#! /usr/bin/env python3 # def smr00 ( ): #*****************************************************************************80 # ## smr00() returns the SMR rule of degree 0. # # Discussion: # # DEGREE: 0 # SYMM.: (X,Y), (-X,-Y) # POINTS CARDINALITY: 1 # NORM INF MOMS. RESIDUAL: 0.00000E+00, # SUM NEGATIVE WEIGHTS: 0.00000E+00, # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*1), the requested rule. # import numpy as np xyw = np.array ( [ \ 0.000000000000000E+00, 0.000000000000000E+00, 4.000000000000000E+00 ] ) return xyw def smr01 ( ): #*****************************************************************************80 # ## smr01 returns the SMR rule of degree 1. # # Discussion: # # DEGREE: 1 # SYMM.: (X,Y), (-X,-Y) # POINTS CARDINALITY: 1 # NORM INF MOMS. RESIDUAL: 0.00000E+00, # SUM NEGATIVE WEIGHTS: 0.00000E+00, # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*1), the requested rule. # import numpy as np xyw = np.array ( [ \ 0.000000000000000E+00, 0.000000000000000E+00, 4.000000000000000E+00 ] ) return xyw def smr02 ( ): #*****************************************************************************80 # ## smr02 returns the SMR rule of degree 2. # # Discussion: # # DEGREE: 2 # POINTS CARDINALITY: 3 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00, # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*3), the requested rule. # import numpy as np xyw = np.array ( [ \ 6.519542382482019E-01, 3.623444315022428E-01, 1.498681096511322E+00, \ -8.070876861583226E-01, 5.322309038833022E-01, 1.051530016968792E+00, \ -8.856086946552445E-02, -7.605904084126465E-01, 1.449788886519887E+00 ] ) return xyw def smr03 ( ): #*****************************************************************************80 # ## smr03 returns the SMR rule of degree 3. # # Discussion: # # DEGREE: 3 # SYMMETRY: (X,Y), (-Y,X), (-X,-Y), (Y,-X) # POINTS CARDINALITY: 4 # NORM INF MOMS. RESIDUAL: 2.22045e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00, # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*4), the requested rule. # import numpy as np xyw = np.array ( [ \ -5.773502691896257E-01, -5.773502691896257E-01, 1.000000000000000E+00, \ -5.773502691896257E-01, 5.773502691896257E-01, 1.000000000000000E+00, \ 5.773502691896257E-01, 5.773502691896257E-01, 1.000000000000000E+00, \ 5.773502691896257E-01, -5.773502691896257E-01, 1.000000000000000E+00 ] ) return xyw def smr04 ( ): #*****************************************************************************80 # ## smr04 returns the SMR rule of degree 4. # # Discussion: # # DEGREE: 4 # POINTS CARDINALITY: 6 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00, # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*6), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.298664473826397E-01, 6.361197473108544E-02, 4.979283660841867E-01, \ -7.329012618874027E-01, 5.903145258425608E-01, 6.883081069413867E-01, \ 3.895446419719248E-01, 8.325323327063485E-01, 6.340849824642651E-01, \ 5.169294362169509E-01, -8.804002381721473E-01, 4.856847322376568E-01, \ -5.223159975544114E-02, -1.540167862605936E-01, 1.180646405191258E+00, \ -7.693563599017555E-01, -6.943687766134327E-01, 5.133474070812475E-01 ] ) return xyw def smr05 ( ): #*****************************************************************************80 # ## smr05 returns the SMR rule of degree 5. # # Discussion: # # DEGREE: 5 # SYMMETRY: (X,Y), (-X,-Y) # POINTS CARDINALITY: 7 # NORM INF MOMS. RESIDUAL: 1.66533e-16 # SUM NEGATIVE WEIGHTS: 0 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*7), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.660917830792960E-01, 0.000000000000000E+00, 3.174603174603175E-01, \ -5.773502691896258E-01, -7.745966692414834E-01, 5.555555555555556E-01, \ -5.773502691896258E-01, 7.745966692414834E-01, 5.555555555555556E-01, \ 0.000000000000000E+00, 0.000000000000000E+00, 1.142857142857143E+00, \ 5.773502691896258E-01, 7.745966692414834E-01, 5.555555555555556E-01, \ 5.773502691896258E-01, -7.745966692414834E-01, 5.555555555555556E-01, \ 9.660917830792960E-01, 0.000000000000000E+00, 3.174603174603175E-01 ] ) return xyw def smr06 ( ): #*****************************************************************************80 # ## smr06 returns the SMR rule of degree 6. # # Discussion: # # DEGREE: 6 # POINTS CARDINALITY: 10 # NORM INF MOMS. RESIDUAL: 9.02056e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*10), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.785155476851563E-01, 2.032663758845348E-01, 2.115144101443901E-01, \ 8.002071174796732E-01, -8.068212789789568E-01, 2.633128596562718E-01, \ 6.478447271179293E-01, 8.174437151345265E-01, 3.765392584231271E-01, \ 4.527740405918522E-01, -2.317108088207500E-01, 7.128261121734308E-01, \ -4.775668731692919E-01, 9.766597077168154E-01, 1.915080888326935E-01, \ -7.569420164799104E-02, 4.409055401533251E-01, 7.647398979197457E-01, \ -1.241563248035317E-01, -8.409222499092199E-01, 4.422079284502612E-01, \ -9.014158913156406E-01, 5.483121720080090E-01, 2.801510395399764E-01, \ -6.560277628978444E-01, -2.866497529648795E-01, 6.536308666716537E-01, \ -9.537871517453275E-01, -8.861523430050633E-01, 1.035695381884487E-01 ] ) return xyw def smr07 ( ): #*****************************************************************************80 # ## smr07 returns the SMR rule of degree 7. # # Discussion: # # DEGREE: 7 # ROTATIONALLY INVARIANT: (X,Y),(-Y,X),(-X,-Y),(Y,-X). # POINTS CARDINALITY: 12 # NORM INF MOMS. RESIDUAL: 2.77556e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*12), the requested rule. # import numpy as np xyw = np.array ( [ \ 3.938313610187890E-01, -3.669979343404274E-01, 5.209286223023044E-01, \ 8.019684762065925E-01, 8.099259297580919E-01, 2.374024056137991E-01, \ -1.832732766424723E-02, 9.259609259310837E-01, 2.416689720838965E-01, \ 3.669979343404274E-01, 3.938313610187890E-01, 5.209286223023044E-01, \ -8.099259297580919E-01, 8.019684762065925E-01, 2.374024056137991E-01, \ -9.259609259310837E-01, -1.832732766424723E-02, 2.416689720838965E-01, \ -3.938313610187890E-01, 3.669979343404274E-01, 5.209286223023044E-01, \ -8.019684762065925E-01, -8.099259297580919E-01, 2.374024056137991E-01, \ 1.832732766424723E-02, -9.259609259310837E-01, 2.416689720838965E-01, \ -3.669979343404274E-01, -3.938313610187890E-01, 5.209286223023044E-01, \ 8.099259297580919E-01, -8.019684762065925E-01, 2.374024056137991E-01, \ 9.259609259310837E-01, 1.832732766424723E-02, 2.416689720838965E-01 ] ) return xyw def smr08 ( ): #*****************************************************************************80 # ## smr08 returns the SMR rule of degree 8. # # Discussion: # # R.COOLS SAYS THERE IS A RULE WITH 15 PTS. # # DEGREE: 8 # POINTS CARDINALITY: 16 # NORM INF MOMS. RESIDUAL: 5.27356e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*16), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.200233979246099E-01, -1.061811254185043E-01, 2.066851970823297E-01, \ 8.930854460206108E-01, 7.538456868810103E-01, 1.637084884729354E-01, \ 6.675369061590991E-01, -6.602769863240182E-01, 3.448725288612837E-01, \ 9.736841855611369E-01, -9.418906397956112E-01, 4.154990098574050E-02, \ 4.634059670545806E-01, 9.713146222867728E-01, 1.207701070516287E-01, \ 5.257251055722159E-01, 3.284384783969826E-01, 4.761612149298055E-01, \ -3.171906088585705E-01, 8.431651719683217E-01, 8.714564872094989E-02, \ -6.189113622341841E-02, 6.853227004655966E-01, 3.755078795520529E-01, \ 6.720825424065331E-02, -2.654137657769545E-01, 5.939493422195995E-01, \ 1.957478656950412E-01, -9.531380985058940E-01, 1.576823081145121E-01, \ -7.280591295595631E-01, 9.245623167165428E-01, 1.261748042046440E-01, \ -5.538775451118830E-01, 1.849451143123379E-01, 4.968422862065046E-01, \ -4.448446986979669E-01, -7.417922043114903E-01, 3.611024723493892E-01, \ -9.421081322947572E-01, 5.652760298758271E-01, 1.413572491732567E-01, \ -8.900106969566213E-01, -3.626326971963237E-01, 2.363188753269229E-01, \ -8.841558907294489E-01, -9.418511077281306E-01, 7.017169674844463E-02 ] ) return xyw def smr09 ( ): #*****************************************************************************80 # ## smr09 returns the SMR rule of degree 9. # # Discussion: # # DEGREE: 9 # ROTATIONALLY INVARIANT: (X,Y),(-Y,X),(-X,-Y),(Y,-X).- # POINTS CARDINALITY: 17 # NORM INF MOMS. RESIDUAL: 2.77556e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*17), the requested rule. # import numpy as np xyw = np.array ( [ \ -6.306801197316687E-01, 9.688499663619777E-01, 8.887937817019871E-02, \ 4.533398211356471E-01, -5.237358202144294E-01, 3.982824392620701E-01, \ 8.526157293336624E-01, -7.620832819261733E-02, 2.690513376397807E-01, \ -7.502770999789007E-01, -9.279616459595696E-01, 1.120996021295965E-01, \ -9.688499663619777E-01, -6.306801197316687E-01, 8.887937817019871E-02, \ 5.237358202144294E-01, 4.533398211356471E-01, 3.982824392620701E-01, \ 7.620832819261733E-02, 8.526157293336624E-01, 2.690513376397807E-01, \ 9.279616459595696E-01, -7.502770999789007E-01, 1.120996021295965E-01, \ 6.306801197316687E-01, -9.688499663619777E-01, 8.887937817019871E-02, \ -4.533398211356471E-01, 5.237358202144294E-01, 3.982824392620701E-01, \ -8.526157293336624E-01, 7.620832819261733E-02, 2.690513376397807E-01, \ 7.502770999789007E-01, 9.279616459595696E-01, 1.120996021295965E-01, \ 9.688499663619777E-01, 6.306801197316687E-01, 8.887937817019871E-02, \ -5.237358202144294E-01, -4.533398211356471E-01, 3.982824392620701E-01, \ -7.620832819261733E-02, -8.526157293336624E-01, 2.690513376397807E-01, \ -9.279616459595696E-01, 7.502770999789007E-01, 1.120996021295965E-01, \ 0.000000000000000E+00, 0.000000000000000E+00, 5.267489711934157E-01 ] ) return xyw def smr10 ( ): #*****************************************************************************80 # ## smr10 returns the SMR rule of degree 10. # # Discussion: # # DEGREE: 10 # POINTS CARDINALITY: 22 # NORM INF MOMS. RESIDUAL: 3.88578e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*22), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.406185571992117E-01, -3.188453596839293E-01, 1.198415853239125E-01, \ 9.817119264047970E-01, 6.258661935323968E-01, 6.326927276111106E-02, \ 8.117151060164873E-01, 9.246684242905354E-01, 8.868620221697536E-02, \ 7.788254159831852E-01, 2.105273891482154E-01, 2.658711347712608E-01, \ 6.476354842626755E-01, -6.474946981752544E-01, 2.305700455337005E-01, \ 9.225481682574119E-01, -8.792348043990323E-01, 6.253794118755233E-02, \ 1.142951736422380E-01, 9.492191314088700E-01, 1.186176720746597E-01, \ 4.711392149070169E-01, 6.666473305982111E-01, 2.839584221827897E-01, \ 3.507267260891899E-01, -1.844717206212197E-01, 3.881144740244089E-01, \ 6.240243795898468E-01, -9.853833119314599E-01, 3.338712924707296E-02, \ -3.924748753960961E-01, 7.631114939243835E-01, 2.582793941034283E-01, \ -3.211002312038658E-02, 3.187935759364070E-01, 4.082419772615457E-01, \ -1.073322786510871E-01, -6.188661913929927E-01, 3.149887822123112E-01, \ 2.065013461988724E-01, -9.119588710357345E-01, 1.346097738619806E-01, \ -7.529656324799602E-01, 9.707183739677747E-01, 5.911019515035110E-02, \ -7.605065507139738E-01, 3.663139167806791E-01, 2.604239768191683E-01, \ -4.732489884927658E-01, -1.655785251003833E-01, 3.717176493089616E-01, \ -5.089131904296067E-01, -9.215290755789827E-01, 1.333773119224012E-01, \ -9.538019223425510E-01, 7.551269206143554E-01, 7.180589876051692E-02, \ -9.663420836873585E-01, -1.043123255663638E-01, 9.794042948413186E-02, \ -8.103749226019182E-01, -6.115967830349249E-01, 2.001832062027751E-01, \ -9.577495916000752E-01, -9.262105001258389E-01, 3.446752558898364E-02 ] ) return xyw def smr11 ( ): #*****************************************************************************80 # ## smr11 returns the SMR rule of degree 11. # # Discussion: # # DEGREE: 11 # ROTATIONALLY INVARIANT: (X,Y),(-Y,X),(-X,-Y),(Y,-X). # POINTS CARDINALITY: 24 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*24), the requested rule. # import numpy as np xyw = np.array ( [ \ -4.165807191202228E-02, 4.248472488486693E-01, 3.511587183982455E-01, \ 3.156234329152542E-01, 8.125205483048132E-01, 2.117363499989486E-01, \ 7.120019130753363E-01, 5.253202503645478E-01, 2.256260617288634E-01, \ 6.980761045495677E-01, 9.826392235408555E-01, 4.802076335072379E-02, \ 9.535395282015321E-01, 1.885861387186419E-01, 9.738677735866817E-02, \ 9.394863828167369E-01, 8.257758359029640E-01, 6.607132916455061E-02, \ -4.248472488486693E-01, -4.165807191202228E-02, 3.511587183982455E-01, \ -8.125205483048132E-01, 3.156234329152542E-01, 2.117363499989486E-01, \ -5.253202503645478E-01, 7.120019130753363E-01, 2.256260617288634E-01, \ -9.826392235408555E-01, 6.980761045495677E-01, 4.802076335072379E-02, \ -1.885861387186419E-01, 9.535395282015321E-01, 9.738677735866817E-02, \ -8.257758359029640E-01, 9.394863828167369E-01, 6.607132916455061E-02, \ 4.165807191202228E-02, -4.248472488486693E-01, 3.511587183982455E-01, \ -3.156234329152542E-01, -8.125205483048132E-01, 2.117363499989486E-01, \ -7.120019130753363E-01, -5.253202503645478E-01, 2.256260617288634E-01, \ -6.980761045495677E-01, -9.826392235408555E-01, 4.802076335072379E-02, \ -9.535395282015321E-01, -1.885861387186419E-01, 9.738677735866817E-02, \ -9.394863828167369E-01, -8.257758359029640E-01, 6.607132916455061E-02, \ 4.248472488486693E-01, 4.165807191202228E-02, 3.511587183982455E-01, \ 8.125205483048132E-01, -3.156234329152542E-01, 2.117363499989486E-01, \ 5.253202503645478E-01, -7.120019130753363E-01, 2.256260617288634E-01, \ 9.826392235408555E-01, -6.980761045495677E-01, 4.802076335072379E-02, \ 1.885861387186419E-01, -9.535395282015321E-01, 9.738677735866817E-02, \ 8.257758359029640E-01, -9.394863828167369E-01, 6.607132916455061E-02 ] ) return xyw def smr12 ( ): #*****************************************************************************80 # ## smr12 returns the SMR rule of degree 12. # # Discussion: # # DEGREE: 12 # POINTS CARDINALITY: 31 # NORM INF MOMS. RESIDUAL: 5.55112e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*31), the requested rule. # import numpy as np xyw = np.array ( [ \ 7.887961133518859E-01, 9.788423074444343E-01, 3.643740653079505E-02, \ 9.636803326457559E-01, -8.325162377112404E-01, 4.156946367307449E-02, \ 5.727054392308150E-01, 7.717261293782711E-01, 1.680361793533787E-01, \ 9.634302613611325E-01, 8.254780463742046E-01, 4.273104217362153E-02, \ 9.850208941660858E-01, 2.929038490713011E-03, 5.527116827932585E-02, \ 8.590486289231106E-01, -4.568247023502062E-01, 1.528634492877730E-01, \ 7.730732984501992E-01, -9.683129045193353E-01, 4.413124147353821E-02, \ -1.779670698164110E-01, 7.009187390097460E-01, 2.328494912954924E-01, \ 8.543638116305748E-01, 4.518538584893645E-01, 1.556045127005831E-01, \ 6.291273683568680E-01, -7.545283511153206E-03, 2.625512570459704E-01, \ 5.528579662023739E-01, -7.445078276040368E-01, 1.822720395257231E-01, \ 2.838402579450193E-01, 4.114855681818982E-01, 2.766169541326807E-01, \ -8.461631704059508E-02, 8.864609533086124E-02, 2.383849367209651E-01, \ 2.425324152553718E-01, -3.742080386362673E-01, 2.920973373876344E-01, \ 1.732349372327210E-01, -9.397208645575091E-01, 1.020918275656317E-01, \ 1.711409536609614E-01, 9.405188030525048E-01, 1.014134103497821E-01, \ -4.125379277895744E-01, 5.932317296236497E-02, 1.455335918991387E-01, \ -2.114002132094871E-01, -2.840983635497378E-01, 7.946218537051837E-02, \ -4.914206209696642E-01, 9.453457692968009E-01, 8.467100517264473E-02, \ -6.078146688229159E-01, 4.486792064962008E-01, 2.211679207393056E-01, \ -5.774993705610445E-01, -3.758525621312278E-01, 2.131288659567110E-01, \ -4.943548938878011E-01, -9.487282033931176E-01, 8.106167025374129E-02, \ -8.307832892042354E-01, 8.056995002918920E-01, 1.095231158786915E-01, \ -8.780106307148161E-01, 1.661245295800410E-01, 9.555205419558256E-02, \ -9.855207994154948E-01, -5.172324935881427E-01, 4.485874655537044E-02, \ -1.843157675090382E-01, -7.106474367504330E-01, 2.242636308727417E-01, \ -9.639808262111604E-01, 9.935149440412500E-01, 1.153343223604792E-02, \ -9.905890478558095E-01, 5.280652625496880E-01, 4.024626264818196E-02, \ -8.720537162767097E-01, -1.329065631973914E-01, 1.058449657495581E-01, \ -9.263657835203469E-01, -9.372594643356640E-01, 3.401287490362680E-02, \ -7.769128911427001E-01, -7.339368334159078E-01, 1.242179600721695E-01 ] ) return xyw def smr13 ( ): #*****************************************************************************80 # ## smr13 returns the SMR rule of degree 13. # # Discussion: # # DEGREE: 13 # ROTATIONALLY INVARIANT: (X,Y),(-Y,X),(-X,-Y),(Y,-X). # POINTS CARDINALITY: 33 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*33), the requested rule. # import numpy as np xyw = np.array ( [ \ 4.758086252182755E-01, 8.500766736997488E-01, 1.188446673005955E-01, \ 3.427165560404069E-01, 4.093045616940387E-01, 2.568707494819678E-01, \ 7.558053565720811E-01, 6.478216371870110E-01, 1.297635503700028E-01, \ 9.413272258729251E-01, 3.907362161294611E-01, 7.749273853310545E-02, \ 9.572976997863074E-01, 8.595560056416388E-01, 3.817442131708364E-02, \ 7.788097115544195E-01, 9.834866824398723E-01, 2.999183886449914E-02, \ -7.074150899644469E-02, 6.962500784917494E-01, 2.133415814571894E-01, \ 1.381834598624650E-01, 9.589251702875350E-01, 6.042492381774981E-02, \ -8.500766736997488E-01, 4.758086252182755E-01, 1.188446673005955E-01, \ -4.093045616940387E-01, 3.427165560404069E-01, 2.568707494819678E-01, \ -6.478216371870110E-01, 7.558053565720811E-01, 1.297635503700028E-01, \ -3.907362161294611E-01, 9.413272258729251E-01, 7.749273853310545E-02, \ -8.595560056416388E-01, 9.572976997863074E-01, 3.817442131708364E-02, \ -9.834866824398723E-01, 7.788097115544195E-01, 2.999183886449914E-02, \ -6.962500784917494E-01, -7.074150899644469E-02, 2.133415814571894E-01, \ -9.589251702875350E-01, 1.381834598624650E-01, 6.042492381774981E-02, \ -4.758086252182755E-01, -8.500766736997488E-01, 1.188446673005955E-01, \ -3.427165560404069E-01, -4.093045616940387E-01, 2.568707494819678E-01, \ -7.558053565720811E-01, -6.478216371870110E-01, 1.297635503700028E-01, \ -9.413272258729251E-01, -3.907362161294611E-01, 7.749273853310545E-02, \ -9.572976997863074E-01, -8.595560056416388E-01, 3.817442131708364E-02, \ -7.788097115544195E-01, -9.834866824398723E-01, 2.999183886449914E-02, \ 7.074150899644469E-02, -6.962500784917494E-01, 2.133415814571894E-01, \ -1.381834598624650E-01, -9.589251702875350E-01, 6.042492381774981E-02, \ 8.500766736997488E-01, -4.758086252182755E-01, 1.188446673005955E-01, \ 4.093045616940387E-01, -3.427165560404069E-01, 2.568707494819678E-01, \ 6.478216371870110E-01, -7.558053565720811E-01, 1.297635503700028E-01, \ 3.907362161294611E-01, -9.413272258729251E-01, 7.749273853310545E-02, \ 8.595560056416388E-01, -9.572976997863074E-01, 3.817442131708364E-02, \ 9.834866824398723E-01, -7.788097115544195E-01, 2.999183886449914E-02, \ 6.962500784917494E-01, 7.074150899644469E-02, 2.133415814571894E-01, \ 9.589251702875350E-01, -1.381834598624650E-01, 6.042492381774981E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 3.003821154312253E-01 ] ) return xyw def smr14 ( ): #*****************************************************************************80 # ## smr14 returns the SMR rule of degree 14. # # Discussion: # # DEGREE: 14 # POINTS CARDINALITY: 40 # NORM INF MOMS. RESIDUAL: 9.57567e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*40), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.784247248091626E-01, 9.849379037345679E-01, 7.042609290974809E-03, \ 9.696033367128390E-01, -3.331633352358324E-01, 5.127000401619231E-02, \ 9.635907900433699E-01, -8.235135827696192E-01, 2.835904116834926E-02, \ 9.609680853689336E-01, -9.665848054209388E-01, 5.802552341290735E-03, \ 8.759175244824323E-01, 8.440519016975554E-01, 6.406839799781101E-02, \ 9.850622977861553E-01, 5.927006882272775E-01, 3.059827453183588E-02, \ 9.132378164262995E-01, 1.686644107446046E-01, 1.015293304177829E-01, \ 8.210255575251280E-01, -6.312138484114799E-01, 1.070566792196576E-01, \ 7.253802697646771E-01, 5.271299424251080E-01, 1.491850201682654E-01, \ 7.129972234617307E-01, -1.746725364206650E-01, 1.672674729613243E-01, \ 5.551781984544302E-01, -8.617677569495097E-01, 1.035166248728787E-01, \ 8.047627946516351E-01, -9.674432786379303E-01, 2.787008138269169E-02, \ 6.424373183439024E-01, 9.660008737161317E-01, 4.265704272492368E-02, \ 4.202620588036903E-01, 7.809596116887254E-01, 1.425075466703280E-01, \ 4.547166615470812E-01, 1.927401717576898E-01, 2.105516162791665E-01, \ 4.259990143599163E-01, -4.962208715768625E-01, 1.867185172918136E-01, \ 9.710021027954509E-02, 9.536977082453567E-01, 6.972182442589203E-02, \ 1.114008919498024E-01, 4.923616289896904E-01, 2.043948618313033E-01, \ 1.209667130758268E-01, -1.503469100876254E-01, 2.335930539280487E-01, \ 7.524097400070873E-02, -7.452253206810735E-01, 1.601269026668343E-01, \ -4.518656196438389E-01, 9.427795716582286E-01, 6.465270834286081E-02, \ -2.040271575380492E-01, 7.591224031418166E-01, 1.466929221365241E-01, \ -2.427862218874625E-01, 1.736708825032474E-01, 2.280281871073875E-01, \ -2.459782585741061E-01, -4.449955936922590E-01, 2.055272577034085E-01, \ 2.124852450722984E-01, -9.810732833242932E-01, 4.316769231929027E-02, \ -7.568108239381779E-01, 7.901122315570046E-01, 9.576721669303179E-02, \ -5.448202693114659E-01, 5.034324548840123E-01, 1.739315171493671E-01, \ -5.908385723762482E-01, -1.268935867110808E-01, 1.941490024297708E-01, \ -2.895046302710989E-01, -9.116133911949098E-01, 9.663345199603172E-02, \ -6.417036777526361E-01, -9.886715561256082E-01, 2.266331268661072E-02, \ -7.921595150813847E-01, 9.955322518565568E-01, 1.393382316893550E-02, \ -9.527313016559716E-01, 5.688243284550245E-01, 5.657603379663307E-02, \ -8.300912488610223E-01, 2.262029630794567E-01, 1.327223448878936E-01, \ -5.758839055540124E-01, -6.756366015563920E-01, 1.369481741372994E-01, \ -7.954880187581953E-01, -8.506684869408652E-01, 6.033321912862107E-02, \ -9.562007514872694E-01, 9.139906777934969E-01, 2.419546581425405E-02, \ -9.839876523259704E-01, -5.381597268716472E-02, 4.116110545021220E-02, \ -8.552518042944189E-01, -4.002028380944249E-01, 1.164178174263354E-01, \ -9.694591723778574E-01, -6.823556992833991E-01, 3.472756253802061E-02, \ -9.468282975367817E-01, -9.506255113908446E-01, 1.793373090014833E-02 ] ) return xyw def smr15 ( ): #*****************************************************************************80 # ## smr15 returns the SMR rule of degree 15. # # Discussion: # # DEGREE: 15 # SYMMETRY: (X,Y), (-X,-Y). # POINTS CARDINALITY: 43 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*43), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.897035809317545E-01, 5.425907314742811E-01, 2.692004637463620E-02, \ -9.844256804341962E-01, -8.630433434831161E-01, 1.749593663841038E-02, \ -9.720740612950027E-01, -3.529770957215327E-01, 4.407397330060381E-02, \ -9.717518222429252E-01, 9.683214017531246E-01, 9.597984117068133E-03, \ -9.192734438999380E-01, 1.159789159156424E-01, 9.186688636374692E-02, \ -8.920718007989080E-01, 8.096447739678093E-01, 6.009039847791869E-02, \ -8.694522415973330E-01, -9.761961093345928E-01, 2.099677952515304E-02, \ -8.685236892209494E-01, -6.756459657106383E-01, 7.822899155683208E-02, \ -7.630389610522654E-01, -4.519651830370793E-01, 4.323794116684067E-02, \ -7.606746138826611E-01, 4.797962173343035E-01, 1.341465202538838E-01, \ -7.151716310198851E-01, -1.863833474025069E-01, 1.456054555637575E-01, \ -6.987339962580051E-01, 9.595571077523438E-01, 4.226674647754744E-02, \ -6.348443155921265E-01, -8.760006464754001E-01, 8.606581576391330E-02, \ -5.034250302130044E-01, 7.544476347964910E-01, 1.336407358940195E-01, \ -4.795655397342558E-01, 1.795809740683987E-01, 2.029010677239986E-01, \ -4.639944974152491E-01, -5.789694673013793E-01, 1.560859171904400E-01, \ -3.244129251598891E-01, -9.815797807964038E-01, 3.669707979316125E-02, \ -2.413326601845606E-01, -2.562094364546668E-01, 1.805943476814126E-01, \ -2.289847857525782E-01, 9.462454193863400E-01, 7.000525056015877E-02, \ -1.648117901013778E-01, 5.076930665870906E-01, 2.008843851797360E-01, \ -1.220776156497820E-01, -8.000225811280368E-01, 1.383276061021405E-01, \ 0.000000000000000E+00, 0.000000000000000E+00, 1.605402685892418E-01, \ 1.220776156497820E-01, 8.000225811280368E-01, 1.383276061021405E-01, \ 1.648117901013778E-01, -5.076930665870906E-01, 2.008843851797360E-01, \ 2.289847857525782E-01, -9.462454193863400E-01, 7.000525056015877E-02, \ 2.413326601845606E-01, 2.562094364546668E-01, 1.805943476814126E-01, \ 3.244129251598891E-01, 9.815797807964038E-01, 3.669707979316125E-02, \ 4.639944974152491E-01, 5.789694673013793E-01, 1.560859171904400E-01, \ 4.795655397342558E-01, -1.795809740683987E-01, 2.029010677239986E-01, \ 5.034250302130044E-01, -7.544476347964910E-01, 1.336407358940195E-01, \ 6.348443155921265E-01, 8.760006464754001E-01, 8.606581576391330E-02, \ 6.987339962580051E-01, -9.595571077523438E-01, 4.226674647754744E-02, \ 7.151716310198851E-01, 1.863833474025069E-01, 1.456054555637575E-01, \ 7.606746138826611E-01, -4.797962173343035E-01, 1.341465202538838E-01, \ 7.630389610522654E-01, 4.519651830370793E-01, 4.323794116684067E-02, \ 8.685236892209494E-01, 6.756459657106383E-01, 7.822899155683208E-02, \ 8.694522415973330E-01, 9.761961093345928E-01, 2.099677952515304E-02, \ 8.920718007989080E-01, -8.096447739678093E-01, 6.009039847791869E-02, \ 9.192734438999380E-01, -1.159789159156424E-01, 9.186688636374692E-02, \ 9.717518222429252E-01, -9.683214017531246E-01, 9.597984117068133E-03, \ 9.720740612950027E-01, 3.529770957215327E-01, 4.407397330060381E-02, \ 9.844256804341962E-01, 8.630433434831161E-01, 1.749593663841038E-02, \ 9.897035809317545E-01, -5.425907314742811E-01, 2.692004637463620E-02 ] ) return xyw def smr16 ( ): #*****************************************************************************80 # ## smr16 returns the SMR rule of degree 16. # # Discussion: # # DEGREE: 16 # POINTS CARDINALITY: 52 # NORM INF MOMS. RESIDUAL: 9.15934e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*52), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.849840927490825E-01, -8.331548011067518E-01, 1.148497840181236E-02, \ 9.872657987157976E-01, 8.588448788294810E-01, 1.473194969200236E-02, \ 9.793426944857834E-01, 3.488215241207180E-01, 3.098444037686296E-02, \ 9.710730712462519E-01, -1.976275486943358E-01, 3.939075140298535E-02, \ 9.543665314722640E-01, -6.214859681775430E-01, 3.181988181461071E-02, \ 8.967156835567945E-01, 6.357233965740013E-01, 6.754726963166503E-02, \ 8.560787402043915E-01, 9.300163636799799E-02, 9.806208102265382E-02, \ 8.352602163787974E-01, -4.546303275105074E-01, 8.007156600306299E-02, \ 9.242704749020406E-01, -9.624752146350085E-01, 1.773036206031470E-02, \ 8.914637296434523E-01, 9.704982463181010E-01, 1.966130427988303E-02, \ 7.225506553250621E-01, 8.352620376414029E-01, 7.379440929879094E-02, \ 6.725198105909391E-01, 3.980674436765583E-01, 1.347645483339404E-01, \ 6.371105617029685E-01, -1.999912055384129E-01, 1.423112416621634E-01, \ 7.808910471981420E-01, -8.134492991124070E-01, 7.085421872868532E-02, \ 6.337062775345687E-01, -9.719980099330250E-01, 2.925279318090791E-02, \ 5.291062928070972E-01, 9.679384351925090E-01, 3.562931685878622E-02, \ 4.244965002466626E-01, 6.479593280988540E-01, 1.310143500409354E-01, \ 3.773110188906150E-01, 1.020856639775450E-01, 1.867695133142744E-01, \ 5.192633407488266E-01, -6.187964471903282E-01, 1.329295627808754E-01, \ 3.642312437714700E-01, -8.863235986829771E-01, 7.576971496593095E-02, \ 5.561745660244605E-02, 9.824987512094673E-01, 2.458923517607215E-02, \ 2.315339247267523E-01, 8.666994462444320E-01, 7.856108542290755E-02, \ 7.921301678093465E-02, 3.983722019927857E-01, 1.821994092983056E-01, \ 2.060553068006480E-01, -3.586293462932311E-01, 1.877843167547426E-01, \ 5.968748053306436E-02, -7.377671587273356E-01, 1.194943798093123E-01, \ 9.345890458174631E-02, -9.856937685796492E-01, 2.683866060217570E-02, \ -2.309174536279237E-01, 9.038233934314195E-01, 5.704293324973451E-02, \ -8.490129042248308E-02, 7.103616948287095E-01, 1.008414737624086E-01, \ -1.156391657288008E-01, -5.831278342511520E-02, 2.065290952798645E-01, \ -2.469994669672659E-01, -5.451953129096770E-01, 1.486152719982061E-01, \ -2.407569095414160E-01, -9.110001765460239E-01, 7.369448825579748E-02, \ -5.483869894552442E-01, -9.876593748951622E-01, 2.052629805335149E-02, \ -4.504247208566849E-01, 9.823752262299734E-01, 2.182431901411460E-02, \ -3.866081747635596E-01, 6.227238096470654E-01, 9.969926465444570E-02, \ -3.830201431115215E-01, 2.758592684399684E-01, 1.620659760964653E-01, \ -5.052430403406701E-01, -2.965505634060009E-01, 1.515331269600610E-01, \ -5.534470349649314E-01, -7.802045621704854E-01, 9.917678556230886E-02, \ -8.118615876869535E-01, -9.295671133984095E-01, 4.092795912351316E-02, \ -6.110904286470239E-01, 8.416598154470650E-01, 7.681751936941439E-02, \ -7.180850315887866E-01, 5.275124303877409E-01, 1.078772215341901E-01, \ -6.717184597177530E-01, 5.190959173969474E-02, 1.274953461648875E-01, \ -7.688067943153316E-01, -5.765647129796945E-01, 9.670064900592909E-02, \ -8.122178392749709E-01, 9.667410754993326E-01, 2.507418689814922E-02, \ -9.001198519620254E-01, 7.660124377216176E-01, 5.337920648061494E-02, \ -8.927917900428630E-01, 2.801343969829519E-01, 7.365567660310912E-02, \ -8.625316023871907E-01, -2.304828850740908E-01, 7.976422028192462E-02, \ -9.444379963884221E-01, -7.886904781685101E-01, 3.680993075145274E-02, \ -9.814383394418308E-01, 9.386107932617476E-01, 1.041932477487203E-02, \ -9.868302403965578E-01, 5.376625218147606E-01, 2.163454704946022E-02, \ -9.782564506674100E-01, -7.629524842176458E-03, 2.926520573014411E-02, \ -9.734724345230769E-01, -4.774981225500561E-01, 2.926793258824966E-02, \ -9.832450869161593E-01, -9.836383787047436E-01, 5.320699842671481E-03 ] ) return xyw def smr17 ( ): #*****************************************************************************80 # ## smr17 returns the SMR rule of degree 17. # # Discussion: # # DEGREE: 17 # SYMMETRY (X,Y), (-X,-Y) # POINTS CARDINALITY: 54 # NORM INF MOMS. RESIDUAL: 4.44089e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*54), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.863407162001064E-01, -5.350413962053188E-01, 2.305601467067279E-02, \ -9.797917920771685E-01, 9.250929106098536E-02, 3.240673241115238E-02, \ -9.759748695590249E-01, -9.216725954273451E-01, 1.270290274356204E-02, \ -9.751604610540874E-01, 8.226615823534071E-01, 6.967658416756498E-03, \ -9.655463590660567E-01, 5.873038194012039E-01, 3.379494459982002E-02, \ -9.580417051272648E-01, 9.392146008421756E-01, 1.490471492599059E-02, \ -8.990410418369936E-01, -2.442899840300571E-01, 8.052033202871829E-02, \ -8.929777462525665E-01, -7.628113086068719E-01, 5.184525239733102E-02, \ -8.684155248367631E-01, -9.940332573157988E-01, 8.888523934900541E-03, \ -8.543834155553983E-01, 3.348609125819369E-01, 8.942431131283363E-02, \ -8.198994002699886E-01, 7.861039744617548E-01, 6.602369125585303E-02, \ -7.927874398654909E-01, 9.867131971602722E-01, 1.519282623398942E-02, \ -7.313489231885142E-01, -5.375736491397500E-01, 1.043702032541429E-01, \ -7.090784726108733E-01, -9.201347632293920E-01, 4.542324896856204E-02, \ -6.903443278598889E-01, 8.463704695540367E-03, 1.345081852973794E-01, \ -6.159136297254387E-01, 5.598744500532884E-01, 1.235292068763380E-01, \ -5.503655196818333E-01, 9.111946838818689E-01, 6.486019261315923E-02, \ -5.088888961572688E-01, -7.826367523208496E-01, 8.485070415264370E-02, \ -4.701395263110675E-01, -3.185012886935781E-01, 1.454492206755823E-01, \ -3.956137656607415E-01, 2.488545706442738E-01, 1.612339647041861E-01, \ -3.787399827823459E-01, -9.766193765657439E-01, 3.251051105156653E-02, \ -2.831429683388207E-01, 7.382031830574145E-01, 1.224068303196167E-01, \ -2.468625326731463E-01, -6.309764352559230E-01, 1.169672902517008E-01, \ -2.225539938942038E-01, 9.838126768040562E-01, 2.855916848841619E-02, \ -1.626641413140420E-01, -1.008646063203129E-01, 1.626132038726945E-01, \ -6.874965210282233E-02, -8.853346747431012E-01, 8.682936644584309E-02, \ -5.847903009448556E-02, 4.510735833781594E-01, 1.501607980965882E-01, \ 5.847903009448556E-02, -4.510735833781594E-01, 1.501607980965882E-01, \ 6.874965210282233E-02, 8.853346747431012E-01, 8.682936644584309E-02, \ 1.626641413140420E-01, 1.008646063203129E-01, 1.626132038726945E-01, \ 2.225539938942038E-01, -9.838126768040562E-01, 2.855916848841619E-02, \ 2.468625326731463E-01, 6.309764352559230E-01, 1.169672902517008E-01, \ 2.831429683388207E-01, -7.382031830574145E-01, 1.224068303196167E-01, \ 3.787399827823459E-01, 9.766193765657439E-01, 3.251051105156653E-02, \ 3.956137656607415E-01, -2.488545706442738E-01, 1.612339647041861E-01, \ 4.701395263110675E-01, 3.185012886935781E-01, 1.454492206755823E-01, \ 5.088888961572688E-01, 7.826367523208496E-01, 8.485070415264370E-02, \ 5.503655196818333E-01, -9.111946838818689E-01, 6.486019261315923E-02, \ 6.159136297254387E-01, -5.598744500532884E-01, 1.235292068763380E-01, \ 6.903443278598889E-01, -8.463704695540367E-03, 1.345081852973794E-01, \ 7.090784726108733E-01, 9.201347632293920E-01, 4.542324896856204E-02, \ 7.313489231885142E-01, 5.375736491397500E-01, 1.043702032541429E-01, \ 7.927874398654909E-01, -9.867131971602722E-01, 1.519282623398942E-02, \ 8.198994002699886E-01, -7.861039744617548E-01, 6.602369125585303E-02, \ 8.543834155553983E-01, -3.348609125819369E-01, 8.942431131283363E-02, \ 8.684155248367631E-01, 9.940332573157988E-01, 8.888523934900541E-03, \ 8.929777462525665E-01, 7.628113086068719E-01, 5.184525239733102E-02, \ 8.990410418369936E-01, 2.442899840300571E-01, 8.052033202871829E-02, \ 9.580417051272648E-01, -9.392146008421756E-01, 1.490471492599059E-02, \ 9.655463590660567E-01, -5.873038194012039E-01, 3.379494459982002E-02, \ 9.751604610540874E-01, -8.226615823534071E-01, 6.967658416756498E-03, \ 9.759748695590249E-01, 9.216725954273451E-01, 1.270290274356204E-02, \ 9.797917920771685E-01, -9.250929106098536E-02, 3.240673241115238E-02, \ 9.863407162001064E-01, 5.350413962053188E-01, 2.305601467067279E-02 ] ) return xyw def smr18 ( ): #*****************************************************************************80 # ## smr18 returns the SMR rule of degree 18. # # Discussion: # # DEGREE: 18 # POINTS CARDINALITY: 64 # NORM INF MOMS. RESIDUAL: 1.80411e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*64), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.901134796801783E-01, -3.636920739279686E-01, 1.924401162821098E-02, \ -9.813479194657442E-01, 2.269728889226950E-01, 2.377081803411145E-02, \ -9.751246202174101E-01, -8.087895536063188E-01, 1.824571677716675E-02, \ -9.741192020631542E-01, 8.966914512186399E-01, 1.040325999881736E-02, \ -9.699879010686473E-01, -9.814171856874379E-01, 5.169228082043371E-03, \ -9.695988425630034E-01, 6.372691271564769E-01, 2.701864190192290E-02, \ -9.502627815202467E-01, 9.663374399441544E-01, 6.832430188474440E-03, \ -9.197723058789439E-01, -5.864804338113919E-02, 5.855723621166473E-02, \ -9.059247381128510E-01, -5.898828597989898E-01, 5.297590163131558E-02, \ -8.627599153540467E-01, 4.164987829940056E-01, 7.111515467482395E-02, \ -8.569855990839045E-01, -9.267827643653366E-01, 2.894383892650155E-02, \ -8.389143776305836E-01, 8.004661957859885E-01, 5.373522067458378E-02, \ -8.065675356071547E-01, 9.834437446052690E-01, 1.315188692146605E-02, \ -7.872448206722253E-01, -2.985727024319632E-01, 8.409595266673971E-02, \ -7.325897102338846E-01, -7.627707340005139E-01, 6.493193699070636E-02, \ -7.108608115543918E-01, 1.482798927069730E-01, 1.059543276308938E-01, \ -6.620192350608188E-01, -9.914865774170796E-01, 1.356692677046532E-02, \ -6.334849400427111E-01, 6.037434357654228E-01, 1.051942339342666E-01, \ -6.014705998319453E-01, 9.143204709310846E-01, 5.210486977766542E-02, \ -5.892324845704049E-01, -5.045342974742788E-01, 9.788981223530169E-02, \ -5.131040457735190E-01, -9.095715109599031E-02, 1.108235515488634E-01, \ -5.033556139567553E-01, -8.956709590819707E-01, 5.541443510056418E-02, \ -3.947567656009430E-01, 3.383853875972697E-01, 1.469566677471172E-01, \ -3.365255254825216E-01, -6.932064968553141E-01, 9.848736935036356E-02, \ -3.344750516678310E-01, 9.866136919798809E-01, 2.170786884754973E-02, \ -3.310287403968845E-01, 7.731192382826196E-01, 1.015778188232984E-01, \ -2.999505641193486E-01, -2.928443015341402E-01, 1.107816184233573E-01, \ -2.331455368936777E-01, -9.731854050766667E-01, 2.884073562303302E-02, \ -1.116980244718904E-01, 4.992438237750351E-02, 1.612001429698854E-01, \ -6.575627688742440E-02, 5.455174655246902E-01, 1.390613750634900E-01, \ -6.089043840299364E-02, -8.562318836763884E-01, 6.853830062046717E-02, \ -4.781118177875937E-02, -4.996330916388668E-01, 1.194580692354339E-01, \ -2.644564050493325E-02, 9.165721602454180E-01, 6.685724630082367E-02, \ 1.924944168163869E-01, -2.367466035142029E-01, 1.491161554688392E-01, \ 1.951330272152753E-01, -7.328036825494620E-01, 8.630902364197904E-02, \ 2.028158693449157E-01, -9.703380537473529E-01, 3.364243858164141E-02, \ 2.092663468167508E-01, 2.662322825395520E-01, 1.486647112920279E-01, \ 2.283553896503115E-01, 7.496185156938090E-01, 1.027379035896721E-01, \ 2.876554348315164E-01, 9.873845509936813E-01, 2.192507210698709E-02, \ 4.237159887642933E-01, -5.535582535086475E-01, 1.058102193186085E-01, \ 4.581157947253051E-01, 5.130944233380290E-01, 1.090905648997083E-01, \ 4.752280776399702E-01, -8.857999997554080E-01, 6.346475038588688E-02, \ 4.831508023294471E-01, -2.549857293827913E-02, 1.337777655566684E-01, \ 5.057868104561423E-01, 8.896750734704260E-01, 6.079360942822091E-02, \ 6.099162517568020E-01, -3.853032051834505E-01, 6.436419858280257E-02, \ 6.559598836045895E-01, 2.795821152702244E-01, 8.177939511493874E-02, \ 6.565622107706015E-01, -9.883582556647157E-01, 1.640381218907065E-02, \ 6.956126158721206E-01, 6.950821057395169E-01, 7.746885102883669E-02, \ 7.094177605066919E-01, -7.370072009566638E-01, 7.788188331156506E-02, \ 7.290386435476074E-01, 9.703386432783726E-01, 2.313579562579107E-02, \ 7.557526341619506E-01, -2.941608525026456E-01, 7.412112987017343E-02, \ 7.912367791054172E-01, 8.744914899411797E-02, 6.420122545616397E-02, \ 8.543844628271234E-01, -9.182475827792237E-01, 3.336594260262386E-02, \ 8.645615995455240E-01, 4.552151496141779E-01, 6.553880387109420E-02, \ 8.705823452020542E-01, 8.420186142289366E-01, 3.949607694089933E-02, \ 8.978579920125014E-01, -5.603807009892569E-01, 5.906741413770155E-02, \ 9.236747719664095E-01, -1.092483343302797E-01, 5.348329279696051E-02, \ 9.440144649649265E-01, 9.743199890031753E-01, 8.946275110809443E-03, \ 9.689413373175574E-01, 6.453835143088201E-01, 2.577199176900479E-02, \ 9.716342103019509E-01, -9.824772013181601E-01, 5.332369479915357E-03, \ 9.729481716901303E-01, -7.936277261963781E-01, 2.070804573643469E-02, \ 9.758025156447697E-01, 2.267876624457436E-01, 2.981298882062168E-02, \ 9.939173935792275E-01, 8.841354641450845E-01, 5.745299494229030E-03, \ 9.953701290021145E-01, -3.661129988733890E-01, 1.543638847873499E-02 ] ) return xyw def smr19 ( ): #*****************************************************************************80 # ## smr19 returns the SMR rule of degree 19. # # Discussion: # # DEGREE: 19 # SYMMETRY: (X,Y), (-X,-Y) # POINTS CARDINALITY: 67 # NORM INF MOMS. RESIDUAL: 4.44089e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*67), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.882811207043626E-01, 5.499680659586386E-02, 2.092785503234627E-02, \ -9.849643667633750E-01, 6.212597907298936E-01, 1.808240699704512E-02, \ -9.813999666122014E-01, -4.952365265213790E-01, 2.248743945205191E-02, \ -9.782104202505005E-01, 9.275801424350509E-01, 1.011830773881234E-02, \ -9.691016249998836E-01, -9.857365066859964E-01, 4.619328461670566E-03, \ -9.683241755943918E-01, -8.352830082748723E-01, 1.956137669036511E-02, \ -9.202706700587867E-01, 3.511851149995373E-01, 5.773555533944277E-02, \ -9.094971072531579E-01, -2.172757421209814E-01, 6.345799736852624E-02, \ -8.955283373897494E-01, 7.976174402318889E-01, 3.990477349231469E-02, \ -8.910382534296201E-01, 9.945369448321910E-01, 6.887461729231832E-03, \ -8.645217306506207E-01, -6.631996105098346E-01, 5.773686209899585E-02, \ -8.361991822628865E-01, -9.403589726574770E-01, 2.822764839262689E-02, \ -7.730414957980034E-01, 8.238831136924889E-02, 1.001138265151715E-01, \ -7.650572339362595E-01, 5.862972313979000E-01, 7.938451847571938E-02, \ -7.339165122981658E-01, 9.301444324799357E-01, 3.698855138726674E-02, \ -7.142591688630336E-01, -4.144687459254282E-01, 9.862108370826694E-02, \ -6.567593878397442E-01, -8.187456800244232E-01, 6.430400825705974E-02, \ -5.911965681070577E-01, -9.890895416891479E-01, 1.619432554055879E-02, \ -5.650612797733545E-01, 3.562777186069158E-01, 1.145600986645687E-01, \ -5.522558344482561E-01, 7.877180001548971E-01, 7.542302799441891E-02, \ -5.204497226646213E-01, -1.319110721429938E-01, 1.271745083852966E-01, \ -4.843104169217222E-01, -6.372481900547796E-01, 7.509621769261574E-02, \ -4.576710954771651E-01, 9.804344277407575E-01, 2.360353464684936E-02, \ -3.501819505299977E-01, -9.155258592028724E-01, 5.647374387294429E-02, \ -3.449909757079617E-01, -5.171112886647338E-01, 6.683630505556533E-02, \ -3.245616103968320E-01, 6.112729098917052E-01, 1.024013654183961E-01, \ -2.899888936344285E-01, 1.640917354232377E-01, 1.271636872050067E-01, \ -2.124604121926062E-01, 8.907682205113933E-01, 6.854209870863227E-02, \ -2.101863370194021E-01, -2.888406804953518E-01, 1.103357066015591E-01, \ -2.061044019817992E-01, -7.806540187071476E-01, 3.167739924216664E-02, \ -6.183281639699825E-02, 4.515274811396188E-01, 1.060858442601201E-01, \ -5.624698000526564E-02, -7.388749473949220E-01, 8.327955875718944E-02, \ -4.730013829225772E-02, -9.811237074398366E-01, 2.608831452074966E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 1.198105245928960E-01, \ 4.730013829225772E-02, 9.811237074398366E-01, 2.608831452074966E-02, \ 5.624698000526564E-02, 7.388749473949220E-01, 8.327955875718944E-02, \ 6.183281639699825E-02, -4.515274811396188E-01, 1.060858442601201E-01, \ 2.061044019817992E-01, 7.806540187071476E-01, 3.167739924216664E-02, \ 2.101863370194021E-01, 2.888406804953518E-01, 1.103357066015591E-01, \ 2.124604121926062E-01, -8.907682205113933E-01, 6.854209870863227E-02, \ 2.899888936344285E-01, -1.640917354232377E-01, 1.271636872050067E-01, \ 3.245616103968320E-01, -6.112729098917052E-01, 1.024013654183961E-01, \ 3.449909757079617E-01, 5.171112886647338E-01, 6.683630505556533E-02, \ 3.501819505299977E-01, 9.155258592028724E-01, 5.647374387294429E-02, \ 4.576710954771651E-01, -9.804344277407575E-01, 2.360353464684936E-02, \ 4.843104169217222E-01, 6.372481900547796E-01, 7.509621769261574E-02, \ 5.204497226646213E-01, 1.319110721429938E-01, 1.271745083852966E-01, \ 5.522558344482561E-01, -7.877180001548971E-01, 7.542302799441891E-02, \ 5.650612797733545E-01, -3.562777186069158E-01, 1.145600986645687E-01, \ 5.911965681070577E-01, 9.890895416891479E-01, 1.619432554055879E-02, \ 6.567593878397442E-01, 8.187456800244232E-01, 6.430400825705974E-02, \ 7.142591688630336E-01, 4.144687459254282E-01, 9.862108370826694E-02, \ 7.339165122981658E-01, -9.301444324799357E-01, 3.698855138726674E-02, \ 7.650572339362595E-01, -5.862972313979000E-01, 7.938451847571938E-02, \ 7.730414957980034E-01, -8.238831136924889E-02, 1.001138265151715E-01, \ 8.361991822628865E-01, 9.403589726574770E-01, 2.822764839262689E-02, \ 8.645217306506207E-01, 6.631996105098346E-01, 5.773686209899585E-02, \ 8.910382534296201E-01, -9.945369448321910E-01, 6.887461729231832E-03, \ 8.955283373897494E-01, -7.976174402318889E-01, 3.990477349231469E-02, \ 9.094971072531579E-01, 2.172757421209814E-01, 6.345799736852624E-02, \ 9.202706700587867E-01, -3.511851149995373E-01, 5.773555533944277E-02, \ 9.683241755943918E-01, 8.352830082748723E-01, 1.956137669036511E-02, \ 9.691016249998836E-01, 9.857365066859964E-01, 4.619328461670566E-03, \ 9.782104202505005E-01, -9.275801424350509E-01, 1.011830773881234E-02, \ 9.813999666122014E-01, 4.952365265213790E-01, 2.248743945205191E-02, \ 9.849643667633750E-01, -6.212597907298936E-01, 1.808240699704512E-02, \ 9.882811207043626E-01, -5.499680659586386E-02, 2.092785503234627E-02 ] ) return xyw def smr19s ( ): #*****************************************************************************80 # ## smr19S returns the rotationally invariant SMR rule of degree 19. # # Discussion: # # DEGREE: 19 # ROTATIONALLY INVARIANT: (X,Y),(-Y,X),(-X,-Y),(Y,-X). # POINTS CARDINALITY: 68 # NORM INF MOMS. RESIDUAL: 2.63678e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*68), the requested rule. # import numpy as np xyw = np.array ( [ \ 6.772712303303220E-02, 1.091623307294788E-01, 5.494509440087280E-02, \ 1.911320239476111E-01, 7.684428790753622E-01, 9.924039371581232E-02, \ 1.293584417049455E-01, 9.843401047067886E-01, 2.298164089064930E-02, \ 2.653188588974263E-01, 3.187377804093571E-01, 1.356277329376223E-01, \ 4.805884103058745E-01, 5.883672104526556E-01, 1.092830463202312E-01, \ 4.353820421144143E-01, 9.253041863610407E-01, 5.332719030254342E-02, \ 5.327122733511525E-01, 5.307888414194004E-02, 1.342811802398570E-01, \ 6.817257899596626E-01, 8.006754071171294E-01, 6.668259225153295E-02, \ 6.897274550636672E-01, 9.904094449990978E-01, 1.399432148751916E-02, \ 8.960307328244307E-01, 1.256777467976840E-01, 6.752580403681208E-02, \ 7.189012994269330E-01, 3.612251785232622E-01, 1.014916530440626E-01, \ 8.636764064784566E-01, 6.273567750914366E-01, 5.639122590523545E-02, \ 8.689071260438135E-01, 9.214958682077944E-01, 2.840189695206082E-02, \ 9.851138463638244E-01, 3.506711929883037E-01, 1.440758011223270E-02, \ 9.604323781459383E-01, 4.868528161195464E-01, 1.812287875530189E-02, \ 9.757200071559576E-01, 7.955215584636620E-01, 1.826958037918748E-02, \ 9.734329880957604E-01, 9.798840213938864E-01, 5.026188268466660E-03, \ -1.091623307294788E-01, 6.772712303303220E-02, 5.494509440087280E-02, \ -7.684428790753622E-01, 1.911320239476111E-01, 9.924039371581232E-02, \ -9.843401047067886E-01, 1.293584417049455E-01, 2.298164089064930E-02, \ -3.187377804093571E-01, 2.653188588974263E-01, 1.356277329376223E-01, \ -5.883672104526556E-01, 4.805884103058745E-01, 1.092830463202312E-01, \ -9.253041863610407E-01, 4.353820421144143E-01, 5.332719030254342E-02, \ -5.307888414194004E-02, 5.327122733511525E-01, 1.342811802398570E-01, \ -8.006754071171294E-01, 6.817257899596626E-01, 6.668259225153295E-02, \ -9.904094449990978E-01, 6.897274550636672E-01, 1.399432148751916E-02, \ -1.256777467976840E-01, 8.960307328244307E-01, 6.752580403681208E-02, \ -3.612251785232622E-01, 7.189012994269330E-01, 1.014916530440626E-01, \ -6.273567750914366E-01, 8.636764064784566E-01, 5.639122590523545E-02, \ -9.214958682077944E-01, 8.689071260438135E-01, 2.840189695206082E-02, \ -3.506711929883037E-01, 9.851138463638244E-01, 1.440758011223270E-02, \ -4.868528161195464E-01, 9.604323781459383E-01, 1.812287875530189E-02, \ -7.955215584636620E-01, 9.757200071559576E-01, 1.826958037918748E-02, \ -9.798840213938864E-01, 9.734329880957604E-01, 5.026188268466660E-03, \ -6.772712303303220E-02, -1.091623307294788E-01, 5.494509440087280E-02, \ -1.911320239476111E-01, -7.684428790753622E-01, 9.924039371581232E-02, \ -1.293584417049455E-01, -9.843401047067886E-01, 2.298164089064930E-02, \ -2.653188588974263E-01, -3.187377804093571E-01, 1.356277329376223E-01, \ -4.805884103058745E-01, -5.883672104526556E-01, 1.092830463202312E-01, \ -4.353820421144143E-01, -9.253041863610407E-01, 5.332719030254342E-02, \ -5.327122733511525E-01, -5.307888414194004E-02, 1.342811802398570E-01, \ -6.817257899596626E-01, -8.006754071171294E-01, 6.668259225153295E-02, \ -6.897274550636672E-01, -9.904094449990978E-01, 1.399432148751916E-02, \ -8.960307328244307E-01, -1.256777467976840E-01, 6.752580403681208E-02, \ -7.189012994269330E-01, -3.612251785232622E-01, 1.014916530440626E-01, \ -8.636764064784566E-01, -6.273567750914366E-01, 5.639122590523545E-02, \ -8.689071260438135E-01, -9.214958682077944E-01, 2.840189695206082E-02, \ -9.851138463638244E-01, -3.506711929883037E-01, 1.440758011223270E-02, \ -9.604323781459383E-01, -4.868528161195464E-01, 1.812287875530189E-02, \ -9.757200071559576E-01, -7.955215584636620E-01, 1.826958037918748E-02, \ -9.734329880957604E-01, -9.798840213938864E-01, 5.026188268466660E-03, \ 1.091623307294788E-01, -6.772712303303220E-02, 5.494509440087280E-02, \ 7.684428790753622E-01, -1.911320239476111E-01, 9.924039371581232E-02, \ 9.843401047067886E-01, -1.293584417049455E-01, 2.298164089064930E-02, \ 3.187377804093571E-01, -2.653188588974263E-01, 1.356277329376223E-01, \ 5.883672104526556E-01, -4.805884103058745E-01, 1.092830463202312E-01, \ 9.253041863610407E-01, -4.353820421144143E-01, 5.332719030254342E-02, \ 5.307888414194004E-02, -5.327122733511525E-01, 1.342811802398570E-01, \ 8.006754071171294E-01, -6.817257899596626E-01, 6.668259225153295E-02, \ 9.904094449990978E-01, -6.897274550636672E-01, 1.399432148751916E-02, \ 1.256777467976840E-01, -8.960307328244307E-01, 6.752580403681208E-02, \ 3.612251785232622E-01, -7.189012994269330E-01, 1.014916530440626E-01, \ 6.273567750914366E-01, -8.636764064784566E-01, 5.639122590523545E-02, \ 9.214958682077944E-01, -8.689071260438135E-01, 2.840189695206082E-02, \ 3.506711929883037E-01, -9.851138463638244E-01, 1.440758011223270E-02, \ 4.868528161195464E-01, -9.604323781459383E-01, 1.812287875530189E-02, \ 7.955215584636620E-01, -9.757200071559576E-01, 1.826958037918748E-02, \ 9.798840213938864E-01, -9.734329880957604E-01, 5.026188268466660E-03 ] ) return xyw def smr20 ( ): #*****************************************************************************80 # ## smr20 returns the SMR rule of degree 20. # # Discussion: # # DEGREE: 20 # POINTS CARDINALITY: 78 # NORM INF MOMS. RESIDUAL: 2.28983e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*78), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.915878317634396E-01, -3.766765890053987E-01, 1.499554515729458E-02, \ -9.848784210298892E-01, 2.360994416770047E-01, 2.023115319845336E-02, \ -9.825526677091110E-01, -8.035427779709161E-01, 1.282555877962797E-02, \ -9.823044706287086E-01, 9.079824601518448E-01, 8.347241351837816E-03, \ -9.779664722705005E-01, 6.550056336206199E-01, 1.862995031692569E-02, \ -9.749883694415311E-01, -9.764755256224437E-01, 4.686323174122413E-03, \ -9.385487288532800E-01, 9.860342433350299E-01, 5.797911563640461E-03, \ -9.382963126427573E-01, -8.801426949855569E-02, 4.706757194633274E-02, \ -9.249968857981914E-01, -6.085959286922041E-01, 4.012822177863082E-02, \ -8.999893404040346E-01, 4.529514070355635E-01, 5.107860141818281E-02, \ -8.920744993132258E-01, -9.198780734342489E-01, 2.159208371061492E-02, \ -8.839154125809222E-01, 8.143818242625289E-01, 3.594236238111754E-02, \ -8.255579083847894E-01, -3.654427417348043E-01, 6.695838633949613E-02, \ -8.150245024284021E-01, 1.358607026009545E-01, 6.745427113661845E-02, \ -7.845038084549548E-01, 9.550568485953186E-01, 2.204090981614230E-02, \ -7.824159434580745E-01, -7.878743325718499E-01, 4.748312482965101E-02, \ -7.695472095330197E-01, -9.958600578952408E-01, 8.095042436189770E-03, \ -7.297305046678980E-01, 6.478626088426425E-01, 7.099765909663569E-02, \ -6.917823169027344E-01, 3.281317067480576E-01, 5.185357866003446E-02, \ -6.707656574849767E-01, -1.664730150689492E-01, 7.925719271981636E-02, \ -6.531604608468555E-01, -6.061553872260436E-01, 6.838834261564096E-02, \ -6.077773437763014E-01, 8.732147826609341E-01, 4.367407053165663E-02, \ -6.066275299755738E-01, -9.326014647185664E-01, 3.595011352210572E-02, \ -5.368890549246464E-01, 9.928457944663468E-01, 1.126554474822698E-02, \ -5.316204099083646E-01, 6.576158887431759E-02, 8.069676572542248E-02, \ -4.990046627082800E-01, 4.435890153276254E-01, 9.122827397472959E-02, \ -4.796158821615813E-01, -4.431584361510255E-01, 8.384497173647569E-02, \ -4.453245842342572E-01, -8.121904960479558E-01, 5.866651296620028E-02, \ -4.339460304187116E-01, 7.546357919895570E-01, 6.052390807315380E-02, \ -3.360460286836234E-01, -1.779527551281239E-01, 9.606753662405314E-02, \ -3.163304450629529E-01, -9.789738490980646E-01, 2.421886578475265E-02, \ -2.973007276058863E-01, 9.384528339104452E-01, 3.945003410423680E-02, \ -2.583665449486478E-01, -6.746223007740130E-01, 7.803382675359716E-02, \ -2.518910778242828E-01, 2.047144992617838E-01, 1.190753521874101E-01, \ -2.350658939126170E-01, 6.176223949714494E-01, 8.152900900964591E-02, \ -1.249372040555246E-01, -4.012798196143892E-01, 9.737789681157598E-02, \ -1.071681420632334E-01, 9.911853557002673E-01, 7.840583991172302E-03, \ -7.990032115620818E-02, -8.881537557485726E-01, 6.417774009554068E-02, \ -4.818581787472142E-02, 8.368871897464495E-01, 6.958137992100039E-02, \ -6.302932436761816E-03, 4.427387497778728E-01, 1.046411531707668E-01, \ 6.282561382377720E-03, -4.735863969094835E-02, 1.283072770780011E-01, \ 7.678421140871043E-02, -6.515968986198225E-01, 7.386235866198392E-02, \ 1.223163344818137E-01, -5.049264867963420E-01, 3.280543393245010E-02, \ 1.476259613184704E-01, 9.693655840355563E-01, 2.767850463294367E-02, \ 1.518625838305689E-01, -9.802704961935971E-01, 2.416012781979250E-02, \ 2.026981528589298E-01, 6.904257555809832E-01, 8.975917019163195E-02, \ 2.329194026833933E-01, 2.327373099667877E-01, 1.156666854710510E-01, \ 2.594187814838830E-01, -2.856358493697289E-01, 1.124110482665555E-01, \ 2.798470302423499E-01, -8.056133086386197E-01, 7.131679353184883E-02, \ 3.814217712474836E-01, 8.883375933116525E-01, 5.600628102613372E-02, \ 4.444592404902306E-01, 5.043261157258173E-01, 1.006394209690602E-01, \ 4.558914387037205E-01, -5.329822923030598E-01, 9.411407048103884E-02, \ 4.614020071813320E-01, 4.486972130091344E-03, 1.101092346172853E-01, \ 4.685495664357138E-01, -9.368544770988728E-01, 4.082934734266681E-02, \ 5.560918457946907E-01, 9.862938876987586E-01, 1.658263314370683E-02, \ 6.138352275991088E-01, 7.500124042821561E-01, 7.207159699616439E-02, \ 6.168426991815920E-01, -7.309006089346149E-01, 6.388336371014162E-02, \ 6.496172646332740E-01, -2.465046206462174E-01, 9.502316165822158E-02, \ 6.597659995735623E-01, 2.810856634851854E-01, 9.635446672099211E-02, \ 6.758048936769788E-01, -9.975229702582141E-01, 8.901892537462009E-03, \ 7.526986651007189E-01, -8.790172927450672E-01, 3.744847919043556E-02, \ 7.612710727469121E-01, 9.187271298549152E-01, 3.541134799086990E-02, \ 7.917231830960033E-01, -4.936809625913063E-01, 6.733975809456394E-02, \ 8.045897042890074E-01, 5.573763685706831E-01, 6.859164893126736E-02, \ 8.267194449217807E-01, 2.268030189899398E-02, 7.832191919270795E-02, \ 8.905802715963324E-01, -9.579826342974288E-01, 1.558785638304684E-02, \ 8.926961921705238E-01, -7.092071287453895E-01, 3.889483241199626E-02, \ 9.008369589898633E-01, 9.865275306057119E-01, 7.998523354461931E-03, \ 9.055629673123163E-01, 7.845529526667002E-01, 3.438925925800883E-02, \ 9.323802074714704E-01, -2.645795079832657E-01, 4.838142723685821E-02, \ 9.345858376931122E-01, 3.200026555755083E-01, 4.824416289256322E-02, \ 9.738506914356970E-01, -8.469006629251953E-01, 1.394893863211126E-02, \ 9.755796434358871E-01, 8.802225242154167E-01, 6.292208457909152E-03, \ 9.843147800221137E-01, -5.383749684018156E-01, 1.737917079753502E-02, \ 9.849316953313286E-01, 9.464841822891732E-01, 4.298012753035497E-03, \ 9.851840541929131E-01, 6.021648971571338E-01, 1.660764544264520E-02, \ 9.870587239914860E-01, -9.834157626132080E-01, 2.426383339927545E-03, \ 9.921802352398980E-01, 2.608826889643944E-02, 1.626098469219482E-02 ] ) return xyw def smr21 ( ): #*****************************************************************************80 # ## smr21 returns the SMR rule of degree 21. # # Discussion: # # DEGREE: 21 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 81 # NORM INF MOMS. RESIDUAL: 4.44089e-15 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*81), the requested rule. # import numpy as np xyw = np.array ( [ \ 2.659786054558319E-01, 2.472943466792205E-01, 1.257081274315271E-01, \ 2.966299561078732E-01, 6.837659120145181E-01, 9.195620074644660E-02, \ 3.476456848560975E-01, 9.391305012893792E-01, 3.823913002575823E-02, \ 5.204899365134467E-01, 4.701056221362075E-01, 9.955659700462254E-02, \ 5.565331479249288E-01, 8.299687476559192E-01, 5.711233679557120E-02, \ 5.608625825041144E-01, 9.938235381537796E-01, 8.125409684532186E-03, \ 7.107545267842089E-01, 2.218786231241980E-01, 8.989795633682901E-02, \ 7.323028382034139E-01, 6.675759613958541E-01, 6.285712965516167E-02, \ 7.248337121391071E-01, 9.556008374660931E-01, 2.068885521020362E-02, \ 8.678958423780866E-01, 4.595394054487673E-01, 5.463376630254965E-02, \ 8.501142309217191E-01, 8.692220828069680E-01, 2.950403142043507E-02, \ 9.142859758630335E-01, 9.852274923275850E-01, 6.850217129206400E-03, \ 9.537223544012101E-01, 2.050108803358328E-01, 3.630414793101230E-02, \ 9.934425198626209E-01, 5.102048128337472E-01, 1.110556726680624E-02, \ 9.448573049959050E-01, 7.218738735054576E-01, 2.723130314700101E-02, \ 9.865716562931908E-01, 8.882998675210052E-01, 6.165546352541271E-03, \ 9.790570750021207E-01, 9.587134606894607E-01, 2.900715554613127E-03, \ 1.944817128807972E-02, 4.950400647800665E-01, 1.165426493105556E-01, \ 5.600805589569329E-02, 8.501230581964183E-01, 6.754741413634147E-02, \ 1.000588448960449E-01, 9.908677016040155E-01, 1.332984242008183E-02, \ -2.472943466792205E-01, 2.659786054558319E-01, 1.257081274315271E-01, \ -6.837659120145181E-01, 2.966299561078732E-01, 9.195620074644660E-02, \ -9.391305012893792E-01, 3.476456848560975E-01, 3.823913002575823E-02, \ -4.701056221362075E-01, 5.204899365134467E-01, 9.955659700462254E-02, \ -8.299687476559192E-01, 5.565331479249288E-01, 5.711233679557120E-02, \ -9.938235381537796E-01, 5.608625825041144E-01, 8.125409684532186E-03, \ -2.218786231241980E-01, 7.107545267842089E-01, 8.989795633682901E-02, \ -6.675759613958541E-01, 7.323028382034139E-01, 6.285712965516167E-02, \ -9.556008374660931E-01, 7.248337121391071E-01, 2.068885521020362E-02, \ -4.595394054487673E-01, 8.678958423780866E-01, 5.463376630254965E-02, \ -8.692220828069680E-01, 8.501142309217191E-01, 2.950403142043507E-02, \ -9.852274923275850E-01, 9.142859758630335E-01, 6.850217129206400E-03, \ -2.050108803358328E-01, 9.537223544012101E-01, 3.630414793101230E-02, \ -5.102048128337472E-01, 9.934425198626209E-01, 1.110556726680624E-02, \ -7.218738735054576E-01, 9.448573049959050E-01, 2.723130314700101E-02, \ -8.882998675210052E-01, 9.865716562931908E-01, 6.165546352541271E-03, \ -9.587134606894607E-01, 9.790570750021207E-01, 2.900715554613127E-03, \ -4.950400647800665E-01, 1.944817128807972E-02, 1.165426493105556E-01, \ -8.501230581964183E-01, 5.600805589569329E-02, 6.754741413634147E-02, \ -9.908677016040155E-01, 1.000588448960449E-01, 1.332984242008183E-02, \ -2.659786054558319E-01, -2.472943466792205E-01, 1.257081274315271E-01, \ -2.966299561078732E-01, -6.837659120145181E-01, 9.195620074644660E-02, \ -3.476456848560975E-01, -9.391305012893792E-01, 3.823913002575823E-02, \ -5.204899365134467E-01, -4.701056221362075E-01, 9.955659700462254E-02, \ -5.565331479249288E-01, -8.299687476559192E-01, 5.711233679557120E-02, \ -5.608625825041144E-01, -9.938235381537796E-01, 8.125409684532186E-03, \ -7.107545267842089E-01, -2.218786231241980E-01, 8.989795633682901E-02, \ -7.323028382034139E-01, -6.675759613958541E-01, 6.285712965516167E-02, \ -7.248337121391071E-01, -9.556008374660931E-01, 2.068885521020362E-02, \ -8.678958423780866E-01, -4.595394054487673E-01, 5.463376630254965E-02, \ -8.501142309217191E-01, -8.692220828069680E-01, 2.950403142043507E-02, \ -9.142859758630335E-01, -9.852274923275850E-01, 6.850217129206400E-03, \ -9.537223544012101E-01, -2.050108803358328E-01, 3.630414793101230E-02, \ -9.934425198626209E-01, -5.102048128337472E-01, 1.110556726680624E-02, \ -9.448573049959050E-01, -7.218738735054576E-01, 2.723130314700101E-02, \ -9.865716562931908E-01, -8.882998675210052E-01, 6.165546352541271E-03, \ -9.790570750021207E-01, -9.587134606894607E-01, 2.900715554613127E-03, \ -1.944817128807972E-02, -4.950400647800665E-01, 1.165426493105556E-01, \ -5.600805589569329E-02, -8.501230581964183E-01, 6.754741413634147E-02, \ -1.000588448960449E-01, -9.908677016040155E-01, 1.332984242008183E-02, \ 2.472943466792205E-01, -2.659786054558319E-01, 1.257081274315271E-01, \ 6.837659120145181E-01, -2.966299561078732E-01, 9.195620074644660E-02, \ 9.391305012893792E-01, -3.476456848560975E-01, 3.823913002575823E-02, \ 4.701056221362075E-01, -5.204899365134467E-01, 9.955659700462254E-02, \ 8.299687476559192E-01, -5.565331479249288E-01, 5.711233679557120E-02, \ 9.938235381537796E-01, -5.608625825041144E-01, 8.125409684532186E-03, \ 2.218786231241980E-01, -7.107545267842089E-01, 8.989795633682901E-02, \ 6.675759613958541E-01, -7.323028382034139E-01, 6.285712965516167E-02, \ 9.556008374660931E-01, -7.248337121391071E-01, 2.068885521020362E-02, \ 4.595394054487673E-01, -8.678958423780866E-01, 5.463376630254965E-02, \ 8.692220828069680E-01, -8.501142309217191E-01, 2.950403142043507E-02, \ 9.852274923275850E-01, -9.142859758630335E-01, 6.850217129206400E-03, \ 2.050108803358328E-01, -9.537223544012101E-01, 3.630414793101230E-02, \ 5.102048128337472E-01, -9.934425198626209E-01, 1.110556726680624E-02, \ 7.218738735054576E-01, -9.448573049959050E-01, 2.723130314700101E-02, \ 8.882998675210052E-01, -9.865716562931908E-01, 6.165546352541271E-03, \ 9.587134606894607E-01, -9.790570750021207E-01, 2.900715554613127E-03, \ 4.950400647800665E-01, -1.944817128807972E-02, 1.165426493105556E-01, \ 8.501230581964183E-01, -5.600805589569329E-02, 6.754741413634147E-02, \ 9.908677016040155E-01, -1.000588448960449E-01, 1.332984242008183E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 1.349722245528155E-01 ] ) return xyw def smr22 ( ): #*****************************************************************************80 # ## smr22 returns the SMR rule of degree 22. # # Discussion: # # DEGREE: 22 # POINTS CARDINALITY: 93 # NORM INF MOMS. RESIDUAL: 9.10296e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*93), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.886329057797582E-01, -1.145674729933659E-01, 1.325842639382102E-02, \ 9.888026938509622E-01, -5.213303149527411E-01, 1.068979190883013E-02, \ 9.661816000824490E-01, -7.555070898927371E-01, 1.743977208490352E-02, \ 9.889031095854282E-01, -9.320977012046493E-01, 5.174381878169184E-03, \ 9.873701927717461E-01, 9.897035459144938E-01, 1.707304801541134E-03, \ 9.905941115128364E-01, 8.327302191279294E-01, 6.754790334156039E-03, \ 9.706393731700478E-01, 5.982438926502055E-01, 2.062095495154808E-02, \ 9.803136579961507E-01, 2.717042647614646E-01, 1.891617092472248E-02, \ 9.341083383086605E-01, -3.353056638554749E-01, 3.390112966783673E-02, \ 8.734893606329978E-01, -6.054983585922311E-01, 3.753341638181854E-02, \ 8.810582900635474E-01, -8.777017334048872E-01, 2.414667023001881E-02, \ 9.308712251904757E-01, -9.880767541958921E-01, 5.413462408552709E-03, \ 9.377374302689546E-01, 9.330744362659844E-01, 1.265810122238417E-02, \ 8.843781920205257E-01, 7.681591801566370E-01, 3.367838185981432E-02, \ 8.775411599331090E-01, 4.195677919703100E-01, 4.701250942104521E-02, \ 9.082100522297584E-01, 4.460741468226298E-02, 4.492517531449552E-02, \ 7.763303548789647E-01, -4.810624802969050E-01, 3.017348276324992E-02, \ 7.230162511431557E-01, -7.596607824735281E-01, 4.911947899024260E-02, \ 7.562342329425361E-01, -9.545271924860271E-01, 1.392058621129393E-02, \ 8.327763332833239E-01, 9.863527280259253E-01, 8.265982196594024E-03, \ 7.412680367128046E-01, 8.954212932861624E-01, 3.350811254077402E-02, \ 7.400126973983402E-01, 6.111125638321177E-01, 5.811729500469508E-02, \ 7.414564617437679E-01, 1.965720776730482E-01, 7.150247641033709E-02, \ 7.867408087541262E-01, -1.930389785977610E-01, 6.417378369478929E-02, \ 5.369437186749637E-01, -6.314307127870589E-01, 4.820720884716240E-02, \ 5.461961159674565E-01, -8.910958585786000E-01, 4.010297901331633E-02, \ 7.505636824335776E-01, -9.781952487239193E-01, 5.423665310144266E-03, \ 5.668739124520142E-01, 9.769610350593898E-01, 1.855890684449772E-02, \ 5.608631907999050E-01, 7.717573834145061E-01, 5.676854811058375E-02, \ 5.612115855209996E-01, 4.088149453043886E-01, 8.333374346661079E-02, \ 5.661336430919435E-01, -4.176475015217607E-02, 9.157138052866115E-02, \ 6.134724653625782E-01, -4.169917924461408E-01, 6.572843506020827E-02, \ 3.374627534596129E-01, -7.953338524031655E-01, 4.698932393055661E-02, \ 5.506194243847290E-01, -9.906600094074560E-01, 6.956589831798293E-03, \ 3.682032600755504E-01, 8.998189655297543E-01, 4.291338908110833E-02, \ 3.503173557999109E-01, 6.043160593908300E-01, 8.199842424347994E-02, \ 3.484934492594987E-01, 1.842187014808652E-01, 1.042545147901201E-01, \ 3.599239753698877E-01, -2.793900622896136E-01, 1.003220388009486E-01, \ 3.352794040120309E-01, -6.090983723997480E-01, 5.250936392916155E-02, \ 1.648479846846835E-01, -9.222811023803827E-01, 3.600095811243217E-02, \ 3.409639556515009E-01, -9.775579820216516E-01, 1.513630382707296E-02, \ 2.013308254889806E-01, 9.817828174442371E-01, 1.803413215387369E-02, \ 1.340901732488610E-01, 7.766562660948982E-01, 6.844087294220280E-02, \ 1.144967045243097E-01, 4.069075707084039E-01, 1.019382263127832E-01, \ 1.189485784665626E-01, -5.433922354403713E-02, 1.136907024324531E-01, \ 1.058758908864689E-01, -4.793787778363424E-01, 9.348793573923811E-02, \ 2.839855852222449E-02, -7.559768193014593E-01, 6.803236606704954E-02, \ -4.712493250696739E-02, -9.874476808665996E-01, 1.515020459751181E-02, \ -1.410549552011679E-01, 9.945136764387909E-01, 7.185771234424889E-03, \ -5.100979131120797E-02, 9.148649196209385E-01, 4.369402100644239E-02, \ -1.137013612566373E-01, 6.139356044623114E-01, 8.777317450897354E-02, \ -1.244170197023402E-01, 1.823653793283892E-01, 1.117684867762398E-01, \ -1.370122651236654E-01, -2.712575708608372E-01, 1.085208525145446E-01, \ -2.232031959837765E-01, -6.067425313332153E-01, 8.558870495241622E-02, \ -1.940829548165339E-01, -8.901639697157221E-01, 4.867603590079570E-02, \ -4.081653916012992E-01, -9.709368148205605E-01, 2.331260017933040E-02, \ -3.533981306028999E-01, 9.616410187563108E-01, 2.242566292797548E-02, \ -3.045652224491460E-01, 7.985802428860417E-01, 6.420737202085385E-02, \ -3.526743970139553E-01, 4.146812551454919E-01, 9.787271335988859E-02, \ -3.720004998868196E-01, -3.666778868685774E-02, 1.068882608071387E-01, \ -4.514888617224385E-01, -4.096349836635951E-01, 9.192684575976928E-02, \ -4.429908638318878E-01, -7.743729186166529E-01, 6.295500628522636E-02, \ -6.815740834481019E-01, -9.928214216661736E-01, 7.026776085145282E-03, \ -5.632109089288005E-01, 9.935896447624268E-01, 6.283490740799424E-03, \ -5.621512958714884E-01, 8.896399470067906E-01, 3.761225364844008E-02, \ -5.382057775784931E-01, 6.382212857626252E-01, 7.506638282008458E-02, \ -5.813167555829912E-01, 2.056862702815186E-01, 9.243697007930982E-02, \ -6.516405814152544E-01, -1.846901900997915E-01, 8.505041739260445E-02, \ -6.506998051630787E-01, -6.087053290037806E-01, 6.818365853952568E-02, \ -6.334805048429584E-01, -8.975976820838455E-01, 3.682517885499488E-02, \ -7.472275238683430E-01, 9.641740358177714E-01, 1.669151214269935E-02, \ -7.482067350979565E-01, 7.780755148965470E-01, 4.495260598024266E-02, \ -7.400821884669309E-01, 4.532491832762973E-01, 6.928645874800578E-02, \ -8.105044748991020E-01, 5.416962245544283E-02, 6.619505274805781E-02, \ -8.156792303551951E-01, -4.060746003340047E-01, 6.042829810764130E-02, \ -8.090136873528386E-01, -7.748312229117293E-01, 4.151899530758620E-02, \ -8.335513136071991E-01, -9.535072625443444E-01, 1.514946999120562E-02, \ -8.872174992437346E-01, 8.965769271361460E-01, 2.104433235476698E-02, \ -8.931086765195151E-01, 6.328025905174818E-01, 3.860028858677801E-02, \ -8.916333811989803E-01, 3.038140953910366E-01, 2.786266023247349E-02, \ -9.292789589232818E-01, -1.761834888463487E-01, 4.117008802426377E-02, \ -9.292197203932411E-01, -6.069529981720342E-01, 3.315912528944302E-02, \ -9.385590119112288E-01, -8.777667192165588E-01, 1.580481441801968E-02, \ -9.284304209620261E-01, -9.951824052865140E-01, 2.664793505134054E-03, \ -9.053874905610783E-01, 9.962748823261235E-01, 3.593987239589643E-03, \ -9.747952911035821E-01, 7.907984327057133E-01, 1.405694455607466E-02, \ -9.866861855312228E-01, 5.118586070736004E-01, 1.306184877568784E-02, \ -9.863703578500000E-01, 6.111749406829102E-02, 1.559138821480461E-02, \ -9.889270365025400E-01, -3.994782279754348E-01, 1.342812184963877E-02, \ -9.908021213083021E-01, -7.596541692019284E-01, 7.741415848728735E-03, \ -9.815692523507022E-01, 9.572922384144454E-01, 5.171764118207254E-03, \ -9.471376718841760E-01, 2.927695425907414E-01, 2.000641714794302E-02, \ -9.874787306662429E-01, -9.621211118728035E-01, 3.377128849473962E-03 ] ) return xyw def smr23 ( ): #*****************************************************************************80 # ## smr23 returns the SMR rule of degree 23. # # Discussion: # # DEGREE: 23 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 96 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*96), the requested rule. # import numpy as np xyw = np.array ( [ \ 1.853314713323298E-01, -1.194182324265387E-02, 6.529202325372914E-02, \ 1.659642315868930E-01, 3.367719887764350E-01, 6.231767492170222E-02, \ 9.876738163488666E-02, 8.306969615801286E-01, 6.201416548818468E-02, \ 8.869002322225777E-02, 9.854102218186098E-01, 1.324109920098785E-02, \ 3.982734759789451E-01, 1.335875115514376E-01, 6.923888037215149E-02, \ 2.307675985221515E-01, 5.659053189940804E-01, 7.857529731333650E-02, \ 4.154938603680680E-01, 7.488761930933899E-01, 6.583136220575310E-02, \ 3.258331163946451E-01, 9.405377066569092E-01, 3.516290651110937E-02, \ 4.718068156165912E-01, 3.742733716935872E-01, 7.391201672123172E-02, \ 6.214843667854110E-01, 5.757611415753823E-01, 6.633209783965152E-02, \ 6.111965358277813E-01, 8.835074910197936E-01, 4.096440841363334E-02, \ 5.425835924085424E-01, 9.934011708856250E-01, 9.791218112671066E-03, \ 6.454787887214178E-01, 7.290903205395782E-02, 7.527535021842932E-02, \ 7.663883133711373E-01, 3.281528217933192E-01, 6.564383307544155E-02, \ 7.763362157153701E-01, 7.457829318163177E-01, 4.507790595281267E-02, \ 7.869974305642068E-01, 9.638578123979478E-01, 1.814838304609862E-02, \ 9.212736070974256E-01, 1.716486762023320E-01, 4.117445213281692E-02, \ 8.886542125222323E-01, 5.442346685704154E-01, 4.215575969073930E-02, \ 9.057049801164405E-01, 8.685411402721253E-01, 2.274825956928111E-02, \ 9.457512810375365E-01, 9.860275528096041E-01, 5.078778817313888E-03, \ 9.878935301664215E-01, 7.759170798217239E-02, 4.765144456210194E-03, \ 9.836661500284433E-01, 4.041056452269987E-01, 1.596460029217852E-02, \ 9.734962304125074E-01, 7.140118690494257E-01, 1.705297096357996E-02, \ 9.936548069316368E-01, 9.210767826681668E-01, 4.241411430955866E-03, \ 1.194182324265387E-02, 1.853314713323298E-01, 6.529202325372914E-02, \ -3.367719887764350E-01, 1.659642315868930E-01, 6.231767492170222E-02, \ -8.306969615801286E-01, 9.876738163488666E-02, 6.201416548818468E-02, \ -9.854102218186098E-01, 8.869002322225777E-02, 1.324109920098785E-02, \ -1.335875115514376E-01, 3.982734759789451E-01, 6.923888037215149E-02, \ -5.659053189940804E-01, 2.307675985221515E-01, 7.857529731333650E-02, \ -7.488761930933899E-01, 4.154938603680680E-01, 6.583136220575310E-02, \ -9.405377066569092E-01, 3.258331163946451E-01, 3.516290651110937E-02, \ -3.742733716935872E-01, 4.718068156165912E-01, 7.391201672123172E-02, \ -5.757611415753823E-01, 6.214843667854110E-01, 6.633209783965152E-02, \ -8.835074910197936E-01, 6.111965358277813E-01, 4.096440841363334E-02, \ -9.934011708856250E-01, 5.425835924085424E-01, 9.791218112671066E-03, \ -7.290903205395782E-02, 6.454787887214178E-01, 7.527535021842932E-02, \ -3.281528217933192E-01, 7.663883133711373E-01, 6.564383307544155E-02, \ -7.457829318163177E-01, 7.763362157153701E-01, 4.507790595281267E-02, \ -9.638578123979478E-01, 7.869974305642068E-01, 1.814838304609862E-02, \ -1.716486762023320E-01, 9.212736070974256E-01, 4.117445213281692E-02, \ -5.442346685704154E-01, 8.886542125222323E-01, 4.215575969073930E-02, \ -8.685411402721253E-01, 9.057049801164405E-01, 2.274825956928111E-02, \ -9.860275528096041E-01, 9.457512810375365E-01, 5.078778817313888E-03, \ -7.759170798217239E-02, 9.878935301664215E-01, 4.765144456210194E-03, \ -4.041056452269987E-01, 9.836661500284433E-01, 1.596460029217852E-02, \ -7.140118690494257E-01, 9.734962304125074E-01, 1.705297096357996E-02, \ -9.210767826681668E-01, 9.936548069316368E-01, 4.241411430955866E-03, \ -1.853314713323298E-01, 1.194182324265387E-02, 6.529202325372914E-02, \ -1.659642315868930E-01, -3.367719887764350E-01, 6.231767492170222E-02, \ -9.876738163488666E-02, -8.306969615801286E-01, 6.201416548818468E-02, \ -8.869002322225777E-02, -9.854102218186098E-01, 1.324109920098785E-02, \ -3.982734759789451E-01, -1.335875115514376E-01, 6.923888037215149E-02, \ -2.307675985221515E-01, -5.659053189940804E-01, 7.857529731333650E-02, \ -4.154938603680680E-01, -7.488761930933899E-01, 6.583136220575310E-02, \ -3.258331163946451E-01, -9.405377066569092E-01, 3.516290651110937E-02, \ -4.718068156165912E-01, -3.742733716935872E-01, 7.391201672123172E-02, \ -6.214843667854110E-01, -5.757611415753823E-01, 6.633209783965152E-02, \ -6.111965358277813E-01, -8.835074910197936E-01, 4.096440841363334E-02, \ -5.425835924085424E-01, -9.934011708856250E-01, 9.791218112671066E-03, \ -6.454787887214178E-01, -7.290903205395782E-02, 7.527535021842932E-02, \ -7.663883133711373E-01, -3.281528217933192E-01, 6.564383307544155E-02, \ -7.763362157153701E-01, -7.457829318163177E-01, 4.507790595281267E-02, \ -7.869974305642068E-01, -9.638578123979478E-01, 1.814838304609862E-02, \ -9.212736070974256E-01, -1.716486762023320E-01, 4.117445213281692E-02, \ -8.886542125222323E-01, -5.442346685704154E-01, 4.215575969073930E-02, \ -9.057049801164405E-01, -8.685411402721253E-01, 2.274825956928111E-02, \ -9.457512810375365E-01, -9.860275528096041E-01, 5.078778817313888E-03, \ -9.878935301664215E-01, -7.759170798217239E-02, 4.765144456210194E-03, \ -9.836661500284433E-01, -4.041056452269987E-01, 1.596460029217852E-02, \ -9.734962304125074E-01, -7.140118690494257E-01, 1.705297096357996E-02, \ -9.936548069316368E-01, -9.210767826681668E-01, 4.241411430955866E-03, \ -1.194182324265387E-02, -1.853314713323298E-01, 6.529202325372914E-02, \ 3.367719887764350E-01, -1.659642315868930E-01, 6.231767492170222E-02, \ 8.306969615801286E-01, -9.876738163488666E-02, 6.201416548818468E-02, \ 9.854102218186098E-01, -8.869002322225777E-02, 1.324109920098785E-02, \ 1.335875115514376E-01, -3.982734759789451E-01, 6.923888037215149E-02, \ 5.659053189940804E-01, -2.307675985221515E-01, 7.857529731333650E-02, \ 7.488761930933899E-01, -4.154938603680680E-01, 6.583136220575310E-02, \ 9.405377066569092E-01, -3.258331163946451E-01, 3.516290651110937E-02, \ 3.742733716935872E-01, -4.718068156165912E-01, 7.391201672123172E-02, \ 5.757611415753823E-01, -6.214843667854110E-01, 6.633209783965152E-02, \ 8.835074910197936E-01, -6.111965358277813E-01, 4.096440841363334E-02, \ 9.934011708856250E-01, -5.425835924085424E-01, 9.791218112671066E-03, \ 7.290903205395782E-02, -6.454787887214178E-01, 7.527535021842932E-02, \ 3.281528217933192E-01, -7.663883133711373E-01, 6.564383307544155E-02, \ 7.457829318163177E-01, -7.763362157153701E-01, 4.507790595281267E-02, \ 9.638578123979478E-01, -7.869974305642068E-01, 1.814838304609862E-02, \ 1.716486762023320E-01, -9.212736070974256E-01, 4.117445213281692E-02, \ 5.442346685704154E-01, -8.886542125222323E-01, 4.215575969073930E-02, \ 8.685411402721253E-01, -9.057049801164405E-01, 2.274825956928111E-02, \ 9.860275528096041E-01, -9.457512810375365E-01, 5.078778817313888E-03, \ 7.759170798217239E-02, -9.878935301664215E-01, 4.765144456210194E-03, \ 4.041056452269987E-01, -9.836661500284433E-01, 1.596460029217852E-02, \ 7.140118690494257E-01, -9.734962304125074E-01, 1.705297096357996E-02, \ 9.210767826681668E-01, -9.936548069316368E-01, 4.241411430955866E-03 ] ) return xyw def smr24 ( ): #*****************************************************************************80 # ## smr24 returns the SMR rule of degree 24. # # Discussion: # # DEGREE: 24 # POINTS CARDINALITY: 109 # NORM INF MOMS. RESIDUAL: 1.33227e-15 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*109), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.947552488434938E-01, -4.385704490896414E-01, 2.698557791124145E-03, \ -9.931097629772323E-01, 6.703739358435329E-01, 7.377682774083533E-03, \ -9.926803856666530E-01, 2.074620875386726E-01, 6.953676686934647E-03, \ -9.906389564778285E-01, 9.389787594673664E-01, 4.005676169355294E-03, \ -9.853982980908041E-01, -1.546975310338203E-01, 1.391680440670080E-02, \ -9.837508975466611E-01, -8.419003469340943E-01, 8.844680842740435E-03, \ -9.834972384053117E-01, -5.844467591604228E-01, 1.101492580337329E-02, \ -9.818922098458703E-01, -9.808906804560406E-01, 2.833762301624789E-03, \ -9.737197710731226E-01, 3.846778957131831E-01, 1.346113092355880E-02, \ -9.500074961120746E-01, 8.209864656561424E-01, 1.735987104490214E-02, \ -9.403701834437002E-01, 9.898046509843106E-01, 4.134638994139726E-03, \ -9.322891009559756E-01, 6.891056205665078E-02, 3.385109951711678E-02, \ -9.291432442434125E-01, -3.649292941055270E-01, 3.313278955371516E-02, \ -9.278770514198088E-01, 5.372507215773373E-01, 2.595775803019849E-02, \ -9.160984294365914E-01, -7.088454133225529E-01, 2.740072723324332E-02, \ -9.158788280467461E-01, -9.354605631847065E-01, 1.341647825529986E-02, \ -8.614049341981235E-01, 9.223186488292008E-01, 1.828556090710842E-02, \ -8.411326781777169E-01, 2.986796133696130E-01, 5.109735452042367E-02, \ -8.399585109946057E-01, 6.941827653602577E-01, 3.578648643426428E-02, \ -8.284250818876616E-01, -1.413597089673544E-01, 5.450666609336831E-02, \ -8.258893393997301E-01, -9.946839974593770E-01, 5.524951523211650E-03, \ -8.061244501112171E-01, -5.249750016790736E-01, 5.069979449576008E-02, \ -8.039912747312149E-01, -8.393703760802331E-01, 3.118857585337858E-02, \ -7.503800600330690E-01, 9.808995135027622E-01, 1.020614373666720E-02, \ -7.159580396066608E-01, 8.204005009530653E-01, 3.345975676433573E-02, \ -7.066954614920985E-01, 5.015305614605768E-01, 6.001952691278750E-02, \ -6.885485793465114E-01, 9.202328849593100E-02, 7.346166114914886E-02, \ -6.800088501791149E-01, -9.443640836874199E-01, 2.298808927262541E-02, \ -6.560939841533527E-01, -3.083819563661853E-01, 7.136431171052350E-02, \ -6.549319709970016E-01, -6.928080924969605E-01, 5.352097766179938E-02, \ -5.986758659840633E-01, 9.036887631193311E-01, 2.206238875433044E-02, \ -5.440986421726908E-01, 6.690288689480005E-01, 5.524621622310746E-02, \ -5.421013331274553E-01, 9.805973671548335E-01, 1.050046021811538E-02, \ -5.117472121011815E-01, 3.140452735180922E-01, 8.289952810298720E-02, \ -5.059194733599800E-01, -9.837457937119135E-01, 1.096035229919467E-02, \ -4.980272781651189E-01, -8.405454275729934E-01, 4.487909208174960E-02, \ -4.827305043646576E-01, -4.980524078016305E-01, 7.003741329201849E-02, \ -4.657032616378755E-01, -8.311620500718582E-02, 9.203159768871901E-02, \ -3.984335431880944E-01, 7.823560336425450E-01, 3.533735180399633E-02, \ -3.812251842054403E-01, 9.211692018557595E-01, 2.479377740140328E-02, \ -3.254324649968378E-01, -6.106485217368141E-01, 1.987123465724002E-02, \ -3.081376572739211E-01, 5.152565145304252E-01, 8.148061878192561E-02, \ -3.061609471247951E-01, -9.953099499439115E-01, 4.421627578115842E-03, \ -3.040806099754977E-01, -6.945205873058414E-01, 4.874084869821138E-02, \ -3.040627168926376E-01, -9.238254614973810E-01, 2.731221830374910E-02, \ -2.730267547433428E-01, 9.914365779967292E-01, 9.183887978612177E-03, \ -2.548424890251378E-01, -3.019158326395579E-01, 9.514384875199645E-02, \ -2.519554856003144E-01, 1.492385558662303E-01, 1.000641506538448E-01, \ -1.931995209634114E-01, 8.232643617111496E-01, 3.769059900817138E-02, \ -1.885349353760669E-01, -8.893470388562837E-01, 8.285027518755494E-03, \ -1.018544959716391E-01, -7.832201508773523E-01, 4.767805838303123E-02, \ -9.655685106805004E-02, 6.703558020663598E-01, 5.541671674358566E-02, \ -7.901309787694769E-02, -9.687392227645953E-01, 1.819078482187320E-02, \ -7.169337674372403E-02, 9.452615682987324E-01, 2.860240343608491E-02, \ -4.349902330261272E-02, -5.144306594431935E-01, 8.777502677071561E-02, \ -2.884848343031785E-02, -7.515483993225638E-02, 1.033082821984657E-01, \ -1.950518268267537E-02, 3.687032706515938E-01, 9.771287132446460E-02, \ 1.000713405257931E-01, -8.778592595775899E-01, 4.025365288851937E-02, \ 1.288386576225213E-01, 8.499166400570952E-01, 4.727125786790465E-02, \ 1.307155265497598E-01, -9.938241813833318E-01, 7.039833852159185E-03, \ 1.308425147211156E-01, 6.526807421421726E-01, 4.979273601404909E-02, \ 1.451164406166477E-01, 9.905591807186089E-01, 1.078258330904423E-02, \ 1.853995153478054E-01, -3.035646033025806E-01, 9.690391758696711E-02, \ 1.943247761163270E-01, -6.769527305130935E-01, 7.109638809439672E-02, \ 2.052879132552834E-01, 1.494567879060908E-01, 1.010903998636895E-01, \ 2.768585369952569E-01, 5.067311062472540E-01, 6.479712852470575E-02, \ 3.149836876173980E-01, -9.498509878332206E-01, 2.600605597250065E-02, \ 3.466439434503832E-01, 9.410184803711036E-01, 2.912818672968244E-02, \ 3.903088921667896E-01, 4.250693093572162E-01, 2.571049499832495E-02, \ 3.993865541451484E-01, 7.683264787575288E-01, 5.493699586057709E-02, \ 4.086593369430472E-01, -4.969944946335217E-01, 7.910634640474691E-02, \ 4.120045473805335E-01, -8.379854233451292E-02, 9.482614431233395E-02, \ 4.170298041496714E-01, -8.110827678737819E-01, 5.059001095427527E-02, \ 4.991948804043371E-01, 2.844383580006540E-01, 7.600131857765238E-02, \ 5.215718300412919E-01, -9.911476542754794E-01, 8.938791600642888E-03, \ 5.358795456370800E-01, 9.892706596240752E-01, 9.652257973711614E-03, \ 5.675663650098263E-01, 6.269930547839709E-01, 5.565333636824790E-02, \ 6.083113501735691E-01, -6.671573460757463E-01, 5.724631842495273E-02, \ 6.091213803480886E-01, -3.002786277521432E-01, 7.620974249495195E-02, \ 6.098130539524327E-01, 8.880641734983817E-01, 3.607781947134865E-02, \ 6.133229089892412E-01, -9.115716813284614E-01, 2.976045072649638E-02, \ 6.644692975845461E-01, 7.278284636752541E-02, 7.402473800633137E-02, \ 7.058360022640749E-01, 4.736368348307747E-01, 5.128474162165504E-02, \ 7.603978094655672E-01, 7.687530787837937E-01, 3.987086504850027E-02, \ 7.680081930648918E-01, 9.719796486153569E-01, 1.425802911781755E-02, \ 7.730566152310493E-01, -8.076103665001979E-01, 3.513944563783513E-02, \ 7.740524973445363E-01, -5.000787609526253E-01, 5.331933422231531E-02, \ 7.765031539359070E-01, -9.744702466310179E-01, 1.298770336406751E-02, \ 8.105891537849745E-01, -1.496106096240346E-01, 5.659879783131575E-02, \ 8.136030860267544E-01, 2.997934729123835E-01, 4.597071032159282E-02, \ 8.738296548638522E-01, 6.252207344858673E-01, 3.235229209061567E-02, \ 8.820767009721266E-01, 8.997350185706089E-01, 1.969080467560540E-02, \ 8.968725800328660E-01, -6.749357059674395E-01, 3.049246549718226E-02, \ 9.008567820439595E-01, -9.076509501580650E-01, 1.724041843190777E-02, \ 9.036351991894711E-01, 1.066673951092828E-01, 3.553262749083069E-02, \ 9.194113498715898E-01, -3.652426921938732E-01, 3.438229944741761E-02, \ 9.235901436599459E-01, 4.967015317618840E-01, 1.373744804296171E-02, \ 9.328830195971040E-01, -9.941380940892665E-01, 2.989382978667606E-03, \ 9.404372628037821E-01, 9.889603686778536E-01, 4.443564861581591E-03, \ 9.607926125333919E-01, 7.879019305115507E-01, 1.649904214759328E-02, \ 9.627435059550357E-01, 3.759293384523862E-01, 1.893234461167443E-02, \ 9.661246051400586E-01, -9.321465960805159E-02, 2.021199306716822E-02, \ 9.772105063681134E-01, -8.054188902050837E-01, 1.143950510739337E-02, \ 9.818083790572272E-01, -5.613562549296841E-01, 1.303588980687769E-02, \ 9.873606864519788E-01, -9.558632391723191E-01, 3.650162385277064E-03, \ 9.909481727417117E-01, 9.350098107984304E-01, 4.199764168210779E-03, \ 9.933228865506706E-01, 1.717028973685849E-01, 7.977198513429708E-03, \ 9.934734927244968E-01, 6.113673375988821E-01, 7.151800672626832E-03, \ 9.958206097496789E-01, -2.883979781434184E-01, 5.617961121686336E-03 ] ) return xyw def smr25 ( ): #*****************************************************************************80 # ## smr25 returns the SMR rule of degree 25. # # Discussion: # # DEGREE: 25 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 113 # NORM INF MOMS. RESIDUAL: 2.04121e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*113), the requested rule. # import numpy as np xyw = np.array ( [ \ 2.408979561244244E-01, 4.202921149345177E-01, 8.649643596540968E-02, \ 2.718022358106373E-01, 7.547569098063632E-01, 5.930450471454697E-02, \ 2.949651173549945E-01, 9.557139743958390E-01, 2.492523876506716E-02, \ 4.390520493777193E-01, 2.026918805813806E-01, 8.650651080976479E-02, \ 4.662064901266157E-01, 5.942245210433184E-01, 6.800866187330593E-02, \ 4.830786617878046E-01, 8.732633185547312E-01, 3.820005521117373E-02, \ 5.045376712354956E-01, 9.940169417092007E-01, 7.120126112016729E-03, \ 7.757488163218268E-01, 1.779409708250335E-01, 5.827884791218824E-02, \ 6.369947479572929E-01, 4.005073391747475E-01, 6.761649569671979E-02, \ 6.535675504807226E-01, 7.533634302760710E-01, 4.601021918794469E-02, \ 6.595342990537197E-01, 9.508745400630684E-01, 1.723971223901597E-02, \ 7.906371918772621E-01, 5.934656821653986E-01, 4.568246307970081E-02, \ 8.055336482199160E-01, 8.773080252379840E-01, 2.484701585804588E-02, \ 7.535373835857363E-01, 9.795331551151395E-01, 4.313716122504384E-03, \ 9.564646592216111E-01, 1.571205964662031E-01, 2.535428637556193E-02, \ 8.902743405153437E-01, 3.914673487680078E-01, 3.753743912008318E-02, \ 9.033639329394400E-01, 7.595177874407598E-01, 2.457091299936516E-02, \ 9.372983112686489E-01, 9.385069580562527E-01, 1.007243031836228E-02, \ 8.636461603424476E-01, 9.896801193034730E-01, 4.961458044877222E-03, \ 9.938360564492993E-01, 3.750300609078687E-01, 7.598805738926257E-03, \ 9.619543373713801E-01, 5.836819379362060E-01, 1.776328589308987E-02, \ 9.918091540820021E-01, 7.176122922535305E-01, 3.747585881528770E-03, \ 9.847916123916505E-01, 8.571417379883992E-01, 6.289982457940641E-03, \ 9.885652833157735E-01, 9.860593798999778E-01, 1.697350354991505E-03, \ 9.233777086225921E-03, 2.208671709154587E-01, 9.688701249182402E-02, \ 3.041113022131709E-02, 6.137415273447637E-01, 7.643513771616485E-02, \ 6.708941821053316E-02, 8.786573477860689E-01, 4.373962481400533E-02, \ 7.276240742442623E-02, 9.928846185998859E-01, 8.791036677341798E-03, \ -4.202921149345177E-01, 2.408979561244244E-01, 8.649643596540968E-02, \ -7.547569098063632E-01, 2.718022358106373E-01, 5.930450471454697E-02, \ -9.557139743958390E-01, 2.949651173549945E-01, 2.492523876506716E-02, \ -2.026918805813806E-01, 4.390520493777193E-01, 8.650651080976479E-02, \ -5.942245210433184E-01, 4.662064901266157E-01, 6.800866187330593E-02, \ -8.732633185547312E-01, 4.830786617878046E-01, 3.820005521117373E-02, \ -9.940169417092007E-01, 5.045376712354956E-01, 7.120126112016729E-03, \ -1.779409708250335E-01, 7.757488163218268E-01, 5.827884791218824E-02, \ -4.005073391747475E-01, 6.369947479572929E-01, 6.761649569671979E-02, \ -7.533634302760710E-01, 6.535675504807226E-01, 4.601021918794469E-02, \ -9.508745400630684E-01, 6.595342990537197E-01, 1.723971223901597E-02, \ -5.934656821653986E-01, 7.906371918772621E-01, 4.568246307970081E-02, \ -8.773080252379840E-01, 8.055336482199160E-01, 2.484701585804588E-02, \ -9.795331551151395E-01, 7.535373835857363E-01, 4.313716122504384E-03, \ -1.571205964662031E-01, 9.564646592216111E-01, 2.535428637556193E-02, \ -3.914673487680078E-01, 8.902743405153437E-01, 3.753743912008318E-02, \ -7.595177874407598E-01, 9.033639329394400E-01, 2.457091299936516E-02, \ -9.385069580562527E-01, 9.372983112686489E-01, 1.007243031836228E-02, \ -9.896801193034730E-01, 8.636461603424476E-01, 4.961458044877222E-03, \ -3.750300609078687E-01, 9.938360564492993E-01, 7.598805738926257E-03, \ -5.836819379362060E-01, 9.619543373713801E-01, 1.776328589308987E-02, \ -7.176122922535305E-01, 9.918091540820021E-01, 3.747585881528770E-03, \ -8.571417379883992E-01, 9.847916123916505E-01, 6.289982457940641E-03, \ -9.860593798999778E-01, 9.885652833157735E-01, 1.697350354991505E-03, \ -2.208671709154587E-01, 9.233777086225921E-03, 9.688701249182402E-02, \ -6.137415273447637E-01, 3.041113022131709E-02, 7.643513771616485E-02, \ -8.786573477860689E-01, 6.708941821053316E-02, 4.373962481400533E-02, \ -9.928846185998859E-01, 7.276240742442623E-02, 8.791036677341798E-03, \ -2.408979561244244E-01, -4.202921149345177E-01, 8.649643596540968E-02, \ -2.718022358106373E-01, -7.547569098063632E-01, 5.930450471454697E-02, \ -2.949651173549945E-01, -9.557139743958390E-01, 2.492523876506716E-02, \ -4.390520493777193E-01, -2.026918805813806E-01, 8.650651080976479E-02, \ -4.662064901266157E-01, -5.942245210433184E-01, 6.800866187330593E-02, \ -4.830786617878046E-01, -8.732633185547312E-01, 3.820005521117373E-02, \ -5.045376712354956E-01, -9.940169417092007E-01, 7.120126112016729E-03, \ -7.757488163218268E-01, -1.779409708250335E-01, 5.827884791218824E-02, \ -6.369947479572929E-01, -4.005073391747475E-01, 6.761649569671979E-02, \ -6.535675504807226E-01, -7.533634302760710E-01, 4.601021918794469E-02, \ -6.595342990537197E-01, -9.508745400630684E-01, 1.723971223901597E-02, \ -7.906371918772621E-01, -5.934656821653986E-01, 4.568246307970081E-02, \ -8.055336482199160E-01, -8.773080252379840E-01, 2.484701585804588E-02, \ -7.535373835857363E-01, -9.795331551151395E-01, 4.313716122504384E-03, \ -9.564646592216111E-01, -1.571205964662031E-01, 2.535428637556193E-02, \ -8.902743405153437E-01, -3.914673487680078E-01, 3.753743912008318E-02, \ -9.033639329394400E-01, -7.595177874407598E-01, 2.457091299936516E-02, \ -9.372983112686489E-01, -9.385069580562527E-01, 1.007243031836228E-02, \ -8.636461603424476E-01, -9.896801193034730E-01, 4.961458044877222E-03, \ -9.938360564492993E-01, -3.750300609078687E-01, 7.598805738926257E-03, \ -9.619543373713801E-01, -5.836819379362060E-01, 1.776328589308987E-02, \ -9.918091540820021E-01, -7.176122922535305E-01, 3.747585881528770E-03, \ -9.847916123916505E-01, -8.571417379883992E-01, 6.289982457940641E-03, \ -9.885652833157735E-01, -9.860593798999778E-01, 1.697350354991505E-03, \ -9.233777086225921E-03, -2.208671709154587E-01, 9.688701249182402E-02, \ -3.041113022131709E-02, -6.137415273447637E-01, 7.643513771616485E-02, \ -6.708941821053316E-02, -8.786573477860689E-01, 4.373962481400533E-02, \ -7.276240742442623E-02, -9.928846185998859E-01, 8.791036677341798E-03, \ 4.202921149345177E-01, -2.408979561244244E-01, 8.649643596540968E-02, \ 7.547569098063632E-01, -2.718022358106373E-01, 5.930450471454697E-02, \ 9.557139743958390E-01, -2.949651173549945E-01, 2.492523876506716E-02, \ 2.026918805813806E-01, -4.390520493777193E-01, 8.650651080976479E-02, \ 5.942245210433184E-01, -4.662064901266157E-01, 6.800866187330593E-02, \ 8.732633185547312E-01, -4.830786617878046E-01, 3.820005521117373E-02, \ 9.940169417092007E-01, -5.045376712354956E-01, 7.120126112016729E-03, \ 1.779409708250335E-01, -7.757488163218268E-01, 5.827884791218824E-02, \ 4.005073391747475E-01, -6.369947479572929E-01, 6.761649569671979E-02, \ 7.533634302760710E-01, -6.535675504807226E-01, 4.601021918794469E-02, \ 9.508745400630684E-01, -6.595342990537197E-01, 1.723971223901597E-02, \ 5.934656821653986E-01, -7.906371918772621E-01, 4.568246307970081E-02, \ 8.773080252379840E-01, -8.055336482199160E-01, 2.484701585804588E-02, \ 9.795331551151395E-01, -7.535373835857363E-01, 4.313716122504384E-03, \ 1.571205964662031E-01, -9.564646592216111E-01, 2.535428637556193E-02, \ 3.914673487680078E-01, -8.902743405153437E-01, 3.753743912008318E-02, \ 7.595177874407598E-01, -9.033639329394400E-01, 2.457091299936516E-02, \ 9.385069580562527E-01, -9.372983112686489E-01, 1.007243031836228E-02, \ 9.896801193034730E-01, -8.636461603424476E-01, 4.961458044877222E-03, \ 3.750300609078687E-01, -9.938360564492993E-01, 7.598805738926257E-03, \ 5.836819379362060E-01, -9.619543373713801E-01, 1.776328589308987E-02, \ 7.176122922535305E-01, -9.918091540820021E-01, 3.747585881528770E-03, \ 8.571417379883992E-01, -9.847916123916505E-01, 6.289982457940641E-03, \ 9.860593798999778E-01, -9.885652833157735E-01, 1.697350354991505E-03, \ 2.208671709154587E-01, -9.233777086225921E-03, 9.688701249182402E-02, \ 6.137415273447637E-01, -3.041113022131709E-02, 7.643513771616485E-02, \ 8.786573477860689E-01, -6.708941821053316E-02, 4.373962481400533E-02, \ 9.928846185998859E-01, -7.276240742442623E-02, 8.791036677341798E-03, \ 0.000000000000000E+00, 0.000000000000000E+00, 1.459027412974250E-05 ] ) return xyw def smr26 ( ): #*****************************************************************************80 # ## smr26 returns the SMR rule of degree 26. # # Discussion: # # DEGREE: 26 # POINTS CARDINALITY: 127 # NORM INF MOMS. RESIDUAL: 2.72785e-16 # SUM NEGATIVE WEIGHTS: 0 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*127), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.954149432053586E-01, -8.467950645561364E-01, 3.684914976298696E-03, \ -9.951846316463983E-01, 4.962239287417011E-01, 5.769468055434405E-03, \ -9.946910061010343E-01, -2.554039039018801E-01, 5.732088976456913E-03, \ -9.919373759022915E-01, 1.036499274958413E-01, 7.852213957780449E-03, \ -9.906494815143384E-01, 8.649856906058798E-01, 5.121508648969548E-03, \ -9.896255204784331E-01, -5.367353086290219E-01, 7.653897829024368E-03, \ -9.883067004873612E-01, 9.892991458592666E-01, 1.353489163893612E-03, \ -9.871269120799574E-01, -9.856243972746432E-01, 1.601609521006031E-03, \ -9.688175505639893E-01, 6.876579842845731E-01, 1.481263227905701E-02, \ -9.623107235333284E-01, -7.113315046485157E-01, 1.467102553035195E-02, \ -9.594699050132816E-01, 3.158494085062999E-01, 2.066592783625548E-02, \ -9.556340329654068E-01, -8.022603946161568E-02, 2.057995991913653E-02, \ -9.551530447389018E-01, -9.306484497591768E-01, 8.053489843056318E-03, \ -9.424969861668707E-01, 9.469477514122181E-01, 8.919732609121192E-03, \ -9.420253084162512E-01, -3.677325230608104E-01, 2.273184282144351E-02, \ -8.987320916561362E-01, 8.122593786261580E-01, 2.096666902511633E-02, \ -8.958607050863848E-01, 5.192884077130218E-01, 3.251925598993868E-02, \ -8.896472695790547E-01, -8.337317899908271E-01, 1.954814636274032E-02, \ -8.855870754573025E-01, -5.696730697875062E-01, 2.769715991416717E-02, \ -8.851975534775430E-01, -9.861706664088894E-01, 5.503686420382153E-03, \ -8.824869023397663E-01, 1.313680696309325E-01, 3.733200212029421E-02, \ -8.536298178066737E-01, 9.912818948096804E-01, 5.124303871062341E-03, \ -8.470126989959706E-01, -1.751543370107349E-01, 3.903031857246672E-02, \ -7.935791896852771E-01, 9.085946391105678E-01, 2.070806621666239E-02, \ -7.916311495402206E-01, -4.081621366651574E-01, 3.398634661189039E-02, \ -7.861405619098327E-01, -9.316104713801209E-01, 1.770750778349851E-02, \ -7.844763488387392E-01, 6.770066879653323E-01, 3.909373917813275E-02, \ -7.812595515556915E-01, -7.208792112743798E-01, 3.206208479847047E-02, \ -7.750802181046658E-01, 3.380282238952111E-01, 5.215291009390418E-02, \ -7.135764412117650E-01, 1.416925255648272E-02, 5.853608843151761E-02, \ -6.828943144695906E-01, -9.907384181599451E-01, 6.548608319199373E-03, \ -6.658796622951563E-01, -5.739095648918578E-01, 4.128887088242855E-02, \ -6.601473080396085E-01, 9.720448999511093E-01, 1.432353654588031E-02, \ -6.579506062388087E-01, -2.844859212870189E-01, 4.720582197472361E-02, \ -6.479646319399198E-01, -8.498157318331752E-01, 3.083452896969299E-02, \ -6.397790086368259E-01, 8.094061184323337E-01, 3.847861173239278E-02, \ -6.249362696077773E-01, 5.216217958951045E-01, 5.859572334726999E-02, \ -5.576842250639873E-01, 2.121572188446747E-01, 6.977200243841351E-02, \ -5.231225720726088E-01, -9.559709376266402E-01, 1.921032430496192E-02, \ -5.108013542724835E-01, -7.271185268803120E-01, 4.267920181533953E-02, \ -4.958822443640539E-01, -1.352950226786132E-01, 6.727743365041994E-02, \ -4.903913278322852E-01, -4.632593578701779E-01, 5.398148692009514E-02, \ -4.716786109784886E-01, 9.096410577420503E-01, 3.072280881059000E-02, \ -4.571089728524948E-01, 9.962395125952335E-01, 5.314155662552198E-03, \ -4.458359027750944E-01, 6.845878478236567E-01, 5.741502788464329E-02, \ -3.761204219053791E-01, 4.027492188232445E-01, 7.244352535381400E-02, \ -3.757270438769368E-01, -8.813300989750833E-01, 2.864804532479737E-02, \ -3.233151458448575E-01, -9.924702614510548E-01, 8.376460295913149E-03, \ -3.214177198641322E-01, 5.465196421581072E-02, 7.825743561587792E-02, \ -3.079596913747666E-01, -6.299193766661012E-01, 5.253252015129221E-02, \ -2.908499987046121E-01, -3.299468222568143E-01, 7.147473944911664E-02, \ -2.711488527112555E-01, -8.141343465894294E-01, 2.066316039292166E-02, \ -2.621892153300335E-01, 9.646535606685744E-01, 1.798911598012612E-02, \ -2.481167506627375E-01, 8.186440564336724E-01, 4.859943151527142E-02, \ -1.791342365314126E-01, 5.748981248381774E-01, 6.765610404074739E-02, \ -1.437544578360581E-01, -9.443574522438600E-01, 2.652222430073281E-02, \ -1.269743475931557E-01, 2.485350964764208E-01, 8.025561424009733E-02, \ -1.038608843226707E-01, -1.432437001920102E-01, 8.120590842585292E-02, \ -8.599298880188963E-02, -7.716801473651607E-01, 4.636752344758587E-02, \ -8.395006281782805E-02, 9.871263594306682E-01, 6.816019493764937E-03, \ -8.371947125930103E-02, -5.208589889223917E-01, 6.747918873878211E-02, \ -1.697646807858736E-02, 9.086536018884021E-01, 3.387459722470887E-02, \ 1.833871143655595E-02, 7.209167099679072E-01, 5.538931339457189E-02, \ 5.565106332452326E-02, -9.889754197418217E-01, 1.032926366015326E-02, \ 7.395330091505788E-02, 4.297944936585988E-01, 7.320349165354346E-02, \ 9.468086843565157E-02, 5.388968586906774E-02, 8.305615985562806E-02, \ 1.024839179112914E-01, -8.834041600598230E-01, 3.604665584816725E-02, \ 1.074857184095777E-01, -3.452094910890526E-01, 7.761121952888624E-02, \ 1.267100636690128E-01, 9.932822811543160E-01, 6.369719109332116E-03, \ 1.534607276530462E-01, -6.678010821258034E-01, 6.156496555816345E-02, \ 2.264963086729804E-01, 8.230177907394701E-01, 3.968243470712332E-02, \ 2.459857454037700E-01, 9.492195041164657E-01, 2.026587105731689E-02, \ 2.573243932667488E-01, 5.876784265758089E-01, 5.691232110819883E-02, \ 2.787299946892420E-01, -8.902304358275253E-01, 6.562216924914964E-03, \ 2.938069266369140E-01, 2.464559758407173E-01, 7.639234774613035E-02, \ 3.031751644439591E-01, -1.498955147329062E-01, 7.988963989267751E-02, \ 3.057176124210453E-01, -9.663294098875163E-01, 1.951951397301675E-02, \ 3.429948224409587E-01, -5.036657844935868E-01, 6.771694379519085E-02, \ 3.468395902763219E-01, -8.106928028976478E-01, 3.534883558238713E-02, \ 4.294715053745923E-01, 6.972444059344115E-01, 4.114854443928950E-02, \ 4.504438324791868E-01, 9.813465089178893E-01, 1.218029689385577E-02, \ 4.587114216458100E-01, 8.757161022302909E-01, 2.985614815263661E-02, \ 4.705023240099300E-01, 4.248914232485290E-01, 6.029605985982594E-02, \ 4.730542337014057E-01, -7.226405060364207E-01, 3.424156109429213E-02, \ 4.939440770258761E-01, 5.066200964988320E-02, 7.407077493593092E-02, \ 5.203715415927748E-01, -3.207475729229982E-01, 6.635966202614821E-02, \ 5.257639785007799E-01, -9.977170958540899E-01, 5.409613333068085E-03, \ 5.313378826806301E-01, -9.170479942929537E-01, 2.720520257275587E-02, \ 6.022923045507941E-01, -5.994501280239045E-01, 4.830919014106976E-02, \ 6.204433975928566E-01, 7.641974295227819E-01, 3.404033553026726E-02, \ 6.209466711991216E-01, 5.494777927720476E-01, 3.791496686575289E-02, \ 6.466689879582136E-01, 9.360734505765457E-01, 1.996022042410962E-02, \ 6.621033564067602E-01, 2.496966370849072E-01, 6.144981322024960E-02, \ 6.789809770063248E-01, -8.212602557120876E-01, 3.236488593000712E-02, \ 6.796918717501631E-01, -1.331309975388194E-01, 5.802989349830448E-02, \ 6.812502176754324E-01, 9.989521401044065E-01, 3.579807875673121E-03, \ 7.266475436540760E-01, -9.675683591285036E-01, 1.484875678494199E-02, \ 7.440642616936161E-01, -4.322014403053586E-01, 4.959179569785551E-02, \ 7.592474840505909E-01, 6.228158958890423E-01, 3.061073682759719E-02, \ 7.651597556914833E-01, 8.643901077992759E-01, 1.594483883723016E-02, \ 7.967436284918096E-01, -6.999653717120403E-01, 3.119771973203415E-02, \ 8.082541716984714E-01, 5.125601506516623E-02, 4.548581114128645E-02, \ 8.109696076652307E-01, 4.100804853037188E-01, 4.010668645708275E-02, \ 8.230542108068375E-01, 7.992506945688510E-01, 1.707575997005541E-02, \ 8.345479402209883E-01, 9.699921801950655E-01, 1.084337625005019E-02, \ 8.501041529924387E-01, -8.905397308072454E-01, 2.036774520670110E-02, \ 8.672176401962716E-01, -2.462270148388496E-01, 4.072777874876069E-02, \ 8.815659674305341E-01, -9.912929489021226E-01, 4.286277790305716E-03, \ 8.884328863679039E-01, -5.630909797598750E-01, 2.665108708356420E-02, \ 9.036096198949736E-01, 6.861746191520888E-01, 2.199046962304617E-02, \ 9.087614696522919E-01, 2.107906691217087E-01, 2.933513900564612E-02, \ 9.227489940536037E-01, 5.030781079388300E-01, 1.792733716201453E-02, \ 9.244232598969854E-01, 8.987785855053358E-01, 1.334853657169367E-02, \ 9.371340023166588E-01, -7.719078499479927E-01, 1.828418899551716E-02, \ 9.533101385624838E-01, -5.893948233744529E-02, 2.493427565247522E-02, \ 9.546218786151554E-01, 9.901100266242597E-01, 2.997669288160739E-03, \ 9.549184254866305E-01, -9.479041510850161E-01, 7.333351181224950E-03, \ 9.584840095307160E-01, -4.174125864174710E-01, 1.906983600300858E-02, \ 9.754885144991214E-01, 3.570890018408184E-01, 1.283253988624834E-02, \ 9.784766134144718E-01, 7.916730646314184E-01, 9.664155967361797E-03, \ 9.878112520788415E-01, 5.881933255153872E-01, 8.019243932869360E-03, \ 9.878730421247439E-01, -6.289972589684678E-01, 8.869256817284361E-03, \ 9.914552412725798E-01, -8.617824090170690E-01, 4.432377107176309E-03, \ 9.929343270174540E-01, -9.907397806148996E-01, 9.278177812673883E-04, \ 9.937639919249919E-01, 9.433436502803851E-01, 2.685285882370453E-03, \ 9.939007341106521E-01, 1.320895377365522E-01, 6.886649912238812E-03, \ 9.952509862842531E-01, -2.550697642134186E-01, 6.463763906756026E-03 ] ) return xyw def smr27 ( ): #*****************************************************************************80 # ## smr27 returns the SMR rule of degree 27. # # Discussion: # # DEGREE: 27 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 132 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*132), the requested rule. # import numpy as np xyw = np.array ( [ \ 1.886005021782720E-03, 5.828566738691298E-01, 6.979680609052895E-02, \ -4.610090446080339E-03, 8.577929872633651E-01, 4.314966506560954E-02, \ -4.155284083838179E-02, 9.888852930552997E-01, 1.072399831167234E-02, \ 2.067872320344404E-01, -6.296477862134920E-04, 8.488483237702206E-02, \ 2.082269167023509E-01, 4.038616639190317E-01, 7.727830308506041E-02, \ 2.052137161358173E-01, 7.394171390837959E-01, 5.621586102413551E-02, \ 1.807393256852824E-01, 9.496265565549702E-01, 2.535911050249288E-02, \ 3.322057475944939E-01, 9.960227386085063E-01, 5.272055511683970E-03, \ 4.045305824612024E-01, 2.059859741136477E-01, 7.726743635049893E-02, \ 4.025837874193514E-01, 5.870128510662224E-01, 6.365147357369046E-02, \ 3.850900136224434E-01, 8.707822203710608E-01, 3.854775533996937E-02, \ 4.961565809611688E-01, 9.726108752621352E-01, 1.194490281825224E-02, \ 7.337041416795138E-01, 2.082446806606209E-01, 5.658941671510189E-02, \ 5.809960989937741E-01, 4.073474789041275E-01, 6.376865298046723E-02, \ 5.677230574148288E-01, 7.531679569108030E-01, 4.625453544861270E-02, \ 6.209259660886249E-01, 9.313450399117541E-01, 1.820437285093996E-02, \ 7.222712946524428E-01, 9.926688332077881E-01, 5.756269356678867E-03, \ 8.472675519335334E-01, 4.202098689198475E-01, 4.046935707697283E-02, \ 7.235313755189597E-01, 6.009001598253331E-01, 4.695366916509310E-02, \ 7.436209196607865E-01, 8.532631127882830E-01, 2.452811191323398E-02, \ 8.078125449235396E-01, 8.865860238557206E-01, 3.599599560868793E-03, \ 8.496011789870433E-01, 9.584740402687207E-01, 1.136717702495919E-02, \ 9.873993632652779E-01, 3.857565023254501E-01, 9.087958640367919E-03, \ 9.407918538992979E-01, 5.806290275537873E-01, 2.155259200865792E-02, \ 8.583622893662932E-01, 7.355260155277167E-01, 2.723142317719206E-02, \ 9.417112190155333E-01, 8.140933233486173E-01, 6.586312510744677E-03, \ 9.293007271718974E-01, 8.976314904285845E-01, 9.170625679716800E-03, \ 9.365522911144204E-01, 2.247649048332172E-01, 2.753902574626484E-02, \ 9.913001320610028E-01, 5.146910772747944E-01, 2.062938898431044E-03, \ 9.892062993684332E-01, 7.177306340863354E-01, 6.213455600316710E-03, \ 9.825794696006162E-01, 8.526916976863245E-01, 3.542165144107640E-03, \ 9.899623983816039E-01, 9.559123039771233E-01, 2.789025209960568E-03, \ 9.454816892922301E-01, 9.931508332329141E-01, 2.641115240694518E-03, \ -5.828566738691298E-01, 1.886005021782720E-03, 6.979680609052895E-02, \ -8.577929872633651E-01, -4.610090446080339E-03, 4.314966506560954E-02, \ -9.888852930552997E-01, -4.155284083838179E-02, 1.072399831167234E-02, \ 6.296477862134920E-04, 2.067872320344404E-01, 8.488483237702206E-02, \ -4.038616639190317E-01, 2.082269167023509E-01, 7.727830308506041E-02, \ -7.394171390837959E-01, 2.052137161358173E-01, 5.621586102413551E-02, \ -9.496265565549702E-01, 1.807393256852824E-01, 2.535911050249288E-02, \ -9.960227386085063E-01, 3.322057475944939E-01, 5.272055511683970E-03, \ -2.059859741136477E-01, 4.045305824612024E-01, 7.726743635049893E-02, \ -5.870128510662224E-01, 4.025837874193514E-01, 6.365147357369046E-02, \ -8.707822203710608E-01, 3.850900136224434E-01, 3.854775533996937E-02, \ -9.726108752621352E-01, 4.961565809611688E-01, 1.194490281825224E-02, \ -2.082446806606209E-01, 7.337041416795138E-01, 5.658941671510189E-02, \ -4.073474789041275E-01, 5.809960989937741E-01, 6.376865298046723E-02, \ -7.531679569108030E-01, 5.677230574148288E-01, 4.625453544861270E-02, \ -9.313450399117541E-01, 6.209259660886249E-01, 1.820437285093996E-02, \ -9.926688332077881E-01, 7.222712946524428E-01, 5.756269356678867E-03, \ -4.202098689198475E-01, 8.472675519335334E-01, 4.046935707697283E-02, \ -6.009001598253331E-01, 7.235313755189597E-01, 4.695366916509310E-02, \ -8.532631127882830E-01, 7.436209196607865E-01, 2.452811191323398E-02, \ -8.865860238557206E-01, 8.078125449235396E-01, 3.599599560868793E-03, \ -9.584740402687207E-01, 8.496011789870433E-01, 1.136717702495919E-02, \ -3.857565023254501E-01, 9.873993632652779E-01, 9.087958640367919E-03, \ -5.806290275537873E-01, 9.407918538992979E-01, 2.155259200865792E-02, \ -7.355260155277167E-01, 8.583622893662932E-01, 2.723142317719206E-02, \ -8.140933233486173E-01, 9.417112190155333E-01, 6.586312510744677E-03, \ -8.976314904285845E-01, 9.293007271718974E-01, 9.170625679716800E-03, \ -2.247649048332172E-01, 9.365522911144204E-01, 2.753902574626484E-02, \ -5.146910772747944E-01, 9.913001320610028E-01, 2.062938898431044E-03, \ -7.177306340863354E-01, 9.892062993684332E-01, 6.213455600316710E-03, \ -8.526916976863245E-01, 9.825794696006162E-01, 3.542165144107640E-03, \ -9.559123039771233E-01, 9.899623983816039E-01, 2.789025209960568E-03, \ -9.931508332329141E-01, 9.454816892922301E-01, 2.641115240694518E-03, \ -1.886005021782720E-03, -5.828566738691298E-01, 6.979680609052895E-02, \ 4.610090446080339E-03, -8.577929872633651E-01, 4.314966506560954E-02, \ 4.155284083838179E-02, -9.888852930552997E-01, 1.072399831167234E-02, \ -2.067872320344404E-01, 6.296477862134920E-04, 8.488483237702206E-02, \ -2.082269167023509E-01, -4.038616639190317E-01, 7.727830308506041E-02, \ -2.052137161358173E-01, -7.394171390837959E-01, 5.621586102413551E-02, \ -1.807393256852824E-01, -9.496265565549702E-01, 2.535911050249288E-02, \ -3.322057475944939E-01, -9.960227386085063E-01, 5.272055511683970E-03, \ -4.045305824612024E-01, -2.059859741136477E-01, 7.726743635049893E-02, \ -4.025837874193514E-01, -5.870128510662224E-01, 6.365147357369046E-02, \ -3.850900136224434E-01, -8.707822203710608E-01, 3.854775533996937E-02, \ -4.961565809611688E-01, -9.726108752621352E-01, 1.194490281825224E-02, \ -7.337041416795138E-01, -2.082446806606209E-01, 5.658941671510189E-02, \ -5.809960989937741E-01, -4.073474789041275E-01, 6.376865298046723E-02, \ -5.677230574148288E-01, -7.531679569108030E-01, 4.625453544861270E-02, \ -6.209259660886249E-01, -9.313450399117541E-01, 1.820437285093996E-02, \ -7.222712946524428E-01, -9.926688332077881E-01, 5.756269356678867E-03, \ -8.472675519335334E-01, -4.202098689198475E-01, 4.046935707697283E-02, \ -7.235313755189597E-01, -6.009001598253331E-01, 4.695366916509310E-02, \ -7.436209196607865E-01, -8.532631127882830E-01, 2.452811191323398E-02, \ -8.078125449235396E-01, -8.865860238557206E-01, 3.599599560868793E-03, \ -8.496011789870433E-01, -9.584740402687207E-01, 1.136717702495919E-02, \ -9.873993632652779E-01, -3.857565023254501E-01, 9.087958640367919E-03, \ -9.407918538992979E-01, -5.806290275537873E-01, 2.155259200865792E-02, \ -8.583622893662932E-01, -7.355260155277167E-01, 2.723142317719206E-02, \ -9.417112190155333E-01, -8.140933233486173E-01, 6.586312510744677E-03, \ -9.293007271718974E-01, -8.976314904285845E-01, 9.170625679716800E-03, \ -9.365522911144204E-01, -2.247649048332172E-01, 2.753902574626484E-02, \ -9.913001320610028E-01, -5.146910772747944E-01, 2.062938898431044E-03, \ -9.892062993684332E-01, -7.177306340863354E-01, 6.213455600316710E-03, \ -9.825794696006162E-01, -8.526916976863245E-01, 3.542165144107640E-03, \ -9.899623983816039E-01, -9.559123039771233E-01, 2.789025209960568E-03, \ -9.454816892922301E-01, -9.931508332329141E-01, 2.641115240694518E-03, \ 5.828566738691298E-01, -1.886005021782720E-03, 6.979680609052895E-02, \ 8.577929872633651E-01, 4.610090446080339E-03, 4.314966506560954E-02, \ 9.888852930552997E-01, 4.155284083838179E-02, 1.072399831167234E-02, \ -6.296477862134920E-04, -2.067872320344404E-01, 8.488483237702206E-02, \ 4.038616639190317E-01, -2.082269167023509E-01, 7.727830308506041E-02, \ 7.394171390837959E-01, -2.052137161358173E-01, 5.621586102413551E-02, \ 9.496265565549702E-01, -1.807393256852824E-01, 2.535911050249288E-02, \ 9.960227386085063E-01, -3.322057475944939E-01, 5.272055511683970E-03, \ 2.059859741136477E-01, -4.045305824612024E-01, 7.726743635049893E-02, \ 5.870128510662224E-01, -4.025837874193514E-01, 6.365147357369046E-02, \ 8.707822203710608E-01, -3.850900136224434E-01, 3.854775533996937E-02, \ 9.726108752621352E-01, -4.961565809611688E-01, 1.194490281825224E-02, \ 2.082446806606209E-01, -7.337041416795138E-01, 5.658941671510189E-02, \ 4.073474789041275E-01, -5.809960989937741E-01, 6.376865298046723E-02, \ 7.531679569108030E-01, -5.677230574148288E-01, 4.625453544861270E-02, \ 9.313450399117541E-01, -6.209259660886249E-01, 1.820437285093996E-02, \ 9.926688332077881E-01, -7.222712946524428E-01, 5.756269356678867E-03, \ 4.202098689198475E-01, -8.472675519335334E-01, 4.046935707697283E-02, \ 6.009001598253331E-01, -7.235313755189597E-01, 4.695366916509310E-02, \ 8.532631127882830E-01, -7.436209196607865E-01, 2.452811191323398E-02, \ 8.865860238557206E-01, -8.078125449235396E-01, 3.599599560868793E-03, \ 9.584740402687207E-01, -8.496011789870433E-01, 1.136717702495919E-02, \ 3.857565023254501E-01, -9.873993632652779E-01, 9.087958640367919E-03, \ 5.806290275537873E-01, -9.407918538992979E-01, 2.155259200865792E-02, \ 7.355260155277167E-01, -8.583622893662932E-01, 2.723142317719206E-02, \ 8.140933233486173E-01, -9.417112190155333E-01, 6.586312510744677E-03, \ 8.976314904285845E-01, -9.293007271718974E-01, 9.170625679716800E-03, \ 2.247649048332172E-01, -9.365522911144204E-01, 2.753902574626484E-02, \ 5.146910772747944E-01, -9.913001320610028E-01, 2.062938898431044E-03, \ 7.177306340863354E-01, -9.892062993684332E-01, 6.213455600316710E-03, \ 8.526916976863245E-01, -9.825794696006162E-01, 3.542165144107640E-03, \ 9.559123039771233E-01, -9.899623983816039E-01, 2.789025209960568E-03, \ 9.931508332329141E-01, -9.454816892922301E-01, 2.641115240694518E-03 ] ) return xyw def smr28 ( ): #*****************************************************************************80 # ## smr28 returns the SMR rule of degree 28. # # Discussion: # # DEGREE: 28 # POINTS CARDINALITY: 146 # NORM INF MOMS. RESIDUAL: 9.93129e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real *XYW(3*146), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.948578576510482E-01, 9.951313777393089E-01, 5.350567115949095E-04, \ 9.942909707974587E-01, 8.766570248036105E-01, 2.791138783606160E-03, \ 9.936073905803642E-01, 6.435920031349868E-01, 4.975936005062567E-03, \ 9.955492434128311E-01, 3.009600560431372E-01, 5.028092846274678E-03, \ 9.953117341967249E-01, -1.155952308989407E-01, 5.404591653487998E-03, \ 9.945568546430053E-01, -4.954371212342698E-01, 4.995854780477920E-03, \ 9.941123224157187E-01, -7.686450662183013E-01, 3.412261550099155E-03, \ 9.973970470314231E-01, -9.477148556565722E-01, 1.256390479179999E-03, \ 9.688973112117140E-01, 9.519148224233880E-01, 4.713673624203035E-03, \ 9.613309496208055E-01, 7.757025845655895E-01, 1.166028423822774E-02, \ 9.659860418437211E-01, 4.681861912724297E-01, 1.519045343561554E-02, \ 9.698532836823804E-01, 9.733476040026384E-02, 1.657048063461714E-02, \ 9.676987141452779E-01, -3.026291805415285E-01, 1.602715348074777E-02, \ 9.652351090613974E-01, -6.421223495984553E-01, 1.210066207543355E-02, \ 9.705483737595868E-01, -8.773547971281066E-01, 6.923308160213495E-03, \ 9.748783800172183E-01, -9.912505022009086E-01, 1.588717379761370E-03, \ 9.166016146066042E-01, 9.861313164544186E-01, 3.329484690768878E-03, \ 8.994804531261812E-01, 8.827649742916205E-01, 1.434726026694510E-02, \ 9.053106430680723E-01, 6.228188101332273E-01, 2.276716021991524E-02, \ 9.071948418179018E-01, 2.805718262681513E-01, 2.888726414871897E-02, \ 9.109240111661969E-01, -9.646023425605603E-02, 2.952643485962895E-02, \ 9.103965861122791E-01, -4.750063547383416E-01, 2.428497272680478E-02, \ 9.135589107435960E-01, -7.731270000889884E-01, 1.598024520842712E-02, \ 9.235219832875176E-01, -9.536909415826325E-01, 7.313384482073473E-03, \ 8.422727743872929E-01, 9.983748940501636E-01, 1.177144882525381E-03, \ 8.021369409522103E-01, 9.526336218686154E-01, 1.233677299331454E-02, \ 8.162908906345308E-01, 7.599008885973428E-01, 2.655091644582969E-02, \ 8.127751861060339E-01, 4.597366883296284E-01, 3.763596042165646E-02, \ 8.129630861903968E-01, 9.176425527693403E-02, 4.284745602911020E-02, \ 8.233720523878740E-01, -2.917598066537037E-01, 3.906509971261103E-02, \ 8.273253984611962E-01, -6.351315017888974E-01, 2.985137841867004E-02, \ 8.410861657858746E-01, -8.770078144051303E-01, 1.678011176333675E-02, \ 8.462927808942150E-01, -9.911001774446370E-01, 4.109086265895744E-03, \ 6.692649802375389E-01, 9.897101791893593E-01, 6.302703194199112E-03, \ 6.959480214373159E-01, 8.669178979407627E-01, 2.525587670248390E-02, \ 6.896592055450543E-01, 6.236755137912841E-01, 4.183562464805562E-02, \ 6.865013864931789E-01, 2.840539118035566E-01, 5.208001068769284E-02, \ 6.962750629039214E-01, -1.115191087063258E-01, 5.256283376203195E-02, \ 7.074126907672926E-01, -4.752442590431704E-01, 4.556426477896882E-02, \ 7.191258343646272E-01, -7.720946761786819E-01, 3.133433453762152E-02, \ 7.381207241833775E-01, -9.459798668063141E-01, 1.409639241355121E-02, \ 6.771073750372986E-01, -9.922518457423063E-01, 2.777359845401900E-03, \ 5.475677331233061E-01, 9.422181957297456E-01, 1.897982231084832E-02, \ 5.400263477570776E-01, 7.619170134687657E-01, 3.998120414157146E-02, \ 5.343007222250298E-01, 4.660852613438181E-01, 5.641016682972110E-02, \ 5.464626157458451E-01, 8.180074857237349E-02, 6.215654744912379E-02, \ 5.520150032550133E-01, -3.052541200774422E-01, 5.923432236764290E-02, \ 5.668728132802315E-01, -6.388668498497777E-01, 4.710391803124826E-02, \ 5.810992753051508E-01, -8.752071635592164E-01, 2.787797798973161E-02, \ 5.671475579878305E-01, -9.796604593842159E-01, 7.793314748885580E-03, \ 3.968756859090636E-01, 9.879827506647261E-01, 8.923994125095943E-03, \ 3.707910234961497E-01, 8.695515088341891E-01, 3.239278927868577E-02, \ 3.620431155247392E-01, 6.294210332481971E-01, 5.436999365883735E-02, \ 3.756691454599630E-01, 2.722208281305576E-01, 6.689872061273545E-02, \ 3.801363136282314E-01, -1.153023476012179E-01, 6.916197504314157E-02, \ 3.870789258805237E-01, -4.852712266367580E-01, 6.069376521414673E-02, \ 4.013748435296351E-01, -7.721926519007076E-01, 4.296137864461146E-02, \ 4.029880643773450E-01, -9.405596605751765E-01, 1.992102855514764E-02, \ 4.035133457630937E-01, -9.984853538421118E-01, 2.668528192375319E-03, \ 1.160216426928697E-01, 9.922413519284493E-01, 5.350102953202783E-03, \ 2.055793223051185E-01, 9.459133372942112E-01, 2.072186274583783E-02, \ 1.776855819898789E-01, 7.668715275107250E-01, 4.612076109466228E-02, \ 1.919764609816849E-01, 4.526549306348999E-01, 6.552641398222167E-02, \ 1.926293216704643E-01, 7.875626396945502E-02, 7.415699880326786E-02, \ 1.985057734993036E-01, -3.060328376638529E-01, 7.072349740661799E-02, \ 2.038466930455823E-01, -6.417616215413990E-01, 5.626372459884906E-02, \ 2.088349228463496E-01, -8.693904617391873E-01, 3.383513644639114E-02, \ 2.112825401519657E-01, -9.795723716889928E-01, 1.129835512516279E-02, \ -5.348117081594564E-02, 9.601197110277508E-01, 1.102425532666331E-02, \ -1.440209295656826E-03, 8.728107413837934E-01, 3.293357956668601E-02, \ 3.475808263467210E-03, 6.154311844205719E-01, 5.809864825359298E-02, \ -1.120628220586241E-03, 2.708231330142061E-01, 7.325167415256556E-02, \ 1.044970007167108E-03, -1.158225951592231E-01, 7.568882188561220E-02, \ 6.384994250920603E-03, -4.809476808243928E-01, 6.617874013219743E-02, \ 4.295452536640910E-03, -7.676008066148449E-01, 4.657600571756004E-02, \ 4.651117956286204E-03, -9.365900032572481E-01, 2.283252555981913E-02, \ 8.237620269373420E-03, -9.962744074089572E-01, 3.786352125662351E-03, \ -1.274891040086490E-01, 9.929001195823554E-01, 4.958467693467626E-03, \ -2.413142327752992E-01, 9.029321598234583E-01, 1.853018716489174E-02, \ -1.832813730805473E-01, 7.525928605307329E-01, 4.713333096331936E-02, \ -1.920382892873746E-01, 4.539454858901587E-01, 6.603945261049947E-02, \ -1.956436793406595E-01, 7.941255257340975E-02, 7.508025050715028E-02, \ -1.923970603608269E-01, -3.024155270841158E-01, 7.084970982103253E-02, \ -1.911944603737556E-01, -6.318610134350573E-01, 5.601846880048385E-02, \ -1.997986481004511E-01, -8.643880734116528E-01, 3.434757868627490E-02, \ -2.040634037532908E-01, -9.778548144980190E-01, 1.259279635934074E-02, \ -2.997076844021980E-01, 9.628107191472532E-01, 1.314095498758601E-02, \ -4.148554476460968E-01, 8.338942142941969E-01, 3.293242786053679E-02, \ -3.779198201034129E-01, 6.158737694305179E-01, 5.508527968607409E-02, \ -3.805490179487411E-01, 2.750443753116855E-01, 6.796131506618697E-02, \ -3.841282487515310E-01, -1.132877025420610E-01, 7.045152003060294E-02, \ -3.804454671026422E-01, -4.720772509930954E-01, 6.002911781360866E-02, \ -3.841911412860247E-01, -7.558248311258943E-01, 4.283433317172849E-02, \ -4.014494726845325E-01, -9.319408172971044E-01, 2.234448515507551E-02, \ -4.134249428005414E-01, -9.971881189618174E-01, 3.879387979882435E-03, \ -4.482484235975709E-01, 9.933540226000461E-01, 5.885518307205129E-03, \ -5.401264617535639E-01, 9.300111343789312E-01, 2.045252873739783E-02, \ -5.846028440856790E-01, 7.267512221362666E-01, 4.025157999677987E-02, \ -5.551715224920534E-01, 4.543430257556506E-01, 5.681533956880705E-02, \ -5.546040128597290E-01, 8.607588431664005E-02, 6.345041073160007E-02, \ -5.590463446310300E-01, -2.987570130168568E-01, 5.984062693812596E-02, \ -5.535005324411616E-01, -6.169692132455251E-01, 4.534179475738604E-02, \ -5.666697445547572E-01, -8.481255174324074E-01, 2.955237828322555E-02, \ -5.928240900022717E-01, -9.728321444146757E-01, 1.207258865550634E-02, \ -6.756466780817323E-01, 9.797748409271184E-01, 9.430834821192467E-03, \ -7.057090125640939E-01, 8.569411643178257E-01, 2.578172152269087E-02, \ -7.324178297883669E-01, 5.881115844344131E-01, 4.112604151501918E-02, \ -7.089833134544923E-01, 2.743227288305772E-01, 5.206048407106920E-02, \ -7.070216898176970E-01, -1.052133696540627E-01, 5.313592538270182E-02, \ -7.140246356433033E-01, -4.665219411497065E-01, 4.523777395980864E-02, \ -7.018378364178222E-01, -7.239136739360896E-01, 2.865845173440685E-02, \ -7.265012674973680E-01, -9.106140002539487E-01, 1.785266500303629E-02, \ -7.502326422653172E-01, -9.941725573151815E-01, 3.753285495396784E-03, \ -8.274846897101481E-01, 9.978010553534403E-01, 2.202140457066555E-03, \ -8.192923347877169E-01, 9.390289816897084E-01, 1.292326356223006E-02, \ -8.313147253414798E-01, 7.529833038926661E-01, 2.592641401983919E-02, \ -8.508397854338550E-01, 4.234950052660812E-01, 3.562268594306770E-02, \ -8.335604271423080E-01, 8.263716754706234E-02, 4.169722943892294E-02, \ -8.333299598244532E-01, -2.871192325820531E-01, 3.873060921878728E-02, \ -8.458562646869368E-01, -5.969821698805272E-01, 2.877988053080015E-02, \ -8.078655554136182E-01, -7.904438964071007E-01, 1.755929774595502E-02, \ -8.447527353299386E-01, -9.573586572433928E-01, 9.057958019613784E-03, \ -9.281623277448025E-01, 9.778973529249545E-01, 4.706571839130655E-03, \ -9.134629368007466E-01, 8.725226493533312E-01, 1.272093703683140E-02, \ -9.189059119013587E-01, 6.228132355945927E-01, 2.081162885166939E-02, \ -9.352972042034906E-01, 2.394035979501314E-01, 2.507345449526446E-02, \ -9.260008242840237E-01, -1.093506648825247E-01, 2.730772032753251E-02, \ -9.322554404281427E-01, -4.325018867770137E-01, 2.166809223221262E-02, \ -9.265407983180678E-01, -6.804488306011519E-01, 1.129035475105887E-02, \ -8.963660879434896E-01, -8.578428981954751E-01, 1.427796928443569E-02, \ -9.228669313126245E-01, -9.903049524081384E-01, 2.936908429948614E-03, \ -9.795076814902403E-01, 9.391999047436536E-01, 3.611764745309799E-03, \ -9.682018722477242E-01, 7.789774445276537E-01, 9.386909970380832E-03, \ -9.723852471142062E-01, 4.752904607817341E-01, 1.284048267253543E-02, \ -9.845164156039091E-01, 4.496231910970377E-02, 1.155742732057478E-02, \ -9.919138468383984E-01, -5.892431915668860E-01, 5.712369221551983E-03, \ -9.653607048671382E-01, -7.514078044040550E-01, 9.247990075208610E-03, \ -9.634968122279486E-01, -9.300634913926976E-01, 6.455717208889276E-03, \ -9.899993900205354E-01, 9.944294353233614E-01, 6.923818612511791E-04, \ -9.957478348818433E-01, 8.751512353190156E-01, 1.727894454945418E-03, \ -9.950143212717456E-01, 6.584454755209226E-01, 3.945702259118487E-03, \ -9.960292127295011E-01, 3.102415165889851E-01, 4.235815708736188E-03, \ -9.868438218892031E-01, -2.632466666320823E-01, 1.048005824445523E-02, \ -9.759292701915939E-01, -4.866196210874411E-01, 4.122542369510386E-03, \ -9.956803593698287E-01, -8.464174810055828E-01, 2.909040478947865E-03, \ -9.918608822862665E-01, -9.833582162145671E-01, 1.201280370154266E-03 ] ) return xyw def smr29 ( ): #*****************************************************************************80 # ## smr29 returns the SMR rule of degree 29. # # Discussion: # # DEGREE: 29 # SYMMETRY: (X, Y), (-X, -Y) # POINTS CARDINALITY: 153 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*153), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.949933127427926E-01, 9.846653902287268E-01, 9.395690393964076E-04, \ -9.947553807807867E-01, -6.565416135023074E-01, 4.902572703976801E-03, \ -9.945746533289254E-01, 8.095347588811120E-01, 3.444322300954131E-03, \ -9.936165836110393E-01, 5.449460871204653E-01, 5.048778280493792E-03, \ -9.916021206491545E-01, -3.020588266272870E-01, 7.856326443021280E-03, \ -9.885493346511697E-01, 3.754426235872674E-02, 9.243463352453171E-03, \ -9.853949921317231E-01, -9.716885948870212E-01, 2.611624046143479E-03, \ -9.850307952194871E-01, -8.619821821525152E-01, 5.756950705760731E-03, \ -9.832827588628299E-01, 3.064831307139635E-01, 1.011037458386165E-02, \ -9.721136174490276E-01, 9.199575449706859E-01, 6.336945711231334E-03, \ -9.629324251458530E-01, 6.898499209334040E-01, 1.253275279199627E-02, \ -9.611009120701418E-01, -5.003853392931935E-01, 1.712154659313199E-02, \ -9.462498240094916E-01, -1.332608625807670E-01, 2.240075719199047E-02, \ -9.411359576419225E-01, -7.505472392355358E-01, 1.603065396164867E-02, \ -9.382448848401312E-01, 4.599118226520993E-01, 1.718439080989034E-02, \ -9.314612798308124E-01, -9.967694998936406E-01, 1.745679805743830E-03, \ -9.295735875484051E-01, 9.848152682310835E-01, 4.103888501222671E-03, \ -9.232310041137312E-01, 1.804372056187648E-01, 2.477443727803194E-02, \ -9.183317763520688E-01, -9.261208167798600E-01, 1.096195080681892E-02, \ -9.116574969716016E-01, 8.271123341203230E-01, 1.601077862848477E-02, \ -8.888912692909274E-01, -3.479987971871291E-01, 2.796225817458692E-02, \ -8.779301509485118E-01, 5.948583749922939E-01, 2.015897400394908E-02, \ -8.637451657209914E-01, -6.139023089531026E-01, 2.808904163947544E-02, \ -8.501310025536610E-01, 9.347168973702518E-01, 1.258009305624949E-02, \ -8.432406244370808E-01, 2.340798283350513E-02, 3.394457013361375E-02, \ -8.333294144744180E-01, -1.839129116833924E-01, 9.917901422164995E-03, \ -8.296887505977431E-01, -8.345532619659806E-01, 2.285324032183532E-02, \ -8.290744150263981E-01, 3.658292544818590E-01, 3.507289015514854E-02, \ -8.187205704950732E-01, -9.788557134648613E-01, 7.722403962482972E-03, \ -8.088673371817973E-01, 7.219103637161282E-01, 2.472789041607375E-02, \ -7.802699772004215E-01, 9.914861448776406E-01, 4.713473975833743E-03, \ -7.752301559048632E-01, -2.171128429124935E-01, 2.378259924133609E-02, \ -7.470829498608977E-01, -4.586599493926842E-01, 4.002928037597185E-02, \ -7.361511371834013E-01, 8.583154508083678E-01, 2.261583569713491E-02, \ -7.287146431973126E-01, -6.873006158071762E-01, 2.251882920671917E-02, \ -7.180886055039243E-01, 2.076767520253592E-01, 4.499352749218116E-02, \ -7.146537939190210E-01, -9.289340401690634E-01, 1.645329992585584E-02, \ -7.067199537433859E-01, 5.424756607903567E-01, 4.335690137047433E-02, \ -6.903679490586278E-01, -7.147862946890238E-02, 3.408763052303377E-02, \ -6.764025157771765E-01, -7.573659452363536E-01, 1.935531604707887E-02, \ -6.506894539762457E-01, 9.564690231494537E-01, 1.464896209687315E-02, \ -6.208513475663459E-01, -9.916051471397467E-01, 6.432187025682493E-03, \ -6.116292887899047E-01, 7.357056852576344E-01, 3.377020044412275E-02, \ -5.979003962373047E-01, -2.796891406409555E-01, 4.888297756206456E-02, \ -5.778077209855854E-01, -8.675249675625395E-01, 2.457244823370517E-02, \ -5.728456567073842E-01, -5.296576709425311E-01, 3.639826598763665E-02, \ -5.602688054023620E-01, 3.829382266085970E-01, 5.473125938490646E-02, \ -5.600226162335806E-01, 7.201761109528224E-02, 4.732804187723799E-02, \ -5.315715479129545E-01, -6.485017442148879E-01, 2.380537349256804E-02, \ -5.213722221542452E-01, 8.717053530032300E-01, 2.354037231951190E-02, \ -5.205683240806913E-01, 9.943357320308036E-01, 5.022863813128614E-03, \ -4.747713831994940E-01, 6.303175260200578E-01, 3.769491458931831E-02, \ -4.518891563243193E-01, -9.565726413410444E-01, 1.899592320434612E-02, \ -4.253276863946355E-01, -1.030467857496181E-01, 5.661499125196553E-02, \ -4.243714642725596E-01, -7.749351121311114E-01, 3.571480883454545E-02, \ -4.208552091936032E-01, 9.360365856546493E-01, 1.371343151498627E-02, \ -3.971426434725366E-01, -3.784299583698726E-01, 5.358828824792165E-02, \ -3.840824803302514E-01, 2.278813318596969E-01, 5.817728003299089E-02, \ -3.537037178838521E-01, 5.212016641539493E-01, 4.215943343810559E-02, \ -3.344249565042606E-01, 7.938301760272564E-01, 3.983164515649597E-02, \ -3.183689681012091E-01, -5.911289985164023E-01, 4.507083618856889E-02, \ -3.099978370992671E-01, 9.775914827530479E-01, 1.070368922033845E-02, \ -2.742873135694627E-01, -9.934217560165197E-01, 7.024959810244680E-03, \ -2.684789526442052E-01, -8.841305328486172E-01, 3.234575636115414E-02, \ -2.236413499576709E-01, 6.847889170584819E-02, 5.715210426473966E-02, \ -2.076813935038102E-01, -1.933246405625380E-01, 5.711938069880197E-02, \ -1.985992354046592E-01, 4.002875818222759E-01, 5.390325679350508E-02, \ -1.731862586703496E-01, 9.086517858862069E-01, 2.785469982257396E-02, \ -1.650094536595912E-01, 6.768962485151462E-01, 4.809572953564538E-02, \ -1.634028445678156E-01, -7.199249170570964E-01, 4.287990357079033E-02, \ -1.548556328765567E-01, -4.247385329928982E-01, 4.815909770521859E-02, \ -8.887107041790254E-02, 9.911658972290777E-01, 7.431729974979581E-03, \ -8.682050121233974E-02, -9.548310793397383E-01, 2.094359269434157E-02, \ -3.424326390343065E-02, 2.534546862921038E-01, 5.738432661390758E-02, \ -3.764571754171391E-03, -5.533592189095456E-01, 4.897606541273797E-02, \ -1.890047137705217E-03, 8.246644534267950E-01, 3.721909074703320E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 5.611678279970572E-02, \ 1.890047137705217E-03, -8.246644534267950E-01, 3.721909074703320E-02, \ 3.764571754171391E-03, 5.533592189095456E-01, 4.897606541273797E-02, \ 3.424326390343065E-02, -2.534546862921038E-01, 5.738432661390758E-02, \ 8.682050121233974E-02, 9.548310793397383E-01, 2.094359269434157E-02, \ 8.887107041790254E-02, -9.911658972290777E-01, 7.431729974979581E-03, \ 1.548556328765567E-01, 4.247385329928982E-01, 4.815909770521859E-02, \ 1.634028445678156E-01, 7.199249170570964E-01, 4.287990357079033E-02, \ 1.650094536595912E-01, -6.768962485151462E-01, 4.809572953564538E-02, \ 1.731862586703496E-01, -9.086517858862069E-01, 2.785469982257396E-02, \ 1.985992354046592E-01, -4.002875818222759E-01, 5.390325679350508E-02, \ 2.076813935038102E-01, 1.933246405625380E-01, 5.711938069880197E-02, \ 2.236413499576709E-01, -6.847889170584819E-02, 5.715210426473966E-02, \ 2.684789526442052E-01, 8.841305328486172E-01, 3.234575636115414E-02, \ 2.742873135694627E-01, 9.934217560165197E-01, 7.024959810244680E-03, \ 3.099978370992671E-01, -9.775914827530479E-01, 1.070368922033845E-02, \ 3.183689681012091E-01, 5.911289985164023E-01, 4.507083618856889E-02, \ 3.344249565042606E-01, -7.938301760272564E-01, 3.983164515649597E-02, \ 3.537037178838521E-01, -5.212016641539493E-01, 4.215943343810559E-02, \ 3.840824803302514E-01, -2.278813318596969E-01, 5.817728003299089E-02, \ 3.971426434725366E-01, 3.784299583698726E-01, 5.358828824792165E-02, \ 4.208552091936032E-01, -9.360365856546493E-01, 1.371343151498627E-02, \ 4.243714642725596E-01, 7.749351121311114E-01, 3.571480883454545E-02, \ 4.253276863946355E-01, 1.030467857496181E-01, 5.661499125196553E-02, \ 4.518891563243193E-01, 9.565726413410444E-01, 1.899592320434612E-02, \ 4.747713831994940E-01, -6.303175260200578E-01, 3.769491458931831E-02, \ 5.205683240806913E-01, -9.943357320308036E-01, 5.022863813128614E-03, \ 5.213722221542452E-01, -8.717053530032300E-01, 2.354037231951190E-02, \ 5.315715479129545E-01, 6.485017442148879E-01, 2.380537349256804E-02, \ 5.600226162335806E-01, -7.201761109528224E-02, 4.732804187723799E-02, \ 5.602688054023620E-01, -3.829382266085970E-01, 5.473125938490646E-02, \ 5.728456567073842E-01, 5.296576709425311E-01, 3.639826598763665E-02, \ 5.778077209855854E-01, 8.675249675625395E-01, 2.457244823370517E-02, \ 5.979003962373047E-01, 2.796891406409555E-01, 4.888297756206456E-02, \ 6.116292887899047E-01, -7.357056852576344E-01, 3.377020044412275E-02, \ 6.208513475663459E-01, 9.916051471397467E-01, 6.432187025682493E-03, \ 6.506894539762457E-01, -9.564690231494537E-01, 1.464896209687315E-02, \ 6.764025157771765E-01, 7.573659452363536E-01, 1.935531604707887E-02, \ 6.903679490586278E-01, 7.147862946890238E-02, 3.408763052303377E-02, \ 7.067199537433859E-01, -5.424756607903567E-01, 4.335690137047433E-02, \ 7.146537939190210E-01, 9.289340401690634E-01, 1.645329992585584E-02, \ 7.180886055039243E-01, -2.076767520253592E-01, 4.499352749218116E-02, \ 7.287146431973126E-01, 6.873006158071762E-01, 2.251882920671917E-02, \ 7.361511371834013E-01, -8.583154508083678E-01, 2.261583569713491E-02, \ 7.470829498608977E-01, 4.586599493926842E-01, 4.002928037597185E-02, \ 7.752301559048632E-01, 2.171128429124935E-01, 2.378259924133609E-02, \ 7.802699772004215E-01, -9.914861448776406E-01, 4.713473975833743E-03, \ 8.088673371817973E-01, -7.219103637161282E-01, 2.472789041607375E-02, \ 8.187205704950732E-01, 9.788557134648613E-01, 7.722403962482972E-03, \ 8.290744150263981E-01, -3.658292544818590E-01, 3.507289015514854E-02, \ 8.296887505977431E-01, 8.345532619659806E-01, 2.285324032183532E-02, \ 8.333294144744180E-01, 1.839129116833924E-01, 9.917901422164995E-03, \ 8.432406244370808E-01, -2.340798283350513E-02, 3.394457013361375E-02, \ 8.501310025536610E-01, -9.347168973702518E-01, 1.258009305624949E-02, \ 8.637451657209914E-01, 6.139023089531026E-01, 2.808904163947544E-02, \ 8.779301509485118E-01, -5.948583749922939E-01, 2.015897400394908E-02, \ 8.888912692909274E-01, 3.479987971871291E-01, 2.796225817458692E-02, \ 9.116574969716016E-01, -8.271123341203230E-01, 1.601077862848477E-02, \ 9.183317763520688E-01, 9.261208167798600E-01, 1.096195080681892E-02, \ 9.232310041137312E-01, -1.804372056187648E-01, 2.477443727803194E-02, \ 9.295735875484051E-01, -9.848152682310835E-01, 4.103888501222671E-03, \ 9.314612798308124E-01, 9.967694998936406E-01, 1.745679805743830E-03, \ 9.382448848401312E-01, -4.599118226520993E-01, 1.718439080989034E-02, \ 9.411359576419225E-01, 7.505472392355358E-01, 1.603065396164867E-02, \ 9.462498240094916E-01, 1.332608625807670E-01, 2.240075719199047E-02, \ 9.611009120701418E-01, 5.003853392931935E-01, 1.712154659313199E-02, \ 9.629324251458530E-01, -6.898499209334040E-01, 1.253275279199627E-02, \ 9.721136174490276E-01, -9.199575449706859E-01, 6.336945711231334E-03, \ 9.832827588628299E-01, -3.064831307139635E-01, 1.011037458386165E-02, \ 9.850307952194871E-01, 8.619821821525152E-01, 5.756950705760731E-03, \ 9.853949921317231E-01, 9.716885948870212E-01, 2.611624046143479E-03, \ 9.885493346511697E-01, -3.754426235872674E-02, 9.243463352453171E-03, \ 9.916021206491545E-01, 3.020588266272870E-01, 7.856326443021280E-03, \ 9.936165836110393E-01, -5.449460871204653E-01, 5.048778280493792E-03, \ 9.945746533289254E-01, -8.095347588811120E-01, 3.444322300954131E-03, \ 9.947553807807867E-01, 6.565416135023074E-01, 4.902572703976801E-03, \ 9.949933127427926E-01, -9.846653902287268E-01, 9.395690393964076E-04 ] ) return xyw def smr29s ( ): #*****************************************************************************80 # ## smr29S returns the rotatonally invariant SMR rule of degree 29. # # Discussion: # # DEGREE: 29 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 153 # NORM INF MOMS. RESIDUAL: 2.70617e-16 # SUM NEGATIVE WEIGHTS: 1.46517E-02, \ # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*153), the requested rule. # import numpy as np xyw = np.array ( [ \ 1.995554510347695E-01, 1.887353707822548E-01, 7.344881047788419E-02, \ 2.130905764129401E-01, 5.455267403580432E-01, 6.209984035978915E-02, \ 2.388895084628246E-01, 8.131809651972651E-01, 4.184384427163037E-02, \ 2.038938767743064E-01, 9.863343822191492E-01, 5.131075694716339E-04, \ 2.698246240215212E-01, 9.643706705539593E-01, 1.712164807226155E-02, \ 3.928345180603147E-01, 3.686184349052021E-01, 6.489527207591311E-02, \ 4.144000559327279E-01, 6.845975817877503E-01, 4.944840913356350E-02, \ 4.402759350876731E-01, 9.010432195863607E-01, 2.757405514679618E-02, \ 4.527181508614157E-01, 9.952152161758490E-01, 4.925532618002394E-03, \ 5.579522261495289E-01, 1.761582819832321E-01, 6.188238970001386E-02, \ 5.753347655779147E-01, 5.292288412881652E-01, 5.168460836650747E-02, \ 5.934515082334419E-01, 8.046750403390426E-01, 3.415204165486681E-02, \ 6.055261390114883E-01, 9.669899640916929E-01, 1.323441713883155E-02, \ 7.154909664472028E-01, 3.523839334728593E-01, 4.846803145137081E-02, \ 7.268010683419225E-01, 6.783203685825908E-01, 3.602990566434557E-02, \ 7.296280734021068E-01, 9.091222948855520E-01, 1.863026896557024E-02, \ 7.685318705419301E-01, 9.932162015282956E-01, 4.367730318652883E-03, \ 8.289969889442530E-01, 1.584524092289804E-01, 4.058748981808668E-02, \ 8.365897953958084E-01, 5.258522155386184E-01, 3.319785897530852E-02, \ 8.316719666113968E-01, 8.204370730256448E-01, 2.075970864095848E-02, \ 8.871860429369979E-01, 9.163805447338561E-01, 3.893022115627323E-03, \ 8.690236026560919E-01, 9.647484296790166E-01, 7.335685071586549E-03, \ 9.187533470826308E-01, 3.499840453590620E-01, 2.626466692941504E-02, \ 9.134702524025524E-01, 7.013486396820177E-01, 1.955810454123038E-02, \ 9.541746623132917E-01, 8.410023019359270E-01, 6.965850473298985E-03, \ 9.475721149242626E-01, 9.269025845479085E-01, 5.802838252293684E-03, \ 9.568636719971328E-01, 9.889975414443256E-01, 3.098510717291335E-03, \ 9.700539003410525E-01, 1.462690094803091E-01, 1.684436628110278E-02, \ 9.961052572257075E-01, 3.632658507871842E-01, 5.146979760206008E-03, \ 9.696607933775031E-01, 5.511605113182357E-01, 1.411592369017692E-02, \ 9.930889935835162E-01, 7.238541535398172E-01, 4.366281743177327E-03, \ 9.861368659264031E-01, 8.483603521407402E-01, 2.558788266617852E-03, \ 9.703225207695876E-01, 9.617299191521864E-01, -3.662923776765502E-03, \ 9.877929897983208E-01, 9.572988789445298E-01, 3.811762688023674E-03, \ 1.110886537223573E-02, 3.805232776392568E-01, 7.048655460716827E-02, \ 2.656770164537742E-02, 7.008980905724834E-01, 5.369718262729808E-02, \ 5.439701833656795E-02, 9.100556589521321E-01, 2.989488274476401E-02, \ 7.142859722990462E-02, 9.946044556670760E-01, 5.849868982269740E-03, \ -1.887353707822548E-01, 1.995554510347695E-01, 7.344881047788419E-02, \ -5.455267403580432E-01, 2.130905764129401E-01, 6.209984035978915E-02, \ -8.131809651972651E-01, 2.388895084628246E-01, 4.184384427163037E-02, \ -9.863343822191492E-01, 2.038938767743064E-01, 5.131075694716339E-04, \ -9.643706705539593E-01, 2.698246240215212E-01, 1.712164807226155E-02, \ -3.686184349052021E-01, 3.928345180603147E-01, 6.489527207591311E-02, \ -6.845975817877503E-01, 4.144000559327279E-01, 4.944840913356350E-02, \ -9.010432195863607E-01, 4.402759350876731E-01, 2.757405514679618E-02, \ -9.952152161758490E-01, 4.527181508614157E-01, 4.925532618002394E-03, \ -1.761582819832321E-01, 5.579522261495289E-01, 6.188238970001386E-02, \ -5.292288412881652E-01, 5.753347655779147E-01, 5.168460836650747E-02, \ -8.046750403390426E-01, 5.934515082334419E-01, 3.415204165486681E-02, \ -9.669899640916929E-01, 6.055261390114883E-01, 1.323441713883155E-02, \ -3.523839334728593E-01, 7.154909664472028E-01, 4.846803145137081E-02, \ -6.783203685825908E-01, 7.268010683419225E-01, 3.602990566434557E-02, \ -9.091222948855520E-01, 7.296280734021068E-01, 1.863026896557024E-02, \ -9.932162015282956E-01, 7.685318705419301E-01, 4.367730318652883E-03, \ -1.584524092289804E-01, 8.289969889442530E-01, 4.058748981808668E-02, \ -5.258522155386184E-01, 8.365897953958084E-01, 3.319785897530852E-02, \ -8.204370730256448E-01, 8.316719666113968E-01, 2.075970864095848E-02, \ -9.163805447338561E-01, 8.871860429369979E-01, 3.893022115627323E-03, \ -9.647484296790166E-01, 8.690236026560919E-01, 7.335685071586549E-03, \ -3.499840453590620E-01, 9.187533470826308E-01, 2.626466692941504E-02, \ -7.013486396820177E-01, 9.134702524025524E-01, 1.955810454123038E-02, \ -8.410023019359270E-01, 9.541746623132917E-01, 6.965850473298985E-03, \ -9.269025845479085E-01, 9.475721149242626E-01, 5.802838252293684E-03, \ -9.889975414443256E-01, 9.568636719971328E-01, 3.098510717291335E-03, \ -1.462690094803091E-01, 9.700539003410525E-01, 1.684436628110278E-02, \ -3.632658507871842E-01, 9.961052572257075E-01, 5.146979760206008E-03, \ -5.511605113182357E-01, 9.696607933775031E-01, 1.411592369017692E-02, \ -7.238541535398172E-01, 9.930889935835162E-01, 4.366281743177327E-03, \ -8.483603521407402E-01, 9.861368659264031E-01, 2.558788266617852E-03, \ -9.617299191521864E-01, 9.703225207695876E-01, -3.662923776765502E-03, \ -9.572988789445298E-01, 9.877929897983208E-01, 3.811762688023674E-03, \ -3.805232776392568E-01, 1.110886537223573E-02, 7.048655460716827E-02, \ -7.008980905724834E-01, 2.656770164537742E-02, 5.369718262729808E-02, \ -9.100556589521321E-01, 5.439701833656795E-02, 2.989488274476401E-02, \ -9.946044556670760E-01, 7.142859722990462E-02, 5.849868982269740E-03, \ -1.995554510347695E-01, -1.887353707822548E-01, 7.344881047788419E-02, \ -2.130905764129401E-01, -5.455267403580432E-01, 6.209984035978915E-02, \ -2.388895084628246E-01, -8.131809651972651E-01, 4.184384427163037E-02, \ -2.038938767743064E-01, -9.863343822191492E-01, 5.131075694716339E-04, \ -2.698246240215212E-01, -9.643706705539593E-01, 1.712164807226155E-02, \ -3.928345180603147E-01, -3.686184349052021E-01, 6.489527207591311E-02, \ -4.144000559327279E-01, -6.845975817877503E-01, 4.944840913356350E-02, \ -4.402759350876731E-01, -9.010432195863607E-01, 2.757405514679618E-02, \ -4.527181508614157E-01, -9.952152161758490E-01, 4.925532618002394E-03, \ -5.579522261495289E-01, -1.761582819832321E-01, 6.188238970001386E-02, \ -5.753347655779147E-01, -5.292288412881652E-01, 5.168460836650747E-02, \ -5.934515082334419E-01, -8.046750403390426E-01, 3.415204165486681E-02, \ -6.055261390114883E-01, -9.669899640916929E-01, 1.323441713883155E-02, \ -7.154909664472028E-01, -3.523839334728593E-01, 4.846803145137081E-02, \ -7.268010683419225E-01, -6.783203685825908E-01, 3.602990566434557E-02, \ -7.296280734021068E-01, -9.091222948855520E-01, 1.863026896557024E-02, \ -7.685318705419301E-01, -9.932162015282956E-01, 4.367730318652883E-03, \ -8.289969889442530E-01, -1.584524092289804E-01, 4.058748981808668E-02, \ -8.365897953958084E-01, -5.258522155386184E-01, 3.319785897530852E-02, \ -8.316719666113968E-01, -8.204370730256448E-01, 2.075970864095848E-02, \ -8.871860429369979E-01, -9.163805447338561E-01, 3.893022115627323E-03, \ -8.690236026560919E-01, -9.647484296790166E-01, 7.335685071586549E-03, \ -9.187533470826308E-01, -3.499840453590620E-01, 2.626466692941504E-02, \ -9.134702524025524E-01, -7.013486396820177E-01, 1.955810454123038E-02, \ -9.541746623132917E-01, -8.410023019359270E-01, 6.965850473298985E-03, \ -9.475721149242626E-01, -9.269025845479085E-01, 5.802838252293684E-03, \ -9.568636719971328E-01, -9.889975414443256E-01, 3.098510717291335E-03, \ -9.700539003410525E-01, -1.462690094803091E-01, 1.684436628110278E-02, \ -9.961052572257075E-01, -3.632658507871842E-01, 5.146979760206008E-03, \ -9.696607933775031E-01, -5.511605113182357E-01, 1.411592369017692E-02, \ -9.930889935835162E-01, -7.238541535398172E-01, 4.366281743177327E-03, \ -9.861368659264031E-01, -8.483603521407402E-01, 2.558788266617852E-03, \ -9.703225207695876E-01, -9.617299191521864E-01, -3.662923776765502E-03, \ -9.877929897983208E-01, -9.572988789445298E-01, 3.811762688023674E-03, \ -1.110886537223573E-02, -3.805232776392568E-01, 7.048655460716827E-02, \ -2.656770164537742E-02, -7.008980905724834E-01, 5.369718262729808E-02, \ -5.439701833656795E-02, -9.100556589521321E-01, 2.989488274476401E-02, \ -7.142859722990462E-02, -9.946044556670760E-01, 5.849868982269740E-03, \ 1.887353707822548E-01, -1.995554510347695E-01, 7.344881047788419E-02, \ 5.455267403580432E-01, -2.130905764129401E-01, 6.209984035978915E-02, \ 8.131809651972651E-01, -2.388895084628246E-01, 4.184384427163037E-02, \ 9.863343822191492E-01, -2.038938767743064E-01, 5.131075694716339E-04, \ 9.643706705539593E-01, -2.698246240215212E-01, 1.712164807226155E-02, \ 3.686184349052021E-01, -3.928345180603147E-01, 6.489527207591311E-02, \ 6.845975817877503E-01, -4.144000559327279E-01, 4.944840913356350E-02, \ 9.010432195863607E-01, -4.402759350876731E-01, 2.757405514679618E-02, \ 9.952152161758490E-01, -4.527181508614157E-01, 4.925532618002394E-03, \ 1.761582819832321E-01, -5.579522261495289E-01, 6.188238970001386E-02, \ 5.292288412881652E-01, -5.753347655779147E-01, 5.168460836650747E-02, \ 8.046750403390426E-01, -5.934515082334419E-01, 3.415204165486681E-02, \ 9.669899640916929E-01, -6.055261390114883E-01, 1.323441713883155E-02, \ 3.523839334728593E-01, -7.154909664472028E-01, 4.846803145137081E-02, \ 6.783203685825908E-01, -7.268010683419225E-01, 3.602990566434557E-02, \ 9.091222948855520E-01, -7.296280734021068E-01, 1.863026896557024E-02, \ 9.932162015282956E-01, -7.685318705419301E-01, 4.367730318652883E-03, \ 1.584524092289804E-01, -8.289969889442530E-01, 4.058748981808668E-02, \ 5.258522155386184E-01, -8.365897953958084E-01, 3.319785897530852E-02, \ 8.204370730256448E-01, -8.316719666113968E-01, 2.075970864095848E-02, \ 9.163805447338561E-01, -8.871860429369979E-01, 3.893022115627323E-03, \ 9.647484296790166E-01, -8.690236026560919E-01, 7.335685071586549E-03, \ 3.499840453590620E-01, -9.187533470826308E-01, 2.626466692941504E-02, \ 7.013486396820177E-01, -9.134702524025524E-01, 1.955810454123038E-02, \ 8.410023019359270E-01, -9.541746623132917E-01, 6.965850473298985E-03, \ 9.269025845479085E-01, -9.475721149242626E-01, 5.802838252293684E-03, \ 9.889975414443256E-01, -9.568636719971328E-01, 3.098510717291335E-03, \ 1.462690094803091E-01, -9.700539003410525E-01, 1.684436628110278E-02, \ 3.632658507871842E-01, -9.961052572257075E-01, 5.146979760206008E-03, \ 5.511605113182357E-01, -9.696607933775031E-01, 1.411592369017692E-02, \ 7.238541535398172E-01, -9.930889935835162E-01, 4.366281743177327E-03, \ 8.483603521407402E-01, -9.861368659264031E-01, 2.558788266617852E-03, \ 9.617299191521864E-01, -9.703225207695876E-01, -3.662923776765502E-03, \ 9.572988789445298E-01, -9.877929897983208E-01, 3.811762688023674E-03, \ 3.805232776392568E-01, -1.110886537223573E-02, 7.048655460716827E-02, \ 7.008980905724834E-01, -2.656770164537742E-02, 5.369718262729808E-02, \ 9.100556589521321E-01, -5.439701833656795E-02, 2.989488274476401E-02, \ 9.946044556670760E-01, -7.142859722990462E-02, 5.849868982269740E-03, \ 0.000000000000000E+00, 0.000000000000000E+00, 7.642673546157117E-02 ] ) return xyw def smr30 ( ): #*****************************************************************************80 # ## smr30 returns the SMR rule of degree 30. # # Discussion: # # DEGREE: 30 # XIAO-GIMBUTAS ESTIMATE: 166 MOELLER-RASPUTIN LOWER BOUND: 128 # POINTS CARDINALITY: 167 # NORM INF MOMS. RESIDUAL: 4.44089e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*167), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.962695953022117E-01, -4.432378837780777E-01, 3.892630177515625E-03, \ -9.954114173626548E-01, 2.643526556843364E-01, 4.534201620636273E-03, \ -9.949269819594637E-01, 5.811458193160586E-01, 3.690610442210943E-03, \ -9.947791036081476E-01, -8.855392187642179E-02, 4.945989612847814E-03, \ -9.940513238712086E-01, -9.629012381127487E-01, 1.529980279640927E-03, \ -9.937009284888235E-01, -7.963627749974038E-01, 3.806704824353705E-03, \ -9.914129974533056E-01, 9.014542533695618E-01, 3.250642010093910E-03, \ -9.912570981356938E-01, 9.920951313914597E-01, 7.737085001637529E-04, \ -9.823632199537923E-01, 7.480690374805677E-01, 7.178107249226476E-03, \ -9.774418651328238E-01, -6.195633189134538E-01, 1.012484081798108E-02, \ -9.706544108267556E-01, -2.729784055929617E-01, 1.355763804090731E-02, \ -9.703903424063889E-01, -9.055390715558742E-01, 3.812394374457089E-03, \ -9.694574072185448E-01, 4.341328372213230E-01, 1.266804574330651E-02, \ -9.690407115962437E-01, 9.341819736700314E-02, 1.394979228044907E-02, \ -9.628802671374306E-01, -9.944496567185225E-01, 1.467879560257003E-03, \ -9.527399448624597E-01, 9.624994157286473E-01, 5.260700927456429E-03, \ -9.514132521336506E-01, -8.829098392211954E-01, 4.907118941168890E-03, \ -9.345046955574380E-01, 8.387639945783492E-01, 1.172001054121250E-02, \ -9.297146520577916E-01, 6.183698468095432E-01, 1.825632348450637E-02, \ -9.293314444347445E-01, -7.435030197515320E-01, 1.482615873422928E-02, \ -9.260149110397602E-01, -4.576849499932223E-01, 2.118348083720268E-02, \ -9.191878620227047E-01, -8.576798396420104E-02, 2.272620841149477E-02, \ -9.158350185631037E-01, 2.692275128511369E-01, 2.304963366190331E-02, \ -9.100695669977138E-01, -9.705559713759557E-01, 3.389088115670371E-03, \ -8.849735191782050E-01, -9.517932989228655E-01, 5.364563594773305E-03, \ -8.808666812238437E-01, 9.943730059848226E-01, 2.875519471334203E-03, \ -8.595716686462112E-01, 9.162278791175735E-01, 1.277710664857529E-02, \ -8.534233518158184E-01, -8.449957910924649E-01, 1.658096280776431E-02, \ -8.532333609215695E-01, -2.640000860004303E-01, 2.911278919189067E-02, \ -8.500329899131518E-01, 4.606540637675913E-01, 2.965001937514069E-02, \ -8.500143920229317E-01, -6.082069619792305E-01, 2.645748804192720E-02, \ -8.454025250745086E-01, 7.354238754987793E-01, 2.316800651593019E-02, \ -8.367229347951246E-01, 8.990264524394226E-02, 3.373621057431971E-02, \ -8.001347673092866E-01, -9.933648582561806E-01, 3.850587028399502E-03, \ -7.695116274930011E-01, -4.118889027088976E-01, 3.034893498538439E-02, \ -7.555576680657612E-01, 9.700425147325877E-01, 1.014999644279535E-02, \ -7.538647716837412E-01, -9.239685866946878E-01, 1.517356711708827E-02, \ -7.462990724884444E-01, -7.378827886824465E-01, 2.842931310687195E-02, \ -7.435929466472898E-01, 2.881630895110476E-01, 4.096030346800239E-02, \ -7.367231344637399E-01, 8.391743049717729E-01, 2.371595352428025E-02, \ -7.360783333119556E-01, 5.954890113834164E-01, 3.505479981673820E-02, \ -7.358357631903044E-01, -9.719765309238697E-02, 4.351226764743989E-02, \ -6.784458770150876E-01, -5.334164281651258E-01, 2.989403195373217E-02, \ -6.323142754086236E-01, -9.756719768853687E-01, 1.050599811708168E-02, \ -6.187413218331049E-01, 9.957562917639060E-01, 3.877141507331312E-03, \ -6.185869146576074E-01, -8.450016714647949E-01, 2.679921705344681E-02, \ -6.169842175479411E-01, 1.078804071378743E-01, 5.004167045667424E-02, \ -6.111438437236484E-01, -2.769425577256663E-01, 4.921646796209538E-02, \ -6.028539652311193E-01, 7.224797085796002E-01, 3.569438969843478E-02, \ -6.024568031179428E-01, 9.184105677646670E-01, 2.045602682082065E-02, \ -6.005929876780286E-01, 4.366655576377152E-01, 4.708714185331756E-02, \ -5.721476752159514E-01, -6.455779128450227E-01, 3.324435055130232E-02, \ -4.821587643276321E-01, -6.552912695280060E-02, 5.000579378842215E-02, \ -4.693508512146036E-01, -9.251514364207605E-01, 2.156482363680663E-02, \ -4.664112078735353E-01, -4.442366390500550E-01, 5.080565593127764E-02, \ -4.618665119648193E-01, -9.967579491010828E-01, 3.816748009617544E-03, \ -4.494143273856875E-01, 8.276470129494764E-01, 3.214308262649934E-02, \ -4.479160038776199E-01, 9.719485124728899E-01, 1.285989649810473E-02, \ -4.448715957603111E-01, 5.834707035806619E-01, 4.762439584447587E-02, \ -4.443814635842437E-01, 2.635713157455042E-01, 5.794249352621746E-02, \ -4.396198113354752E-01, -7.548969208964118E-01, 3.428224841661166E-02, \ -3.657940226461420E-01, -2.006533706330268E-01, 3.755546975167398E-02, \ -3.068381707303870E-01, -5.934274157892239E-01, 4.806217780828576E-02, \ -2.967415958337351E-01, 9.138477267737024E-01, 2.179374136407983E-02, \ -2.843623923239886E-01, -9.723235086081026E-01, 1.370404412777051E-02, \ -2.841773158810993E-01, -8.502214939557524E-01, 3.069486488068529E-02, \ -2.774502955157072E-01, 7.783800443548269E-02, 6.485367831170855E-02, \ -2.754822583044234E-01, 7.120414326285063E-01, 4.331711859331076E-02, \ -2.687871739273696E-01, 4.269851621611526E-01, 5.836353670839110E-02, \ -2.567436168928061E-01, 9.945360458235195E-01, 5.240836616582418E-03, \ -2.513499007569119E-01, -3.210828524214602E-01, 4.844638715484986E-02, \ -1.598590614299937E-01, 8.482252908489760E-01, 1.682030776305622E-02, \ -1.427799257579916E-01, -7.170460184955041E-01, 3.915904236744100E-02, \ -1.091853236351570E-01, 9.580261183543186E-01, 1.474658041347025E-02, \ -1.022992873259765E-01, -1.104785543258961E-01, 6.661932528640521E-02, \ -1.015416677161510E-01, -9.200676756186152E-01, 2.329668513832093E-02, \ -9.412889158601399E-02, -4.688846642550997E-01, 5.469210938337690E-02, \ -8.907000954456333E-02, 2.513213963693643E-01, 6.571594126284511E-02, \ -8.744029029762249E-02, 5.785381919572421E-01, 5.300724353175888E-02, \ -7.712410713884485E-02, -9.943194119246959E-01, 5.499112875651152E-03, \ -6.523473573640569E-02, 7.983102424409952E-01, 2.517854943448727E-02, \ -1.095721736720509E-02, -7.962228644585386E-01, 2.085587531389086E-02, \ 2.518303411594268E-02, 9.860853647300887E-01, 6.488533578084030E-03, \ 6.649367018609328E-02, 8.934359950937619E-01, 2.271313073139822E-02, \ 7.864093675987820E-02, -2.918181793455348E-01, 6.374671736339137E-02, \ 8.230594852824862E-02, -6.128716323876445E-01, 5.036688164272618E-02, \ 8.994595584407042E-02, 6.378488548700582E-02, 6.747055946750249E-02, \ 9.331414467274024E-02, 4.264112897435890E-01, 5.762076485371190E-02, \ 1.036274934285688E-01, -9.654170079830869E-01, 1.528097665571535E-02, \ 1.062379679357248E-01, 7.045294352966426E-01, 4.336208027576573E-02, \ 1.070563588959354E-01, -8.518818738785342E-01, 2.527278435887043E-02, \ 1.702241024982263E-01, 9.972150656853269E-01, 2.645999354440326E-03, \ 1.941498146775931E-01, 9.416958566669819E-01, 1.299271762491835E-02, \ 2.382851494989787E-01, 2.794121411070278E-01, 3.900619436018987E-02, \ 2.597216208260207E-01, -4.600772470944473E-01, 5.666664739064187E-02, \ 2.633608715116675E-01, -7.382703813686664E-01, 4.094242606634930E-02, \ 2.680422728449567E-01, -1.237008749685800E-01, 6.430917939062639E-02, \ 2.709535102430495E-01, -9.946277851787007E-01, 4.995330134500549E-03, \ 2.717768185055764E-01, 8.206386870412736E-01, 3.322490081159339E-02, \ 2.860865029604455E-01, 5.750046796390000E-01, 5.163715243954464E-02, \ 2.919629207724195E-01, -9.126523283762582E-01, 2.290547444002006E-02, \ 3.221994725736586E-01, 9.739873036170995E-01, 9.709787500403095E-03, \ 3.238916864531801E-01, 1.871152636079638E-01, 3.786953410800285E-02, \ 4.326883824490022E-01, 9.054252916722543E-01, 2.179426150033381E-02, \ 4.334112862933560E-01, -6.113886295669552E-01, 4.619739021387417E-02, \ 4.393894435610020E-01, -3.042985645127746E-01, 5.679993404477694E-02, \ 4.457707596424073E-01, 4.135856200591693E-01, 5.369039030443149E-02, \ 4.480222422807119E-01, -9.699096000438506E-01, 1.284524266997323E-02, \ 4.481245405662154E-01, 7.226095819651619E-01, 3.875267371369672E-02, \ 4.548106144879556E-01, -8.323081975450645E-01, 3.014220006377240E-02, \ 4.581780858586828E-01, 3.469977407352812E-02, 5.500861406890217E-02, \ 4.703860920439117E-01, 9.947418373536940E-01, 3.780014001903630E-03, \ 5.804007745393400E-01, 9.618079992566787E-01, 1.161053553740031E-02, \ 5.833354854251170E-01, 5.930231848340044E-01, 3.799033003205411E-02, \ 5.930856097062387E-01, 2.373877943575770E-01, 5.084589261923814E-02, \ 5.965641353176369E-01, -4.730726160978409E-01, 4.627028009154758E-02, \ 6.019409638213139E-01, 8.388951235924025E-01, 2.676118014960469E-02, \ 6.025337137784932E-01, -1.408542441091471E-01, 4.904466589737274E-02, \ 6.035685372806677E-01, -9.184860893047954E-01, 1.930940686592521E-02, \ 6.054544565337695E-01, -9.957236600655665E-01, 3.768877425809975E-03, \ 6.057207734020840E-01, -7.322512010108688E-01, 3.339567747677206E-02, \ 6.875670307888612E-01, 4.627278058070344E-01, 2.947065495054275E-02, \ 7.023177466590736E-01, 9.928205536558483E-01, 3.885728390925337E-03, \ 7.195170980700635E-01, 7.305873329417671E-01, 2.847807814619499E-02, \ 7.238446910374424E-01, 5.561690048457465E-02, 4.419832996135477E-02, \ 7.240210652949475E-01, -3.007014261972007E-01, 3.439575422315153E-02, \ 7.371020667711963E-01, 9.252595362582127E-01, 1.536785201342859E-02, \ 7.384195707426535E-01, -8.438380733571678E-01, 2.235510768691872E-02, \ 7.405499034588905E-01, -6.188990137603514E-01, 3.246295613758222E-02, \ 7.440604692168796E-01, -9.713408547253161E-01, 9.607479120263517E-03, \ 7.685900922442980E-01, 3.465057508910690E-01, 2.776338673026480E-02, \ 7.954329735534109E-01, -4.109341533557886E-01, 1.857369110661608E-02, \ 8.140461518894649E-01, 5.964637576338830E-01, 2.604275460103966E-02, \ 8.298209513184971E-01, 8.417188363600208E-01, 1.770911353888088E-02, \ 8.337255108415906E-01, -1.237521420338796E-01, 3.477363818844623E-02, \ 8.450338467672839E-01, 9.803989034344278E-01, 6.318914249788773E-03, \ 8.499053424569023E-01, -7.513598048680518E-01, 2.131459811435620E-02, \ 8.505494208495452E-01, 2.034903566768354E-01, 2.898559224509574E-02, \ 8.534375448038033E-01, -9.226288272371441E-01, 1.212457346099878E-02, \ 8.655964520277111E-01, -9.954157466834472E-01, 2.574302443652325E-03, \ 8.685850946711341E-01, -5.228140183251604E-01, 2.217355893689261E-02, \ 8.943292225583946E-01, 4.595261118728072E-01, 2.187541877465294E-02, \ 9.006171857996548E-01, 7.180830553785196E-01, 1.636671200905273E-02, \ 9.075612511758971E-01, 9.205481097893897E-01, 7.889096906380533E-03, \ 9.108243128554621E-01, -3.093255095271237E-01, 2.247790975299426E-02, \ 9.242976221883992E-01, 4.079387457619278E-02, 2.269368117980306E-02, \ 9.336780332840566E-01, -8.547607055279791E-01, 1.092484696375260E-02, \ 9.387265328139205E-01, -6.592057435752858E-01, 1.490210373726517E-02, \ 9.446037800832677E-01, -9.693489449953010E-01, 4.898536170872587E-03, \ 9.479408185885666E-01, 9.575588886071763E-01, 2.997578905083853E-03, \ 9.495353577945340E-01, 3.186288923971684E-01, 1.513823435852647E-02, \ 9.520042531581182E-01, 9.980612732198122E-01, 1.202725556369299E-03, \ 9.525533437955715E-01, 8.141508738554407E-01, 8.188829215294804E-03, \ 9.641212854564828E-01, 5.940993549166920E-01, 1.301642639806175E-02, \ 9.664957432070073E-01, -1.581005636616589E-01, 1.326365917546207E-02, \ 9.683352852913805E-01, -4.679098763469015E-01, 1.225127303731581E-02, \ 9.842518603414726E-01, 1.836896830126595E-01, 8.499315253887113E-03, \ 9.846619943535420E-01, -7.799717728866817E-01, 5.965044619806711E-03, \ 9.852422761112879E-01, 8.861974810453618E-01, 3.934308818294981E-03, \ 9.891880847194036E-01, -9.191530362600531E-01, 3.253203726665571E-03, \ 9.897009343507575E-01, -9.931297876049714E-01, 7.600893882678305E-04, \ 9.922603853169076E-01, 9.719335327349238E-01, 1.435167883917694E-03, \ 9.936305551862550E-01, -1.510608205895069E-02, 4.418790732679170E-03, \ 9.941000705774204E-01, 4.425041797515226E-01, 5.144918479154803E-03, \ 9.941101780466588E-01, 7.280757215015392E-01, 3.867855257271212E-03, \ 9.950172763856067E-01, -6.114888124308911E-01, 3.581501248642710E-03, \ 9.951171305214461E-01, -3.168085664517462E-01, 4.336888090484613E-03 ] ) return xyw def smr31 ( ): #*****************************************************************************80 # ## smr31 returns the SMR rule of degree 31. # # Discussion: # # DEGREE: 31 # POINTS CARDINALITY: 172 # NORM INF MOMS. RESIDUAL: 2.07733e-16 # SUM NEGATIVE WEIGHTS: 0 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*172), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.955496296346447E-01, -2.757893737712724E-02, 3.952828126515200E-03, \ -9.952093636515903E-01, 3.078672596656606E-01, 4.465674926565594E-03, \ -9.949219293696708E-01, -4.293313749761587E-01, 4.734653786951149E-03, \ -9.947777289433332E-01, 6.082007753656643E-01, 3.687083706716762E-03, \ -9.947711657807963E-01, -7.291135575065112E-01, 3.567753282746309E-03, \ -9.898665478412323E-01, 9.927280498683013E-01, 7.900353557535870E-04, \ -9.896201133119824E-01, 9.148303804608103E-01, 3.248339703605548E-03, \ -9.894221797194233E-01, -8.963309110540300E-01, 2.680927365865937E-03, \ -9.891613515312806E-01, -9.745514901909140E-01, 1.655992514072826E-03, \ -9.847115459075805E-01, 7.760597415217361E-01, 5.791133619187665E-03, \ -9.822216835749852E-01, -1.858981354343795E-01, 6.958199118327337E-03, \ -9.688290280461213E-01, 1.346435658626332E-01, 1.394269523344841E-02, \ -9.681141160941403E-01, 4.618217642366224E-01, 1.249777398451523E-02, \ -9.680653032337156E-01, -5.892528308394193E-01, 1.229021380297149E-02, \ -9.621105113004819E-01, -8.293868331873653E-01, 7.471001060877273E-03, \ -9.565888110363844E-01, -2.955138587991344E-01, 1.254260666301101E-02, \ -9.469790068617381E-01, -9.968106327216375E-01, 1.362946951896202E-03, \ -9.464971595212447E-01, 9.668261260754121E-01, 5.057521838548747E-03, \ -9.404074979033311E-01, 6.594952112812067E-01, 1.377422226180171E-02, \ -9.386071275818250E-01, -9.447266737672761E-01, 4.408092682116897E-03, \ -9.340283957363398E-01, 8.488905145274273E-01, 1.096662540259541E-02, \ -9.198052061978775E-01, -5.136717870605163E-02, 2.325563069027812E-02, \ -9.125069846160752E-01, 2.965175005985400E-01, 2.317349030282014E-02, \ -9.123983052278903E-01, -7.247489113905282E-01, 1.632786836774140E-02, \ -9.068677187647651E-01, -4.445873104662686E-01, 2.188675357029590E-02, \ -9.055659136341394E-01, -9.175374320754922E-01, 5.491385731273308E-03, \ -8.774069425333418E-01, 5.321738640857572E-01, 1.982544206254361E-02, \ -8.706320657782287E-01, 9.948789461128177E-01, 2.722659841902658E-03, \ -8.559872594373867E-01, 9.178926105523973E-01, 1.239374987476905E-02, \ -8.487413771127457E-01, 7.442213847925441E-01, 2.151797328509033E-02, \ -8.475645530398180E-01, -2.209115672323100E-01, 2.832498125828596E-02, \ -8.449119525088070E-01, -9.790174363372415E-01, 6.490465735794747E-03, \ -8.388493423999792E-01, -8.442105015209006E-01, 1.741719558530361E-02, \ -8.320878189683433E-01, 1.145771146767555E-01, 3.439308836971967E-02, \ -8.290267482829156E-01, -5.972601809233826E-01, 2.702368742037717E-02, \ -8.034575695173080E-01, 4.094748377144478E-01, 2.509623581221141E-02, \ -7.760357257316899E-01, -3.548922765484357E-01, 2.268460217050950E-02, \ -7.509248997072229E-01, 9.692871949519603E-01, 9.979338077119586E-03, \ -7.387062791288017E-01, 8.375261790603876E-01, 2.279562252991799E-02, \ -7.382550697652832E-01, 6.100825289389331E-01, 3.294515892662506E-02, \ -7.363260972595160E-01, -9.253776418251520E-01, 1.584321780127163E-02, \ -7.298334096260589E-01, -7.360653624762051E-01, 2.903866461556321E-02, \ -7.251547137883499E-01, -6.996863675606819E-02, 4.370775795972342E-02, \ -7.113581145093257E-01, 2.702313355967329E-01, 3.714680586412551E-02, \ -7.071807441641457E-01, -9.944876613499617E-01, 3.480514785349274E-03, \ -7.039820156247814E-01, -4.654525806221809E-01, 3.069975493264972E-02, \ -6.184086297782805E-01, 9.955258965189302E-01, 3.881568620917195E-03, \ -6.077218310997582E-01, 9.148419450019303E-01, 1.991703166278273E-02, \ -6.034954341682667E-01, 7.237932367497814E-01, 3.389141507458358E-02, \ -6.013041765209197E-01, -8.425771299300596E-01, 2.713141610820029E-02, \ -5.995171839175090E-01, 4.575307437971686E-01, 4.553732637405976E-02, \ -5.987747492273197E-01, -2.555243484270794E-01, 5.002646306167845E-02, \ -5.927778548664734E-01, -6.036103424582507E-01, 3.911054484449386E-02, \ -5.901440107668018E-01, 1.060198712260184E-01, 4.821287790488322E-02, \ -5.784913015945842E-01, -9.666586674693635E-01, 1.173664788888666E-02, \ -4.588198301439419E-01, 9.693486333009571E-01, 1.313666284266309E-02, \ -4.567271123348693E-01, 8.253817273249296E-01, 3.056135412459628E-02, \ -4.537069399424983E-01, -4.303216184624180E-01, 5.246566824474671E-02, \ -4.528331550744691E-01, -6.765968580901423E-02, 5.225928157201407E-02, \ -4.472686223717481E-01, -7.308744706376724E-01, 3.864973973872291E-02, \ -4.434291687664805E-01, 2.865506865407869E-01, 5.621007974099101E-02, \ -4.406325252658753E-01, -9.951861574277165E-01, 3.942690951645789E-03, \ -4.393137941615871E-01, 5.923410411408412E-01, 4.592935024129758E-02, \ -4.286656345744738E-01, -9.110553186427821E-01, 2.189185972353471E-02, \ -3.378031689425344E-01, -2.004187762207998E-01, 2.823318588167162E-02, \ -3.044251614615452E-01, 9.086361595553306E-01, 2.309284749670321E-02, \ -2.928456536563019E-01, -9.712927609897977E-01, 1.017404407973292E-02, \ -2.912502627343641E-01, -5.842088648173278E-01, 4.974674817513107E-02, \ -2.811322114845757E-01, 9.943304190452436E-01, 5.253366355617619E-03, \ -2.766540265223294E-01, 7.185096774489679E-01, 4.096115975792532E-02, \ -2.748922538693097E-01, 1.033654937792176E-01, 6.398840590311936E-02, \ -2.658691893989600E-01, -8.278100124889359E-01, 3.306728584127568E-02, \ -2.638448388909397E-01, 4.383380334499116E-01, 5.665306321736824E-02, \ -2.509255177911933E-01, -2.932348684939356E-01, 4.608256320492199E-02, \ -1.873924507634162E-01, -9.941405263712252E-01, 2.154767334708834E-03, \ -1.623725117112911E-01, -9.393770105705175E-01, 1.234737326017698E-02, \ -1.321095433217891E-01, 8.321796504932829E-01, 2.707477268062864E-02, \ -1.248486574319150E-01, 9.596829430320998E-01, 1.572343508516491E-02, \ -1.160794606213587E-01, -7.051458563086379E-01, 3.871928288060491E-02, \ -9.862627315703923E-02, -8.426927609780714E-02, 6.684928152189812E-02, \ -9.324738040737274E-02, -4.443546718135858E-01, 5.655998204740964E-02, \ -9.000433791884935E-02, 5.901154946888999E-01, 5.092306051816564E-02, \ -8.193230202578333E-02, 2.677472052197009E-01, 6.437330348690143E-02, \ -4.921447280582370E-02, -8.948195724899560E-01, 2.115122029930462E-02, \ -2.766233245972495E-02, -9.904468342292223E-01, 6.140727614369517E-03, \ -1.010525418227002E-02, 7.724429823094344E-01, 1.672977767715024E-02, \ 1.010525418227002E-02, -7.724429823094344E-01, 1.672977767715024E-02, \ 2.766233245972495E-02, 9.904468342292223E-01, 6.140727614369517E-03, \ 4.921447280582370E-02, 8.948195724899560E-01, 2.115122029930462E-02, \ 8.193230202578333E-02, -2.677472052197009E-01, 6.437330348690143E-02, \ 9.000433791884935E-02, -5.901154946888999E-01, 5.092306051816564E-02, \ 9.324738040737274E-02, 4.443546718135858E-01, 5.655998204740964E-02, \ 9.862627315703923E-02, 8.426927609780714E-02, 6.684928152189812E-02, \ 1.160794606213587E-01, 7.051458563086379E-01, 3.871928288060491E-02, \ 1.248486574319150E-01, -9.596829430320998E-01, 1.572343508516491E-02, \ 1.321095433217891E-01, -8.321796504932829E-01, 2.707477268062864E-02, \ 1.623725117112911E-01, 9.393770105705175E-01, 1.234737326017698E-02, \ 1.873924507634162E-01, 9.941405263712252E-01, 2.154767334708834E-03, \ 2.509255177911933E-01, 2.932348684939356E-01, 4.608256320492199E-02, \ 2.638448388909397E-01, -4.383380334499116E-01, 5.665306321736824E-02, \ 2.658691893989600E-01, 8.278100124889359E-01, 3.306728584127568E-02, \ 2.748922538693097E-01, -1.033654937792176E-01, 6.398840590311936E-02, \ 2.766540265223294E-01, -7.185096774489679E-01, 4.096115975792532E-02, \ 2.811322114845757E-01, -9.943304190452436E-01, 5.253366355617619E-03, \ 2.912502627343641E-01, 5.842088648173278E-01, 4.974674817513107E-02, \ 2.928456536563019E-01, 9.712927609897977E-01, 1.017404407973292E-02, \ 3.044251614615452E-01, -9.086361595553306E-01, 2.309284749670321E-02, \ 3.378031689425344E-01, 2.004187762207998E-01, 2.823318588167162E-02, \ 4.286656345744738E-01, 9.110553186427821E-01, 2.189185972353471E-02, \ 4.393137941615871E-01, -5.923410411408412E-01, 4.592935024129758E-02, \ 4.406325252658753E-01, 9.951861574277165E-01, 3.942690951645789E-03, \ 4.434291687664805E-01, -2.865506865407869E-01, 5.621007974099101E-02, \ 4.472686223717481E-01, 7.308744706376724E-01, 3.864973973872291E-02, \ 4.528331550744691E-01, 6.765968580901423E-02, 5.225928157201407E-02, \ 4.537069399424983E-01, 4.303216184624180E-01, 5.246566824474671E-02, \ 4.567271123348693E-01, -8.253817273249296E-01, 3.056135412459628E-02, \ 4.588198301439419E-01, -9.693486333009571E-01, 1.313666284266309E-02, \ 5.784913015945842E-01, 9.666586674693635E-01, 1.173664788888666E-02, \ 5.901440107668018E-01, -1.060198712260184E-01, 4.821287790488322E-02, \ 5.927778548664734E-01, 6.036103424582507E-01, 3.911054484449386E-02, \ 5.987747492273197E-01, 2.555243484270794E-01, 5.002646306167845E-02, \ 5.995171839175090E-01, -4.575307437971686E-01, 4.553732637405976E-02, \ 6.013041765209197E-01, 8.425771299300596E-01, 2.713141610820029E-02, \ 6.034954341682667E-01, -7.237932367497814E-01, 3.389141507458358E-02, \ 6.077218310997582E-01, -9.148419450019303E-01, 1.991703166278273E-02, \ 6.184086297782805E-01, -9.955258965189302E-01, 3.881568620917195E-03, \ 7.039820156247814E-01, 4.654525806221809E-01, 3.069975493264972E-02, \ 7.071807441641457E-01, 9.944876613499617E-01, 3.480514785349274E-03, \ 7.113581145093257E-01, -2.702313355967329E-01, 3.714680586412551E-02, \ 7.251547137883499E-01, 6.996863675606819E-02, 4.370775795972342E-02, \ 7.298334096260589E-01, 7.360653624762051E-01, 2.903866461556321E-02, \ 7.363260972595160E-01, 9.253776418251520E-01, 1.584321780127163E-02, \ 7.382550697652832E-01, -6.100825289389331E-01, 3.294515892662506E-02, \ 7.387062791288017E-01, -8.375261790603876E-01, 2.279562252991799E-02, \ 7.509248997072229E-01, -9.692871949519603E-01, 9.979338077119586E-03, \ 7.760357257316899E-01, 3.548922765484357E-01, 2.268460217050950E-02, \ 8.034575695173080E-01, -4.094748377144478E-01, 2.509623581221141E-02, \ 8.290267482829156E-01, 5.972601809233826E-01, 2.702368742037717E-02, \ 8.320878189683433E-01, -1.145771146767555E-01, 3.439308836971967E-02, \ 8.388493423999792E-01, 8.442105015209006E-01, 1.741719558530361E-02, \ 8.449119525088070E-01, 9.790174363372415E-01, 6.490465735794747E-03, \ 8.475645530398180E-01, 2.209115672323100E-01, 2.832498125828596E-02, \ 8.487413771127457E-01, -7.442213847925441E-01, 2.151797328509033E-02, \ 8.559872594373867E-01, -9.178926105523973E-01, 1.239374987476905E-02, \ 8.706320657782287E-01, -9.948789461128177E-01, 2.722659841902658E-03, \ 8.774069425333418E-01, -5.321738640857572E-01, 1.982544206254361E-02, \ 9.055659136341394E-01, 9.175374320754922E-01, 5.491385731273308E-03, \ 9.068677187647651E-01, 4.445873104662686E-01, 2.188675357029590E-02, \ 9.123983052278903E-01, 7.247489113905282E-01, 1.632786836774140E-02, \ 9.125069846160752E-01, -2.965175005985400E-01, 2.317349030282014E-02, \ 9.198052061978775E-01, 5.136717870605163E-02, 2.325563069027812E-02, \ 9.340283957363398E-01, -8.488905145274273E-01, 1.096662540259541E-02, \ 9.386071275818250E-01, 9.447266737672761E-01, 4.408092682116897E-03, \ 9.404074979033311E-01, -6.594952112812067E-01, 1.377422226180171E-02, \ 9.464971595212447E-01, -9.668261260754121E-01, 5.057521838548747E-03, \ 9.469790068617381E-01, 9.968106327216375E-01, 1.362946951896202E-03, \ 9.565888110363844E-01, 2.955138587991344E-01, 1.254260666301101E-02, \ 9.621105113004819E-01, 8.293868331873653E-01, 7.471001060877273E-03, \ 9.680653032337156E-01, 5.892528308394193E-01, 1.229021380297149E-02, \ 9.681141160941403E-01, -4.618217642366224E-01, 1.249777398451523E-02, \ 9.688290280461213E-01, -1.346435658626332E-01, 1.394269523344841E-02, \ 9.822216835749852E-01, 1.858981354343795E-01, 6.958199118327337E-03, \ 9.847115459075805E-01, -7.760597415217361E-01, 5.791133619187665E-03, \ 9.891613515312806E-01, 9.745514901909140E-01, 1.655992514072826E-03, \ 9.894221797194233E-01, 8.963309110540300E-01, 2.680927365865937E-03, \ 9.896201133119824E-01, -9.148303804608103E-01, 3.248339703605548E-03, \ 9.898665478412323E-01, -9.927280498683013E-01, 7.900353557535870E-04, \ 9.947711657807963E-01, 7.291135575065112E-01, 3.567753282746309E-03, \ 9.947777289433332E-01, -6.082007753656643E-01, 3.687083706716762E-03, \ 9.949219293696708E-01, 4.293313749761587E-01, 4.734653786951149E-03, \ 9.952093636515903E-01, -3.078672596656606E-01, 4.465674926565594E-03, \ 9.955496296346447E-01, 2.757893737712724E-02, 3.952828126515200E-03 ] ) return xyw def smr31s ( ): #*****************************************************************************80 # ## smr31S returns the rotationally invariant SMR rule of degree 31. # # Discussion: # # DEGREE: 31 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 172 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 2.84496E-03, \ # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*172), the requested rule. # import numpy as np xyw = np.array ( [ \ -3.904806549599655E-02, -4.335393037614890E-02, 1.983961989686983E-02, \ 1.361882296394248E-01, 5.339885716159022E-01, 5.606290851087755E-02, \ -6.237898572307624E-02, 6.650680443410015E-01, 4.954926631685492E-02, \ 1.043081290265589E-01, 7.978188386199707E-01, 3.954352049027991E-02, \ 8.175663994339752E-02, 9.536337842041479E-01, 1.819407316290299E-02, \ 1.326909285794375E-01, 9.985967754075993E-01, 2.198741271493517E-03, \ 3.573200269387108E-01, 3.083812309752531E-02, 6.275382718191864E-02, \ 1.711251846005631E-01, 2.023226798991783E-01, 6.312752392564865E-02, \ 3.301558760691319E-01, 3.890928730006515E-01, 5.784814622385932E-02, \ 2.990255438330413E-01, 6.899278622152941E-01, 4.599430975257399E-02, \ 2.743945607890017E-01, 8.969874117510032E-01, 2.722794626350406E-02, \ 2.930343597574347E-01, 9.866371893249537E-01, 7.297804329258834E-03, \ 4.811149130969350E-01, 5.627097593501477E-01, 4.813376158498228E-02, \ 4.577756563378687E-01, 8.164852603726748E-01, 3.369675352996792E-02, \ 4.576603028130140E-01, 9.581255271049165E-01, 1.483779460064700E-02, \ 5.011717697509331E-01, 9.967514621307949E-01, 1.375821755782986E-03, \ 5.066615476347207E-01, 2.279797220835331E-01, 5.617345067788202E-02, \ 6.414891770627443E-01, 4.165197368067110E-01, 4.637789988502160E-02, \ 6.218437939846863E-01, 7.124331860455828E-01, 3.611694132069662E-02, \ 6.189705671147399E-01, 9.055771549707593E-01, 2.142589064473523E-02, \ 6.257695254024579E-01, 9.920525612037021E-01, 4.604781337595676E-03, \ 7.773558757000041E-01, 2.587982643359955E-01, 3.995025536141079E-02, \ 7.602620921526432E-01, 5.866806545003377E-01, 3.454986715153591E-02, \ 8.080239490235996E-01, 7.466133969130114E-01, -7.112408612016088E-04, \ 7.578022960040215E-01, 8.250210799807152E-01, 2.415241529771807E-02, \ 7.572699136795021E-01, 9.658518182607879E-01, 1.066322723829567E-02, \ 8.838106230790593E-01, 9.517499798893064E-02, 3.021344380673574E-02, \ 8.690870146928319E-01, 4.428796688721532E-01, 2.841376547681653E-02, \ 8.664188675223524E-01, 7.215367573910633E-01, 2.259238404505909E-02, \ 8.662357931878873E-01, 9.115792712550360E-01, 1.298465964143997E-02, \ 8.668639312200342E-01, 9.955281129139882E-01, 2.678582771124035E-03, \ 9.464084279482877E-01, 2.901035303505874E-01, 1.924589937161483E-02, \ 9.432116671128417E-01, 5.914789709627410E-01, 1.601261396001407E-02, \ 9.621603453340629E-01, 7.421113162391834E-01, 2.850658278802631E-03, \ 9.424551010209468E-01, 8.371341836669535E-01, 1.039571899572164E-02, \ 9.455364284543073E-01, 9.674856486387888E-01, 5.118117255528941E-03, \ 9.860981807821748E-01, 1.062982665761813E-01, 8.507743310820945E-03, \ 9.968354200302058E-01, 2.730105297008364E-01, 1.865603977042027E-03, \ 9.874604632806666E-01, 4.594240145656220E-01, 7.587442385373269E-03, \ 9.914773043212965E-01, 6.790808250554563E-01, 3.856894243772012E-03, \ 9.892581143506071E-01, 7.901123155310413E-01, 2.579633577944600E-03, \ 9.893015185233809E-01, 9.146983422640488E-01, 3.312018439594244E-03, \ 9.898894503566366E-01, 9.925022404589151E-01, 7.995136114829527E-04, \ 4.335393037614890E-02, -3.904806549599655E-02, 1.983961989686983E-02, \ -5.339885716159022E-01, 1.361882296394248E-01, 5.606290851087755E-02, \ -6.650680443410015E-01, -6.237898572307624E-02, 4.954926631685492E-02, \ -7.978188386199707E-01, 1.043081290265589E-01, 3.954352049027991E-02, \ -9.536337842041479E-01, 8.175663994339752E-02, 1.819407316290299E-02, \ -9.985967754075993E-01, 1.326909285794375E-01, 2.198741271493517E-03, \ -3.083812309752531E-02, 3.573200269387108E-01, 6.275382718191864E-02, \ -2.023226798991783E-01, 1.711251846005631E-01, 6.312752392564865E-02, \ -3.890928730006515E-01, 3.301558760691319E-01, 5.784814622385932E-02, \ -6.899278622152941E-01, 2.990255438330413E-01, 4.599430975257399E-02, \ -8.969874117510032E-01, 2.743945607890017E-01, 2.722794626350406E-02, \ -9.866371893249537E-01, 2.930343597574347E-01, 7.297804329258834E-03, \ -5.627097593501477E-01, 4.811149130969350E-01, 4.813376158498228E-02, \ -8.164852603726748E-01, 4.577756563378687E-01, 3.369675352996792E-02, \ -9.581255271049165E-01, 4.576603028130140E-01, 1.483779460064700E-02, \ -9.967514621307949E-01, 5.011717697509331E-01, 1.375821755782986E-03, \ -2.279797220835331E-01, 5.066615476347207E-01, 5.617345067788202E-02, \ -4.165197368067110E-01, 6.414891770627443E-01, 4.637789988502160E-02, \ -7.124331860455828E-01, 6.218437939846863E-01, 3.611694132069662E-02, \ -9.055771549707593E-01, 6.189705671147399E-01, 2.142589064473523E-02, \ -9.920525612037021E-01, 6.257695254024579E-01, 4.604781337595676E-03, \ -2.587982643359955E-01, 7.773558757000041E-01, 3.995025536141079E-02, \ -5.866806545003377E-01, 7.602620921526432E-01, 3.454986715153591E-02, \ -7.466133969130114E-01, 8.080239490235996E-01, -7.112408612016088E-04, \ -8.250210799807152E-01, 7.578022960040215E-01, 2.415241529771807E-02, \ -9.658518182607879E-01, 7.572699136795021E-01, 1.066322723829567E-02, \ -9.517499798893064E-02, 8.838106230790593E-01, 3.021344380673574E-02, \ -4.428796688721532E-01, 8.690870146928319E-01, 2.841376547681653E-02, \ -7.215367573910633E-01, 8.664188675223524E-01, 2.259238404505909E-02, \ -9.115792712550360E-01, 8.662357931878873E-01, 1.298465964143997E-02, \ -9.955281129139882E-01, 8.668639312200342E-01, 2.678582771124035E-03, \ -2.901035303505874E-01, 9.464084279482877E-01, 1.924589937161483E-02, \ -5.914789709627410E-01, 9.432116671128417E-01, 1.601261396001407E-02, \ -7.421113162391834E-01, 9.621603453340629E-01, 2.850658278802631E-03, \ -8.371341836669535E-01, 9.424551010209468E-01, 1.039571899572164E-02, \ -9.674856486387888E-01, 9.455364284543073E-01, 5.118117255528941E-03, \ -1.062982665761813E-01, 9.860981807821748E-01, 8.507743310820945E-03, \ -2.730105297008364E-01, 9.968354200302058E-01, 1.865603977042027E-03, \ -4.594240145656220E-01, 9.874604632806666E-01, 7.587442385373269E-03, \ -6.790808250554563E-01, 9.914773043212965E-01, 3.856894243772012E-03, \ -7.901123155310413E-01, 9.892581143506071E-01, 2.579633577944600E-03, \ -9.146983422640488E-01, 9.893015185233809E-01, 3.312018439594244E-03, \ -9.925022404589151E-01, 9.898894503566366E-01, 7.995136114829527E-04, \ 3.904806549599655E-02, 4.335393037614890E-02, 1.983961989686983E-02, \ -1.361882296394248E-01, -5.339885716159022E-01, 5.606290851087755E-02, \ 6.237898572307624E-02, -6.650680443410015E-01, 4.954926631685492E-02, \ -1.043081290265589E-01, -7.978188386199707E-01, 3.954352049027991E-02, \ -8.175663994339752E-02, -9.536337842041479E-01, 1.819407316290299E-02, \ -1.326909285794375E-01, -9.985967754075993E-01, 2.198741271493517E-03, \ -3.573200269387108E-01, -3.083812309752531E-02, 6.275382718191864E-02, \ -1.711251846005631E-01, -2.023226798991783E-01, 6.312752392564865E-02, \ -3.301558760691319E-01, -3.890928730006515E-01, 5.784814622385932E-02, \ -2.990255438330413E-01, -6.899278622152941E-01, 4.599430975257399E-02, \ -2.743945607890017E-01, -8.969874117510032E-01, 2.722794626350406E-02, \ -2.930343597574347E-01, -9.866371893249537E-01, 7.297804329258834E-03, \ -4.811149130969350E-01, -5.627097593501477E-01, 4.813376158498228E-02, \ -4.577756563378687E-01, -8.164852603726748E-01, 3.369675352996792E-02, \ -4.576603028130140E-01, -9.581255271049165E-01, 1.483779460064700E-02, \ -5.011717697509331E-01, -9.967514621307949E-01, 1.375821755782986E-03, \ -5.066615476347207E-01, -2.279797220835331E-01, 5.617345067788202E-02, \ -6.414891770627443E-01, -4.165197368067110E-01, 4.637789988502160E-02, \ -6.218437939846863E-01, -7.124331860455828E-01, 3.611694132069662E-02, \ -6.189705671147399E-01, -9.055771549707593E-01, 2.142589064473523E-02, \ -6.257695254024579E-01, -9.920525612037021E-01, 4.604781337595676E-03, \ -7.773558757000041E-01, -2.587982643359955E-01, 3.995025536141079E-02, \ -7.602620921526432E-01, -5.866806545003377E-01, 3.454986715153591E-02, \ -8.080239490235996E-01, -7.466133969130114E-01, -7.112408612016088E-04, \ -7.578022960040215E-01, -8.250210799807152E-01, 2.415241529771807E-02, \ -7.572699136795021E-01, -9.658518182607879E-01, 1.066322723829567E-02, \ -8.838106230790593E-01, -9.517499798893064E-02, 3.021344380673574E-02, \ -8.690870146928319E-01, -4.428796688721532E-01, 2.841376547681653E-02, \ -8.664188675223524E-01, -7.215367573910633E-01, 2.259238404505909E-02, \ -8.662357931878873E-01, -9.115792712550360E-01, 1.298465964143997E-02, \ -8.668639312200342E-01, -9.955281129139882E-01, 2.678582771124035E-03, \ -9.464084279482877E-01, -2.901035303505874E-01, 1.924589937161483E-02, \ -9.432116671128417E-01, -5.914789709627410E-01, 1.601261396001407E-02, \ -9.621603453340629E-01, -7.421113162391834E-01, 2.850658278802631E-03, \ -9.424551010209468E-01, -8.371341836669535E-01, 1.039571899572164E-02, \ -9.455364284543073E-01, -9.674856486387888E-01, 5.118117255528941E-03, \ -9.860981807821748E-01, -1.062982665761813E-01, 8.507743310820945E-03, \ -9.968354200302058E-01, -2.730105297008364E-01, 1.865603977042027E-03, \ -9.874604632806666E-01, -4.594240145656220E-01, 7.587442385373269E-03, \ -9.914773043212965E-01, -6.790808250554563E-01, 3.856894243772012E-03, \ -9.892581143506071E-01, -7.901123155310413E-01, 2.579633577944600E-03, \ -9.893015185233809E-01, -9.146983422640488E-01, 3.312018439594244E-03, \ -9.898894503566366E-01, -9.925022404589151E-01, 7.995136114829527E-04, \ -4.335393037614890E-02, 3.904806549599655E-02, 1.983961989686983E-02, \ 5.339885716159022E-01, -1.361882296394248E-01, 5.606290851087755E-02, \ 6.650680443410015E-01, 6.237898572307624E-02, 4.954926631685492E-02, \ 7.978188386199707E-01, -1.043081290265589E-01, 3.954352049027991E-02, \ 9.536337842041479E-01, -8.175663994339752E-02, 1.819407316290299E-02, \ 9.985967754075993E-01, -1.326909285794375E-01, 2.198741271493517E-03, \ 3.083812309752531E-02, -3.573200269387108E-01, 6.275382718191864E-02, \ 2.023226798991783E-01, -1.711251846005631E-01, 6.312752392564865E-02, \ 3.890928730006515E-01, -3.301558760691319E-01, 5.784814622385932E-02, \ 6.899278622152941E-01, -2.990255438330413E-01, 4.599430975257399E-02, \ 8.969874117510032E-01, -2.743945607890017E-01, 2.722794626350406E-02, \ 9.866371893249537E-01, -2.930343597574347E-01, 7.297804329258834E-03, \ 5.627097593501477E-01, -4.811149130969350E-01, 4.813376158498228E-02, \ 8.164852603726748E-01, -4.577756563378687E-01, 3.369675352996792E-02, \ 9.581255271049165E-01, -4.576603028130140E-01, 1.483779460064700E-02, \ 9.967514621307949E-01, -5.011717697509331E-01, 1.375821755782986E-03, \ 2.279797220835331E-01, -5.066615476347207E-01, 5.617345067788202E-02, \ 4.165197368067110E-01, -6.414891770627443E-01, 4.637789988502160E-02, \ 7.124331860455828E-01, -6.218437939846863E-01, 3.611694132069662E-02, \ 9.055771549707593E-01, -6.189705671147399E-01, 2.142589064473523E-02, \ 9.920525612037021E-01, -6.257695254024579E-01, 4.604781337595676E-03, \ 2.587982643359955E-01, -7.773558757000041E-01, 3.995025536141079E-02, \ 5.866806545003377E-01, -7.602620921526432E-01, 3.454986715153591E-02, \ 7.466133969130114E-01, -8.080239490235996E-01, -7.112408612016088E-04, \ 8.250210799807152E-01, -7.578022960040215E-01, 2.415241529771807E-02, \ 9.658518182607879E-01, -7.572699136795021E-01, 1.066322723829567E-02, \ 9.517499798893064E-02, -8.838106230790593E-01, 3.021344380673574E-02, \ 4.428796688721532E-01, -8.690870146928319E-01, 2.841376547681653E-02, \ 7.215367573910633E-01, -8.664188675223524E-01, 2.259238404505909E-02, \ 9.115792712550360E-01, -8.662357931878873E-01, 1.298465964143997E-02, \ 9.955281129139882E-01, -8.668639312200342E-01, 2.678582771124035E-03, \ 2.901035303505874E-01, -9.464084279482877E-01, 1.924589937161483E-02, \ 5.914789709627410E-01, -9.432116671128417E-01, 1.601261396001407E-02, \ 7.421113162391834E-01, -9.621603453340629E-01, 2.850658278802631E-03, \ 8.371341836669535E-01, -9.424551010209468E-01, 1.039571899572164E-02, \ 9.674856486387888E-01, -9.455364284543073E-01, 5.118117255528941E-03, \ 1.062982665761813E-01, -9.860981807821748E-01, 8.507743310820945E-03, \ 2.730105297008364E-01, -9.968354200302058E-01, 1.865603977042027E-03, \ 4.594240145656220E-01, -9.874604632806666E-01, 7.587442385373269E-03, \ 6.790808250554563E-01, -9.914773043212965E-01, 3.856894243772012E-03, \ 7.901123155310413E-01, -9.892581143506071E-01, 2.579633577944600E-03, \ 9.146983422640488E-01, -9.893015185233809E-01, 3.312018439594244E-03, \ 9.925022404589151E-01, -9.898894503566366E-01, 7.995136114829527E-04 ] ) return xyw def smr32 ( ): #*****************************************************************************80 # ## smr32 returns the SMR rule of degree 32. # # Discussion: # # DEGREE: 32 # POINTS CARDINALITY: 189 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*189), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.961443158376487E-01, -6.887572767977012E-01, 3.176265881806332E-03, \ -9.955150539895966E-01, 6.626971407249244E-01, 3.280265060152129E-03, \ -9.953673174806560E-01, -3.490320479685254E-02, 4.675890937959332E-03, \ -9.953301148958117E-01, 8.868398804037936E-01, 2.284058312905218E-03, \ -9.949536289138113E-01, -3.776956946778952E-01, 4.510771123627496E-03, \ -9.947581001027488E-01, 3.329076528027972E-01, 4.813891020740236E-03, \ -9.941343268456251E-01, 9.936112061216035E-01, 5.375112498857630E-04, \ -9.932824877107631E-01, -9.089949394457987E-01, 2.496612709475389E-03, \ -9.901718606538452E-01, -9.916407321742867E-01, 7.701138529293439E-04, \ -9.751008630866578E-01, 5.195777161215037E-01, 9.359036791703322E-03, \ -9.723977826522521E-01, 1.379087148825411E-01, 1.181986792189326E-02, \ -9.716123205144245E-01, -8.031016796856173E-01, 7.898808335562373E-03, \ -9.711842977478065E-01, -5.430726346303393E-01, 1.151176330250413E-02, \ -9.704055489123288E-01, 7.804584258849506E-01, 8.644818596664990E-03, \ -9.694199058988444E-01, 9.557067749284750E-01, 4.223280833025587E-03, \ -9.683411874625077E-01, -2.103323587190609E-01, 1.388419379439329E-02, \ -9.567808007888505E-01, -9.626987460709516E-01, 4.415431329419894E-03, \ -9.437425354265615E-01, 4.414088771841401E-01, 6.832573539725157E-03, \ -9.402218788200302E-01, 2.637892865469118E-01, 1.016860955591373E-02, \ -9.217551019965182E-01, 8.766772417195136E-01, 1.065665181655526E-02, \ -9.201345036606068E-01, -6.784459223365346E-01, 1.669398948968993E-02, \ -9.187137927257295E-01, -8.800989100992515E-01, 9.591064623401077E-03, \ -9.181947091905479E-01, -3.841738613909663E-01, 2.059591744256289E-02, \ -9.181637384564565E-01, 6.508430144443661E-01, 1.797283563699723E-02, \ -9.180866951945609E-01, -3.534323022121689E-02, 2.220774903033375E-02, \ -9.162233942094903E-01, 9.905273384808887E-01, 2.842827696268136E-03, \ -8.942375422053964E-01, -9.940021310654177E-01, 2.526325882162393E-03, \ -8.925004548103099E-01, 3.675577608041817E-01, 1.740206879654378E-02, \ -8.567376342667298E-01, 1.327464071241374E-01, 2.320747945421362E-02, \ -8.527049285163805E-01, -5.173331471639295E-01, 1.823135215166509E-02, \ -8.500346292659974E-01, 9.424744256560323E-01, 9.628825949603207E-03, \ -8.495936622225249E-01, -9.366589616617220E-01, 8.808214017805906E-03, \ -8.420958026145372E-01, 7.746496697546652E-01, 2.038980506805041E-02, \ -8.405229008591695E-01, -2.146465103993396E-01, 3.115686395982564E-02, \ -8.400130747502382E-01, -7.833828505922565E-01, 1.867972088056950E-02, \ -8.251520015911556E-01, 5.249712695416556E-01, 2.828908020393419E-02, \ -7.960746843247288E-01, -5.942990648607921E-01, 1.818720327698928E-02, \ -7.884200501943553E-01, 2.431068089032147E-01, 2.161873511289656E-02, \ -7.832198580393690E-01, 9.882893671904269E-01, 4.201313239030647E-03, \ -7.691956377515223E-01, -9.767479568418154E-01, 6.899965676153335E-03, \ -7.509072411287868E-01, -2.719575746898528E-02, 3.742043760045523E-02, \ -7.427461156257692E-01, 8.707027609907575E-01, 1.919642121969817E-02, \ -7.393846173049607E-01, -8.675695987661742E-01, 1.783672443816834E-02, \ -7.351194183949288E-01, -3.774494681673472E-01, 3.738148314393595E-02, \ -7.213398259926092E-01, 6.655990116514867E-01, 3.145176228542881E-02, \ -7.120543004828920E-01, 3.695232160325304E-01, 3.307881993920563E-02, \ -7.013785314229773E-01, -6.985386189309318E-01, 2.798941131398564E-02, \ -6.889047528617022E-01, 9.602183527522339E-01, 7.162747081491355E-03, \ -6.522280372437145E-01, -9.963873207253509E-01, 2.915037219722206E-03, \ -6.294141334037263E-01, -9.321941144432188E-01, 1.469357873203910E-02, \ -6.289236482231599E-01, 1.335531135944628E-01, 4.333999853931410E-02, \ -6.250143551668971E-01, -1.909837821647839E-01, 4.450992385162815E-02, \ -6.162479185474388E-01, 9.957592249563421E-01, 2.859071377057288E-03, \ -6.099556060400831E-01, -5.265301674660628E-01, 3.737333144755796E-02, \ -6.035692437775674E-01, 5.068951570189404E-01, 3.542431096817152E-02, \ -5.957398931434491E-01, 7.867544741614058E-01, 2.991054273162196E-02, \ -5.880720673778793E-01, 9.278338224868491E-01, 1.311047438579956E-02, \ -5.642943955874409E-01, -8.045488845290898E-01, 2.887379909514902E-02, \ -5.341453289511777E-01, -6.580308812592266E-01, 8.231881868308998E-03, \ -5.037785265285627E-01, 2.911261252936324E-01, 4.463898222861209E-02, \ -5.035520020780221E-01, 6.164678558380017E-01, 2.375628980516375E-02, \ -4.988776272469410E-01, -9.742698071302808E-01, 9.972534732384969E-03, \ -4.880950860424961E-01, -3.570330104924047E-01, 4.487865776129120E-02, \ -4.782873763449944E-01, -3.311071102284526E-02, 4.988651815705654E-02, \ -4.611263669660518E-01, 9.776538472171752E-01, 9.547170864365405E-03, \ -4.460940172737087E-01, -5.617163266009875E-01, 1.057733340125433E-02, \ -4.344215560289689E-01, 8.756198694104429E-01, 2.433238295221333E-02, \ -4.303464547840762E-01, -6.717475726140401E-01, 3.186301410699670E-02, \ -4.140771909387703E-01, -8.929909921505204E-01, 2.416865558364916E-02, \ -4.106621334605041E-01, 6.984143047391834E-01, 2.962064813188227E-02, \ -3.860009662973919E-01, 4.525655697932027E-01, 3.233946990986691E-02, \ -3.484793436284917E-01, -9.955996498738462E-01, 3.793172976457341E-03, \ -3.391951567840935E-01, 1.226820429084983E-01, 4.753908343744886E-02, \ -3.357809356696743E-01, -2.224706747610833E-01, 4.615497828125666E-02, \ -3.250278129966869E-01, 3.756115481576739E-01, 1.811254509132181E-02, \ -3.056089159859502E-01, -4.920724555612009E-01, 4.554710841070758E-02, \ -2.961214860982124E-01, 9.974527284699805E-01, 3.060823576685151E-03, \ -2.847932366229927E-01, -7.838348732823106E-01, 3.404104052520678E-02, \ -2.713478176538165E-01, 9.439481248438524E-01, 1.788329467008652E-02, \ -2.623891895744691E-01, 7.934963660422401E-01, 3.215348099890328E-02, \ -2.474541407740861E-01, -9.552431364916144E-01, 1.619837106218808E-02, \ -2.350008942691768E-01, 5.720771765501166E-01, 4.318782866021313E-02, \ -2.029577973797018E-01, -8.943368639764357E-02, 4.553097782784060E-02, \ -1.990670168540228E-01, 2.443876445322615E-01, 4.110363868615158E-02, \ -1.549456091317803E-01, -6.415558836799513E-01, 4.267610300710221E-02, \ -1.347331997024815E-01, -3.592068358004468E-01, 5.074071162472863E-02, \ -1.193212615110174E-01, -8.772608465003254E-01, 2.680897358145306E-02, \ -9.608366181884005E-02, 8.811478309456120E-01, 2.657134265114752E-02, \ -8.724674317423464E-02, 9.829741829813902E-01, 9.730625947232925E-03, \ -8.357262181047176E-02, 4.013140117181199E-01, 4.841144500118764E-02, \ -7.663657189401872E-02, -9.904382181654797E-01, 6.943274642780526E-03, \ -7.506542665125431E-02, 6.928415737526518E-01, 4.014342124479778E-02, \ -6.814560175398696E-02, 4.856261470453426E-02, 4.844065720660989E-02, \ 1.062473558727759E-02, -7.650288124962303E-01, 3.558799833293477E-02, \ 1.660017546118934E-02, -2.180239260173989E-01, 4.831607231731554E-02, \ 2.272453179480726E-02, -5.268496064565723E-01, 4.537055458358597E-02, \ 4.931212356041427E-02, -9.458603059209817E-01, 1.758790356906201E-02, \ 7.613140727060182E-02, 5.418798866250614E-01, 4.818153253307554E-02, \ 7.853294280823510E-02, 2.224042128166391E-01, 5.465464269071678E-02, \ 8.372125557287705E-02, 9.435131549853616E-01, 1.786409990626899E-02, \ 9.337887407842871E-02, 8.001140509910943E-01, 3.410288806782028E-02, \ 1.089074910813305E-01, -3.010076469468967E-02, 2.723309734230703E-02, \ 1.411908890075358E-01, 9.960717448990448E-01, 3.569321191002430E-03, \ 1.751413474655890E-01, -3.997261685283053E-01, 4.541750739879684E-02, \ 1.756054472282782E-01, -8.658339890881421E-01, 2.662577185951133E-02, \ 1.864598899283486E-01, -6.697382946526751E-01, 3.827435555232931E-02, \ 2.015902009534723E-01, -9.883931352101503E-01, 7.887679303175682E-03, \ 2.044045426953899E-01, -1.421919981535460E-01, 3.558139723631710E-02, \ 2.378932317489774E-01, 3.802228852670115E-01, 5.139141457782884E-02, \ 2.453419557836962E-01, 6.743539422739147E-01, 4.230440026330508E-02, \ 2.673924056388006E-01, 8.857386065554180E-01, 2.512168130932855E-02, \ 2.794321878522678E-01, 8.071672703911634E-02, 5.195889525876823E-02, \ 2.852750321228393E-01, 9.766942081801527E-01, 8.542384805675192E-03, \ 3.366919097882969E-01, -5.582614071904248E-01, 3.957781174651530E-02, \ 3.382140442187983E-01, -9.401781089769999E-01, 1.829722847974778E-02, \ 3.432642241169637E-01, -7.908855951561965E-01, 2.972251194098460E-02, \ 3.455152732870559E-01, -2.966429396872311E-01, 4.443118022793111E-02, \ 3.916837958172765E-01, 5.230067770696570E-01, 4.184441753133104E-02, \ 4.120040722413747E-01, 7.890179305884122E-01, 3.275969268754896E-02, \ 4.238156081215504E-01, 9.950429590804639E-01, 2.471843473128421E-03, \ 4.287156692418698E-01, 2.431531997648373E-01, 5.098740815593964E-02, \ 4.406392416503330E-01, -9.421351055228980E-02, 4.952434585624959E-02, \ 4.435754669288457E-01, 9.470031795306957E-01, 1.407985409716778E-02, \ 4.558595671892888E-01, -9.896709958176498E-01, 6.495456224860164E-03, \ 4.873417746475680E-01, -6.968841503239952E-01, 3.193924196689053E-02, \ 4.970448498999819E-01, -4.587836752559167E-01, 4.009098722323794E-02, \ 5.026246934476013E-01, -8.799728934510729E-01, 2.251236322931963E-02, \ 5.142480616051717E-01, 6.332295493966821E-01, 2.628145641746948E-02, \ 5.635007809294439E-01, 8.830661523985979E-01, 2.138158866985076E-02, \ 5.760177960925376E-01, 4.034390879812669E-01, 4.461725888680534E-02, \ 5.786951907000567E-01, 7.200913403128530E-02, 4.714224835011449E-02, \ 5.850240866763193E-01, 9.892820474952123E-01, 5.400839750748531E-03, \ 5.851379143554923E-01, -2.686399203625244E-01, 4.255109067146633E-02, \ 6.039149631797995E-01, -9.595657522395640E-01, 1.243029383620673E-02, \ 6.085940759319246E-01, 7.188102110043890E-01, 2.414801307071736E-02, \ 6.367455861073830E-01, -6.091087379827170E-01, 3.181043163725066E-02, \ 6.389771216716220E-01, -8.001263004879462E-01, 2.306016831136437E-02, \ 6.923848443111713E-01, 9.536668248480320E-01, 1.203359878310568E-02, \ 7.027796911591175E-01, -9.965270954213804E-01, 3.064467191573918E-03, \ 7.057525331398022E-01, -1.091230879464752E-01, 3.965634211274827E-02, \ 7.065644544049037E-01, 5.577016427729737E-01, 3.480317597803997E-02, \ 7.069599688705653E-01, 2.377081331437708E-01, 4.015277537380656E-02, \ 7.089592747680905E-01, -4.373982847931744E-01, 3.119546438021227E-02, \ 7.146942471573201E-01, 8.178315170110126E-01, 2.161251683469453E-02, \ 7.307538954522923E-01, -9.007096403390665E-01, 1.565402681403319E-02, \ 7.704504545341444E-01, -7.396567334921220E-01, 2.067477223680419E-02, \ 7.897818448390646E-01, -3.232780509941606E-01, 1.880267861755378E-02, \ 7.934484404832058E-01, 9.926504167490636E-01, 3.776050573673320E-03, \ 8.026728771155266E-01, -9.655537841075670E-01, 7.156659310810854E-03, \ 8.087651311032129E-01, -5.934295716161285E-01, 2.201032582341064E-02, \ 8.095585492822206E-01, 5.131014033000776E-02, 3.161252035941158E-02, \ 8.113041827662109E-01, 4.018532940895451E-01, 2.993617375756685E-02, \ 8.140746090133947E-01, 6.999506065348030E-01, 2.452891312211182E-02, \ 8.175220739845873E-01, 9.045678533269281E-01, 1.408878624403073E-02, \ 8.442244744987026E-01, -2.330660680257271E-01, 2.137248847571907E-02, \ 8.577022609864510E-01, -8.347496637512480E-01, 1.302733239156259E-02, \ 8.740997306450817E-01, -9.016947723266606E-01, 5.700088397798577E-03, \ 8.760720409171439E-01, 1.798424501465092E-01, 1.242534941969138E-02, \ 8.776595540145247E-01, -9.871736549700062E-01, 3.023298480841919E-03, \ 8.876770756008736E-01, -4.737591614279884E-01, 2.114261952758863E-02, \ 8.893257290546359E-01, 5.497239097424972E-01, 1.883916296392102E-02, \ 8.966119498774410E-01, 9.684306041089270E-01, 6.514509999621678E-03, \ 9.005134923798872E-01, 8.160726922491325E-01, 1.492277961359557E-02, \ 9.028454350969399E-01, 2.628603055474125E-01, 1.525753840078711E-02, \ 9.099332057150961E-01, -9.463222058681031E-02, 2.114989721521207E-02, \ 9.116851421787586E-01, -6.958768581382581E-01, 1.656213645188111E-02, \ 9.380791852794695E-01, -9.390761885813872E-01, 6.505278755513709E-03, \ 9.395276649285043E-01, 6.496946928511224E-01, 9.668304772455727E-03, \ 9.473470605468867E-01, -3.346050342634356E-01, 1.585630013135186E-02, \ 9.491070785582369E-01, -9.969373733490615E-01, 9.281179028714037E-04, \ 9.509854262005244E-01, 3.980404983361944E-01, 1.284569365696251E-02, \ 9.538750327616107E-01, 4.953599709321822E-02, 1.055872402608265E-02, \ 9.578780270631901E-01, 9.103067048312464E-01, 6.968260865746103E-03, \ 9.592991308680465E-01, 9.968731654931796E-01, 1.210463692085719E-03, \ 9.601302552519683E-01, -8.180789200488630E-01, 8.683841565713000E-03, \ 9.694392229219877E-01, -5.715033820344755E-01, 1.159851379681130E-02, \ 9.703910299123225E-01, 1.632899951759109E-01, 7.363467408097404E-03, \ 9.719159673797005E-01, 7.411274370572497E-01, 7.318477013269155E-03, \ 9.829103770479058E-01, 5.055355492737967E-01, 6.282928001932651E-03, \ 9.833554207795926E-01, -1.837381133019218E-01, 8.880000815180237E-03, \ 9.874031706544697E-01, -9.781008326752658E-01, 1.660786069380725E-03, \ 9.915132744979969E-01, -8.960126036794243E-01, 2.711324914646742E-03, \ 9.917024709452258E-01, 9.678533470873883E-01, 1.688735729327407E-03, \ 9.937579585467250E-01, -7.180615094407097E-01, 3.871787826906220E-03, \ 9.940901871599539E-01, 8.430528621092570E-01, 2.741339818214634E-03, \ 9.941340765584503E-01, 2.870098965170506E-01, 4.589322892855804E-03, \ 9.949661609261387E-01, 6.084106757497423E-03, 3.583734039365401E-03, \ 9.960704002907521E-01, -4.220415957631232E-01, 4.045718926806529E-03, \ 9.968040423856127E-01, 6.246991365652024E-01, 2.405030444120247E-03 ] ) return xyw def smr33 ( ): #*****************************************************************************80 # ## smr33 returns the SMR rule of degree 33. # # Discussion: # # DEGREE: 33 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 197 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*197), the requested rule. # import numpy as np xyw = np.array ( [ \ 1.485098538731679E-01, 1.694663949097438E-01, 4.808148867803772E-02, \ 1.172505996395537E-01, 5.208793654128182E-01, 4.731056174816773E-02, \ 1.066031447166868E-01, 7.778079973351806E-01, 3.516295123254670E-02, \ 1.132061108674796E-01, 9.316643176349618E-01, 1.951472105421867E-02, \ 1.073615219898776E-01, 9.959676005278353E-01, 3.976501444162358E-03, \ 3.462608583072413E-01, 2.127438914067375E-01, 2.293908286621284E-02, \ 2.637306543835957E-01, 3.722947344432351E-01, 4.432068637015522E-02, \ 2.693795841838618E-01, 6.682002420169654E-01, 3.897921421448901E-02, \ 2.875348204916399E-01, 8.670452225998134E-01, 2.660382508243975E-02, \ 2.893753551193369E-01, 9.757288452382227E-01, 1.105346348813268E-02, \ 5.338546425019925E-01, 2.183801117113716E-01, 3.966360973156654E-02, \ 4.549680885072975E-01, 3.744677210475233E-01, 2.597222014353591E-02, \ 4.090144024608169E-01, 5.458954883248048E-01, 3.713648914135518E-02, \ 5.663026752204063E-01, 6.734659888883729E-01, 2.933590367319608E-02, \ 4.400187284568344E-01, 7.788448587064940E-01, 3.047735039849236E-02, \ 4.582598509566294E-01, 9.355376236278888E-01, 1.725142829363587E-02, \ 4.582752827247127E-01, 9.968603726644156E-01, 3.162797947778954E-03, \ 6.759309027563951E-01, 3.646480880237580E-01, 3.217426321537782E-02, \ 5.907301259704386E-01, 4.949340946812834E-01, 2.734110543912327E-02, \ 7.146893160300763E-01, 6.329648433025803E-01, 1.940442339199639E-02, \ 5.953318104316343E-01, 8.701483739421072E-01, 2.120649987549222E-02, \ 6.160860838046369E-01, 9.794286822210785E-01, 8.362497816308373E-03, \ 7.767420410261425E-01, 2.222325062449502E-01, 3.296613956707922E-02, \ 7.831882183207082E-01, 5.287992062720019E-01, 2.386573699307072E-02, \ 7.041851604707902E-01, 7.847889458751023E-01, 2.058221303838324E-02, \ 7.290534382081308E-01, 9.388309009733727E-01, 1.190900733146451E-02, \ 7.820133071823339E-01, 9.948308715565458E-01, 3.147989159421966E-03, \ 8.652684158240387E-01, 4.011976196638404E-01, 2.438236797329849E-02, \ 8.642300806994567E-01, 6.861574436903071E-01, 1.727637663346140E-02, \ 8.162582507393171E-01, 7.697617350233709E-01, 9.484139746590401E-03, \ 8.182773560074186E-01, 8.794302700865166E-01, 1.280268009696023E-02, \ 8.763977475275423E-01, 9.668867982051652E-01, 6.900853588227474E-03, \ 9.328617706321541E-01, 2.521078906774078E-01, 1.887531974376769E-02, \ 9.761739411206226E-01, 4.312566462575608E-01, 1.066375643199943E-02, \ 9.303430517898699E-01, 5.710543042726919E-01, 1.625052256486291E-02, \ 9.235378662628289E-01, 8.205750108473285E-01, 1.032788782555771E-02, \ 9.162909962693953E-01, 9.020219304490703E-01, 4.456178267147566E-03, \ 9.687563884966668E-01, 9.315860338184979E-01, 4.698545579229029E-03, \ 9.479068758778074E-01, 9.935126494654830E-01, 1.772982851226346E-03, \ 9.962467362996064E-01, 2.548705123657606E-01, 3.847516809883929E-03, \ 9.961740044729398E-01, 6.047358347062713E-01, 3.352228907155900E-03, \ 9.715483507430605E-01, 7.273867424892582E-01, 8.746651111990895E-03, \ 9.934251724726507E-01, 8.497187134082044E-01, 2.995115265626365E-03, \ 9.944169188618658E-01, 9.785612572781918E-01, 1.006759244687949E-03, \ 7.126217736993628E-03, 2.946754002433002E-01, 3.527142153616744E-02, \ -6.246434173781462E-02, 4.078563905320223E-01, 3.051711732786730E-02, \ -5.410706476354973E-02, 6.561935311635315E-01, 4.279129134457323E-02, \ -6.740481034767548E-02, 8.680969463101411E-01, 2.696044145284995E-02, \ -7.268739448152371E-02, 9.746198602047339E-01, 1.183714051929051E-02, \ -1.694663949097438E-01, 1.485098538731679E-01, 4.808148867803772E-02, \ -5.208793654128182E-01, 1.172505996395537E-01, 4.731056174816773E-02, \ -7.778079973351806E-01, 1.066031447166868E-01, 3.516295123254670E-02, \ -9.316643176349618E-01, 1.132061108674796E-01, 1.951472105421867E-02, \ -9.959676005278353E-01, 1.073615219898776E-01, 3.976501444162358E-03, \ -2.127438914067375E-01, 3.462608583072413E-01, 2.293908286621284E-02, \ -3.722947344432351E-01, 2.637306543835957E-01, 4.432068637015522E-02, \ -6.682002420169654E-01, 2.693795841838618E-01, 3.897921421448901E-02, \ -8.670452225998134E-01, 2.875348204916399E-01, 2.660382508243975E-02, \ -9.757288452382227E-01, 2.893753551193369E-01, 1.105346348813268E-02, \ -2.183801117113716E-01, 5.338546425019925E-01, 3.966360973156654E-02, \ -3.744677210475233E-01, 4.549680885072975E-01, 2.597222014353591E-02, \ -5.458954883248048E-01, 4.090144024608169E-01, 3.713648914135518E-02, \ -6.734659888883729E-01, 5.663026752204063E-01, 2.933590367319608E-02, \ -7.788448587064940E-01, 4.400187284568344E-01, 3.047735039849236E-02, \ -9.355376236278888E-01, 4.582598509566294E-01, 1.725142829363587E-02, \ -9.968603726644156E-01, 4.582752827247127E-01, 3.162797947778954E-03, \ -3.646480880237580E-01, 6.759309027563951E-01, 3.217426321537782E-02, \ -4.949340946812834E-01, 5.907301259704386E-01, 2.734110543912327E-02, \ -6.329648433025803E-01, 7.146893160300763E-01, 1.940442339199639E-02, \ -8.701483739421072E-01, 5.953318104316343E-01, 2.120649987549222E-02, \ -9.794286822210785E-01, 6.160860838046369E-01, 8.362497816308373E-03, \ -2.222325062449502E-01, 7.767420410261425E-01, 3.296613956707922E-02, \ -5.287992062720019E-01, 7.831882183207082E-01, 2.386573699307072E-02, \ -7.847889458751023E-01, 7.041851604707902E-01, 2.058221303838324E-02, \ -9.388309009733727E-01, 7.290534382081308E-01, 1.190900733146451E-02, \ -9.948308715565458E-01, 7.820133071823339E-01, 3.147989159421966E-03, \ -4.011976196638404E-01, 8.652684158240387E-01, 2.438236797329849E-02, \ -6.861574436903071E-01, 8.642300806994567E-01, 1.727637663346140E-02, \ -7.697617350233709E-01, 8.162582507393171E-01, 9.484139746590401E-03, \ -8.794302700865166E-01, 8.182773560074186E-01, 1.280268009696023E-02, \ -9.668867982051652E-01, 8.763977475275423E-01, 6.900853588227474E-03, \ -2.521078906774078E-01, 9.328617706321541E-01, 1.887531974376769E-02, \ -4.312566462575608E-01, 9.761739411206226E-01, 1.066375643199943E-02, \ -5.710543042726919E-01, 9.303430517898699E-01, 1.625052256486291E-02, \ -8.205750108473285E-01, 9.235378662628289E-01, 1.032788782555771E-02, \ -9.020219304490703E-01, 9.162909962693953E-01, 4.456178267147566E-03, \ -9.315860338184979E-01, 9.687563884966668E-01, 4.698545579229029E-03, \ -9.935126494654830E-01, 9.479068758778074E-01, 1.772982851226346E-03, \ -2.548705123657606E-01, 9.962467362996064E-01, 3.847516809883929E-03, \ -6.047358347062713E-01, 9.961740044729398E-01, 3.352228907155900E-03, \ -7.273867424892582E-01, 9.715483507430605E-01, 8.746651111990895E-03, \ -8.497187134082044E-01, 9.934251724726507E-01, 2.995115265626365E-03, \ -9.785612572781918E-01, 9.944169188618658E-01, 1.006759244687949E-03, \ -2.946754002433002E-01, 7.126217736993628E-03, 3.527142153616744E-02, \ -4.078563905320223E-01, -6.246434173781462E-02, 3.051711732786730E-02, \ -6.561935311635315E-01, -5.410706476354973E-02, 4.279129134457323E-02, \ -8.680969463101411E-01, -6.740481034767548E-02, 2.696044145284995E-02, \ -9.746198602047339E-01, -7.268739448152371E-02, 1.183714051929051E-02, \ -1.485098538731679E-01, -1.694663949097438E-01, 4.808148867803772E-02, \ -1.172505996395537E-01, -5.208793654128182E-01, 4.731056174816773E-02, \ -1.066031447166868E-01, -7.778079973351806E-01, 3.516295123254670E-02, \ -1.132061108674796E-01, -9.316643176349618E-01, 1.951472105421867E-02, \ -1.073615219898776E-01, -9.959676005278353E-01, 3.976501444162358E-03, \ -3.462608583072413E-01, -2.127438914067375E-01, 2.293908286621284E-02, \ -2.637306543835957E-01, -3.722947344432351E-01, 4.432068637015522E-02, \ -2.693795841838618E-01, -6.682002420169654E-01, 3.897921421448901E-02, \ -2.875348204916399E-01, -8.670452225998134E-01, 2.660382508243975E-02, \ -2.893753551193369E-01, -9.757288452382227E-01, 1.105346348813268E-02, \ -5.338546425019925E-01, -2.183801117113716E-01, 3.966360973156654E-02, \ -4.549680885072975E-01, -3.744677210475233E-01, 2.597222014353591E-02, \ -4.090144024608169E-01, -5.458954883248048E-01, 3.713648914135518E-02, \ -5.663026752204063E-01, -6.734659888883729E-01, 2.933590367319608E-02, \ -4.400187284568344E-01, -7.788448587064940E-01, 3.047735039849236E-02, \ -4.582598509566294E-01, -9.355376236278888E-01, 1.725142829363587E-02, \ -4.582752827247127E-01, -9.968603726644156E-01, 3.162797947778954E-03, \ -6.759309027563951E-01, -3.646480880237580E-01, 3.217426321537782E-02, \ -5.907301259704386E-01, -4.949340946812834E-01, 2.734110543912327E-02, \ -7.146893160300763E-01, -6.329648433025803E-01, 1.940442339199639E-02, \ -5.953318104316343E-01, -8.701483739421072E-01, 2.120649987549222E-02, \ -6.160860838046369E-01, -9.794286822210785E-01, 8.362497816308373E-03, \ -7.767420410261425E-01, -2.222325062449502E-01, 3.296613956707922E-02, \ -7.831882183207082E-01, -5.287992062720019E-01, 2.386573699307072E-02, \ -7.041851604707902E-01, -7.847889458751023E-01, 2.058221303838324E-02, \ -7.290534382081308E-01, -9.388309009733727E-01, 1.190900733146451E-02, \ -7.820133071823339E-01, -9.948308715565458E-01, 3.147989159421966E-03, \ -8.652684158240387E-01, -4.011976196638404E-01, 2.438236797329849E-02, \ -8.642300806994567E-01, -6.861574436903071E-01, 1.727637663346140E-02, \ -8.162582507393171E-01, -7.697617350233709E-01, 9.484139746590401E-03, \ -8.182773560074186E-01, -8.794302700865166E-01, 1.280268009696023E-02, \ -8.763977475275423E-01, -9.668867982051652E-01, 6.900853588227474E-03, \ -9.328617706321541E-01, -2.521078906774078E-01, 1.887531974376769E-02, \ -9.761739411206226E-01, -4.312566462575608E-01, 1.066375643199943E-02, \ -9.303430517898699E-01, -5.710543042726919E-01, 1.625052256486291E-02, \ -9.235378662628289E-01, -8.205750108473285E-01, 1.032788782555771E-02, \ -9.162909962693953E-01, -9.020219304490703E-01, 4.456178267147566E-03, \ -9.687563884966668E-01, -9.315860338184979E-01, 4.698545579229029E-03, \ -9.479068758778074E-01, -9.935126494654830E-01, 1.772982851226346E-03, \ -9.962467362996064E-01, -2.548705123657606E-01, 3.847516809883929E-03, \ -9.961740044729398E-01, -6.047358347062713E-01, 3.352228907155900E-03, \ -9.715483507430605E-01, -7.273867424892582E-01, 8.746651111990895E-03, \ -9.934251724726507E-01, -8.497187134082044E-01, 2.995115265626365E-03, \ -9.944169188618658E-01, -9.785612572781918E-01, 1.006759244687949E-03, \ -7.126217736993628E-03, -2.946754002433002E-01, 3.527142153616744E-02, \ 6.246434173781462E-02, -4.078563905320223E-01, 3.051711732786730E-02, \ 5.410706476354973E-02, -6.561935311635315E-01, 4.279129134457323E-02, \ 6.740481034767548E-02, -8.680969463101411E-01, 2.696044145284995E-02, \ 7.268739448152371E-02, -9.746198602047339E-01, 1.183714051929051E-02, \ 1.694663949097438E-01, -1.485098538731679E-01, 4.808148867803772E-02, \ 5.208793654128182E-01, -1.172505996395537E-01, 4.731056174816773E-02, \ 7.778079973351806E-01, -1.066031447166868E-01, 3.516295123254670E-02, \ 9.316643176349618E-01, -1.132061108674796E-01, 1.951472105421867E-02, \ 9.959676005278353E-01, -1.073615219898776E-01, 3.976501444162358E-03, \ 2.127438914067375E-01, -3.462608583072413E-01, 2.293908286621284E-02, \ 3.722947344432351E-01, -2.637306543835957E-01, 4.432068637015522E-02, \ 6.682002420169654E-01, -2.693795841838618E-01, 3.897921421448901E-02, \ 8.670452225998134E-01, -2.875348204916399E-01, 2.660382508243975E-02, \ 9.757288452382227E-01, -2.893753551193369E-01, 1.105346348813268E-02, \ 2.183801117113716E-01, -5.338546425019925E-01, 3.966360973156654E-02, \ 3.744677210475233E-01, -4.549680885072975E-01, 2.597222014353591E-02, \ 5.458954883248048E-01, -4.090144024608169E-01, 3.713648914135518E-02, \ 6.734659888883729E-01, -5.663026752204063E-01, 2.933590367319608E-02, \ 7.788448587064940E-01, -4.400187284568344E-01, 3.047735039849236E-02, \ 9.355376236278888E-01, -4.582598509566294E-01, 1.725142829363587E-02, \ 9.968603726644156E-01, -4.582752827247127E-01, 3.162797947778954E-03, \ 3.646480880237580E-01, -6.759309027563951E-01, 3.217426321537782E-02, \ 4.949340946812834E-01, -5.907301259704386E-01, 2.734110543912327E-02, \ 6.329648433025803E-01, -7.146893160300763E-01, 1.940442339199639E-02, \ 8.701483739421072E-01, -5.953318104316343E-01, 2.120649987549222E-02, \ 9.794286822210785E-01, -6.160860838046369E-01, 8.362497816308373E-03, \ 2.222325062449502E-01, -7.767420410261425E-01, 3.296613956707922E-02, \ 5.287992062720019E-01, -7.831882183207082E-01, 2.386573699307072E-02, \ 7.847889458751023E-01, -7.041851604707902E-01, 2.058221303838324E-02, \ 9.388309009733727E-01, -7.290534382081308E-01, 1.190900733146451E-02, \ 9.948308715565458E-01, -7.820133071823339E-01, 3.147989159421966E-03, \ 4.011976196638404E-01, -8.652684158240387E-01, 2.438236797329849E-02, \ 6.861574436903071E-01, -8.642300806994567E-01, 1.727637663346140E-02, \ 7.697617350233709E-01, -8.162582507393171E-01, 9.484139746590401E-03, \ 8.794302700865166E-01, -8.182773560074186E-01, 1.280268009696023E-02, \ 9.668867982051652E-01, -8.763977475275423E-01, 6.900853588227474E-03, \ 2.521078906774078E-01, -9.328617706321541E-01, 1.887531974376769E-02, \ 4.312566462575608E-01, -9.761739411206226E-01, 1.066375643199943E-02, \ 5.710543042726919E-01, -9.303430517898699E-01, 1.625052256486291E-02, \ 8.205750108473285E-01, -9.235378662628289E-01, 1.032788782555771E-02, \ 9.020219304490703E-01, -9.162909962693953E-01, 4.456178267147566E-03, \ 9.315860338184979E-01, -9.687563884966668E-01, 4.698545579229029E-03, \ 9.935126494654830E-01, -9.479068758778074E-01, 1.772982851226346E-03, \ 2.548705123657606E-01, -9.962467362996064E-01, 3.847516809883929E-03, \ 6.047358347062713E-01, -9.961740044729398E-01, 3.352228907155900E-03, \ 7.273867424892582E-01, -9.715483507430605E-01, 8.746651111990895E-03, \ 8.497187134082044E-01, -9.934251724726507E-01, 2.995115265626365E-03, \ 9.785612572781918E-01, -9.944169188618658E-01, 1.006759244687949E-03, \ 2.946754002433002E-01, -7.126217736993628E-03, 3.527142153616744E-02, \ 4.078563905320223E-01, 6.246434173781462E-02, 3.051711732786730E-02, \ 6.561935311635315E-01, 5.410706476354973E-02, 4.279129134457323E-02, \ 8.680969463101411E-01, 6.740481034767548E-02, 2.696044145284995E-02, \ 9.746198602047339E-01, 7.268739448152371E-02, 1.183714051929051E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 5.152213536694609E-02 ] ) return xyw def smr34 ( ): #*****************************************************************************80 # ## smr34 returns the SMR rule of degree 34. # # Discussion: # # DEGREE: 34 # POINTS CARDINALITY: 211 # NORM INF MOMS. RESIDUAL: 1.28603e-15 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*211), the requested rule. # import numpy as np xyw = np.array ( [ \ 9.957894049234940E-01, 9.315910675787362E-01, 1.269921938742754E-03, \ 9.966819226158441E-01, 1.990628617847345E-01, 2.824785894655117E-03, \ 9.964232568659287E-01, -8.647711926777550E-02, 2.645466616758639E-03, \ 9.956972863904161E-01, -3.319481955508262E-01, 2.579394947779080E-03, \ 9.970019011095760E-01, -9.813822644968530E-01, 5.121822735027154E-04, \ 9.927566324556228E-01, 9.934870866426487E-01, 4.095595153407374E-04, \ 9.703323011961618E-01, 9.728958623239660E-01, 2.212600752526410E-03, \ 9.900242513895626E-01, 8.165046961752659E-01, 3.489632874382814E-03, \ 9.902525852068462E-01, 6.514930247782849E-01, 4.815598056643366E-03, \ 9.917712097306959E-01, 4.326945836209130E-01, 4.941854039948059E-03, \ 9.773024985383031E-01, 5.683940605635036E-02, 8.460270092591574E-03, \ 9.765396060948102E-01, -2.098648339912204E-01, 7.323452637054356E-03, \ 9.880323477406699E-01, -5.045486513331958E-01, 5.591335677415872E-03, \ 9.944122733775166E-01, -7.025141307156174E-01, 3.181105696378461E-03, \ 9.958204649863345E-01, -8.811936722293690E-01, 1.679399407542441E-03, \ 9.739851411479190E-01, -9.961982985684296E-01, 6.089390050721569E-04, \ 9.254838810436582E-01, 9.958919316136239E-01, 1.271037344372932E-03, \ 9.587557132884421E-01, 8.944112789567285E-01, 5.640872717691950E-03, \ 9.478849514864001E-01, 7.463373175773630E-01, 1.008027250286055E-02, \ 9.549410582182760E-01, 5.355951225176204E-01, 1.161336024599024E-02, \ 9.613314688856274E-01, 2.819596780094841E-01, 1.253554272417035E-02, \ 9.371448388483095E-01, -8.017182518756116E-02, 1.355567725840021E-02, \ 9.492637368076354E-01, -3.697133117565873E-01, 1.281170011512887E-02, \ 9.566739186062905E-01, -6.179209188638126E-01, 1.016499900104730E-02, \ 9.690740057689825E-01, -8.076324709283432E-01, 7.066159092569420E-03, \ 9.749406372948716E-01, -9.432315538275444E-01, 3.241771014445550E-03, \ 9.028278454473605E-01, 9.506719573551936E-01, 5.718690511681701E-03, \ 8.866581548182707E-01, 8.445040467901622E-01, 1.175179682399269E-02, \ 8.903706483869364E-01, 6.377461105727130E-01, 1.554746970297020E-02, \ 8.969144590540912E-01, 3.956118985338431E-01, 1.953552168957224E-02, \ 9.053329661179432E-01, 1.228611554470282E-01, 2.024486874693669E-02, \ 8.842030747448643E-01, -2.282562902715039E-01, 2.040134384913240E-02, \ 8.946404670250787E-01, -4.984799138722827E-01, 1.782084645269496E-02, \ 9.062802014741841E-01, -7.288543903373946E-01, 1.354418113376059E-02, \ 9.198811888280545E-01, -8.922009039806831E-01, 8.721191397819752E-03, \ 9.293075634720418E-01, -9.788256460307448E-01, 3.013136362612083E-03, \ 8.307416649103097E-01, 9.847272069450065E-01, 3.863549341320347E-03, \ 7.989018093580924E-01, 9.174533264327734E-01, 1.128961407311655E-02, \ 8.153857983509745E-01, 7.467362479932101E-01, 1.716850446840271E-02, \ 8.106585959801085E-01, 5.188318587780150E-01, 2.320252631505465E-02, \ 8.162893718776413E-01, 2.444840500980434E-01, 2.728966404029472E-02, \ 8.215905935547697E-01, -3.780686241256082E-02, 2.873816438714253E-02, \ 8.072057239710502E-01, -3.681756246884155E-01, 2.561572339256985E-02, \ 8.197749309285268E-01, -6.248305963346963E-01, 2.157459899366617E-02, \ 8.339165476219796E-01, -8.250462105756355E-01, 1.506332709846787E-02, \ 8.437899588814044E-01, -9.504266038421356E-01, 7.899470455295205E-03, \ 8.682228958168398E-01, -9.969291267643441E-01, 1.326374275614798E-03, \ 7.414965930896726E-01, 9.976180923017504E-01, 1.275494804255145E-03, \ 6.896123397952399E-01, 9.672239781292444E-01, 8.487518731202960E-03, \ 7.211153759242311E-01, 8.337039311560572E-01, 1.641194543039353E-02, \ 7.110494018863930E-01, 6.441550914790497E-01, 2.560376586419488E-02, \ 7.120710037407173E-01, 3.843983266067464E-01, 3.118328085454265E-02, \ 7.082337843919169E-01, 9.533642358177043E-02, 3.479648766166858E-02, \ 7.187206312556610E-01, -1.999543274853690E-01, 3.480535416060045E-02, \ 7.099505499909835E-01, -5.055377353405510E-01, 2.961142270210251E-02, \ 7.231776378051314E-01, -7.385609605003077E-01, 2.311015021964838E-02, \ 7.369495741211172E-01, -9.005396614377654E-01, 1.415501795415763E-02, \ 7.505952660477123E-01, -9.861825097580426E-01, 4.832952601963804E-03, \ 5.629653024363824E-01, 9.941135664776372E-01, 3.633655134392321E-03, \ 6.141214240396574E-01, 8.998790302041257E-01, 1.392167112523221E-02, \ 5.931921073513758E-01, 7.527920640845824E-01, 2.481829833350465E-02, \ 5.899871025319341E-01, 5.223942064090121E-01, 3.423115609409048E-02, \ 5.883574941173312E-01, 2.456253195175061E-01, 3.801938621563456E-02, \ 5.866522692423990E-01, -6.354514810462418E-02, 4.033761673976392E-02, \ 5.956977300877557E-01, -3.566931332257176E-01, 3.883131233055023E-02, \ 5.927782889432014E-01, -6.336224604245022E-01, 3.122552426886264E-02, \ 6.039926786166937E-01, -8.337208546028212E-01, 2.203539439992588E-02, \ 6.254100151918139E-01, -9.560918196311188E-01, 1.059755194349184E-02, \ 6.138060651734009E-01, -9.979430080887202E-01, 1.564596443077996E-03, \ 5.022165322679116E-01, 9.482480846379436E-01, 1.084348902106024E-02, \ 4.589509327363929E-01, 8.404994158661170E-01, 2.205645658430699E-02, \ 4.535417272429489E-01, 6.512962979642629E-01, 3.348745611830561E-02, \ 4.510904524624095E-01, 3.881579570291138E-01, 4.047512990695875E-02, \ 4.531813432716658E-01, 9.229245238599951E-02, 4.393288153714553E-02, \ 4.488470929336799E-01, -2.197179800757668E-01, 4.388737292644242E-02, \ 4.563145412677839E-01, -5.038653497135700E-01, 4.012853694760013E-02, \ 4.562655526794984E-01, -7.462651889579118E-01, 3.008472851353892E-02, \ 4.727430836168379E-01, -9.110093097588490E-01, 1.799703635920556E-02, \ 4.843396113021201E-01, -9.856160975683469E-01, 5.547598452760956E-03, \ 3.782074525681371E-01, 9.816291834100873E-01, 7.597211525403482E-03, \ 3.210021971883614E-01, 9.073748618669065E-01, 1.712946714791248E-02, \ 2.971150388089600E-01, 7.594439443864908E-01, 3.119492749262633E-02, \ 3.085827486636639E-01, 5.288161042011519E-01, 3.927023314753940E-02, \ 3.026283090386810E-01, 2.403811853574280E-01, 4.600362243085380E-02, \ 3.035481141969048E-01, -6.382973969918371E-02, 4.775119284718515E-02, \ 2.994451040546098E-01, -3.704131087942491E-01, 4.493238986528309E-02, \ 3.026913839582241E-01, -6.362750245744471E-01, 3.848554817804676E-02, \ 3.121563314492936E-01, -8.444884638792907E-01, 2.592723046024846E-02, \ 3.177377527975286E-01, -9.623829050564436E-01, 1.196800170196079E-02, \ 3.522562949226852E-01, -9.977574902186489E-01, 1.465730151083379E-03, \ 2.252906962715443E-01, 9.978350295394129E-01, 2.641867829058960E-03, \ 1.870003268404008E-01, 9.519167862352040E-01, 1.192465747101495E-02, \ 1.307262219235918E-01, 8.489253631104906E-01, 2.661740954067537E-02, \ 1.460202234422147E-01, 6.479061469473005E-01, 3.731070624469975E-02, \ 1.551732848359904E-01, 3.937810190186502E-01, 4.428770255029615E-02, \ 1.446818601451690E-01, 8.694181210571608E-02, 4.921582512367255E-02, \ 1.447233210916806E-01, -2.195027813449513E-01, 4.906351937807495E-02, \ 1.412640048285802E-01, -5.107425247720647E-01, 4.323240844139490E-02, \ 1.466417969010396E-01, -7.557347294477489E-01, 3.399928104285673E-02, \ 1.513983361920271E-01, -9.178835711763990E-01, 1.968326070317311E-02, \ 1.600169709826858E-01, -9.920169758816885E-01, 5.106715024206334E-03, \ 4.623093501161722E-02, 9.801351468257945E-01, 8.170216576549613E-03, \ -4.319669651670000E-02, 9.166149692153970E-01, 2.022961085099902E-02, \ -2.230730777996857E-02, 7.523423884761198E-01, 3.290525410921873E-02, \ -1.392477655643914E-02, 5.228385485756610E-01, 4.239225481578053E-02, \ -2.183676694863989E-03, 2.501384326494425E-01, 4.695791528007733E-02, \ -1.771073397997970E-02, -6.845314069841779E-02, 4.998518364759874E-02, \ -1.918022708935162E-02, -3.696927200439754E-01, 4.749247254760981E-02, \ -1.474661089836961E-02, -6.423393807595678E-01, 3.916228450022604E-02, \ -1.910959910763293E-02, -8.510668952524700E-01, 2.737517696135046E-02, \ -1.100089784272918E-02, -9.691167342202294E-01, 1.213622924790588E-02, \ -3.847492042854418E-02, -9.987599455147976E-01, 5.258835064828757E-04, \ -1.160040389320081E-01, 9.958817619644164E-01, 3.406278974443858E-03, \ -2.185121444211190E-01, 9.631241177105265E-01, 1.268502876701255E-02, \ -1.937132212208339E-01, 8.383996125115697E-01, 2.675583510478743E-02, \ -1.826019579662390E-01, 6.413756225205492E-01, 3.761719838478075E-02, \ -1.735927428003249E-01, 3.847679978445431E-01, 4.506880832422441E-02, \ -1.594820599810335E-01, 1.021893850082368E-01, 4.732469156429694E-02, \ -1.797927762716425E-01, -2.215868153351966E-01, 4.805977741575223E-02, \ -1.784086402180959E-01, -5.142300281088545E-01, 4.362591086259024E-02, \ -1.745465205857428E-01, -7.537366611960344E-01, 3.293031384181930E-02, \ -1.828492149475154E-01, -9.245139444740262E-01, 1.949340077252138E-02, \ -1.789613218613975E-01, -9.949810109450419E-01, 4.016610904884734E-03, \ -3.800099111129797E-01, 9.908974338803321E-01, 5.688273109814698E-03, \ -3.586039156258787E-01, 9.068849508020077E-01, 1.913010526360378E-02, \ -3.496397464654761E-01, 7.438459923959813E-01, 3.124476168334308E-02, \ -3.364944138026182E-01, 5.149360180314989E-01, 3.983236757275106E-02, \ -3.294605072590807E-01, 2.384445970652024E-01, 4.513790568866929E-02, \ -3.122746998671402E-01, -4.678649257141996E-02, 4.548014560760486E-02, \ -3.341423047428589E-01, -3.709042921640023E-01, 4.429219382577024E-02, \ -3.354222464209633E-01, -6.423389313071104E-01, 3.714968452645009E-02, \ -3.286029525442455E-01, -8.464666976755009E-01, 2.548880688148467E-02, \ -3.423506685296714E-01, -9.732216431261292E-01, 1.101466595660109E-02, \ -5.138042906159611E-01, 9.558781663655185E-01, 1.229885705467326E-02, \ -5.033240255512550E-01, 8.325996634815285E-01, 2.342997859462644E-02, \ -4.934184358754027E-01, 6.313367991374997E-01, 3.314341950516837E-02, \ -4.810231379698435E-01, 3.779456066296256E-01, 3.930146102742181E-02, \ -4.764387898456861E-01, 8.757235735790503E-02, 4.263018853028100E-02, \ -4.572408337995446E-01, -1.943807931912226E-01, 4.242015879601867E-02, \ -4.802078301948393E-01, -5.087552615537000E-01, 3.799154907843184E-02, \ -4.816737135589465E-01, -7.533088525220843E-01, 2.921009462864135E-02, \ -4.733119659070418E-01, -9.179909803583359E-01, 1.746139256900922E-02, \ -4.990207194253169E-01, -9.955235014987277E-01, 3.570668877927755E-03, \ -6.062998022698073E-01, 9.932404164712231E-01, 3.708370634578858E-03, \ -6.491078687880649E-01, 8.991595936933783E-01, 1.661359748562513E-02, \ -6.321366293284888E-01, 7.379522674184295E-01, 2.543791270192361E-02, \ -6.224588096649009E-01, 5.058658625167738E-01, 3.217812029858986E-02, \ -6.117601892971127E-01, 2.344646477708566E-01, 3.626413991737416E-02, \ -6.122438295935009E-01, -6.118231673822243E-02, 3.846524273667296E-02, \ -5.905469375569611E-01, -3.379271094668896E-01, 3.725605813241765E-02, \ -6.122926561666857E-01, -6.332620144806621E-01, 3.045025547248366E-02, \ -6.117420843079315E-01, -8.439605906500176E-01, 2.063725984389774E-02, \ -6.116108912175794E-01, -9.645394242789779E-01, 1.003007390672613E-02, \ -7.202064450714707E-01, 9.687351621558032E-01, 7.343535416630068E-03, \ -7.640489552162673E-01, 8.186646209837353E-01, 1.863562117417300E-02, \ -7.436443095834101E-01, 6.262385938114700E-01, 2.495426940021197E-02, \ -7.331951159558409E-01, 3.722915352073840E-01, 2.875505251303774E-02, \ -7.291744483592270E-01, 9.368940286691475E-02, 3.156945503308321E-02, \ -7.288163979760982E-01, -2.086415233438004E-01, 3.215315002188151E-02, \ -7.098973709325594E-01, -4.751240313065653E-01, 3.076312488254992E-02, \ -7.268316303036324E-01, -7.421205012809852E-01, 2.255876744610365E-02, \ -7.264152089003056E-01, -9.083680633160397E-01, 1.267855278207347E-02, \ -7.233502526295543E-01, -9.921398900464297E-01, 3.600327870316919E-03, \ -7.944789979709225E-01, 9.959607742122426E-01, 1.854529264151413E-03, \ -8.147179926759360E-01, 9.259971742330974E-01, 9.286071545967561E-03, \ -8.358777763260274E-01, 5.001749403101742E-01, 2.223492620715524E-02, \ -8.280513515003269E-01, 2.411582059883278E-01, 2.368666725498836E-02, \ -8.243355863622386E-01, -4.998572152583577E-02, 2.569483374962900E-02, \ -8.253626145601571E-01, -3.493120592376261E-01, 2.490342922131878E-02, \ -8.121903650291438E-01, -6.033292859790981E-01, 2.346341699504689E-02, \ -8.243577863456620E-01, -8.312302356419400E-01, 1.465176915755172E-02, \ -8.082617618985660E-01, -9.574178572790982E-01, 6.560728336041037E-03, \ -8.769708382829380E-01, 9.770175617614344E-01, 3.974309788574307E-03, \ -8.880540245245994E-01, 8.666033220470682E-01, 9.800468993344479E-03, \ -8.568819581968040E-01, 7.165122557426438E-01, 1.790497672791658E-02, \ -9.108965422368728E-01, 3.666364065180091E-01, 1.733578039890229E-02, \ -8.999292387149525E-01, 1.038339307709946E-01, 1.840663934478885E-02, \ -8.998152788908981E-01, -1.919839007449358E-01, 1.937803424050972E-02, \ -9.011685721899708E-01, -4.791884508086222E-01, 1.781696597031558E-02, \ -8.923912156383284E-01, -7.214601312758249E-01, 1.500532951025639E-02, \ -8.907008410401606E-01, -9.129470624567904E-01, 7.655314254685561E-03, \ -8.676939171104242E-01, -9.904314861849869E-01, 2.705031002848760E-03, \ -9.188556339019280E-01, 9.977441709649485E-01, 6.651528764616177E-04, \ -9.393146671802626E-01, 9.406875019616726E-01, 4.907287875623333E-03, \ -9.427004725205717E-01, 7.884492668449667E-01, 8.999020685128650E-03, \ -9.254983409374398E-01, 5.949923406312909E-01, 1.449266443485655E-02, \ -9.623402050786286E-01, 2.203675962432235E-01, 1.154948473266472E-02, \ -9.534726655584184E-01, -3.595939510894143E-02, 1.281508516722223E-02, \ -9.562602062411448E-01, -3.265233934409525E-01, 1.289425537223051E-02, \ -9.499571065866433E-01, -6.131217314929267E-01, 1.037125192483871E-02, \ -9.414372674717216E-01, -8.421925517112083E-01, 7.635598833311997E-03, \ -9.395229108692154E-01, -9.677418086529198E-01, 3.716167310778579E-03, \ -9.663743388828732E-01, 9.850068209277927E-01, 1.420844648930481E-03, \ -9.793571344458664E-01, 8.835824849533620E-01, 4.236370836658044E-03, \ -9.784131895253078E-01, 6.860465632928617E-01, 6.466485198832629E-03, \ -9.720790479760727E-01, 4.609381343239562E-01, 9.123045248824293E-03, \ -9.922349973191166E-01, 7.408980516640630E-02, 5.036903551023158E-03, \ -9.884518154282259E-01, -1.661796274498394E-01, 6.407263174244769E-03, \ -9.837613800395109E-01, -4.904211187466530E-01, 6.284479940669028E-03, \ -9.762934256514504E-01, -7.589006865381343E-01, 5.806817236490501E-03, \ -9.802746096908096E-01, -9.188419450488240E-01, 3.548038742379143E-03, \ -9.621555816212115E-01, -9.997532394165864E-01, 5.926783687992160E-04, \ -9.896332869499853E-01, 9.951276758066656E-01, 3.200747405907301E-04, \ -9.951132917806931E-01, 9.549806547758480E-01, 1.112585947085899E-03, \ -9.971587223315985E-01, 7.967223653947199E-01, 1.766856809395384E-03, \ -9.966946507532868E-01, 5.656259514453754E-01, 2.374570144278089E-03, \ -9.948421084318764E-01, 3.184211137190651E-01, 3.508527197107025E-03, \ -9.985195040394224E-01, -3.568719965932207E-01, 1.842016463896301E-03, \ -9.952776313728143E-01, -6.518074202281385E-01, 2.603732985806352E-03, \ -9.985034101792289E-01, -8.450489535939099E-01, 1.326109663812068E-03, \ -9.930680364844743E-01, -9.794233688312636E-01, 9.749008815310916E-04 ] ) return xyw def smr35 ( ): #*****************************************************************************80 # ## smr35 returns the SMR rule of degree 35. # # Discussion: # # DEGREE: 35 # SYMMETRY: (X, Y), (-X, -Y) # POINTS CARDINALITY: 220 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*220), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.963054076831271E-01, 5.895227652492729E-01, 3.040448117975760E-03, \ -9.959258876623405E-01, 8.226232166208993E-01, 1.978505799274471E-03, \ -9.954067560360648E-01, -9.074145716693054E-01, 1.810898452206362E-03, \ -9.952722138287154E-01, 2.785041956973013E-01, 4.045664611880734E-03, \ -9.949775104476455E-01, -7.198973208744759E-01, 2.841977406946536E-03, \ -9.943750550352027E-01, -3.487179202856331E-02, 4.548201806973092E-03, \ -9.943677037885296E-01, 9.710410041880194E-01, 1.118097006661641E-03, \ -9.937038655576630E-01, -9.931050540649843E-01, 4.830386117047890E-04, \ -9.930202681222473E-01, -3.214092657950156E-01, 4.905950396961080E-03, \ -9.861727841676639E-01, -5.400704381496431E-01, 6.797444141494801E-03, \ -9.810071147719678E-01, 8.985653300431585E-01, 3.181435032108599E-03, \ -9.740062631571137E-01, 7.162386303873299E-01, 7.887232214456035E-03, \ -9.739587062789258E-01, 4.439901118287898E-01, 1.034505230549930E-02, \ -9.726572697503230E-01, -8.181619946621148E-01, 6.464658905526641E-03, \ -9.698067055262342E-01, -9.633285091443817E-01, 3.282158060938487E-03, \ -9.694166462805192E-01, 1.256612526452283E-01, 1.203688131505905E-02, \ -9.658674622089268E-01, 9.953452266059633E-01, 1.102717947131251E-03, \ -9.638166221951805E-01, -1.751088896720577E-01, 1.281494987287384E-02, \ -9.504683215166834E-01, 9.376314986069719E-01, 4.086139127613287E-03, \ -9.449990557642718E-01, -6.629472122415720E-01, 1.284843891927071E-02, \ -9.446169086076862E-01, -4.135452324650374E-01, 1.479906753649862E-02, \ -9.317772095678226E-01, 8.201150672577782E-01, 9.940838732765474E-03, \ -9.290486544464471E-01, -8.950190921642169E-01, 7.779964394420137E-03, \ -9.283184737295814E-01, 5.879017021514434E-01, 1.561783824168382E-02, \ -9.245462285990703E-01, 2.974342857591706E-01, 1.847140993304593E-02, \ -9.211763298375819E-01, -9.934526556341349E-01, 2.003191789183488E-03, \ -9.119151052554647E-01, -4.274927442267495E-02, 1.424779189715308E-02, \ -9.057117846078058E-01, 4.659054057320846E-02, 9.353615677783169E-03, \ -8.999935234232900E-01, 9.752903231391948E-01, 4.574852292020883E-03, \ -8.829230087690153E-01, -7.770114466508429E-01, 1.555785382570586E-02, \ -8.824467573040489E-01, -2.752146559569857E-01, 2.057326622412542E-02, \ -8.735663725309100E-01, -5.411359973847757E-01, 2.141510206682392E-02, \ -8.722180260064613E-01, 8.841005984426642E-01, 8.223856754800985E-03, \ -8.688253850828861E-01, -9.504355153693655E-01, 7.016335896084859E-03, \ -8.610711834248425E-01, 7.150978677167033E-01, 1.850564562244901E-02, \ -8.562600324120904E-01, 4.495124318073283E-01, 2.357983853078307E-02, \ -8.358095013326707E-01, 1.733093930153186E-01, 2.670539971994917E-02, \ -8.228302442461702E-01, -1.697016693626475E-01, 1.342647121783435E-02, \ -8.174385098192266E-01, 9.961711079884141E-01, 2.165794610184791E-03, \ -8.166426016882831E-01, 9.271485107406205E-01, 7.934960713327414E-03, \ -7.985152091160521E-01, -8.693626506598062E-01, 1.561754453690349E-02, \ -7.981120997224805E-01, -9.863110488956950E-01, 4.428350131300970E-03, \ -7.904587180395604E-01, -3.698232163504092E-02, 2.186616762504613E-02, \ -7.887652330718642E-01, -6.709289186517926E-01, 2.371430123275542E-02, \ -7.796834866912661E-01, -3.994715783200819E-01, 2.994104825767884E-02, \ -7.704963456494349E-01, 5.900999992322654E-01, 2.533980569560729E-02, \ -7.640326515570037E-01, 8.125887805195392E-01, 1.949174894848284E-02, \ -7.450492234413376E-01, 3.427381908986717E-01, 2.313801537268639E-02, \ -7.328136392431331E-01, 2.875348312510743E-01, 1.087089248290535E-02, \ -7.295286264509984E-01, 9.665226078227548E-01, 8.147629083103793E-03, \ -7.084311098316746E-01, -1.768747230410797E-01, 2.397513960514677E-02, \ -7.005552670374735E-01, -9.406601330339404E-01, 1.246369990823231E-02, \ -6.897531031934704E-01, 6.782883935108303E-01, 6.655878361359627E-03, \ -6.848525475182752E-01, -7.813397580356689E-01, 2.347027715648843E-02, \ -6.787362302215644E-01, 8.353105038445782E-02, 3.660462342407370E-02, \ -6.758525517932752E-01, -5.427274842488018E-01, 3.178580319617729E-02, \ -6.598249437273979E-01, -9.948642685624477E-01, 2.808772731098325E-03, \ -6.499799074317244E-01, 8.924083156022753E-01, 1.749067931565174E-02, \ -6.406772691253437E-01, 7.139228812806040E-01, 2.272673241453971E-02, \ -6.404909510129633E-01, 4.864679391303438E-01, 2.960589457868493E-02, \ -6.308221736554908E-01, -2.945267523482654E-01, 3.146868659787020E-02, \ -6.143455982549889E-01, 9.920826636566066E-01, 4.351963504883606E-03, \ -5.844710675512947E-01, 2.592109992058108E-01, 2.283706283744573E-02, \ -5.748230680261558E-01, -8.760965122066653E-01, 1.943926421467558E-02, \ -5.572474716940677E-01, -6.686420737982589E-01, 3.083669208006901E-02, \ -5.482102814487624E-01, 4.226896138717067E-01, 1.428889064276768E-02, \ -5.435737968160658E-01, -7.127399923480068E-02, 4.496806151459203E-02, \ -5.391683921956473E-01, -9.726355827179098E-01, 9.266285418087179E-03, \ -5.207225999437588E-01, 2.085864473946192E-01, 2.344644441982280E-02, \ -5.185875206855339E-01, 8.093271136372929E-01, 2.465400557427630E-02, \ -5.177821997159030E-01, -4.860941365404695E-01, 4.035705383914671E-03, \ -5.159801356223465E-01, 9.489058642290333E-01, 1.356103767266921E-02, \ -5.158924660295786E-01, -4.251904122231722E-01, 3.560324497451925E-02, \ -4.994044935070279E-01, 6.099462217677528E-01, 3.154922279377764E-02, \ -4.542210356062989E-01, -7.958468688022844E-01, 1.794582284359643E-02, \ -4.056267255080869E-01, 5.341375520421459E-01, 1.152087899889739E-02, \ -4.055948117557182E-01, -9.243438360258911E-01, 1.650133309775475E-02, \ -4.040537647708318E-01, -9.964418579498329E-01, 3.051316164369587E-03, \ -4.039882331666476E-01, -2.369652785329704E-01, 4.786645009346951E-02, \ -4.035957925466688E-01, -7.396121234399951E-01, 1.283147906403060E-02, \ -3.998139656878879E-01, 3.785894153380550E-01, 3.993632109430833E-02, \ -3.963413695053817E-01, 9.888743963929636E-01, 6.292415031278153E-03, \ -3.916192571372809E-01, 8.570203854231701E-02, 4.709957356606227E-02, \ -3.781489380730715E-01, -5.664445529989698E-01, 3.920699629566945E-02, \ -3.716587536775290E-01, 8.852446618690641E-01, 2.141062768778597E-02, \ -3.634328788865228E-01, 7.287742400150319E-01, 2.448742112847983E-02, \ -2.987755245919356E-01, 6.636636932174717E-01, 1.342406173089754E-02, \ -2.968276435525883E-01, -8.304928792595524E-01, 1.658848141268110E-02, \ -2.730446394137964E-01, -9.731854164765670E-01, 9.487914154560882E-03, \ -2.527215209939402E-01, -3.953707636595537E-01, 4.787894718529206E-02, \ -2.484030447599341E-01, 9.526421508958445E-01, 1.422151685597499E-02, \ -2.449636454507225E-01, -7.846110838738764E-02, 5.146237215684395E-02, \ -2.425768385346887E-01, 5.209707813340320E-01, 3.945757174858697E-02, \ -2.350501139206987E-01, 2.470184275136251E-01, 4.984023350983210E-02, \ -2.242013177906116E-01, -6.901076261298711E-01, 3.533647809963283E-02, \ -2.185301091710398E-01, -8.814048828689003E-01, 1.288022793213647E-02, \ -2.041253198436666E-01, 7.913052621344840E-01, 2.097344678642826E-02, \ -1.711186961614260E-01, 8.484142146354349E-01, 1.191006595550569E-02, \ -1.706560382250964E-01, 9.949901599692252E-01, 3.586815258663693E-03, \ -1.215442732714673E-01, -9.952093452521580E-01, 3.571400312739183E-03, \ -1.212739677278976E-01, -9.375172954719908E-01, 1.267403468943651E-02, \ -9.463646218871977E-02, -5.420702319082150E-01, 4.444769202139284E-02, \ -8.912243328958734E-02, 6.529263044412255E-01, 3.773327086808358E-02, \ -8.859975837369544E-02, -2.416302562834947E-01, 5.169192291225042E-02, \ -8.213238766551616E-02, -8.377296354933957E-01, 1.300368186580167E-02, \ -7.960209828358143E-02, 8.301571435730447E-02, 5.326449572668888E-02, \ -6.910083831974916E-02, 3.985144846429817E-01, 4.829901192754266E-02, \ -6.703676747477079E-02, 9.036691320042987E-01, 1.766559618844168E-02, \ -3.859244773141641E-02, -7.670969426559235E-01, 2.567105291338053E-02, \ -2.835677761623644E-02, 9.748999327824780E-01, 8.816515305029195E-03, \ 2.835677761623644E-02, -9.748999327824780E-01, 8.816515305029195E-03, \ 3.859244773141641E-02, 7.670969426559235E-01, 2.567105291338053E-02, \ 6.703676747477079E-02, -9.036691320042987E-01, 1.766559618844168E-02, \ 6.910083831974916E-02, -3.985144846429817E-01, 4.829901192754266E-02, \ 7.960209828358143E-02, -8.301571435730447E-02, 5.326449572668888E-02, \ 8.213238766551616E-02, 8.377296354933957E-01, 1.300368186580167E-02, \ 8.859975837369544E-02, 2.416302562834947E-01, 5.169192291225042E-02, \ 8.912243328958734E-02, -6.529263044412255E-01, 3.773327086808358E-02, \ 9.463646218871977E-02, 5.420702319082150E-01, 4.444769202139284E-02, \ 1.212739677278976E-01, 9.375172954719908E-01, 1.267403468943651E-02, \ 1.215442732714673E-01, 9.952093452521580E-01, 3.571400312739183E-03, \ 1.706560382250964E-01, -9.949901599692252E-01, 3.586815258663693E-03, \ 1.711186961614260E-01, -8.484142146354349E-01, 1.191006595550569E-02, \ 2.041253198436666E-01, -7.913052621344840E-01, 2.097344678642826E-02, \ 2.185301091710398E-01, 8.814048828689003E-01, 1.288022793213647E-02, \ 2.242013177906116E-01, 6.901076261298711E-01, 3.533647809963283E-02, \ 2.350501139206987E-01, -2.470184275136251E-01, 4.984023350983210E-02, \ 2.425768385346887E-01, -5.209707813340320E-01, 3.945757174858697E-02, \ 2.449636454507225E-01, 7.846110838738764E-02, 5.146237215684395E-02, \ 2.484030447599341E-01, -9.526421508958445E-01, 1.422151685597499E-02, \ 2.527215209939402E-01, 3.953707636595537E-01, 4.787894718529206E-02, \ 2.730446394137964E-01, 9.731854164765670E-01, 9.487914154560882E-03, \ 2.968276435525883E-01, 8.304928792595524E-01, 1.658848141268110E-02, \ 2.987755245919356E-01, -6.636636932174717E-01, 1.342406173089754E-02, \ 3.634328788865228E-01, -7.287742400150319E-01, 2.448742112847983E-02, \ 3.716587536775290E-01, -8.852446618690641E-01, 2.141062768778597E-02, \ 3.781489380730715E-01, 5.664445529989698E-01, 3.920699629566945E-02, \ 3.916192571372809E-01, -8.570203854231701E-02, 4.709957356606227E-02, \ 3.963413695053817E-01, -9.888743963929636E-01, 6.292415031278153E-03, \ 3.998139656878879E-01, -3.785894153380550E-01, 3.993632109430833E-02, \ 4.035957925466688E-01, 7.396121234399951E-01, 1.283147906403060E-02, \ 4.039882331666476E-01, 2.369652785329704E-01, 4.786645009346951E-02, \ 4.040537647708318E-01, 9.964418579498329E-01, 3.051316164369587E-03, \ 4.055948117557182E-01, 9.243438360258911E-01, 1.650133309775475E-02, \ 4.056267255080869E-01, -5.341375520421459E-01, 1.152087899889739E-02, \ 4.542210356062989E-01, 7.958468688022844E-01, 1.794582284359643E-02, \ 4.994044935070279E-01, -6.099462217677528E-01, 3.154922279377764E-02, \ 5.158924660295786E-01, 4.251904122231722E-01, 3.560324497451925E-02, \ 5.159801356223465E-01, -9.489058642290333E-01, 1.356103767266921E-02, \ 5.177821997159030E-01, 4.860941365404695E-01, 4.035705383914671E-03, \ 5.185875206855339E-01, -8.093271136372929E-01, 2.465400557427630E-02, \ 5.207225999437588E-01, -2.085864473946192E-01, 2.344644441982280E-02, \ 5.391683921956473E-01, 9.726355827179098E-01, 9.266285418087179E-03, \ 5.435737968160658E-01, 7.127399923480068E-02, 4.496806151459203E-02, \ 5.482102814487624E-01, -4.226896138717067E-01, 1.428889064276768E-02, \ 5.572474716940677E-01, 6.686420737982589E-01, 3.083669208006901E-02, \ 5.748230680261558E-01, 8.760965122066653E-01, 1.943926421467558E-02, \ 5.844710675512947E-01, -2.592109992058108E-01, 2.283706283744573E-02, \ 6.143455982549889E-01, -9.920826636566066E-01, 4.351963504883606E-03, \ 6.308221736554908E-01, 2.945267523482654E-01, 3.146868659787020E-02, \ 6.404909510129633E-01, -4.864679391303438E-01, 2.960589457868493E-02, \ 6.406772691253437E-01, -7.139228812806040E-01, 2.272673241453971E-02, \ 6.499799074317244E-01, -8.924083156022753E-01, 1.749067931565174E-02, \ 6.598249437273979E-01, 9.948642685624477E-01, 2.808772731098325E-03, \ 6.758525517932752E-01, 5.427274842488018E-01, 3.178580319617729E-02, \ 6.787362302215644E-01, -8.353105038445782E-02, 3.660462342407370E-02, \ 6.848525475182752E-01, 7.813397580356689E-01, 2.347027715648843E-02, \ 6.897531031934704E-01, -6.782883935108303E-01, 6.655878361359627E-03, \ 7.005552670374735E-01, 9.406601330339404E-01, 1.246369990823231E-02, \ 7.084311098316746E-01, 1.768747230410797E-01, 2.397513960514677E-02, \ 7.295286264509984E-01, -9.665226078227548E-01, 8.147629083103793E-03, \ 7.328136392431331E-01, -2.875348312510743E-01, 1.087089248290535E-02, \ 7.450492234413376E-01, -3.427381908986717E-01, 2.313801537268639E-02, \ 7.640326515570037E-01, -8.125887805195392E-01, 1.949174894848284E-02, \ 7.704963456494349E-01, -5.900999992322654E-01, 2.533980569560729E-02, \ 7.796834866912661E-01, 3.994715783200819E-01, 2.994104825767884E-02, \ 7.887652330718642E-01, 6.709289186517926E-01, 2.371430123275542E-02, \ 7.904587180395604E-01, 3.698232163504092E-02, 2.186616762504613E-02, \ 7.981120997224805E-01, 9.863110488956950E-01, 4.428350131300970E-03, \ 7.985152091160521E-01, 8.693626506598062E-01, 1.561754453690349E-02, \ 8.166426016882831E-01, -9.271485107406205E-01, 7.934960713327414E-03, \ 8.174385098192266E-01, -9.961711079884141E-01, 2.165794610184791E-03, \ 8.228302442461702E-01, 1.697016693626475E-01, 1.342647121783435E-02, \ 8.358095013326707E-01, -1.733093930153186E-01, 2.670539971994917E-02, \ 8.562600324120904E-01, -4.495124318073283E-01, 2.357983853078307E-02, \ 8.610711834248425E-01, -7.150978677167033E-01, 1.850564562244901E-02, \ 8.688253850828861E-01, 9.504355153693655E-01, 7.016335896084859E-03, \ 8.722180260064613E-01, -8.841005984426642E-01, 8.223856754800985E-03, \ 8.735663725309100E-01, 5.411359973847757E-01, 2.141510206682392E-02, \ 8.824467573040489E-01, 2.752146559569857E-01, 2.057326622412542E-02, \ 8.829230087690153E-01, 7.770114466508429E-01, 1.555785382570586E-02, \ 8.999935234232900E-01, -9.752903231391948E-01, 4.574852292020883E-03, \ 9.057117846078058E-01, -4.659054057320846E-02, 9.353615677783169E-03, \ 9.119151052554647E-01, 4.274927442267495E-02, 1.424779189715308E-02, \ 9.211763298375819E-01, 9.934526556341349E-01, 2.003191789183488E-03, \ 9.245462285990703E-01, -2.974342857591706E-01, 1.847140993304593E-02, \ 9.283184737295814E-01, -5.879017021514434E-01, 1.561783824168382E-02, \ 9.290486544464471E-01, 8.950190921642169E-01, 7.779964394420137E-03, \ 9.317772095678226E-01, -8.201150672577782E-01, 9.940838732765474E-03, \ 9.446169086076862E-01, 4.135452324650374E-01, 1.479906753649862E-02, \ 9.449990557642718E-01, 6.629472122415720E-01, 1.284843891927071E-02, \ 9.504683215166834E-01, -9.376314986069719E-01, 4.086139127613287E-03, \ 9.638166221951805E-01, 1.751088896720577E-01, 1.281494987287384E-02, \ 9.658674622089268E-01, -9.953452266059633E-01, 1.102717947131251E-03, \ 9.694166462805192E-01, -1.256612526452283E-01, 1.203688131505905E-02, \ 9.698067055262342E-01, 9.633285091443817E-01, 3.282158060938487E-03, \ 9.726572697503230E-01, 8.181619946621148E-01, 6.464658905526641E-03, \ 9.739587062789258E-01, -4.439901118287898E-01, 1.034505230549930E-02, \ 9.740062631571137E-01, -7.162386303873299E-01, 7.887232214456035E-03, \ 9.810071147719678E-01, -8.985653300431585E-01, 3.181435032108599E-03, \ 9.861727841676639E-01, 5.400704381496431E-01, 6.797444141494801E-03, \ 9.930202681222473E-01, 3.214092657950156E-01, 4.905950396961080E-03, \ 9.937038655576630E-01, 9.931050540649843E-01, 4.830386117047890E-04, \ 9.943677037885296E-01, -9.710410041880194E-01, 1.118097006661641E-03, \ 9.943750550352027E-01, 3.487179202856331E-02, 4.548201806973092E-03, \ 9.949775104476455E-01, 7.198973208744759E-01, 2.841977406946536E-03, \ 9.952722138287154E-01, -2.785041956973013E-01, 4.045664611880734E-03, \ 9.954067560360648E-01, 9.074145716693054E-01, 1.810898452206362E-03, \ 9.959258876623405E-01, -8.226232166208993E-01, 1.978505799274471E-03, \ 9.963054076831271E-01, -5.895227652492729E-01, 3.040448117975760E-03 ] ) return xyw def smr35s ( ): #*****************************************************************************80 # ## smr35S returns the rotationally invariant SMR rule of degree 35. # # Discussion: # # DEGREE: 35 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 220 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 6.54962E-03, \ # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*220), the requested rule. # import numpy as np xyw = np.array ( [ \ 4.889904361809121E-03, 1.619503174532069E-01, 5.226179892467336E-02, \ 1.430680275835659E-02, 4.693240762340044E-01, 4.679625079080703E-02, \ 1.814469250768224E-01, 6.009339848917693E-01, 4.158929555209646E-02, \ 3.513535787046233E-02, 9.092730028762068E-01, 2.186232237110550E-02, \ 7.640565697368758E-02, 9.941574902382558E-01, 4.878857836280798E-03, \ 1.713276929018882E-01, 3.150081208611397E-01, 4.954187274939539E-02, \ 1.878090789211163E-01, 8.240874417949644E-01, 2.885775015170009E-02, \ 3.641585032828187E-01, 8.926397561302795E-01, 1.380108158872173E-02, \ 3.369795025432279E-01, 8.976793330525874E-01, 7.578776426504399E-03, \ 2.085987555621641E-01, 9.589188503432696E-01, 1.412626006558690E-02, \ 3.243221451814440E-01, 1.522018736597065E-01, 4.954596092265034E-02, \ 3.340889484224165E-01, 4.585908563274512E-01, 4.430990763422363E-02, \ 3.416707320282502E-01, 7.180689168234468E-01, 3.441280383837739E-02, \ 5.024923591323561E-01, 8.083923344052878E-01, 2.637941189985826E-02, \ 4.874255868918486E-01, 9.513870810486795E-01, 1.250237621770788E-02, \ 3.540377809173803E-01, 9.907757451385623E-01, 5.795738840614077E-03, \ 6.111391703621065E-01, 1.419989823593704E-01, 4.138723814719325E-02, \ 4.786194165434669E-01, 3.040699140137090E-01, 4.424656646443821E-02, \ 4.861267145306208E-01, 5.913669578961687E-01, 3.721264812187189E-02, \ 6.345277961643816E-01, 6.987872435915059E-01, 2.910424842344178E-02, \ 6.280256760699003E-01, 8.900123914565822E-01, 1.728479546144200E-02, \ 5.638455934275640E-01, 9.906924665049914E-01, 3.999894615639466E-03, \ 7.357593544096634E-01, 2.940516185138239E-01, 3.430970133414903E-02, \ 6.187418092262584E-01, 4.486490710363784E-01, 3.718438978370203E-02, \ 7.505794530276153E-01, 5.696684149936826E-01, 2.884692065902148E-02, \ 7.475454182228141E-01, 8.033938822693132E-01, 2.018681888060652E-02, \ 6.695740390881190E-01, 9.620089635211753E-01, 5.992235715031513E-03, \ 7.137131446338533E-01, 9.946730046954464E-01, 2.252933356555567E-03, \ 7.266647735941557E-01, -2.452226684020481E-02, 3.613466911375480E-02, \ 8.470677884177439E-01, 4.244997249111068E-01, 2.562278510791793E-02, \ 8.461060260934473E-01, 6.944065541165793E-01, 2.014809941680893E-02, \ 7.673369976264737E-01, 9.139571921846420E-01, 5.720892850954219E-03, \ 7.837945110129694E-01, 9.598803080155067E-01, 5.594606457330472E-03, \ 8.527052966458518E-01, 9.899482390180141E-01, 3.064017911530195E-03, \ 8.330453451104365E-01, 1.306648127961336E-01, 2.910519731720890E-02, \ 9.208363926514060E-01, 5.648082314710416E-01, 1.681694481057345E-02, \ 8.555714597948697E-01, 8.421130303734168E-01, 3.389803494740707E-03, \ 8.569746510423235E-01, 8.904703192599482E-01, 8.892049582448583E-03, \ 9.163957789950904E-01, 9.512153808029943E-01, 5.736088538001383E-03, \ 9.468183474113080E-01, 9.935269656304787E-01, 1.198934044159158E-03, \ 9.709743906771017E-01, 1.015883859290755E-01, 1.259776829311839E-02, \ 9.211304080943010E-01, 2.672344770872243E-01, 2.012412691259350E-02, \ 9.720064559847991E-01, 4.216836904760396E-01, 1.141976686833465E-02, \ 9.932227888701425E-01, 6.482010598302427E-01, -1.475608411232590E-03, \ 9.826552234357039E-01, 6.932083351123020E-01, 4.286571189420782E-03, \ 9.238348699268808E-01, 7.973265219048701E-01, 1.108551064645477E-02, \ 9.785171113227352E-01, 9.731930158842385E-01, 1.481797407435137E-03, \ 9.963425748043122E-01, 2.646515091977871E-01, 3.893391747905868E-03, \ 9.988925112672711E-01, 4.106568212342961E-01, -1.617960722779276E-04, \ 9.959215572099368E-01, 5.751170429423320E-01, 3.902216245624410E-03, \ 9.640572980293431E-01, 6.867546611123180E-01, 5.691309854696837E-03, \ 9.945462995891214E-01, 8.085573402233180E-01, 2.563895647702530E-03, \ 9.670114428073955E-01, 8.888800101355042E-01, 5.609754500116319E-03, \ 9.958210056699377E-01, 9.383693663697456E-01, 1.047624717542818E-03, \ 9.943379392579890E-01, 9.949415630191232E-01, 2.607250337397194E-04, \ -1.619503174532069E-01, 4.889904361809121E-03, 5.226179892467336E-02, \ -4.693240762340044E-01, 1.430680275835659E-02, 4.679625079080703E-02, \ -6.009339848917693E-01, 1.814469250768224E-01, 4.158929555209646E-02, \ -9.092730028762068E-01, 3.513535787046233E-02, 2.186232237110550E-02, \ -9.941574902382558E-01, 7.640565697368758E-02, 4.878857836280798E-03, \ -3.150081208611397E-01, 1.713276929018882E-01, 4.954187274939539E-02, \ -8.240874417949644E-01, 1.878090789211163E-01, 2.885775015170009E-02, \ -8.926397561302795E-01, 3.641585032828187E-01, 1.380108158872173E-02, \ -8.976793330525874E-01, 3.369795025432279E-01, 7.578776426504399E-03, \ -9.589188503432696E-01, 2.085987555621641E-01, 1.412626006558690E-02, \ -1.522018736597065E-01, 3.243221451814440E-01, 4.954596092265034E-02, \ -4.585908563274512E-01, 3.340889484224165E-01, 4.430990763422363E-02, \ -7.180689168234468E-01, 3.416707320282502E-01, 3.441280383837739E-02, \ -8.083923344052878E-01, 5.024923591323561E-01, 2.637941189985826E-02, \ -9.513870810486795E-01, 4.874255868918486E-01, 1.250237621770788E-02, \ -9.907757451385623E-01, 3.540377809173803E-01, 5.795738840614077E-03, \ -1.419989823593704E-01, 6.111391703621065E-01, 4.138723814719325E-02, \ -3.040699140137090E-01, 4.786194165434669E-01, 4.424656646443821E-02, \ -5.913669578961687E-01, 4.861267145306208E-01, 3.721264812187189E-02, \ -6.987872435915059E-01, 6.345277961643816E-01, 2.910424842344178E-02, \ -8.900123914565822E-01, 6.280256760699003E-01, 1.728479546144200E-02, \ -9.906924665049914E-01, 5.638455934275640E-01, 3.999894615639466E-03, \ -2.940516185138239E-01, 7.357593544096634E-01, 3.430970133414903E-02, \ -4.486490710363784E-01, 6.187418092262584E-01, 3.718438978370203E-02, \ -5.696684149936826E-01, 7.505794530276153E-01, 2.884692065902148E-02, \ -8.033938822693132E-01, 7.475454182228141E-01, 2.018681888060652E-02, \ -9.620089635211753E-01, 6.695740390881190E-01, 5.992235715031513E-03, \ -9.946730046954464E-01, 7.137131446338533E-01, 2.252933356555567E-03, \ 2.452226684020481E-02, 7.266647735941557E-01, 3.613466911375480E-02, \ -4.244997249111068E-01, 8.470677884177439E-01, 2.562278510791793E-02, \ -6.944065541165793E-01, 8.461060260934473E-01, 2.014809941680893E-02, \ -9.139571921846420E-01, 7.673369976264737E-01, 5.720892850954219E-03, \ -9.598803080155067E-01, 7.837945110129694E-01, 5.594606457330472E-03, \ -9.899482390180141E-01, 8.527052966458518E-01, 3.064017911530195E-03, \ -1.306648127961336E-01, 8.330453451104365E-01, 2.910519731720890E-02, \ -5.648082314710416E-01, 9.208363926514060E-01, 1.681694481057345E-02, \ -8.421130303734168E-01, 8.555714597948697E-01, 3.389803494740707E-03, \ -8.904703192599482E-01, 8.569746510423235E-01, 8.892049582448583E-03, \ -9.512153808029943E-01, 9.163957789950904E-01, 5.736088538001383E-03, \ -9.935269656304787E-01, 9.468183474113080E-01, 1.198934044159158E-03, \ -1.015883859290755E-01, 9.709743906771017E-01, 1.259776829311839E-02, \ -2.672344770872243E-01, 9.211304080943010E-01, 2.012412691259350E-02, \ -4.216836904760396E-01, 9.720064559847991E-01, 1.141976686833465E-02, \ -6.482010598302427E-01, 9.932227888701425E-01, -1.475608411232590E-03, \ -6.932083351123020E-01, 9.826552234357039E-01, 4.286571189420782E-03, \ -7.973265219048701E-01, 9.238348699268808E-01, 1.108551064645477E-02, \ -9.731930158842385E-01, 9.785171113227352E-01, 1.481797407435137E-03, \ -2.646515091977871E-01, 9.963425748043122E-01, 3.893391747905868E-03, \ -4.106568212342961E-01, 9.988925112672711E-01, -1.617960722779276E-04, \ -5.751170429423320E-01, 9.959215572099368E-01, 3.902216245624410E-03, \ -6.867546611123180E-01, 9.640572980293431E-01, 5.691309854696837E-03, \ -8.085573402233180E-01, 9.945462995891214E-01, 2.563895647702530E-03, \ -8.888800101355042E-01, 9.670114428073955E-01, 5.609754500116319E-03, \ -9.383693663697456E-01, 9.958210056699377E-01, 1.047624717542818E-03, \ -9.949415630191232E-01, 9.943379392579890E-01, 2.607250337397194E-04, \ -4.889904361809121E-03, -1.619503174532069E-01, 5.226179892467336E-02, \ -1.430680275835659E-02, -4.693240762340044E-01, 4.679625079080703E-02, \ -1.814469250768224E-01, -6.009339848917693E-01, 4.158929555209646E-02, \ -3.513535787046233E-02, -9.092730028762068E-01, 2.186232237110550E-02, \ -7.640565697368758E-02, -9.941574902382558E-01, 4.878857836280798E-03, \ -1.713276929018882E-01, -3.150081208611397E-01, 4.954187274939539E-02, \ -1.878090789211163E-01, -8.240874417949644E-01, 2.885775015170009E-02, \ -3.641585032828187E-01, -8.926397561302795E-01, 1.380108158872173E-02, \ -3.369795025432279E-01, -8.976793330525874E-01, 7.578776426504399E-03, \ -2.085987555621641E-01, -9.589188503432696E-01, 1.412626006558690E-02, \ -3.243221451814440E-01, -1.522018736597065E-01, 4.954596092265034E-02, \ -3.340889484224165E-01, -4.585908563274512E-01, 4.430990763422363E-02, \ -3.416707320282502E-01, -7.180689168234468E-01, 3.441280383837739E-02, \ -5.024923591323561E-01, -8.083923344052878E-01, 2.637941189985826E-02, \ -4.874255868918486E-01, -9.513870810486795E-01, 1.250237621770788E-02, \ -3.540377809173803E-01, -9.907757451385623E-01, 5.795738840614077E-03, \ -6.111391703621065E-01, -1.419989823593704E-01, 4.138723814719325E-02, \ -4.786194165434669E-01, -3.040699140137090E-01, 4.424656646443821E-02, \ -4.861267145306208E-01, -5.913669578961687E-01, 3.721264812187189E-02, \ -6.345277961643816E-01, -6.987872435915059E-01, 2.910424842344178E-02, \ -6.280256760699003E-01, -8.900123914565822E-01, 1.728479546144200E-02, \ -5.638455934275640E-01, -9.906924665049914E-01, 3.999894615639466E-03, \ -7.357593544096634E-01, -2.940516185138239E-01, 3.430970133414903E-02, \ -6.187418092262584E-01, -4.486490710363784E-01, 3.718438978370203E-02, \ -7.505794530276153E-01, -5.696684149936826E-01, 2.884692065902148E-02, \ -7.475454182228141E-01, -8.033938822693132E-01, 2.018681888060652E-02, \ -6.695740390881190E-01, -9.620089635211753E-01, 5.992235715031513E-03, \ -7.137131446338533E-01, -9.946730046954464E-01, 2.252933356555567E-03, \ -7.266647735941557E-01, 2.452226684020481E-02, 3.613466911375480E-02, \ -8.470677884177439E-01, -4.244997249111068E-01, 2.562278510791793E-02, \ -8.461060260934473E-01, -6.944065541165793E-01, 2.014809941680893E-02, \ -7.673369976264737E-01, -9.139571921846420E-01, 5.720892850954219E-03, \ -7.837945110129694E-01, -9.598803080155067E-01, 5.594606457330472E-03, \ -8.527052966458518E-01, -9.899482390180141E-01, 3.064017911530195E-03, \ -8.330453451104365E-01, -1.306648127961336E-01, 2.910519731720890E-02, \ -9.208363926514060E-01, -5.648082314710416E-01, 1.681694481057345E-02, \ -8.555714597948697E-01, -8.421130303734168E-01, 3.389803494740707E-03, \ -8.569746510423235E-01, -8.904703192599482E-01, 8.892049582448583E-03, \ -9.163957789950904E-01, -9.512153808029943E-01, 5.736088538001383E-03, \ -9.468183474113080E-01, -9.935269656304787E-01, 1.198934044159158E-03, \ -9.709743906771017E-01, -1.015883859290755E-01, 1.259776829311839E-02, \ -9.211304080943010E-01, -2.672344770872243E-01, 2.012412691259350E-02, \ -9.720064559847991E-01, -4.216836904760396E-01, 1.141976686833465E-02, \ -9.932227888701425E-01, -6.482010598302427E-01, -1.475608411232590E-03, \ -9.826552234357039E-01, -6.932083351123020E-01, 4.286571189420782E-03, \ -9.238348699268808E-01, -7.973265219048701E-01, 1.108551064645477E-02, \ -9.785171113227352E-01, -9.731930158842385E-01, 1.481797407435137E-03, \ -9.963425748043122E-01, -2.646515091977871E-01, 3.893391747905868E-03, \ -9.988925112672711E-01, -4.106568212342961E-01, -1.617960722779276E-04, \ -9.959215572099368E-01, -5.751170429423320E-01, 3.902216245624410E-03, \ -9.640572980293431E-01, -6.867546611123180E-01, 5.691309854696837E-03, \ -9.945462995891214E-01, -8.085573402233180E-01, 2.563895647702530E-03, \ -9.670114428073955E-01, -8.888800101355042E-01, 5.609754500116319E-03, \ -9.958210056699377E-01, -9.383693663697456E-01, 1.047624717542818E-03, \ -9.943379392579890E-01, -9.949415630191232E-01, 2.607250337397194E-04, \ 1.619503174532069E-01, -4.889904361809121E-03, 5.226179892467336E-02, \ 4.693240762340044E-01, -1.430680275835659E-02, 4.679625079080703E-02, \ 6.009339848917693E-01, -1.814469250768224E-01, 4.158929555209646E-02, \ 9.092730028762068E-01, -3.513535787046233E-02, 2.186232237110550E-02, \ 9.941574902382558E-01, -7.640565697368758E-02, 4.878857836280798E-03, \ 3.150081208611397E-01, -1.713276929018882E-01, 4.954187274939539E-02, \ 8.240874417949644E-01, -1.878090789211163E-01, 2.885775015170009E-02, \ 8.926397561302795E-01, -3.641585032828187E-01, 1.380108158872173E-02, \ 8.976793330525874E-01, -3.369795025432279E-01, 7.578776426504399E-03, \ 9.589188503432696E-01, -2.085987555621641E-01, 1.412626006558690E-02, \ 1.522018736597065E-01, -3.243221451814440E-01, 4.954596092265034E-02, \ 4.585908563274512E-01, -3.340889484224165E-01, 4.430990763422363E-02, \ 7.180689168234468E-01, -3.416707320282502E-01, 3.441280383837739E-02, \ 8.083923344052878E-01, -5.024923591323561E-01, 2.637941189985826E-02, \ 9.513870810486795E-01, -4.874255868918486E-01, 1.250237621770788E-02, \ 9.907757451385623E-01, -3.540377809173803E-01, 5.795738840614077E-03, \ 1.419989823593704E-01, -6.111391703621065E-01, 4.138723814719325E-02, \ 3.040699140137090E-01, -4.786194165434669E-01, 4.424656646443821E-02, \ 5.913669578961687E-01, -4.861267145306208E-01, 3.721264812187189E-02, \ 6.987872435915059E-01, -6.345277961643816E-01, 2.910424842344178E-02, \ 8.900123914565822E-01, -6.280256760699003E-01, 1.728479546144200E-02, \ 9.906924665049914E-01, -5.638455934275640E-01, 3.999894615639466E-03, \ 2.940516185138239E-01, -7.357593544096634E-01, 3.430970133414903E-02, \ 4.486490710363784E-01, -6.187418092262584E-01, 3.718438978370203E-02, \ 5.696684149936826E-01, -7.505794530276153E-01, 2.884692065902148E-02, \ 8.033938822693132E-01, -7.475454182228141E-01, 2.018681888060652E-02, \ 9.620089635211753E-01, -6.695740390881190E-01, 5.992235715031513E-03, \ 9.946730046954464E-01, -7.137131446338533E-01, 2.252933356555567E-03, \ -2.452226684020481E-02, -7.266647735941557E-01, 3.613466911375480E-02, \ 4.244997249111068E-01, -8.470677884177439E-01, 2.562278510791793E-02, \ 6.944065541165793E-01, -8.461060260934473E-01, 2.014809941680893E-02, \ 9.139571921846420E-01, -7.673369976264737E-01, 5.720892850954219E-03, \ 9.598803080155067E-01, -7.837945110129694E-01, 5.594606457330472E-03, \ 9.899482390180141E-01, -8.527052966458518E-01, 3.064017911530195E-03, \ 1.306648127961336E-01, -8.330453451104365E-01, 2.910519731720890E-02, \ 5.648082314710416E-01, -9.208363926514060E-01, 1.681694481057345E-02, \ 8.421130303734168E-01, -8.555714597948697E-01, 3.389803494740707E-03, \ 8.904703192599482E-01, -8.569746510423235E-01, 8.892049582448583E-03, \ 9.512153808029943E-01, -9.163957789950904E-01, 5.736088538001383E-03, \ 9.935269656304787E-01, -9.468183474113080E-01, 1.198934044159158E-03, \ 1.015883859290755E-01, -9.709743906771017E-01, 1.259776829311839E-02, \ 2.672344770872243E-01, -9.211304080943010E-01, 2.012412691259350E-02, \ 4.216836904760396E-01, -9.720064559847991E-01, 1.141976686833465E-02, \ 6.482010598302427E-01, -9.932227888701425E-01, -1.475608411232590E-03, \ 6.932083351123020E-01, -9.826552234357039E-01, 4.286571189420782E-03, \ 7.973265219048701E-01, -9.238348699268808E-01, 1.108551064645477E-02, \ 9.731930158842385E-01, -9.785171113227352E-01, 1.481797407435137E-03, \ 2.646515091977871E-01, -9.963425748043122E-01, 3.893391747905868E-03, \ 4.106568212342961E-01, -9.988925112672711E-01, -1.617960722779276E-04, \ 5.751170429423320E-01, -9.959215572099368E-01, 3.902216245624410E-03, \ 6.867546611123180E-01, -9.640572980293431E-01, 5.691309854696837E-03, \ 8.085573402233180E-01, -9.945462995891214E-01, 2.563895647702530E-03, \ 8.888800101355042E-01, -9.670114428073955E-01, 5.609754500116319E-03, \ 9.383693663697456E-01, -9.958210056699377E-01, 1.047624717542818E-03, \ 9.949415630191232E-01, -9.943379392579890E-01, 2.607250337397194E-04 ] ) return xyw def smr36 ( ): #*****************************************************************************80 # ## smr36 returns the SMR rule of degree 36. # # Discussion: # # DEGREE: 36 # POINTS CARDINALITY: 238 # NORM INF MOMS. RESIDUAL: 4.27609e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*238), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.978817227614055E-01, -8.890076517204608E-04, 2.330741632674278E-03, \ -9.973711646404451E-01, -9.532092615783677E-01, 9.627969193226537E-04, \ -9.961692635944124E-01, 9.688495936611794E-01, 8.898973486835064E-04, \ -9.959497922009879E-01, -3.098803144458146E-01, 2.832831652522147E-03, \ -9.959465092993447E-01, -5.592627350774092E-01, 2.519247595249725E-03, \ -9.954980310007229E-01, 6.046856101951658E-01, 2.958064214592169E-03, \ -9.946662450102303E-01, 3.416260049342602E-01, 3.892327512506448E-03, \ -9.934973736752050E-01, -7.316617433785163E-01, 2.288706827417947E-03, \ -9.917053480435074E-01, 8.702611598150070E-01, 1.958941400105963E-03, \ -9.916694420714898E-01, 7.809558409845563E-01, 2.395428553360631E-03, \ -9.895910809889403E-01, -8.396046316830745E-01, 2.802701148321813E-03, \ -9.831331889300642E-01, 1.393223594054985E-01, 6.694472389602429E-03, \ -9.807631633241672E-01, -1.600365161997248E-01, 7.382399101251368E-03, \ -9.798886059262791E-01, -9.915282494038506E-01, 1.128746425663043E-03, \ -9.750680034434991E-01, -4.311357357378125E-01, 7.832140397353063E-03, \ -9.728412562557132E-01, 9.944489940720668E-01, 1.002140135620488E-03, \ -9.710537275206133E-01, 4.830250325748792E-01, 9.568264880729656E-03, \ -9.689535066576080E-01, -9.071389361410935E-01, 4.309260818499709E-03, \ -9.687604103109784E-01, -6.302344727365032E-01, 6.664551467651576E-03, \ -9.687211535263930E-01, 9.237100995654350E-01, 4.080017523260788E-03, \ -9.668485420668568E-01, 7.049532664378062E-01, 7.415218794906055E-03, \ -9.535784368796688E-01, 2.490218550690452E-01, 1.037891180826214E-02, \ -9.512663640224540E-01, -7.491171041425378E-01, 7.422605405628350E-03, \ -9.493818109732231E-01, -2.852036250206639E-02, 1.195246886959401E-02, \ -9.367870389253897E-01, 8.258762212688808E-01, 8.844488878029041E-03, \ -9.363513457140649E-01, -2.859985380532227E-01, 1.380555928314730E-02, \ -9.360696971408200E-01, -9.644084451245751E-01, 4.146894859108681E-03, \ -9.239202364264265E-01, 9.695178305424945E-01, 4.259509443297511E-03, \ -9.225706959239526E-01, -5.058509463174830E-01, 1.253905649616530E-02, \ -9.179832388286352E-01, 6.014333969026019E-01, 1.426678903924167E-02, \ -9.149034273351938E-01, -8.372226403884956E-01, 9.334389760441908E-03, \ -9.138551873238143E-01, 3.754959341345724E-01, 1.452036035160031E-02, \ -8.996791165793870E-01, 9.328644693068573E-02, 1.734677366105503E-02, \ -8.885447268542435E-01, -6.386179822823047E-01, 1.367023050135804E-02, \ -8.871714117838472E-01, -9.948601599114012E-01, 1.899222828399880E-03, \ -8.816880330919030E-01, -1.586021131310660E-01, 1.669820902512087E-02, \ -8.812403173103464E-01, 8.951164258907871E-01, 8.364155027998615E-03, \ -8.656692388301289E-01, 7.350500859830660E-01, 1.548010198333609E-02, \ -8.643529629348047E-01, -9.173100142874313E-01, 9.120730562086893E-03, \ -8.641286582087778E-01, 9.950657916116978E-01, 1.918170304192286E-03, \ -8.522612942302550E-01, -3.788264332914240E-01, 2.087884271099431E-02, \ -8.422113258119911E-01, 2.446382041130486E-01, 2.002609499764870E-02, \ -8.416694599504575E-01, 4.814984345703843E-01, 1.925007441204762E-02, \ -8.360902062521303E-01, -7.477119396150796E-01, 1.554744797988430E-02, \ -8.203145632717700E-01, -5.613317466249494E-02, 1.901567227303284E-02, \ -8.199490742198897E-01, 9.428287492604916E-01, 7.056116422992586E-03, \ -7.984923809331644E-01, -9.722593485667060E-01, 6.504144377884679E-03, \ -7.937886622074718E-01, -5.311719776256463E-01, 2.203842796899376E-02, \ -7.898800883541095E-01, 8.213759805863565E-01, 1.360908524722615E-02, \ -7.857456450301465E-01, 6.109453946109499E-01, 1.776520678097427E-02, \ -7.707528347691809E-01, 1.109546864852665E-01, 2.039092251468907E-02, \ -7.702900422534331E-01, -8.487764338033230E-01, 1.532480873697326E-02, \ -7.576331295741205E-01, -2.435713966271017E-01, 2.854257229107140E-02, \ -7.569151133259240E-01, 9.814581630123478E-01, 4.921916895711927E-03, \ -7.438369227242233E-01, 3.482222843377805E-01, 2.451979727480189E-02, \ -7.241630175636773E-01, -6.592065655597069E-01, 2.199849707676197E-02, \ -7.176692539981274E-01, 8.801116546686418E-01, 1.112305619521462E-02, \ -7.124686946589255E-01, 6.945133493012733E-01, 1.771156252011625E-02, \ -7.069737778502420E-01, -9.962628623410572E-01, 2.374966048245442E-03, \ -6.963043004286823E-01, -8.135105429081526E-03, 2.318695224198078E-02, \ -6.921249477814184E-01, 4.700703121100537E-01, 1.655699575608719E-02, \ -6.892915677631921E-01, -9.267197507187467E-01, 1.257447358342760E-02, \ -6.785922159896439E-01, -4.067666128583923E-01, 2.999698423607718E-02, \ -6.552506919956539E-01, 9.423928975555224E-01, 9.667568404627368E-03, \ -6.449800715385902E-01, -7.742900371415136E-01, 2.163194611984287E-02, \ -6.384020750298662E-01, 2.053842735458858E-01, 3.298168414587938E-02, \ -6.376845625430727E-01, 9.961884415103500E-01, 2.510551666922923E-03, \ -6.198393609997173E-01, 7.788946966190957E-01, 2.119226728365691E-02, \ -6.187213657289741E-01, -1.433838420063922E-01, 3.147480251378770E-02, \ -6.160766221019519E-01, 5.525549239562721E-01, 2.501384151648360E-02, \ -5.942484471471827E-01, -5.523398131727161E-01, 2.880932433502099E-02, \ -5.886645820614776E-01, -9.742244390227165E-01, 7.791673063038694E-03, \ -5.491885966414285E-01, -8.701566014002242E-01, 1.925267375227190E-02, \ -5.454451806767899E-01, 8.873611141110606E-01, 1.421144648662051E-02, \ -5.363668460871786E-01, 3.689903490268424E-01, 3.551950638985276E-02, \ -5.288973102226180E-01, -3.000753546210893E-01, 3.577864794644277E-02, \ -5.228971037176965E-01, 5.511893622125074E-02, 3.559238125168576E-02, \ -5.149484349272324E-01, 9.736990573228385E-01, 8.663852126555528E-03, \ -5.034028322638731E-01, -6.810046891007370E-01, 2.770229125683340E-02, \ -5.018240598484098E-01, 6.610827773551222E-01, 2.955164458688282E-02, \ -4.836723369928086E-01, -9.951317872137048E-01, 2.432216069339591E-03, \ -4.472178273697551E-01, 8.261234039804835E-01, 1.723994440057944E-02, \ -4.351671626526074E-01, -9.405635523740720E-01, 1.391944650569191E-02, \ -4.325000537322283E-01, -4.571254404046099E-01, 3.550196939096451E-02, \ -4.221899486344116E-01, 2.072870640590052E-01, 2.856147506087960E-02, \ -4.184381906407810E-01, -9.486272782368495E-02, 3.647913743103923E-02, \ -4.051084329362841E-01, 4.968069795284735E-01, 3.427981654195449E-02, \ -3.996415711088327E-01, -7.922180602255362E-01, 2.534465150429595E-02, \ -3.802275025133069E-01, 9.957850696595502E-01, 3.171371339804449E-03, \ -3.746724165491376E-01, 9.322066554008961E-01, 1.474166848943957E-02, \ -3.507030139156035E-01, 7.411784897062579E-01, 2.164321207016425E-02, \ -3.396094592441956E-01, 2.851648864371023E-01, 2.378767233475549E-02, \ -3.373067518851020E-01, -9.891744514862336E-01, 4.703010171973971E-03, \ -3.310224303024400E-01, -2.403265390297470E-01, 3.423310351714857E-02, \ -3.277966873918430E-01, -5.977752159941997E-01, 3.339651184485331E-02, \ -2.908043265646401E-01, 5.910702778731858E-01, 2.096575868118241E-02, \ -2.890360016090808E-01, -8.852915279552505E-01, 1.911208855887150E-02, \ -2.761160035464659E-01, 7.095757720766041E-02, 4.278824944215505E-02, \ -2.702812218851570E-01, 8.808141244965264E-01, 1.053036550496354E-02, \ -2.649298324354653E-01, 7.864553422973282E-01, 8.647185905965778E-03, \ -2.401609050863505E-01, 9.806596979744967E-01, 5.868860421996299E-03, \ -2.377667595528341E-01, -3.801643379704139E-01, 3.628804159235034E-02, \ -2.206216268941887E-01, -7.204121124667704E-01, 2.854623272707025E-02, \ -2.201538989416436E-01, 3.913115801581338E-01, 3.894518817033470E-02, \ -2.193792333441053E-01, -9.646669064229157E-01, 1.014429441651051E-02, \ -1.934707182262981E-01, 6.432496392898787E-01, 2.233474208920316E-02, \ -1.772628853095497E-01, 9.609427885428339E-01, 7.154337173291553E-03, \ -1.729141076933932E-01, 8.539977338065532E-01, 1.673175151833196E-02, \ -1.718150507993583E-01, -9.405721790034696E-02, 4.086787977428533E-02, \ -1.328625066941062E-01, -8.318318453990768E-01, 1.982971921305763E-02, \ -1.307387810744456E-01, -5.185641556580906E-01, 3.616547559993144E-02, \ -1.100824617462925E-01, 2.107790367554701E-01, 4.576013746563733E-02, \ -9.984259485045630E-02, -9.955064961031446E-01, 3.717433056480130E-03, \ -9.328608102993199E-02, 7.332290790832092E-01, 2.071715580387419E-02, \ -6.793914116753401E-02, -2.506459841110294E-01, 4.089224120208960E-02, \ -6.741335673585816E-02, -9.267152274199159E-01, 1.602534157276938E-02, \ -6.637788288034263E-02, 5.124518645869145E-01, 3.844362321627411E-02, \ -5.192619879677355E-02, 9.952626224499167E-01, 3.973984013870450E-03, \ -4.256393926237442E-02, -6.587648588333753E-01, 2.554184333603511E-02, \ -3.928908743269727E-02, 9.249275328206857E-01, 1.717155965123946E-02, \ -8.616254706753439E-03, 7.863971003772713E-01, 1.617333783082740E-02, \ 3.445686005032637E-03, 3.438556195988679E-02, 4.484896925422164E-02, \ 2.162783184909196E-02, -7.869560221084054E-01, 2.154792738605269E-02, \ 4.685825299635766E-02, -4.020978227292492E-01, 4.049427770416184E-02, \ 5.479814290878701E-02, 3.514969350769057E-01, 4.422512667927580E-02, \ 6.774629290604679E-02, -9.760182750123766E-01, 9.963602473671930E-03, \ 7.328667269147976E-02, -5.930557986747867E-01, 1.877217900127421E-02, \ 8.018258564306395E-02, 6.365101735574987E-01, 3.483121330550053E-02, \ 1.073043308069154E-01, 8.535066059079015E-01, 2.227117133691220E-02, \ 1.113229411695483E-01, -8.835075472889613E-01, 1.949085547150652E-02, \ 1.114570513525386E-01, 9.729484455626918E-01, 1.101932189177536E-02, \ 1.153437593007439E-01, -1.317768141870329E-01, 4.247315097231750E-02, \ 1.690835216382367E-01, 1.764988836591127E-01, 4.458603343706025E-02, \ 1.753955610939935E-01, -7.156031949485488E-01, 2.527623764375623E-02, \ 1.976972674748326E-01, -5.279953242568892E-01, 3.026255490382024E-02, \ 2.116967467449395E-01, 4.926985242614755E-01, 4.098066738615446E-02, \ 2.235223377254471E-01, 7.379223803362939E-01, 2.795309201248948E-02, \ 2.258353983807109E-01, -2.868829397355061E-01, 3.947306768337931E-02, \ 2.264823571880064E-01, -9.969471381094707E-01, 3.073985454466239E-03, \ 2.490851417470266E-01, -9.447796629842063E-01, 1.396431826192642E-02, \ 2.508519660769009E-01, 9.195561800757367E-01, 1.768832443081297E-02, \ 2.680482539332619E-01, -8.226935415045739E-01, 1.981797389395326E-02, \ 2.680721351751811E-01, 9.958511445825230E-01, 3.640429024869928E-03, \ 2.821534236058784E-01, 7.446925967702267E-03, 4.211100109823734E-02, \ 3.247146118763189E-01, 3.224964883167490E-01, 4.234100652772199E-02, \ 3.343254479054538E-01, -6.422924772737209E-01, 2.425454643455124E-02, \ 3.453396235355017E-01, -4.291253398815807E-01, 3.317163396355886E-02, \ 3.462605320455555E-01, 8.161845863833764E-01, 1.987362322109004E-02, \ 3.651493677371224E-01, 6.182965874272552E-01, 3.559824694190696E-02, \ 3.854996236485986E-01, -1.532257150482036E-01, 3.742508791404799E-02, \ 3.870016759773888E-01, -7.585686209099854E-01, 1.501299544256757E-02, \ 3.938946116638710E-01, 9.662848771953462E-01, 1.068691773232336E-02, \ 3.982573856142398E-01, -8.950554117718855E-01, 1.602448842253433E-02, \ 4.016801936992866E-01, -9.813691194805932E-01, 7.892152840793696E-03, \ 4.371070566774968E-01, 1.511026982040890E-01, 4.102768020962930E-02, \ 4.544035146465257E-01, 8.763928228014183E-01, 1.634600741893583E-02, \ 4.558293123288908E-01, -5.713496230258187E-01, 2.252028952268153E-02, \ 4.732557000280899E-01, 4.583389381205352E-01, 3.776384470597906E-02, \ 4.810692207812149E-01, -3.081467734409822E-01, 3.206248778671018E-02, \ 5.077103930139962E-01, -8.274029452105797E-01, 1.494395639519947E-02, \ 5.078271770180696E-01, 7.302517937446340E-01, 2.869995132952615E-02, \ 5.184597430790860E-01, 9.915516893623654E-01, 4.063313365916709E-03, \ 5.243768590626090E-01, -7.095143454551895E-01, 1.946548740642335E-02, \ 5.347672174839160E-01, -2.303639928245786E-02, 3.592243824739078E-02, \ 5.378718338501072E-01, -9.453203497305898E-01, 1.131041403550440E-02, \ 5.604528611741826E-01, -4.738251057279866E-01, 2.716710521567537E-02, \ 5.649480860981207E-01, -9.961787956204670E-01, 2.686662642257578E-03, \ 5.694785456537736E-01, 9.306241376040423E-01, 1.310983188725784E-02, \ 5.797726075345430E-01, 2.904464196731755E-01, 3.707917140022222E-02, \ 6.073441340190595E-01, 5.863537474015226E-01, 3.123083612446972E-02, \ 6.146619349973880E-01, -1.954577444891345E-01, 3.004097012228125E-02, \ 6.310711580799437E-01, -8.865377678376085E-01, 1.239250785539078E-02, \ 6.369188707330101E-01, 8.251358672704174E-01, 2.109369809774988E-02, \ 6.397822146063097E-01, 9.933516960588022E-01, 1.566823050510530E-03, \ 6.447025783419807E-01, -7.748327398433732E-01, 1.353919524034135E-02, \ 6.490923224989641E-01, -6.210654215758872E-01, 2.453036222700825E-02, \ 6.652852081461884E-01, 1.056429932263364E-01, 3.235059149781160E-02, \ 6.769243424161306E-01, -9.791782695964194E-01, 4.843329361124712E-03, \ 6.812487855144383E-01, -3.677376001017615E-01, 2.767580050018398E-02, \ 6.881611881783396E-01, 9.690785564088401E-01, 7.180152922776447E-03, \ 7.029917084563276E-01, 4.285118331295772E-01, 3.086990327791525E-02, \ 7.164764656784520E-01, -9.518583821949328E-01, 5.355105147941908E-03, \ 7.246902454799630E-01, 7.020207625777104E-01, 2.375449102290038E-02, \ 7.325693440295951E-01, -8.399374390925475E-01, 1.036024466955918E-02, \ 7.351112383538153E-01, -7.951756972515223E-02, 2.785001849780098E-02, \ 7.509928361696643E-01, 8.988638838541747E-01, 1.368741903606304E-02, \ 7.607007202364793E-01, -5.206337661298087E-01, 2.328103635760096E-02, \ 7.690593533802963E-01, -7.201514627550166E-01, 1.811779028755979E-02, \ 7.720233247908281E-01, 2.383646904389616E-01, 2.697895164503969E-02, \ 7.861129856968502E-01, 9.953733636825969E-01, 2.204660432176242E-03, \ 7.932635688940682E-01, -2.545931233040153E-01, 2.360509584832022E-02, \ 7.934795953540076E-01, -9.940911141191972E-01, 2.578022439771223E-03, \ 7.986501480724928E-01, -9.141670055638340E-01, 9.844477819414077E-03, \ 8.061029566945606E-01, 5.593366976508258E-01, 2.355691263970365E-02, \ 8.243070351881039E-01, 8.000279479141921E-01, 1.625476526376125E-02, \ 8.349061461503988E-01, 5.242989783303436E-02, 2.396763947561963E-02, \ 8.387086026393442E-01, 9.590800307491609E-01, 6.799333697297724E-03, \ 8.514060544957516E-01, -4.143618409619704E-01, 1.824968840166299E-02, \ 8.564000533604161E-01, 3.680409247826315E-01, 2.048685538595784E-02, \ 8.586490931530540E-01, -8.172679381074797E-01, 1.319146184667337E-02, \ 8.603733614050693E-01, -6.314782677843042E-01, 1.724870287833661E-02, \ 8.708025881828373E-01, -9.671023391671761E-01, 5.636725309105074E-03, \ 8.801258067547251E-01, -1.305377170691088E-01, 1.777128791266185E-02, \ 8.888526668725696E-01, 6.765021487498224E-01, 1.606206650402240E-02, \ 8.933099031235968E-01, 8.952281659692933E-01, 8.296408662073707E-03, \ 9.113602853210563E-01, 9.899169943701300E-01, 2.463722493435422E-03, \ 9.118722066757234E-01, 1.929776411231569E-01, 1.825776248523375E-02, \ 9.163929674501358E-01, -2.990041843102318E-01, 1.314634212775509E-02, \ 9.189017721547910E-01, 4.858317388925585E-01, 1.362028136343246E-02, \ 9.207066423332223E-01, -8.980672622897176E-01, 7.718082091266390E-03, \ 9.272785007117844E-01, -5.207581337916093E-01, 1.312690216075551E-02, \ 9.311020805101690E-01, 8.243210513505537E-01, 6.095543309002014E-03, \ 9.312327541844606E-01, -9.944089524999217E-01, 1.544072841043584E-03, \ 9.326765355471089E-01, -7.345782056816920E-01, 1.147121027748882E-02, \ 9.403087384697171E-01, -8.071436851387262E-03, 1.176918657324237E-02, \ 9.533497236250201E-01, 9.491647170059687E-01, 4.270793656586557E-03, \ 9.581432174025166E-01, 7.516220759263724E-01, 6.745942316173472E-03, \ 9.604046590298700E-01, 5.830153275767322E-01, 7.784720252720092E-03, \ 9.631077811144789E-01, -1.757985976531334E-01, 8.688657559223576E-03, \ 9.646721058936349E-01, 3.325578173839724E-01, 1.132962868101588E-02, \ 9.647811822781394E-01, -9.547975852433266E-01, 3.342959180531801E-03, \ 9.692409843048421E-01, -3.948453480534794E-01, 8.200365271055058E-03, \ 9.748844113653906E-01, -8.353669805015749E-01, 5.733917618965338E-03, \ 9.765605657096736E-01, -6.223778160859140E-01, 7.479750101379069E-03, \ 9.777781151583427E-01, 1.008331484661780E-01, 7.466802821144819E-03, \ 9.823248797734118E-01, 9.908257848386118E-01, 1.055477347697845E-03, \ 9.824013057546825E-01, 8.793077972340478E-01, 3.946153214787464E-03, \ 9.896592863949374E-01, 6.524183287421559E-01, 3.684068604731808E-03, \ 9.901852458780420E-01, -9.879591744269937E-01, 8.501750539953944E-04, \ 9.924040123666048E-01, -2.695088450767503E-01, 3.730991030920448E-03, \ 9.927679196128025E-01, 4.643954909265275E-01, 4.248272970481418E-03, \ 9.938098745051424E-01, -6.272470872855707E-02, 3.793703053258545E-03, \ 9.960268905980724E-01, -9.143875891227382E-01, 1.458149770534853E-03, \ 9.960772480893844E-01, 7.831338729008818E-01, 1.769564456969298E-03, \ 9.962805481813658E-01, -7.386272660484093E-01, 2.258142891171576E-03, \ 9.962980942352860E-01, -4.897161915618530E-01, 2.721379560273475E-03, \ 9.963851076303689E-01, 2.242470825907724E-01, 2.871929785587053E-03, \ 9.983360376701429E-01, 9.526320578956575E-01, 7.769150734629690E-04 ] ) return xyw def smr37 ( ): #*****************************************************************************80 # ## smr37 returns the SMR rule of degree 37. # # Discussion: # # DEGREE: 37 # ROTATIONALLY INVARIANT: (X, Y), (-Y, X), (-X, -Y), (Y, -X). # POINTS CARDINALITY: 245 # NORM INF MOMS. RESIDUAL: 1.97628e-15 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*245), the requested rule. # import numpy as np xyw = np.array ( [ \ 1.688689515698905E-01, 1.899855310442196E-01, 1.879076889689011E-02, \ 1.664922672701527E-01, 3.429140133623845E-01, 3.449917667815708E-02, \ 1.789345703476781E-01, 5.923725055750423E-01, 3.712580251685875E-02, \ 1.912828097143278E-01, 8.047865391631479E-01, 2.804589806906416E-02, \ 1.909000554810340E-01, 9.526563151843329E-01, 1.317147780067464E-02, \ 1.197461382570857E-01, 9.934656721499447E-01, 3.246786042836229E-03, \ 3.142942982925143E-01, 1.085212763112808E-01, 4.073944662145704E-02, \ 3.136430658350363E-01, 3.168853969514266E-01, 1.888769495196758E-02, \ 3.257592735310023E-01, 4.744364447040339E-01, 3.338316795412049E-02, \ 3.370767611845376E-01, 7.018261748212855E-01, 3.160597567460757E-02, \ 3.228638369287264E-01, 8.961218476259737E-01, 1.882298564453669E-02, \ 3.240794429041066E-01, 9.907076643667728E-01, 5.242591968441962E-03, \ 4.573043899331568E-01, 2.595246348757670E-01, 3.729781542768577E-02, \ 4.752591359356870E-01, 4.488205755197494E-01, 1.479677650128667E-02, \ 4.758333073820230E-01, 5.902241348085835E-01, 2.899670157191689E-02, \ 5.652930131354381E-01, 7.267134552411152E-01, 2.191839430308059E-02, \ 4.508159401323132E-01, 8.204509229358563E-01, 2.228800060943608E-02, \ 4.475176031554735E-01, 9.598714005292409E-01, 1.115771006747028E-02, \ 5.961940658067776E-01, 1.285519929807882E-01, 3.745963783702447E-02, \ 5.958894993059283E-01, 4.008434952939153E-01, 3.161819475642853E-02, \ 6.758517622961954E-01, 5.420453939309517E-01, 1.197569541821857E-02, \ 6.440973695595638E-01, 6.074025740384232E-01, 1.687104351509356E-02, \ 6.599539606557937E-01, 8.196857529727558E-01, 1.433025041492978E-02, \ 5.662112657592980E-01, 9.051653639016278E-01, 1.517136608765207E-02, \ 6.604704311527990E-01, 9.545232264955925E-01, 5.954681784138311E-03, \ 5.550021925411663E-01, 9.938020253544084E-01, 3.779613188841330E-03, \ 7.175598471168050E-01, 2.730403569607258E-01, 3.181466382684873E-02, \ 7.689529149485085E-01, 4.849501945095196E-01, 2.205707035359098E-02, \ 7.225244519379806E-01, 7.346670194240615E-01, 8.555695820639366E-03, \ 7.402191126180568E-01, 8.767789551273115E-01, 1.086516778783751E-02, \ 6.901879840655373E-01, 9.774065816278240E-01, 4.413949586651726E-03, \ 8.145402907615753E-01, 1.194770600468978E-01, 2.773238005998524E-02, \ 8.468674880069054E-01, 3.677292203050513E-01, 2.040170735025986E-02, \ 7.709894430969280E-01, 6.883167579089596E-01, 1.537385690938401E-02, \ 8.412324448391584E-01, 8.049116063955287E-01, 1.469009646857076E-02, \ 8.046126375110838E-01, 9.350177341085882E-01, 8.737871041426535E-03, \ 7.820614187450875E-01, 9.953174665105079E-01, 2.315496884250784E-03, \ 9.508079160816079E-01, 1.063127388777120E-01, 1.140349599008745E-02, \ 9.083772470189286E-01, 2.392578185017081E-01, 1.649605664974265E-02, \ 8.623376059969516E-01, 6.074887398627125E-01, 1.799944191342780E-02, \ 9.049650989085555E-01, 8.906584714348453E-01, 8.885404075061408E-03, \ 9.414987804698027E-01, 9.972662607622250E-01, 1.012999506114864E-03, \ 8.784002089990299E-01, 9.767224278002355E-01, 4.609542770434277E-03, \ 9.277718380370786E-01, 4.868377946168942E-01, 1.482235294209374E-02, \ 9.740284280473888E-01, 6.153952571724473E-01, 8.444452079041077E-03, \ 9.261384032176685E-01, 7.279402581589705E-01, 1.230535711494119E-02, \ 9.679546133670914E-01, 8.320886256235162E-01, 6.228411019066719E-03, \ 9.563820929391198E-01, 9.496839487816863E-01, 4.116804695327055E-03, \ 9.926061411961665E-01, 2.123910718029504E-01, 4.298821847813497E-03, \ 9.709143978580982E-01, 3.514215085134095E-01, 9.842825211091850E-03, \ 9.964469722990946E-01, 4.826995164323201E-01, 3.063734063870583E-03, \ 9.948590950034147E-01, 7.363116181982159E-01, 2.686189437945335E-03, \ 9.924033492665334E-01, 8.341694790656329E-01, 4.583425786943879E-04, \ 9.936078762597962E-01, 9.109429166275763E-01, 1.832840176946247E-03, \ 9.897652124914369E-01, 9.843626854080677E-01, 1.073091219432144E-03, \ 3.032916166693916E-02, 1.723425646848686E-01, 3.655713458299797E-02, \ 2.217294601980654E-02, 4.663686154054668E-01, 4.027271183981319E-02, \ 2.814942665710626E-02, 7.102048981913600E-01, 3.373438958414005E-02, \ 4.438627067827642E-02, 8.900063168860698E-01, 2.195827523559744E-02, \ 6.744822333126831E-03, 9.762502292316360E-01, 5.490273279461521E-03, \ -4.982446329191517E-02, 9.956312481563887E-01, 1.436535699659639E-03, \ -1.899855310442196E-01, 1.688689515698905E-01, 1.879076889689011E-02, \ -3.429140133623845E-01, 1.664922672701527E-01, 3.449917667815708E-02, \ -5.923725055750423E-01, 1.789345703476781E-01, 3.712580251685875E-02, \ -8.047865391631479E-01, 1.912828097143278E-01, 2.804589806906416E-02, \ -9.526563151843329E-01, 1.909000554810340E-01, 1.317147780067464E-02, \ -9.934656721499447E-01, 1.197461382570857E-01, 3.246786042836229E-03, \ -1.085212763112808E-01, 3.142942982925143E-01, 4.073944662145704E-02, \ -3.168853969514266E-01, 3.136430658350363E-01, 1.888769495196758E-02, \ -4.744364447040339E-01, 3.257592735310023E-01, 3.338316795412049E-02, \ -7.018261748212855E-01, 3.370767611845376E-01, 3.160597567460757E-02, \ -8.961218476259737E-01, 3.228638369287264E-01, 1.882298564453669E-02, \ -9.907076643667728E-01, 3.240794429041066E-01, 5.242591968441962E-03, \ -2.595246348757670E-01, 4.573043899331568E-01, 3.729781542768577E-02, \ -4.488205755197494E-01, 4.752591359356870E-01, 1.479677650128667E-02, \ -5.902241348085835E-01, 4.758333073820230E-01, 2.899670157191689E-02, \ -7.267134552411152E-01, 5.652930131354381E-01, 2.191839430308059E-02, \ -8.204509229358563E-01, 4.508159401323132E-01, 2.228800060943608E-02, \ -9.598714005292409E-01, 4.475176031554735E-01, 1.115771006747028E-02, \ -1.285519929807882E-01, 5.961940658067776E-01, 3.745963783702447E-02, \ -4.008434952939153E-01, 5.958894993059283E-01, 3.161819475642853E-02, \ -5.420453939309517E-01, 6.758517622961954E-01, 1.197569541821857E-02, \ -6.074025740384232E-01, 6.440973695595638E-01, 1.687104351509356E-02, \ -8.196857529727558E-01, 6.599539606557937E-01, 1.433025041492978E-02, \ -9.051653639016278E-01, 5.662112657592980E-01, 1.517136608765207E-02, \ -9.545232264955925E-01, 6.604704311527990E-01, 5.954681784138311E-03, \ -9.938020253544084E-01, 5.550021925411663E-01, 3.779613188841330E-03, \ -2.730403569607258E-01, 7.175598471168050E-01, 3.181466382684873E-02, \ -4.849501945095196E-01, 7.689529149485085E-01, 2.205707035359098E-02, \ -7.346670194240615E-01, 7.225244519379806E-01, 8.555695820639366E-03, \ -8.767789551273115E-01, 7.402191126180568E-01, 1.086516778783751E-02, \ -9.774065816278240E-01, 6.901879840655373E-01, 4.413949586651726E-03, \ -1.194770600468978E-01, 8.145402907615753E-01, 2.773238005998524E-02, \ -3.677292203050513E-01, 8.468674880069054E-01, 2.040170735025986E-02, \ -6.883167579089596E-01, 7.709894430969280E-01, 1.537385690938401E-02, \ -8.049116063955287E-01, 8.412324448391584E-01, 1.469009646857076E-02, \ -9.350177341085882E-01, 8.046126375110838E-01, 8.737871041426535E-03, \ -9.953174665105079E-01, 7.820614187450875E-01, 2.315496884250784E-03, \ -1.063127388777120E-01, 9.508079160816079E-01, 1.140349599008745E-02, \ -2.392578185017081E-01, 9.083772470189286E-01, 1.649605664974265E-02, \ -6.074887398627125E-01, 8.623376059969516E-01, 1.799944191342780E-02, \ -8.906584714348453E-01, 9.049650989085555E-01, 8.885404075061408E-03, \ -9.972662607622250E-01, 9.414987804698027E-01, 1.012999506114864E-03, \ -9.767224278002355E-01, 8.784002089990299E-01, 4.609542770434277E-03, \ -4.868377946168942E-01, 9.277718380370786E-01, 1.482235294209374E-02, \ -6.153952571724473E-01, 9.740284280473888E-01, 8.444452079041077E-03, \ -7.279402581589705E-01, 9.261384032176685E-01, 1.230535711494119E-02, \ -8.320886256235162E-01, 9.679546133670914E-01, 6.228411019066719E-03, \ -9.496839487816863E-01, 9.563820929391198E-01, 4.116804695327055E-03, \ -2.123910718029504E-01, 9.926061411961665E-01, 4.298821847813497E-03, \ -3.514215085134095E-01, 9.709143978580982E-01, 9.842825211091850E-03, \ -4.826995164323201E-01, 9.964469722990946E-01, 3.063734063870583E-03, \ -7.363116181982159E-01, 9.948590950034147E-01, 2.686189437945335E-03, \ -8.341694790656329E-01, 9.924033492665334E-01, 4.583425786943879E-04, \ -9.109429166275763E-01, 9.936078762597962E-01, 1.832840176946247E-03, \ -9.843626854080677E-01, 9.897652124914369E-01, 1.073091219432144E-03, \ -1.723425646848686E-01, 3.032916166693916E-02, 3.655713458299797E-02, \ -4.663686154054668E-01, 2.217294601980654E-02, 4.027271183981319E-02, \ -7.102048981913600E-01, 2.814942665710626E-02, 3.373438958414005E-02, \ -8.900063168860698E-01, 4.438627067827642E-02, 2.195827523559744E-02, \ -9.762502292316360E-01, 6.744822333126831E-03, 5.490273279461521E-03, \ -9.956312481563887E-01, -4.982446329191517E-02, 1.436535699659639E-03, \ -1.688689515698905E-01, -1.899855310442196E-01, 1.879076889689011E-02, \ -1.664922672701527E-01, -3.429140133623845E-01, 3.449917667815708E-02, \ -1.789345703476781E-01, -5.923725055750423E-01, 3.712580251685875E-02, \ -1.912828097143278E-01, -8.047865391631479E-01, 2.804589806906416E-02, \ -1.909000554810340E-01, -9.526563151843329E-01, 1.317147780067464E-02, \ -1.197461382570857E-01, -9.934656721499447E-01, 3.246786042836229E-03, \ -3.142942982925143E-01, -1.085212763112808E-01, 4.073944662145704E-02, \ -3.136430658350363E-01, -3.168853969514266E-01, 1.888769495196758E-02, \ -3.257592735310023E-01, -4.744364447040339E-01, 3.338316795412049E-02, \ -3.370767611845376E-01, -7.018261748212855E-01, 3.160597567460757E-02, \ -3.228638369287264E-01, -8.961218476259737E-01, 1.882298564453669E-02, \ -3.240794429041066E-01, -9.907076643667728E-01, 5.242591968441962E-03, \ -4.573043899331568E-01, -2.595246348757670E-01, 3.729781542768577E-02, \ -4.752591359356870E-01, -4.488205755197494E-01, 1.479677650128667E-02, \ -4.758333073820230E-01, -5.902241348085835E-01, 2.899670157191689E-02, \ -5.652930131354381E-01, -7.267134552411152E-01, 2.191839430308059E-02, \ -4.508159401323132E-01, -8.204509229358563E-01, 2.228800060943608E-02, \ -4.475176031554735E-01, -9.598714005292409E-01, 1.115771006747028E-02, \ -5.961940658067776E-01, -1.285519929807882E-01, 3.745963783702447E-02, \ -5.958894993059283E-01, -4.008434952939153E-01, 3.161819475642853E-02, \ -6.758517622961954E-01, -5.420453939309517E-01, 1.197569541821857E-02, \ -6.440973695595638E-01, -6.074025740384232E-01, 1.687104351509356E-02, \ -6.599539606557937E-01, -8.196857529727558E-01, 1.433025041492978E-02, \ -5.662112657592980E-01, -9.051653639016278E-01, 1.517136608765207E-02, \ -6.604704311527990E-01, -9.545232264955925E-01, 5.954681784138311E-03, \ -5.550021925411663E-01, -9.938020253544084E-01, 3.779613188841330E-03, \ -7.175598471168050E-01, -2.730403569607258E-01, 3.181466382684873E-02, \ -7.689529149485085E-01, -4.849501945095196E-01, 2.205707035359098E-02, \ -7.225244519379806E-01, -7.346670194240615E-01, 8.555695820639366E-03, \ -7.402191126180568E-01, -8.767789551273115E-01, 1.086516778783751E-02, \ -6.901879840655373E-01, -9.774065816278240E-01, 4.413949586651726E-03, \ -8.145402907615753E-01, -1.194770600468978E-01, 2.773238005998524E-02, \ -8.468674880069054E-01, -3.677292203050513E-01, 2.040170735025986E-02, \ -7.709894430969280E-01, -6.883167579089596E-01, 1.537385690938401E-02, \ -8.412324448391584E-01, -8.049116063955287E-01, 1.469009646857076E-02, \ -8.046126375110838E-01, -9.350177341085882E-01, 8.737871041426535E-03, \ -7.820614187450875E-01, -9.953174665105079E-01, 2.315496884250784E-03, \ -9.508079160816079E-01, -1.063127388777120E-01, 1.140349599008745E-02, \ -9.083772470189286E-01, -2.392578185017081E-01, 1.649605664974265E-02, \ -8.623376059969516E-01, -6.074887398627125E-01, 1.799944191342780E-02, \ -9.049650989085555E-01, -8.906584714348453E-01, 8.885404075061408E-03, \ -9.414987804698027E-01, -9.972662607622250E-01, 1.012999506114864E-03, \ -8.784002089990299E-01, -9.767224278002355E-01, 4.609542770434277E-03, \ -9.277718380370786E-01, -4.868377946168942E-01, 1.482235294209374E-02, \ -9.740284280473888E-01, -6.153952571724473E-01, 8.444452079041077E-03, \ -9.261384032176685E-01, -7.279402581589705E-01, 1.230535711494119E-02, \ -9.679546133670914E-01, -8.320886256235162E-01, 6.228411019066719E-03, \ -9.563820929391198E-01, -9.496839487816863E-01, 4.116804695327055E-03, \ -9.926061411961665E-01, -2.123910718029504E-01, 4.298821847813497E-03, \ -9.709143978580982E-01, -3.514215085134095E-01, 9.842825211091850E-03, \ -9.964469722990946E-01, -4.826995164323201E-01, 3.063734063870583E-03, \ -9.948590950034147E-01, -7.363116181982159E-01, 2.686189437945335E-03, \ -9.924033492665334E-01, -8.341694790656329E-01, 4.583425786943879E-04, \ -9.936078762597962E-01, -9.109429166275763E-01, 1.832840176946247E-03, \ -9.897652124914369E-01, -9.843626854080677E-01, 1.073091219432144E-03, \ -3.032916166693916E-02, -1.723425646848686E-01, 3.655713458299797E-02, \ -2.217294601980654E-02, -4.663686154054668E-01, 4.027271183981319E-02, \ -2.814942665710626E-02, -7.102048981913600E-01, 3.373438958414005E-02, \ -4.438627067827642E-02, -8.900063168860698E-01, 2.195827523559744E-02, \ -6.744822333126831E-03, -9.762502292316360E-01, 5.490273279461521E-03, \ 4.982446329191517E-02, -9.956312481563887E-01, 1.436535699659639E-03, \ 1.899855310442196E-01, -1.688689515698905E-01, 1.879076889689011E-02, \ 3.429140133623845E-01, -1.664922672701527E-01, 3.449917667815708E-02, \ 5.923725055750423E-01, -1.789345703476781E-01, 3.712580251685875E-02, \ 8.047865391631479E-01, -1.912828097143278E-01, 2.804589806906416E-02, \ 9.526563151843329E-01, -1.909000554810340E-01, 1.317147780067464E-02, \ 9.934656721499447E-01, -1.197461382570857E-01, 3.246786042836229E-03, \ 1.085212763112808E-01, -3.142942982925143E-01, 4.073944662145704E-02, \ 3.168853969514266E-01, -3.136430658350363E-01, 1.888769495196758E-02, \ 4.744364447040339E-01, -3.257592735310023E-01, 3.338316795412049E-02, \ 7.018261748212855E-01, -3.370767611845376E-01, 3.160597567460757E-02, \ 8.961218476259737E-01, -3.228638369287264E-01, 1.882298564453669E-02, \ 9.907076643667728E-01, -3.240794429041066E-01, 5.242591968441962E-03, \ 2.595246348757670E-01, -4.573043899331568E-01, 3.729781542768577E-02, \ 4.488205755197494E-01, -4.752591359356870E-01, 1.479677650128667E-02, \ 5.902241348085835E-01, -4.758333073820230E-01, 2.899670157191689E-02, \ 7.267134552411152E-01, -5.652930131354381E-01, 2.191839430308059E-02, \ 8.204509229358563E-01, -4.508159401323132E-01, 2.228800060943608E-02, \ 9.598714005292409E-01, -4.475176031554735E-01, 1.115771006747028E-02, \ 1.285519929807882E-01, -5.961940658067776E-01, 3.745963783702447E-02, \ 4.008434952939153E-01, -5.958894993059283E-01, 3.161819475642853E-02, \ 5.420453939309517E-01, -6.758517622961954E-01, 1.197569541821857E-02, \ 6.074025740384232E-01, -6.440973695595638E-01, 1.687104351509356E-02, \ 8.196857529727558E-01, -6.599539606557937E-01, 1.433025041492978E-02, \ 9.051653639016278E-01, -5.662112657592980E-01, 1.517136608765207E-02, \ 9.545232264955925E-01, -6.604704311527990E-01, 5.954681784138311E-03, \ 9.938020253544084E-01, -5.550021925411663E-01, 3.779613188841330E-03, \ 2.730403569607258E-01, -7.175598471168050E-01, 3.181466382684873E-02, \ 4.849501945095196E-01, -7.689529149485085E-01, 2.205707035359098E-02, \ 7.346670194240615E-01, -7.225244519379806E-01, 8.555695820639366E-03, \ 8.767789551273115E-01, -7.402191126180568E-01, 1.086516778783751E-02, \ 9.774065816278240E-01, -6.901879840655373E-01, 4.413949586651726E-03, \ 1.194770600468978E-01, -8.145402907615753E-01, 2.773238005998524E-02, \ 3.677292203050513E-01, -8.468674880069054E-01, 2.040170735025986E-02, \ 6.883167579089596E-01, -7.709894430969280E-01, 1.537385690938401E-02, \ 8.049116063955287E-01, -8.412324448391584E-01, 1.469009646857076E-02, \ 9.350177341085882E-01, -8.046126375110838E-01, 8.737871041426535E-03, \ 9.953174665105079E-01, -7.820614187450875E-01, 2.315496884250784E-03, \ 1.063127388777120E-01, -9.508079160816079E-01, 1.140349599008745E-02, \ 2.392578185017081E-01, -9.083772470189286E-01, 1.649605664974265E-02, \ 6.074887398627125E-01, -8.623376059969516E-01, 1.799944191342780E-02, \ 8.906584714348453E-01, -9.049650989085555E-01, 8.885404075061408E-03, \ 9.972662607622250E-01, -9.414987804698027E-01, 1.012999506114864E-03, \ 9.767224278002355E-01, -8.784002089990299E-01, 4.609542770434277E-03, \ 4.868377946168942E-01, -9.277718380370786E-01, 1.482235294209374E-02, \ 6.153952571724473E-01, -9.740284280473888E-01, 8.444452079041077E-03, \ 7.279402581589705E-01, -9.261384032176685E-01, 1.230535711494119E-02, \ 8.320886256235162E-01, -9.679546133670914E-01, 6.228411019066719E-03, \ 9.496839487816863E-01, -9.563820929391198E-01, 4.116804695327055E-03, \ 2.123910718029504E-01, -9.926061411961665E-01, 4.298821847813497E-03, \ 3.514215085134095E-01, -9.709143978580982E-01, 9.842825211091850E-03, \ 4.826995164323201E-01, -9.964469722990946E-01, 3.063734063870583E-03, \ 7.363116181982159E-01, -9.948590950034147E-01, 2.686189437945335E-03, \ 8.341694790656329E-01, -9.924033492665334E-01, 4.583425786943879E-04, \ 9.109429166275763E-01, -9.936078762597962E-01, 1.832840176946247E-03, \ 9.843626854080677E-01, -9.897652124914369E-01, 1.073091219432144E-03, \ 1.723425646848686E-01, -3.032916166693916E-02, 3.655713458299797E-02, \ 4.663686154054668E-01, -2.217294601980654E-02, 4.027271183981319E-02, \ 7.102048981913600E-01, -2.814942665710626E-02, 3.373438958414005E-02, \ 8.900063168860698E-01, -4.438627067827642E-02, 2.195827523559744E-02, \ 9.762502292316360E-01, -6.744822333126831E-03, 5.490273279461521E-03, \ 9.956312481563887E-01, 4.982446329191517E-02, 1.436535699659639E-03, \ 0.000000000000000E+00, 0.000000000000000E+00, 2.733962437974891E-02 ] ) return xyw def smr38 ( ): #*****************************************************************************80 # ## smr38 returns the SMR rule of degree 38. # # Discussion: # # DEGREE: 38 # POINTS CARDINALITY: 265 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*265), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.986728061698944E-01, 7.022053437776367E-01, 1.480107210669759E-03, \ -9.982717636746820E-01, -9.054654092610701E-01, 1.075250999194606E-03, \ -9.967818426696908E-01, 2.010254208991262E-01, 2.641794509284354E-03, \ -9.961752169855568E-01, -4.510641362412657E-01, 2.262884166375447E-03, \ -9.956850333584866E-01, -2.104763459288764E-01, 2.878520269955461E-03, \ -9.954228554916262E-01, -6.464904618069326E-01, 2.018600540825626E-03, \ -9.952874532053829E-01, 4.651922890152825E-01, 2.686536492992849E-03, \ -9.948147421400011E-01, 8.983435291372217E-01, 1.575355209064770E-03, \ -9.944162554551003E-01, 9.804886839517453E-01, 7.123537841476463E-04, \ -9.941508164951945E-01, -9.924193701187594E-01, 4.124555173483122E-04, \ -9.895909168262721E-01, -7.760059158658976E-01, 3.335123807315742E-03, \ -9.884130043110948E-01, -6.828120541211876E-03, 5.966363865455931E-03, \ -9.825019022108045E-01, 8.025512121835557E-01, 4.473439125255699E-03, \ -9.808025717173898E-01, 5.928703642747596E-01, 5.654233758485060E-03, \ -9.789202260574441E-01, -9.600751096501493E-01, 2.400023758037121E-03, \ -9.780946430895284E-01, 3.312033086392446E-01, 7.232443622428314E-03, \ -9.768400253233941E-01, -3.363809641049628E-01, 6.810652491435815E-03, \ -9.766127586199059E-01, -5.507973729936958E-01, 5.502878410512012E-03, \ -9.709970420576878E-01, 9.982493459462520E-01, 5.220890807668551E-04, \ -9.699274049351875E-01, 9.472087194394833E-01, 3.027446723606712E-03, \ -9.687234644693394E-01, -8.597252944572178E-01, 4.921184172578546E-03, \ -9.579599016628263E-01, 1.346951753939543E-01, 1.158893898492868E-02, \ -9.565118929757315E-01, -1.489920158469925E-01, 1.130253568365422E-02, \ -9.553009304164504E-01, -6.804355607895213E-01, 8.027637882625688E-03, \ -9.511658622347594E-01, 6.971063358211608E-01, 8.324574726565883E-03, \ -9.437446561733596E-01, 4.732467184275191E-01, 1.096804727700399E-02, \ -9.430645590398508E-01, 8.721609246940591E-01, 6.497332370837135E-03, \ -9.424278783556489E-01, -9.922571454686503E-01, 1.636770445566413E-03, \ -9.398691006571868E-01, -4.560244625614296E-01, 8.895278250957981E-03, \ -9.292771715176156E-01, -9.225625756492970E-01, 5.669237451343602E-03, \ -9.249858311739745E-01, 9.811603990754799E-01, 2.809384277239985E-03, \ -9.180677638423977E-01, -7.800607674872433E-01, 9.623850741009066E-03, \ -9.177060680740887E-01, -3.177972997817269E-01, 1.019917034278841E-02, \ -9.174754746776520E-01, 3.041897807994299E-01, 1.201129866345285E-02, \ -9.079474620384712E-01, -1.522732468440084E-02, 1.645827217241348E-02, \ -8.989880442284409E-01, -5.721449662059714E-01, 1.288528291339345E-02, \ -8.981089387121135E-01, 7.784183494868725E-01, 1.067299862517563E-02, \ -8.932346929455569E-01, 5.887798321389541E-01, 1.418723684484729E-02, \ -8.844628907549286E-01, 9.298461890098859E-01, 6.826913613669788E-03, \ -8.785753240387332E-01, 1.874264068388238E-01, 1.280230079204341E-02, \ -8.769155610558782E-01, -9.702794097426992E-01, 4.732604136822726E-03, \ -8.745143973474696E-01, -2.287312677692649E-01, 1.419838785220286E-02, \ -8.616355979293774E-01, -8.599524645119671E-01, 1.033767954867920E-02, \ -8.543820371352494E-01, 9.950509885730230E-01, 1.586566768400716E-03, \ -8.524166456930568E-01, 4.012946300633538E-01, 1.310477717253685E-02, \ -8.456839492120051E-01, -6.831067002350120E-01, 1.516421735877612E-02, \ -8.383382188368550E-01, -4.319298337860406E-01, 1.921462523307014E-02, \ -8.264198166719673E-01, 8.543820715032787E-01, 1.170776794008535E-02, \ -8.238644456887115E-01, 4.631329546631612E-01, 1.038537538791454E-02, \ -8.223392361684277E-01, 6.288554440206344E-02, 1.667203720394711E-02, \ -8.211280022738077E-01, 6.855811948721302E-01, 1.601478444956828E-02, \ -8.199277985385334E-01, -9.968372670905445E-01, 1.661577894515087E-03, \ -8.129329692738561E-01, -1.273992868913358E-01, 1.875947652746525E-02, \ -8.011794106051470E-01, 9.669501083215283E-01, 5.767768497940699E-03, \ -7.929367673515950E-01, -9.266258905147980E-01, 9.411444971101739E-03, \ -7.900564493377547E-01, 2.381148763558590E-01, 1.647531191140429E-02, \ -7.731467279987423E-01, -7.797397671681381E-01, 1.601496823099040E-02, \ -7.623964593130932E-01, -5.501193940493972E-01, 1.159218418929015E-02, \ -7.584255224981719E-01, -3.184791336183493E-01, 2.091892442653742E-02, \ -7.519475217388361E-01, -5.791824818686737E-01, 1.205989910558337E-02, \ -7.479661500312423E-01, 5.530676731141679E-01, 2.158851143401081E-02, \ -7.352203999162555E-01, 7.734652586603286E-01, 1.630985619573579E-02, \ -7.301302673120450E-01, 9.132724657488548E-01, 1.112141678436374E-02, \ -7.256956958727250E-01, 3.329739597626992E-01, 2.022428576496201E-02, \ -7.239178205154017E-01, -9.768043840489384E-01, 5.995264547827235E-03, \ -7.144660932162712E-01, 9.939502544860596E-01, 2.623316720141714E-03, \ -7.134918721775755E-01, -8.299044913428447E-02, 1.940442510934155E-02, \ -7.119027324460611E-01, 8.578636631641405E-02, 2.131075003508226E-02, \ -6.885657387083151E-01, -8.646581939789911E-01, 1.508744259539114E-02, \ -6.815796916450431E-01, -2.520940863406625E-01, 1.530753004805380E-02, \ -6.642578820959111E-01, -6.852634338827157E-01, 2.278049969875701E-02, \ -6.473518575748209E-01, 6.592583222880233E-01, 2.271475467380947E-02, \ -6.437258851335323E-01, -4.477173879758088E-01, 2.975639615479566E-02, \ -6.355112635497605E-01, 4.378956512417215E-01, 2.521762558761123E-02, \ -6.325124605614381E-01, 8.407501306388737E-01, 1.460590022059716E-02, \ -6.315677583266991E-01, 9.662034393812413E-01, 7.808742737505493E-03, \ -6.196042474875053E-01, -9.963363069708174E-01, 2.238568005909896E-03, \ -6.140032205110788E-01, 2.010897045841556E-01, 2.855123742414878E-02, \ -6.129576438043784E-01, -9.390322728980965E-01, 1.034926062595989E-02, \ -5.875439691207275E-01, -2.193439986467143E-02, 2.499512527874338E-02, \ -5.799105261064157E-01, -2.023065726805473E-01, 2.524717784018200E-02, \ -5.639961982962394E-01, -7.885570098234548E-01, 2.129350870359041E-02, \ -5.596787042093025E-01, 9.043275540829417E-01, 9.506472361159410E-03, \ -5.352404064125716E-01, -5.820386013748505E-01, 2.975207132885310E-02, \ -5.296093245457807E-01, 7.468713682804629E-01, 2.126630472576444E-02, \ -5.287674931826091E-01, 5.463207389216995E-01, 2.634684268285789E-02, \ -5.219567374887893E-01, 9.934029903982332E-01, 3.621614418679607E-03, \ -5.149216590929167E-01, -9.004320190387479E-01, 7.688847109621289E-03, \ -5.011828192721633E-01, 3.227765374618168E-01, 3.053941514246194E-02, \ -4.984369209637762E-01, -9.785989702329311E-01, 6.782679629517108E-03, \ -4.936061758540524E-01, -3.486445503736601E-01, 3.330194686505883E-02, \ -4.708043838891184E-01, 9.397512604542692E-01, 9.223376930093745E-03, \ -4.700530607377321E-01, 9.067704013502087E-02, 3.194924782643185E-02, \ -4.421006521894345E-01, -8.668776943903029E-01, 1.365222130557064E-02, \ -4.322459166260278E-01, 8.364964883317925E-01, 1.748429055313385E-02, \ -4.274779754835013E-01, -1.078954532368429E-01, 3.224879248144154E-02, \ -4.198312559908789E-01, -7.021715466719177E-01, 2.768892576177184E-02, \ -4.084458907612225E-01, 6.401570118208092E-01, 2.499005578311043E-02, \ -3.854852212643881E-01, 4.349492407425390E-01, 2.817381856722252E-02, \ -3.774830229936222E-01, -4.844006263231227E-01, 3.385700109477467E-02, \ -3.733125787412826E-01, -9.970755357985500E-01, 2.170942883821916E-03, \ -3.727797012921453E-01, 9.754151248075028E-01, 7.281188512200446E-03, \ -3.688270887346273E-01, -9.468451854156112E-01, 1.073492503946515E-02, \ -3.400601966223295E-01, 2.175481788735125E-01, 3.596233825588648E-02, \ -3.309577504370512E-01, -2.409725722453500E-01, 3.299006641898251E-02, \ -3.139120548586594E-01, 8.944387687131167E-01, 1.499808244204078E-02, \ -3.077283461062756E-01, 7.430289388062856E-01, 2.298506594699816E-02, \ -3.068704930295912E-01, -8.068905304677897E-01, 2.173679496778064E-02, \ -2.858215339736228E-01, 9.963809140996434E-01, 2.123402062955704E-03, \ -2.752650785602830E-01, 5.229667081821272E-01, 2.373528701602919E-02, \ -2.741878663975621E-01, 1.806172412531546E-02, 3.809014012672781E-02, \ -2.567719567007165E-01, -6.119240851225661E-01, 3.194011296016801E-02, \ -2.486412305697790E-01, -9.068815421904441E-01, 1.217810020482826E-02, \ -2.449174300564486E-01, -9.850991839405564E-01, 4.904448003786544E-03, \ -2.187168991298080E-01, -3.684600845707849E-01, 3.494313486419826E-02, \ -2.033117249838243E-01, 9.468738387846685E-01, 1.197619385623436E-02, \ -2.010080284425486E-01, 3.460129359512604E-01, 3.625695619354579E-02, \ -1.826355317918911E-01, 6.262632974300691E-01, 2.662590215392095E-02, \ -1.790215484342411E-01, 8.175236068900705E-01, 2.125277683247088E-02, \ -1.620973947089955E-01, -1.254151736109939E-01, 3.616346313257308E-02, \ -1.539052421137992E-01, -7.363057881237680E-01, 2.507618881866903E-02, \ -1.509748710751692E-01, -9.644785457571827E-01, 7.018739561734089E-03, \ -1.493613992998394E-01, 9.916687319806494E-01, 3.018026062389521E-03, \ -1.222783616692547E-01, 1.555419729513029E-01, 3.996865738603259E-02, \ -1.217834179658884E-01, -8.665867966847536E-01, 1.614918555107364E-02, \ -9.954568034561521E-02, -4.983049956809532E-01, 3.480237785300572E-02, \ -6.355783962147189E-02, 4.834454631547017E-01, 3.435231211682938E-02, \ -5.980328238804704E-02, -9.959405331674103E-01, 3.043977853817699E-03, \ -5.539568797194713E-02, 8.900885330680616E-01, 1.816753046217396E-02, \ -5.044959347909641E-02, 7.147609138031071E-01, 2.708098053621957E-02, \ -4.957845184210880E-02, -2.517606346179521E-01, 3.400381338647362E-02, \ -3.882145970770993E-02, 9.753666286618804E-01, 7.353902601259136E-03, \ -1.876732002789969E-02, -9.356601897044989E-01, 1.223556469983839E-02, \ -1.249886771851880E-02, -6.467617699294321E-01, 2.729244897787926E-02, \ -2.013003655499770E-03, 6.804392691959212E-03, 3.855008975037510E-02, \ 1.402682997558021E-02, 3.138839948744481E-01, 3.388937184270214E-02, \ 1.858848688086966E-02, -8.036198891624267E-01, 2.153717804647764E-02, \ 6.003092973120553E-02, -3.753272041106706E-01, 3.397898340796751E-02, \ 7.672497416901625E-02, 5.912600487498983E-01, 3.121782785742061E-02, \ 8.150239020231834E-02, 8.067824202268138E-01, 2.407531651957368E-02, \ 8.668589264981116E-02, 9.969497157386084E-01, 2.701504620609339E-03, \ 9.231571720996709E-02, -9.780482238991313E-01, 7.785551665765360E-03, \ 9.737323505829255E-02, 9.384929736173514E-01, 1.338210888613317E-02, \ 1.128012445661176E-01, 1.896414997815953E-01, 3.128705789253182E-02, \ 1.143511803097085E-01, -1.243491400435504E-01, 3.392864370862653E-02, \ 1.176787443821946E-01, -5.474612454684378E-01, 2.746213627764317E-02, \ 1.268891351439016E-01, -8.839456725175053E-01, 1.672616556795388E-02, \ 1.631426909205751E-01, -7.177106221484078E-01, 2.625147736220446E-02, \ 1.758741383852967E-01, 4.265421432395542E-01, 3.797964446958128E-02, \ 2.006154550504023E-01, 6.951418864446643E-01, 2.545733408956723E-02, \ 2.152860030071384E-01, -2.422132475961240E-01, 3.100597045992737E-02, \ 2.185770634825280E-01, 6.907417504035727E-02, 3.492638326125608E-02, \ 2.236246288520670E-01, -9.963809891717132E-01, 2.645997507264436E-03, \ 2.288887051657028E-01, 8.754003178432914E-01, 1.912737808424751E-02, \ 2.333826052338914E-01, 9.779009358962610E-01, 8.217956207171995E-03, \ 2.396650307918395E-01, -9.403475642021211E-01, 1.212182944813937E-02, \ 2.400346653041813E-01, -4.372367795710141E-01, 2.750818762763818E-02, \ 2.748295966460754E-01, -8.146962266181857E-01, 2.119754629186746E-02, \ 2.987201821315680E-01, -6.058548502859488E-01, 2.839877337228632E-02, \ 3.045773430811280E-01, 2.755917979498074E-01, 3.925796207971420E-02, \ 3.076075819952085E-01, 5.616633852300046E-01, 3.047990578805131E-02, \ 3.287712171984706E-01, 7.700477537553330E-01, 2.209664204066767E-02, \ 3.353060396411924E-01, -6.713224338700050E-02, 3.731512968063742E-02, \ 3.590192167691809E-01, -3.124154796685937E-01, 2.690461091828352E-02, \ 3.599858348938447E-01, -9.772275522212224E-01, 7.322166085339412E-03, \ 3.633366721464262E-01, 9.346084117544282E-01, 1.354702461771435E-02, \ 3.764020834512444E-01, 9.961755944581749E-01, 2.780135787415783E-03, \ 3.890228459314153E-01, -8.890435602042946E-01, 1.607523732193323E-02, \ 4.027914291932886E-01, -7.160255035244310E-01, 2.387070910106874E-02, \ 4.097421894946350E-01, 4.452381475461492E-01, 2.464804897575283E-02, \ 4.229178797439392E-01, -4.701825939351019E-01, 2.729336096379032E-02, \ 4.340848616284464E-01, 1.248473223854657E-01, 3.829435373976316E-02, \ 4.470213771246104E-01, 8.458186314958444E-01, 1.848706583481758E-02, \ 4.529246621415263E-01, 6.588844784476522E-01, 2.807897061918352E-02, \ 4.691823411918916E-01, -1.894802637910654E-01, 3.053879012802178E-02, \ 4.783450123946249E-01, -9.966085192019259E-01, 2.372775192102795E-03, \ 4.895259810138424E-01, 3.534144616221834E-01, 2.351128491079622E-02, \ 4.959734262824529E-01, 9.740444635499416E-01, 7.710763334339463E-03, \ 5.035757619767235E-01, -9.439613658930373E-01, 1.096738800807791E-02, \ 5.065601845768776E-01, -5.790286708924139E-01, 2.135179779707459E-02, \ 5.085183945179361E-01, -8.074877657027639E-01, 1.929376564778246E-02, \ 5.522864200597388E-01, -2.345289122385255E-02, 3.173415604312580E-02, \ 5.570494428224395E-01, 9.133422840649569E-01, 1.040230474694315E-02, \ 5.592614360711528E-01, -3.522697411422632E-01, 3.062865653271522E-02, \ 5.701115871183835E-01, 5.306977130285789E-01, 2.961992797000797E-02, \ 5.715387605890363E-01, 7.590559568198023E-01, 2.163444564883412E-02, \ 5.835624398896593E-01, -6.686734742923499E-01, 1.834802018964697E-02, \ 5.852476417677183E-01, 2.370919609747132E-01, 3.031865232259109E-02, \ 6.022583849974138E-01, 8.935147959329210E-01, 4.687076326332230E-03, \ 6.126343242580223E-01, 9.948806624831008E-01, 2.738111925376468E-03, \ 6.130380835098971E-01, -9.809871456541636E-01, 6.008330808378468E-03, \ 6.137772669975574E-01, -8.823362281279877E-01, 1.455389914650117E-02, \ 6.503113146309555E-01, -4.923990275537434E-01, 2.548798440031706E-02, \ 6.557363354466152E-01, -1.827492834052264E-01, 2.943913000621533E-02, \ 6.632308515099845E-01, -7.513836134228538E-01, 1.603729849717827E-02, \ 6.733087762907948E-01, 7.458312789499499E-02, 2.620926808459537E-02, \ 6.777745043586945E-01, 6.498008245436880E-01, 2.305772728455377E-02, \ 6.801215770962631E-01, 9.582506362246405E-01, 8.570728995577852E-03, \ 6.812691836007740E-01, 3.950396235783185E-01, 2.866215400698846E-02, \ 6.845867333636126E-01, 8.369868628766669E-01, 1.511423850063031E-02, \ 7.142144737185003E-01, -9.401517749959084E-01, 9.679186610760252E-03, \ 7.273928279094639E-01, -9.968690745004373E-01, 1.839049038220150E-03, \ 7.351794320872288E-01, -3.295931784311009E-01, 2.303520052753472E-02, \ 7.366016686661473E-01, -6.141664794256717E-01, 2.025486074750510E-02, \ 7.410876578755918E-01, -8.243736678762867E-01, 1.265159478674391E-02, \ 7.551110132205514E-01, 2.093562914164269E-01, 2.349869126796357E-02, \ 7.702496257050028E-01, -6.565803371865064E-02, 2.585856694796258E-02, \ 7.725680221187270E-01, 9.904023414650684E-01, 3.400468248188160E-03, \ 7.738393121081201E-01, 5.296366886950493E-01, 2.210916654329989E-02, \ 7.749611837963317E-01, 9.058131786659659E-01, 1.041506168806316E-02, \ 7.760702944135377E-01, 7.489596799092613E-01, 1.652307042159280E-02, \ 8.027353439778935E-01, -4.573336361960537E-01, 1.831340868862391E-02, \ 8.124305771363060E-01, -9.759706592062355E-01, 5.062161724834427E-03, \ 8.147149488148366E-01, -8.861421984181819E-01, 9.631215601485367E-03, \ 8.163753750967859E-01, -7.177004379126865E-01, 1.541261476754118E-02, \ 8.258640864298581E-01, 3.417271576604571E-01, 1.986204459592654E-02, \ 8.385288085877484E-01, -2.304198329903687E-01, 2.068650913588178E-02, \ 8.480262557901783E-01, 9.584500401922721E-01, 5.818073292341461E-03, \ 8.499406855634883E-01, 8.311541485724494E-02, 2.138582032495064E-02, \ 8.542395824011385E-01, 6.470836810764854E-01, 1.548189977556605E-02, \ 8.551735349936741E-01, 8.361408239071259E-01, 1.113210052356122E-02, \ 8.682126765591526E-01, -5.724226374325766E-01, 1.512163401783132E-02, \ 8.862702936910032E-01, -8.045997586076709E-01, 1.081270580739009E-02, \ 8.864333814317719E-01, -9.343418320939790E-01, 6.185112577237470E-03, \ 8.887165787912253E-01, 4.737933027545716E-01, 1.532406329926187E-02, \ 8.909110194387325E-01, -9.952080704120854E-01, 1.557095545851028E-03, \ 8.969514630808822E-01, 9.930243801730180E-01, 1.899826340411995E-03, \ 8.975959754390993E-01, -3.806019598663427E-01, 1.487375295518117E-02, \ 9.030468245555767E-01, -9.390288889102749E-02, 1.549257621043731E-02, \ 9.085939371709327E-01, 2.350241676754213E-01, 1.558218899145559E-02, \ 9.140361598405574E-01, 9.095155793512008E-01, 6.544935838415903E-03, \ 9.171230192628999E-01, 7.511379775519837E-01, 1.001948867534600E-02, \ 9.268871231165261E-01, -6.775251262894855E-01, 1.088618566292480E-02, \ 9.416935102978777E-01, 6.013078832211158E-01, 1.017124306808582E-02, \ 9.433556271573456E-01, -8.749994999185291E-01, 6.277143297506312E-03, \ 9.434325703715991E-01, 3.225727122372022E-02, 9.237465593827822E-03, \ 9.437308091058394E-01, -9.711971052517493E-01, 3.026949149785576E-03, \ 9.439963213838909E-01, -2.608317409688558E-01, 9.360240633006462E-03, \ 9.484876843189004E-01, -5.004997732310644E-01, 1.009870421315387E-02, \ 9.499243743977762E-01, 3.801906587509148E-01, 9.818422202948377E-03, \ 9.514871432590463E-01, 9.671631794962331E-01, 3.146221524837508E-03, \ 9.609489550655589E-01, 8.428332536315430E-01, 5.730637488550284E-03, \ 9.662829103996791E-01, 1.468518597297787E-01, 7.207542405549267E-03, \ 9.696872558843541E-01, -1.605437913785572E-01, 5.981560914072205E-03, \ 9.702856060632504E-01, -7.717575893450904E-01, 5.993654542760810E-03, \ 9.760573100533793E-01, 9.966116994495912E-01, 5.808298238542816E-04, \ 9.778854166720647E-01, -9.945815670139703E-01, 7.405440773791397E-04, \ 9.789726619300820E-01, 7.196402966212632E-01, 5.322542886910651E-03, \ 9.792756889708635E-01, 5.073451727037140E-01, 5.506244507295100E-03, \ 9.811303210024424E-01, -6.060022042631865E-01, 5.278083219704399E-03, \ 9.821031078208879E-01, -3.681824090938130E-01, 6.200855551112159E-03, \ 9.823346110259005E-01, -9.302538972721487E-01, 2.710453922448771E-03, \ 9.862095221362329E-01, 2.895216427234739E-01, 5.194439945195447E-03, \ 9.864268580437249E-01, 9.195586194143690E-01, 2.646059688376799E-03, \ 9.880369774377964E-01, -3.549566919434279E-02, 5.082042661181035E-03, \ 9.945896034737212E-01, -8.501279475990717E-01, 1.873959291274505E-03, \ 9.954239677428349E-01, 6.245266829365560E-01, 2.088928242308500E-03, \ 9.961170766979618E-01, 9.777701767940108E-01, 6.025320119282685E-04, \ 9.966190752080943E-01, -7.030873365364748E-01, 1.672495855073975E-03, \ 9.973338514057413E-01, -4.871402038403967E-01, 1.840226666996993E-03, \ 9.975779076043548E-01, -2.229904598382893E-01, 2.112563470049513E-03, \ 9.976658933368316E-01, 1.309914613948673E-01, 1.954166630091224E-03, \ 9.977174090396262E-01, 8.188675476038971E-01, 1.472509815415101E-03, \ 9.983759366126691E-01, -9.751850545004921E-01, 4.748950672235257E-04, \ 9.984440204501318E-01, 4.288187400230707E-01, 1.459369339895693E-03 ] ) return xyw def smr39 ( ): #*****************************************************************************80 # ## smr39 returns the SMR rule of degree 39. # # Discussion: # # DEGREE: 39 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 274 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*274), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.983507138390728E-01, 2.846923651716276E-02, 1.946248040917511E-03, \ -9.974803510397799E-01, 5.723617700464594E-01, 1.730177315995435E-03, \ -9.970436400762405E-01, 8.380584517844631E-01, 1.474635255954523E-03, \ -9.966780331371223E-01, 9.694002319896394E-01, 7.243867200693780E-04, \ -9.966744182696170E-01, -5.085108565093430E-01, 1.980803681920541E-03, \ -9.958948247928820E-01, 3.162381906315679E-01, 2.750378228739487E-03, \ -9.957989442071229E-01, -2.946071658312556E-01, 2.310642786475657E-03, \ -9.951431493831727E-01, -9.317895250779106E-01, 1.311747532188187E-03, \ -9.947425612275775E-01, -6.937725695763057E-01, 2.327244406193416E-03, \ -9.946606993258253E-01, -9.946657556011911E-01, 3.187304244494703E-04, \ -9.891970457464104E-01, -8.249338141061554E-01, 3.217331206511223E-03, \ -9.882776096714541E-01, 6.996008607192892E-01, 3.762641387033618E-03, \ -9.863969994171303E-01, -1.393885680294662E-01, 5.467653298722175E-03, \ -9.815404512250665E-01, 1.578509309909750E-01, 6.740930954579635E-03, \ -9.808343955917264E-01, 9.119881406240292E-01, 3.204352632730979E-03, \ -9.801636812194632E-01, 4.593560896100384E-01, 6.656001065255846E-03, \ -9.781563938994409E-01, 9.946089769037700E-01, 7.827411078516896E-04, \ -9.778060661329431E-01, -3.970269563950553E-01, 6.040841876140015E-03, \ -9.732806127131356E-01, -5.909702866713498E-01, 6.577441961101425E-03, \ -9.719927242736324E-01, -9.738032840708760E-01, 2.184317380157956E-03, \ -9.672092676086640E-01, 7.825063090118517E-01, 5.021658745346757E-03, \ -9.603776991602971E-01, -2.153921649724314E-02, 8.448862253501903E-03, \ -9.590320135912280E-01, -8.917513123920264E-01, 5.150986564054207E-03, \ -9.545890590274086E-01, -7.377847025903865E-01, 8.094745379189257E-03, \ -9.518800297972723E-01, 6.005875476668143E-01, 1.012666553714644E-02, \ -9.515429157747712E-01, 2.941640121000471E-01, 1.034277329324190E-02, \ -9.490472836637540E-01, 9.596558694888836E-01, 3.220645239038979E-03, \ -9.474949611934800E-01, -2.528714063790848E-01, 1.171512879678826E-02, \ -9.373768292011957E-01, 8.493689030467824E-01, 5.846679077116532E-03, \ -9.316184094587854E-01, -4.719381834645925E-01, 1.149946336342146E-02, \ -9.286585069364643E-01, -9.958860857406989E-01, 1.228760288290566E-03, \ -9.267775091062305E-01, 8.114744510060384E-02, 1.023519688964817E-02, \ -9.163559242547217E-01, 4.235110040036954E-01, 1.200757888591889E-02, \ -9.121815833695173E-01, 9.882371567284969E-01, 2.019136532361037E-03, \ -9.109849110758503E-01, -9.453953022277268E-01, 5.441926862298386E-03, \ -9.037513800248385E-01, 7.152403666234081E-01, 1.254893510280643E-02, \ -9.029200480204936E-01, -8.212018233771367E-01, 1.010629097307952E-02, \ -9.017715031500836E-01, -6.268263259886000E-01, 1.344763853761130E-02, \ -8.966208411354669E-01, 9.032456722718886E-01, 6.128920772776423E-03, \ -8.949592560928252E-01, -1.162935700588350E-01, 1.704399639079853E-02, \ -8.840140563237966E-01, 1.969976541674721E-01, 1.596015406249639E-02, \ -8.746116719331715E-01, -3.448361698711476E-01, 1.765094462924452E-02, \ -8.710753346416532E-01, 5.340745871340347E-01, 1.443864424160225E-02, \ -8.484438717285120E-01, 9.509156312117837E-01, 5.738054352556750E-03, \ -8.458535483524889E-01, -9.815128577523679E-01, 4.137548861495137E-03, \ -8.398481586927637E-01, 9.961877079907046E-01, 1.304263243999687E-03, \ -8.380687425956748E-01, 8.117290446268374E-01, 1.347035082702432E-02, \ -8.338881116659986E-01, -8.932750703415656E-01, 1.036216371830049E-02, \ -8.323418772294408E-01, -7.249676279524006E-01, 1.575346317085866E-02, \ -8.249812915580336E-01, 3.366002739808117E-01, 2.128624669032709E-02, \ -8.240658406348467E-01, 2.473915430588143E-02, 2.254370190641922E-02, \ -8.235861595693262E-01, -5.100296033516193E-01, 2.030894605456216E-02, \ -8.077195745093785E-01, 6.402169882573437E-01, 1.719971170125941E-02, \ -7.994401076934280E-01, -2.090758091368732E-01, 2.285093214933729E-02, \ -7.630151789434809E-01, 8.944374728168084E-01, 1.178494783231054E-02, \ -7.595914562260390E-01, 9.774953228487998E-01, 5.007040345181551E-03, \ -7.582407204546612E-01, -9.977747817904907E-01, 1.471436198785488E-03, \ -7.479025577044630E-01, 4.742891505995823E-01, 2.322814942159416E-02, \ -7.476388136248332E-01, -9.482109321336361E-01, 8.869792121065277E-03, \ -7.467703985197518E-01, -8.150373305425095E-01, 1.612171337958705E-02, \ -7.437239011702286E-01, 1.745124876671426E-01, 2.695721316522005E-02, \ -7.347330924126372E-01, -6.233626922279565E-01, 2.200766479881018E-02, \ -7.315599487238387E-01, -3.750364118349838E-01, 2.628156017590748E-02, \ -7.287657206722611E-01, 7.405217467057846E-01, 1.766147427786541E-02, \ -7.068497539323653E-01, -5.980644840754300E-02, 2.389888208127354E-02, \ -6.810402042857588E-01, -1.522180405710772E-01, 9.694473603796364E-03, \ -6.732322428485551E-01, 3.420204047422755E-01, 1.378566447967479E-02, \ -6.671777044407723E-01, 9.965429698430747E-01, 2.043998547474421E-03, \ -6.661024488936084E-01, 8.365632468531969E-01, 1.043213484692862E-02, \ -6.574739030221062E-01, 6.056292870332995E-01, 1.928874088451468E-02, \ -6.471433178579986E-01, 9.435400364191848E-01, 1.053431875912228E-02, \ -6.450928247980198E-01, -8.897594199253124E-01, 1.467091129012532E-02, \ -6.450169863776212E-01, -9.837401664708233E-01, 5.320225765195333E-03, \ -6.356111898627910E-01, 2.888888071755747E-01, 1.689616308681305E-02, \ -6.353365310873343E-01, -7.289411912040862E-01, 2.112609662944668E-02, \ -6.298334119568398E-01, -4.991303444532345E-01, 2.693509156798771E-02, \ -6.291453725213981E-01, 5.401236508742461E-01, 8.067204019727233E-03, \ -6.052836931615376E-01, -2.550054118031913E-01, 3.145439290857988E-02, \ -6.020155389610803E-01, 7.193745911974410E-02, 3.280026289766638E-02, \ -5.864000058451709E-01, 8.398830909360200E-01, 9.794020060223996E-03, \ -5.844053681740743E-01, 7.439581399260577E-01, 9.673537687961857E-03, \ -5.595952952122188E-01, 4.183137864951066E-01, 2.109228735521581E-02, \ -5.426224610168304E-01, 6.721678667912533E-01, 1.507682570233586E-02, \ -5.392718444436758E-01, -6.640373564025523E-01, 6.853039280534112E-03, \ -5.392273233424993E-01, -9.497301018552529E-01, 1.000131088526367E-02, \ -5.352356532684714E-01, -5.949900365542921E-01, 1.257623121836303E-02, \ -5.323778014446715E-01, 9.820204941474223E-01, 6.618755503045249E-03, \ -5.217356658216146E-01, -8.191869945411094E-01, 1.965283477527441E-02, \ -5.005240240607661E-01, 9.025303947810552E-01, 1.461332246120154E-02, \ -4.938892072238822E-01, -9.399631019971544E-02, 3.808292738661537E-02, \ -4.937487614230233E-01, -9.959198263215358E-01, 2.729762079728744E-03, \ -4.900963037914226E-01, -3.938750807407649E-01, 3.202384141512818E-02, \ -4.882533660406217E-01, 2.148638214494721E-01, 3.418958389588500E-02, \ -4.867250611982683E-01, 5.069290645382520E-01, 2.181757841571514E-02, \ -4.652861756571924E-01, -6.195234647797874E-01, 1.584655621464966E-02, \ -4.606315835191566E-01, 7.592681033169186E-01, 1.498569479673017E-02, \ -4.247086062086841E-01, -9.049304493933019E-01, 1.318933688912641E-02, \ -4.065029720082786E-01, 6.264617368348774E-01, 1.614341656613300E-02, \ -3.964381931274395E-01, -7.402485185211833E-01, 2.066230577186247E-02, \ -3.917275322790500E-01, -2.763915160061775E-01, 2.066535103271340E-02, \ -3.832536927501162E-01, 9.979855334480493E-01, 2.234175560395208E-03, \ -3.794623453333835E-01, 9.538177413235013E-01, 1.114591704523323E-02, \ -3.772235876850343E-01, 3.495735710597775E-01, 3.119665329913849E-02, \ -3.717776952778286E-01, 8.276226068123943E-01, 1.892035069295494E-02, \ -3.653673059860704E-01, -9.753012851813677E-01, 8.368304519228926E-03, \ -3.645712799913758E-01, 5.949773008037845E-02, 4.066487888089951E-02, \ -3.538124036025474E-01, 5.741754846631917E-01, 1.454074748757973E-02, \ -3.469245014798072E-01, -5.093114780151489E-01, 3.377755276109650E-02, \ -3.282417053015600E-01, -2.037015005394916E-01, 2.733887753306074E-02, \ -3.131220942783493E-01, -8.518113941722779E-01, 1.597548862353881E-02, \ -2.898525204314484E-01, 4.261338334628221E-01, 1.508608675885359E-02, \ -2.882387623730816E-01, -6.853570019217500E-01, 1.688354844281806E-02, \ -2.702465413583358E-01, 7.030983141548524E-01, 2.434400019199495E-02, \ -2.508609565354079E-01, 8.968720007287277E-01, 1.702860129891579E-02, \ -2.295191348329352E-01, 2.120242218321433E-01, 4.168382939934718E-02, \ -2.272941564596992E-01, -9.960184881945845E-01, 3.049828038296397E-03, \ -2.264708864968271E-01, -9.349035701784980E-01, 1.391154926700919E-02, \ -2.246333439376893E-01, 9.827415964495356E-01, 7.017267263314176E-03, \ -2.114669394714854E-01, -3.735617108580254E-01, 3.956793096822071E-02, \ -2.089912056577438E-01, -7.231174948680190E-02, 4.093460500440146E-02, \ -2.088716807934302E-01, 5.073561793189525E-01, 2.832407460904032E-02, \ -1.854458909022641E-01, -7.951187042517341E-01, 2.077334257293032E-02, \ -1.842272015612801E-01, -6.069003654432927E-01, 2.779454600167818E-02, \ -1.777934970536059E-01, 7.780240581694521E-01, 1.585670340057501E-02, \ -1.355056850182737E-01, 9.495952359773809E-01, 4.847063927629738E-03, \ -9.279375419038796E-02, 6.222406899096711E-01, 3.101829992759421E-02, \ -8.902511936497644E-02, 8.391229312717673E-01, 1.695975469484219E-02, \ -8.734458962076150E-02, 3.558214042720322E-01, 3.984235442334169E-02, \ -8.571835501122597E-02, -9.754128963485780E-01, 8.697179874291300E-03, \ -7.422536842735775E-02, -8.831710824906397E-01, 1.813390976222609E-02, \ -7.156922510987426E-02, -2.275959622954337E-01, 4.227714481951355E-02, \ -7.101258554499701E-02, 7.775804214199432E-02, 4.334052544550671E-02, \ -6.035205037448012E-02, -7.014869129344957E-01, 1.646744774690809E-02, \ -6.004312209068092E-02, 9.389290315999793E-01, 1.055063932869926E-02, \ -5.380430609957936E-02, 9.956336871057816E-01, 3.141838490889661E-03, \ -5.001273890650990E-02, -4.928052077494132E-01, 3.665549033605845E-02, \ -9.807961584190060E-03, -7.518448026748643E-01, 1.483105676671131E-02, \ 9.807961584190060E-03, 7.518448026748643E-01, 1.483105676671131E-02, \ 5.001273890650990E-02, 4.928052077494132E-01, 3.665549033605845E-02, \ 5.380430609957936E-02, -9.956336871057816E-01, 3.141838490889661E-03, \ 6.004312209068092E-02, -9.389290315999793E-01, 1.055063932869926E-02, \ 6.035205037448012E-02, 7.014869129344957E-01, 1.646744774690809E-02, \ 7.101258554499701E-02, -7.775804214199432E-02, 4.334052544550671E-02, \ 7.156922510987426E-02, 2.275959622954337E-01, 4.227714481951355E-02, \ 7.422536842735775E-02, 8.831710824906397E-01, 1.813390976222609E-02, \ 8.571835501122597E-02, 9.754128963485780E-01, 8.697179874291300E-03, \ 8.734458962076150E-02, -3.558214042720322E-01, 3.984235442334169E-02, \ 8.902511936497644E-02, -8.391229312717673E-01, 1.695975469484219E-02, \ 9.279375419038796E-02, -6.222406899096711E-01, 3.101829992759421E-02, \ 1.355056850182737E-01, -9.495952359773809E-01, 4.847063927629738E-03, \ 1.777934970536059E-01, -7.780240581694521E-01, 1.585670340057501E-02, \ 1.842272015612801E-01, 6.069003654432927E-01, 2.779454600167818E-02, \ 1.854458909022641E-01, 7.951187042517341E-01, 2.077334257293032E-02, \ 2.088716807934302E-01, -5.073561793189525E-01, 2.832407460904032E-02, \ 2.089912056577438E-01, 7.231174948680190E-02, 4.093460500440146E-02, \ 2.114669394714854E-01, 3.735617108580254E-01, 3.956793096822071E-02, \ 2.246333439376893E-01, -9.827415964495356E-01, 7.017267263314176E-03, \ 2.264708864968271E-01, 9.349035701784980E-01, 1.391154926700919E-02, \ 2.272941564596992E-01, 9.960184881945845E-01, 3.049828038296397E-03, \ 2.295191348329352E-01, -2.120242218321433E-01, 4.168382939934718E-02, \ 2.508609565354079E-01, -8.968720007287277E-01, 1.702860129891579E-02, \ 2.702465413583358E-01, -7.030983141548524E-01, 2.434400019199495E-02, \ 2.882387623730816E-01, 6.853570019217500E-01, 1.688354844281806E-02, \ 2.898525204314484E-01, -4.261338334628221E-01, 1.508608675885359E-02, \ 3.131220942783493E-01, 8.518113941722779E-01, 1.597548862353881E-02, \ 3.282417053015600E-01, 2.037015005394916E-01, 2.733887753306074E-02, \ 3.469245014798072E-01, 5.093114780151489E-01, 3.377755276109650E-02, \ 3.538124036025474E-01, -5.741754846631917E-01, 1.454074748757973E-02, \ 3.645712799913758E-01, -5.949773008037845E-02, 4.066487888089951E-02, \ 3.653673059860704E-01, 9.753012851813677E-01, 8.368304519228926E-03, \ 3.717776952778286E-01, -8.276226068123943E-01, 1.892035069295494E-02, \ 3.772235876850343E-01, -3.495735710597775E-01, 3.119665329913849E-02, \ 3.794623453333835E-01, -9.538177413235013E-01, 1.114591704523323E-02, \ 3.832536927501162E-01, -9.979855334480493E-01, 2.234175560395208E-03, \ 3.917275322790500E-01, 2.763915160061775E-01, 2.066535103271340E-02, \ 3.964381931274395E-01, 7.402485185211833E-01, 2.066230577186247E-02, \ 4.065029720082786E-01, -6.264617368348774E-01, 1.614341656613300E-02, \ 4.247086062086841E-01, 9.049304493933019E-01, 1.318933688912641E-02, \ 4.606315835191566E-01, -7.592681033169186E-01, 1.498569479673017E-02, \ 4.652861756571924E-01, 6.195234647797874E-01, 1.584655621464966E-02, \ 4.867250611982683E-01, -5.069290645382520E-01, 2.181757841571514E-02, \ 4.882533660406217E-01, -2.148638214494721E-01, 3.418958389588500E-02, \ 4.900963037914226E-01, 3.938750807407649E-01, 3.202384141512818E-02, \ 4.937487614230233E-01, 9.959198263215358E-01, 2.729762079728744E-03, \ 4.938892072238822E-01, 9.399631019971544E-02, 3.808292738661537E-02, \ 5.005240240607661E-01, -9.025303947810552E-01, 1.461332246120154E-02, \ 5.217356658216146E-01, 8.191869945411094E-01, 1.965283477527441E-02, \ 5.323778014446715E-01, -9.820204941474223E-01, 6.618755503045249E-03, \ 5.352356532684714E-01, 5.949900365542921E-01, 1.257623121836303E-02, \ 5.392273233424993E-01, 9.497301018552529E-01, 1.000131088526367E-02, \ 5.392718444436758E-01, 6.640373564025523E-01, 6.853039280534112E-03, \ 5.426224610168304E-01, -6.721678667912533E-01, 1.507682570233586E-02, \ 5.595952952122188E-01, -4.183137864951066E-01, 2.109228735521581E-02, \ 5.844053681740743E-01, -7.439581399260577E-01, 9.673537687961857E-03, \ 5.864000058451709E-01, -8.398830909360200E-01, 9.794020060223996E-03, \ 6.020155389610803E-01, -7.193745911974410E-02, 3.280026289766638E-02, \ 6.052836931615376E-01, 2.550054118031913E-01, 3.145439290857988E-02, \ 6.291453725213981E-01, -5.401236508742461E-01, 8.067204019727233E-03, \ 6.298334119568398E-01, 4.991303444532345E-01, 2.693509156798771E-02, \ 6.353365310873343E-01, 7.289411912040862E-01, 2.112609662944668E-02, \ 6.356111898627910E-01, -2.888888071755747E-01, 1.689616308681305E-02, \ 6.450169863776212E-01, 9.837401664708233E-01, 5.320225765195333E-03, \ 6.450928247980198E-01, 8.897594199253124E-01, 1.467091129012532E-02, \ 6.471433178579986E-01, -9.435400364191848E-01, 1.053431875912228E-02, \ 6.574739030221062E-01, -6.056292870332995E-01, 1.928874088451468E-02, \ 6.661024488936084E-01, -8.365632468531969E-01, 1.043213484692862E-02, \ 6.671777044407723E-01, -9.965429698430747E-01, 2.043998547474421E-03, \ 6.732322428485551E-01, -3.420204047422755E-01, 1.378566447967479E-02, \ 6.810402042857588E-01, 1.522180405710772E-01, 9.694473603796364E-03, \ 7.068497539323653E-01, 5.980644840754300E-02, 2.389888208127354E-02, \ 7.287657206722611E-01, -7.405217467057846E-01, 1.766147427786541E-02, \ 7.315599487238387E-01, 3.750364118349838E-01, 2.628156017590748E-02, \ 7.347330924126372E-01, 6.233626922279565E-01, 2.200766479881018E-02, \ 7.437239011702286E-01, -1.745124876671426E-01, 2.695721316522005E-02, \ 7.467703985197518E-01, 8.150373305425095E-01, 1.612171337958705E-02, \ 7.476388136248332E-01, 9.482109321336361E-01, 8.869792121065277E-03, \ 7.479025577044630E-01, -4.742891505995823E-01, 2.322814942159416E-02, \ 7.582407204546612E-01, 9.977747817904907E-01, 1.471436198785488E-03, \ 7.595914562260390E-01, -9.774953228487998E-01, 5.007040345181551E-03, \ 7.630151789434809E-01, -8.944374728168084E-01, 1.178494783231054E-02, \ 7.994401076934280E-01, 2.090758091368732E-01, 2.285093214933729E-02, \ 8.077195745093785E-01, -6.402169882573437E-01, 1.719971170125941E-02, \ 8.235861595693262E-01, 5.100296033516193E-01, 2.030894605456216E-02, \ 8.240658406348467E-01, -2.473915430588143E-02, 2.254370190641922E-02, \ 8.249812915580336E-01, -3.366002739808117E-01, 2.128624669032709E-02, \ 8.323418772294408E-01, 7.249676279524006E-01, 1.575346317085866E-02, \ 8.338881116659986E-01, 8.932750703415656E-01, 1.036216371830049E-02, \ 8.380687425956748E-01, -8.117290446268374E-01, 1.347035082702432E-02, \ 8.398481586927637E-01, -9.961877079907046E-01, 1.304263243999687E-03, \ 8.458535483524889E-01, 9.815128577523679E-01, 4.137548861495137E-03, \ 8.484438717285120E-01, -9.509156312117837E-01, 5.738054352556750E-03, \ 8.710753346416532E-01, -5.340745871340347E-01, 1.443864424160225E-02, \ 8.746116719331715E-01, 3.448361698711476E-01, 1.765094462924452E-02, \ 8.840140563237966E-01, -1.969976541674721E-01, 1.596015406249639E-02, \ 8.949592560928252E-01, 1.162935700588350E-01, 1.704399639079853E-02, \ 8.966208411354669E-01, -9.032456722718886E-01, 6.128920772776423E-03, \ 9.017715031500836E-01, 6.268263259886000E-01, 1.344763853761130E-02, \ 9.029200480204936E-01, 8.212018233771367E-01, 1.010629097307952E-02, \ 9.037513800248385E-01, -7.152403666234081E-01, 1.254893510280643E-02, \ 9.109849110758503E-01, 9.453953022277268E-01, 5.441926862298386E-03, \ 9.121815833695173E-01, -9.882371567284969E-01, 2.019136532361037E-03, \ 9.163559242547217E-01, -4.235110040036954E-01, 1.200757888591889E-02, \ 9.267775091062305E-01, -8.114744510060384E-02, 1.023519688964817E-02, \ 9.286585069364643E-01, 9.958860857406989E-01, 1.228760288290566E-03, \ 9.316184094587854E-01, 4.719381834645925E-01, 1.149946336342146E-02, \ 9.373768292011957E-01, -8.493689030467824E-01, 5.846679077116532E-03, \ 9.474949611934800E-01, 2.528714063790848E-01, 1.171512879678826E-02, \ 9.490472836637540E-01, -9.596558694888836E-01, 3.220645239038979E-03, \ 9.515429157747712E-01, -2.941640121000471E-01, 1.034277329324190E-02, \ 9.518800297972723E-01, -6.005875476668143E-01, 1.012666553714644E-02, \ 9.545890590274086E-01, 7.377847025903865E-01, 8.094745379189257E-03, \ 9.590320135912280E-01, 8.917513123920264E-01, 5.150986564054207E-03, \ 9.603776991602971E-01, 2.153921649724314E-02, 8.448862253501903E-03, \ 9.672092676086640E-01, -7.825063090118517E-01, 5.021658745346757E-03, \ 9.719927242736324E-01, 9.738032840708760E-01, 2.184317380157956E-03, \ 9.732806127131356E-01, 5.909702866713498E-01, 6.577441961101425E-03, \ 9.778060661329431E-01, 3.970269563950553E-01, 6.040841876140015E-03, \ 9.781563938994409E-01, -9.946089769037700E-01, 7.827411078516896E-04, \ 9.801636812194632E-01, -4.593560896100384E-01, 6.656001065255846E-03, \ 9.808343955917264E-01, -9.119881406240292E-01, 3.204352632730979E-03, \ 9.815404512250665E-01, -1.578509309909750E-01, 6.740930954579635E-03, \ 9.863969994171303E-01, 1.393885680294662E-01, 5.467653298722175E-03, \ 9.882776096714541E-01, -6.996008607192892E-01, 3.762641387033618E-03, \ 9.891970457464104E-01, 8.249338141061554E-01, 3.217331206511223E-03, \ 9.946606993258253E-01, 9.946657556011911E-01, 3.187304244494703E-04, \ 9.947425612275775E-01, 6.937725695763057E-01, 2.327244406193416E-03, \ 9.951431493831727E-01, 9.317895250779106E-01, 1.311747532188187E-03, \ 9.957989442071229E-01, 2.946071658312556E-01, 2.310642786475657E-03, \ 9.958948247928820E-01, -3.162381906315679E-01, 2.750378228739487E-03, \ 9.966744182696170E-01, 5.085108565093430E-01, 1.980803681920541E-03, \ 9.966780331371223E-01, -9.694002319896394E-01, 7.243867200693780E-04, \ 9.970436400762405E-01, -8.380584517844631E-01, 1.474635255954523E-03, \ 9.974803510397799E-01, -5.723617700464594E-01, 1.730177315995435E-03, \ 9.983507138390728E-01, -2.846923651716276E-02, 1.946248040917511E-03 ] ) return xyw def smr40 ( ): #*****************************************************************************80 # ## smr40 returns the SMR rule of degree 40. # # Discussion: # # DEGREE: 40 # POINTS CARDINALITY: 296 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*296), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.980037227196614E-01, 1.255939443038006E-01, 2.053102393463664E-03, \ -9.975374042816840E-01, 5.936108405943805E-01, 1.276187489810420E-03, \ -9.972861466402049E-01, -6.627439420820114E-01, 1.580298156253981E-03, \ -9.968592673741854E-01, 8.736423351683437E-01, 1.202945592410809E-03, \ -9.966589451189311E-01, -4.369849380251707E-01, 2.115586380569520E-03, \ -9.965219690837533E-01, -1.944638806631471E-01, 2.429919318140257E-03, \ -9.964358393204891E-01, 4.092031891829934E-01, 2.182777026867640E-03, \ -9.963941450446951E-01, 9.775574537230374E-01, 5.781357112514488E-04, \ -9.955864247426816E-01, -9.784933334191470E-01, 6.423485659734820E-04, \ -9.955242411687316E-01, -8.201261852647251E-01, 1.452148584658119E-03, \ -9.913130830294992E-01, 7.451950336474148E-01, 3.099740554076827E-03, \ -9.900337734476057E-01, -9.112486663047842E-01, 2.026525375041507E-03, \ -9.844939696556546E-01, -3.396948505159310E-02, 6.297322525864257E-03, \ -9.828708241253864E-01, 2.672014458471039E-01, 6.110796337925116E-03, \ -9.813352997502048E-01, 9.317282602187734E-01, 2.388338374639091E-03, \ -9.812506993249306E-01, -5.599844336596295E-01, 5.433547359777527E-03, \ -9.811994633761572E-01, 5.954700474743184E-01, 3.855922634832198E-03, \ -9.787064347309005E-01, -3.245284003636001E-01, 6.507740619311661E-03, \ -9.780647700362322E-01, -7.464363616852314E-01, 4.386694918546395E-03, \ -9.768709333873531E-01, 9.964868257322258E-01, 5.743979761358160E-04, \ -9.743127159036291E-01, -9.969203399240063E-01, 5.885958513598154E-04, \ -9.719890138043383E-01, 4.635529385440017E-01, 5.543426475209034E-03, \ -9.663961744212400E-01, 8.297161334267321E-01, 5.377245930028534E-03, \ -9.624486391679733E-01, -9.552403379650487E-01, 2.935271926976710E-03, \ -9.571101155486035E-01, -8.504016909299451E-01, 5.548045896834978E-03, \ -9.569508072526900E-01, 1.145259922791730E-01, 1.019364727373913E-02, \ -9.539620291105575E-01, 9.656118875216714E-01, 2.000317967473577E-03, \ -9.531361804534030E-01, -1.756012259335100E-01, 1.012788272053494E-02, \ -9.503256987566595E-01, 6.828228592655408E-01, 8.213806957862843E-03, \ -9.455690174869477E-01, -4.553679978362609E-01, 1.002546929027743E-02, \ -9.444080894387320E-01, -6.600309149596145E-01, 8.342165274488325E-03, \ -9.363352068572794E-01, 3.305989409491193E-01, 1.063637549554008E-02, \ -9.344111368509483E-01, 5.018191785468655E-01, 7.093229113292136E-03, \ -9.250445674046065E-01, 8.992422617422033E-01, 6.279305248680532E-03, \ -9.225703808148057E-01, 9.858292479280879E-01, 1.834573979737579E-03, \ -9.165441617582062E-01, -9.853128908447532E-01, 2.565324347525059E-03, \ -9.150614770382599E-01, -3.139530918232870E-02, 1.359896871759167E-02, \ -9.103915600727824E-01, -9.092647756707973E-01, 6.216724896190497E-03, \ -9.074945980525453E-01, -3.110157725349993E-01, 1.298683840693059E-02, \ -9.043535181463653E-01, -7.713160602214696E-01, 1.024303332784389E-02, \ -9.025325558225301E-01, 7.743255817267981E-01, 1.011918005042377E-02, \ -8.936138114540279E-01, 1.960899239677014E-01, 1.411969841594799E-02, \ -8.921757562307675E-01, 5.847775228961032E-01, 1.223494929054215E-02, \ -8.914413155620955E-01, -5.644405075920796E-01, 1.287350206631372E-02, \ -8.651606789959365E-01, 9.507227302652309E-01, 5.817570712124294E-03, \ -8.624964059071404E-01, 4.007509803672114E-01, 1.631963389227952E-02, \ -8.624016491888394E-01, 9.973607974975222E-01, 1.085292256544525E-03, \ -8.571481676731489E-01, -1.732871980674100E-01, 1.643819257648864E-02, \ -8.511908836822574E-01, -4.127628928140689E-01, 1.185185065054727E-02, \ -8.471275338153255E-01, -9.533530423203328E-01, 5.827596397572629E-03, \ -8.433676706517138E-01, 5.983417524756374E-02, 1.569370700632547E-02, \ -8.424649352939378E-01, 8.531606755621376E-01, 1.000254175836821E-02, \ -8.382814166059266E-01, -9.973371948408554E-01, 1.236406010086881E-03, \ -8.380565845515963E-01, -8.466246757209853E-01, 1.074234765384687E-02, \ -8.321936110008199E-01, -6.779831075876902E-01, 1.522781703701599E-02, \ -8.286278033800711E-01, 6.833732733978219E-01, 1.509304227664999E-02, \ -8.055255758765038E-01, -4.763880300923605E-01, 1.085366933632746E-02, \ -7.971673647784905E-01, 2.532323209821991E-01, 2.052836615250460E-02, \ -7.910441928184301E-01, 5.077971678500216E-01, 1.780077542770354E-02, \ -7.859172990177037E-01, -7.833283965104983E-02, 1.472595970793188E-02, \ -7.798224683613482E-01, 9.817158588687893E-01, 4.411372664168903E-03, \ -7.733447858053083E-01, -2.912095449947633E-01, 2.109987317572403E-02, \ -7.707288564403509E-01, 9.135259150232076E-01, 8.345329225642115E-03, \ -7.578198426154767E-01, -9.796098169168449E-01, 4.456574433684158E-03, \ -7.562414896721606E-01, -9.049214717524879E-01, 1.001882084525143E-02, \ -7.548211869038036E-01, 7.785365721991255E-01, 1.478039679943451E-02, \ -7.494378413286128E-01, -7.662608330090768E-01, 1.581956505815484E-02, \ -7.445473618861123E-01, -5.699700714382581E-01, 1.889632922544271E-02, \ -7.423038822674627E-01, 7.897961507665216E-02, 1.715604114405427E-02, \ -7.170452369551987E-01, 6.041689391836269E-01, 1.721434133773814E-02, \ -7.096177258303671E-01, 3.669023638814550E-01, 2.303538633973196E-02, \ -6.947187172157958E-01, -9.098243292500578E-02, 1.600840192685054E-02, \ -6.827474344539016E-01, 8.632122010101693E-01, 9.488912002746175E-03, \ -6.766766916048634E-01, -4.118520712505950E-01, 2.365726668658341E-02, \ -6.757537207484740E-01, 9.965428761249577E-01, 1.913682375287724E-03, \ -6.716977448629430E-01, 9.507129459344548E-01, 7.775380155384150E-03, \ -6.705672963967729E-01, -2.084540920008020E-01, 1.628326394109379E-02, \ -6.634191394897307E-01, -9.956567399175887E-01, 2.049561637770933E-03, \ -6.628050205606234E-01, 1.672916166402376E-01, 2.265410339187529E-02, \ -6.572284494011310E-01, -9.451593820143880E-01, 8.033722247688203E-03, \ -6.502802198668451E-01, -6.663478504843525E-01, 2.086896333372951E-02, \ -6.500944652911421E-01, -8.388046887319990E-01, 1.533892815116460E-02, \ -6.494395416059597E-01, 6.978896106401927E-01, 1.632586135380591E-02, \ -6.182525423851862E-01, 4.772666066191493E-01, 2.314379901273175E-02, \ -6.097521926338272E-01, 8.178387432803899E-01, 1.027570595259021E-02, \ -5.857038932505656E-01, -1.750697876397254E-03, 2.826026275637352E-02, \ -5.765612790071245E-01, -5.184987079049800E-01, 2.276145801578116E-02, \ -5.737142051029732E-01, -3.132765352046541E-01, 1.443899895963975E-02, \ -5.644865970292597E-01, 9.783893306945404E-01, 5.710986844724012E-03, \ -5.644553463342945E-01, 2.782921931969836E-01, 2.781479815231922E-02, \ -5.580769546100564E-01, -9.759275455445522E-01, 5.684058667060024E-03, \ -5.542741288051631E-01, 9.016977074485676E-01, 1.168589067769203E-02, \ -5.542073588689838E-01, -2.043031348070334E-01, 1.827083660577868E-02, \ -5.433087051306172E-01, 5.922649560095551E-01, 1.990937282981727E-02, \ -5.386567969465166E-01, -8.983031172510674E-01, 1.272427456995568E-02, \ -5.373382383966947E-01, -7.520144164271236E-01, 2.091503656277224E-02, \ -5.224304686125945E-01, 7.455130741439847E-01, 1.698684695502466E-02, \ -4.893827154330137E-01, -5.941538126001544E-01, 1.598966080652984E-02, \ -4.722069619254669E-01, -3.587550371799506E-01, 2.132063146049633E-02, \ -4.718832732594200E-01, -9.958106507002302E-01, 2.226108918584357E-03, \ -4.706670553696944E-01, 1.154506383897263E-01, 2.935766164731613E-02, \ -4.626454569472719E-01, 9.963250210519803E-01, 2.223046715737653E-03, \ -4.600264076712823E-01, 3.966582665227552E-01, 2.629091387627286E-02, \ -4.481481045273694E-01, 9.395445338170469E-01, 8.839978177696708E-03, \ -4.415878841168007E-01, -1.062065683181053E-01, 3.058245417110486E-02, \ -4.412583635452328E-01, 5.087399017780769E-01, 1.125492379082715E-02, \ -4.304912794659402E-01, -4.469668566457143E-01, 1.012062172404055E-02, \ -4.287211566152106E-01, 8.321571485937996E-01, 1.786605784125267E-02, \ -4.223793646176035E-01, -8.333753189124466E-01, 1.730213472188374E-02, \ -4.222588890220841E-01, -9.452641667145504E-01, 1.007216794776104E-02, \ -4.083597732182007E-01, 6.509919047599022E-01, 2.181242775531822E-02, \ -3.998205203687450E-01, -6.594190487482490E-01, 2.190933309032257E-02, \ -3.695693944824219E-01, 2.193101954125042E-01, 2.327576101611239E-02, \ -3.676144523897173E-01, 9.682350478689863E-01, 4.815232646045845E-03, \ -3.591049460581930E-01, -4.614598488900264E-01, 1.852799716750301E-02, \ -3.447647402371574E-01, -2.381537435610105E-01, 2.808527790039856E-02, \ -3.341217099662899E-01, -9.826197273812773E-01, 5.494849259173287E-03, \ -3.093195936880301E-01, 3.287238905146597E-01, 2.185303504037471E-02, \ -3.072048398998126E-01, 9.859602190406442E-01, 3.831362623751753E-03, \ -3.058002206640513E-01, 2.103076331772531E-02, 3.459647562394031E-02, \ -3.044867199555938E-01, 5.186120611581733E-01, 2.833979791519306E-02, \ -3.028681432998989E-01, -7.600469172213820E-01, 1.964686881716537E-02, \ -3.024605574449728E-01, 8.931659138204667E-01, 1.538434812191329E-02, \ -3.011532601990519E-01, 7.437794313731125E-01, 2.273787326209627E-02, \ -2.887440306182171E-01, -8.957912044678301E-01, 1.555524233275056E-02, \ -2.644411240015258E-01, -5.502788852260921E-01, 2.671171545840637E-02, \ -2.400609781144449E-01, -3.260570838043731E-01, 2.569267849167105E-02, \ -2.246489878361267E-01, -9.978033236073471E-01, 1.770873804828288E-03, \ -2.066616281756470E-01, -1.045383048279050E-01, 2.497609050660571E-02, \ -2.009374136079489E-01, 2.040282941161825E-01, 2.267428085593906E-02, \ -1.909926939589495E-01, 9.968668571166585E-01, 2.126801518422638E-03, \ -1.887172076094760E-01, -9.549438196754605E-01, 1.035110388694925E-02, \ -1.885639548532559E-01, -6.847997847346543E-01, 2.014138051533820E-02, \ -1.856269263888624E-01, 9.475270956402012E-01, 1.146925671119005E-02, \ -1.790760401308231E-01, 6.312120892250483E-01, 2.910873684757638E-02, \ -1.707661353723164E-01, 8.213933035442971E-01, 2.057181928201535E-02, \ -1.702074855482027E-01, 4.002072179476484E-01, 2.982548255683739E-02, \ -1.505878349304818E-01, -8.293254383680554E-01, 2.076026265668495E-02, \ -1.380074232134180E-01, 1.170336739663703E-01, 2.527234775085595E-02, \ -1.268389913099443E-01, -4.236318257465341E-01, 3.117645114412499E-02, \ -1.153288220374788E-01, -1.747226323716413E-01, 2.609156073209279E-02, \ -8.202442049825323E-02, -6.034256289197292E-01, 2.293044125103543E-02, \ -6.778022692220509E-02, -9.864359427377531E-01, 5.537492701577899E-03, \ -5.134750275993507E-02, 9.806699464341012E-01, 7.025195533489713E-03, \ -4.796731115368809E-02, 5.109816289271156E-01, 2.949281042166952E-02, \ -4.605994163927313E-02, 8.940716194171991E-01, 1.696854743218261E-02, \ -4.447210172626447E-02, -9.096553765331403E-01, 1.548395021034487E-02, \ -4.115113842285135E-02, 7.297743920654538E-01, 2.604976478474774E-02, \ -2.744836558183677E-02, 4.417586914136311E-03, 3.387227419183413E-02, \ -1.995488830453244E-02, 2.898374142768337E-01, 3.548548223572283E-02, \ -9.393841375026718E-03, -7.464248084281863E-01, 2.510074937831712E-02, \ 5.604522124288533E-03, -2.838153304903738E-01, 3.557931287068862E-02, \ 3.379282258563019E-02, -5.108284849354834E-01, 2.741093593275501E-02, \ 7.396931495071729E-02, 6.103364495915078E-01, 2.553255759952799E-02, \ 7.811073060419052E-02, -9.596104105748841E-01, 9.711338256956472E-03, \ 8.053272615641659E-02, 1.616603676436590E-01, 2.424025867338976E-02, \ 8.332876758512328E-02, -9.980434804933414E-01, 1.698291109393467E-03, \ 8.611110621478242E-02, 9.972454574738652E-01, 2.305464957382294E-03, \ 9.098018561909829E-02, 9.458495772991818E-01, 1.224095474595298E-02, \ 9.177090470118981E-02, 8.205555321043025E-01, 2.227240136214740E-02, \ 9.706026488340756E-02, -8.463187115614078E-01, 2.019012230112588E-02, \ 9.815256847947500E-02, -9.239456937873544E-02, 2.644315338527209E-02, \ 1.222602596423681E-01, 4.213511759613903E-01, 3.341374966024566E-02, \ 1.323057369500668E-01, -6.509117254364495E-01, 2.871043880147142E-02, \ 1.476438086930435E-01, -4.017405050343198E-01, 2.837624979369559E-02, \ 1.700850694113563E-01, -1.780332539520100E-01, 2.291185695253523E-02, \ 1.736805569574461E-01, 1.096612012416960E-01, 2.405540809236990E-02, \ 1.843432890535553E-01, 6.990228911926680E-01, 2.163148537165614E-02, \ 1.995648926700597E-01, -9.818731842028169E-01, 3.370075215701449E-03, \ 2.081596610552691E-01, 2.925076496248445E-01, 1.903382067011115E-02, \ 2.211797307297267E-01, -9.164694403878136E-01, 1.468906732639756E-02, \ 2.277074094032160E-01, 9.805932530165899E-01, 7.084751090497078E-03, \ 2.292021628595871E-01, 8.912694976681395E-01, 1.721353195733831E-02, \ 2.353608895201955E-01, -3.491298395101170E-01, 9.892666536128697E-03, \ 2.385004221656652E-01, -7.689128083096237E-01, 2.393352337395165E-02, \ 2.613881314139023E-01, 5.471551577512984E-01, 3.040265099653250E-02, \ 2.662205097670882E-01, -9.919548226778696E-01, 2.707867154217599E-03, \ 2.680565017395204E-01, -5.400402346502616E-01, 3.088207638947784E-02, \ 2.833408004935626E-01, -6.718319274714699E-03, 3.511070135380980E-02, \ 2.921989695479881E-01, 7.730713136429667E-01, 1.950015697008031E-02, \ 2.932051140793899E-01, -2.568476496223008E-01, 2.600581679576460E-02, \ 3.010766919534110E-01, 3.879280619333716E-01, 1.093142774025551E-02, \ 3.103865035997045E-01, 2.499428455332039E-01, 2.499586360508493E-02, \ 3.585933886911649E-01, -8.576820377675525E-01, 1.842882832290949E-02, \ 3.596570955415763E-01, -9.615962408411522E-01, 9.068153972939736E-03, \ 3.618929539106814E-01, 9.449875484526220E-01, 1.169739415667232E-02, \ 3.672563754612045E-01, 9.968578675032447E-01, 2.310464434967522E-03, \ 3.689758663333720E-01, -6.723055595123385E-01, 2.553001008106885E-02, \ 3.871364360677614E-01, -3.963308613870815E-01, 2.492421215216349E-02, \ 3.982469712949650E-01, 4.487336172829021E-01, 2.309608167942591E-02, \ 3.983155249621386E-01, 6.561427847972009E-01, 2.730674172786235E-02, \ 4.034252589810011E-01, 8.423386731412055E-01, 1.707487237256047E-02, \ 4.102541856930609E-01, -1.410736134292944E-01, 3.151312043028231E-02, \ 4.168183088396271E-01, 1.263343252035515E-01, 3.270130716222084E-02, \ 4.356104174313109E-01, -9.957058788304909E-01, 2.363557214215902E-03, \ 4.405318740860549E-01, -4.926398721055529E-01, 1.608280706132078E-02, \ 4.649771622601932E-01, 3.483599503333080E-01, 1.925449126504078E-02, \ 4.709325171484977E-01, -7.695942184085469E-01, 1.705050367502311E-02, \ 4.850638966079184E-01, -9.216775010693871E-01, 1.252775237505845E-02, \ 4.932957374397012E-01, 9.795648836635775E-01, 6.463044419371160E-03, \ 5.128665631816022E-01, 9.033981066102003E-01, 1.292621422635387E-02, \ 5.150863190443300E-01, -5.934248074499449E-01, 2.363213862387783E-02, \ 5.156373648667533E-01, 5.651053767086885E-01, 1.423781492860490E-02, \ 5.181912316625248E-01, -2.922194304405071E-01, 2.989079134667543E-02, \ 5.251717070662635E-01, 7.552962710143433E-01, 2.242429087194216E-02, \ 5.269679036105911E-01, -2.177852596986115E-02, 2.944698631679846E-02, \ 5.359327347133740E-01, -8.200294790454760E-01, 8.860113200433273E-03, \ 5.388079818555839E-01, -9.812499958704087E-01, 4.680745828233062E-03, \ 5.434833238763666E-01, 2.380283686509251E-01, 2.395538344613452E-02, \ 5.496379512343986E-01, 5.253805284097529E-01, 1.632157824790180E-02, \ 6.051493656005358E-01, -4.503578461535495E-01, 2.612344895845866E-02, \ 6.124277898034318E-01, 9.967024781187570E-01, 2.002070456520778E-03, \ 6.140603542011213E-01, 3.676905093247132E-01, 1.890620847606754E-02, \ 6.149248157512081E-01, -8.737165849180063E-01, 1.296667270713843E-02, \ 6.154648019220623E-01, -7.039292064085437E-01, 2.124810385786090E-02, \ 6.216520374448096E-01, 9.489344195184967E-01, 8.530620092099012E-03, \ 6.262996333546856E-01, -9.603966937474196E-01, 6.014411655091729E-03, \ 6.266507568536149E-01, -1.753112127213321E-01, 2.574430846684179E-02, \ 6.320748250590934E-01, 9.236778723276985E-02, 2.509516970454762E-02, \ 6.371103207708532E-01, 8.421673270141240E-01, 1.637617879409531E-02, \ 6.445697045015427E-01, 6.589930041457702E-01, 2.309339250212301E-02, \ 6.611641817999792E-01, -9.971250985273443E-01, 1.780949246753485E-03, \ 6.827225489763870E-01, 4.582089303489358E-01, 1.967115820258447E-02, \ 7.007607922685678E-01, -5.793001008608837E-01, 2.187824067436787E-02, \ 7.074131809621955E-01, -3.372902789247548E-01, 2.360006012075187E-02, \ 7.117739087420435E-01, 2.241359340497962E-01, 2.258162720143967E-02, \ 7.151943805770620E-01, -7.271602060694378E-02, 2.063320130758209E-02, \ 7.155680922709143E-01, -7.994435082716885E-01, 1.620969075703751E-02, \ 7.187947908611272E-01, -9.289105584767267E-01, 8.674348771692817E-03, \ 7.188580147804288E-01, 9.801870566125678E-01, 4.556848768699447E-03, \ 7.407850806335647E-01, 9.092174747735176E-01, 1.069960175297740E-02, \ 7.414535252324259E-01, 7.627992252808989E-01, 1.713716583993931E-02, \ 7.620781689289542E-01, 5.682929391541718E-01, 1.992594154989019E-02, \ 7.635939132299792E-01, -9.831481015790724E-01, 4.153559323873574E-03, \ 7.797638735837149E-01, 4.665676142002305E-02, 1.954090589438721E-02, \ 7.867620038671331E-01, 3.403489048139350E-01, 1.972374555702004E-02, \ 7.883553505223821E-01, -6.893416107380125E-01, 1.663667575800614E-02, \ 7.942764870013759E-01, -4.707153685105653E-01, 1.983755770035392E-02, \ 7.952669529963022E-01, -2.273770055235256E-01, 2.028000921211288E-02, \ 7.990872541216331E-01, 9.962955158284175E-01, 1.408927698874655E-03, \ 8.066178878802995E-01, -8.762511423208362E-01, 1.090696275036013E-02, \ 8.274679999131711E-01, 8.480202028380042E-01, 1.137803861452648E-02, \ 8.297408153069072E-01, 9.581886918512165E-01, 5.948632265683609E-03, \ 8.377680145222012E-01, 6.811297101045124E-01, 1.536534914781161E-02, \ 8.427716005452982E-01, -9.571708221478029E-01, 4.952439619855199E-03, \ 8.488271945024087E-01, 1.666337693793623E-01, 1.887388216602816E-02, \ 8.525662030669592E-01, 4.592708043695782E-01, 1.653498201879920E-02, \ 8.561315417874497E-01, -9.598113535151943E-02, 1.680778035994472E-02, \ 8.606876078808835E-01, -9.969922689109865E-01, 1.288211684632280E-03, \ 8.613581542207239E-01, -7.784610468370953E-01, 1.096644364207657E-02, \ 8.690885595988450E-01, -5.894733063271762E-01, 1.503337345041933E-02, \ 8.723930444088900E-01, -3.621107058578862E-01, 1.641608892157977E-02, \ 8.962187117350728E-01, 9.900514429185334E-01, 2.177703335659953E-03, \ 8.978901908775218E-01, 9.150513717072788E-01, 6.528697758436882E-03, \ 8.995842578268963E-01, -9.234484518613306E-01, 5.137110006320958E-03, \ 9.026936084906036E-01, 7.808928092755504E-01, 1.012526399216284E-02, \ 9.070441620900885E-01, 3.009963311241410E-01, 1.501588480324425E-02, \ 9.077878820329093E-01, 5.794983066365614E-01, 1.246940196306337E-02, \ 9.111551364648940E-01, -8.412973077435701E-01, 5.641113054429737E-03, \ 9.142518109635371E-01, 2.169517484726380E-02, 1.439386845586924E-02, \ 9.173217644911268E-01, -2.254212884222193E-01, 1.167670360384378E-02, \ 9.282555961436508E-01, -6.912520433990101E-01, 9.933776930685268E-03, \ 9.284877628036031E-01, -9.817037571629690E-01, 2.694281259701618E-03, \ 9.334452240614641E-01, -4.859399349804389E-01, 1.184281101417954E-02, \ 9.468439730471343E-01, 9.657765158699502E-01, 3.003223815105551E-03, \ 9.506625037743694E-01, 4.376710347741515E-01, 1.025469033794625E-02, \ 9.520896121093332E-01, 8.643710868609885E-01, 5.555972363422187E-03, \ 9.523271992044501E-01, 6.913007415265950E-01, 7.990950689265556E-03, \ 9.545272982243453E-01, -8.811333722531620E-01, 3.828862340862868E-03, \ 9.554958506512122E-01, 1.588668533845889E-01, 1.058860881322785E-02, \ 9.598844841990601E-01, -3.304786335896162E-01, 6.696028105510322E-03, \ 9.612092716134895E-01, -1.252637834195337E-01, 8.918983273981967E-03, \ 9.664864057745631E-01, -7.771023857020345E-01, 5.108888381040824E-03, \ 9.696658884223082E-01, -9.486617819335378E-01, 2.629252771609383E-03, \ 9.714461152005505E-01, 9.966817132006599E-01, 6.382221125358519E-04, \ 9.756072026722676E-01, -9.972566545264508E-01, 5.380433266276414E-04, \ 9.756270675128569E-01, -5.974850205967676E-01, 6.836267790083512E-03, \ 9.794527164689676E-01, 5.643324681844055E-01, 5.410131191715718E-03, \ 9.826866520761600E-01, 7.911127382228441E-01, 3.928246838882010E-03, \ 9.831392239644022E-01, 9.303396888012979E-01, 2.423589086603377E-03, \ 9.832274416154096E-01, 3.033661616270960E-01, 6.310915040526618E-03, \ 9.843450993838505E-01, -4.150221010386896E-01, 4.095407382162835E-03, \ 9.849932890167565E-01, 7.572227591204869E-03, 5.802629795760786E-03, \ 9.909963827975042E-01, -2.639507972140410E-01, 3.395140293721511E-03, \ 9.912765561948801E-01, -8.332891526969999E-01, 1.953926311905468E-03, \ 9.934327301490941E-01, 6.231882587178860E-01, 9.287993595683975E-04, \ 9.937448936136122E-01, -9.092710501130503E-01, 1.256142182103206E-03, \ 9.948882230658729E-01, -7.050697257712721E-01, 2.287960809703529E-03, \ 9.951704470679726E-01, 9.801745622873680E-01, 6.475410324288955E-04, \ 9.952340236934687E-01, -9.783971899965007E-01, 6.447054298301821E-04, \ 9.963792308208721E-01, 6.981957876294371E-01, 1.512427084884079E-03, \ 9.970264968246741E-01, 4.457495638028096E-01, 2.107128717380615E-03, \ 9.977348846785328E-01, -1.427747693558082E-01, 1.552913600795280E-03, \ 9.977388598284106E-01, 1.545000376629158E-01, 2.038498731858248E-03, \ 9.982891584585788E-01, 8.710523206892243E-01, 9.529077858582162E-04, \ 9.991656973291163E-01, -5.021799411346501E-01, 1.444993876112607E-03 ] ) return xyw def smr41 ( ): #*****************************************************************************80 # ## smr41 returns the SMR rule of degree 41. # # Discussion: # # DEGREE: 41 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 303 # NORM INF MOMS. RESIDUAL: 1.77636e-15 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*303), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.979788599279722E-01, -8.620321171404657E-01, 9.843080418879427E-04, \ -9.972233023651127E-01, -1.689643304774283E-01, 2.334603070096216E-03, \ -9.968865665492763E-01, 1.264946845449128E-01, 2.336585497171821E-03, \ -9.967543799903597E-01, 3.758322880625192E-01, 1.965952058779777E-03, \ -9.966030911672050E-01, -4.414700559329136E-01, 2.103309187930437E-03, \ -9.965848495106024E-01, -6.842725498070605E-01, 1.783337849517576E-03, \ -9.961989059670616E-01, 9.525971037206539E-01, 6.660472520224310E-04, \ -9.955131940127476E-01, 8.558413309721239E-01, 1.466862509992409E-03, \ -9.955121819465780E-01, -9.789979211029449E-01, 6.407210056305082E-04, \ -9.954861320163209E-01, 5.681416527913361E-01, 2.181094091195068E-03, \ -9.929582393871068E-01, -5.370347553708347E-01, 6.365700160628349E-04, \ -9.918341858607898E-01, 7.250215468408083E-01, 2.925047225366992E-03, \ -9.897982334464747E-01, 9.889847320679855E-01, 6.578382364688170E-04, \ -9.850276191493494E-01, -9.248683981506678E-01, 2.259102932718402E-03, \ -9.820959231331791E-01, -7.821855489421354E-01, 4.084862972791807E-03, \ -9.818366925634343E-01, -2.156090420260150E-02, 6.852107137072102E-03, \ -9.808975723862894E-01, -3.112518230537506E-01, 6.733976982472782E-03, \ -9.803016487147558E-01, 2.539985793768113E-01, 6.144467944923415E-03, \ -9.791585763360798E-01, -5.756466500202441E-01, 5.476389537369480E-03, \ -9.767561034338471E-01, 9.143771666367756E-01, 2.776979717116026E-03, \ -9.758317798625764E-01, 4.558745215283740E-01, 5.758484945330961E-03, \ -9.733634369985799E-01, -9.966978125597651E-01, 6.175342802324851E-04, \ -9.675664657866050E-01, 6.206279941904160E-01, 6.157178279661575E-03, \ -9.667526686680565E-01, 8.023493190515092E-01, 5.052013954468514E-03, \ -9.574847616595294E-01, 9.991852307452070E-01, 4.156752677850517E-04, \ -9.551655794629224E-01, 9.662000026762417E-01, 2.519263815744828E-03, \ -9.541283709855817E-01, -9.615200131743211E-01, 2.770123594982525E-03, \ -9.529627107888853E-01, -8.594308951734482E-01, 5.521466103754615E-03, \ -9.511137028620014E-01, 1.537123214377626E-01, 1.548656739539656E-03, \ -9.501218449448332E-01, -1.679843056344594E-01, 1.129203236633850E-02, \ -9.486279733146294E-01, -6.865588686606500E-01, 8.287308334158514E-03, \ -9.483377728448769E-01, 1.079182983808205E-01, 9.649772007405522E-03, \ -9.481698863829746E-01, -4.482511579023943E-01, 1.058846772781884E-02, \ -9.376659862954376E-01, 3.320927786395850E-01, 9.853104948952236E-03, \ -9.306103944301639E-01, 8.662316655121048E-01, 5.280103565555265E-03, \ -9.300699834315862E-01, 7.014618847802435E-01, 8.344725482478233E-03, \ -9.280108673251274E-01, 4.983380051452493E-01, 9.333950017742142E-03, \ -9.095843629981852E-01, -9.870451124979706E-01, 2.291616065068371E-03, \ -9.045872993270916E-01, 9.244231244080491E-01, 4.633234288837451E-03, \ -9.035282359913408E-01, -9.127575798900944E-01, 6.195061068875661E-03, \ -9.023427661156972E-01, -3.102537604841927E-01, 1.518789863772203E-02, \ -9.023191697919575E-01, 9.860953439377561E-01, 2.287777730391639E-03, \ -9.018609313605185E-01, -3.168234272327462E-02, 1.540631304873537E-02, \ -9.009350039678510E-01, -7.782630377583909E-01, 1.005814342536296E-02, \ -8.995512373198538E-01, -5.752687860358924E-01, 1.333914316671023E-02, \ -8.862410073156858E-01, 2.023135190038032E-01, 1.419438960724134E-02, \ -8.799510611339678E-01, 7.804272229598096E-01, 9.800822621659112E-03, \ -8.779133156049225E-01, 5.858583967917332E-01, 1.273340964065398E-02, \ -8.655996427765849E-01, 3.758701133077118E-01, 1.356217699235571E-02, \ -8.409266136580046E-01, -4.471234082886604E-01, 1.725729695008926E-02, \ -8.400990403804555E-01, -9.553728108586558E-01, 5.756357460449216E-03, \ -8.396784302276527E-01, -1.756139328191055E-01, 1.921157782857880E-02, \ -8.378454530446884E-01, 9.530099558379057E-01, 5.399408829933249E-03, \ -8.351166757877715E-01, -9.976562452857387E-01, 1.078286714786108E-03, \ -8.318210977517786E-01, -8.478689190545843E-01, 1.077737568013724E-02, \ -8.316813659365053E-01, -6.810571166632299E-01, 1.554511865335202E-02, \ -8.305330238628740E-01, 8.626294758901784E-01, 9.402009758617824E-03, \ -8.294785607894918E-01, 9.967444014424583E-01, 1.208238555914957E-03, \ -8.257889703732273E-01, 7.178314536082597E-02, 1.768899055141865E-02, \ -8.110197774934704E-01, 6.807113046668994E-01, 1.523540797814434E-02, \ -8.029840820822153E-01, 4.688347153306865E-01, 1.679016485272365E-02, \ -7.832130052321671E-01, 2.499268458076058E-01, 1.971664557932711E-02, \ -7.801221870591962E-01, -5.296331251016586E-01, 3.661339198539565E-03, \ -7.680489268476366E-01, -3.239665253282490E-01, 2.029577519777635E-02, \ -7.568982042081489E-01, -6.469903320156577E-02, 1.929849800043277E-02, \ -7.519799147310821E-01, -9.820165683081348E-01, 4.279421611368336E-03, \ -7.503688437977389E-01, -9.065793653546036E-01, 1.014558607042340E-02, \ -7.503013634605583E-01, 9.802360242338881E-01, 4.439623982463855E-03, \ -7.497536820115352E-01, -5.698053761201402E-01, 1.779839962659180E-02, \ -7.446422046307247E-01, 9.102156841025124E-01, 9.086171802680322E-03, \ -7.445500034233367E-01, 7.848047539654122E-01, 1.480460601233261E-02, \ -7.420314577338432E-01, -7.669296945893275E-01, 1.649262306205733E-02, \ -7.232254143511531E-01, 5.713056680823388E-01, 2.016548810406117E-02, \ -7.062208864591450E-01, 9.503977235942600E-02, 1.928783830209237E-02, \ -7.031430448656599E-01, 3.539369545569842E-01, 2.086333365650514E-02, \ -6.910760386360507E-01, -2.202589299389135E-01, 1.824693519009817E-02, \ -6.711541165821081E-01, -4.470179997221566E-01, 1.982448992952755E-02, \ -6.531718048226814E-01, 9.967997404348319E-01, 1.851797920829879E-03, \ -6.510982873867898E-01, -9.494836825061095E-01, 8.282094698086110E-03, \ -6.495359763175098E-01, -9.967203887198085E-01, 1.840591604616235E-03, \ -6.473927602298331E-01, 6.932779937556659E-01, 1.958957103753717E-02, \ -6.464452229923815E-01, 8.552721751249167E-01, 1.167683626501659E-02, \ -6.459328707826928E-01, -6.630485503781940E-01, 2.204591732276851E-02, \ -6.422957416183844E-01, 9.498995336148190E-01, 8.184904472780722E-03, \ -6.411208000593052E-01, -8.428969978933917E-01, 1.568169438177813E-02, \ -6.376753802962584E-01, -7.106433457042012E-02, 1.835262838211505E-02, \ -6.277916196017650E-01, 1.869178545078614E-01, 2.243995725960829E-02, \ -6.151521573306764E-01, 4.575647790357444E-01, 2.332139121086357E-02, \ -6.110490337662942E-01, -3.716909293029730E-01, 1.353424810977647E-02, \ -5.789585639318591E-01, 8.116111501687501E-01, 8.239538289259576E-03, \ -5.719445376985364E-01, -2.076230901972163E-01, 1.980619800036562E-02, \ -5.503010082245448E-01, -5.351187300277593E-01, 2.203583241136872E-02, \ -5.448020739951114E-01, 5.943977618827134E-01, 2.119679939093152E-02, \ -5.405717934730448E-01, 2.398766500666945E-02, 2.753053261097250E-02, \ -5.379183131495114E-01, -9.794968398169707E-01, 5.852700601431832E-03, \ -5.351808255772759E-01, 9.807921885374170E-01, 5.695018653828906E-03, \ -5.307318203931908E-01, -7.548959411509537E-01, 2.161368448540176E-02, \ -5.295874335958505E-01, 2.972675778301046E-01, 2.831405936915660E-02, \ -5.286141781682451E-01, -9.043560824552355E-01, 1.301083261420718E-02, \ -5.174239052084288E-01, 9.052729023030037E-01, 1.310577146977484E-02, \ -5.002001743362517E-01, 7.536126162564385E-01, 1.877702249835676E-02, \ -4.949149883106970E-01, -3.239151523715213E-01, 2.413732904338590E-02, \ -4.926819371575777E-01, -5.863264530268616E-01, 9.252700572850187E-03, \ -4.572955824770646E-01, 5.174797928661199E-01, 1.280901341961230E-02, \ -4.330661622416971E-01, -1.162896573168444E-01, 3.094672746065751E-02, \ -4.265146037440953E-01, 1.431197872276920E-01, 3.097439241585212E-02, \ -4.261542183676564E-01, 4.217014688490645E-01, 2.299426219446216E-02, \ -4.260965440692615E-01, -9.965783521197458E-01, 2.184951478119829E-03, \ -4.195965641842235E-01, 9.968712678138757E-01, 2.102981801155398E-03, \ -4.122399178795176E-01, -4.475194975775657E-01, 1.989673839306039E-02, \ -4.105366827946999E-01, -8.373589753274594E-01, 1.841138617779475E-02, \ -4.018650475100398E-01, -6.569857706362335E-01, 2.531099347585827E-02, \ -4.011312302189050E-01, -9.485309748736876E-01, 1.036126977964170E-02, \ -3.965687446957954E-01, 9.512021797025086E-01, 1.007429601084097E-02, \ -3.886867567687322E-01, 8.415221322242826E-01, 1.867865037165336E-02, \ -3.863072449479136E-01, 6.585305620664139E-01, 2.494229959731991E-02, \ -3.558089768700468E-01, -4.173145393898551E-01, 1.256145253990760E-02, \ -3.361006797113043E-01, -2.320489871510133E-01, 2.411745034362549E-02, \ -3.273064092637250E-01, 2.552981701918742E-01, 1.731337482356964E-02, \ -3.143235654002606E-01, 3.434855626045295E-01, 1.768325686985408E-02, \ -2.969988871235867E-01, 1.512212631139971E-02, 3.451049222856652E-02, \ -2.851682496889180E-01, -9.823368483892302E-01, 6.076427259472100E-03, \ -2.842287026196041E-01, -7.573701654746426E-01, 2.254851231334031E-02, \ -2.763872051458339E-01, 9.848430016399402E-01, 4.391195859850334E-03, \ -2.757570191887748E-01, 5.328644045211444E-01, 3.039500110542442E-02, \ -2.689789570111630E-01, -8.976396396474979E-01, 1.589379778474137E-02, \ -2.666695494019358E-01, -5.458482771574984E-01, 3.009909572762831E-02, \ -2.655053034213333E-01, 9.771787699513292E-01, 1.894385891729340E-03, \ -2.627557017089030E-01, 7.555588777373272E-01, 2.363679764618126E-02, \ -2.562363324756580E-01, 9.047634768272976E-01, 1.523993759370399E-02, \ -2.401694466154886E-01, -3.082397101256352E-01, 2.545591145933639E-02, \ -1.999384860986652E-01, 1.995960452917006E-01, 2.644981232826374E-02, \ -1.934165548136490E-01, -1.001228826623429E-01, 2.353802509227792E-02, \ -1.605338025079172E-01, -9.977634540883650E-01, 1.896784969760382E-03, \ -1.596836572730810E-01, 3.941151625223360E-01, 3.004459538308863E-02, \ -1.582769934825167E-01, -6.689987456876101E-01, 2.405213561825666E-02, \ -1.454325940338082E-01, -9.514097712610464E-01, 1.102950511878142E-02, \ -1.436551253873852E-01, 6.453308106984021E-01, 2.877227939270967E-02, \ -1.364207441182524E-01, 9.973928878261128E-01, 2.062325710829592E-03, \ -1.323616733693008E-01, -8.292521434719048E-01, 2.101390827968778E-02, \ -1.284662135957239E-01, -4.199690393178734E-01, 3.292903599927027E-02, \ -1.272488031447826E-01, 8.354138942117858E-01, 2.022653122178670E-02, \ -1.242239684265682E-01, 9.539196646941631E-01, 1.076287752752471E-02, \ -1.099650016306503E-01, 1.001181481554234E-01, 2.776239604781384E-02, \ -1.058473836439364E-01, -1.676489858375358E-01, 2.632360797858480E-02, \ -4.887769924515067E-02, 4.984873757664716E-01, 2.452379021441048E-02, \ -4.878511560715085E-02, -5.810857563657668E-01, 2.200867989097806E-02, \ -1.487759494787105E-02, -9.841897690617597E-01, 6.148525047866293E-03, \ -9.715667325046100E-03, 2.841665712486741E-01, 3.560311127234845E-02, \ -7.133604297269260E-03, -9.026737353005819E-01, 1.596380767648381E-02, \ -5.357202966277515E-03, 7.436791749793509E-01, 2.516341018429965E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 3.080626042474933E-02, \ 5.357202966277515E-03, -7.436791749793509E-01, 2.516341018429965E-02, \ 7.133604297269260E-03, 9.026737353005819E-01, 1.596380767648381E-02, \ 9.715667325046100E-03, -2.841665712486741E-01, 3.560311127234845E-02, \ 1.487759494787105E-02, 9.841897690617597E-01, 6.148525047866293E-03, \ 4.878511560715085E-02, 5.810857563657668E-01, 2.200867989097806E-02, \ 4.887769924515067E-02, -4.984873757664716E-01, 2.452379021441048E-02, \ 1.058473836439364E-01, 1.676489858375358E-01, 2.632360797858480E-02, \ 1.099650016306503E-01, -1.001181481554234E-01, 2.776239604781384E-02, \ 1.242239684265682E-01, -9.539196646941631E-01, 1.076287752752471E-02, \ 1.272488031447826E-01, -8.354138942117858E-01, 2.022653122178670E-02, \ 1.284662135957239E-01, 4.199690393178734E-01, 3.292903599927027E-02, \ 1.323616733693008E-01, 8.292521434719048E-01, 2.101390827968778E-02, \ 1.364207441182524E-01, -9.973928878261128E-01, 2.062325710829592E-03, \ 1.436551253873852E-01, -6.453308106984021E-01, 2.877227939270967E-02, \ 1.454325940338082E-01, 9.514097712610464E-01, 1.102950511878142E-02, \ 1.582769934825167E-01, 6.689987456876101E-01, 2.405213561825666E-02, \ 1.596836572730810E-01, -3.941151625223360E-01, 3.004459538308863E-02, \ 1.605338025079172E-01, 9.977634540883650E-01, 1.896784969760382E-03, \ 1.934165548136490E-01, 1.001228826623429E-01, 2.353802509227792E-02, \ 1.999384860986652E-01, -1.995960452917006E-01, 2.644981232826374E-02, \ 2.401694466154886E-01, 3.082397101256352E-01, 2.545591145933639E-02, \ 2.562363324756580E-01, -9.047634768272976E-01, 1.523993759370399E-02, \ 2.627557017089030E-01, -7.555588777373272E-01, 2.363679764618126E-02, \ 2.655053034213333E-01, -9.771787699513292E-01, 1.894385891729340E-03, \ 2.666695494019358E-01, 5.458482771574984E-01, 3.009909572762831E-02, \ 2.689789570111630E-01, 8.976396396474979E-01, 1.589379778474137E-02, \ 2.757570191887748E-01, -5.328644045211444E-01, 3.039500110542442E-02, \ 2.763872051458339E-01, -9.848430016399402E-01, 4.391195859850334E-03, \ 2.842287026196041E-01, 7.573701654746426E-01, 2.254851231334031E-02, \ 2.851682496889180E-01, 9.823368483892302E-01, 6.076427259472100E-03, \ 2.969988871235867E-01, -1.512212631139971E-02, 3.451049222856652E-02, \ 3.143235654002606E-01, -3.434855626045295E-01, 1.768325686985408E-02, \ 3.273064092637250E-01, -2.552981701918742E-01, 1.731337482356964E-02, \ 3.361006797113043E-01, 2.320489871510133E-01, 2.411745034362549E-02, \ 3.558089768700468E-01, 4.173145393898551E-01, 1.256145253990760E-02, \ 3.863072449479136E-01, -6.585305620664139E-01, 2.494229959731991E-02, \ 3.886867567687322E-01, -8.415221322242826E-01, 1.867865037165336E-02, \ 3.965687446957954E-01, -9.512021797025086E-01, 1.007429601084097E-02, \ 4.011312302189050E-01, 9.485309748736876E-01, 1.036126977964170E-02, \ 4.018650475100398E-01, 6.569857706362335E-01, 2.531099347585827E-02, \ 4.105366827946999E-01, 8.373589753274594E-01, 1.841138617779475E-02, \ 4.122399178795176E-01, 4.475194975775657E-01, 1.989673839306039E-02, \ 4.195965641842235E-01, -9.968712678138757E-01, 2.102981801155398E-03, \ 4.260965440692615E-01, 9.965783521197458E-01, 2.184951478119829E-03, \ 4.261542183676564E-01, -4.217014688490645E-01, 2.299426219446216E-02, \ 4.265146037440953E-01, -1.431197872276920E-01, 3.097439241585212E-02, \ 4.330661622416971E-01, 1.162896573168444E-01, 3.094672746065751E-02, \ 4.572955824770646E-01, -5.174797928661199E-01, 1.280901341961230E-02, \ 4.926819371575777E-01, 5.863264530268616E-01, 9.252700572850187E-03, \ 4.949149883106970E-01, 3.239151523715213E-01, 2.413732904338590E-02, \ 5.002001743362517E-01, -7.536126162564385E-01, 1.877702249835676E-02, \ 5.174239052084288E-01, -9.052729023030037E-01, 1.310577146977484E-02, \ 5.286141781682451E-01, 9.043560824552355E-01, 1.301083261420718E-02, \ 5.295874335958505E-01, -2.972675778301046E-01, 2.831405936915660E-02, \ 5.307318203931908E-01, 7.548959411509537E-01, 2.161368448540176E-02, \ 5.351808255772759E-01, -9.807921885374170E-01, 5.695018653828906E-03, \ 5.379183131495114E-01, 9.794968398169707E-01, 5.852700601431832E-03, \ 5.405717934730448E-01, -2.398766500666945E-02, 2.753053261097250E-02, \ 5.448020739951114E-01, -5.943977618827134E-01, 2.119679939093152E-02, \ 5.503010082245448E-01, 5.351187300277593E-01, 2.203583241136872E-02, \ 5.719445376985364E-01, 2.076230901972163E-01, 1.980619800036562E-02, \ 5.789585639318591E-01, -8.116111501687501E-01, 8.239538289259576E-03, \ 6.110490337662942E-01, 3.716909293029730E-01, 1.353424810977647E-02, \ 6.151521573306764E-01, -4.575647790357444E-01, 2.332139121086357E-02, \ 6.277916196017650E-01, -1.869178545078614E-01, 2.243995725960829E-02, \ 6.376753802962584E-01, 7.106433457042012E-02, 1.835262838211505E-02, \ 6.411208000593052E-01, 8.428969978933917E-01, 1.568169438177813E-02, \ 6.422957416183844E-01, -9.498995336148190E-01, 8.184904472780722E-03, \ 6.459328707826928E-01, 6.630485503781940E-01, 2.204591732276851E-02, \ 6.464452229923815E-01, -8.552721751249167E-01, 1.167683626501659E-02, \ 6.473927602298331E-01, -6.932779937556659E-01, 1.958957103753717E-02, \ 6.495359763175098E-01, 9.967203887198085E-01, 1.840591604616235E-03, \ 6.510982873867898E-01, 9.494836825061095E-01, 8.282094698086110E-03, \ 6.531718048226814E-01, -9.967997404348319E-01, 1.851797920829879E-03, \ 6.711541165821081E-01, 4.470179997221566E-01, 1.982448992952755E-02, \ 6.910760386360507E-01, 2.202589299389135E-01, 1.824693519009817E-02, \ 7.031430448656599E-01, -3.539369545569842E-01, 2.086333365650514E-02, \ 7.062208864591450E-01, -9.503977235942600E-02, 1.928783830209237E-02, \ 7.232254143511531E-01, -5.713056680823388E-01, 2.016548810406117E-02, \ 7.420314577338432E-01, 7.669296945893275E-01, 1.649262306205733E-02, \ 7.445500034233367E-01, -7.848047539654122E-01, 1.480460601233261E-02, \ 7.446422046307247E-01, -9.102156841025124E-01, 9.086171802680322E-03, \ 7.497536820115352E-01, 5.698053761201402E-01, 1.779839962659180E-02, \ 7.503013634605583E-01, -9.802360242338881E-01, 4.439623982463855E-03, \ 7.503688437977389E-01, 9.065793653546036E-01, 1.014558607042340E-02, \ 7.519799147310821E-01, 9.820165683081348E-01, 4.279421611368336E-03, \ 7.568982042081489E-01, 6.469903320156577E-02, 1.929849800043277E-02, \ 7.680489268476366E-01, 3.239665253282490E-01, 2.029577519777635E-02, \ 7.801221870591962E-01, 5.296331251016586E-01, 3.661339198539565E-03, \ 7.832130052321671E-01, -2.499268458076058E-01, 1.971664557932711E-02, \ 8.029840820822153E-01, -4.688347153306865E-01, 1.679016485272365E-02, \ 8.110197774934704E-01, -6.807113046668994E-01, 1.523540797814434E-02, \ 8.257889703732273E-01, -7.178314536082597E-02, 1.768899055141865E-02, \ 8.294785607894918E-01, -9.967444014424583E-01, 1.208238555914957E-03, \ 8.305330238628740E-01, -8.626294758901784E-01, 9.402009758617824E-03, \ 8.316813659365053E-01, 6.810571166632299E-01, 1.554511865335202E-02, \ 8.318210977517786E-01, 8.478689190545843E-01, 1.077737568013724E-02, \ 8.351166757877715E-01, 9.976562452857387E-01, 1.078286714786108E-03, \ 8.378454530446884E-01, -9.530099558379057E-01, 5.399408829933249E-03, \ 8.396784302276527E-01, 1.756139328191055E-01, 1.921157782857880E-02, \ 8.400990403804555E-01, 9.553728108586558E-01, 5.756357460449216E-03, \ 8.409266136580046E-01, 4.471234082886604E-01, 1.725729695008926E-02, \ 8.655996427765849E-01, -3.758701133077118E-01, 1.356217699235571E-02, \ 8.779133156049225E-01, -5.858583967917332E-01, 1.273340964065398E-02, \ 8.799510611339678E-01, -7.804272229598096E-01, 9.800822621659112E-03, \ 8.862410073156858E-01, -2.023135190038032E-01, 1.419438960724134E-02, \ 8.995512373198538E-01, 5.752687860358924E-01, 1.333914316671023E-02, \ 9.009350039678510E-01, 7.782630377583909E-01, 1.005814342536296E-02, \ 9.018609313605185E-01, 3.168234272327462E-02, 1.540631304873537E-02, \ 9.023191697919575E-01, -9.860953439377561E-01, 2.287777730391639E-03, \ 9.023427661156972E-01, 3.102537604841927E-01, 1.518789863772203E-02, \ 9.035282359913408E-01, 9.127575798900944E-01, 6.195061068875661E-03, \ 9.045872993270916E-01, -9.244231244080491E-01, 4.633234288837451E-03, \ 9.095843629981852E-01, 9.870451124979706E-01, 2.291616065068371E-03, \ 9.280108673251274E-01, -4.983380051452493E-01, 9.333950017742142E-03, \ 9.300699834315862E-01, -7.014618847802435E-01, 8.344725482478233E-03, \ 9.306103944301639E-01, -8.662316655121048E-01, 5.280103565555265E-03, \ 9.376659862954376E-01, -3.320927786395850E-01, 9.853104948952236E-03, \ 9.481698863829746E-01, 4.482511579023943E-01, 1.058846772781884E-02, \ 9.483377728448769E-01, -1.079182983808205E-01, 9.649772007405522E-03, \ 9.486279733146294E-01, 6.865588686606500E-01, 8.287308334158514E-03, \ 9.501218449448332E-01, 1.679843056344594E-01, 1.129203236633850E-02, \ 9.511137028620014E-01, -1.537123214377626E-01, 1.548656739539656E-03, \ 9.529627107888853E-01, 8.594308951734482E-01, 5.521466103754615E-03, \ 9.541283709855817E-01, 9.615200131743211E-01, 2.770123594982525E-03, \ 9.551655794629224E-01, -9.662000026762417E-01, 2.519263815744828E-03, \ 9.574847616595294E-01, -9.991852307452070E-01, 4.156752677850517E-04, \ 9.667526686680565E-01, -8.023493190515092E-01, 5.052013954468514E-03, \ 9.675664657866050E-01, -6.206279941904160E-01, 6.157178279661575E-03, \ 9.733634369985799E-01, 9.966978125597651E-01, 6.175342802324851E-04, \ 9.758317798625764E-01, -4.558745215283740E-01, 5.758484945330961E-03, \ 9.767561034338471E-01, -9.143771666367756E-01, 2.776979717116026E-03, \ 9.791585763360798E-01, 5.756466500202441E-01, 5.476389537369480E-03, \ 9.803016487147558E-01, -2.539985793768113E-01, 6.144467944923415E-03, \ 9.808975723862894E-01, 3.112518230537506E-01, 6.733976982472782E-03, \ 9.818366925634343E-01, 2.156090420260150E-02, 6.852107137072102E-03, \ 9.820959231331791E-01, 7.821855489421354E-01, 4.084862972791807E-03, \ 9.850276191493494E-01, 9.248683981506678E-01, 2.259102932718402E-03, \ 9.897982334464747E-01, -9.889847320679855E-01, 6.578382364688170E-04, \ 9.918341858607898E-01, -7.250215468408083E-01, 2.925047225366992E-03, \ 9.929582393871068E-01, 5.370347553708347E-01, 6.365700160628349E-04, \ 9.954861320163209E-01, -5.681416527913361E-01, 2.181094091195068E-03, \ 9.955121819465780E-01, 9.789979211029449E-01, 6.407210056305082E-04, \ 9.955131940127476E-01, -8.558413309721239E-01, 1.466862509992409E-03, \ 9.961989059670616E-01, -9.525971037206539E-01, 6.660472520224310E-04, \ 9.965848495106024E-01, 6.842725498070605E-01, 1.783337849517576E-03, \ 9.966030911672050E-01, 4.414700559329136E-01, 2.103309187930437E-03, \ 9.967543799903597E-01, -3.758322880625192E-01, 1.965952058779777E-03, \ 9.968865665492763E-01, -1.264946845449128E-01, 2.336585497171821E-03, \ 9.972233023651127E-01, 1.689643304774283E-01, 2.334603070096216E-03, \ 9.979788599279722E-01, 8.620321171404657E-01, 9.843080418879427E-04 ] ) return xyw def smr42 ( ): #*****************************************************************************80 # ## smr42 returns the SMR rule of degree 42. # # Discussion: # # DEGREE: 42 # POINTS CARDINALITY: 326 # NORM INF MOMS. RESIDUAL: 8.67145e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*326), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.983895853811665E-01, 2.969737627802563E-01, 1.238150356046483E-03, \ -9.977615781174913E-01, -7.709519815994472E-01, 1.081616267165998E-03, \ -9.975604363093720E-01, 5.337316075161648E-01, 1.249737376093271E-03, \ -9.975457919908404E-01, 9.770830229535153E-01, 4.470299430512570E-04, \ -9.969809246965443E-01, -2.451005993701799E-01, 2.074243379361551E-03, \ -9.968120260128331E-01, 8.514136675024221E-01, 1.167341137105932E-03, \ -9.966778899972677E-01, -9.176221669397234E-01, 8.041981836080290E-04, \ -9.964245708711565E-01, -4.889240550109979E-01, 2.074108808482804E-03, \ -9.960265424615615E-01, -3.206262163873343E-03, 2.541774019152315E-03, \ -9.957193536867802E-01, 6.973486149261381E-01, 1.833470374408153E-03, \ -9.954906184608173E-01, -9.834651303414434E-01, 4.837448015994170E-04, \ -9.923170394980639E-01, -6.488504511621852E-01, 2.300838549325460E-03, \ -9.894941295318366E-01, 1.816206171244922E-01, 3.686717692046918E-03, \ -9.874887743325775E-01, -8.588958391844354E-01, 1.934675349668603E-03, \ -9.873676197128440E-01, 4.258048442933274E-01, 3.995262993123166E-03, \ -9.872315968340971E-01, 9.256499485066579E-01, 2.010548420182620E-03, \ -9.817076131502388E-01, -3.607331662659895E-01, 5.403841252241704E-03, \ -9.810397049156565E-01, 9.959675054022549E-01, 5.131550081223118E-04, \ -9.788010746558530E-01, 7.823002392178441E-01, 4.112245929337191E-03, \ -9.779826267946542E-01, -1.280907393842539E-01, 6.825619620264833E-03, \ -9.778857566817490E-01, -7.070297596348967E-01, 2.333933933327752E-03, \ -9.770873279965435E-01, 5.991400956941817E-01, 5.320539361361202E-03, \ -9.765278890669798E-01, -9.531509988501621E-01, 2.086667535123516E-03, \ -9.761966529808779E-01, -9.980243997428009E-01, 3.926872153298788E-04, \ -9.726562997502463E-01, -5.585474334620195E-01, 4.784629701022005E-03, \ -9.726043123727997E-01, -8.113170875896518E-01, 2.635483305155019E-03, \ -9.682147583093088E-01, 8.904719493506889E-02, 6.698723958291691E-03, \ -9.634445582523827E-01, 3.139599897908095E-01, 7.954619210267289E-03, \ -9.610169069361439E-01, 9.666011711506927E-01, 2.268817275848690E-03, \ -9.551948115536512E-01, 8.710650846109909E-01, 4.964920743527174E-03, \ -9.505460777198159E-01, -4.343062948294107E-01, 6.106499989272643E-03, \ -9.482223349262576E-01, -7.448087682906291E-01, 5.255811938574469E-03, \ -9.479658383534716E-01, -8.987701284133403E-01, 4.635769935190221E-03, \ -9.436143895358713E-01, 6.959041714345351E-01, 7.863254576614227E-03, \ -9.436039683315387E-01, -6.104452737087587E-01, 4.434535145882001E-03, \ -9.433758303285367E-01, 4.906689218494150E-01, 9.429821854040199E-03, \ -9.423237187354413E-01, -2.467823489744650E-01, 1.076584727710253E-02, \ -9.391182625762966E-01, -9.826638214851392E-01, 2.109364556787303E-03, \ -9.350615084246884E-01, -1.659457024937119E-02, 1.048767996389870E-02, \ -9.217645802840572E-01, 9.907869871400011E-01, 1.616360403829918E-03, \ -9.215474836204731E-01, 2.043715053498819E-01, 1.216781578897710E-02, \ -9.126031690605523E-01, 9.291576693756454E-01, 5.032494622473610E-03, \ -9.108376159034378E-01, -4.897424808873326E-01, 8.527008883353277E-03, \ -9.064530353685755E-01, 7.992951966595492E-01, 8.733726687076370E-03, \ -9.056607152087032E-01, -8.272477088723909E-01, 7.878562829643663E-03, \ -9.044219288728528E-01, -6.636706870428218E-01, 8.309150810743564E-03, \ -8.947784500749467E-01, -9.451248056062111E-01, 4.977957482614220E-03, \ -8.942957719772126E-01, 3.854833600681813E-01, 1.263526180235866E-02, \ -8.914509500717330E-01, 5.988572449686976E-01, 1.236911144033898E-02, \ -8.852322112438892E-01, -1.236708436669904E-01, 1.426043676836211E-02, \ -8.841579338925228E-01, -3.412926369849601E-01, 1.325394767927102E-02, \ -8.801771943577119E-01, -9.966091035909469E-01, 1.109347862822931E-03, \ -8.662960901298091E-01, 8.948961991555911E-02, 1.538814023759737E-02, \ -8.547901173562468E-01, 9.685970327546581E-01, 4.221229608246627E-03, \ -8.513281464403821E-01, 9.987701957017139E-01, 6.276947609934688E-04, \ -8.493965412767819E-01, 8.750994636081615E-01, 8.702080207924946E-03, \ -8.486190442117658E-01, -5.636240679874738E-01, 1.285521591384748E-02, \ -8.463705738558919E-01, -7.448243067394232E-01, 1.130500524300540E-02, \ -8.405308044871470E-01, 3.043148488295061E-01, 1.046140819688675E-02, \ -8.398358181977051E-01, 7.161435779598875E-01, 1.314151256378980E-02, \ -8.383653549203041E-01, -8.878539286502376E-01, 8.430171578574307E-03, \ -8.210741123697933E-01, -9.766488081068017E-01, 4.098354002811169E-03, \ -8.208707647886223E-01, 4.974203597708007E-01, 1.710985289131320E-02, \ -8.146158417958415E-01, -2.198432016525242E-01, 1.701739186308798E-02, \ -8.118659561962476E-01, 2.211043698771638E-01, 8.434215380175943E-03, \ -8.109301081611654E-01, -4.211295967806792E-01, 1.412782056675765E-02, \ -8.011290535296839E-01, -1.248581495063462E-02, 1.560092136756764E-02, \ -7.735252515593568E-01, 9.309650034206048E-01, 7.961026263346178E-03, \ -7.716408539520909E-01, 9.890328536125180E-01, 2.627819279756719E-03, \ -7.713122237357826E-01, -6.510284878473606E-01, 1.538601522963826E-02, \ -7.707190051131479E-01, 2.324471573934027E-01, 9.036405673615943E-03, \ -7.702424235973540E-01, 8.084384767368644E-01, 1.275881172676499E-02, \ -7.669148226628323E-01, -8.144012723914440E-01, 1.203610936905808E-02, \ -7.563615651755403E-01, -9.344574350143551E-01, 7.162428695194032E-03, \ -7.549356580691885E-01, 6.261159426797993E-01, 1.790785421685001E-02, \ -7.388091269205519E-01, -9.953991842940237E-01, 1.935302554193668E-03, \ -7.378692050124985E-01, -8.521050209128646E-02, 1.377372412683884E-02, \ -7.377023207292610E-01, -4.941261650174635E-01, 1.380544592194696E-02, \ -7.331931178475477E-01, 3.913893482110728E-01, 2.143967325273679E-02, \ -7.270864834829239E-01, 1.139187591845308E-01, 1.516896982460334E-02, \ -7.267695434410246E-01, -3.082489183913576E-01, 1.881115737108218E-02, \ -6.899885699483223E-01, -8.821573559917478E-01, 4.925947047330577E-03, \ -6.813723030880324E-01, 9.984161114829040E-01, 7.885438697656719E-04, \ -6.794320916451463E-01, 8.785358277598266E-01, 1.205922032830251E-02, \ -6.784703765570435E-01, -7.297133387630516E-01, 1.598916748258378E-02, \ -6.776012969063153E-01, 1.391839047743928E-01, 9.832835902747970E-03, \ -6.764723618609201E-01, 9.685324267578785E-01, 5.859512706387141E-03, \ -6.738460375138086E-01, -9.651002679024745E-01, 4.767009187250398E-03, \ -6.737243836937874E-01, 7.342773798093677E-01, 1.709899970138294E-02, \ -6.644539826425694E-01, -5.635537416067942E-01, 1.564317167183973E-02, \ -6.634751213533232E-01, -1.604215873631951E-01, 1.935734255198524E-02, \ -6.619502670840386E-01, -8.649428894817014E-01, 7.118057258260406E-03, \ -6.549827012606614E-01, 5.282752967927656E-01, 2.240760255327129E-02, \ -6.306600511355206E-01, -3.919448791059551E-01, 1.900513660573725E-02, \ -6.297817200305971E-01, 2.823803712729075E-01, 2.502986526281338E-02, \ -6.216953173007335E-01, 5.643843021717805E-03, 1.796402412073861E-02, \ -6.140165745664186E-01, -9.859418938622825E-01, 3.212423164931555E-03, \ -5.771270411761599E-01, -9.215133237530594E-01, 9.668925716545904E-03, \ -5.748435613862279E-01, 9.327577622499963E-01, 9.757429923397945E-03, \ -5.737485473796465E-01, -7.972486291015727E-01, 1.508656680428934E-02, \ -5.718887760630267E-01, -6.370333746969838E-01, 1.848456636165576E-02, \ -5.707074067500586E-01, 9.922102608817531E-01, 2.881990914702140E-03, \ -5.688961239076191E-01, 3.298702902382509E-02, 1.047465657364413E-02, \ -5.675251115967979E-01, 8.169896013111752E-01, 1.640586553806266E-02, \ -5.655659214306783E-01, 6.509750976080372E-01, 2.125680475231248E-02, \ -5.571510587648792E-01, -2.467810374030457E-01, 2.398602658758524E-02, \ -5.507102005306738E-01, -4.616455796605000E-01, 1.436780242522091E-02, \ -5.419415518233097E-01, 4.248295257169304E-01, 2.626823745716256E-02, \ -5.218547423997800E-01, -9.976415918771692E-01, 1.583196126084757E-03, \ -5.149992864069691E-01, -9.423558398261378E-02, 1.076036322418040E-02, \ -5.132180036238988E-01, 1.711550456896960E-01, 2.785354108817730E-02, \ -4.829210648831740E-01, -9.616162988487118E-01, 7.469943358099489E-03, \ -4.688160566868244E-01, -8.611456662935529E-01, 1.398190185303191E-02, \ -4.677745958608924E-01, -5.249766577809418E-01, 2.002854227312364E-02, \ -4.669496773079832E-01, 9.726887728674144E-01, 6.450395357727730E-03, \ -4.658245441037069E-01, -8.858372256137174E-02, 1.784446157965224E-02, \ -4.628895760753138E-01, -7.133269525288682E-01, 1.912050315315815E-02, \ -4.535449668032904E-01, 8.866031212139555E-01, 1.401926812957357E-02, \ -4.478788754500803E-01, 5.600753093630753E-01, 2.492544822075299E-02, \ -4.457854778948153E-01, 7.446400102911364E-01, 2.064381447286162E-02, \ -4.369470824412445E-01, -3.431724701283002E-01, 2.658713998880457E-02, \ -4.185328241266283E-01, 3.170545750718476E-01, 2.922560369899428E-02, \ -3.890877209652377E-01, 9.971081288565442E-01, 1.796661084966019E-03, \ -3.864446656766595E-01, 5.863091742160163E-02, 3.003146041596166E-02, \ -3.831955458377362E-01, -1.740817521363409E-01, 1.214811438718327E-02, \ -3.735932973145009E-01, -9.868758698413692E-01, 4.788684591089814E-03, \ -3.613111294101750E-01, -9.165044324691506E-01, 1.212237717515227E-02, \ -3.538765488045220E-01, -6.105807051018285E-01, 2.342111343448623E-02, \ -3.470851761320838E-01, -7.893958214407354E-01, 1.847852212603510E-02, \ -3.391198332478134E-01, 9.420920789488475E-01, 1.053753340465246E-02, \ -3.259626426410726E-01, -2.132438198328835E-01, 2.050933783996452E-02, \ -3.225863338681545E-01, 4.621171913143386E-01, 2.803762474902662E-02, \ -3.223116544172475E-01, 8.281765786009968E-01, 1.845884999832045E-02, \ -3.181331758231921E-01, 6.624003884340418E-01, 2.410899398588486E-02, \ -3.097545730889024E-01, -4.424649187010514E-01, 2.680988640221558E-02, \ -2.884650031184056E-01, 9.884147622938702E-01, 2.472347723619564E-03, \ -2.873088695274083E-01, 2.062472424818550E-01, 3.118760247446968E-02, \ -2.512791493091187E-01, -5.135873454190604E-02, 3.099744003973420E-02, \ -2.423641370999858E-01, -9.577710745485877E-01, 9.265732928547869E-03, \ -2.328824316631447E-01, -9.978364337209883E-01, 1.779978256713267E-03, \ -2.263780767365199E-01, -7.000400004124890E-01, 2.322442438266213E-02, \ -2.263399639641023E-01, -8.582209349267874E-01, 1.680208369151338E-02, \ -2.087812004974775E-01, 9.770858608961845E-01, 5.302771699443291E-03, \ -2.083614303693334E-01, -3.073111903430377E-01, 2.784736930013426E-02, \ -1.999283175075603E-01, 8.989837030255559E-01, 1.499199948128067E-02, \ -1.909845816734380E-01, 3.575369873843971E-01, 3.046703330507673E-02, \ -1.884716472361604E-01, 5.724569389790787E-01, 2.632448749251792E-02, \ -1.869410921110642E-01, 7.565028038405339E-01, 2.233491028950177E-02, \ -1.843841115545689E-01, -5.395615455530922E-01, 2.494019997742770E-02, \ -1.498332978393480E-01, 9.424107635111555E-02, 3.190590627327158E-02, \ -1.195770040560849E-01, 9.976785699720651E-01, 1.708610445747687E-03, \ -1.128810472678152E-01, -1.621115180942063E-01, 3.095358985546368E-02, \ -1.020657000747672E-01, -9.827964093930615E-01, 5.862490005379920E-03, \ -9.932663283884499E-02, -9.143596686063581E-01, 1.369553699475923E-02, \ -9.274767285187367E-02, -7.822730372488192E-01, 2.164311512564077E-02, \ -8.103825378906829E-02, -4.096519478108676E-01, 2.759310160331856E-02, \ -7.489973868725409E-02, 9.518169186995218E-01, 1.035496878834830E-02, \ -6.335698901293590E-02, -6.250608749966023E-01, 2.255920523045297E-02, \ -6.166904446316302E-02, 4.784389475960453E-01, 2.676383008544048E-02, \ -5.970836208331559E-02, 8.405649967632023E-01, 1.908548342904795E-02, \ -5.501382393331618E-02, 2.467531511014508E-01, 3.173197137193996E-02, \ -5.061788078599418E-02, 6.732401322495646E-01, 2.516076352162443E-02, \ -1.015615433395733E-02, -2.055972514442930E-02, 3.182295725284823E-02, \ 9.042710639563842E-03, 9.901284880011576E-01, 3.036532554395697E-03, \ 2.455819938982937E-02, -2.746511791380577E-01, 3.058344887912262E-02, \ 3.009510952559026E-02, -9.957979450703934E-01, 2.230092699402469E-03, \ 4.161126623700789E-02, -8.541692940023290E-01, 1.832620914421112E-02, \ 4.315071485893791E-02, -9.531546367603930E-01, 1.004404501682993E-02, \ 4.980781610591364E-02, -5.055026057272577E-01, 2.695393126406910E-02, \ 5.614259373801662E-02, 3.839891266510965E-01, 2.555881058966561E-02, \ 5.653066870778246E-02, -7.009049065775056E-01, 2.162651797501659E-02, \ 6.431492052043117E-02, 9.094943484367410E-01, 1.442924487724422E-02, \ 7.954502210454595E-02, 7.677175431668712E-01, 2.242255949995469E-02, \ 8.170982374355797E-02, 5.812890091744177E-01, 2.612319135336336E-02, \ 8.304206805112350E-02, 1.303122834290349E-01, 3.197796594776971E-02, \ 9.579669178358458E-02, 9.786128840932780E-01, 4.858466607668643E-03, \ 1.298140716395927E-01, -1.364129934454575E-01, 3.153849046439230E-02, \ 1.448602053653137E-01, -9.993997310860954E-01, 5.187655461501736E-04, \ 1.637794332334225E-01, 2.917847592352579E-01, 2.372133318277343E-02, \ 1.656376032948203E-01, -3.792766926420451E-01, 3.002828141125498E-02, \ 1.762292877481467E-01, -7.767882983828635E-01, 2.024589761678427E-02, \ 1.814953063827089E-01, -9.796863149731511E-01, 6.038716138269680E-03, \ 1.834852661942361E-01, -5.949216461693253E-01, 2.588018863116454E-02, \ 1.867990480390358E-01, -9.082909202013399E-01, 1.438268457601201E-02, \ 1.997745797864829E-01, 8.521395692935436E-01, 1.769908491854464E-02, \ 2.012879315451541E-01, 4.865204987031345E-01, 2.424802585375267E-02, \ 2.073540200015715E-01, 9.979690495625936E-01, 1.871839129499010E-03, \ 2.092466713865647E-01, 9.536237467670772E-01, 9.197918109386862E-03, \ 2.142508728125625E-01, 6.811733554860471E-01, 2.453455227667186E-02, \ 2.222235734801500E-01, 1.329690651656386E-02, 3.153867440259803E-02, \ 2.552587195458114E-01, 2.135868866634151E-01, 1.710171709003340E-02, \ 2.738405728748159E-01, -2.432353447249460E-01, 3.084667141478646E-02, \ 3.037543314031991E-01, 3.985764917009157E-01, 2.212002672383645E-02, \ 3.062582671628846E-01, -4.779029541794464E-01, 2.841632130217824E-02, \ 3.073771915996136E-01, -9.932860050681348E-01, 2.560967478145304E-03, \ 3.085884559918400E-01, -6.853150635640251E-01, 2.335501600448783E-02, \ 3.097655269975939E-01, -8.409329107501455E-01, 1.745461988433493E-02, \ 3.264090470748552E-01, 7.799958670008352E-01, 1.976931010135947E-02, \ 3.269506077033738E-01, 1.528597292687391E-01, 1.880416143417532E-02, \ 3.287397793338149E-01, -9.499963119187408E-01, 1.015995287897780E-02, \ 3.299686062924967E-01, 9.136754073945763E-01, 1.223211496544324E-02, \ 3.399940734865946E-01, 9.843406124989522E-01, 5.358533964816193E-03, \ 3.414386037016686E-01, 5.837599078463863E-01, 2.531201093274045E-02, \ 3.626455120418416E-01, -9.420914031009561E-02, 2.954195879994616E-02, \ 4.071626746871289E-01, 3.109774847555636E-01, 2.432492670918727E-02, \ 4.140936135772086E-01, -3.459697602487943E-01, 2.904643863705676E-02, \ 4.145550075939219E-01, -9.984668858105441E-01, 8.704393591207662E-04, \ 4.248119738620462E-01, 7.344623137957502E-02, 2.290584551728990E-02, \ 4.327427543879804E-01, -5.800952441542988E-01, 2.542846350942939E-02, \ 4.378605680904344E-01, -7.622695385405753E-01, 1.990561596716723E-02, \ 4.398019895929731E-01, 8.590468375941196E-01, 1.424593076230482E-02, \ 4.409957188846723E-01, -8.964515554446453E-01, 1.360912679478925E-02, \ 4.446633915248027E-01, 6.971747211943454E-01, 2.079224858597253E-02, \ 4.561120813077312E-01, 9.583286368134947E-01, 7.651874640364773E-03, \ 4.578378135836055E-01, 4.858442710495443E-01, 2.286780694222276E-02, \ 4.673508637290545E-01, -9.782167962078963E-01, 6.029168541655493E-03, \ 4.743480302386265E-01, 9.967031114708308E-01, 1.646439778827267E-03, \ 4.982830846776936E-01, -1.973451409716288E-01, 2.712296241805855E-02, \ 5.053791029402219E-01, -4.887386159139488E-02, 8.213397938570224E-03, \ 5.182457807020877E-01, 2.160333823951996E-01, 2.436046657122245E-02, \ 5.382900510803214E-01, -4.567938591720622E-01, 2.598020239337663E-02, \ 5.431714974163138E-01, 2.867426624023640E-02, 1.502442733748493E-02, \ 5.450456322230584E-01, 7.938839184396489E-01, 1.592965984721472E-02, \ 5.460671166844733E-01, 4.143453777845346E-01, 1.419118265364266E-02, \ 5.483280208744600E-01, 9.203785964981086E-01, 9.152425543104364E-03, \ 5.538810843207090E-01, 6.108588585460906E-01, 2.034833182220751E-02, \ 5.568932657964470E-01, -6.692481046679927E-01, 2.157498392901168E-02, \ 5.596381875735323E-01, 9.921593115140971E-01, 1.608865885491389E-03, \ 5.597407146364283E-01, -8.307068015467881E-01, 1.582771127386430E-02, \ 5.662708737165433E-01, -9.399876147283586E-01, 9.394744050751306E-03, \ 5.918239732225662E-01, -9.949593941852612E-01, 2.396290467084638E-03, \ 6.132912672442516E-01, -3.146039051646457E-01, 2.212711650881879E-02, \ 6.138426634662881E-01, -6.118802903793545E-02, 1.806733793235598E-02, \ 6.142784830337650E-01, 3.453724863115886E-01, 1.864729091061658E-02, \ 6.182773578473880E-01, 9.740513097221366E-01, 5.410977905903992E-03, \ 6.396787787836092E-01, 8.728694805818825E-01, 1.137048039230828E-02, \ 6.406468508438566E-01, 1.468000595369991E-01, 2.043212465588637E-02, \ 6.467851189666363E-01, 7.205388161010090E-01, 1.703077749193565E-02, \ 6.488127284463796E-01, -2.007299075262801E-01, 1.095427143818548E-02, \ 6.517007603679420E-01, 5.283348578512921E-01, 1.809208934701153E-02, \ 6.559512407902149E-01, -5.555135149722775E-01, 2.234826148158751E-02, \ 6.690244056582569E-01, -7.508923368689349E-01, 1.710484161723342E-02, \ 6.718714751553437E-01, -8.884291476865778E-01, 1.150781632550147E-02, \ 6.771644395694760E-01, -9.722288077426058E-01, 5.528569852248240E-03, \ 7.083681501678855E-01, 6.248980851431146E-02, 1.314715640510330E-02, \ 7.097149683060735E-01, 9.954900449580694E-01, 1.976100218099145E-03, \ 7.138402644040628E-01, 9.387924343684284E-01, 8.164980595434149E-03, \ 7.198490951545802E-01, 2.812564715356937E-01, 1.789583577642915E-02, \ 7.215588783892570E-01, -1.159998849132680E-01, 1.652956139432900E-02, \ 7.226187070333294E-01, -4.079425951229357E-01, 2.112863498184051E-02, \ 7.265292300868345E-01, 4.469086468315797E-01, 1.420616050890493E-02, \ 7.331775979965447E-01, 8.135825128068572E-01, 1.307598884661690E-02, \ 7.416232943868383E-01, 6.401664396369919E-01, 1.652038500895329E-02, \ 7.474274447805114E-01, -2.490193226057417E-01, 9.746025489521986E-03, \ 7.577219445007012E-01, -6.503099455495434E-01, 1.766386441308518E-02, \ 7.585692250178416E-01, -9.940238473548991E-01, 2.133367947374089E-03, \ 7.673603283405851E-01, -8.229326660746660E-01, 1.248597476302831E-02, \ 7.692530439279005E-01, -9.355395173554912E-01, 7.514322260630891E-03, \ 7.854444511977640E-01, 2.685123392480584E-02, 1.533947945855647E-02, \ 7.951738457011064E-01, 9.766083680702315E-01, 4.356175996997274E-03, \ 7.985748483813998E-01, 2.025555068725613E-01, 1.564386357005296E-02, \ 8.040234894621253E-01, -2.042597387565252E-01, 7.710958187140682E-03, \ 8.057295032357437E-01, 8.915828031028744E-01, 9.355613099192112E-03, \ 8.088604175612499E-01, 4.023062626041685E-01, 1.273706153435572E-02, \ 8.120135674815725E-01, -5.076674583210536E-01, 1.736448568443276E-02, \ 8.133759777422149E-01, 5.487782375682692E-01, 1.217998404158868E-02, \ 8.184347733263844E-01, 7.425426026236549E-01, 1.279679392158505E-02, \ 8.235558633092787E-01, -3.024959465991686E-01, 1.287819098925984E-02, \ 8.421681940961352E-01, -9.736872041616552E-01, 4.112192665900335E-03, \ 8.426583009273289E-01, -7.378407924120958E-01, 1.274069526022431E-02, \ 8.491855987208501E-01, -8.846256408253794E-01, 8.283446027511682E-03, \ 8.516898507135523E-01, -7.990981970042101E-02, 1.580891087490480E-02, \ 8.583531941070754E-01, 9.966311518784791E-01, 1.191591564881406E-03, \ 8.707932748733679E-01, -9.983455554915148E-01, 6.345865698137260E-04, \ 8.719292766173237E-01, 3.244559296210806E-01, 1.339462628650847E-02, \ 8.741706562832676E-01, 1.282050668916198E-01, 1.359136343527793E-02, \ 8.746739329394990E-01, 9.458932113235630E-01, 5.483866186101370E-03, \ 8.754686572917406E-01, 6.486907444035410E-01, 9.118856886512235E-03, \ 8.810154998962139E-01, 8.328762658091308E-01, 8.944431517124202E-03, \ 8.838623245418704E-01, 5.232758761535393E-01, 8.099355551928950E-03, \ 8.840131826785472E-01, -6.067031031846036E-01, 1.277176198724360E-02, \ 8.857877394173622E-01, -3.901273813669436E-01, 1.389624600553866E-02, \ 9.091784209404282E-01, -9.377849360846731E-01, 4.939598298332105E-03, \ 9.095211566710759E-01, -1.967240155892789E-01, 1.315977866277586E-02, \ 9.097092205890601E-01, -8.157851178868343E-01, 8.243125043271836E-03, \ 9.196079033409038E-01, 7.363362622288353E-01, 5.921333683728877E-03, \ 9.227347373981668E-01, 2.518050384938889E-02, 1.062691558572691E-02, \ 9.248521839866148E-01, 9.836500044365560E-01, 2.345619531278534E-03, \ 9.251563778586870E-01, 4.438563917317115E-01, 9.900476467889377E-03, \ 9.257255001153735E-01, -9.889449924089616E-01, 1.597653710972395E-03, \ 9.343954029970296E-01, 9.015214103086258E-01, 5.328104999186108E-03, \ 9.369174879213626E-01, 2.389817273899876E-01, 1.111346808242325E-02, \ 9.383511550992609E-01, 6.373581080663476E-01, 5.774002588554636E-03, \ 9.387517764149524E-01, -4.968798107682113E-01, 1.020259840078752E-02, \ 9.387607494306587E-01, -7.000259293912848E-01, 8.261643223094358E-03, \ 9.539697271844676E-01, 7.975969707432101E-01, 4.649762577280237E-03, \ 9.552276863128365E-01, -3.035710530293175E-01, 9.006117332227408E-03, \ 9.569172017920470E-01, -8.842472974692178E-01, 4.741019829465620E-03, \ 9.595675104913648E-01, -7.355852323028661E-02, 7.652758779266264E-03, \ 9.644864346894841E-01, -9.667641619200008E-01, 2.030067204957960E-03, \ 9.656087615773162E-01, 5.543437727025696E-01, 6.351762240325599E-03, \ 9.688546673876272E-01, 9.558880345442317E-01, 2.480910477329663E-03, \ 9.704101090001410E-01, 9.981808611338953E-01, 4.561152547158576E-04, \ 9.727514081123080E-01, 1.110004091109647E-01, 6.093769602114571E-03, \ 9.729878975391641E-01, 3.616245012182894E-01, 6.843942401499502E-03, \ 9.756932294462006E-01, -6.036471845921362E-01, 5.800134625750472E-03, \ 9.760900548932613E-01, -7.838246719005716E-01, 4.407536360315319E-03, \ 9.782973640835879E-01, -9.971684762652360E-01, 4.311602698318422E-04, \ 9.807900912370063E-01, 7.129244508544674E-01, 4.127102044979779E-03, \ 9.808939118005312E-01, 8.613001240894053E-01, 2.999414636157759E-03, \ 9.835779953552617E-01, -4.135902303116288E-01, 5.032085033161774E-03, \ 9.854244802470254E-01, -1.682373835033575E-01, 4.864699918722623E-03, \ 9.871873668187979E-01, 1.693824175740657E-01, 2.336035230228115E-03, \ 9.897390691072502E-01, -9.305936554854670E-01, 1.645629389008965E-03, \ 9.934973942415222E-01, 4.709702784519761E-01, 2.855403033244952E-03, \ 9.941323665942218E-01, 9.840689837610336E-01, 5.975302834838432E-04, \ 9.948473950532203E-01, 9.223043056827241E-01, 1.118642207825798E-03, \ 9.948570811646354E-01, 6.241948125538140E-01, 1.966746818044319E-03, \ 9.955141358332547E-01, -7.009139270684177E-01, 1.973528831634365E-03, \ 9.955332555186237E-01, -8.505509962676160E-01, 1.399475221966474E-03, \ 9.959646721127126E-01, -4.250651416434814E-04, 2.683953315797548E-03, \ 9.966503083795464E-01, 2.697627971477953E-01, 2.110801603897598E-03, \ 9.966625578128554E-01, -9.821401814469173E-01, 4.298915672048476E-04, \ 9.972191681750349E-01, -5.232937991459530E-01, 1.621857507529301E-03, \ 9.977589931512456E-01, -2.851699647482527E-01, 1.679574685965640E-03, \ 9.982095733525613E-01, 7.942486273250328E-01, 1.122778646693857E-03 ] ) return xyw def smr43 ( ): #*****************************************************************************80 # ## smr43 returns the SMR rule of degree 43. # # Discussion: # # DEGREE: 43 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 331 # NORM INF MOMS. RESIDUAL: 6.57894e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*331), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.991322806157538E-01, -7.967757949667039E-01, 8.678616486509684E-04, \ -9.982000639809739E-01, 3.046004953209935E-01, 1.439841751685133E-03, \ -9.980850962629690E-01, 9.781664509229353E-01, 3.796649877334044E-04, \ -9.980230789357751E-01, -2.518043976244231E-01, 1.843703555135520E-03, \ -9.977169911523626E-01, 5.459548078849698E-01, 1.239809456010988E-03, \ -9.960955981451255E-01, 1.323322402607845E-02, 2.563511060458582E-03, \ -9.949822864151898E-01, -9.238195120237386E-01, 9.266737007306744E-04, \ -9.949201671743397E-01, 7.003454609915903E-01, 2.006603012946033E-03, \ -9.948772524482939E-01, 8.407859395090261E-01, 1.605442474502514E-03, \ -9.948541523937408E-01, -9.833293028860037E-01, 5.491048194068317E-04, \ -9.947061632621746E-01, -6.355790382588226E-01, 1.778286578522554E-03, \ -9.945229623313124E-01, -4.853023018396496E-01, 2.560515852421350E-03, \ -9.892614872423598E-01, 9.260146296311070E-01, 1.799734507689385E-03, \ -9.871939619842668E-01, -8.755067171008981E-01, 1.519837361369944E-03, \ -9.870688041516782E-01, 1.860477389466161E-01, 4.518470382030127E-03, \ -9.867444463087381E-01, 4.389464150281105E-01, 4.224292354075523E-03, \ -9.834968499928717E-01, -7.202131341080557E-01, 3.339955375858229E-03, \ -9.821598385319343E-01, 9.959978097052690E-01, 4.727038168393605E-04, \ -9.821204851739278E-01, -1.368717477114345E-01, 4.757586602695279E-03, \ -9.797140053995109E-01, -3.605450203749538E-01, 5.952555069740412E-03, \ -9.748774429719304E-01, 6.046447974749469E-01, 5.546938866694710E-03, \ -9.734413327253255E-01, -9.978546421321081E-01, 4.474703090515473E-04, \ -9.734116599154365E-01, -8.128285861906330E-02, 2.741115844813457E-03, \ -9.726507374329582E-01, 7.726414313517832E-01, 4.741572721729229E-03, \ -9.714591142922610E-01, -8.274759240878854E-01, 3.381861982854643E-03, \ -9.707758044034546E-01, -9.550455839865367E-01, 2.339780436266730E-03, \ -9.675614571152631E-01, -5.690626658543524E-01, 6.088138066683147E-03, \ -9.643580663040768E-01, 9.675657234336767E-01, 2.156284749425144E-03, \ -9.620411392118244E-01, 8.827193644891181E-02, 7.524938344770951E-03, \ -9.613825223406508E-01, 3.274157880119070E-01, 8.329588693656027E-03, \ -9.572105649891679E-01, 8.779211539499637E-01, 4.677019870857324E-03, \ -9.482779256977600E-01, -6.571793975487423E-01, 3.415065808643305E-03, \ -9.442203741741305E-01, -2.396912099299458E-01, 1.053267886519870E-02, \ -9.414082069989970E-01, -4.455867154949159E-01, 7.955507648643412E-03, \ -9.399484869570831E-01, 5.017481363429027E-01, 9.346304112770374E-03, \ -9.387730081468121E-01, -8.994764149206039E-01, 5.120889482069984E-03, \ -9.381605799832013E-01, -7.581359176425346E-01, 6.330117595761937E-03, \ -9.324895156315322E-01, 6.876092944131506E-01, 8.757387580269081E-03, \ -9.303980205538308E-01, -2.287492239980876E-02, 9.878323399096202E-03, \ -9.300897829687235E-01, -9.834052375669528E-01, 2.235790741981890E-03, \ -9.235245729050272E-01, 9.918027925163878E-01, 1.542906053318116E-03, \ -9.175260810911099E-01, 2.167671303064032E-01, 1.277769691913465E-02, \ -9.152022665122554E-01, 9.349908468306158E-01, 4.721132707483059E-03, \ -9.085212108480799E-01, 8.115960772910453E-01, 8.234979199618303E-03, \ -9.005451856752491E-01, -6.470132016778298E-01, 9.072910191199055E-03, \ -8.993217981371787E-01, -5.116431205683809E-01, 8.049099608777895E-03, \ -8.927214238682213E-01, 4.039129384019244E-01, 1.176810878122849E-02, \ -8.881186605619299E-01, -8.304324891473370E-01, 8.581965557258065E-03, \ -8.876535679652159E-01, -3.361428192098763E-01, 1.273089714018281E-02, \ -8.857085475134302E-01, -1.254112109470145E-01, 1.296699198587140E-02, \ -8.821398112805722E-01, -9.453230958968664E-01, 5.328273493767261E-03, \ -8.750237163459592E-01, 5.925043126358809E-01, 1.336532935350772E-02, \ -8.681630157484973E-01, -9.968478564406162E-01, 1.108072915590710E-03, \ -8.654982773274537E-01, 8.883753842636366E-02, 1.557578581133525E-02, \ -8.563237880711940E-01, 9.727943477844379E-01, 3.899549565205258E-03, \ -8.529385601042461E-01, 8.850063664849166E-01, 8.114118976527893E-03, \ -8.416510529475818E-01, 7.343186487220238E-01, 1.255955264577050E-02, \ -8.384749004002887E-01, 3.197575534100762E-01, 1.323030988966136E-02, \ -8.382565684334965E-01, -7.304981145627908E-01, 1.224239155066108E-02, \ -8.367263219641764E-01, 9.989783711881817E-01, 6.905843510793296E-04, \ -8.317712773416662E-01, -5.574060797969008E-01, 1.237820673005956E-02, \ -8.211388015093348E-01, -4.085976590181732E-01, 1.240477807928645E-02, \ -8.200424695478955E-01, -2.132333832998874E-01, 1.547445721646811E-02, \ -8.166284772848996E-01, -8.902469000574972E-01, 9.021259420998788E-03, \ -8.064166934103733E-01, -9.770750896183711E-01, 4.237570484423649E-03, \ -8.007534551335261E-01, 2.023658932297688E-01, 1.164039038671748E-02, \ -8.007277480191897E-01, -2.104803054778272E-02, 1.569505703943440E-02, \ -8.004502220252274E-01, 4.920509614468455E-01, 1.783350078263945E-02, \ -7.777206426895686E-01, 9.379771024961836E-01, 7.326924906570778E-03, \ -7.728688446320272E-01, 8.237137982084558E-01, 1.213629881907029E-02, \ -7.580631733732273E-01, -8.027077015709957E-01, 1.251455028114069E-02, \ -7.577866929033681E-01, 6.473964743724965E-01, 1.731376923259042E-02, \ -7.553675037695931E-01, 9.890969808970442E-01, 2.691505001410149E-03, \ -7.542249834026444E-01, -6.390864016792512E-01, 1.601212151097312E-02, \ -7.477885480587728E-01, 2.427391554099002E-01, 1.018027057488272E-02, \ -7.429209417585371E-01, -4.572389551800778E-01, 1.367871025169973E-02, \ -7.371197753463775E-01, -2.906469452332063E-01, 1.778595422410749E-02, \ -7.324580428326298E-01, -8.991331137587374E-02, 1.376411964043993E-02, \ -7.298747767373949E-01, -9.377223151384039E-01, 7.856423898031506E-03, \ -7.216457298390802E-01, -9.955998257315364E-01, 1.925204978765617E-03, \ -7.198181678973603E-01, 9.304616811847628E-02, 1.635290663392455E-02, \ -7.130017786063146E-01, 3.849140372358901E-01, 2.099925831266623E-02, \ -6.825679163672110E-01, 8.905466207929580E-01, 1.126602938845450E-02, \ -6.763401791869282E-01, 7.520777122204155E-01, 1.664378870053760E-02, \ -6.745643364827608E-01, -8.606759404486958E-01, 9.423794484989551E-03, \ -6.692634952197962E-01, 5.097498990430799E-01, 3.490301165694596E-03, \ -6.678673365644893E-01, 9.692798398364254E-01, 5.426070381428601E-03, \ -6.643115741452658E-01, -5.309653253850217E-01, 1.761400113990701E-02, \ -6.606757146764088E-01, -7.200291927434657E-01, 1.686289443033400E-02, \ -6.567913888935971E-01, 5.564860922255590E-01, 1.944041905076146E-02, \ -6.534475768044156E-01, -1.614337947470229E-01, 1.995971702129454E-02, \ -6.524650541104557E-01, 9.984813564068824E-01, 8.021305622560764E-04, \ -6.485591953402302E-01, 1.462165876218090E-01, 1.245039847543152E-02, \ -6.399859555346357E-01, -9.716158671859889E-01, 5.166264959182605E-03, \ -6.305799776467085E-01, -3.579775654349885E-01, 1.953568169826047E-02, \ -6.267627879174098E-01, -8.871690949497815E-01, 4.520535674923600E-03, \ -6.120426992404430E-01, 2.869750962968468E-03, 1.860789887443906E-02, \ -6.088744531800644E-01, 2.804875419270162E-01, 2.332988515386343E-02, \ -5.749843157741534E-01, -9.904789673241521E-01, 2.362095702578418E-03, \ -5.718072946653548E-01, 8.322456115066252E-01, 1.553421465906625E-02, \ -5.675480158302344E-01, 9.377249812058859E-01, 9.005466515286650E-03, \ -5.664486963280643E-01, -6.135983682693644E-01, 2.017210091127541E-02, \ -5.657771979464153E-01, 6.704839134317745E-01, 2.109811178256368E-02, \ -5.585579279296714E-01, -7.943301890435838E-01, 1.609461230917944E-02, \ -5.579555277532646E-01, -9.225093413353801E-01, 9.166625675892499E-03, \ -5.577648940591486E-01, 9.919460143463890E-01, 2.677714001127571E-03, \ -5.482310238931972E-01, 4.436263081953605E-01, 2.595341256088991E-02, \ -5.447318792923874E-01, -4.312874087466062E-01, 1.584488792236623E-02, \ -5.329070463527521E-01, -2.338802504012752E-01, 2.422380287073101E-02, \ -5.252362328960822E-01, 3.532940066961791E-02, 9.744250397514996E-03, \ -5.130671510975665E-01, -6.775266904189804E-02, 1.459619277289368E-02, \ -4.960740015643434E-01, 1.706460416978806E-01, 2.591008998522666E-02, \ -4.808128433935768E-01, -9.974703436931273E-01, 1.443156609799716E-03, \ -4.623102743179813E-01, -9.610162776458973E-01, 7.615494645822680E-03, \ -4.600618171289382E-01, -4.996628273183154E-01, 2.060900455474742E-02, \ -4.564322622275068E-01, -6.991541335990263E-01, 2.068903174625100E-02, \ -4.548079347101475E-01, 9.746241299392923E-01, 6.067456845050942E-03, \ -4.515547213045702E-01, -8.598202981137183E-01, 1.439130083445319E-02, \ -4.503129032330394E-01, 7.633185764987656E-01, 1.967366980699904E-02, \ -4.502426979449590E-01, 5.735143166228439E-01, 2.537869809042589E-02, \ -4.496670834961325E-01, 8.946719781100732E-01, 1.311990862370523E-02, \ -4.251260023953483E-01, 3.328741198230487E-01, 2.923686270121404E-02, \ -4.102747237675974E-01, -3.287465817704832E-01, 2.653855839458294E-02, \ -4.097742235858718E-01, -1.135690075591068E-01, 2.264588400082614E-02, \ -3.821379964609022E-01, 9.977278116070721E-01, 1.492947570302465E-03, \ -3.710645184035626E-01, 6.451693464263640E-02, 2.822176831273999E-02, \ -3.481673778720014E-01, -5.903202117641789E-01, 2.447652324050865E-02, \ -3.448938453586106E-01, -9.856166934989374E-01, 5.018022434939532E-03, \ -3.422130750204260E-01, -9.147110358303762E-01, 1.211341740570449E-02, \ -3.378211193742023E-01, -7.806996115904031E-01, 1.966729409903938E-02, \ -3.293359567236023E-01, 6.802105984639650E-01, 2.316447832146869E-02, \ -3.271120843566677E-01, 9.451621148227166E-01, 1.023548496461210E-02, \ -3.229115509093045E-01, 4.710955737486453E-01, 2.874889270545898E-02, \ -3.211530646437794E-01, 8.398359715224299E-01, 1.720122054179252E-02, \ -3.191122714012474E-01, -1.905915965306147E-01, 1.407630952884238E-02, \ -2.905224871790252E-01, 2.219174453896190E-01, 3.135886233490107E-02, \ -2.868275827924473E-01, -4.287232032846321E-01, 2.644181346508640E-02, \ -2.813268043035183E-01, 9.900617341002494E-01, 2.531900366243961E-03, \ -2.489834837398367E-01, -2.386259984115299E-01, 2.038703880401185E-02, \ -2.348227489146337E-01, -3.642259826195845E-02, 2.974478219547869E-02, \ -2.229672705935626E-01, -9.536956599040048E-01, 8.925090234945601E-03, \ -2.217237803712502E-01, -6.844325665508253E-01, 2.424626466446409E-02, \ -2.128621594472864E-01, -8.526186852917771E-01, 1.756834142926637E-02, \ -2.125561177477307E-01, -9.980480071481969E-01, 1.726623494738264E-03, \ -2.054220511368849E-01, 5.927379621951687E-01, 2.476004812382263E-02, \ -1.954822662555086E-01, 7.701425309943154E-01, 2.069081296177256E-02, \ -1.899491393527934E-01, 9.774606174758702E-01, 5.458708894084326E-03, \ -1.869931902994500E-01, 3.648439403146066E-01, 3.090130558081868E-02, \ -1.869854048603779E-01, 9.026780626332723E-01, 1.464880341973280E-02, \ -1.679896766248765E-01, -5.248629640600491E-01, 2.470645077115440E-02, \ -1.465102454558500E-01, 1.123409399107938E-01, 3.177165363173588E-02, \ -1.385073680894356E-01, -3.298408069038985E-01, 2.620563217542392E-02, \ -1.134715731110063E-01, -9.780057138044185E-01, 4.706880211425860E-03, \ -1.021222696160731E-01, 9.977141232529759E-01, 1.651355185248162E-03, \ -9.405687967364605E-02, -1.438416812367627E-01, 3.079509771216723E-02, \ -8.817076361552034E-02, -7.703079005902046E-01, 2.232155693784380E-02, \ -8.704255665377880E-02, 5.068242195166577E-01, 2.401020117466116E-02, \ -7.913623635980109E-02, -9.095514118294697E-01, 1.423838918529654E-02, \ -6.929449557918647E-02, 6.932074779450002E-01, 2.267377008668297E-02, \ -5.631165265722810E-02, 9.521617930920341E-01, 1.005557273422889E-02, \ -5.146821758475675E-02, -6.119016003137178E-01, 2.335034055431550E-02, \ -4.992117521864334E-02, 8.431401729697686E-01, 1.893911020782059E-02, \ -4.672957151157093E-02, 2.554909810874523E-01, 3.137166376170161E-02, \ -2.525132080623741E-02, -9.900183656322150E-01, 3.101973828036974E-03, \ -2.362106216876548E-02, -4.221330758506368E-01, 2.444427008848211E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 3.168017196709776E-02, \ 2.362106216876548E-02, 4.221330758506368E-01, 2.444427008848211E-02, \ 2.525132080623741E-02, 9.900183656322150E-01, 3.101973828036974E-03, \ 4.672957151157093E-02, -2.554909810874523E-01, 3.137166376170161E-02, \ 4.992117521864334E-02, -8.431401729697686E-01, 1.893911020782059E-02, \ 5.146821758475675E-02, 6.119016003137178E-01, 2.335034055431550E-02, \ 5.631165265722810E-02, -9.521617930920341E-01, 1.005557273422889E-02, \ 6.929449557918647E-02, -6.932074779450002E-01, 2.267377008668297E-02, \ 7.913623635980109E-02, 9.095514118294697E-01, 1.423838918529654E-02, \ 8.704255665377880E-02, -5.068242195166577E-01, 2.401020117466116E-02, \ 8.817076361552034E-02, 7.703079005902046E-01, 2.232155693784380E-02, \ 9.405687967364605E-02, 1.438416812367627E-01, 3.079509771216723E-02, \ 1.021222696160731E-01, -9.977141232529759E-01, 1.651355185248162E-03, \ 1.134715731110063E-01, 9.780057138044185E-01, 4.706880211425860E-03, \ 1.385073680894356E-01, 3.298408069038985E-01, 2.620563217542392E-02, \ 1.465102454558500E-01, -1.123409399107938E-01, 3.177165363173588E-02, \ 1.679896766248765E-01, 5.248629640600491E-01, 2.470645077115440E-02, \ 1.869854048603779E-01, -9.026780626332723E-01, 1.464880341973280E-02, \ 1.869931902994500E-01, -3.648439403146066E-01, 3.090130558081868E-02, \ 1.899491393527934E-01, -9.774606174758702E-01, 5.458708894084326E-03, \ 1.954822662555086E-01, -7.701425309943154E-01, 2.069081296177256E-02, \ 2.054220511368849E-01, -5.927379621951687E-01, 2.476004812382263E-02, \ 2.125561177477307E-01, 9.980480071481969E-01, 1.726623494738264E-03, \ 2.128621594472864E-01, 8.526186852917771E-01, 1.756834142926637E-02, \ 2.217237803712502E-01, 6.844325665508253E-01, 2.424626466446409E-02, \ 2.229672705935626E-01, 9.536956599040048E-01, 8.925090234945601E-03, \ 2.348227489146337E-01, 3.642259826195845E-02, 2.974478219547869E-02, \ 2.489834837398367E-01, 2.386259984115299E-01, 2.038703880401185E-02, \ 2.813268043035183E-01, -9.900617341002494E-01, 2.531900366243961E-03, \ 2.868275827924473E-01, 4.287232032846321E-01, 2.644181346508640E-02, \ 2.905224871790252E-01, -2.219174453896190E-01, 3.135886233490107E-02, \ 3.191122714012474E-01, 1.905915965306147E-01, 1.407630952884238E-02, \ 3.211530646437794E-01, -8.398359715224299E-01, 1.720122054179252E-02, \ 3.229115509093045E-01, -4.710955737486453E-01, 2.874889270545898E-02, \ 3.271120843566677E-01, -9.451621148227166E-01, 1.023548496461210E-02, \ 3.293359567236023E-01, -6.802105984639650E-01, 2.316447832146869E-02, \ 3.378211193742023E-01, 7.806996115904031E-01, 1.966729409903938E-02, \ 3.422130750204260E-01, 9.147110358303762E-01, 1.211341740570449E-02, \ 3.448938453586106E-01, 9.856166934989374E-01, 5.018022434939532E-03, \ 3.481673778720014E-01, 5.903202117641789E-01, 2.447652324050865E-02, \ 3.710645184035626E-01, -6.451693464263640E-02, 2.822176831273999E-02, \ 3.821379964609022E-01, -9.977278116070721E-01, 1.492947570302465E-03, \ 4.097742235858718E-01, 1.135690075591068E-01, 2.264588400082614E-02, \ 4.102747237675974E-01, 3.287465817704832E-01, 2.653855839458294E-02, \ 4.251260023953483E-01, -3.328741198230487E-01, 2.923686270121404E-02, \ 4.496670834961325E-01, -8.946719781100732E-01, 1.311990862370523E-02, \ 4.502426979449590E-01, -5.735143166228439E-01, 2.537869809042589E-02, \ 4.503129032330394E-01, -7.633185764987656E-01, 1.967366980699904E-02, \ 4.515547213045702E-01, 8.598202981137183E-01, 1.439130083445319E-02, \ 4.548079347101475E-01, -9.746241299392923E-01, 6.067456845050942E-03, \ 4.564322622275068E-01, 6.991541335990263E-01, 2.068903174625100E-02, \ 4.600618171289382E-01, 4.996628273183154E-01, 2.060900455474742E-02, \ 4.623102743179813E-01, 9.610162776458973E-01, 7.615494645822680E-03, \ 4.808128433935768E-01, 9.974703436931273E-01, 1.443156609799716E-03, \ 4.960740015643434E-01, -1.706460416978806E-01, 2.591008998522666E-02, \ 5.130671510975665E-01, 6.775266904189804E-02, 1.459619277289368E-02, \ 5.252362328960822E-01, -3.532940066961791E-02, 9.744250397514996E-03, \ 5.329070463527521E-01, 2.338802504012752E-01, 2.422380287073101E-02, \ 5.447318792923874E-01, 4.312874087466062E-01, 1.584488792236623E-02, \ 5.482310238931972E-01, -4.436263081953605E-01, 2.595341256088991E-02, \ 5.577648940591486E-01, -9.919460143463890E-01, 2.677714001127571E-03, \ 5.579555277532646E-01, 9.225093413353801E-01, 9.166625675892499E-03, \ 5.585579279296714E-01, 7.943301890435838E-01, 1.609461230917944E-02, \ 5.657771979464153E-01, -6.704839134317745E-01, 2.109811178256368E-02, \ 5.664486963280643E-01, 6.135983682693644E-01, 2.017210091127541E-02, \ 5.675480158302344E-01, -9.377249812058859E-01, 9.005466515286650E-03, \ 5.718072946653548E-01, -8.322456115066252E-01, 1.553421465906625E-02, \ 5.749843157741534E-01, 9.904789673241521E-01, 2.362095702578418E-03, \ 6.088744531800644E-01, -2.804875419270162E-01, 2.332988515386343E-02, \ 6.120426992404430E-01, -2.869750962968468E-03, 1.860789887443906E-02, \ 6.267627879174098E-01, 8.871690949497815E-01, 4.520535674923600E-03, \ 6.305799776467085E-01, 3.579775654349885E-01, 1.953568169826047E-02, \ 6.399859555346357E-01, 9.716158671859889E-01, 5.166264959182605E-03, \ 6.485591953402302E-01, -1.462165876218090E-01, 1.245039847543152E-02, \ 6.524650541104557E-01, -9.984813564068824E-01, 8.021305622560764E-04, \ 6.534475768044156E-01, 1.614337947470229E-01, 1.995971702129454E-02, \ 6.567913888935971E-01, -5.564860922255590E-01, 1.944041905076146E-02, \ 6.606757146764088E-01, 7.200291927434657E-01, 1.686289443033400E-02, \ 6.643115741452658E-01, 5.309653253850217E-01, 1.761400113990701E-02, \ 6.678673365644893E-01, -9.692798398364254E-01, 5.426070381428601E-03, \ 6.692634952197962E-01, -5.097498990430799E-01, 3.490301165694596E-03, \ 6.745643364827608E-01, 8.606759404486958E-01, 9.423794484989551E-03, \ 6.763401791869282E-01, -7.520777122204155E-01, 1.664378870053760E-02, \ 6.825679163672110E-01, -8.905466207929580E-01, 1.126602938845450E-02, \ 7.130017786063146E-01, -3.849140372358901E-01, 2.099925831266623E-02, \ 7.198181678973603E-01, -9.304616811847628E-02, 1.635290663392455E-02, \ 7.216457298390802E-01, 9.955998257315364E-01, 1.925204978765617E-03, \ 7.298747767373949E-01, 9.377223151384039E-01, 7.856423898031506E-03, \ 7.324580428326298E-01, 8.991331137587374E-02, 1.376411964043993E-02, \ 7.371197753463775E-01, 2.906469452332063E-01, 1.778595422410749E-02, \ 7.429209417585371E-01, 4.572389551800778E-01, 1.367871025169973E-02, \ 7.477885480587728E-01, -2.427391554099002E-01, 1.018027057488272E-02, \ 7.542249834026444E-01, 6.390864016792512E-01, 1.601212151097312E-02, \ 7.553675037695931E-01, -9.890969808970442E-01, 2.691505001410149E-03, \ 7.577866929033681E-01, -6.473964743724965E-01, 1.731376923259042E-02, \ 7.580631733732273E-01, 8.027077015709957E-01, 1.251455028114069E-02, \ 7.728688446320272E-01, -8.237137982084558E-01, 1.213629881907029E-02, \ 7.777206426895686E-01, -9.379771024961836E-01, 7.326924906570778E-03, \ 8.004502220252274E-01, -4.920509614468455E-01, 1.783350078263945E-02, \ 8.007277480191897E-01, 2.104803054778272E-02, 1.569505703943440E-02, \ 8.007534551335261E-01, -2.023658932297688E-01, 1.164039038671748E-02, \ 8.064166934103733E-01, 9.770750896183711E-01, 4.237570484423649E-03, \ 8.166284772848996E-01, 8.902469000574972E-01, 9.021259420998788E-03, \ 8.200424695478955E-01, 2.132333832998874E-01, 1.547445721646811E-02, \ 8.211388015093348E-01, 4.085976590181732E-01, 1.240477807928645E-02, \ 8.317712773416662E-01, 5.574060797969008E-01, 1.237820673005956E-02, \ 8.367263219641764E-01, -9.989783711881817E-01, 6.905843510793296E-04, \ 8.382565684334965E-01, 7.304981145627908E-01, 1.224239155066108E-02, \ 8.384749004002887E-01, -3.197575534100762E-01, 1.323030988966136E-02, \ 8.416510529475818E-01, -7.343186487220238E-01, 1.255955264577050E-02, \ 8.529385601042461E-01, -8.850063664849166E-01, 8.114118976527893E-03, \ 8.563237880711940E-01, -9.727943477844379E-01, 3.899549565205258E-03, \ 8.654982773274537E-01, -8.883753842636366E-02, 1.557578581133525E-02, \ 8.681630157484973E-01, 9.968478564406162E-01, 1.108072915590710E-03, \ 8.750237163459592E-01, -5.925043126358809E-01, 1.336532935350772E-02, \ 8.821398112805722E-01, 9.453230958968664E-01, 5.328273493767261E-03, \ 8.857085475134302E-01, 1.254112109470145E-01, 1.296699198587140E-02, \ 8.876535679652159E-01, 3.361428192098763E-01, 1.273089714018281E-02, \ 8.881186605619299E-01, 8.304324891473370E-01, 8.581965557258065E-03, \ 8.927214238682213E-01, -4.039129384019244E-01, 1.176810878122849E-02, \ 8.993217981371787E-01, 5.116431205683809E-01, 8.049099608777895E-03, \ 9.005451856752491E-01, 6.470132016778298E-01, 9.072910191199055E-03, \ 9.085212108480799E-01, -8.115960772910453E-01, 8.234979199618303E-03, \ 9.152022665122554E-01, -9.349908468306158E-01, 4.721132707483059E-03, \ 9.175260810911099E-01, -2.167671303064032E-01, 1.277769691913465E-02, \ 9.235245729050272E-01, -9.918027925163878E-01, 1.542906053318116E-03, \ 9.300897829687235E-01, 9.834052375669528E-01, 2.235790741981890E-03, \ 9.303980205538308E-01, 2.287492239980876E-02, 9.878323399096202E-03, \ 9.324895156315322E-01, -6.876092944131506E-01, 8.757387580269081E-03, \ 9.381605799832013E-01, 7.581359176425346E-01, 6.330117595761937E-03, \ 9.387730081468121E-01, 8.994764149206039E-01, 5.120889482069984E-03, \ 9.399484869570831E-01, -5.017481363429027E-01, 9.346304112770374E-03, \ 9.414082069989970E-01, 4.455867154949159E-01, 7.955507648643412E-03, \ 9.442203741741305E-01, 2.396912099299458E-01, 1.053267886519870E-02, \ 9.482779256977600E-01, 6.571793975487423E-01, 3.415065808643305E-03, \ 9.572105649891679E-01, -8.779211539499637E-01, 4.677019870857324E-03, \ 9.613825223406508E-01, -3.274157880119070E-01, 8.329588693656027E-03, \ 9.620411392118244E-01, -8.827193644891181E-02, 7.524938344770951E-03, \ 9.643580663040768E-01, -9.675657234336767E-01, 2.156284749425144E-03, \ 9.675614571152631E-01, 5.690626658543524E-01, 6.088138066683147E-03, \ 9.707758044034546E-01, 9.550455839865367E-01, 2.339780436266730E-03, \ 9.714591142922610E-01, 8.274759240878854E-01, 3.381861982854643E-03, \ 9.726507374329582E-01, -7.726414313517832E-01, 4.741572721729229E-03, \ 9.734116599154365E-01, 8.128285861906330E-02, 2.741115844813457E-03, \ 9.734413327253255E-01, 9.978546421321081E-01, 4.474703090515473E-04, \ 9.748774429719304E-01, -6.046447974749469E-01, 5.546938866694710E-03, \ 9.797140053995109E-01, 3.605450203749538E-01, 5.952555069740412E-03, \ 9.821204851739278E-01, 1.368717477114345E-01, 4.757586602695279E-03, \ 9.821598385319343E-01, -9.959978097052690E-01, 4.727038168393605E-04, \ 9.834968499928717E-01, 7.202131341080557E-01, 3.339955375858229E-03, \ 9.867444463087381E-01, -4.389464150281105E-01, 4.224292354075523E-03, \ 9.870688041516782E-01, -1.860477389466161E-01, 4.518470382030127E-03, \ 9.871939619842668E-01, 8.755067171008981E-01, 1.519837361369944E-03, \ 9.892614872423598E-01, -9.260146296311070E-01, 1.799734507689385E-03, \ 9.945229623313124E-01, 4.853023018396496E-01, 2.560515852421350E-03, \ 9.947061632621746E-01, 6.355790382588226E-01, 1.778286578522554E-03, \ 9.948541523937408E-01, 9.833293028860037E-01, 5.491048194068317E-04, \ 9.948772524482939E-01, -8.407859395090261E-01, 1.605442474502514E-03, \ 9.949201671743397E-01, -7.003454609915903E-01, 2.006603012946033E-03, \ 9.949822864151898E-01, 9.238195120237386E-01, 9.266737007306744E-04, \ 9.960955981451255E-01, -1.323322402607845E-02, 2.563511060458582E-03, \ 9.977169911523626E-01, -5.459548078849698E-01, 1.239809456010988E-03, \ 9.980230789357751E-01, 2.518043976244231E-01, 1.843703555135520E-03, \ 9.980850962629690E-01, -9.781664509229353E-01, 3.796649877334044E-04, \ 9.982000639809739E-01, -3.046004953209935E-01, 1.439841751685133E-03, \ 9.991322806157538E-01, 7.967757949667039E-01, 8.678616486509684E-04 ] ) return xyw def smr44 ( ): #*****************************************************************************80 # ## smr44 returns the SMR rule of degree 44. # # Discussion: # # DEGREE: 44 # POINTS CARDINALITY: 353 # NORM INF MOMS. RESIDUAL: 1.39699e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*353), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.984320392366739E-01, -8.069907738631789E-01, 9.129188297919674E-04, \ -9.983184531837725E-01, 9.305063618730227E-01, 5.320673982755963E-04, \ -9.978244272094350E-01, 2.010518994335128E-01, 1.598745058561678E-03, \ -9.974547076089806E-01, 4.442097888110615E-01, 1.587226283438206E-03, \ -9.971550888623897E-01, -5.768131021729579E-02, 1.901977649434094E-03, \ -9.967647638775373E-01, 8.058203134817903E-01, 1.263686704072662E-03, \ -9.963702759402693E-01, 9.957226369845009E-01, 1.818612016165590E-04, \ -9.963181710633270E-01, -6.304189998071564E-01, 1.671127161151113E-03, \ -9.961268807224163E-01, 6.456711899254686E-01, 1.750825399677425E-03, \ -9.957522090105495E-01, -9.275216968816482E-01, 8.507815083388259E-04, \ -9.951693924758787E-01, -2.761138658566978E-01, 2.436900445069140E-03, \ -9.950054666513565E-01, -9.849707705106929E-01, 4.757246968341718E-04, \ -9.946541882949513E-01, -4.583314062976532E-01, 2.366650251412720E-03, \ -9.887114315163458E-01, 9.660230724784559E-01, 8.879418773849759E-04, \ -9.846991374239497E-01, 7.976665855520176E-02, 5.012110624120673E-03, \ -9.844761515180129E-01, 3.207459712592796E-01, 4.876181551671285E-03, \ -9.842610329585771E-01, -8.709872191992893E-01, 2.295666225344954E-03, \ -9.839028036500266E-01, -7.269350704556350E-01, 3.598356544188341E-03, \ -9.834521968435078E-01, 8.788181549694504E-01, 2.662295402621843E-03, \ -9.825404996126923E-01, 5.377600798078346E-01, 4.243392110291322E-03, \ -9.791830807570596E-01, 7.300801609052650E-01, 4.174881751974668E-03, \ -9.789536888169472E-01, -1.541839686056489E-01, 5.635575613152338E-03, \ -9.754623934517895E-01, -9.985001905507400E-01, 3.451126367359588E-04, \ -9.754074605989603E-01, -5.489105297220782E-01, 5.119253227374393E-03, \ -9.743732738644221E-01, -9.576680228121058E-01, 1.885947698906212E-03, \ -9.727071455292210E-01, 9.854153480279049E-01, 9.090447956991166E-04, \ -9.724216540568620E-01, -3.604921321100248E-01, 5.763676619977396E-03, \ -9.613138962914113E-01, -8.110561453053367E-01, 3.754018364329767E-03, \ -9.569550751753445E-01, 9.321525496230852E-01, 3.154552805737187E-03, \ -9.556428656633877E-01, 2.033112164565538E-01, 8.655618940100654E-03, \ -9.549267697092383E-01, 4.267664542473830E-01, 7.666973204798044E-03, \ -9.533681225680328E-01, -1.542928806337710E-02, 8.164452383475256E-03, \ -9.527049674156014E-01, 6.174677639259242E-01, 6.608979468596846E-03, \ -9.515654916231491E-01, 8.125776987261066E-01, 5.354225267337657E-03, \ -9.490456638939141E-01, -6.481440018182706E-01, 6.672612545168258E-03, \ -9.458175364481419E-01, -9.060068746246541E-01, 4.013235135085827E-03, \ -9.440126918917942E-01, 9.976234060121431E-01, 5.680139121819110E-04, \ -9.437045246883812E-01, -4.180391499005318E-01, 4.052305718583254E-03, \ -9.416958977488444E-01, -9.832610660242087E-01, 1.644473802134468E-03, \ -9.406877057002140E-01, -2.319813480159833E-01, 8.705386624332852E-03, \ -9.296781480094017E-01, -7.566364668417300E-01, 4.783429752162442E-03, \ -9.248302265385766E-01, -4.861577371922396E-01, 7.748939834534853E-03, \ -9.202441950236100E-01, 9.674488696318712E-01, 2.660205689239971E-03, \ -9.178390013250890E-01, 7.064362568998120E-01, 7.919583195340947E-03, \ -9.135758448462131E-01, 8.754421512868488E-01, 5.404549032231900E-03, \ -9.119456444341953E-01, 3.233647958995216E-01, 1.083291124444676E-02, \ -9.079717560919897E-01, -8.773647290343602E-02, 9.522960144764343E-03, \ -9.067025869022671E-01, 1.076010187739800E-01, 1.170317912042211E-02, \ -9.051126411361261E-01, 5.170998371398160E-01, 1.099643030005613E-02, \ -9.001351500517843E-01, -9.461649530258005E-01, 4.028247494909381E-03, \ -9.000620333263829E-01, -8.422658056671526E-01, 6.586062353219417E-03, \ -8.994849690542454E-01, -9.938608373644522E-01, 9.520566362941994E-04, \ -8.941680642100808E-01, -3.104307200910414E-01, 9.898803205596610E-03, \ -8.932311675008094E-01, -5.876846915824177E-01, 7.570892945063220E-03, \ -8.795126005531750E-01, -7.053987104996297E-01, 8.491984407075194E-03, \ -8.784492099639224E-01, 9.883243937096547E-01, 1.809730927741861E-03, \ -8.693740466112758E-01, 9.210068898056959E-01, 4.897281085790932E-03, \ -8.693401894440411E-01, 7.856297245279599E-01, 9.261454593228968E-03, \ -8.562011220892315E-01, -3.962460994060516E-01, 9.981754074698595E-03, \ -8.548549835925230E-01, 2.399548122908549E-01, 1.209333227731901E-02, \ -8.532888443992166E-01, 6.222509726831481E-01, 1.233013730701336E-02, \ -8.528074077558421E-01, -1.579638544671366E-01, 1.324588980901926E-02, \ -8.444113766994861E-01, -9.992229866877739E-01, 4.723975132108903E-04, \ -8.432057487089938E-01, 3.235108142044065E-02, 1.319558395099830E-02, \ -8.430373389996317E-01, -8.928430380538469E-01, 6.787529444568871E-03, \ -8.425055028423227E-01, -5.289098324323593E-01, 8.580086025567452E-03, \ -8.396012261206522E-01, -9.728858072059390E-01, 3.439212998921980E-03, \ -8.382826128298011E-01, 4.169643647390908E-01, 1.529603938770566E-02, \ -8.216846795004334E-01, -7.826199200643963E-01, 1.066116384062461E-02, \ -8.180509590829773E-01, 9.976706498590422E-01, 8.622182721712620E-04, \ -8.168446401782580E-01, 9.569871415452944E-01, 4.642547532189030E-03, \ -8.059705646063106E-01, 8.562279695272285E-01, 9.713220584480500E-03, \ -7.985378237516410E-01, -6.361943884365141E-01, 1.288799983989059E-02, \ -7.874963351816394E-01, 7.136737011098295E-01, 1.328855758833727E-02, \ -7.873181180776506E-01, 1.717693790572155E-01, 1.456745869621430E-02, \ -7.867043322440256E-01, -2.603635734391026E-01, 1.766717913659451E-02, \ -7.837010537620064E-01, -4.338871119370292E-01, 1.153873491612521E-02, \ -7.718371515252632E-01, -9.328817815076849E-01, 6.466448787081487E-03, \ -7.714891987669056E-01, -4.239834940027459E-02, 1.628468473942501E-02, \ -7.713192309659846E-01, 5.319196451075733E-01, 1.658253232258541E-02, \ -7.617253581469365E-01, -9.897388221915862E-01, 2.488625548037977E-03, \ -7.506982895864639E-01, 3.204233011897250E-01, 1.685029450873451E-02, \ -7.448534415599564E-01, 9.829922539741698E-01, 3.520796639776173E-03, \ -7.421873132631707E-01, -8.453867233878035E-01, 1.088288447448831E-02, \ -7.293425876035039E-01, 9.154064068042572E-01, 8.936809305882937E-03, \ -7.223446846603496E-01, -7.141244471949223E-01, 1.414814648905025E-02, \ -7.219135429448188E-01, -5.263185876605118E-01, 1.575035952702964E-02, \ -7.098617300046203E-01, 7.947984896859370E-01, 1.339686789384787E-02, \ -6.988495988698514E-01, 4.052943040220409E-01, 9.837663715320634E-03, \ -6.984909504155071E-01, -1.429846401852013E-01, 1.896573077123497E-02, \ -6.975652345893874E-01, 9.525558491386997E-02, 2.060322580221702E-02, \ -6.900736961878055E-01, 6.326479337076335E-01, 1.728656050260011E-02, \ -6.869058806489352E-01, -3.499362651285792E-01, 2.042431472019608E-02, \ -6.838451466610610E-01, -9.632238434827868E-01, 5.536575368407264E-03, \ -6.601354229220036E-01, -9.978926285407612E-01, 1.118308079993473E-03, \ -6.591611069246858E-01, 9.972971332925751E-01, 1.393373155547319E-03, \ -6.496630709138930E-01, -8.968850821145237E-01, 9.867235398314472E-03, \ -6.435615255682987E-01, 4.745725306260367E-01, 1.695728879109135E-02, \ -6.382152417385206E-01, 9.593302235740115E-01, 6.948544515653850E-03, \ -6.368057767453273E-01, -6.105621900036199E-01, 1.773677383165920E-02, \ -6.352930402436240E-01, 2.440334398061165E-01, 2.247199576089053E-02, \ -6.302597734646941E-01, -7.836990702094097E-01, 1.442675294839290E-02, \ -6.222316612499560E-01, 8.650945015472389E-01, 1.244266398906457E-02, \ -6.142105393288021E-01, -3.115349747226613E-02, 1.267213816470802E-02, \ -5.999445700339456E-01, 7.231403345609435E-01, 1.705107902581306E-02, \ -5.985364302471942E-01, -2.220826177325775E-01, 2.068460393331641E-02, \ -5.874715162971924E-01, -4.537860718695650E-01, 2.256935531509155E-02, \ -5.805876391669599E-01, 1.164148986297675E-02, 1.455966199822115E-02, \ -5.761875109801690E-01, -9.834901963379014E-01, 4.021379301366000E-03, \ -5.536892203872140E-01, 5.713476331182120E-01, 2.021949241318215E-02, \ -5.482191724466468E-01, -9.351120650991530E-01, 7.900752509637180E-03, \ -5.443795454192639E-01, 3.668375708005358E-01, 2.231767290088453E-02, \ -5.356710284369979E-01, -6.904452102919497E-01, 1.837686099829941E-02, \ -5.352962150371631E-01, 9.876776882519422E-01, 4.155389888548638E-03, \ -5.257781590187137E-01, -8.445781803925743E-01, 1.356203757752880E-02, \ -5.248342428534777E-01, 9.219407641844128E-01, 1.026387297173803E-02, \ -5.174066557246780E-01, 1.518777346465177E-01, 2.518880761805230E-02, \ -5.036594510447880E-01, 8.035723784673375E-01, 1.586067262933542E-02, \ -5.034025143249927E-01, -3.126938402863565E-01, 2.210632272995924E-02, \ -4.806633025223544E-01, -1.069134743166169E-01, 2.522706612518943E-02, \ -4.768202265102032E-01, -5.503872364548488E-01, 2.284324106026750E-02, \ -4.646325900518826E-01, -9.961732199116691E-01, 1.946334569341992E-03, \ -4.547884920410544E-01, 6.649539370735507E-01, 1.931316094733287E-02, \ -4.421806574347436E-01, -9.613324393854693E-01, 6.002473078471003E-03, \ -4.394327628517760E-01, 4.730023882906435E-01, 2.198395890845260E-02, \ -4.232998688209890E-01, 2.883435479068856E-01, 2.182550754053004E-02, \ -4.226231099797195E-01, -7.634216829847481E-01, 1.777618548814907E-02, \ -4.220890965407914E-01, 9.630811547877729E-01, 6.855160079679186E-03, \ -4.112420604475592E-01, -8.937882050869647E-01, 1.158849916478484E-02, \ -4.024593442610409E-01, 8.726238717970590E-01, 1.358874265349387E-02, \ -4.002269679736949E-01, -4.051442349677620E-01, 2.393039425904835E-02, \ -3.993267478943860E-01, 5.176385479657997E-02, 2.702588719348437E-02, \ -3.923849152916527E-01, 9.981789733855365E-01, 1.591517314127669E-03, \ -3.906313798231402E-01, -1.840437971511796E-01, 1.351522769629539E-02, \ -3.582740394972692E-01, 7.469437554790193E-01, 1.688419511612995E-02, \ -3.576445111330830E-01, -6.381016019538316E-01, 2.217271254303683E-02, \ -3.471390596376763E-01, 9.751558114236266E-01, 1.414687365431868E-03, \ -3.410270978511928E-01, 5.659016258527511E-01, 1.929118341000195E-02, \ -3.395129208825403E-01, -9.824778005139284E-01, 4.415576863417267E-03, \ -3.331346997723381E-01, 2.223766929597974E-01, 1.646772259494828E-02, \ -3.252463389952233E-01, -2.451189274367319E-01, 2.240870404470034E-02, \ -3.009376392714923E-01, -8.266673670128765E-01, 1.591461362539792E-02, \ -2.981870657864640E-01, 3.966510337158281E-01, 2.346801013649629E-02, \ -2.952430335911029E-01, 9.272338125092218E-01, 1.052839956257688E-02, \ -2.925795365681464E-01, -9.317251622707681E-01, 9.101328501500838E-03, \ -2.837411558415489E-01, -4.979776736270173E-01, 2.506976148361703E-02, \ -2.806344135463510E-01, -4.809162882996374E-02, 2.782770459634624E-02, \ -2.656701164804061E-01, 8.179772293299151E-01, 1.481544909528898E-02, \ -2.542370551980483E-01, 9.856209199785680E-01, 4.824829120437116E-03, \ -2.521259754556285E-01, -9.973002828723974E-01, 1.620836943142523E-03, \ -2.497736261853112E-01, 6.474134806850792E-01, 1.852942792640709E-02, \ -2.494952225569154E-01, 1.582011504522273E-01, 2.190214882403085E-02, \ -2.324705240257510E-01, -7.170067419800342E-01, 2.080073547457119E-02, \ -2.104466559805069E-01, -3.406566669476734E-01, 2.720075219951604E-02, \ -2.099261409117430E-01, 4.786906023524469E-01, 1.185954144951369E-02, \ -1.861486176729608E-01, -9.634767979371285E-01, 6.737017697973697E-03, \ -1.756023068664000E-01, -8.797164554325823E-01, 1.312819960371862E-02, \ -1.662816084102881E-01, 8.799028024337228E-01, 1.284862663386604E-02, \ -1.657193846143792E-01, 3.172098063693634E-01, 2.614101117655917E-02, \ -1.615402128474088E-01, -1.512617629404641E-01, 2.870683831769700E-02, \ -1.562119970212992E-01, -5.878544646273842E-01, 2.490102418715279E-02, \ -1.534073739178984E-01, 7.313740308801530E-01, 1.907865171993343E-02, \ -1.468820128344276E-01, 7.454986763836169E-02, 2.515116960979389E-02, \ -1.456132526020360E-01, 9.547929947534334E-01, 8.009904149647161E-03, \ -1.411022235577947E-01, 5.402822094147779E-01, 1.985276171591949E-02, \ -1.145203437993708E-01, 9.971336236185711E-01, 1.976988745961730E-03, \ -1.083747697202039E-01, -9.898130243123879E-01, 3.355317427073141E-03, \ -1.034956048479747E-01, -7.889452083356127E-01, 1.855933599799289E-02, \ -9.518052933052586E-02, -4.313306509695957E-01, 2.120680416955437E-02, \ -5.764780880949349E-02, -9.255412926001291E-01, 1.041178057147584E-02, \ -4.945963945071411E-02, 8.139429446246940E-01, 1.695154845553709E-02, \ -4.694483372115068E-02, 2.260246749730705E-01, 2.750563040286702E-02, \ -3.710556308317932E-02, -2.550849012394165E-01, 2.916267630869709E-02, \ -3.589386545922083E-02, -2.053720558161740E-02, 2.801912438135100E-02, \ -3.529301810325418E-02, 4.374449384609287E-01, 2.490206851452144E-02, \ -3.174169125194722E-02, 6.397258205734582E-01, 2.335214947901313E-02, \ -2.807946922203877E-02, 9.747008686677923E-01, 4.510619199652917E-03, \ -2.585228714382427E-02, -6.752836809385544E-01, 2.280749223644548E-02, \ -1.289238997994259E-02, -4.843864246438258E-01, 1.556053198827482E-02, \ -1.223860458201907E-02, 9.149372658820439E-01, 1.142835906607102E-02, \ -1.086355028359328E-02, -9.753777328721651E-01, 3.249297484258564E-03, \ 2.708179220842590E-02, -8.547719772455804E-01, 1.569718188959173E-02, \ 4.149479523966346E-02, -9.979599963961665E-01, 1.565335881756029E-03, \ 5.689776414251970E-02, 9.891551358091155E-01, 3.282255117781437E-03, \ 6.075582703243104E-02, -5.668334256989663E-01, 1.153844244336376E-02, \ 7.101224496756312E-02, -9.575012140957714E-01, 6.335543760258588E-03, \ 7.535912927721751E-02, 1.235303669187323E-01, 2.997948351699728E-02, \ 7.592224478984431E-02, 7.415381032881689E-01, 2.029679101450883E-02, \ 7.750653209648602E-02, 3.539562134043134E-01, 2.426431231808029E-02, \ 8.652690668833830E-02, -1.247447983933045E-01, 2.991558956158543E-02, \ 9.446479482059529E-02, -3.553535264925528E-01, 2.880322792020771E-02, \ 9.779012576626916E-02, 5.494194161163839E-01, 2.608420815396981E-02, \ 1.012772299308512E-01, -7.581900569606719E-01, 1.947312434746350E-02, \ 1.030203458432020E-01, 8.661062919924195E-01, 1.346630675248675E-02, \ 1.062220246130106E-01, -5.577336014290080E-01, 1.363056491610594E-02, \ 1.327284751168050E-01, 9.519418660538810E-01, 9.110450516946341E-03, \ 1.563331097859266E-01, -9.095402453421066E-01, 1.228782579110563E-02, \ 1.701527767472629E-01, 9.984157843452909E-01, 1.295448963991591E-03, \ 1.741393635207433E-01, -9.854144027813655E-01, 4.755824748909084E-03, \ 1.879938370487562E-01, 2.630174862645962E-01, 2.621178775149382E-02, \ 2.002223207104934E-01, -6.587656605309330E-01, 2.189481233525649E-02, \ 2.033135424032844E-01, 1.226680906571880E-02, 3.091880266293206E-02, \ 2.073867973374402E-01, 6.656736012079840E-01, 2.289758057394497E-02, \ 2.165364146034749E-01, 8.131469595412018E-01, 1.546367066744115E-02, \ 2.186815288972714E-01, -2.296610279178752E-01, 2.995732867358852E-02, \ 2.218162837289157E-01, -4.581289072758777E-01, 2.642830689906846E-02, \ 2.263761239474323E-01, 4.557960959181672E-01, 2.667293537062659E-02, \ 2.289231298283811E-01, -8.289790576270621E-01, 1.613294129345465E-02, \ 2.527251024651854E-01, 9.135017973841686E-01, 1.092935602260977E-02, \ 2.621462888782247E-01, 9.816181546275472E-01, 5.528965474505003E-03, \ 2.823739032553990E-01, -9.532140949241149E-01, 8.906935903531529E-03, \ 2.955081211245678E-01, 1.689963046033540E-01, 2.153510784480399E-02, \ 2.985636391106877E-01, -9.974664868313298E-01, 1.671486096091834E-03, \ 3.232078531359192E-01, -7.439006988246658E-01, 1.855709405036384E-02, \ 3.279464627695976E-01, -5.713898766443788E-01, 2.281029102796516E-02, \ 3.338179507930596E-01, 5.793637325547847E-01, 2.428395685755850E-02, \ 3.362148410933743E-01, -9.818025366828656E-02, 3.019903785775920E-02, \ 3.385127772310140E-01, 7.540230240429753E-01, 1.856265624620952E-02, \ 3.419562637644176E-01, -3.435538342382597E-01, 2.733858964505634E-02, \ 3.471461374896801E-01, 3.553265509457362E-01, 2.648696947548793E-02, \ 3.502303936426706E-01, -8.883940691302195E-01, 1.279371820180086E-02, \ 3.556091773799562E-01, 8.707051502073961E-01, 1.047555741127083E-02, \ 3.556899139550058E-01, 1.128080696436079E-01, 1.321188723958388E-02, \ 3.841288497521308E-01, 9.553718729947618E-01, 8.119912907486298E-03, \ 3.946422029579690E-01, 9.964039498775228E-01, 2.112349660084158E-03, \ 4.050330117544253E-01, -9.814927725279841E-01, 5.157104944908028E-03, \ 4.362849601968560E-01, 9.019016117216835E-01, 2.940968659036344E-03, \ 4.379541949910271E-01, -6.683641513610455E-01, 1.846439396156306E-02, \ 4.420456441645449E-01, -4.713347319581990E-01, 2.365595165327062E-02, \ 4.472336730065484E-01, -8.167105914183533E-01, 1.590868587912039E-02, \ 4.492188628877602E-01, 3.464784069711753E-02, 2.599642724440654E-02, \ 4.516598503772268E-01, -2.248848786742561E-01, 2.605750990330061E-02, \ 4.534848886303145E-01, 4.821787086314744E-01, 2.470370157097336E-02, \ 4.558094575502872E-01, 6.776999314380787E-01, 2.063485603141766E-02, \ 4.597299209841112E-01, 2.512300079082298E-01, 2.520816228387497E-02, \ 4.664792245356821E-01, -9.343321639127969E-01, 9.316460572589282E-03, \ 4.676049536388429E-01, 8.280983665613982E-01, 1.378155136701219E-02, \ 5.125021470312456E-01, -9.961912026741276E-01, 1.787642568838215E-03, \ 5.134945143382650E-01, 9.255730990320611E-01, 8.514600636975230E-03, \ 5.166884966564118E-01, 9.825109005210685E-01, 5.038395003621559E-03, \ 5.363347257603982E-01, -1.095695413413886E-01, 1.941023977299713E-02, \ 5.399965994699566E-01, -5.859352676802068E-01, 1.854304744927082E-02, \ 5.464942478849923E-01, -3.640970433686203E-01, 2.338117168332904E-02, \ 5.581611838771341E-01, -7.440467570644548E-01, 1.656347514164712E-02, \ 5.627502014020098E-01, -8.788042385170552E-01, 1.221723450900345E-02, \ 5.642272201418791E-01, 3.770370382758487E-01, 2.374317220254762E-02, \ 5.673319233898169E-01, 5.874729567335129E-01, 2.128053054223834E-02, \ 5.674460469518047E-01, 1.540150684251285E-01, 2.257605869396812E-02, \ 5.707186911322696E-01, 7.641772183668017E-01, 1.625295655282468E-02, \ 5.742168074270232E-01, -9.682555557935811E-01, 5.994073320670981E-03, \ 5.959490795665168E-01, -1.948187074408299E-02, 1.530634182479124E-02, \ 6.062396124913686E-01, 8.797986377073432E-01, 1.088748308713618E-02, \ 6.229319420659956E-01, 9.975455983379399E-01, 1.521861509028911E-03, \ 6.295610198351687E-01, -4.991220308747384E-01, 1.739885853059415E-02, \ 6.324276873199660E-01, -2.471665977726898E-01, 2.093917940469638E-02, \ 6.355497887094055E-01, -9.952129871832354E-01, 1.099875629037961E-03, \ 6.410901541595502E-01, 9.583614862393586E-01, 7.156911768526562E-03, \ 6.605190644019022E-01, -6.630669125378098E-01, 1.682341496394070E-02, \ 6.618975494369205E-01, -8.156394553988217E-01, 1.300052108247076E-02, \ 6.673842000772493E-01, 2.749077536864489E-01, 2.067282662025163E-02, \ 6.680484006462090E-01, -9.288814872355221E-01, 8.563893166362068E-03, \ 6.686812125950333E-01, 4.866788467643654E-01, 2.039892342110449E-02, \ 6.700985984918092E-01, 6.842265838658567E-01, 1.713021812997701E-02, \ 6.769960821664744E-01, 8.318062288950726E-02, 1.684726166034979E-02, \ 6.859697885605170E-01, -1.260093282101731E-01, 1.484254174402420E-02, \ 6.926497230416636E-01, -9.859783123599433E-01, 2.705348861376380E-03, \ 6.959863573791213E-01, 8.238747062055407E-01, 1.204055197449034E-02, \ 6.977679871466710E-01, -4.161601763333563E-01, 1.335373628024542E-02, \ 7.368622503416473E-01, 9.864017859775360E-01, 3.620239739614126E-03, \ 7.375774852972609E-01, 9.169799988402917E-01, 8.825252453784535E-03, \ 7.438254372505340E-01, -3.279021941386523E-01, 1.463105332863874E-02, \ 7.440253522657176E-01, -1.400891582182774E-02, 1.425466175849190E-02, \ 7.495595182168627E-01, -5.717554727395397E-01, 1.640815363214294E-02, \ 7.530771473618030E-01, -7.446510104634911E-01, 1.295670791695812E-02, \ 7.544901018164238E-01, -8.766498669907319E-01, 9.526725213141853E-03, \ 7.587437942011223E-01, 5.908863410878806E-01, 1.647006558144315E-02, \ 7.593851565749156E-01, 3.839941762215441E-01, 1.723107403577913E-02, \ 7.639885454115690E-01, 1.980228289731446E-01, 1.519597994741737E-02, \ 7.685687728456019E-01, -9.630400573145438E-01, 5.001848985499082E-03, \ 7.770428027301898E-01, -9.982843164373418E-01, 8.745652562061165E-04, \ 7.772871884934368E-01, 7.542035650256003E-01, 1.251996742574017E-02, \ 7.825025147503595E-01, -1.834533183514675E-01, 1.579709193200259E-02, \ 8.150533231289440E-01, 1.014695483551139E-01, 1.256924687457834E-02, \ 8.181863818318679E-01, -4.606542231051104E-01, 1.549715675497659E-02, \ 8.193847399280907E-01, 8.611191119341332E-01, 9.398125531125533E-03, \ 8.207989728131910E-01, 9.591480451070792E-01, 5.279791002982384E-03, \ 8.297368239121403E-01, -6.631813144059097E-01, 1.224002342014436E-02, \ 8.320106005459350E-01, -8.152569987720697E-01, 9.323523497601202E-03, \ 8.320408056110908E-01, 9.977249436063439E-01, 1.033282992509946E-03, \ 8.329105693070811E-01, 4.871128705837552E-01, 1.348907133473504E-02, \ 8.365337282424045E-01, -9.243522188950283E-01, 6.014070108326465E-03, \ 8.434092146075628E-01, -5.376676824572151E-02, 1.449901864773636E-02, \ 8.449004755072183E-01, 3.093947633052660E-01, 1.245158207072536E-02, \ 8.465147750656848E-01, 6.700666235615695E-01, 1.175161455116867E-02, \ 8.478350019505928E-01, -2.985362344057802E-01, 1.366010228359022E-02, \ 8.496498343126059E-01, -9.871021978521631E-01, 2.415904636287212E-03, \ 8.796260274253024E-01, 2.138443454392648E-01, 9.339618669988453E-03, \ 8.845751363465439E-01, 7.907698638866625E-01, 8.893129746809459E-03, \ 8.866321017241603E-01, -5.623269734279417E-01, 1.150129922332423E-02, \ 8.882047697517171E-01, 9.164586294991613E-01, 5.951354500731454E-03, \ 8.938627976408585E-01, -7.430539467366774E-01, 8.289403676208404E-03, \ 8.949156789984212E-01, 5.661161599991380E-01, 8.566550012330865E-03, \ 8.954010799494210E-01, -8.753539964754327E-01, 5.837845483486322E-03, \ 8.973716972615503E-01, 9.833889194543620E-01, 2.511910121955958E-03, \ 9.001148478941252E-01, -1.724880329303405E-01, 1.268999061952536E-02, \ 9.023269610303840E-01, 6.533036389509404E-02, 1.173221023616003E-02, \ 9.023726303973623E-01, -9.609883325303766E-01, 3.360315770311110E-03, \ 9.081093855357991E-01, -3.974545530931652E-01, 1.116292038350684E-02, \ 9.082458364338479E-01, 4.160787215946197E-01, 9.411679613649818E-03, \ 9.201288583031026E-01, -9.973298211676691E-01, 7.257268851225051E-04, \ 9.288000531532276E-01, 7.013943012440006E-01, 7.037823616626887E-03, \ 9.329884007773763E-01, 3.304494336614532E-01, 5.904281068176790E-03, \ 9.384251860650527E-01, 8.571626242598636E-01, 5.623306077628070E-03, \ 9.387709463419280E-01, -6.569247138091421E-01, 7.505461254587439E-03, \ 9.390362481895664E-01, -8.140965237093258E-01, 4.977781534664430E-03, \ 9.431435157432486E-01, 5.870360626983142E-01, 5.191324447454316E-03, \ 9.450773084819802E-01, -9.221219392424895E-01, 3.393763295106028E-03, \ 9.453915273808479E-01, 1.895221840939932E-01, 8.348594654611519E-03, \ 9.456536724677754E-01, 9.539239527027603E-01, 3.022785644899445E-03, \ 9.473577935390517E-01, -5.193485262434305E-02, 9.670046203567387E-03, \ 9.489719119922718E-01, 9.971737186812124E-01, 6.141238201223769E-04, \ 9.513861085801828E-01, -2.782244198545041E-01, 9.083776210637055E-03, \ 9.524619245554554E-01, -5.009630638627496E-01, 7.585592261208418E-03, \ 9.570396759412962E-01, -9.818217124953741E-01, 1.504963278061301E-03, \ 9.651084193076095E-01, 4.764381514817677E-01, 6.804854306822511E-03, \ 9.673991604949321E-01, 7.692810312148867E-01, 4.520963014240378E-03, \ 9.730917870009820E-01, -7.458190017187750E-01, 4.241383153444730E-03, \ 9.734392697290727E-01, -8.673592113403571E-01, 2.810476896561892E-03, \ 9.763607543792061E-01, 3.048040261918404E-01, 5.276457875981873E-03, \ 9.768475228065115E-01, 9.082588824000043E-01, 2.643888308901319E-03, \ 9.782469107965639E-01, 7.857190536343943E-02, 6.186986811631052E-03, \ 9.798711093359943E-01, 6.455315254229357E-01, 4.130331043787127E-03, \ 9.801558211147705E-01, 9.831284518138658E-01, 1.028657890512397E-03, \ 9.817934561418729E-01, -6.004957048608559E-01, 4.153182683219009E-03, \ 9.822023634787357E-01, -9.520064075525696E-01, 1.488447743427078E-03, \ 9.824823278531268E-01, -1.588192490530472E-01, 5.597811173658705E-03, \ 9.824823551297321E-01, -3.937517188889684E-01, 5.138454426652030E-03, \ 9.866504547608295E-01, -9.955835634824257E-01, 3.961208092085676E-04, \ 9.905327362354205E-01, 8.309506492911954E-01, 2.069825511375866E-03, \ 9.942355332758673E-01, 3.974103619286143E-01, 2.413263541158905E-03, \ 9.945084471405289E-01, 5.494932527943799E-01, 2.193364858292885E-03, \ 9.945305554986960E-01, -8.135327323625892E-01, 1.514406390792948E-03, \ 9.947615068172242E-01, 9.545658333888697E-01, 7.423836783813612E-04, \ 9.949517157579387E-01, -9.067668333653325E-01, 9.864959809811758E-04, \ 9.957818259075973E-01, 1.993953840265955E-01, 2.396827736651728E-03, \ 9.962141216868449E-01, -6.903174371098946E-01, 1.476800783658664E-03, \ 9.968687603178163E-01, -2.875773812112470E-02, 2.072108287711335E-03, \ 9.971393163063961E-01, 7.214186037213960E-01, 1.344741266208887E-03, \ 9.972431159527100E-01, -5.064881469083564E-01, 1.610896725802623E-03, \ 9.974246740827564E-01, 9.967061334165134E-01, 1.310709895846009E-04, \ 9.974788575004648E-01, -2.791676769769759E-01, 1.765107353951216E-03, \ 9.989309477716464E-01, -9.759800757253289E-01, 2.868352447506991E-04, \ 9.999408488515129E-01, 8.953088235569292E-01, 3.456123608241670E-04 ] ) return xyw def smr45 ( ): #*****************************************************************************80 # ## smr45 returns the SMR rule of degree 45. # # Discussion: # # DEGREE: 45 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 359 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*359), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.987809239831112E-01, 9.748368623655366E-01, 2.993356033786765E-04, \ -9.985808631696838E-01, -8.990756328646153E-01, 5.055415778287732E-04, \ -9.985157152594889E-01, -9.971971012987678E-01, 9.821637011466654E-05, \ -9.976075303722897E-01, 2.495954379536609E-01, 1.726273349986223E-03, \ -9.975896723770977E-01, -7.481282641542352E-01, 1.186765908765057E-03, \ -9.970359077153589E-01, -4.973042782590862E-03, 1.976200444087838E-03, \ -9.970034303329453E-01, 4.805125358625656E-01, 1.717119689979895E-03, \ -9.961579504388610E-01, -2.339319461038794E-01, 2.197631276825098E-03, \ -9.959759411587524E-01, 8.966138075526434E-01, 9.460145783264427E-04, \ -9.955607724070924E-01, 6.629654417179892E-01, 1.734396121578630E-03, \ -9.944882643568679E-01, -5.822713014974841E-01, 2.130704201950450E-03, \ -9.944839549832385E-01, -4.305503528241359E-01, 2.332655357182134E-03, \ -9.943103084508153E-01, -9.589447862560037E-01, 7.154329251248137E-04, \ -9.942971011761540E-01, 7.923589246102194E-01, 1.676928772166950E-03, \ -9.879109700683048E-01, -8.401442342078335E-01, 2.254477068544381E-03, \ -9.871570448287768E-01, 9.953040717606414E-01, 4.014919822858868E-04, \ -9.834657898675960E-01, 9.464917816489062E-01, 1.606043238725865E-03, \ -9.833305319309631E-01, 1.263457021753157E-01, 5.419689142545006E-03, \ -9.826246063168834E-01, 3.638393037687699E-01, 5.148686860161606E-03, \ -9.810868050137430E-01, -9.856276869865556E-01, 8.700281868935982E-04, \ -9.802648322311707E-01, -6.750032224988851E-01, 3.955250863364047E-03, \ -9.799852473516794E-01, 5.711769167233038E-01, 4.435133168562443E-03, \ -9.796202659342652E-01, -1.139693876952825E-01, 5.831373899382246E-03, \ -9.771712814502167E-01, -3.337491350874086E-01, 5.138702967736385E-03, \ -9.753612107572261E-01, 8.542575822594997E-01, 2.939880020404475E-03, \ -9.750871880034563E-01, -9.181022714139108E-01, 2.418384903446744E-03, \ -9.712009645368384E-01, 7.236074445113848E-01, 4.632318546295927E-03, \ -9.664706318878840E-01, -5.062808601831001E-01, 6.514641073677681E-03, \ -9.635773411406924E-01, -7.811935286068071E-01, 4.341305455620128E-03, \ -9.592551721099858E-01, 9.800077457957908E-01, 1.583793112109460E-03, \ -9.527470555424390E-01, 2.452206198184587E-01, 8.934499397490152E-03, \ -9.512217505973695E-01, -9.975809114133117E-01, 5.139248565810932E-04, \ -9.509238027788980E-01, 4.671808125048466E-01, 7.778845637088972E-03, \ -9.502795953661248E-01, 1.665956085226044E-02, 9.244882696179383E-03, \ -9.483846862528557E-01, 9.121585564057219E-01, 3.515812117215462E-03, \ -9.464214946937899E-01, -2.174055880473181E-01, 8.183789662861353E-03, \ -9.462416352500443E-01, -9.599078291538412E-01, 2.602348449588172E-03, \ -9.419837071661598E-01, -6.127904283944557E-01, 5.775655266427641E-03, \ -9.391238991374505E-01, 7.989714235337833E-01, 5.179018142204592E-03, \ -9.378086513718291E-01, -8.695603466712696E-01, 5.169665843353311E-03, \ -9.370137281757169E-01, 6.282649414142087E-01, 7.623356356150477E-03, \ -9.356961338262859E-01, -3.645584063625137E-01, 6.010631113438040E-03, \ -9.253974646921507E-01, -7.190198240417008E-01, 6.336440252338264E-03, \ -9.248470794804491E-01, 9.972632014604238E-01, 7.216535092722727E-04, \ -9.102216394091136E-01, 9.552115242137005E-01, 3.429119254261080E-03, \ -9.090014113055961E-01, -4.456272486278706E-01, 9.085459391365453E-03, \ -9.077061721157841E-01, 3.609878414025458E-01, 1.119544980789453E-02, \ -9.044718083850251E-01, -9.248380504679798E-02, 1.138730334189965E-02, \ -9.041052183788196E-01, 1.370275081676114E-01, 1.231280001099448E-02, \ -9.003272138921747E-01, -9.855131239038005E-01, 2.142261107197177E-03, \ -8.998267130073949E-01, 8.611867551994773E-01, 5.652454680674074E-03, \ -8.964517879623641E-01, 7.184571948644249E-01, 8.121078281162448E-03, \ -8.906894622641233E-01, -5.845154566197192E-01, 8.308665412941993E-03, \ -8.897286914429898E-01, -9.254565139699565E-01, 5.359918872844426E-03, \ -8.856328610403172E-01, 5.303622802964915E-01, 1.168547747268816E-02, \ -8.854742809240306E-01, -8.063045923419880E-01, 8.148233321624298E-03, \ -8.834346561856141E-01, -2.466770217389220E-01, 9.493619529933141E-03, \ -8.629850430376032E-01, 9.846794003258130E-01, 2.528739364876000E-03, \ -8.506693908403453E-01, 9.125903996034499E-01, 5.849578632842550E-03, \ -8.492900289400127E-01, 2.609008872385714E-01, 1.361563690700432E-02, \ -8.474472786288211E-01, -6.901503323404313E-01, 1.100649739704037E-02, \ -8.464217718205864E-01, 2.909630308393418E-02, 1.381846696789304E-02, \ -8.459950759889058E-01, -3.370889407226870E-01, 1.214993895881173E-02, \ -8.408627217827968E-01, 7.927942230163550E-01, 9.201701596927991E-03, \ -8.370863536953854E-01, -9.980212613540562E-01, 8.867352167594041E-04, \ -8.323965789758532E-01, 6.377990761410410E-01, 1.217271062025909E-02, \ -8.314738798895785E-01, -5.062045685366845E-01, 1.274593131055984E-02, \ -8.240227041551308E-01, -9.642226450420159E-01, 4.656297575580126E-03, \ -8.233464165343024E-01, -8.728783340437961E-01, 8.558990866905701E-03, \ -8.220591736941830E-01, -1.243862989299787E-01, 1.244606872559087E-02, \ -8.188844823185363E-01, 4.261617662513782E-01, 1.558630923706844E-02, \ -7.969896207737629E-01, 9.976480667995195E-01, 9.937781058818520E-04, \ -7.918069891410763E-01, 9.552496571182889E-01, 5.247432489034864E-03, \ -7.839313303459738E-01, 1.577452094536468E-01, 1.531782499550762E-02, \ -7.808186099816705E-01, -7.721253866618816E-01, 1.174558344919606E-02, \ -7.735975996435843E-01, 8.594993334079274E-01, 9.569255855638928E-03, \ -7.673513409414942E-01, -2.186521333866828E-01, 1.604398689184609E-02, \ -7.634767876646369E-01, -6.119083101507623E-01, 1.551125361015980E-02, \ -7.604924395747599E-01, -4.040521641808663E-01, 1.640483106687547E-02, \ -7.598303762668254E-01, 7.223972889507986E-01, 1.294995516437059E-02, \ -7.546147648023375E-01, 5.450635784714123E-01, 1.627134395977775E-02, \ -7.477268693062509E-01, -1.178617906350497E-03, 1.534766967987536E-02, \ -7.441981398623979E-01, -9.248122192057350E-01, 7.952214175998626E-03, \ -7.411794309655517E-01, -9.883378955524539E-01, 3.149005459627492E-03, \ -7.396577473534641E-01, 3.065734892201429E-01, 1.696772838146242E-02, \ -7.173231621338175E-01, 9.835540032598186E-01, 3.576914417052623E-03, \ -7.013275658365165E-01, -8.389991135422733E-01, 1.116556601175833E-02, \ -6.972792709156885E-01, 9.171883050550365E-01, 8.783301477841914E-03, \ -6.889056647928331E-01, 4.105476960488628E-01, 1.322143695866550E-02, \ -6.791491171576957E-01, -9.973182946735697E-02, 1.835334682967442E-02, \ -6.785344806438597E-01, -7.028760007459759E-01, 1.603405486470507E-02, \ -6.778885853526038E-01, 7.985598896411525E-01, 1.305296371184325E-02, \ -6.767414083720775E-01, 1.216983833611472E-01, 1.702881131982138E-02, \ -6.767037258823436E-01, -5.089593879681761E-01, 1.929956845223450E-02, \ -6.693168433164310E-01, -2.985847484238517E-01, 2.053896928599153E-02, \ -6.681575030734345E-01, 6.391753535023200E-01, 1.675821395824656E-02, \ -6.490686401640144E-01, -9.624589736537986E-01, 6.433329913117225E-03, \ -6.299677977917032E-01, 9.975283667931077E-01, 1.307683705358367E-03, \ -6.269567681651597E-01, 4.853810354287711E-01, 1.557881532766953E-02, \ -6.251430706398415E-01, -9.977234181855117E-01, 1.373432556349576E-03, \ -6.246231931149462E-01, 2.373991342623364E-01, 1.859631127917601E-02, \ -6.135737153470906E-01, -8.913530795649121E-01, 9.807279239964804E-03, \ -6.099509227115107E-01, 9.609069768683841E-01, 6.626684869311525E-03, \ -5.906682339894699E-01, 8.667890507859654E-01, 1.214231245428204E-02, \ -5.902315633378371E-01, 7.656704700409119E-03, 1.553617180174587E-02, \ -5.827340699533451E-01, -7.799185004279106E-01, 1.506550662060840E-02, \ -5.800597214330994E-01, -6.076368281751579E-01, 1.994641910743171E-02, \ -5.731297492992956E-01, 7.245305917039069E-01, 1.666027168900788E-02, \ -5.720751096895411E-01, -1.782643294102043E-01, 2.248088421841022E-02, \ -5.704963535556302E-01, -4.059198759788438E-01, 2.319074978994265E-02, \ -5.499812366523558E-01, 3.491130804137083E-01, 2.143412266902755E-02, \ -5.413499891114516E-01, 5.699276014351697E-01, 1.818656471958422E-02, \ -5.404313099098355E-01, 7.035913506382468E-02, 1.450685080017977E-02, \ -5.241201775879956E-01, -9.836142249086132E-01, 4.533301530515161E-03, \ -5.211800788850269E-01, -9.318333678975942E-01, 7.829122810295861E-03, \ -5.091471437000489E-01, 9.883443269909445E-01, 3.852866247300155E-03, \ -4.999904832068175E-01, 9.243318111693436E-01, 9.722335283461081E-03, \ -4.827891808826871E-01, -8.404726014611830E-01, 1.259532628864143E-02, \ -4.758599005186578E-01, 8.031297625877543E-01, 1.563421315582868E-02, \ -4.739367439717606E-01, -6.948299595246461E-01, 1.902025287597122E-02, \ -4.725182717643259E-01, 1.906085429772531E-01, 2.556026449129186E-02, \ -4.685979592711882E-01, -2.811429587683000E-01, 2.475198280486229E-02, \ -4.617764304558508E-01, -5.116467385712951E-01, 2.392689042225338E-02, \ -4.543098644742484E-01, -6.357162836142750E-02, 2.429812363005727E-02, \ -4.514514457659036E-01, 4.524814600085829E-01, 2.178659688025009E-02, \ -4.454674266029482E-01, -9.088658429301943E-01, 1.921862701385430E-03, \ -4.442220408374918E-01, 6.539255470454639E-01, 1.815962112706960E-02, \ -4.037641494006043E-01, -9.963492843723524E-01, 2.019937935352191E-03, \ -3.994965424916097E-01, 9.652033889320616E-01, 6.696722911338705E-03, \ -3.949679284272561E-01, -9.580785434262290E-01, 7.330895788726833E-03, \ -3.839587310522242E-01, 8.749726658353748E-01, 1.286006475529313E-02, \ -3.774779250407504E-01, -8.809520347205344E-01, 9.629793742675348E-03, \ -3.724254271641495E-01, 3.180527134728118E-01, 2.421744890018692E-02, \ -3.706962390305071E-01, -1.391738691222885E-01, 1.415158967598348E-02, \ -3.635222351976187E-01, 9.976906542407633E-01, 1.690203137096647E-03, \ -3.634271195533723E-01, -7.666438656111270E-01, 1.659518137533172E-02, \ -3.588134811520187E-01, -3.863706837941547E-01, 2.562066896160286E-02, \ -3.511410895989978E-01, 7.598657097017213E-02, 2.910832017440310E-02, \ -3.466859823064926E-01, 7.342599349174546E-01, 1.755602838304911E-02, \ -3.437157470820955E-01, -6.085084561101284E-01, 2.330640521520084E-02, \ -3.427496011843691E-01, 5.493351398103018E-01, 2.167791054401352E-02, \ -2.977464025093953E-01, -2.106175113605862E-01, 2.369155711000212E-02, \ -2.841131225980947E-01, 2.454441303908954E-01, 1.128244322556367E-02, \ -2.838181184983802E-01, 9.294716603915232E-01, 9.657842880004704E-03, \ -2.734308898435502E-01, -9.821535582823072E-01, 5.186520389550382E-03, \ -2.686875707529910E-01, -9.183318465397052E-01, 1.013872822805395E-02, \ -2.659505623760141E-01, 9.790699184449342E-01, 2.972586627418943E-03, \ -2.597785379692306E-01, 8.165639824525108E-01, 1.545056567597512E-02, \ -2.524367426587176E-01, 4.306497620594896E-01, 2.413813532250804E-02, \ -2.521254582882448E-01, -8.208877915065049E-01, 1.380175215808280E-02, \ -2.416100067508830E-01, -4.864539918350533E-01, 2.540579845521675E-02, \ -2.295904421272411E-01, 6.423345387430144E-01, 2.156902469663802E-02, \ -2.257486484336952E-01, -3.648215238588141E-02, 2.987778176615610E-02, \ -2.220343030041925E-01, 1.957161674328358E-01, 2.195717424950444E-02, \ -2.179684508686903E-01, -6.927362944979131E-01, 2.155320590936663E-02, \ -2.125785431554086E-01, 9.877070401926165E-01, 3.018182936437289E-03, \ -1.882237242340730E-01, -9.986463574985669E-01, 1.183175228276184E-03, \ -1.861290129251524E-01, -3.113784253755371E-01, 2.679220781431789E-02, \ -1.612964698946688E-01, 8.840734468407453E-01, 1.245957990550999E-02, \ -1.460578395314807E-01, -9.538340166911464E-01, 8.610066632546907E-03, \ -1.453751285806197E-01, 5.230712405315956E-01, 1.269762461159384E-02, \ -1.367296766455244E-01, 7.427957482907744E-01, 1.891959592837709E-02, \ -1.361199669288722E-01, -8.678102051101638E-01, 1.300544655252503E-02, \ -1.297519722477037E-01, 3.446333134156687E-01, 2.525956832091458E-02, \ -1.260626917855079E-01, 9.523539560424874E-01, 7.832872314688318E-03, \ -1.171007843208515E-01, -5.778453790284559E-01, 2.438894687265387E-02, \ -1.122739223228800E-01, 1.017082445961973E-01, 2.710215456491743E-02, \ -1.036241515184341E-01, -1.486588557732932E-01, 2.899957751330600E-02, \ -9.450221416605288E-02, 5.591570240316848E-01, 1.413344321715599E-02, \ -9.300307584944975E-02, 9.974712889340351E-01, 1.727683826252121E-03, \ -8.814000629237449E-02, -7.646007397219974E-01, 1.862769502398370E-02, \ -7.747007763111526E-02, -4.031347072028282E-01, 2.085048513843114E-02, \ -7.227524974688553E-02, -9.894515397095711E-01, 3.355911821480428E-03, \ -4.023801246392568E-02, 8.277576362873151E-01, 1.555793756126800E-02, \ -2.080615617949091E-02, 9.742774768032481E-01, 4.593636973363114E-03, \ -1.411339171791895E-02, 2.524618422545646E-01, 2.675098480014549E-02, \ -1.258443439627821E-02, -9.143387117035456E-01, 1.160220639371127E-02, \ -9.858909067684239E-03, 6.635856125497768E-01, 2.179583092424484E-02, \ -9.552055799839686E-03, 4.656768245300902E-01, 1.833743720043940E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 2.726382862976956E-02, \ 9.552055799839686E-03, -4.656768245300902E-01, 1.833743720043940E-02, \ 9.858909067684239E-03, -6.635856125497768E-01, 2.179583092424484E-02, \ 1.258443439627821E-02, 9.143387117035456E-01, 1.160220639371127E-02, \ 1.411339171791895E-02, -2.524618422545646E-01, 2.675098480014549E-02, \ 2.080615617949091E-02, -9.742774768032481E-01, 4.593636973363114E-03, \ 4.023801246392568E-02, -8.277576362873151E-01, 1.555793756126800E-02, \ 7.227524974688553E-02, 9.894515397095711E-01, 3.355911821480428E-03, \ 7.747007763111526E-02, 4.031347072028282E-01, 2.085048513843114E-02, \ 8.814000629237449E-02, 7.646007397219974E-01, 1.862769502398370E-02, \ 9.300307584944975E-02, -9.974712889340351E-01, 1.727683826252121E-03, \ 9.450221416605288E-02, -5.591570240316848E-01, 1.413344321715599E-02, \ 1.036241515184341E-01, 1.486588557732932E-01, 2.899957751330600E-02, \ 1.122739223228800E-01, -1.017082445961973E-01, 2.710215456491743E-02, \ 1.171007843208515E-01, 5.778453790284559E-01, 2.438894687265387E-02, \ 1.260626917855079E-01, -9.523539560424874E-01, 7.832872314688318E-03, \ 1.297519722477037E-01, -3.446333134156687E-01, 2.525956832091458E-02, \ 1.361199669288722E-01, 8.678102051101638E-01, 1.300544655252503E-02, \ 1.367296766455244E-01, -7.427957482907744E-01, 1.891959592837709E-02, \ 1.453751285806197E-01, -5.230712405315956E-01, 1.269762461159384E-02, \ 1.460578395314807E-01, 9.538340166911464E-01, 8.610066632546907E-03, \ 1.612964698946688E-01, -8.840734468407453E-01, 1.245957990550999E-02, \ 1.861290129251524E-01, 3.113784253755371E-01, 2.679220781431789E-02, \ 1.882237242340730E-01, 9.986463574985669E-01, 1.183175228276184E-03, \ 2.125785431554086E-01, -9.877070401926165E-01, 3.018182936437289E-03, \ 2.179684508686903E-01, 6.927362944979131E-01, 2.155320590936663E-02, \ 2.220343030041925E-01, -1.957161674328358E-01, 2.195717424950444E-02, \ 2.257486484336952E-01, 3.648215238588141E-02, 2.987778176615610E-02, \ 2.295904421272411E-01, -6.423345387430144E-01, 2.156902469663802E-02, \ 2.416100067508830E-01, 4.864539918350533E-01, 2.540579845521675E-02, \ 2.521254582882448E-01, 8.208877915065049E-01, 1.380175215808280E-02, \ 2.524367426587176E-01, -4.306497620594896E-01, 2.413813532250804E-02, \ 2.597785379692306E-01, -8.165639824525108E-01, 1.545056567597512E-02, \ 2.659505623760141E-01, -9.790699184449342E-01, 2.972586627418943E-03, \ 2.686875707529910E-01, 9.183318465397052E-01, 1.013872822805395E-02, \ 2.734308898435502E-01, 9.821535582823072E-01, 5.186520389550382E-03, \ 2.838181184983802E-01, -9.294716603915232E-01, 9.657842880004704E-03, \ 2.841131225980947E-01, -2.454441303908954E-01, 1.128244322556367E-02, \ 2.977464025093953E-01, 2.106175113605862E-01, 2.369155711000212E-02, \ 3.427496011843691E-01, -5.493351398103018E-01, 2.167791054401352E-02, \ 3.437157470820955E-01, 6.085084561101284E-01, 2.330640521520084E-02, \ 3.466859823064926E-01, -7.342599349174546E-01, 1.755602838304911E-02, \ 3.511410895989978E-01, -7.598657097017213E-02, 2.910832017440310E-02, \ 3.588134811520187E-01, 3.863706837941547E-01, 2.562066896160286E-02, \ 3.634271195533723E-01, 7.666438656111270E-01, 1.659518137533172E-02, \ 3.635222351976187E-01, -9.976906542407633E-01, 1.690203137096647E-03, \ 3.706962390305071E-01, 1.391738691222885E-01, 1.415158967598348E-02, \ 3.724254271641495E-01, -3.180527134728118E-01, 2.421744890018692E-02, \ 3.774779250407504E-01, 8.809520347205344E-01, 9.629793742675348E-03, \ 3.839587310522242E-01, -8.749726658353748E-01, 1.286006475529313E-02, \ 3.949679284272561E-01, 9.580785434262290E-01, 7.330895788726833E-03, \ 3.994965424916097E-01, -9.652033889320616E-01, 6.696722911338705E-03, \ 4.037641494006043E-01, 9.963492843723524E-01, 2.019937935352191E-03, \ 4.442220408374918E-01, -6.539255470454639E-01, 1.815962112706960E-02, \ 4.454674266029482E-01, 9.088658429301943E-01, 1.921862701385430E-03, \ 4.514514457659036E-01, -4.524814600085829E-01, 2.178659688025009E-02, \ 4.543098644742484E-01, 6.357162836142750E-02, 2.429812363005727E-02, \ 4.617764304558508E-01, 5.116467385712951E-01, 2.392689042225338E-02, \ 4.685979592711882E-01, 2.811429587683000E-01, 2.475198280486229E-02, \ 4.725182717643259E-01, -1.906085429772531E-01, 2.556026449129186E-02, \ 4.739367439717606E-01, 6.948299595246461E-01, 1.902025287597122E-02, \ 4.758599005186578E-01, -8.031297625877543E-01, 1.563421315582868E-02, \ 4.827891808826871E-01, 8.404726014611830E-01, 1.259532628864143E-02, \ 4.999904832068175E-01, -9.243318111693436E-01, 9.722335283461081E-03, \ 5.091471437000489E-01, -9.883443269909445E-01, 3.852866247300155E-03, \ 5.211800788850269E-01, 9.318333678975942E-01, 7.829122810295861E-03, \ 5.241201775879956E-01, 9.836142249086132E-01, 4.533301530515161E-03, \ 5.404313099098355E-01, -7.035913506382468E-02, 1.450685080017977E-02, \ 5.413499891114516E-01, -5.699276014351697E-01, 1.818656471958422E-02, \ 5.499812366523558E-01, -3.491130804137083E-01, 2.143412266902755E-02, \ 5.704963535556302E-01, 4.059198759788438E-01, 2.319074978994265E-02, \ 5.720751096895411E-01, 1.782643294102043E-01, 2.248088421841022E-02, \ 5.731297492992956E-01, -7.245305917039069E-01, 1.666027168900788E-02, \ 5.800597214330994E-01, 6.076368281751579E-01, 1.994641910743171E-02, \ 5.827340699533451E-01, 7.799185004279106E-01, 1.506550662060840E-02, \ 5.902315633378371E-01, -7.656704700409119E-03, 1.553617180174587E-02, \ 5.906682339894699E-01, -8.667890507859654E-01, 1.214231245428204E-02, \ 6.099509227115107E-01, -9.609069768683841E-01, 6.626684869311525E-03, \ 6.135737153470906E-01, 8.913530795649121E-01, 9.807279239964804E-03, \ 6.246231931149462E-01, -2.373991342623364E-01, 1.859631127917601E-02, \ 6.251430706398415E-01, 9.977234181855117E-01, 1.373432556349576E-03, \ 6.269567681651597E-01, -4.853810354287711E-01, 1.557881532766953E-02, \ 6.299677977917032E-01, -9.975283667931077E-01, 1.307683705358367E-03, \ 6.490686401640144E-01, 9.624589736537986E-01, 6.433329913117225E-03, \ 6.681575030734345E-01, -6.391753535023200E-01, 1.675821395824656E-02, \ 6.693168433164310E-01, 2.985847484238517E-01, 2.053896928599153E-02, \ 6.767037258823436E-01, 5.089593879681761E-01, 1.929956845223450E-02, \ 6.767414083720775E-01, -1.216983833611472E-01, 1.702881131982138E-02, \ 6.778885853526038E-01, -7.985598896411525E-01, 1.305296371184325E-02, \ 6.785344806438597E-01, 7.028760007459759E-01, 1.603405486470507E-02, \ 6.791491171576957E-01, 9.973182946735697E-02, 1.835334682967442E-02, \ 6.889056647928331E-01, -4.105476960488628E-01, 1.322143695866550E-02, \ 6.972792709156885E-01, -9.171883050550365E-01, 8.783301477841914E-03, \ 7.013275658365165E-01, 8.389991135422733E-01, 1.116556601175833E-02, \ 7.173231621338175E-01, -9.835540032598186E-01, 3.576914417052623E-03, \ 7.396577473534641E-01, -3.065734892201429E-01, 1.696772838146242E-02, \ 7.411794309655517E-01, 9.883378955524539E-01, 3.149005459627492E-03, \ 7.441981398623979E-01, 9.248122192057350E-01, 7.952214175998626E-03, \ 7.477268693062509E-01, 1.178617906350497E-03, 1.534766967987536E-02, \ 7.546147648023375E-01, -5.450635784714123E-01, 1.627134395977775E-02, \ 7.598303762668254E-01, -7.223972889507986E-01, 1.294995516437059E-02, \ 7.604924395747599E-01, 4.040521641808663E-01, 1.640483106687547E-02, \ 7.634767876646369E-01, 6.119083101507623E-01, 1.551125361015980E-02, \ 7.673513409414942E-01, 2.186521333866828E-01, 1.604398689184609E-02, \ 7.735975996435843E-01, -8.594993334079274E-01, 9.569255855638928E-03, \ 7.808186099816705E-01, 7.721253866618816E-01, 1.174558344919606E-02, \ 7.839313303459738E-01, -1.577452094536468E-01, 1.531782499550762E-02, \ 7.918069891410763E-01, -9.552496571182889E-01, 5.247432489034864E-03, \ 7.969896207737629E-01, -9.976480667995195E-01, 9.937781058818520E-04, \ 8.188844823185363E-01, -4.261617662513782E-01, 1.558630923706844E-02, \ 8.220591736941830E-01, 1.243862989299787E-01, 1.244606872559087E-02, \ 8.233464165343024E-01, 8.728783340437961E-01, 8.558990866905701E-03, \ 8.240227041551308E-01, 9.642226450420159E-01, 4.656297575580126E-03, \ 8.314738798895785E-01, 5.062045685366845E-01, 1.274593131055984E-02, \ 8.323965789758532E-01, -6.377990761410410E-01, 1.217271062025909E-02, \ 8.370863536953854E-01, 9.980212613540562E-01, 8.867352167594041E-04, \ 8.408627217827968E-01, -7.927942230163550E-01, 9.201701596927991E-03, \ 8.459950759889058E-01, 3.370889407226870E-01, 1.214993895881173E-02, \ 8.464217718205864E-01, -2.909630308393418E-02, 1.381846696789304E-02, \ 8.474472786288211E-01, 6.901503323404313E-01, 1.100649739704037E-02, \ 8.492900289400127E-01, -2.609008872385714E-01, 1.361563690700432E-02, \ 8.506693908403453E-01, -9.125903996034499E-01, 5.849578632842550E-03, \ 8.629850430376032E-01, -9.846794003258130E-01, 2.528739364876000E-03, \ 8.834346561856141E-01, 2.466770217389220E-01, 9.493619529933141E-03, \ 8.854742809240306E-01, 8.063045923419880E-01, 8.148233321624298E-03, \ 8.856328610403172E-01, -5.303622802964915E-01, 1.168547747268816E-02, \ 8.897286914429898E-01, 9.254565139699565E-01, 5.359918872844426E-03, \ 8.906894622641233E-01, 5.845154566197192E-01, 8.308665412941993E-03, \ 8.964517879623641E-01, -7.184571948644249E-01, 8.121078281162448E-03, \ 8.998267130073949E-01, -8.611867551994773E-01, 5.652454680674074E-03, \ 9.003272138921747E-01, 9.855131239038005E-01, 2.142261107197177E-03, \ 9.041052183788196E-01, -1.370275081676114E-01, 1.231280001099448E-02, \ 9.044718083850251E-01, 9.248380504679798E-02, 1.138730334189965E-02, \ 9.077061721157841E-01, -3.609878414025458E-01, 1.119544980789453E-02, \ 9.090014113055961E-01, 4.456272486278706E-01, 9.085459391365453E-03, \ 9.102216394091136E-01, -9.552115242137005E-01, 3.429119254261080E-03, \ 9.248470794804491E-01, -9.972632014604238E-01, 7.216535092722727E-04, \ 9.253974646921507E-01, 7.190198240417008E-01, 6.336440252338264E-03, \ 9.356961338262859E-01, 3.645584063625137E-01, 6.010631113438040E-03, \ 9.370137281757169E-01, -6.282649414142087E-01, 7.623356356150477E-03, \ 9.378086513718291E-01, 8.695603466712696E-01, 5.169665843353311E-03, \ 9.391238991374505E-01, -7.989714235337833E-01, 5.179018142204592E-03, \ 9.419837071661598E-01, 6.127904283944557E-01, 5.775655266427641E-03, \ 9.462416352500443E-01, 9.599078291538412E-01, 2.602348449588172E-03, \ 9.464214946937899E-01, 2.174055880473181E-01, 8.183789662861353E-03, \ 9.483846862528557E-01, -9.121585564057219E-01, 3.515812117215462E-03, \ 9.502795953661248E-01, -1.665956085226044E-02, 9.244882696179383E-03, \ 9.509238027788980E-01, -4.671808125048466E-01, 7.778845637088972E-03, \ 9.512217505973695E-01, 9.975809114133117E-01, 5.139248565810932E-04, \ 9.527470555424390E-01, -2.452206198184587E-01, 8.934499397490152E-03, \ 9.592551721099858E-01, -9.800077457957908E-01, 1.583793112109460E-03, \ 9.635773411406924E-01, 7.811935286068071E-01, 4.341305455620128E-03, \ 9.664706318878840E-01, 5.062808601831001E-01, 6.514641073677681E-03, \ 9.712009645368384E-01, -7.236074445113848E-01, 4.632318546295927E-03, \ 9.750871880034563E-01, 9.181022714139108E-01, 2.418384903446744E-03, \ 9.753612107572261E-01, -8.542575822594997E-01, 2.939880020404475E-03, \ 9.771712814502167E-01, 3.337491350874086E-01, 5.138702967736385E-03, \ 9.796202659342652E-01, 1.139693876952825E-01, 5.831373899382246E-03, \ 9.799852473516794E-01, -5.711769167233038E-01, 4.435133168562443E-03, \ 9.802648322311707E-01, 6.750032224988851E-01, 3.955250863364047E-03, \ 9.810868050137430E-01, 9.856276869865556E-01, 8.700281868935982E-04, \ 9.826246063168834E-01, -3.638393037687699E-01, 5.148686860161606E-03, \ 9.833305319309631E-01, -1.263457021753157E-01, 5.419689142545006E-03, \ 9.834657898675960E-01, -9.464917816489062E-01, 1.606043238725865E-03, \ 9.871570448287768E-01, -9.953040717606414E-01, 4.014919822858868E-04, \ 9.879109700683048E-01, 8.401442342078335E-01, 2.254477068544381E-03, \ 9.942971011761540E-01, -7.923589246102194E-01, 1.676928772166950E-03, \ 9.943103084508153E-01, 9.589447862560037E-01, 7.154329251248137E-04, \ 9.944839549832385E-01, 4.305503528241359E-01, 2.332655357182134E-03, \ 9.944882643568679E-01, 5.822713014974841E-01, 2.130704201950450E-03, \ 9.955607724070924E-01, -6.629654417179892E-01, 1.734396121578630E-03, \ 9.959759411587524E-01, -8.966138075526434E-01, 9.460145783264427E-04, \ 9.961579504388610E-01, 2.339319461038794E-01, 2.197631276825098E-03, \ 9.970034303329453E-01, -4.805125358625656E-01, 1.717119689979895E-03, \ 9.970359077153589E-01, 4.973042782590862E-03, 1.976200444087838E-03, \ 9.975896723770977E-01, 7.481282641542352E-01, 1.186765908765057E-03, \ 9.976075303722897E-01, -2.495954379536609E-01, 1.726273349986223E-03, \ 9.985157152594889E-01, 9.971971012987678E-01, 9.821637011466654E-05, \ 9.985808631696838E-01, 8.990756328646153E-01, 5.055415778287732E-04, \ 9.987809239831112E-01, -9.748368623655366E-01, 2.993356033786765E-04 ] ) return xyw def smr46 ( ): #*****************************************************************************80 # ## smr46 returns the SMR rule of degree 46. # # Discussion: # # DEGREE: 46 # POINTS CARDINALITY: 387 # NORM INF MOMS. RESIDUAL: 2.03396e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*387), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.983111423300403E-01, 5.288463379177194E-01, 1.077877162071936E-03, \ -9.980165536240384E-01, 9.771577113964515E-01, 3.358785950069629E-04, \ -9.980057366593107E-01, 8.627358726346877E-01, 6.003479857328445E-04, \ -9.979683379344829E-01, -6.942209080688336E-01, 1.101994373218053E-03, \ -9.978846063972665E-01, 7.248634355141237E-01, 9.622706165518573E-04, \ -9.976343783636701E-01, -4.901932224780105E-01, 1.459301786243793E-03, \ -9.975456640840761E-01, 3.145719096243388E-01, 1.435508298339834E-03, \ -9.974305941584383E-01, -8.537788458635189E-01, 8.063821753970214E-04, \ -9.963467450618418E-01, -9.821437303584432E-01, 4.013000811661125E-04, \ -9.963009121112316E-01, -2.704146437985034E-01, 2.094359395819190E-03, \ -9.962806106099757E-01, 1.123075934443736E-01, 1.888774287809683E-03, \ -9.940902248165704E-01, -9.316901409499205E-01, 8.495707747103506E-04, \ -9.938933215260991E-01, -7.079039559931181E-02, 2.912153811018539E-03, \ -9.917585881160206E-01, 9.225449661005339E-01, 1.208278868867505E-03, \ -9.877765791917548E-01, 6.288297749314813E-01, 3.125282998079219E-03, \ -9.868078584857646E-01, 8.017653629554962E-01, 2.384264480882027E-03, \ -9.864405958010823E-01, -7.802922340742308E-01, 2.766257703102030E-03, \ -9.861374381057205E-01, 4.302599938856595E-01, 3.896596604742260E-03, \ -9.860561184001005E-01, 9.959625949335185E-01, 3.768462609684377E-04, \ -9.851999106336341E-01, -5.993676873167308E-01, 3.897179923118708E-03, \ -9.823744385328851E-01, 2.224305198952116E-01, 4.389361116586368E-03, \ -9.823717033752213E-01, -3.922448187993621E-01, 4.866053077993799E-03, \ -9.816324879121784E-01, -9.972824585879037E-01, 3.539318490028104E-04, \ -9.808402316764249E-01, -8.969081857937120E-01, 1.430112081567521E-03, \ -9.755886861073786E-01, 9.593223831278707E-01, 1.537597902797862E-03, \ -9.743498206750085E-01, -1.814564543728963E-01, 6.160694758533645E-03, \ -9.723572538186456E-01, -9.608004605969592E-01, 1.775385419876353E-03, \ -9.722382292526556E-01, 4.575052264951963E-02, 6.359444615009903E-03, \ -9.674256064855085E-01, 8.719589137075090E-01, 3.343864470517355E-03, \ -9.655171991563514E-01, 7.180035091780340E-01, 4.785905400994727E-03, \ -9.624420464882796E-01, -8.488914199258957E-01, 3.342352186086261E-03, \ -9.624375637065791E-01, 5.378256410738799E-01, 6.214733942070574E-03, \ -9.609564853325729E-01, -6.987107790974231E-01, 5.634701956686364E-03, \ -9.582534487467066E-01, 3.329644217027720E-01, 6.778705946888507E-03, \ -9.553330912989174E-01, -5.085340714542828E-01, 7.366493334985202E-03, \ -9.513324008400423E-01, 9.856312840827730E-01, 1.330643418748665E-03, \ -9.462216299986661E-01, -3.074523531561095E-01, 8.518829293626153E-03, \ -9.423577772939717E-01, -9.868227254586934E-01, 1.516125769939738E-03, \ -9.393806145622896E-01, -6.393001117132881E-02, 9.254712550028325E-03, \ -9.380581290975274E-01, -9.143951836207059E-01, 3.592402661502303E-03, \ -9.370997481849076E-01, 9.247112445714407E-01, 3.596998195741029E-03, \ -9.370408950027029E-01, 1.701035315993199E-01, 9.761731824542692E-03, \ -9.331125695054737E-01, 7.991178696492102E-01, 6.010555876145078E-03, \ -9.264553050234512E-01, 6.367471939422996E-01, 8.013247394678898E-03, \ -9.257833020863018E-01, -7.851138118520632E-01, 6.465654027360096E-03, \ -9.232295614388404E-01, 4.373930707289740E-01, 8.924951728810733E-03, \ -9.169304968245420E-01, -6.173156236169133E-01, 9.176842979353183E-03, \ -9.158461010077630E-01, 9.983551814323244E-01, 5.272476313713648E-04, \ -9.051276758776533E-01, -4.239566904643302E-01, 1.072046479438868E-02, \ -9.032419077912952E-01, -9.530184538306384E-01, 3.182051544793368E-03, \ -9.021102524547485E-01, -1.916184311444890E-01, 1.130998717609783E-02, \ -8.980961459025067E-01, 9.646542499645536E-01, 3.178751154593399E-03, \ -8.930078393151207E-01, -9.981508615033944E-01, 6.570920554362360E-04, \ -8.906744958940082E-01, 5.331652102117236E-02, 1.270902532675199E-02, \ -8.905389004793887E-01, 8.675870875563284E-01, 6.336364651974894E-03, \ -8.886387309148650E-01, 2.919115286844978E-01, 1.269563275681320E-02, \ -8.854149145655548E-01, -8.605083285679000E-01, 6.622620311336960E-03, \ -8.793037622856232E-01, 7.261357982998039E-01, 9.242333645649367E-03, \ -8.771808942835173E-01, 5.369791516940807E-01, 1.078396362232102E-02, \ -8.678439739737586E-01, -7.154028908195939E-01, 1.017271142495267E-02, \ -8.547339766301599E-01, -9.781932956431606E-01, 2.678930288181945E-03, \ -8.537315103377962E-01, -5.343331860669793E-01, 1.242332352924924E-02, \ -8.520164840234268E-01, -3.094551247900096E-01, 1.305829147586281E-02, \ -8.488681825198992E-01, 9.896255593087030E-01, 2.002616403722711E-03, \ -8.416507788252385E-01, -8.265115783740917E-02, 1.490207091803921E-02, \ -8.392425787263469E-01, 9.232660535378425E-01, 5.881955508762292E-03, \ -8.354077924594627E-01, -9.142725948542541E-01, 5.674810428887848E-03, \ -8.308359345629498E-01, 1.725487547473738E-01, 1.533431714809703E-02, \ -8.274841967106447E-01, 4.088159141245927E-01, 1.501736541467763E-02, \ -8.238115079964703E-01, 8.060487501731384E-01, 9.429758324133860E-03, \ -8.197373702496686E-01, 6.306005588539771E-01, 1.221854856004642E-02, \ -8.119207537103786E-01, -8.024258568330985E-01, 1.017584060240601E-02, \ -7.934808337088018E-01, -6.360553805785052E-01, 1.319241564428063E-02, \ -7.914436664499496E-01, -4.207932036862586E-01, 1.447292693321381E-02, \ -7.887191070259210E-01, -9.936283345929116E-01, 1.752216334037365E-03, \ -7.817594477527704E-01, 9.649444494603818E-01, 4.403270919820491E-03, \ -7.806968676724935E-01, -2.127005818706033E-01, 1.590915338247300E-02, \ -7.787206463899139E-01, -9.502131272522223E-01, 4.429611018981373E-03, \ -7.729716977649312E-01, 3.504231727683854E-02, 1.730216063737120E-02, \ -7.615475168534998E-01, 9.970713335225059E-01, 1.105751104522964E-03, \ -7.613774270772271E-01, 8.732384669131723E-01, 8.765009909401999E-03, \ -7.605658209205032E-01, 2.873715524000673E-01, 1.724853309888603E-02, \ -7.545102898776130E-01, 5.185064654385597E-01, 1.653260406179394E-02, \ -7.543179046928901E-01, 7.203533180047458E-01, 1.279648077347124E-02, \ -7.462096105686143E-01, -8.716832704900178E-01, 8.965204163025747E-03, \ -7.297551839636630E-01, -7.294705145359583E-01, 1.257733002011545E-02, \ -7.242201288685997E-01, -5.260417553686566E-01, 1.491064590305035E-02, \ -7.111976203431433E-01, -3.418767681380177E-01, 1.372933284312857E-02, \ -7.108504678954995E-01, -1.039300655680135E-01, 1.688080640592963E-02, \ -7.080091377554032E-01, -9.738542524510675E-01, 3.832949073991781E-03, \ -6.993005032215379E-01, 9.292838315386169E-01, 6.854783787218264E-03, \ -6.945010624970885E-01, 1.490753875762792E-01, 1.908181406615000E-02, \ -6.829539157895229E-01, 3.943661912129811E-01, 1.775227360298309E-02, \ -6.824522164896524E-01, 9.828020464230726E-01, 3.461480537140765E-03, \ -6.811161448382028E-01, 8.009485101920445E-01, 1.247548617968576E-02, \ -6.740874841537527E-01, -9.203828537769473E-01, 6.499214840639783E-03, \ -6.740590762912708E-01, 6.234582056824679E-01, 1.710880207528098E-02, \ -6.667283792866656E-01, -9.966870351134982E-01, 1.345631389649490E-03, \ -6.627500062251878E-01, -2.629897031536784E-01, 1.253500094538003E-02, \ -6.622225214428993E-01, -8.059108267523946E-01, 1.065281011757487E-02, \ -6.557914154525895E-01, -6.273988439708652E-01, 1.444872151803694E-02, \ -6.348709267896325E-01, -4.673203468046226E-01, 1.172736214570953E-02, \ -6.328413233255047E-01, -6.452211008886946E-04, 1.869025751288091E-02, \ -6.118719359252214E-01, 8.762829386426818E-01, 1.033274390128391E-02, \ -6.110556896889493E-01, 2.560001034291458E-01, 1.917352404679710E-02, \ -6.092675868512063E-01, 9.974932063614328E-01, 1.111770360271985E-03, \ -6.089001735150132E-01, 4.894606407282653E-01, 1.493304221615996E-02, \ -5.957728962033498E-01, -9.442775669731837E-01, 5.152774389043164E-03, \ -5.934378260544972E-01, -8.618789798012082E-01, 8.671109578031069E-03, \ -5.919685431225901E-01, 9.532093633373470E-01, 6.000008339596521E-03, \ -5.919111534153291E-01, -3.881929105751961E-01, 1.404997546066828E-02, \ -5.877361965725245E-01, -1.659039454745879E-01, 1.965458127599791E-02, \ -5.877226304090875E-01, 7.189942447153720E-01, 1.660443704063239E-02, \ -5.853917259329147E-01, -7.157079059870500E-01, 1.335893581504478E-02, \ -5.787373200325358E-01, -9.819349338509461E-01, 3.724690335082629E-03, \ -5.515089331602092E-01, -5.600319273292009E-01, 1.459416036801704E-02, \ -5.469704321502723E-01, 5.581230180424370E-01, 1.320231485769863E-02, \ -5.448756607377084E-01, 1.052883744135819E-01, 2.111827618977989E-02, \ -5.340427010083240E-01, 3.528051735252741E-01, 1.689752990450137E-02, \ -5.315744106126522E-01, 9.832382229796701E-01, 2.995609026491748E-03, \ -5.148064070837848E-01, 8.147217984009684E-01, 1.345617174772626E-02, \ -5.087680119024051E-01, -2.788763652823787E-01, 1.994337766154448E-02, \ -5.061581233455268E-01, -7.892496183565814E-01, 1.286508149092348E-02, \ -5.012203894259853E-01, -8.990231192240392E-01, 8.956058330470088E-03, \ -4.936349963135775E-01, -9.968369463719365E-01, 1.575947703548631E-03, \ -4.911326875959225E-01, 9.149214659234989E-01, 9.293367007494500E-03, \ -4.879661301700524E-01, -4.800056817263576E-02, 2.227718283981051E-02, \ -4.847914361880020E-01, -4.546071876863588E-01, 1.526526777579720E-02, \ -4.846822250085249E-01, -6.418342427755345E-01, 1.219156161879653E-02, \ -4.760256114114479E-01, 6.375375872806944E-01, 1.720769987743707E-02, \ -4.621007151616755E-01, -9.579502546478819E-01, 6.554088731066456E-03, \ -4.612967110110002E-01, 9.966660407011948E-01, 1.217481758961742E-03, \ -4.569206283268340E-01, 4.345123071178997E-01, 1.839698391377606E-02, \ -4.496803127775477E-01, 2.202902900476915E-01, 2.241266821911760E-02, \ -4.278915134934840E-01, 9.671114926361384E-01, 5.191064069034339E-03, \ -4.146363040355858E-01, 7.473511052485697E-01, 1.508362820205234E-02, \ -4.076400871388755E-01, -7.062801223113114E-01, 1.443945184922928E-02, \ -4.070553182360229E-01, -1.526895844070415E-01, 2.047617240956142E-02, \ -4.022172104649683E-01, -3.511189153921571E-01, 1.888641854799721E-02, \ -4.005903401571346E-01, -8.436497390055564E-01, 1.164332051477943E-02, \ -3.942704527579263E-01, -5.429006006269239E-01, 1.763233210715006E-02, \ -3.920322092784385E-01, 8.675390012920151E-01, 1.041096047388326E-02, \ -3.846660086832624E-01, 8.917470150450708E-02, 1.892693797908766E-02, \ -3.729863115263242E-01, -9.859184869614498E-01, 4.095961239144511E-03, \ -3.716740791814342E-01, 5.310297213894640E-01, 2.083126621383546E-02, \ -3.486558657245032E-01, -9.194138838445431E-01, 9.698505131349492E-03, \ -3.433349546665356E-01, 3.230449465905588E-01, 2.374293118970489E-02, \ -3.344389712170940E-01, 9.921091261971137E-01, 2.869305970347512E-03, \ -3.339313518662538E-01, 9.384366607395505E-01, 7.681016742585266E-03, \ -3.325417016336327E-01, 1.286602408259136E-02, 1.557157921087293E-02, \ -3.282638864870970E-01, -7.785798295099498E-01, 9.483406458745599E-03, \ -3.219994475413112E-01, 6.704477854046392E-01, 1.550078134528658E-02, \ -3.159420291185248E-01, 8.270797065832005E-01, 8.524811430984630E-03, \ -3.092399396317421E-01, -2.277117057375501E-01, 2.112662086798820E-02, \ -2.968279429238752E-01, -4.396378070292698E-01, 2.129314196872056E-02, \ -2.905204845049371E-01, -6.277035890195538E-01, 1.949076619182426E-02, \ -2.660737641019463E-01, 4.255724500180151E-01, 1.406940792473095E-02, \ -2.657259347700068E-01, -9.983145161338485E-01, 1.297107633585316E-03, \ -2.557040513029764E-01, -9.607724968354249E-01, 7.076847711496876E-03, \ -2.507469864960903E-01, 1.885266112795361E-01, 2.719835405580567E-02, \ -2.465621618464433E-01, -6.302324636139266E-02, 2.220715080388317E-02, \ -2.422173156650345E-01, 7.716949471630073E-01, 1.461225419981911E-02, \ -2.397259575954650E-01, -7.537162650009356E-01, 1.272707785511618E-02, \ -2.382433304389768E-01, -8.636962693408693E-01, 1.314939728605020E-02, \ -2.348523931292380E-01, 5.954466740476743E-01, 1.696950549956305E-02, \ -2.302678163192251E-01, 8.980662833826019E-01, 1.075143067263782E-02, \ -2.280326790666749E-01, 9.731664665061597E-01, 5.788926660667668E-03, \ -2.067449089627632E-01, -3.142157476434185E-01, 2.065950705760577E-02, \ -1.998822841751484E-01, 4.556559275603105E-01, 1.452445159282058E-02, \ -1.780348710790272E-01, -5.294356781067937E-01, 2.293930129672077E-02, \ -1.729154221323040E-01, 8.947634588886424E-02, 9.633358448521607E-03, \ -1.679785686773150E-01, 9.977004810664578E-01, 1.580660537042458E-03, \ -1.513615578790225E-01, -1.408023440657114E-01, 1.999321020575889E-02, \ -1.510049533511834E-01, -9.857568554875824E-01, 4.171489211283228E-03, \ -1.397908366129535E-01, -6.831910361461173E-01, 1.843457361864874E-02, \ -1.388453696223859E-01, -9.202453076597740E-01, 1.063712403558069E-02, \ -1.364042879497747E-01, 3.148557325219815E-01, 2.642864804518861E-02, \ -1.357676378587967E-01, -3.700839091893132E-01, 1.007003471287555E-02, \ -1.341336818342906E-01, 6.962786900689967E-01, 1.930661907444524E-02, \ -1.268063328385695E-01, 8.405755822951979E-01, 1.421554079635553E-02, \ -1.159584802313210E-01, 6.193763651449499E-02, 2.189180449837289E-02, \ -1.136601056222965E-01, 9.411644534061605E-01, 8.852548392145691E-03, \ -1.021809090852591E-01, -8.116890139416293E-01, 1.638446296121459E-02, \ -9.957974534510225E-02, 5.465537117483713E-01, 1.936985897602384E-02, \ -6.013303858641021E-02, -2.228487583791975E-01, 2.265701874040998E-02, \ -5.169586652442786E-02, 9.835122859254263E-01, 4.824215443618791E-03, \ -5.139510564692561E-02, -4.291434980038135E-01, 2.272752478914381E-02, \ -3.882804828978392E-02, -9.973934768928572E-01, 1.457851894270487E-03, \ -3.342710705704959E-02, 2.161596108865151E-01, 2.137936125066629E-02, \ -3.218752249323631E-02, -9.607936917182006E-01, 7.314373566869228E-03, \ -3.017152289296703E-02, -5.994190919388979E-01, 2.040979936959506E-02, \ -1.867008238226461E-02, 4.362811533647392E-01, 2.208258553134326E-02, \ -1.343806034595350E-02, 7.734825117081163E-01, 1.719967834300143E-02, \ -1.185114610879654E-02, -3.481367504384966E-02, 2.423341772064624E-02, \ -7.919342463364545E-04, 8.945837010426477E-01, 1.232847827313112E-02, \ 4.919452919873997E-03, -8.809812407295396E-01, 1.354090072320326E-02, \ 1.305827593618624E-02, 6.297679760756248E-01, 2.008240810469282E-02, \ 1.779271432032194E-02, -7.377081209970429E-01, 1.876486052772664E-02, \ 4.884160865441580E-02, 1.507066653383158E-01, 1.871250815547388E-02, \ 5.990126302514630E-02, 9.969795355703539E-01, 1.692710307507148E-03, \ 6.006717209602051E-02, -3.083136689294216E-01, 2.565724966279625E-02, \ 6.393909219067830E-02, 3.594993165616777E-01, 1.509548787122363E-02, \ 7.175408292024850E-02, 9.554637730216967E-01, 8.306658405607603E-03, \ 7.525461672292501E-02, -5.160683941502094E-01, 1.874790249909374E-02, \ 8.110183649610606E-02, -9.867585187826022E-01, 4.076210204008766E-03, \ 8.141967150319139E-02, -1.189705745248058E-01, 2.032608743176999E-02, \ 1.124880105553899E-01, -9.359171673996224E-01, 9.571932927888115E-03, \ 1.165489339636398E-01, 8.367961024670041E-01, 1.506162267493892E-02, \ 1.210277013276357E-01, 7.092707728848469E-01, 1.701632734469468E-02, \ 1.226974308970525E-01, 5.269692986000968E-01, 2.428603200993640E-02, \ 1.229083911931521E-01, -8.182540440119128E-01, 1.570235696766660E-02, \ 1.350112470613993E-01, -6.538504393209962E-01, 2.030628583177083E-02, \ 1.399181256835766E-01, 3.015348908887893E-01, 2.019291503816718E-02, \ 1.404257985465581E-01, 6.092746217029241E-02, 2.461307617903064E-02, \ 1.537383644071319E-01, -4.285399646581668E-01, 1.729562302093782E-02, \ 1.793831484355051E-01, 9.848486617613754E-01, 4.373304719358010E-03, \ 1.885276528802143E-01, -1.946570197424425E-01, 2.437822908681812E-02, \ 1.913490446236383E-01, 9.136669626572853E-01, 1.136057870401207E-02, \ 1.950733760684369E-01, -9.988883757089664E-01, 1.115917379491008E-03, \ 2.202349038604578E-01, -8.872502852695510E-01, 1.183870475738118E-02, \ 2.266103135304583E-01, -9.724019023500025E-01, 6.089563321336039E-03, \ 2.334514056216084E-01, 2.100250708586558E-01, 2.242983008197881E-02, \ 2.346890297758962E-01, -7.430696053291979E-01, 1.611144382586636E-02, \ 2.371854897054120E-01, 6.277158377811654E-01, 1.998985840392359E-02, \ 2.381551058710785E-01, -2.728024275968237E-02, 1.867617065182177E-02, \ 2.403845626744464E-01, -5.494371080987960E-01, 1.919163292548581E-02, \ 2.406566753219083E-01, 7.709850451400717E-01, 1.548587357826445E-02, \ 2.437892485634663E-01, 4.312692590040306E-01, 2.500208999773301E-02, \ 2.457113471217321E-01, -3.504488987179999E-01, 2.076259214573411E-02, \ 2.787975217317672E-01, 9.987709148054594E-01, 1.074439970173681E-03, \ 2.874526689515157E-01, 9.610687558161728E-01, 6.639643775994492E-03, \ 3.050701074537157E-01, 8.576858834243071E-01, 1.330354503175670E-02, \ 3.079020816595327E-01, -6.341747220801298E-01, 1.232930413128336E-02, \ 3.129207107515677E-01, -8.153811415487545E-01, 1.088352641587536E-02, \ 3.235238534770942E-01, -9.348385551501034E-01, 8.405733683243891E-03, \ 3.249461420324165E-01, 1.195055866712430E-01, 2.059445277234703E-02, \ 3.259332646765282E-01, -8.115322717293480E-02, 1.921450979679603E-02, \ 3.418019449964280E-01, -9.921627760081128E-01, 2.876179862337243E-03, \ 3.441463742468578E-01, -2.507586930846943E-01, 2.246920139880491E-02, \ 3.454157311797964E-01, 3.196442608280841E-01, 1.949168155726703E-02, \ 3.522858087462989E-01, 5.473292954828115E-01, 2.052211824025522E-02, \ 3.550612724894830E-01, -4.622644021251900E-01, 2.237322821452582E-02, \ 3.628206389441777E-01, 6.996588792810672E-01, 1.611470867455308E-02, \ 3.803124073211717E-01, 9.267629522530908E-01, 7.864925821108384E-03, \ 3.837527955162833E-01, -7.107409299987680E-01, 1.416444264486913E-02, \ 3.851917500153872E-01, 9.887591655242265E-01, 3.339189896709617E-03, \ 3.854269547410605E-01, -8.618469546717433E-01, 9.610742279852392E-03, \ 4.019225793782901E-01, 4.016798585964549E-01, 1.012917154681300E-02, \ 4.127391066428609E-01, 7.903342236233291E-01, 1.269130304446248E-02, \ 4.206237377241268E-01, -9.659761107125491E-01, 5.178093920336236E-03, \ 4.299310943181327E-01, -5.994572508065145E-01, 1.557080469778748E-02, \ 4.307413834300436E-01, 4.658662181207777E-02, 2.219196980426284E-02, \ 4.405340685608884E-01, 2.335295068344127E-01, 1.865946407826078E-02, \ 4.489137849532947E-01, -1.476957002369098E-01, 2.137580876989588E-02, \ 4.553257248925679E-01, -3.592620025020420E-01, 2.194266456909868E-02, \ 4.596003509315073E-01, 8.854184724628273E-01, 8.841941691903296E-03, \ 4.709725837444826E-01, 4.828558460588853E-01, 1.704907169399865E-02, \ 4.739134209792026E-01, -9.952544731037134E-01, 1.384022073294283E-03, \ 4.744311818429655E-01, -9.091663251538931E-01, 9.407209766944927E-03, \ 4.754339111432121E-01, 9.677012363182328E-01, 5.151968481850169E-03, \ 4.756400085409440E-01, -7.846592391745022E-01, 1.479999552925989E-02, \ 4.797722514467903E-01, 6.266312294749810E-01, 1.517363837511235E-02, \ 5.100902189441707E-01, -5.204709881652611E-01, 1.794265819609321E-02, \ 5.114213495330481E-01, 7.063838369295402E-01, 9.385769008220548E-03, \ 5.154702873160621E-01, 9.970261558990023E-01, 1.418938295959134E-03, \ 5.206787479692746E-01, -9.804693890194831E-01, 2.602127396219503E-03, \ 5.248386664133297E-01, 8.240594713994390E-01, 1.015762604252224E-02, \ 5.292261493359739E-01, 3.532128983853009E-01, 1.761372213704019E-02, \ 5.412455238586017E-01, 1.663089169562654E-01, 1.981488239826455E-02, \ 5.422636874412113E-01, -3.888952643040450E-02, 2.029645493692368E-02, \ 5.490686000308411E-01, -6.800871557244708E-01, 1.778082318788007E-02, \ 5.506497016063064E-01, -2.569823972423157E-01, 2.040618638507255E-02, \ 5.558484982602493E-01, 9.370085805481705E-01, 6.860313942207178E-03, \ 5.730289132425076E-01, -8.539043933599846E-01, 1.199840964520873E-02, \ 5.743172499325917E-01, -9.493748534639627E-01, 6.446458905888820E-03, \ 5.933561550270604E-01, -9.973165046518369E-01, 1.106220941881708E-03, \ 5.958409370787153E-01, 5.800079660836041E-01, 1.671078508710501E-02, \ 5.988069851863091E-01, 7.502260051414449E-01, 1.282898642169325E-02, \ 5.990481942679082E-01, -4.246825001870817E-01, 1.984169743778542E-02, \ 6.005986331257841E-01, 4.554769692975677E-01, 1.334287115720346E-02, \ 6.040160922907698E-01, 9.854671530856786E-01, 2.994287695803976E-03, \ 6.148479609092942E-01, 8.841220860695742E-01, 9.043118053822746E-03, \ 6.290329677665637E-01, 6.473056660736756E-02, 1.770611661233833E-02, \ 6.357508149775565E-01, 2.792335526293019E-01, 1.792883669549749E-02, \ 6.359115381229695E-01, -1.533221513721983E-01, 1.866471728653944E-02, \ 6.428347625670869E-01, -5.860865379095112E-01, 1.800068148760219E-02, \ 6.431770915314418E-01, -7.673033465075149E-01, 1.415629485620442E-02, \ 6.629470916951145E-01, -9.814101628847763E-01, 3.828055463736441E-03, \ 6.635620751159940E-01, 9.669552929922944E-01, 3.573941812000668E-03, \ 6.662663601364237E-01, -9.116551120171078E-01, 8.464264999754742E-03, \ 6.826809651786937E-01, 6.740553403014049E-01, 1.482537895685379E-02, \ 6.841894614722424E-01, 9.991626816274169E-01, 6.403585593440745E-04, \ 6.879813211979059E-01, -3.164327346746020E-01, 1.950390211841089E-02, \ 6.895381114908021E-01, 8.244385950006391E-01, 1.107283514053267E-02, \ 6.951293081922316E-01, 3.848652923305114E-01, 1.205406495559543E-02, \ 7.071941862038644E-01, 1.557551547343111E-01, 1.487157194009795E-02, \ 7.088392130891149E-01, 9.311081105556229E-01, 6.403186257497955E-03, \ 7.103489145184514E-01, 5.128671353459157E-01, 1.447349152743848E-02, \ 7.112523777541994E-01, -5.343627919039270E-02, 1.622337417018616E-02, \ 7.269363794433283E-01, -6.840991876519299E-01, 1.435100659999861E-02, \ 7.279049704858229E-01, -8.426704238412119E-01, 1.045402040085113E-02, \ 7.285342993988090E-01, -4.839061792889138E-01, 1.728103414529436E-02, \ 7.452814605775970E-01, -9.968228546357361E-01, 1.246345264724730E-03, \ 7.453280291188794E-01, 9.911483462347401E-01, 1.772175614234971E-03, \ 7.500124480157498E-01, -9.547637231472251E-01, 5.631122806171691E-03, \ 7.660136246691086E-01, 2.540733190060072E-01, 1.368648950065803E-02, \ 7.691308291829931E-01, 7.612449038860015E-01, 1.157990272462695E-02, \ 7.695653758500861E-01, -2.017051775800784E-01, 1.788941594689514E-02, \ 7.757855546099112E-01, 6.120139510322031E-01, 1.234795524473133E-02, \ 7.783422194325996E-01, 8.857643892793224E-01, 8.021465975032427E-03, \ 7.794925507276567E-01, 3.834881273142750E-02, 1.394353531135586E-02, \ 7.881718171116056E-01, 3.986996175544144E-01, 1.286848339449679E-02, \ 7.897308006236938E-01, 9.695228604931504E-01, 3.758196130226270E-03, \ 8.005617072950878E-01, -7.714759314806717E-01, 1.082717845154526E-02, \ 8.014647958275422E-01, -5.914754924105888E-01, 1.372540088894792E-02, \ 8.048586654976113E-01, -3.760191806026097E-01, 1.578196274558745E-02, \ 8.074198214828329E-01, -9.002944432867208E-01, 7.509326689239254E-03, \ 8.229471194855432E-01, -9.844354012048210E-01, 2.780744450891915E-03, \ 8.350468397869657E-01, 5.190039957049550E-01, 1.164754105169609E-02, \ 8.365299137297749E-01, 1.412585586299757E-01, 1.308242784832346E-02, \ 8.413421178380436E-01, -8.484860532171155E-02, 1.504535328855272E-02, \ 8.458961337160322E-01, 6.994870213051259E-01, 1.009460273201535E-02, \ 8.469985537754668E-01, 8.338344678958003E-01, 8.168632261528704E-03, \ 8.488085430055092E-01, 9.947858132674051E-01, 1.443650552126127E-03, \ 8.500645149945468E-01, 9.373507720718434E-01, 5.137934922700379E-03, \ 8.546242903977276E-01, 3.051629507870270E-01, 1.089091512734386E-02, \ 8.641763900405030E-01, -6.889448486764105E-01, 1.039249251041895E-02, \ 8.659703474188424E-01, -4.920675442015341E-01, 1.232231682369118E-02, \ 8.693776571618932E-01, -9.487224468680494E-01, 4.354062518153025E-03, \ 8.694914780269520E-01, -2.629599405001600E-01, 1.349510193140824E-02, \ 8.700002668817390E-01, -8.383123670557577E-01, 7.781670768080279E-03, \ 8.855489975037527E-01, -9.979953692358957E-01, 7.195696835960152E-04, \ 8.915724133557099E-01, 4.333952149598865E-01, 9.718531146073172E-03, \ 8.968125829421709E-01, 6.154154698482395E-01, 9.130732879751960E-03, \ 8.995352955639010E-01, 3.727433236704860E-02, 1.210455078959554E-02, \ 9.044176738266044E-01, 9.759589325906001E-01, 2.784595965114452E-03, \ 9.047127613663705E-01, 2.206198562862635E-01, 8.552543877154380E-03, \ 9.068881151497454E-01, 7.787953338368784E-01, 7.037593396418797E-03, \ 9.083011281987010E-01, 8.960176782874899E-01, 5.423153331182166E-03, \ 9.173132897326095E-01, -5.972448898522749E-01, 9.084632723408663E-03, \ 9.175159859708392E-01, -9.030480944892180E-01, 4.616231117242107E-03, \ 9.181461241031550E-01, -3.851974576496667E-01, 1.023307955068548E-02, \ 9.208135196421833E-01, -1.434373337472792E-01, 1.050231657558337E-02, \ 9.217303926670013E-01, -7.644491631725594E-01, 7.188933837018584E-03, \ 9.227515342181415E-01, -9.791268272110957E-01, 2.161611001412200E-03, \ 9.390812942639490E-01, 3.458046057721214E-01, 8.001729417607994E-03, \ 9.391736486952373E-01, 5.304895199343252E-01, 7.122316398716251E-03, \ 9.430600573892549E-01, 9.966709231907848E-01, 7.129053481620616E-04, \ 9.454576615044328E-01, 7.052920398449620E-01, 6.071748103577099E-03, \ 9.496345360898582E-01, 1.521627208076305E-01, 7.676594864205592E-03, \ 9.524245393681409E-01, 9.458296922698042E-01, 3.034421018413787E-03, \ 9.549490689468429E-01, 8.452832051303726E-01, 4.625534494986953E-03, \ 9.549952747196216E-01, -8.482826904953155E-01, 3.945366388858040E-03, \ 9.561903566881326E-01, -2.674325744283451E-01, 7.592688481937286E-03, \ 9.574313570023540E-01, -4.955636512788343E-01, 7.063311775228204E-03, \ 9.589118653680453E-01, -9.459098456977220E-01, 2.498821388791289E-03, \ 9.592027558752809E-01, -2.347640435515468E-02, 7.496102409709891E-03, \ 9.609958781667891E-01, -6.801431473140105E-01, 5.715602788126438E-03, \ 9.627398206459263E-01, -9.951247808234173E-01, 6.592649205000905E-04, \ 9.728989108861091E-01, 4.499381661270909E-01, 5.032786439355391E-03, \ 9.740714589903327E-01, 6.233281153298854E-01, 4.526374604487227E-03, \ 9.768548600134053E-01, -7.949632055922030E-01, 2.082313300604911E-03, \ 9.782650771098491E-01, 2.726194163361467E-01, 5.185181641231907E-03, \ 9.786925055378212E-01, 9.827582996544191E-01, 1.141047824238659E-03, \ 9.822091362390636E-01, 7.746068528251591E-01, 3.392981026324791E-03, \ 9.828825653139780E-01, -3.788927753616619E-01, 4.587476394453676E-03, \ 9.831832567744532E-01, -1.495359315198227E-01, 4.796541548146330E-03, \ 9.845823512703257E-01, 9.041799806417141E-01, 2.254648011248501E-03, \ 9.848729561355289E-01, -9.008616462537060E-01, 2.041681903834455E-03, \ 9.858543382964763E-01, -9.755482569442001E-01, 9.339547720854347E-04, \ 9.862811960229013E-01, -5.856501611199811E-01, 3.641915309288278E-03, \ 9.864821493614616E-01, 8.874301057952583E-02, 4.193190248767370E-03, \ 9.891882478301796E-01, -7.505304865321339E-01, 1.890478947988027E-03, \ 9.940951241861832E-01, 5.432137582110499E-01, 2.245016939288178E-03, \ 9.953374929604664E-01, 3.836092124240039E-01, 2.043871336953785E-03, \ 9.960416279394205E-01, 9.972986154465028E-01, 1.461982700921600E-04, \ 9.961174988510967E-01, -9.950835645943196E-01, 1.717741433409342E-04, \ 9.961527671803110E-01, 6.918580060078352E-01, 1.525847569674391E-03, \ 9.966559754610508E-01, 9.557295127448442E-01, 6.302051569265952E-04, \ 9.970214929502554E-01, -2.644098315766063E-01, 1.749852740750748E-03, \ 9.973200872809646E-01, -3.826590124697109E-02, 1.645309636276182E-03, \ 9.973259273035801E-01, -8.408771000383591E-01, 8.974177017096658E-04, \ 9.974702963631498E-01, -4.748457085080076E-01, 1.419898311116791E-03, \ 9.979804912008889E-01, 2.058903880121162E-01, 1.332855555539681E-03, \ 9.980187128543290E-01, 8.423741210647242E-01, 8.934394663320126E-04, \ 9.983634077785508E-01, -9.445962296620326E-01, 4.424225813983324E-04, \ 9.983713812941385E-01, -6.766009567160710E-01, 9.089763434524134E-04 ] ) return xyw def smr47 ( ): #*****************************************************************************80 # ## smr47 returns the SMR rule of degree 47. # # Discussion: # # DEGREE: 47 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 396 # NORM INF MOMS. RESIDUAL: 1.56234e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*396), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.988860641396040E-01, -2.373189065242698E-01, 1.059226498023405E-03, \ -9.984308298705356E-01, 6.810115040142974E-01, 8.742573242503645E-04, \ -9.982849649115821E-01, 9.436218579698744E-01, 4.239310404841323E-04, \ -9.975891711682796E-01, -9.308337785182597E-01, 5.005025838481359E-04, \ -9.975758902464168E-01, -8.292104265892648E-01, 8.758182348185454E-04, \ -9.975527094081703E-01, -6.722468138431469E-01, 1.228393951475139E-03, \ -9.975229416008712E-01, 8.411146681674510E-01, 8.259054712338016E-04, \ -9.974354703237893E-01, -9.972347569712511E-01, 1.178428627156954E-04, \ -9.973323543291763E-01, 4.909591129622543E-01, 1.363609590112511E-03, \ -9.971337685886393E-01, 7.632359805747738E-02, 1.695014196901724E-03, \ -9.969508496154019E-01, 9.951320518801803E-01, 1.406624476607038E-04, \ -9.967221454497780E-01, 2.967880150220837E-01, 1.788242723078713E-03, \ -9.958488160214992E-01, -4.963853591618409E-01, 1.871218692254807E-03, \ -9.922776511892646E-01, -3.473204119330540E-01, 2.073619684302503E-03, \ -9.908388235274806E-01, -8.317660908501920E-02, 3.661061584693876E-03, \ -9.904720670548077E-01, -9.710213211789278E-01, 8.475646284885832E-04, \ -9.888702332586248E-01, 7.575946249394171E-01, 2.014228686820058E-03, \ -9.874342455637046E-01, 9.765233090751630E-01, 8.334380630773419E-04, \ -9.862543531528728E-01, 5.965690502576685E-01, 3.417223744136484E-03, \ -9.858704720189189E-01, 9.012846007723281E-01, 1.872665686706367E-03, \ -9.844078028285480E-01, -7.576106510429415E-01, 3.160151211848773E-03, \ -9.842497345754406E-01, -8.869330623714193E-01, 2.084899867143594E-03, \ -9.830502038887345E-01, 1.855914572695679E-01, 4.596336081266426E-03, \ -9.817085463008139E-01, 4.080671844783566E-01, 4.517002995396259E-03, \ -9.808958789729733E-01, -5.936214063681421E-01, 4.206620288925534E-03, \ -9.763487274404036E-01, 8.040608258571258E-01, 1.735576449905203E-03, \ -9.758618568064553E-01, -4.021500807907098E-01, 4.191420631437088E-03, \ -9.739747222412156E-01, -2.170070835355472E-01, 5.848357083847142E-03, \ -9.698875102419363E-01, -9.910520236356811E-01, 8.725558215646179E-04, \ -9.668937072725421E-01, 9.958238219074350E-01, 5.454007647675571E-04, \ -9.667753163257026E-01, 3.477910291429498E-02, 6.924394568068183E-03, \ -9.629858793094620E-01, -9.381408744361764E-01, 2.554368802597983E-03, \ -9.625096668136147E-01, 9.481536769647175E-01, 2.281103018635964E-03, \ -9.621099147673235E-01, 6.897553564879744E-01, 5.294641784299885E-03, \ -9.575259606392211E-01, 8.526222258903702E-01, 3.522351032086693E-03, \ -9.565093211986069E-01, -8.285414929426780E-01, 4.524164566301950E-03, \ -9.560668264177599E-01, 2.992407743127743E-01, 7.187486995447770E-03, \ -9.551892905468934E-01, 5.215279150021472E-01, 6.895698107002057E-03, \ -9.529413061166492E-01, -6.848663302380273E-01, 6.115869631822169E-03, \ -9.499379163273817E-01, -4.990544089847970E-01, 7.157918511939649E-03, \ -9.417225429447996E-01, -1.010399506491120E-01, 8.545115482104066E-03, \ -9.376385227666459E-01, -3.149592118756698E-01, 8.640152266819899E-03, \ -9.296009678982454E-01, 1.579161826917062E-01, 1.000831611323566E-02, \ -9.294596181015237E-01, 9.813684731390790E-01, 1.920664927315008E-03, \ -9.278797101416244E-01, -9.706959780392181E-01, 2.420070122891078E-03, \ -9.250982605210959E-01, 7.735956141038276E-01, 6.643173932293495E-03, \ -9.231065278766845E-01, 9.076886759912991E-01, 4.277169811976498E-03, \ -9.217831985976003E-01, -9.985289666041468E-01, 5.078696283821862E-04, \ -9.195935562112217E-01, -8.913327000110681E-01, 5.052649337869474E-03, \ -9.181270575285391E-01, 4.122328505086459E-01, 9.601387120539102E-03, \ -9.148831482219597E-01, 6.224206774261293E-01, 8.741538710357355E-03, \ -9.106078414366331E-01, -7.633798877459725E-01, 7.390023577666990E-03, \ -9.082567296294581E-01, -5.961320469495873E-01, 9.396878139328617E-03, \ -8.956547894973423E-01, -1.969077394197896E-01, 1.052048363646446E-02, \ -8.947837985257842E-01, 1.554349304099888E-02, 1.207505504176275E-02, \ -8.934682220664112E-01, -4.216540388538755E-01, 1.073747532386832E-02, \ -8.887805555572472E-01, 9.980469645264131E-01, 6.927987848988626E-04, \ -8.788480167168854E-01, 2.792330855544344E-01, 1.282453595081661E-02, \ -8.781614570655271E-01, 9.532957838212304E-01, 3.986319116448455E-03, \ -8.763285336755390E-01, 8.465920091250118E-01, 7.228076122988736E-03, \ -8.707970024861261E-01, -9.370668393694276E-01, 4.607127648721668E-03, \ -8.676827987392443E-01, 5.159125990270553E-01, 1.149515499866792E-02, \ -8.651527837557776E-01, -9.866988624485060E-01, 2.118506810134428E-03, \ -8.624098290914860E-01, 7.126189995166746E-01, 9.861047155006141E-03, \ -8.592237506008711E-01, -8.341324721077372E-01, 7.928559898856604E-03, \ -8.522596697975072E-01, -6.840670787785538E-01, 1.062952046635244E-02, \ -8.422263654558482E-01, -3.015292326049363E-01, 1.287800406757572E-02, \ -8.373962094750010E-01, -5.186387354716220E-01, 1.230119470881243E-02, \ -8.369983523769275E-01, 1.347222940319437E-01, 1.460708731761451E-02, \ -8.357310902097985E-01, -9.723800805043467E-02, 1.374148019748794E-02, \ -8.269374328956414E-01, 9.850869495918245E-01, 2.648428928686930E-03, \ -8.179672372442700E-01, 9.076223036675563E-01, 6.892206214578204E-03, \ -8.148639002101447E-01, 3.932890823416910E-01, 1.520502153610768E-02, \ -8.058634520423256E-01, 6.117159879145377E-01, 1.279254088338618E-02, \ -8.004833550779242E-01, 7.919528617574970E-01, 1.006437035257496E-02, \ -7.983956784496398E-01, -8.914942533713631E-01, 7.267362334258530E-03, \ -7.966190004094728E-01, -9.968334127996725E-01, 1.036781499468538E-03, \ -7.957314634069883E-01, -9.607527680221649E-01, 4.059074074883998E-03, \ -7.862399052534020E-01, -7.635989572508247E-01, 1.120659033007899E-02, \ -7.766600189797701E-01, -4.041663776132322E-01, 1.451699415444131E-02, \ -7.752582668662442E-01, 1.137400097769025E-02, 1.483822376274713E-02, \ -7.718688019814154E-01, -6.087164044214350E-01, 1.281755532683666E-02, \ -7.664905651113335E-01, -2.123608448367788E-01, 1.521536630069221E-02, \ -7.658473206792390E-01, 2.470075232375816E-01, 1.699291241018386E-02, \ -7.570188231121615E-01, 9.562983797766917E-01, 5.269367781364454E-03, \ -7.480114600555077E-01, 9.967592933390678E-01, 1.243409201000067E-03, \ -7.391128608011459E-01, 5.011842297262301E-01, 1.677675545049549E-02, \ -7.344946046482385E-01, 7.002770707813594E-01, 1.339498521201928E-02, \ -7.331498071508773E-01, 8.596337901924931E-01, 9.291892667177389E-03, \ -7.258177950289607E-01, -9.805030048690940E-01, 2.984765845250313E-03, \ -7.157802360889779E-01, -8.336762449322652E-01, 1.012482548177606E-02, \ -7.072078419693140E-01, -9.234919823555481E-01, 6.841723221210096E-03, \ -7.053541655207917E-01, 1.073889554567113E-01, 1.602910466636588E-02, \ -7.052090371098516E-01, -1.119584635184487E-01, 1.420955705467702E-02, \ -7.011205173485494E-01, -5.092216197809605E-01, 1.524066877662247E-02, \ -6.978846262070233E-01, -3.414874362228780E-01, 1.076367185856306E-02, \ -6.960765595225886E-01, -6.880190026120154E-01, 1.357698223373921E-02, \ -6.857267249496155E-01, 3.551782556666386E-01, 1.835639998551701E-02, \ -6.718996078310749E-01, 9.187863739753772E-01, 7.227260623084868E-03, \ -6.688694553842166E-01, -9.962634726340323E-01, 1.299102531809083E-03, \ -6.680438282278643E-01, 9.807419818799499E-01, 3.734416537582896E-03, \ -6.562162894928593E-01, 7.813381408111647E-01, 1.314356882014099E-02, \ -6.539068033827653E-01, 6.025223400436617E-01, 1.747705500021484E-02, \ -6.508182477278392E-01, -2.656608209143835E-01, 1.482527461108588E-02, \ -6.371638788293418E-01, -2.566889805750509E-02, 1.632793168239773E-02, \ -6.291434547685805E-01, 2.023189788534562E-01, 1.795321661628254E-02, \ -6.285276641730166E-01, -9.557558207146426E-01, 5.222692046521106E-03, \ -6.243785655726330E-01, -7.677131072866508E-01, 1.213021892933221E-02, \ -6.153035647870176E-01, -4.406604449329651E-01, 1.315774503238905E-02, \ -6.101810791749840E-01, -8.730802950223981E-01, 9.810988876956505E-03, \ -6.058276827683423E-01, 9.969104641392599E-01, 1.067957112281833E-03, \ -6.050277497663656E-01, -5.991789076131454E-01, 1.720383270245636E-02, \ -6.010977897838671E-01, 4.554853809841653E-01, 1.796395971673612E-02, \ -5.862984837774434E-01, 8.612555834742029E-01, 1.061579515310207E-02, \ -5.768270943940413E-01, 9.454129989500087E-01, 5.910967881352096E-03, \ -5.750197447578449E-01, -9.850659057962179E-01, 3.114356971775973E-03, \ -5.702248508469594E-01, -1.587490643869126E-01, 2.016275464017900E-02, \ -5.631550904449273E-01, 6.970949553808866E-01, 1.710763838261802E-02, \ -5.506357337723290E-01, 7.306393615078814E-02, 2.031057229536963E-02, \ -5.479124054422221E-01, 9.758854402340520E-01, 2.479427756255549E-03, \ -5.470345570052684E-01, -3.529314403402576E-01, 1.664817380826956E-02, \ -5.440713379383119E-01, 3.006296094832735E-01, 1.989408266036578E-02, \ -5.285706246264491E-01, -9.197245554796940E-01, 7.615187153561376E-03, \ -5.252972416610120E-01, -7.002954752760404E-01, 1.432680033700977E-02, \ -5.217907594059557E-01, 5.400272741858242E-01, 1.528186481468926E-02, \ -5.089619423128140E-01, -5.059056477462620E-01, 1.501904216932111E-02, \ -5.078115420044046E-01, -8.111235694116724E-01, 1.195709426495920E-02, \ -4.969587258871904E-01, 8.017211919716127E-01, 1.201247603705383E-02, \ -4.968199837157944E-01, -9.980749914312900E-01, 1.166586821104947E-03, \ -4.959353636879837E-01, 9.946393860645547E-01, 1.686433249616119E-03, \ -4.730248940935154E-01, 9.059843124829209E-01, 9.865671699789467E-03, \ -4.695306511179968E-01, -4.012372094823102E-02, 2.020512288389702E-02, \ -4.684490949568364E-01, -9.635515324500772E-01, 5.666260551094232E-03, \ -4.662090360870560E-01, -2.413919218504774E-01, 1.957608008114237E-02, \ -4.507847851393222E-01, 1.821342046391818E-01, 2.224205809945713E-02, \ -4.504408392645829E-01, 6.157745693132981E-01, 1.569673318119340E-02, \ -4.495408838986024E-01, 3.997386347652018E-01, 2.144177767812802E-02, \ -4.494943818222650E-01, -6.112785695796794E-01, 1.388627516731650E-02, \ -4.395708346821193E-01, 9.678474058357293E-01, 5.077033132428894E-03, \ -4.321562916730266E-01, -4.268668982636962E-01, 1.400797089606991E-02, \ -4.307037407356070E-01, -8.725201945024389E-01, 9.278527778245265E-03, \ -4.168964278432936E-01, 7.450104874315282E-01, 1.219395278659381E-02, \ -3.874730976670355E-01, -7.119235377808760E-01, 1.294126106740710E-02, \ -3.805985421896226E-01, -1.079747078834100E-01, 1.723299400705402E-02, \ -3.785199405738555E-01, -9.876371778523105E-01, 3.684675193016349E-03, \ -3.775068034484436E-01, -7.905403853269520E-01, 1.033847725718908E-02, \ -3.734584665565494E-01, 8.558256846730252E-01, 1.067328374347898E-02, \ -3.655903961329190E-01, -3.266752580040530E-01, 1.908074633576273E-02, \ -3.612230477553254E-01, -9.267019889154319E-01, 8.280449836489664E-03, \ -3.611495490628304E-01, 8.388928253840910E-02, 1.815199832909277E-02, \ -3.544575658069047E-01, 9.925869383206430E-01, 2.882266155274377E-03, \ -3.523952800132275E-01, 5.022785378730914E-01, 2.168828448212548E-02, \ -3.522817929012660E-01, -5.348680504702295E-01, 1.723090656172525E-02, \ -3.413724045500098E-01, 2.868713230288657E-01, 2.351641706301941E-02, \ -3.376590699608993E-01, 6.730406677101659E-01, 1.510911918727652E-02, \ -3.363380915928801E-01, 9.381057218930409E-01, 8.380841067557760E-03, \ -3.054308661239457E-01, 8.161565054705295E-01, 7.871489934535132E-03, \ -2.911339093732676E-01, -1.871048424026023E-01, 2.156968793388712E-02, \ -2.909958284611122E-01, -6.500113551280087E-01, 1.132941951059163E-02, \ -2.866402453607698E-01, 2.784499095490639E-02, 1.703845446866903E-02, \ -2.781698350684899E-01, -8.610025448278995E-01, 1.244171703315526E-02, \ -2.687238931740498E-01, -9.617339692504230E-01, 6.543696094444514E-03, \ -2.646563355865805E-01, -9.979985340168123E-01, 1.301749448971297E-03, \ -2.616214122538829E-01, -4.278716843777844E-01, 2.187272120725739E-02, \ -2.497917994325549E-01, 3.866154000884120E-01, 1.753377798849834E-02, \ -2.407157278594363E-01, -7.680657426891803E-01, 1.428720407246563E-02, \ -2.382131093495637E-01, -6.122566385532253E-01, 1.138418395778662E-02, \ -2.374961081733647E-01, 5.896199791481574E-01, 1.985721981262199E-02, \ -2.368860581759901E-01, 9.742068851942397E-01, 5.931341045087387E-03, \ -2.366505826732369E-01, 7.562399666814275E-01, 1.546898361371274E-02, \ -2.265278487364104E-01, 8.931328439685737E-01, 1.159210102063848E-02, \ -2.209747362024745E-01, 1.884122436616868E-01, 2.568250169412151E-02, \ -1.950442902755774E-01, -2.811626958807719E-01, 2.058667944338659E-02, \ -1.887947955157539E-01, -5.488181437676766E-02, 2.412519217314849E-02, \ -1.874042727370219E-01, 9.985870256064080E-01, 1.332128559441302E-03, \ -1.811513910117983E-01, 4.469187039158583E-01, 1.435518386826230E-02, \ -1.692436690540040E-01, -9.152720547405664E-01, 1.114841347262132E-02, \ -1.607696194805920E-01, -9.844697592632383E-01, 4.214417557364065E-03, \ -1.460884104029156E-01, -5.230400107152748E-01, 2.273359239371198E-02, \ -1.354171446842564E-01, -6.995287211759852E-01, 1.740459683896718E-02, \ -1.250146267020614E-01, 6.790330316810501E-01, 1.950903133230569E-02, \ -1.229292048107615E-01, 8.290159292480069E-01, 1.515992221010223E-02, \ -1.200344097155717E-01, 9.404504623511184E-01, 9.138948896183798E-03, \ -1.126043088126702E-01, 1.039969994189184E-01, 1.948734738016160E-02, \ -1.098342248198241E-01, -8.290702847459517E-01, 1.543693536615040E-02, \ -1.062616019354709E-01, -3.544622956747235E-01, 1.741587972206798E-02, \ -1.054516940373236E-01, 3.111820934533777E-01, 2.489503857532097E-02, \ -9.124174526481066E-02, -1.510286762878782E-01, 2.131519019223245E-02, \ -8.948050655152551E-02, 5.281952357331835E-01, 2.017160434945273E-02, \ -6.799375882563330E-02, 9.851240571486062E-01, 4.627482783799522E-03, \ -5.194154553379345E-02, -9.566399970108974E-01, 8.026920571106742E-03, \ -5.040318666219792E-02, -9.971099379170584E-01, 1.609275224242142E-03, \ -3.734302745905130E-02, 3.768691967771551E-02, 1.732149882179709E-02, \ -2.601415514808519E-02, -6.149995401127395E-01, 2.079979843878833E-02, \ -1.166789681045224E-02, -4.291998918000027E-01, 2.197612010503848E-02, \ -8.044650945002080E-03, 7.582402904728758E-01, 1.762484494418019E-02, \ -7.099519309103105E-03, 8.900638838242294E-01, 1.286870713319578E-02, \ -1.955928951485019E-03, -2.282207401564467E-01, 2.008962148147744E-02, \ 1.955928951485019E-03, 2.282207401564467E-01, 2.008962148147744E-02, \ 7.099519309103105E-03, -8.900638838242294E-01, 1.286870713319578E-02, \ 8.044650945002080E-03, -7.582402904728758E-01, 1.762484494418019E-02, \ 1.166789681045224E-02, 4.291998918000027E-01, 2.197612010503848E-02, \ 2.601415514808519E-02, 6.149995401127395E-01, 2.079979843878833E-02, \ 3.734302745905130E-02, -3.768691967771551E-02, 1.732149882179709E-02, \ 5.040318666219792E-02, 9.971099379170584E-01, 1.609275224242142E-03, \ 5.194154553379345E-02, 9.566399970108974E-01, 8.026920571106742E-03, \ 6.799375882563330E-02, -9.851240571486062E-01, 4.627482783799522E-03, \ 8.948050655152551E-02, -5.281952357331835E-01, 2.017160434945273E-02, \ 9.124174526481066E-02, 1.510286762878782E-01, 2.131519019223245E-02, \ 1.054516940373236E-01, -3.111820934533777E-01, 2.489503857532097E-02, \ 1.062616019354709E-01, 3.544622956747235E-01, 1.741587972206798E-02, \ 1.098342248198241E-01, 8.290702847459517E-01, 1.543693536615040E-02, \ 1.126043088126702E-01, -1.039969994189184E-01, 1.948734738016160E-02, \ 1.200344097155717E-01, -9.404504623511184E-01, 9.138948896183798E-03, \ 1.229292048107615E-01, -8.290159292480069E-01, 1.515992221010223E-02, \ 1.250146267020614E-01, -6.790330316810501E-01, 1.950903133230569E-02, \ 1.354171446842564E-01, 6.995287211759852E-01, 1.740459683896718E-02, \ 1.460884104029156E-01, 5.230400107152748E-01, 2.273359239371198E-02, \ 1.607696194805920E-01, 9.844697592632383E-01, 4.214417557364065E-03, \ 1.692436690540040E-01, 9.152720547405664E-01, 1.114841347262132E-02, \ 1.811513910117983E-01, -4.469187039158583E-01, 1.435518386826230E-02, \ 1.874042727370219E-01, -9.985870256064080E-01, 1.332128559441302E-03, \ 1.887947955157539E-01, 5.488181437676766E-02, 2.412519217314849E-02, \ 1.950442902755774E-01, 2.811626958807719E-01, 2.058667944338659E-02, \ 2.209747362024745E-01, -1.884122436616868E-01, 2.568250169412151E-02, \ 2.265278487364104E-01, -8.931328439685737E-01, 1.159210102063848E-02, \ 2.366505826732369E-01, -7.562399666814275E-01, 1.546898361371274E-02, \ 2.368860581759901E-01, -9.742068851942397E-01, 5.931341045087387E-03, \ 2.374961081733647E-01, -5.896199791481574E-01, 1.985721981262199E-02, \ 2.382131093495637E-01, 6.122566385532253E-01, 1.138418395778662E-02, \ 2.407157278594363E-01, 7.680657426891803E-01, 1.428720407246563E-02, \ 2.497917994325549E-01, -3.866154000884120E-01, 1.753377798849834E-02, \ 2.616214122538829E-01, 4.278716843777844E-01, 2.187272120725739E-02, \ 2.646563355865805E-01, 9.979985340168123E-01, 1.301749448971297E-03, \ 2.687238931740498E-01, 9.617339692504230E-01, 6.543696094444514E-03, \ 2.781698350684899E-01, 8.610025448278995E-01, 1.244171703315526E-02, \ 2.866402453607698E-01, -2.784499095490639E-02, 1.703845446866903E-02, \ 2.909958284611122E-01, 6.500113551280087E-01, 1.132941951059163E-02, \ 2.911339093732676E-01, 1.871048424026023E-01, 2.156968793388712E-02, \ 3.054308661239457E-01, -8.161565054705295E-01, 7.871489934535132E-03, \ 3.363380915928801E-01, -9.381057218930409E-01, 8.380841067557760E-03, \ 3.376590699608993E-01, -6.730406677101659E-01, 1.510911918727652E-02, \ 3.413724045500098E-01, -2.868713230288657E-01, 2.351641706301941E-02, \ 3.522817929012660E-01, 5.348680504702295E-01, 1.723090656172525E-02, \ 3.523952800132275E-01, -5.022785378730914E-01, 2.168828448212548E-02, \ 3.544575658069047E-01, -9.925869383206430E-01, 2.882266155274377E-03, \ 3.611495490628304E-01, -8.388928253840910E-02, 1.815199832909277E-02, \ 3.612230477553254E-01, 9.267019889154319E-01, 8.280449836489664E-03, \ 3.655903961329190E-01, 3.266752580040530E-01, 1.908074633576273E-02, \ 3.734584665565494E-01, -8.558256846730252E-01, 1.067328374347898E-02, \ 3.775068034484436E-01, 7.905403853269520E-01, 1.033847725718908E-02, \ 3.785199405738555E-01, 9.876371778523105E-01, 3.684675193016349E-03, \ 3.805985421896226E-01, 1.079747078834100E-01, 1.723299400705402E-02, \ 3.874730976670355E-01, 7.119235377808760E-01, 1.294126106740710E-02, \ 4.168964278432936E-01, -7.450104874315282E-01, 1.219395278659381E-02, \ 4.307037407356070E-01, 8.725201945024389E-01, 9.278527778245265E-03, \ 4.321562916730266E-01, 4.268668982636962E-01, 1.400797089606991E-02, \ 4.395708346821193E-01, -9.678474058357293E-01, 5.077033132428894E-03, \ 4.494943818222650E-01, 6.112785695796794E-01, 1.388627516731650E-02, \ 4.495408838986024E-01, -3.997386347652018E-01, 2.144177767812802E-02, \ 4.504408392645829E-01, -6.157745693132981E-01, 1.569673318119340E-02, \ 4.507847851393222E-01, -1.821342046391818E-01, 2.224205809945713E-02, \ 4.662090360870560E-01, 2.413919218504774E-01, 1.957608008114237E-02, \ 4.684490949568364E-01, 9.635515324500772E-01, 5.666260551094232E-03, \ 4.695306511179968E-01, 4.012372094823102E-02, 2.020512288389702E-02, \ 4.730248940935154E-01, -9.059843124829209E-01, 9.865671699789467E-03, \ 4.959353636879837E-01, -9.946393860645547E-01, 1.686433249616119E-03, \ 4.968199837157944E-01, 9.980749914312900E-01, 1.166586821104947E-03, \ 4.969587258871904E-01, -8.017211919716127E-01, 1.201247603705383E-02, \ 5.078115420044046E-01, 8.111235694116724E-01, 1.195709426495920E-02, \ 5.089619423128140E-01, 5.059056477462620E-01, 1.501904216932111E-02, \ 5.217907594059557E-01, -5.400272741858242E-01, 1.528186481468926E-02, \ 5.252972416610120E-01, 7.002954752760404E-01, 1.432680033700977E-02, \ 5.285706246264491E-01, 9.197245554796940E-01, 7.615187153561376E-03, \ 5.440713379383119E-01, -3.006296094832735E-01, 1.989408266036578E-02, \ 5.470345570052684E-01, 3.529314403402576E-01, 1.664817380826956E-02, \ 5.479124054422221E-01, -9.758854402340520E-01, 2.479427756255549E-03, \ 5.506357337723290E-01, -7.306393615078814E-02, 2.031057229536963E-02, \ 5.631550904449273E-01, -6.970949553808866E-01, 1.710763838261802E-02, \ 5.702248508469594E-01, 1.587490643869126E-01, 2.016275464017900E-02, \ 5.750197447578449E-01, 9.850659057962179E-01, 3.114356971775973E-03, \ 5.768270943940413E-01, -9.454129989500087E-01, 5.910967881352096E-03, \ 5.862984837774434E-01, -8.612555834742029E-01, 1.061579515310207E-02, \ 6.010977897838671E-01, -4.554853809841653E-01, 1.796395971673612E-02, \ 6.050277497663656E-01, 5.991789076131454E-01, 1.720383270245636E-02, \ 6.058276827683423E-01, -9.969104641392599E-01, 1.067957112281833E-03, \ 6.101810791749840E-01, 8.730802950223981E-01, 9.810988876956505E-03, \ 6.153035647870176E-01, 4.406604449329651E-01, 1.315774503238905E-02, \ 6.243785655726330E-01, 7.677131072866508E-01, 1.213021892933221E-02, \ 6.285276641730166E-01, 9.557558207146426E-01, 5.222692046521106E-03, \ 6.291434547685805E-01, -2.023189788534562E-01, 1.795321661628254E-02, \ 6.371638788293418E-01, 2.566889805750509E-02, 1.632793168239773E-02, \ 6.508182477278392E-01, 2.656608209143835E-01, 1.482527461108588E-02, \ 6.539068033827653E-01, -6.025223400436617E-01, 1.747705500021484E-02, \ 6.562162894928593E-01, -7.813381408111647E-01, 1.314356882014099E-02, \ 6.680438282278643E-01, -9.807419818799499E-01, 3.734416537582896E-03, \ 6.688694553842166E-01, 9.962634726340323E-01, 1.299102531809083E-03, \ 6.718996078310749E-01, -9.187863739753772E-01, 7.227260623084868E-03, \ 6.857267249496155E-01, -3.551782556666386E-01, 1.835639998551701E-02, \ 6.960765595225886E-01, 6.880190026120154E-01, 1.357698223373921E-02, \ 6.978846262070233E-01, 3.414874362228780E-01, 1.076367185856306E-02, \ 7.011205173485494E-01, 5.092216197809605E-01, 1.524066877662247E-02, \ 7.052090371098516E-01, 1.119584635184487E-01, 1.420955705467702E-02, \ 7.053541655207917E-01, -1.073889554567113E-01, 1.602910466636588E-02, \ 7.072078419693140E-01, 9.234919823555481E-01, 6.841723221210096E-03, \ 7.157802360889779E-01, 8.336762449322652E-01, 1.012482548177606E-02, \ 7.258177950289607E-01, 9.805030048690940E-01, 2.984765845250313E-03, \ 7.331498071508773E-01, -8.596337901924931E-01, 9.291892667177389E-03, \ 7.344946046482385E-01, -7.002770707813594E-01, 1.339498521201928E-02, \ 7.391128608011459E-01, -5.011842297262301E-01, 1.677675545049549E-02, \ 7.480114600555077E-01, -9.967592933390678E-01, 1.243409201000067E-03, \ 7.570188231121615E-01, -9.562983797766917E-01, 5.269367781364454E-03, \ 7.658473206792390E-01, -2.470075232375816E-01, 1.699291241018386E-02, \ 7.664905651113335E-01, 2.123608448367788E-01, 1.521536630069221E-02, \ 7.718688019814154E-01, 6.087164044214350E-01, 1.281755532683666E-02, \ 7.752582668662442E-01, -1.137400097769025E-02, 1.483822376274713E-02, \ 7.766600189797701E-01, 4.041663776132322E-01, 1.451699415444131E-02, \ 7.862399052534020E-01, 7.635989572508247E-01, 1.120659033007899E-02, \ 7.957314634069883E-01, 9.607527680221649E-01, 4.059074074883998E-03, \ 7.966190004094728E-01, 9.968334127996725E-01, 1.036781499468538E-03, \ 7.983956784496398E-01, 8.914942533713631E-01, 7.267362334258530E-03, \ 8.004833550779242E-01, -7.919528617574970E-01, 1.006437035257496E-02, \ 8.058634520423256E-01, -6.117159879145377E-01, 1.279254088338618E-02, \ 8.148639002101447E-01, -3.932890823416910E-01, 1.520502153610768E-02, \ 8.179672372442700E-01, -9.076223036675563E-01, 6.892206214578204E-03, \ 8.269374328956414E-01, -9.850869495918245E-01, 2.648428928686930E-03, \ 8.357310902097985E-01, 9.723800805043467E-02, 1.374148019748794E-02, \ 8.369983523769275E-01, -1.347222940319437E-01, 1.460708731761451E-02, \ 8.373962094750010E-01, 5.186387354716220E-01, 1.230119470881243E-02, \ 8.422263654558482E-01, 3.015292326049363E-01, 1.287800406757572E-02, \ 8.522596697975072E-01, 6.840670787785538E-01, 1.062952046635244E-02, \ 8.592237506008711E-01, 8.341324721077372E-01, 7.928559898856604E-03, \ 8.624098290914860E-01, -7.126189995166746E-01, 9.861047155006141E-03, \ 8.651527837557776E-01, 9.866988624485060E-01, 2.118506810134428E-03, \ 8.676827987392443E-01, -5.159125990270553E-01, 1.149515499866792E-02, \ 8.707970024861261E-01, 9.370668393694276E-01, 4.607127648721668E-03, \ 8.763285336755390E-01, -8.465920091250118E-01, 7.228076122988736E-03, \ 8.781614570655271E-01, -9.532957838212304E-01, 3.986319116448455E-03, \ 8.788480167168854E-01, -2.792330855544344E-01, 1.282453595081661E-02, \ 8.887805555572472E-01, -9.980469645264131E-01, 6.927987848988626E-04, \ 8.934682220664112E-01, 4.216540388538755E-01, 1.073747532386832E-02, \ 8.947837985257842E-01, -1.554349304099888E-02, 1.207505504176275E-02, \ 8.956547894973423E-01, 1.969077394197896E-01, 1.052048363646446E-02, \ 9.082567296294581E-01, 5.961320469495873E-01, 9.396878139328617E-03, \ 9.106078414366331E-01, 7.633798877459725E-01, 7.390023577666990E-03, \ 9.148831482219597E-01, -6.224206774261293E-01, 8.741538710357355E-03, \ 9.181270575285391E-01, -4.122328505086459E-01, 9.601387120539102E-03, \ 9.195935562112217E-01, 8.913327000110681E-01, 5.052649337869474E-03, \ 9.217831985976003E-01, 9.985289666041468E-01, 5.078696283821862E-04, \ 9.231065278766845E-01, -9.076886759912991E-01, 4.277169811976498E-03, \ 9.250982605210959E-01, -7.735956141038276E-01, 6.643173932293495E-03, \ 9.278797101416244E-01, 9.706959780392181E-01, 2.420070122891078E-03, \ 9.294596181015237E-01, -9.813684731390790E-01, 1.920664927315008E-03, \ 9.296009678982454E-01, -1.579161826917062E-01, 1.000831611323566E-02, \ 9.376385227666459E-01, 3.149592118756698E-01, 8.640152266819899E-03, \ 9.417225429447996E-01, 1.010399506491120E-01, 8.545115482104066E-03, \ 9.499379163273817E-01, 4.990544089847970E-01, 7.157918511939649E-03, \ 9.529413061166492E-01, 6.848663302380273E-01, 6.115869631822169E-03, \ 9.551892905468934E-01, -5.215279150021472E-01, 6.895698107002057E-03, \ 9.560668264177599E-01, -2.992407743127743E-01, 7.187486995447770E-03, \ 9.565093211986069E-01, 8.285414929426780E-01, 4.524164566301950E-03, \ 9.575259606392211E-01, -8.526222258903702E-01, 3.522351032086693E-03, \ 9.621099147673235E-01, -6.897553564879744E-01, 5.294641784299885E-03, \ 9.625096668136147E-01, -9.481536769647175E-01, 2.281103018635964E-03, \ 9.629858793094620E-01, 9.381408744361764E-01, 2.554368802597983E-03, \ 9.667753163257026E-01, -3.477910291429498E-02, 6.924394568068183E-03, \ 9.668937072725421E-01, -9.958238219074350E-01, 5.454007647675571E-04, \ 9.698875102419363E-01, 9.910520236356811E-01, 8.725558215646179E-04, \ 9.739747222412156E-01, 2.170070835355472E-01, 5.848357083847142E-03, \ 9.758618568064553E-01, 4.021500807907098E-01, 4.191420631437088E-03, \ 9.763487274404036E-01, -8.040608258571258E-01, 1.735576449905203E-03, \ 9.808958789729733E-01, 5.936214063681421E-01, 4.206620288925534E-03, \ 9.817085463008139E-01, -4.080671844783566E-01, 4.517002995396259E-03, \ 9.830502038887345E-01, -1.855914572695679E-01, 4.596336081266426E-03, \ 9.842497345754406E-01, 8.869330623714193E-01, 2.084899867143594E-03, \ 9.844078028285480E-01, 7.576106510429415E-01, 3.160151211848773E-03, \ 9.858704720189189E-01, -9.012846007723281E-01, 1.872665686706367E-03, \ 9.862543531528728E-01, -5.965690502576685E-01, 3.417223744136484E-03, \ 9.874342455637046E-01, -9.765233090751630E-01, 8.334380630773419E-04, \ 9.888702332586248E-01, -7.575946249394171E-01, 2.014228686820058E-03, \ 9.904720670548077E-01, 9.710213211789278E-01, 8.475646284885832E-04, \ 9.908388235274806E-01, 8.317660908501920E-02, 3.661061584693876E-03, \ 9.922776511892646E-01, 3.473204119330540E-01, 2.073619684302503E-03, \ 9.958488160214992E-01, 4.963853591618409E-01, 1.871218692254807E-03, \ 9.967221454497780E-01, -2.967880150220837E-01, 1.788242723078713E-03, \ 9.969508496154019E-01, -9.951320518801803E-01, 1.406624476607038E-04, \ 9.971337685886393E-01, -7.632359805747738E-02, 1.695014196901724E-03, \ 9.973323543291763E-01, -4.909591129622543E-01, 1.363609590112511E-03, \ 9.974354703237893E-01, 9.972347569712511E-01, 1.178428627156954E-04, \ 9.975229416008712E-01, -8.411146681674510E-01, 8.259054712338016E-04, \ 9.975527094081703E-01, 6.722468138431469E-01, 1.228393951475139E-03, \ 9.975758902464168E-01, 8.292104265892648E-01, 8.758182348185454E-04, \ 9.975891711682796E-01, 9.308337785182597E-01, 5.005025838481359E-04, \ 9.982849649115821E-01, -9.436218579698744E-01, 4.239310404841323E-04, \ 9.984308298705356E-01, -6.810115040142974E-01, 8.742573242503645E-04, \ 9.988860641396040E-01, 2.373189065242698E-01, 1.059226498023405E-03 ] ) return xyw def smr48 ( ): #*****************************************************************************80 # ## smr48 returns the SMR rule of degree 48. # # Discussion: # # DEGREE: 48 # POINTS CARDINALITY: 417 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*417), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.990552580516567E-01, -7.479254608809505E-01, 4.845844320013029E-04, \ -9.988760883998153E-01, 2.568938088751835E-01, 8.877453242046397E-04, \ -9.986091048294213E-01, 1.475403353286808E-02, 8.040816649406732E-04, \ -9.985122425173576E-01, -5.059783159128129E-01, 1.125983578847775E-03, \ -9.984530690329705E-01, -9.196817917920462E-01, 3.211292464713594E-04, \ -9.982842816947866E-01, 4.893019742012896E-01, 8.282364851453019E-04, \ -9.982520488850405E-01, 9.821235324863609E-01, 2.422927481790814E-04, \ -9.973280389800840E-01, 6.756520485620866E-01, 8.237504025536671E-04, \ -9.967449468871785E-01, 7.716874829711365E-01, 7.452334436535652E-04, \ -9.964365335122727E-01, 8.681515615582738E-01, 8.902528711682726E-04, \ -9.962098577937705E-01, -2.857266397360828E-01, 1.937344458762579E-03, \ -9.957795050622651E-01, -9.876433080318017E-01, 3.429533984696887E-04, \ -9.946778211699915E-01, -8.474215921378356E-01, 1.194026452801634E-03, \ -9.945109495244129E-01, -6.711427250073166E-01, 1.419745783388957E-03, \ -9.940837925205557E-01, -1.077708304941221E-01, 2.223464254615778E-03, \ -9.925155388861520E-01, 9.388248000765870E-01, 1.047480811500816E-03, \ -9.919901944290620E-01, 5.686557912949334E-01, 1.838793597622181E-03, \ -9.917306363878621E-01, -9.478395921965526E-01, 7.802173870853395E-04, \ -9.910822911638744E-01, 1.331031266923891E-01, 2.938508672222513E-03, \ -9.908515335539425E-01, 3.685202933287459E-01, 2.830526597142672E-03, \ -9.866307668467350E-01, 9.966272831969996E-01, 2.933195451028031E-04, \ -9.858792923413487E-01, -4.118290444180076E-01, 3.755509131978820E-03, \ -9.855194095112306E-01, 7.159397591374761E-01, 1.535917055011706E-03, \ -9.837772596137903E-01, -5.934253159283669E-01, 3.377108351701475E-03, \ -9.819497692855043E-01, -7.782643779166490E-01, 2.756877484994091E-03, \ -9.812266425695817E-01, 8.130580129104829E-01, 2.309363670601080E-03, \ -9.771749693182564E-01, -9.984960207754501E-01, 2.822482441259009E-04, \ -9.763974116368401E-01, -1.934951329958478E-01, 5.027497830243744E-03, \ -9.759936629550091E-01, -8.954485094924929E-01, 2.449068285191341E-03, \ -9.754641485200377E-01, 8.434179079015775E-03, 5.273299242251507E-03, \ -9.741421449181825E-01, 6.292753411868561E-01, 3.568019735683563E-03, \ -9.730819722375790E-01, 9.724521292180650E-01, 1.382948896073604E-03, \ -9.730789870204469E-01, 2.472883400161374E-01, 5.460293273811428E-03, \ -9.726640066871888E-01, 4.651672305117452E-01, 4.813551654491207E-03, \ -9.717010087770350E-01, -9.703771901004872E-01, 1.394234729269292E-03, \ -9.714960642729723E-01, 8.970281595932642E-01, 2.562951198781977E-03, \ -9.617362473444955E-01, -7.027703241908005E-01, 4.605971076568484E-03, \ -9.607210672269872E-01, -3.322709269921182E-01, 5.431302361324639E-03, \ -9.602445514242340E-01, 7.612260341568599E-01, 2.456698577190253E-03, \ -9.579948900288462E-01, -5.112746901351274E-01, 6.253400316621933E-03, \ -9.484290775926218E-01, -8.341736274933066E-01, 4.531225726400182E-03, \ -9.451917183607923E-01, 1.238808781931126E-01, 8.201814840229081E-03, \ -9.432653194808177E-01, -8.861458353897265E-02, 8.008713660300900E-03, \ -9.428586367673794E-01, 9.934004622465014E-01, 9.547156202731789E-04, \ -9.428418829683745E-01, 7.043511955026499E-01, 4.669981461123601E-03, \ -9.427846854068982E-01, 3.530751008963562E-01, 7.832254190109047E-03, \ -9.414741499351150E-01, 5.507528104239781E-01, 6.583790177049798E-03, \ -9.405199230043805E-01, -9.336896767870310E-01, 3.192075832607225E-03, \ -9.398430171859361E-01, 9.410585382180106E-01, 2.918746684002447E-03, \ -9.380601617332789E-01, 8.443007256893251E-01, 4.531934577547019E-03, \ -9.357722262152627E-01, -9.892798298875611E-01, 1.357757734504045E-03, \ -9.297135605148458E-01, -6.291547793730226E-01, 6.754868314277823E-03, \ -9.287300178800064E-01, -2.543930308185366E-01, 7.243849160815757E-03, \ -9.161728844949248E-01, -4.239962588280450E-01, 9.299369071546468E-03, \ -9.122999452276054E-01, -7.650962839278904E-01, 6.505328730774483E-03, \ -9.027195651058045E-01, 2.343213824631600E-01, 1.070153334345670E-02, \ -9.002481970024863E-01, 1.787948642362641E-02, 1.028208803766175E-02, \ -8.994716034464636E-01, 4.509467480279049E-01, 9.722518509241976E-03, \ -8.993299181171596E-01, 6.366994301022654E-01, 8.088190471646505E-03, \ -8.989185508841521E-01, 9.746279357779196E-01, 2.489656257649104E-03, \ -8.973598832577063E-01, -8.839606479669895E-01, 5.558455108410310E-03, \ -8.960324839944227E-01, 7.780412959093933E-01, 6.945480690212927E-03, \ -8.937261594542628E-01, 8.990377097685573E-01, 4.960137962212837E-03, \ -8.894524278225060E-01, -9.645087195310335E-01, 3.234691525597815E-03, \ -8.852845185346627E-01, -1.644249224842236E-01, 1.054311506523360E-02, \ -8.832749949602599E-01, -5.540463681956116E-01, 9.519966984097020E-03, \ -8.763116175834303E-01, -9.976476645275696E-01, 7.363515432897181E-04, \ -8.681923940787308E-01, 9.972359969871393E-01, 8.113364667770608E-04, \ -8.668394917625060E-01, -6.993705565874477E-01, 7.872179533786066E-03, \ -8.613634360731458E-01, -3.261475318345773E-01, 1.232507953462154E-02, \ -8.509299252626037E-01, 1.169899980428923E-01, 1.136757785818936E-02, \ -8.482538929392435E-01, 3.393726360408879E-01, 1.267378157246283E-02, \ -8.451523222407388E-01, 5.453005687235306E-01, 1.130491811792810E-02, \ -8.449087456035432E-01, -8.224590938386219E-01, 8.042605075076493E-03, \ -8.412671406367855E-01, 9.446888202667849E-01, 4.514535531844399E-03, \ -8.389136147784579E-01, 8.439972605417678E-01, 7.433693180569364E-03, \ -8.388809490720153E-01, 7.089485738913401E-01, 9.353324994663370E-03, \ -8.309124445900310E-01, -9.265465930991434E-01, 5.703635540067962E-03, \ -8.274670608886809E-01, -6.041854831216104E-02, 1.386142916565396E-02, \ -8.236973795101074E-01, -4.667582208856409E-01, 1.279580075793840E-02, \ -8.174330288251811E-01, -9.840873060176719E-01, 2.642923071487787E-03, \ -8.120012776170108E-01, -6.342612806052523E-01, 1.021716402717029E-02, \ -8.050460479697321E-01, 9.843510759586377E-01, 2.619831715043517E-03, \ -7.963298579913790E-01, 2.091194063771606E-01, 1.291867519635318E-02, \ -7.946735264586758E-01, -2.195828771062506E-01, 1.512054362089480E-02, \ -7.827811955363804E-01, 4.402675008295936E-01, 1.430859367414026E-02, \ -7.808856870805703E-01, -7.574581885514182E-01, 9.891673069466232E-03, \ -7.745104986488009E-01, 6.271495747138331E-01, 1.211509248039978E-02, \ -7.742852249721359E-01, 9.016812565623727E-01, 7.058444102029891E-03, \ -7.712501309180960E-01, 7.818205620509094E-01, 9.871384023520356E-03, \ -7.644957465687958E-01, -8.749115601199623E-01, 8.398169418965080E-03, \ -7.569201207717521E-01, 5.030282021695773E-02, 1.660514828868849E-02, \ -7.523794410765668E-01, -3.660105878543244E-01, 1.584334374567671E-02, \ -7.455561476506094E-01, -9.573278361059363E-01, 5.090662283402881E-03, \ -7.449421292184407E-01, -9.968633522754683E-01, 1.161090043869617E-03, \ -7.446132349955634E-01, -5.547266254690082E-01, 1.386801984803096E-02, \ -7.369394855016965E-01, 9.975277318664320E-01, 1.006571180791874E-03, \ -7.314430658691584E-01, 9.585376926340167E-01, 4.835999288723090E-03, \ -7.300796275468885E-01, 3.048033260490218E-01, 1.561003081144107E-02, \ -7.168671655213190E-01, -1.074176336475728E-01, 1.755811473136017E-02, \ -7.109858048794567E-01, -6.930842326296686E-01, 1.103274111420899E-02, \ -7.042131099438929E-01, 5.325994952276727E-01, 1.503724999824317E-02, \ -6.966126002275308E-01, 7.081800737356690E-01, 1.259320917995288E-02, \ -6.964513605087373E-01, 8.482976774714664E-01, 9.697594807909158E-03, \ -6.865327730089299E-01, -8.144546391445805E-01, 1.072836825388296E-02, \ -6.753051999581515E-01, 1.623967218674537E-01, 1.866107345822792E-02, \ -6.704437071455894E-01, -2.555701283341775E-01, 1.828130593919578E-02, \ -6.688090823093042E-01, -9.158922580375838E-01, 7.745824340518855E-03, \ -6.654346461416878E-01, -4.581318541855599E-01, 1.715362559535030E-02, \ -6.622715641926926E-01, -9.815849224623253E-01, 3.264022763125851E-03, \ -6.569729367129702E-01, 9.843252854264678E-01, 3.107653612709843E-03, \ -6.490814825652859E-01, 9.219379527553472E-01, 7.273589045997255E-03, \ -6.490772877820512E-01, 4.032488941882870E-01, 1.750178260989192E-02, \ -6.403967267747678E-01, -6.234176969692687E-01, 1.335506042885241E-02, \ -6.321887611571272E-01, -9.956439648928699E-01, 7.346686354790276E-04, \ -6.290834033601033E-01, 7.216244083470421E-03, 1.947776642467306E-02, \ -6.171162584505504E-01, 6.223647914691047E-01, 1.549230086365143E-02, \ -6.112516621704388E-01, 7.831776557256033E-01, 1.255020376848972E-02, \ -5.985853482566683E-01, -7.497385410641988E-01, 1.263727710129047E-02, \ -5.869424988010886E-01, 9.973980234326894E-01, 1.017364927160106E-03, \ -5.839168637130311E-01, -8.616887542657947E-01, 9.710010662354636E-03, \ -5.838249969862671E-01, 2.718839290695758E-01, 1.987995004105253E-02, \ -5.785506719608396E-01, -1.394134201304520E-01, 2.006270434602024E-02, \ -5.776106646583016E-01, -3.488508238645545E-01, 1.954400064690151E-02, \ -5.759454975927832E-01, -9.501573801694301E-01, 5.909368816766506E-03, \ -5.641159090423106E-01, 9.599854139458381E-01, 5.586746910682514E-03, \ -5.633216281680778E-01, 8.755125598060366E-01, 9.255164778582764E-03, \ -5.607747764243531E-01, -5.381763644015136E-01, 1.699095923630616E-02, \ -5.600305973998688E-01, -9.806167661958205E-01, 1.262483548230043E-03, \ -5.567454205492522E-01, 5.026048129003556E-01, 1.827080325916463E-02, \ -5.341810753346672E-01, -9.969266028026199E-01, 1.301907496370608E-03, \ -5.329787205184003E-01, 1.215536852040537E-01, 2.056858991083391E-02, \ -5.216420701735659E-01, 7.059660023740130E-01, 1.551296508436025E-02, \ -5.172659165257237E-01, -6.815002930550295E-01, 1.311160294691172E-02, \ -5.149399834555580E-01, -8.911544014546450E-01, 3.106710974499213E-03, \ -4.954671722032739E-01, 9.877262447568889E-01, 2.704444947872211E-03, \ -4.865772270036066E-01, 3.790795935677761E-01, 2.015371460883953E-02, \ -4.820537324578744E-01, -2.316193655903357E-01, 2.104746654078359E-02, \ -4.809419330248884E-01, 8.244191675015446E-01, 1.014591526088192E-02, \ -4.787129350153638E-01, -1.934329117484134E-02, 2.070508811124076E-02, \ -4.782751005587915E-01, -8.029894135918636E-01, 1.336764814038257E-02, \ -4.770175275669148E-01, -9.699883462880337E-01, 3.399274611185233E-03, \ -4.724003494477093E-01, -4.356324025404807E-01, 1.986953131882142E-02, \ -4.689391598576622E-01, 9.240111512762571E-01, 7.965383957108562E-03, \ -4.658911980881860E-01, -9.126526757581364E-01, 7.367814824582447E-03, \ -4.549738262686863E-01, 5.964200891972189E-01, 1.827733026219556E-02, \ -4.416949290061132E-01, -6.094657082125391E-01, 1.513501533289796E-02, \ -4.308781935067766E-01, 2.346747589224954E-01, 2.059752932220561E-02, \ -4.237214429183968E-01, 9.988429740989183E-01, 7.468909138370148E-04, \ -4.162231798125762E-01, -9.881086636947707E-01, 2.889752971892923E-03, \ -4.039955476728034E-01, 7.698207973252635E-01, 1.213731648511270E-02, \ -4.022743536629942E-01, 9.678771998474882E-01, 4.855326691856050E-03, \ -3.856816592054024E-01, -1.046220184544868E-01, 1.985451526323344E-02, \ -3.842028783258495E-01, 4.782357222377692E-01, 1.944910685094546E-02, \ -3.786287262961593E-01, -7.317696143997668E-01, 1.545284771037087E-02, \ -3.774042657220710E-01, 1.071473163945458E-01, 1.828035198356040E-02, \ -3.767581689748362E-01, -3.215686449173350E-01, 2.187073763613115E-02, \ -3.751374240015725E-01, 8.801101468531496E-01, 9.395413302507984E-03, \ -3.683490409041832E-01, -9.428181074008333E-01, 6.588189243834728E-03, \ -3.629438583461049E-01, -8.569398241270274E-01, 1.243551011498686E-02, \ -3.588340459663644E-01, -5.198877431352260E-01, 1.898803694431077E-02, \ -3.464473861083704E-01, 6.804932722717799E-01, 1.665356435051682E-02, \ -3.299311445310920E-01, 3.361312544479299E-01, 1.885441897381050E-02, \ -3.219997348518502E-01, 9.895504501564032E-01, 2.761328697047235E-03, \ -3.198808254382448E-01, -9.980928088447467E-01, 1.234974434831144E-03, \ -3.037501615875154E-01, 9.368481435389949E-01, 7.207594725661396E-03, \ -3.001889723102260E-01, 3.829984631352593E-02, 1.749110699980297E-02, \ -2.952842276415655E-01, -1.831220068752724E-01, 1.884429765898816E-02, \ -2.933788342322968E-01, -6.564781732148162E-01, 1.409372395800510E-02, \ -2.896454119116090E-01, 8.350902239498463E-01, 1.042215860220357E-02, \ -2.813733871881473E-01, -9.706700162800450E-01, 5.210254763353661E-03, \ -2.803796107520479E-01, 5.666580371271599E-01, 1.769551985203818E-02, \ -2.646649728993916E-01, -4.140438773807713E-01, 2.201548097535621E-02, \ -2.558406082629252E-01, 2.189136718964751E-01, 2.131050014957573E-02, \ -2.512104300954118E-01, -7.918292212992303E-01, 1.562248186161317E-02, \ -2.488917545593868E-01, -9.038959168898448E-01, 1.025510969508195E-02, \ -2.438092787887342E-01, 4.188288491033791E-01, 1.475732864033983E-02, \ -2.346445346959175E-01, 7.613261048327971E-01, 1.455391668451701E-02, \ -2.271156542693553E-01, -5.887245648490607E-01, 1.434999190758240E-02, \ -2.247073731789063E-01, 9.979933451517716E-01, 1.039791944866300E-03, \ -2.163763876756374E-01, 9.677392729427614E-01, 4.990957116044046E-03, \ -2.103558829810385E-01, -2.574697338318033E-01, 1.764960446990464E-02, \ -2.095250370525197E-01, -4.031736543450098E-02, 2.178465331938922E-02, \ -1.927828958465816E-01, 8.982684824267485E-01, 1.042589527917258E-02, \ -1.871159934019396E-01, 6.474212617254689E-01, 1.535750116524344E-02, \ -1.806658576765277E-01, -9.896867624509934E-01, 3.408734541691759E-03, \ -1.633259573375413E-01, 1.400955882739857E-01, 1.959106088770077E-02, \ -1.562364680645740E-01, 4.925045888845677E-01, 1.737804918299484E-02, \ -1.491971854353493E-01, -7.098622267114059E-01, 1.806240202498965E-02, \ -1.452318661461631E-01, -9.437776536061130E-01, 7.890722263129550E-03, \ -1.439290914451357E-01, -5.038374394299656E-01, 2.033901736325344E-02, \ -1.357808182391570E-01, 3.334065136263061E-01, 2.200934208245402E-02, \ -1.313016026395862E-01, -8.511650652628034E-01, 1.347969997761506E-02, \ -1.245113984567057E-01, 9.861958682207052E-01, 3.308916883269708E-03, \ -1.229885666993439E-01, -3.334500618371383E-01, 1.933435335874882E-02, \ -1.144529387813882E-01, 8.314993434856852E-01, 1.360965950150718E-02, \ -1.095687849917511E-01, -1.301117874964884E-01, 2.211874730643872E-02, \ -9.411332760666641E-02, 7.176378070213986E-01, 1.463449452671732E-02, \ -8.388626313485989E-02, 9.413401035627339E-01, 8.138348671609086E-03, \ -7.111096756881072E-02, 5.901854458702823E-02, 2.159648899983570E-02, \ -5.596535842806818E-02, -9.985986389503078E-01, 1.152035315802443E-03, \ -5.519377855670472E-02, 5.804621131957924E-01, 1.951093459498052E-02, \ -5.083880286421506E-02, -6.184685667120825E-01, 1.949335828949948E-02, \ -4.232428288883773E-02, -9.721213788531580E-01, 5.459634326563773E-03, \ -3.362895942304555E-02, 2.473398037721315E-01, 2.225550633881426E-02, \ -2.878763707909897E-02, 9.974212143963649E-01, 1.392150791806729E-03, \ -2.701947130628778E-02, -7.792634752677781E-01, 1.635358938483053E-02, \ -2.099733154867333E-02, -4.174896614559798E-01, 2.064580833064765E-02, \ -1.942942890989090E-02, -9.030039921748615E-01, 1.075920755862384E-02, \ -1.025241776704336E-02, -2.209004411746912E-01, 2.189514896760084E-02, \ -5.603709661495010E-03, 4.376284944061901E-01, 2.305488563112960E-02, \ 5.160807557708119E-03, 8.883127314312923E-01, 1.173589844777346E-02, \ 1.478755859639245E-02, 7.805710255221150E-01, 1.419483273432981E-02, \ 2.203211920457429E-02, 9.710286258778940E-01, 5.352311200607812E-03, \ 2.667969840358058E-02, -3.169899165421439E-02, 2.212058357439342E-02, \ 4.419649539576614E-02, -5.358738509280914E-01, 1.537849072244061E-02, \ 5.645986923166345E-02, 6.654224239023853E-01, 1.852457014689922E-02, \ 7.014561544903802E-02, 1.539138394301714E-01, 2.361180582820691E-02, \ 7.382490787646279E-02, -9.888797183102520E-01, 3.401063622770633E-03, \ 7.677748557728954E-02, -6.950549395483447E-01, 1.891944949236252E-02, \ 8.334400516372700E-02, -9.420248129445080E-01, 7.428425442889059E-03, \ 8.811404198697755E-02, -8.425744879388839E-01, 1.354320033736116E-02, \ 9.428202794142194E-02, -3.130508677914989E-01, 2.260130066690366E-02, \ 1.010204727329467E-01, 3.441432117443262E-01, 2.223504878996065E-02, \ 1.118057634342426E-01, 9.901984397677133E-01, 2.866107790272031E-03, \ 1.196298840971513E-01, 5.382727379580559E-01, 2.270074787659283E-02, \ 1.209411181337108E-01, -4.799090158464530E-01, 1.152147426491700E-02, \ 1.219850999637117E-01, -1.218612532860722E-01, 2.101568083502077E-02, \ 1.232292464562112E-01, 9.343108083094505E-01, 9.206323005860302E-03, \ 1.295669785368222E-01, 8.406880568875401E-01, 1.287955106877277E-02, \ 1.735905842899504E-01, 7.429177350779718E-01, 1.571431921804362E-02, \ 1.755724480028529E-01, 5.338528258468570E-02, 2.372489552516464E-02, \ 1.757472783291680E-01, -5.979131889853080E-01, 1.794402481478493E-02, \ 1.842105709085970E-01, -8.912854841712154E-01, 7.954070193779422E-03, \ 1.849994792854633E-01, -9.651899282978637E-01, 5.064149534933845E-03, \ 1.883621786044712E-01, -9.977844639120534E-01, 1.248646247932006E-03, \ 1.936423269701602E-01, -7.695301946784334E-01, 1.610490406496761E-02, \ 2.014762149232713E-01, -4.110301142644528E-01, 1.885365723952532E-02, \ 2.036789289831738E-01, 2.505729164783445E-01, 2.177691306082853E-02, \ 2.124821840633064E-01, 9.983678654418292E-01, 1.013308752600118E-03, \ 2.186440916146861E-01, -2.099360144286631E-01, 2.166303561905097E-02, \ 2.266009299450756E-01, 4.361972923038600E-01, 2.158994434128180E-02, \ 2.315646394710894E-01, 9.701295500103406E-01, 6.079344492651117E-03, \ 2.356865468776172E-01, 6.370910939235934E-01, 1.931745618038865E-02, \ 2.454088634004036E-01, 8.937656157434565E-01, 1.097036321751639E-02, \ 2.483612800101855E-01, -9.144118112672673E-01, 5.880986220439612E-03, \ 2.738636464954728E-01, -4.180479898913641E-02, 1.973225599622812E-02, \ 2.741334945816214E-01, -6.688097177458799E-01, 1.552583691672160E-02, \ 2.806967904899877E-01, -9.837566472737467E-01, 3.668812731548744E-03, \ 2.878146592243341E-01, 8.096216755413393E-01, 1.248593716069912E-02, \ 2.928095492516591E-01, -8.296492444850465E-01, 1.002982078393012E-02, \ 3.003707713405964E-01, 1.574001974071592E-01, 2.081647115457695E-02, \ 3.032112900280739E-01, -3.213476683127075E-01, 1.986943316524076E-02, \ 3.038778633328361E-01, -5.155279822940786E-01, 2.132140323091509E-02, \ 3.189416740657732E-01, 5.301239563235857E-01, 1.599311728650303E-02, \ 3.379458538210279E-01, 3.380078043017812E-01, 2.231047709478462E-02, \ 3.414315269801313E-01, -9.447221797790122E-01, 7.193479552256923E-03, \ 3.451501869255189E-01, 9.911045296989844E-01, 3.150815381449179E-03, \ 3.459501416944350E-01, 9.412460482178074E-01, 7.581328265611393E-03, \ 3.498025442310060E-01, 7.259867843713310E-01, 1.534088761786192E-02, \ 3.506298151283278E-01, -1.110943927993918E-01, 1.551666339044610E-02, \ 3.508944053443432E-01, -8.597690806797168E-01, 6.780738534373333E-03, \ 3.676203412527344E-01, -7.355441788616041E-01, 1.449363179369764E-02, \ 3.775941728027782E-01, -9.966110448377157E-01, 1.588376651423708E-03, \ 3.860519270960796E-01, 7.302449463643648E-02, 1.674967274353688E-02, \ 3.908175824545033E-01, 6.040163725706776E-01, 1.278149700085847E-02, \ 3.932995953514418E-01, 8.586784918787448E-01, 9.330747431728702E-03, \ 4.009583889628902E-01, -2.237036393799572E-01, 1.892604307935697E-02, \ 4.132872901647590E-01, -4.161374351557686E-01, 2.138066163226836E-02, \ 4.156626605778777E-01, -6.064541375879013E-01, 1.924814510794154E-02, \ 4.275837181210796E-01, 9.094238876105997E-01, 4.770828940366273E-03, \ 4.328418582000582E-01, 4.496319777430270E-01, 1.936747828289653E-02, \ 4.385174796956023E-01, -8.999264574814262E-01, 9.370005851764580E-03, \ 4.416854437364063E-01, -9.738073510248620E-01, 4.796346619556446E-03, \ 4.421330688920201E-01, 2.374107327854063E-01, 2.181532535184939E-02, \ 4.550615803392936E-01, 9.726655099206181E-01, 5.179676710206462E-03, \ 4.569654688277525E-01, 6.884355926489272E-03, 1.583552991175338E-02, \ 4.632819243713829E-01, -8.003126851100022E-01, 1.316681225047508E-02, \ 4.689306146948844E-01, 6.814262213200711E-01, 1.334579482569558E-02, \ 4.696207639607174E-01, 7.988154952920899E-01, 1.184787022608413E-02, \ 4.857658052760571E-01, 9.984893866977577E-01, 1.096119304476565E-03, \ 4.993823494452720E-01, -1.215115809417293E-01, 1.866094748126752E-02, \ 5.147227675195748E-01, -3.085631716120487E-01, 2.105349795001905E-02, \ 5.165019514631053E-01, 5.527052226731102E-01, 1.594523958184094E-02, \ 5.184998491048611E-01, -5.122582772507516E-01, 1.944936029664543E-02, \ 5.212882108068023E-01, 8.912280598565898E-01, 6.430590724186390E-03, \ 5.216196172575923E-01, -6.918653721187973E-01, 1.673261806644407E-02, \ 5.267404688211808E-01, -9.928234349336557E-01, 2.264249969231592E-03, \ 5.337628878538487E-01, 3.562767541456822E-01, 1.973968319676171E-02, \ 5.362462702301273E-01, -9.419621269592201E-01, 7.018123899882877E-03, \ 5.376377966884078E-01, 9.405432980109936E-01, 5.735139534376493E-03, \ 5.414492290361640E-01, 1.392734385435706E-01, 2.077403754645742E-02, \ 5.609107809910865E-01, -8.610602440350434E-01, 1.065010493507847E-02, \ 5.657856622042965E-01, 7.599631423795741E-01, 1.071300749042643E-02, \ 5.853656077435417E-01, 9.875390366974179E-01, 3.152366608701943E-03, \ 5.901716003152813E-01, 6.434525496875014E-01, 1.295115318701735E-02, \ 5.926475181039332E-01, -1.394312891636593E-02, 1.831016768731409E-02, \ 6.004152984409479E-01, 8.529159644062866E-01, 9.481026402361680E-03, \ 6.117360608723036E-01, -1.986847607827743E-01, 1.980214313193597E-02, \ 6.130824033534686E-01, -4.095714300275702E-01, 1.917012065007447E-02, \ 6.151072377903102E-01, 4.701060842696129E-01, 1.706729076110463E-02, \ 6.159307791132325E-01, -7.726284834690805E-01, 1.314127931857205E-02, \ 6.178862021937575E-01, -6.037568023506926E-01, 1.700517763869981E-02, \ 6.233140115752496E-01, -9.990478475611962E-01, 5.756607762407137E-04, \ 6.233882556383349E-01, -9.736906648802569E-01, 4.400416908080170E-03, \ 6.293004246408224E-01, 2.602964866719539E-01, 1.911043777425127E-02, \ 6.354013023790106E-01, 9.594829356193809E-01, 3.875984169380209E-03, \ 6.531860907351404E-01, -9.129935732773705E-01, 7.993871581045829E-03, \ 6.669095378699366E-01, 7.212125041562338E-01, 1.115937328874872E-02, \ 6.682888522038171E-01, 9.170080181860093E-01, 6.711591614310012E-03, \ 6.733698677832002E-01, 9.531068015393949E-02, 1.704322733008138E-02, \ 6.867975790725386E-01, 5.732210324621596E-01, 1.405118611426179E-02, \ 6.877498285966892E-01, 9.972377597170190E-01, 1.171144176394094E-03, \ 6.919530077164939E-01, 8.183966376302371E-01, 8.546002645004975E-03, \ 7.006699775901079E-01, -3.018130078739841E-01, 1.797963536109381E-02, \ 7.007378604415206E-01, -6.967393023705793E-01, 1.347242645942421E-02, \ 7.011706428762506E-01, -8.645955499455821E-02, 1.805455337163264E-02, \ 7.046359024076116E-01, -8.408642058193949E-01, 1.001402071103762E-02, \ 7.050184040815621E-01, -5.062475643165765E-01, 1.662718203829281E-02, \ 7.059713500450162E-01, 3.789436426580511E-01, 1.673848305527229E-02, \ 7.069046616445557E-01, -9.908001304861944E-01, 1.978600063893940E-03, \ 7.266691397063710E-01, 9.764485842045145E-01, 3.196135869015411E-03, \ 7.363406109597423E-01, -9.531023692016642E-01, 5.413055258221468E-03, \ 7.430250973663187E-01, 2.035056651546192E-01, 1.504638709941723E-02, \ 7.535644399389860E-01, 8.879258118131659E-01, 7.006171198702037E-03, \ 7.563574258683842E-01, 6.568574070169740E-01, 1.127645966819047E-02, \ 7.667442271787138E-01, 7.756805658723509E-01, 8.207817118717271E-03, \ 7.701722119351029E-01, 9.513283511378082E-01, 3.288073973455126E-03, \ 7.726397716060590E-01, 4.891287757524024E-01, 1.380985802819005E-02, \ 7.763819833434896E-01, -6.108424957683033E-01, 1.316465009375289E-02, \ 7.765876970003720E-01, -9.983175720029679E-01, 5.530803312446341E-04, \ 7.783135272478848E-01, 3.067088271297034E-02, 1.617867766579491E-02, \ 7.789758903483420E-01, -7.755784522131605E-01, 1.024240381182082E-02, \ 7.794951515725598E-01, -1.900547136170159E-01, 1.605547922328266E-02, \ 7.827786520173903E-01, -4.013994693137274E-01, 1.542333829511010E-02, \ 7.859968639285212E-01, -8.957991066819440E-01, 7.388246252798941E-03, \ 8.019277506261744E-01, 3.096569162287749E-01, 1.321462723675400E-02, \ 8.046989562620047E-01, 9.934698121858433E-01, 1.620975163901152E-03, \ 8.116271678470535E-01, -9.812368844557581E-01, 2.805354005606401E-03, \ 8.271120113357940E-01, 8.445310805164534E-01, 7.391494649958003E-03, \ 8.315475863435614E-01, 9.349719428861505E-01, 4.319512065933182E-03, \ 8.321584209664755E-01, 7.156459468065629E-01, 8.211658184356523E-03, \ 8.346880955680183E-01, 5.790843779334668E-01, 1.053843380670116E-02, \ 8.421200025145761E-01, -5.163218277007364E-01, 1.214654046014649E-02, \ 8.428358142326123E-01, -7.004905652156834E-01, 9.807944160460698E-03, \ 8.429068230233057E-01, 1.506850609766789E-01, 1.392052411787133E-02, \ 8.469443668153608E-01, -7.373217636068097E-02, 1.387616447908254E-02, \ 8.499231814765066E-01, -2.903842316704804E-01, 1.345748857648198E-02, \ 8.509676963874204E-01, -9.421501714518346E-01, 4.512282801925937E-03, \ 8.513842034584429E-01, -8.385682243825499E-01, 7.589918785203049E-03, \ 8.529297252064996E-01, 9.788650415840999E-01, 1.767999675129546E-03, \ 8.548119318481671E-01, 4.129920008983965E-01, 1.142134843011626E-02, \ 8.743399003663345E-01, -9.965501332313196E-01, 8.866545706261915E-04, \ 8.868589131988083E-01, 7.813550256000477E-01, 7.028611053580085E-03, \ 8.882097576725707E-01, 8.967871781921426E-01, 5.131933562814728E-03, \ 8.940437357261795E-01, 6.448353054197643E-01, 7.532981116414975E-03, \ 8.951043245737870E-01, 2.701305401459678E-01, 1.119698691900426E-02, \ 8.957988629549595E-01, -6.172417311892393E-01, 8.745996105562806E-03, \ 8.966637138539476E-01, -4.139876550907898E-01, 1.042345398687548E-02, \ 8.972477740164735E-01, 9.688428320077953E-01, 2.185864494768297E-03, \ 9.009266678826738E-01, 9.978009702135497E-01, 6.895418046666433E-04, \ 9.018821552007310E-01, 4.650154498011889E-02, 1.144764316389570E-02, \ 9.031198283499343E-01, -8.990561632189207E-01, 4.723822492423395E-03, \ 9.045602400259568E-01, -7.701264771658067E-01, 7.053104592289312E-03, \ 9.053380379607494E-01, -1.746480109218232E-01, 1.103438645893049E-02, \ 9.054411149232872E-01, -9.744873584378785E-01, 2.378102961922232E-03, \ 9.055326931403324E-01, 5.042853365036326E-01, 8.843909529693304E-03, \ 9.343926720143196E-01, 8.408281722676378E-01, 4.939252078872689E-03, \ 9.369672998076496E-01, 9.392509664822630E-01, 3.036071275593237E-03, \ 9.370649990477178E-01, -5.263980680715866E-01, 7.197501644580989E-03, \ 9.375084976458372E-01, 3.772288160090471E-01, 7.723756326362103E-03, \ 9.381535834200617E-01, 7.106235070910863E-01, 5.902848304746877E-03, \ 9.397089401153526E-01, -3.064559939391279E-01, 8.183193061824199E-03, \ 9.430513485839862E-01, -8.453991555068732E-01, 4.259151291048153E-03, \ 9.439138207794857E-01, 1.694346027653371E-01, 8.711608432261320E-03, \ 9.453640500952915E-01, -6.918818219382270E-01, 5.811160329023696E-03, \ 9.458401661756128E-01, -9.433047135677757E-01, 2.666991866215932E-03, \ 9.474931749108476E-01, -9.934540488719975E-01, 9.077513966991803E-04, \ 9.480260033412141E-01, -5.528363383644061E-02, 8.344368695609054E-03, \ 9.515094736278008E-01, 9.869714675506723E-01, 1.367495384365193E-03, \ 9.522042365240376E-01, 5.775886113807980E-01, 6.278213478960007E-03, \ 9.666835796199322E-01, 4.481624968499795E-01, 3.204558585936675E-03, \ 9.674418063223464E-01, -4.304000963196550E-01, 5.347598797243928E-03, \ 9.701359035367135E-01, -7.802525506646220E-01, 3.115557673116472E-03, \ 9.701857271817536E-01, 8.938055399198392E-01, 2.864900302668842E-03, \ 9.708930152297497E-01, -1.958004635679564E-01, 5.654816581606078E-03, \ 9.714573561311842E-01, 7.782560227882267E-01, 3.821062888660015E-03, \ 9.738224913796117E-01, -6.066878673454835E-01, 4.238239901525744E-03, \ 9.743870386597691E-01, -9.005600796222234E-01, 2.292879276270914E-03, \ 9.748694751568308E-01, 2.872115060189273E-01, 5.488782914198373E-03, \ 9.770534257331674E-01, -9.733442069702187E-01, 1.220396530498849E-03, \ 9.773487838243448E-01, 6.742991425576679E-02, 5.516141834251902E-03, \ 9.807262602523558E-01, 9.605757763822972E-01, 1.453483834542216E-03, \ 9.821557641147268E-01, 6.556398036205757E-01, 3.678998334252915E-03, \ 9.839106243620387E-01, 9.977561756217526E-01, 2.768302865456187E-04, \ 9.847751712912336E-01, 4.874332090983019E-01, 3.074449052250624E-03, \ 9.872347823081763E-01, -8.347683105720206E-01, 1.269040121422027E-03, \ 9.873631625273047E-01, -3.284258517966067E-01, 3.314654538180889E-03, \ 9.878645619258249E-01, -9.970787084309179E-01, 2.392045469575733E-04, \ 9.891124753817594E-01, -7.120059529034396E-01, 2.190875058685215E-03, \ 9.904843680686551E-01, -8.399228923374426E-02, 3.184383491092044E-03, \ 9.911486992958609E-01, -5.172577211992232E-01, 2.483935260660239E-03, \ 9.926946438637168E-01, 8.406144684615959E-01, 1.680655250200566E-03, \ 9.940864938813981E-01, -9.401988730146373E-01, 8.590139939992197E-04, \ 9.941987746944642E-01, 1.912235208694665E-01, 2.518562325519789E-03, \ 9.960483559226059E-01, 3.732328466642290E-01, 1.950601561707686E-03, \ 9.962534123813316E-01, 9.225251976350251E-01, 7.835582462513657E-04, \ 9.966184286027521E-01, -8.738768172094957E-01, 6.340506805099443E-04, \ 9.968580870618724E-01, 7.336608062965726E-01, 1.218635259088649E-03, \ 9.972221719684324E-01, 9.836266811867312E-01, 3.070667564929675E-04, \ 9.973502464780108E-01, 5.703835859132225E-01, 1.316377370815025E-03, \ 9.977903571993221E-01, -2.217334569601657E-01, 1.243787387237352E-03, \ 9.981467866635252E-01, -7.852760517081546E-01, 5.930241241924707E-04, \ 9.983950085519884E-01, -6.322084663179760E-01, 8.416135676187133E-04, \ 9.984871758203762E-01, -9.838507269098428E-01, 1.976555370458795E-04, \ 9.985986690813101E-01, -4.178930731294047E-01, 8.254856487030795E-04, \ 9.989532297601191E-01, 3.236183825764132E-02, 9.014418551948622E-04 ] ) return xyw def smr49 ( ): #*****************************************************************************80 # ## smr49 returns the SMR rule of degree 49. # # Discussion: # # DEGREE: 49 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 427 # NORM INF MOMS. RESIDUAL: 4.24357e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*427), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.987179482199477E-01, -6.341055456784180E-02, 9.427263494251746E-04, \ -9.985820051950299E-01, 4.311577677096960E-01, 8.506787489756313E-04, \ -9.985812215892117E-01, 2.098862069679553E-01, 9.932558396288942E-04, \ -9.984853824993025E-01, -7.518363345257131E-01, 6.752050933944545E-04, \ -9.984416520882323E-01, -8.814083896367437E-01, 4.548127997472904E-04, \ -9.983293539476047E-01, 9.835120159252404E-01, 2.181997023647311E-04, \ -9.982115219214424E-01, 6.305047404346029E-01, 8.136830618787968E-04, \ -9.978435386703776E-01, 7.692080150297662E-01, 6.598609318533428E-04, \ -9.977221586114358E-01, -6.019952067889782E-01, 5.964708123101566E-04, \ -9.966209533584591E-01, -3.237318892379179E-01, 1.736701233968157E-03, \ -9.963148656482692E-01, -9.861307505276973E-01, 3.364793817721787E-04, \ -9.959458468526172E-01, 8.639404647925895E-01, 9.127209022448868E-04, \ -9.955419051779023E-01, -5.028006893760714E-01, 1.625315064214383E-03, \ -9.939777572418940E-01, 9.377670381442861E-01, 9.071335269558794E-04, \ -9.931100571448706E-01, -9.398758417699402E-01, 9.653046269879767E-04, \ -9.914404533622192E-01, 7.370377576026632E-02, 3.114508431996894E-03, \ -9.910529016163073E-01, -1.720232075920507E-01, 2.834840262020965E-03, \ -9.904412956303582E-01, 5.265151744794012E-01, 2.514644595413010E-03, \ -9.897745584940826E-01, 3.209639101085088E-01, 3.026155349324961E-03, \ -9.896878613799838E-01, -6.734414823238595E-01, 2.206204039428005E-03, \ -9.896446181606325E-01, -8.258526268641876E-01, 1.761173631057456E-03, \ -9.882983824911455E-01, 7.029568166797684E-01, 2.101767111893595E-03, \ -9.870995148246587E-01, 9.971266172517755E-01, 2.522985579422540E-04, \ -9.828402728207225E-01, 8.130859429654207E-01, 1.813569870463969E-03, \ -9.805838302292789E-01, -4.186960243528708E-01, 4.224419641522761E-03, \ -9.799683347097561E-01, -9.982787940792663E-01, 2.802539460088801E-04, \ -9.768576153531923E-01, 9.720516240923431E-01, 1.260176677733168E-03, \ -9.737646096663447E-01, 8.979365374145354E-01, 2.417846375635086E-03, \ -9.736351786214140E-01, -5.825032309876242E-01, 4.276722297762739E-03, \ -9.734565439099904E-01, -8.924228057613435E-01, 2.621925808197151E-03, \ -9.729306672713298E-01, 1.937971855968040E-01, 5.661441805111854E-03, \ -9.728709777782690E-01, -9.691292467666289E-01, 1.466141068305907E-03, \ -9.726983304977663E-01, -4.425763588680746E-02, 5.881914856745899E-03, \ -9.715318079839266E-01, 6.114344673195419E-01, 4.212935529909797E-03, \ -9.711831524640260E-01, -7.579747866842650E-01, 3.663853318492690E-03, \ -9.709279126257970E-01, -2.562383260371136E-01, 5.255024629747484E-03, \ -9.708137869429159E-01, 4.239389021325329E-01, 5.141869518483292E-03, \ -9.664977673747553E-01, 7.669983680205528E-01, 2.614941215020715E-03, \ -9.469548060003440E-01, 9.927873239383316E-01, 9.693950321163949E-04, \ -9.450858475738110E-01, -5.025373008969878E-01, 6.252666523418040E-03, \ -9.448077504847031E-01, 9.425192762886759E-01, 2.715142333531406E-03, \ -9.432745759141794E-01, -3.578284894473978E-01, 6.177743639544537E-03, \ -9.432551757252079E-01, -6.778512313399264E-01, 5.997726172859794E-03, \ -9.425924799508709E-01, 7.723036765423268E-02, 8.594457541849910E-03, \ -9.424045442737207E-01, 6.965818136607429E-01, 5.492047852799914E-03, \ -9.422279295242960E-01, 8.430010110128885E-01, 4.356685968058319E-03, \ -9.421296116189286E-01, 3.072458818807862E-01, 8.166950645809414E-03, \ -9.414068461363603E-01, -8.319946383779213E-01, 4.899221558401311E-03, \ -9.401222897124206E-01, 5.208371173674092E-01, 7.080933689521712E-03, \ -9.396692618824576E-01, -9.333268377293767E-01, 3.176964275867470E-03, \ -9.387594609269243E-01, -9.896419412770018E-01, 1.315181972642427E-03, \ -9.376865583713452E-01, -1.472997681505319E-01, 8.802757771504873E-03, \ -9.058866443920447E-01, -2.915118591864504E-01, 7.312514214991043E-03, \ -9.033753194459962E-01, 9.739301226929417E-01, 2.430898666967969E-03, \ -9.026928782557422E-01, -5.971154860482422E-01, 8.134575081016936E-03, \ -9.021900638531539E-01, 8.986885201991707E-01, 4.735976500809632E-03, \ -9.006876027333818E-01, 7.738025214543742E-01, 6.953572521005407E-03, \ -9.000160662012473E-01, 1.936545205467035E-01, 1.105560603537899E-02, \ -8.994183334513204E-01, -7.589002650753883E-01, 7.412012270186419E-03, \ -8.991432933902236E-01, 6.161569102595980E-01, 8.649321074038529E-03, \ -8.990136642719798E-01, 4.154161042204226E-01, 1.027033600307130E-02, \ -8.955650716170729E-01, -2.889828380654945E-02, 1.141690753127995E-02, \ -8.934822042254417E-01, -8.849206485200981E-01, 5.481269950434707E-03, \ -8.925866230961302E-01, -9.651738737461483E-01, 3.087139101703460E-03, \ -8.916399066676414E-01, -4.478690090838509E-01, 8.958243051785242E-03, \ -8.787467882854940E-01, -9.974975541031985E-01, 7.520196736734306E-04, \ -8.768368119879948E-01, 9.972195337276928E-01, 7.824958500505416E-04, \ -8.688111752985119E-01, -2.062730881400507E-01, 1.032123607597266E-02, \ -8.488444646215817E-01, 9.417487190138607E-01, 4.527482466935922E-03, \ -8.483308513877643E-01, 8.420081277059801E-01, 7.356656581421614E-03, \ -8.465974052776020E-01, -6.804500384380086E-01, 9.439844848201484E-03, \ -8.457711905447103E-01, 3.060565758105315E-01, 1.313083077355583E-02, \ -8.454498037908205E-01, 5.197883189451455E-01, 1.190856918137506E-02, \ -8.440484090367564E-01, 6.995813955156258E-01, 9.801510245897441E-03, \ -8.420990261538619E-01, 8.700843845073450E-02, 1.361576981188029E-02, \ -8.387107616534492E-01, -8.225135460279916E-01, 8.023995882685042E-03, \ -8.342806635072800E-01, -3.686663614256265E-01, 1.185649053487261E-02, \ -8.341324042868387E-01, -5.413042996556211E-01, 1.028726411584244E-02, \ -8.328917808999070E-01, -9.275746498999357E-01, 5.345327410698648E-03, \ -8.222752044712189E-01, -9.828983653726329E-01, 2.569844448228937E-03, \ -8.181510041117529E-01, -1.013221207184385E-01, 1.380702843362417E-02, \ -8.152169502901689E-01, 9.831801913034185E-01, 2.619950174549044E-03, \ -7.828790059504277E-01, 8.970932838288118E-01, 7.123319843648826E-03, \ -7.814359340875883E-01, 4.148826331713472E-01, 1.479944058585885E-02, \ -7.801982799083059E-01, 7.770472357073510E-01, 1.015003094959520E-02, \ -7.785783303955014E-01, 6.125037703604832E-01, 1.287366180571384E-02, \ -7.781640573729546E-01, 1.995944750196611E-01, 1.546595460903855E-02, \ -7.780033996472984E-01, -2.651062610509234E-01, 1.437115393673534E-02, \ -7.761306169624727E-01, -7.501004998319117E-01, 9.930943224422817E-03, \ -7.715857235482023E-01, 9.983428621580931E-01, 5.452222266440912E-04, \ -7.655483726416725E-01, -8.750797093910616E-01, 7.985877894766822E-03, \ -7.650517717498729E-01, -4.715771704307840E-01, 1.255037589648692E-02, \ -7.638158346191554E-01, -6.256899643054369E-01, 1.089753036742033E-02, \ -7.586912864075982E-01, -9.961911332837330E-01, 1.179272785443735E-03, \ -7.531768231132037E-01, 1.201386227993326E-02, 1.642203608617212E-02, \ -7.525943724917873E-01, -9.538377812626558E-01, 4.657805305389900E-03, \ -7.425465126897265E-01, 9.565892784834152E-01, 4.976897852233662E-03, \ -7.120337647362697E-01, -1.543105022946922E-01, 1.667558344244733E-02, \ -7.058491208433765E-01, 9.915756755872566E-01, 1.790261844614419E-03, \ -7.050966153827319E-01, 3.088933084722713E-01, 1.701475236717927E-02, \ -7.050386520037029E-01, 5.147871049065931E-01, 1.577829434551910E-02, \ -7.044541730236628E-01, 8.417075739142680E-01, 9.820401163435438E-03, \ -7.038938546524356E-01, 6.992970712529386E-01, 1.317427859481092E-02, \ -7.030786952640691E-01, -3.737683313436290E-01, 1.533113926314000E-02, \ -6.952697432642575E-01, -8.074711595576919E-01, 9.903249938089028E-03, \ -6.874559480675843E-01, -9.781638816357989E-01, 3.101643133626598E-03, \ -6.843864494264393E-01, -5.640703334807048E-01, 1.247073498122494E-02, \ -6.791674419638026E-01, -6.963055362251113E-01, 1.115720692184079E-02, \ -6.763078266684166E-01, 1.264181240942355E-01, 1.836539066857489E-02, \ -6.743529219450092E-01, -9.106698394539678E-01, 7.349919293946242E-03, \ -6.621044246635598E-01, 9.176320041970745E-01, 7.378997680603661E-03, \ -6.431249402968114E-01, -9.960239767584596E-01, 1.189113707782781E-03, \ -6.349167527421143E-01, -4.120238337350225E-02, 1.855565407496183E-02, \ -6.332996010231378E-01, 9.748499154546882E-01, 3.858727420800304E-03, \ -6.308194378333426E-01, -2.632109226108148E-01, 1.804417109814068E-02, \ -6.216612560681409E-01, 4.121887181945136E-01, 1.799934456348149E-02, \ -6.209382034591413E-01, 6.097444447472842E-01, 1.619622888897558E-02, \ -6.184436204963421E-01, 7.739873263881869E-01, 1.280285540627544E-02, \ -6.181782824659667E-01, -4.720385956358120E-01, 1.570128558680570E-02, \ -6.088138333002981E-01, 9.988834235712669E-01, 6.368095509394178E-04, \ -6.065399576093181E-01, -8.463858971291857E-01, 8.079219530748298E-03, \ -5.996620894961030E-01, -9.482291632711998E-01, 5.540693800633477E-03, \ -5.902607741689768E-01, 2.385643885392057E-01, 1.956867882471149E-02, \ -5.879157685226737E-01, -6.347809747856457E-01, 1.176279561786886E-02, \ -5.837357122734029E-01, -7.476017166168016E-01, 1.139197942656491E-02, \ -5.736831191631178E-01, 8.680031315190274E-01, 9.765401515377791E-03, \ -5.642269847367442E-01, -9.833709030918961E-01, 2.797162890164879E-03, \ -5.513432891392764E-01, 9.450770682538761E-01, 6.170899375503570E-03, \ -5.500959245098467E-01, -8.702213264603355E-01, 4.396899487663076E-03, \ -5.483041549056678E-01, 7.179049125370220E-02, 1.968682836966377E-02, \ -5.464176822976653E-01, -1.467074339338491E-01, 2.005834944791575E-02, \ -5.403151496840451E-01, -3.630610758750227E-01, 1.886598318155659E-02, \ -5.340189262268797E-01, 9.912655376872981E-01, 2.067175993092469E-03, \ -5.310500417455106E-01, 5.118198224616344E-01, 1.858069243154359E-02, \ -5.266542221288756E-01, 6.945596957359338E-01, 1.591896408992095E-02, \ -5.205326762839934E-01, -5.526298443835523E-01, 1.463536127791667E-02, \ -5.077007528436556E-01, -9.110215108206120E-01, 6.879755450888522E-03, \ -4.983192797981136E-01, -9.976115668643906E-01, 1.171541751761967E-03, \ -4.951332232653569E-01, 3.460504369406958E-01, 2.023874109373681E-02, \ -4.835426583725593E-01, 8.111430213132370E-01, 1.157971471365758E-02, \ -4.813959504258653E-01, -7.906922160702855E-01, 1.227086240600740E-02, \ -4.710786595525681E-01, -6.776468702229034E-01, 1.309017893729792E-02, \ -4.684016915514839E-01, -9.631060061929865E-01, 5.069810155479069E-03, \ -4.601634273592006E-01, 9.736184752433025E-01, 3.981032410636509E-03, \ -4.586406152579688E-01, 9.067429858222903E-01, 8.151450352060937E-03, \ -4.581246913316372E-01, 1.846374671629571E-01, 1.859836421630574E-02, \ -4.542591579155089E-01, -2.533998951051241E-02, 2.019107274450048E-02, \ -4.507016433960112E-01, -2.452585642576526E-01, 2.097607879874488E-02, \ -4.405266836969018E-01, -4.527844645321407E-01, 1.865598696449664E-02, \ -4.313857093444732E-01, 6.040918064374622E-01, 1.842506376270006E-02, \ -4.267485951806373E-01, -8.688547899404195E-01, 6.723705742819690E-03, \ -4.131499625978771E-01, 9.970815492711668E-01, 1.271249087845813E-03, \ -3.986015122530552E-01, 7.510577780393508E-01, 1.269074691033858E-02, \ -3.967149116103497E-01, -6.041689107858602E-01, 1.192636288654412E-02, \ -3.961555040155331E-01, 4.470760721116281E-01, 2.010362718935436E-02, \ -3.870311898550397E-01, -9.875044282645365E-01, 3.406124439417308E-03, \ -3.759111439580939E-01, 8.681044983359713E-01, 7.567587310258595E-03, \ -3.733018295823582E-01, 1.124745920090000E-01, 1.444272159271557E-02, \ -3.698211803848768E-01, 9.497944995362068E-01, 5.588072557089718E-03, \ -3.677520025284451E-01, -9.304735975401455E-01, 7.985180614906596E-03, \ -3.647799432566780E-01, -1.113354938202836E-01, 1.869502288898936E-02, \ -3.564395741412303E-01, -7.281106510086501E-01, 1.411781032844452E-02, \ -3.557949371891208E-01, -8.330285597968599E-01, 9.641510028740691E-03, \ -3.555243523154669E-01, 2.839179571854041E-01, 1.993717563297461E-02, \ -3.484889009386569E-01, -3.392883270625222E-01, 2.140162840707676E-02, \ -3.283812713294078E-01, -5.303954087605249E-01, 1.601217072102609E-02, \ -3.195420634648112E-01, 9.856964924833570E-01, 3.355668049705953E-03, \ -3.183691341673544E-01, 6.823032199063920E-01, 1.502246554463540E-02, \ -3.044813423163074E-01, 8.293787725761752E-01, 1.046325726611303E-02, \ -2.987630526075223E-01, 4.684092365905865E-02, 1.926775266958230E-02, \ -2.936532335470334E-01, 5.403974535032333E-01, 1.910165254855807E-02, \ -2.839114443643144E-01, -9.982115043292803E-01, 1.188632971361439E-03, \ -2.838714383237747E-01, 9.229409872704248E-01, 6.670754525457344E-03, \ -2.810131840539091E-01, -1.888679679442530E-01, 1.832810176225835E-02, \ -2.687507311235811E-01, -9.661991515046374E-01, 6.311482289862918E-03, \ -2.656987431438242E-01, -6.579434003777319E-01, 1.182247248408541E-02, \ -2.614828276593449E-01, 3.765883630233104E-01, 1.796650685355945E-02, \ -2.531943910872507E-01, -8.899457540567935E-01, 1.092169990171894E-02, \ -2.406846427640522E-01, -7.855631193658050E-01, 1.359117656318325E-02, \ -2.391816880092877E-01, -4.306619043003660E-01, 2.108838808511827E-02, \ -2.355724334549767E-01, 2.049280038734326E-01, 2.190235001744360E-02, \ -2.230244166633031E-01, 9.979412002068919E-01, 1.240219580715109E-03, \ -2.143016309053875E-01, 7.672825366517191E-01, 1.532929818887211E-02, \ -2.084210826685112E-01, -6.026618831861471E-01, 1.266723448088261E-02, \ -2.074608754565781E-01, 9.668302372454330E-01, 5.784281081186120E-03, \ -1.994470236746966E-01, -4.262641530424785E-02, 2.336758693844741E-02, \ -1.953909451600504E-01, 8.884510132587173E-01, 9.639725933265000E-03, \ -1.947973443282949E-01, 6.327934412393972E-01, 1.604045001285653E-02, \ -1.934348429848317E-01, -2.676344080255245E-01, 1.945754749492376E-02, \ -1.731674619232558E-01, 4.594347331929800E-01, 1.701418105871642E-02, \ -1.581108634025118E-01, -9.886241341680647E-01, 3.738115075160524E-03, \ -1.422635614677805E-01, -9.353836759115295E-01, 9.131973629103902E-03, \ -1.361305424868328E-01, 1.223782786800707E-01, 2.022098154521878E-02, \ -1.332706201055330E-01, -7.135796064753009E-01, 1.658816867334942E-02, \ -1.279679844994012E-01, -8.428571211216312E-01, 1.270368784787859E-02, \ -1.215680553809675E-01, -5.177010109986793E-01, 2.044565322938263E-02, \ -1.191841609577679E-01, 3.166199536093801E-01, 2.232566149349017E-02, \ -1.030306575568989E-01, 5.564353141202014E-01, 1.319022417392010E-02, \ -1.010032725708720E-01, 8.358781872733483E-01, 1.317927677377359E-02, \ -9.793911367017349E-02, -3.496629047055283E-01, 2.036641167270025E-02, \ -9.632162801653921E-02, 9.888966773648641E-01, 3.635491187724198E-03, \ -9.413622131664506E-02, -1.384648595071072E-01, 2.325132772759284E-02, \ -9.173762319021858E-02, 9.377720732845000E-01, 8.484100706145753E-03, \ -8.621270959290740E-02, 7.067235284679263E-01, 1.663872363860805E-02, \ -4.600495484763667E-02, 4.189736454726613E-02, 2.011405200689851E-02, \ -3.846886242278941E-02, 5.343444763759839E-01, 7.629129920225949E-03, \ -3.114682416899431E-02, -9.984328758619065E-01, 1.215239197082301E-03, \ -3.079267631383417E-02, -6.283320709748856E-01, 1.866968865866494E-02, \ -2.943594515930726E-02, -9.691705324016726E-01, 6.300149444345140E-03, \ -1.716717474844928E-02, -7.802924106209882E-01, 1.460622280342255E-02, \ -1.471848835947739E-02, -8.938525086535020E-01, 1.128301163750197E-02, \ -9.971581147176094E-03, 2.306776723300077E-01, 2.246786582285274E-02, \ -9.401058469724652E-03, 4.283083438750301E-01, 2.037055156805384E-02, \ 0.000000000000000E+00, 0.000000000000000E+00, 5.253249918853668E-04, \ 9.401058469724652E-03, -4.283083438750301E-01, 2.037055156805384E-02, \ 9.971581147176094E-03, -2.306776723300077E-01, 2.246786582285274E-02, \ 1.471848835947739E-02, 8.938525086535020E-01, 1.128301163750197E-02, \ 1.716717474844928E-02, 7.802924106209882E-01, 1.460622280342255E-02, \ 2.943594515930726E-02, 9.691705324016726E-01, 6.300149444345140E-03, \ 3.079267631383417E-02, 6.283320709748856E-01, 1.866968865866494E-02, \ 3.114682416899431E-02, 9.984328758619065E-01, 1.215239197082301E-03, \ 3.846886242278941E-02, -5.343444763759839E-01, 7.629129920225949E-03, \ 4.600495484763667E-02, -4.189736454726613E-02, 2.011405200689851E-02, \ 8.621270959290740E-02, -7.067235284679263E-01, 1.663872363860805E-02, \ 9.173762319021858E-02, -9.377720732845000E-01, 8.484100706145753E-03, \ 9.413622131664506E-02, 1.384648595071072E-01, 2.325132772759284E-02, \ 9.632162801653921E-02, -9.888966773648641E-01, 3.635491187724198E-03, \ 9.793911367017349E-02, 3.496629047055283E-01, 2.036641167270025E-02, \ 1.010032725708720E-01, -8.358781872733483E-01, 1.317927677377359E-02, \ 1.030306575568989E-01, -5.564353141202014E-01, 1.319022417392010E-02, \ 1.191841609577679E-01, -3.166199536093801E-01, 2.232566149349017E-02, \ 1.215680553809675E-01, 5.177010109986793E-01, 2.044565322938263E-02, \ 1.279679844994012E-01, 8.428571211216312E-01, 1.270368784787859E-02, \ 1.332706201055330E-01, 7.135796064753009E-01, 1.658816867334942E-02, \ 1.361305424868328E-01, -1.223782786800707E-01, 2.022098154521878E-02, \ 1.422635614677805E-01, 9.353836759115295E-01, 9.131973629103902E-03, \ 1.581108634025118E-01, 9.886241341680647E-01, 3.738115075160524E-03, \ 1.731674619232558E-01, -4.594347331929800E-01, 1.701418105871642E-02, \ 1.934348429848317E-01, 2.676344080255245E-01, 1.945754749492376E-02, \ 1.947973443282949E-01, -6.327934412393972E-01, 1.604045001285653E-02, \ 1.953909451600504E-01, -8.884510132587173E-01, 9.639725933265000E-03, \ 1.994470236746966E-01, 4.262641530424785E-02, 2.336758693844741E-02, \ 2.074608754565781E-01, -9.668302372454330E-01, 5.784281081186120E-03, \ 2.084210826685112E-01, 6.026618831861471E-01, 1.266723448088261E-02, \ 2.143016309053875E-01, -7.672825366517191E-01, 1.532929818887211E-02, \ 2.230244166633031E-01, -9.979412002068919E-01, 1.240219580715109E-03, \ 2.355724334549767E-01, -2.049280038734326E-01, 2.190235001744360E-02, \ 2.391816880092877E-01, 4.306619043003660E-01, 2.108838808511827E-02, \ 2.406846427640522E-01, 7.855631193658050E-01, 1.359117656318325E-02, \ 2.531943910872507E-01, 8.899457540567935E-01, 1.092169990171894E-02, \ 2.614828276593449E-01, -3.765883630233104E-01, 1.796650685355945E-02, \ 2.656987431438242E-01, 6.579434003777319E-01, 1.182247248408541E-02, \ 2.687507311235811E-01, 9.661991515046374E-01, 6.311482289862918E-03, \ 2.810131840539091E-01, 1.888679679442530E-01, 1.832810176225835E-02, \ 2.838714383237747E-01, -9.229409872704248E-01, 6.670754525457344E-03, \ 2.839114443643144E-01, 9.982115043292803E-01, 1.188632971361439E-03, \ 2.936532335470334E-01, -5.403974535032333E-01, 1.910165254855807E-02, \ 2.987630526075223E-01, -4.684092365905865E-02, 1.926775266958230E-02, \ 3.044813423163074E-01, -8.293787725761752E-01, 1.046325726611303E-02, \ 3.183691341673544E-01, -6.823032199063920E-01, 1.502246554463540E-02, \ 3.195420634648112E-01, -9.856964924833570E-01, 3.355668049705953E-03, \ 3.283812713294078E-01, 5.303954087605249E-01, 1.601217072102609E-02, \ 3.484889009386569E-01, 3.392883270625222E-01, 2.140162840707676E-02, \ 3.555243523154669E-01, -2.839179571854041E-01, 1.993717563297461E-02, \ 3.557949371891208E-01, 8.330285597968599E-01, 9.641510028740691E-03, \ 3.564395741412303E-01, 7.281106510086501E-01, 1.411781032844452E-02, \ 3.647799432566780E-01, 1.113354938202836E-01, 1.869502288898936E-02, \ 3.677520025284451E-01, 9.304735975401455E-01, 7.985180614906596E-03, \ 3.698211803848768E-01, -9.497944995362068E-01, 5.588072557089718E-03, \ 3.733018295823582E-01, -1.124745920090000E-01, 1.444272159271557E-02, \ 3.759111439580939E-01, -8.681044983359713E-01, 7.567587310258595E-03, \ 3.870311898550397E-01, 9.875044282645365E-01, 3.406124439417308E-03, \ 3.961555040155331E-01, -4.470760721116281E-01, 2.010362718935436E-02, \ 3.967149116103497E-01, 6.041689107858602E-01, 1.192636288654412E-02, \ 3.986015122530552E-01, -7.510577780393508E-01, 1.269074691033858E-02, \ 4.131499625978771E-01, -9.970815492711668E-01, 1.271249087845813E-03, \ 4.267485951806373E-01, 8.688547899404195E-01, 6.723705742819690E-03, \ 4.313857093444732E-01, -6.040918064374622E-01, 1.842506376270006E-02, \ 4.405266836969018E-01, 4.527844645321407E-01, 1.865598696449664E-02, \ 4.507016433960112E-01, 2.452585642576526E-01, 2.097607879874488E-02, \ 4.542591579155089E-01, 2.533998951051241E-02, 2.019107274450048E-02, \ 4.581246913316372E-01, -1.846374671629571E-01, 1.859836421630574E-02, \ 4.586406152579688E-01, -9.067429858222903E-01, 8.151450352060937E-03, \ 4.601634273592006E-01, -9.736184752433025E-01, 3.981032410636509E-03, \ 4.684016915514839E-01, 9.631060061929865E-01, 5.069810155479069E-03, \ 4.710786595525681E-01, 6.776468702229034E-01, 1.309017893729792E-02, \ 4.813959504258653E-01, 7.906922160702855E-01, 1.227086240600740E-02, \ 4.835426583725593E-01, -8.111430213132370E-01, 1.157971471365758E-02, \ 4.951332232653569E-01, -3.460504369406958E-01, 2.023874109373681E-02, \ 4.983192797981136E-01, 9.976115668643906E-01, 1.171541751761967E-03, \ 5.077007528436556E-01, 9.110215108206120E-01, 6.879755450888522E-03, \ 5.205326762839934E-01, 5.526298443835523E-01, 1.463536127791667E-02, \ 5.266542221288756E-01, -6.945596957359338E-01, 1.591896408992095E-02, \ 5.310500417455106E-01, -5.118198224616344E-01, 1.858069243154359E-02, \ 5.340189262268797E-01, -9.912655376872981E-01, 2.067175993092469E-03, \ 5.403151496840451E-01, 3.630610758750227E-01, 1.886598318155659E-02, \ 5.464176822976653E-01, 1.467074339338491E-01, 2.005834944791575E-02, \ 5.483041549056678E-01, -7.179049125370220E-02, 1.968682836966377E-02, \ 5.500959245098467E-01, 8.702213264603355E-01, 4.396899487663076E-03, \ 5.513432891392764E-01, -9.450770682538761E-01, 6.170899375503570E-03, \ 5.642269847367442E-01, 9.833709030918961E-01, 2.797162890164879E-03, \ 5.736831191631178E-01, -8.680031315190274E-01, 9.765401515377791E-03, \ 5.837357122734029E-01, 7.476017166168016E-01, 1.139197942656491E-02, \ 5.879157685226737E-01, 6.347809747856457E-01, 1.176279561786886E-02, \ 5.902607741689768E-01, -2.385643885392057E-01, 1.956867882471149E-02, \ 5.996620894961030E-01, 9.482291632711998E-01, 5.540693800633477E-03, \ 6.065399576093181E-01, 8.463858971291857E-01, 8.079219530748298E-03, \ 6.088138333002981E-01, -9.988834235712669E-01, 6.368095509394178E-04, \ 6.181782824659667E-01, 4.720385956358120E-01, 1.570128558680570E-02, \ 6.184436204963421E-01, -7.739873263881869E-01, 1.280285540627544E-02, \ 6.209382034591413E-01, -6.097444447472842E-01, 1.619622888897558E-02, \ 6.216612560681409E-01, -4.121887181945136E-01, 1.799934456348149E-02, \ 6.308194378333426E-01, 2.632109226108148E-01, 1.804417109814068E-02, \ 6.332996010231378E-01, -9.748499154546882E-01, 3.858727420800304E-03, \ 6.349167527421143E-01, 4.120238337350225E-02, 1.855565407496183E-02, \ 6.431249402968114E-01, 9.960239767584596E-01, 1.189113707782781E-03, \ 6.621044246635598E-01, -9.176320041970745E-01, 7.378997680603661E-03, \ 6.743529219450092E-01, 9.106698394539678E-01, 7.349919293946242E-03, \ 6.763078266684166E-01, -1.264181240942355E-01, 1.836539066857489E-02, \ 6.791674419638026E-01, 6.963055362251113E-01, 1.115720692184079E-02, \ 6.843864494264393E-01, 5.640703334807048E-01, 1.247073498122494E-02, \ 6.874559480675843E-01, 9.781638816357989E-01, 3.101643133626598E-03, \ 6.952697432642575E-01, 8.074711595576919E-01, 9.903249938089028E-03, \ 7.030786952640691E-01, 3.737683313436290E-01, 1.533113926314000E-02, \ 7.038938546524356E-01, -6.992970712529386E-01, 1.317427859481092E-02, \ 7.044541730236628E-01, -8.417075739142680E-01, 9.820401163435438E-03, \ 7.050386520037029E-01, -5.147871049065931E-01, 1.577829434551910E-02, \ 7.050966153827319E-01, -3.088933084722713E-01, 1.701475236717927E-02, \ 7.058491208433765E-01, -9.915756755872566E-01, 1.790261844614419E-03, \ 7.120337647362697E-01, 1.543105022946922E-01, 1.667558344244733E-02, \ 7.425465126897265E-01, -9.565892784834152E-01, 4.976897852233662E-03, \ 7.525943724917873E-01, 9.538377812626558E-01, 4.657805305389900E-03, \ 7.531768231132037E-01, -1.201386227993326E-02, 1.642203608617212E-02, \ 7.586912864075982E-01, 9.961911332837330E-01, 1.179272785443735E-03, \ 7.638158346191554E-01, 6.256899643054369E-01, 1.089753036742033E-02, \ 7.650517717498729E-01, 4.715771704307840E-01, 1.255037589648692E-02, \ 7.655483726416725E-01, 8.750797093910616E-01, 7.985877894766822E-03, \ 7.715857235482023E-01, -9.983428621580931E-01, 5.452222266440912E-04, \ 7.761306169624727E-01, 7.501004998319117E-01, 9.930943224422817E-03, \ 7.780033996472984E-01, 2.651062610509234E-01, 1.437115393673534E-02, \ 7.781640573729546E-01, -1.995944750196611E-01, 1.546595460903855E-02, \ 7.785783303955014E-01, -6.125037703604832E-01, 1.287366180571384E-02, \ 7.801982799083059E-01, -7.770472357073510E-01, 1.015003094959520E-02, \ 7.814359340875883E-01, -4.148826331713472E-01, 1.479944058585885E-02, \ 7.828790059504277E-01, -8.970932838288118E-01, 7.123319843648826E-03, \ 8.152169502901689E-01, -9.831801913034185E-01, 2.619950174549044E-03, \ 8.181510041117529E-01, 1.013221207184385E-01, 1.380702843362417E-02, \ 8.222752044712189E-01, 9.828983653726329E-01, 2.569844448228937E-03, \ 8.328917808999070E-01, 9.275746498999357E-01, 5.345327410698648E-03, \ 8.341324042868387E-01, 5.413042996556211E-01, 1.028726411584244E-02, \ 8.342806635072800E-01, 3.686663614256265E-01, 1.185649053487261E-02, \ 8.387107616534492E-01, 8.225135460279916E-01, 8.023995882685042E-03, \ 8.420990261538619E-01, -8.700843845073450E-02, 1.361576981188029E-02, \ 8.440484090367564E-01, -6.995813955156258E-01, 9.801510245897441E-03, \ 8.454498037908205E-01, -5.197883189451455E-01, 1.190856918137506E-02, \ 8.457711905447103E-01, -3.060565758105315E-01, 1.313083077355583E-02, \ 8.465974052776020E-01, 6.804500384380086E-01, 9.439844848201484E-03, \ 8.483308513877643E-01, -8.420081277059801E-01, 7.356656581421614E-03, \ 8.488444646215817E-01, -9.417487190138607E-01, 4.527482466935922E-03, \ 8.688111752985119E-01, 2.062730881400507E-01, 1.032123607597266E-02, \ 8.768368119879948E-01, -9.972195337276928E-01, 7.824958500505416E-04, \ 8.787467882854940E-01, 9.974975541031985E-01, 7.520196736734306E-04, \ 8.916399066676414E-01, 4.478690090838509E-01, 8.958243051785242E-03, \ 8.925866230961302E-01, 9.651738737461483E-01, 3.087139101703460E-03, \ 8.934822042254417E-01, 8.849206485200981E-01, 5.481269950434707E-03, \ 8.955650716170729E-01, 2.889828380654945E-02, 1.141690753127995E-02, \ 8.990136642719798E-01, -4.154161042204226E-01, 1.027033600307130E-02, \ 8.991432933902236E-01, -6.161569102595980E-01, 8.649321074038529E-03, \ 8.994183334513204E-01, 7.589002650753883E-01, 7.412012270186419E-03, \ 9.000160662012473E-01, -1.936545205467035E-01, 1.105560603537899E-02, \ 9.006876027333818E-01, -7.738025214543742E-01, 6.953572521005407E-03, \ 9.021900638531539E-01, -8.986885201991707E-01, 4.735976500809632E-03, \ 9.026928782557422E-01, 5.971154860482422E-01, 8.134575081016936E-03, \ 9.033753194459962E-01, -9.739301226929417E-01, 2.430898666967969E-03, \ 9.058866443920447E-01, 2.915118591864504E-01, 7.312514214991043E-03, \ 9.376865583713452E-01, 1.472997681505319E-01, 8.802757771504873E-03, \ 9.387594609269243E-01, 9.896419412770018E-01, 1.315181972642427E-03, \ 9.396692618824576E-01, 9.333268377293767E-01, 3.176964275867470E-03, \ 9.401222897124206E-01, -5.208371173674092E-01, 7.080933689521712E-03, \ 9.414068461363603E-01, 8.319946383779213E-01, 4.899221558401311E-03, \ 9.421296116189286E-01, -3.072458818807862E-01, 8.166950645809414E-03, \ 9.422279295242960E-01, -8.430010110128885E-01, 4.356685968058319E-03, \ 9.424045442737207E-01, -6.965818136607429E-01, 5.492047852799914E-03, \ 9.425924799508709E-01, -7.723036765423268E-02, 8.594457541849910E-03, \ 9.432551757252079E-01, 6.778512313399264E-01, 5.997726172859794E-03, \ 9.432745759141794E-01, 3.578284894473978E-01, 6.177743639544537E-03, \ 9.448077504847031E-01, -9.425192762886759E-01, 2.715142333531406E-03, \ 9.450858475738110E-01, 5.025373008969878E-01, 6.252666523418040E-03, \ 9.469548060003440E-01, -9.927873239383316E-01, 9.693950321163949E-04, \ 9.664977673747553E-01, -7.669983680205528E-01, 2.614941215020715E-03, \ 9.708137869429159E-01, -4.239389021325329E-01, 5.141869518483292E-03, \ 9.709279126257970E-01, 2.562383260371136E-01, 5.255024629747484E-03, \ 9.711831524640260E-01, 7.579747866842650E-01, 3.663853318492690E-03, \ 9.715318079839266E-01, -6.114344673195419E-01, 4.212935529909797E-03, \ 9.726983304977663E-01, 4.425763588680746E-02, 5.881914856745899E-03, \ 9.728709777782690E-01, 9.691292467666289E-01, 1.466141068305907E-03, \ 9.729306672713298E-01, -1.937971855968040E-01, 5.661441805111854E-03, \ 9.734565439099904E-01, 8.924228057613435E-01, 2.621925808197151E-03, \ 9.736351786214140E-01, 5.825032309876242E-01, 4.276722297762739E-03, \ 9.737646096663447E-01, -8.979365374145354E-01, 2.417846375635086E-03, \ 9.768576153531923E-01, -9.720516240923431E-01, 1.260176677733168E-03, \ 9.799683347097561E-01, 9.982787940792663E-01, 2.802539460088801E-04, \ 9.805838302292789E-01, 4.186960243528708E-01, 4.224419641522761E-03, \ 9.828402728207225E-01, -8.130859429654207E-01, 1.813569870463969E-03, \ 9.870995148246587E-01, -9.971266172517755E-01, 2.522985579422540E-04, \ 9.882983824911455E-01, -7.029568166797684E-01, 2.101767111893595E-03, \ 9.896446181606325E-01, 8.258526268641876E-01, 1.761173631057456E-03, \ 9.896878613799838E-01, 6.734414823238595E-01, 2.206204039428005E-03, \ 9.897745584940826E-01, -3.209639101085088E-01, 3.026155349324961E-03, \ 9.904412956303582E-01, -5.265151744794012E-01, 2.514644595413010E-03, \ 9.910529016163073E-01, 1.720232075920507E-01, 2.834840262020965E-03, \ 9.914404533622192E-01, -7.370377576026632E-02, 3.114508431996894E-03, \ 9.931100571448706E-01, 9.398758417699402E-01, 9.653046269879767E-04, \ 9.939777572418940E-01, -9.377670381442861E-01, 9.071335269558794E-04, \ 9.955419051779023E-01, 5.028006893760714E-01, 1.625315064214383E-03, \ 9.959458468526172E-01, -8.639404647925895E-01, 9.127209022448868E-04, \ 9.963148656482692E-01, 9.861307505276973E-01, 3.364793817721787E-04, \ 9.966209533584591E-01, 3.237318892379179E-01, 1.736701233968157E-03, \ 9.977221586114358E-01, 6.019952067889782E-01, 5.964708123101566E-04, \ 9.978435386703776E-01, -7.692080150297662E-01, 6.598609318533428E-04, \ 9.982115219214424E-01, -6.305047404346029E-01, 8.136830618787968E-04, \ 9.983293539476047E-01, -9.835120159252404E-01, 2.181997023647311E-04, \ 9.984416520882323E-01, 8.814083896367437E-01, 4.548127997472904E-04, \ 9.984853824993025E-01, 7.518363345257131E-01, 6.752050933944545E-04, \ 9.985812215892117E-01, -2.098862069679553E-01, 9.932558396288942E-04, \ 9.985820051950299E-01, -4.311577677096960E-01, 8.506787489756313E-04, \ 9.987179482199477E-01, 6.341055456784180E-02, 9.427263494251746E-04 ] ) return xyw def smr50 ( ): #*****************************************************************************80 # ## smr50 returns the SMR rule of degree 50. # # Discussion: # # DEGREE: 50 # POINTS CARDINALITY: 454 # NORM INF MOMS. RESIDUAL: 1.97162e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*454), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.985305923732772E-01, 9.480346609653949E-01, 3.637016044890175E-04, \ -9.983266574377337E-01, -7.135200571279965E-01, 8.681375001274842E-04, \ -9.982410599710965E-01, -5.061487385182745E-02, 1.210422814431021E-03, \ -9.981979630190073E-01, 1.943963798210550E-01, 1.209667416017868E-03, \ -9.981164101550407E-01, 4.217828123427281E-01, 1.100221981712261E-03, \ -9.980251256813344E-01, 8.409407151717826E-01, 6.790256958329296E-04, \ -9.978977416561483E-01, -5.175396836215825E-01, 1.209910288842294E-03, \ -9.977749235731450E-01, -8.787383894116004E-01, 6.804808145574241E-04, \ -9.974790513531082E-01, -2.987478462479398E-01, 1.485043396561256E-03, \ -9.973044005791738E-01, 9.966139708183203E-01, 1.024593234561320E-04, \ -9.965354581345114E-01, -9.625283354808352E-01, 5.086867261717252E-04, \ -9.959776528397177E-01, 5.865612330340912E-01, 1.475073552829635E-03, \ -9.958674494848857E-01, 7.184881012827657E-01, 1.314678451882094E-03, \ -9.958634171963171E-01, -9.964330603430479E-01, 1.378555297245596E-04, \ -9.899892964541681E-01, -8.034025241583582E-01, 2.063321727799165E-03, \ -9.890089603003986E-01, -1.607654105825233E-01, 3.171831815687111E-03, \ -9.889269890822903E-01, 9.792253114023887E-01, 6.925166147590135E-04, \ -9.888556249081619E-01, 9.011374451124298E-01, 1.524076231835903E-03, \ -9.883405484188146E-01, 3.140956912031643E-01, 3.326070006645496E-03, \ -9.882926852196964E-01, 7.591140506738633E-02, 3.713229391963024E-03, \ -9.879532633546659E-01, -6.253049497236600E-01, 2.968377985270547E-03, \ -9.862738466801083E-01, -4.136828994040758E-01, 3.792003832590160E-03, \ -9.840867690629249E-01, -9.225459592561057E-01, 1.716688686998262E-03, \ -9.834561801290923E-01, 7.913470127721602E-01, 2.467251464100417E-03, \ -9.829084684207806E-01, 4.958738236441704E-01, 3.605246991559088E-03, \ -9.799751230610935E-01, -9.858070723372447E-01, 8.062256820069726E-04, \ -9.773121022170035E-01, 6.531868802837602E-01, 3.655328649772478E-03, \ -9.727540699799997E-01, -2.463858035039539E-01, 3.968311046518957E-03, \ -9.722508392684289E-01, 2.227204587069684E-01, 2.881691797859937E-03, \ -9.706187607468760E-01, -7.290537686894693E-01, 3.938655209703868E-03, \ -9.704346881779157E-01, 9.463998760417839E-01, 1.815054306514290E-03, \ -9.690510704309230E-01, 9.956152727894065E-01, 4.874122727335260E-04, \ -9.675183125664917E-01, -3.873668624805015E-02, 6.258912209048882E-03, \ -9.670967144416286E-01, -5.346820717217893E-01, 5.020688484630141E-03, \ -9.655166141119431E-01, -8.589490689754655E-01, 3.424882118788690E-03, \ -9.627685982819859E-01, 8.574258075931914E-01, 3.211357083932979E-03, \ -9.611985315766414E-01, 1.735034523650290E-01, 4.470806430187272E-03, \ -9.597845726633061E-01, 3.970047952525823E-01, 6.128594443133615E-03, \ -9.569446290012320E-01, -3.378216199983041E-01, 5.083719898994831E-03, \ -9.565067320986410E-01, -9.583763747944724E-01, 2.042573269760935E-03, \ -9.529509863706143E-01, 7.367253684069424E-01, 4.607147767328114E-03, \ -9.509009916467068E-01, -9.982452717308193E-01, 4.171743785231584E-04, \ -9.498639131139113E-01, 5.672749857805497E-01, 5.975731307616273E-03, \ -9.428689649793603E-01, -6.526060553577299E-01, 5.505889774975882E-03, \ -9.422311181031663E-01, 9.769229657788217E-01, 1.605353293384605E-03, \ -9.375241836457983E-01, -4.577530187027701E-01, 5.705829120945821E-03, \ -9.362131629000300E-01, -1.507446207119618E-01, 8.504765626649076E-03, \ -9.339474938107682E-01, 9.120768210172238E-01, 3.338622941804765E-03, \ -9.316644572520522E-01, -7.908094170683131E-01, 5.751538344933908E-03, \ -9.314325437683882E-01, 7.308639756184374E-02, 8.950456494516651E-03, \ -9.304457837028240E-01, -9.108477682553909E-01, 3.622093803410868E-03, \ -9.262042777363618E-01, 2.926429789075467E-01, 8.847143966496282E-03, \ -9.205873982096271E-01, 8.098896505724084E-01, 5.174844527226764E-03, \ -9.162051560377870E-01, -9.832510479457329E-01, 1.819552993042389E-03, \ -9.145628768323527E-01, -2.911965871109570E-01, 6.354190461823213E-03, \ -9.144568861286890E-01, 6.634543776500917E-01, 6.992029249399327E-03, \ -9.134662288030968E-01, 4.776130498503005E-01, 8.193380404605263E-03, \ -9.126046852400858E-01, 9.959169009245570E-01, 7.303402358793004E-04, \ -9.084013096944704E-01, -5.810944597640583E-01, 6.912234750082650E-03, \ -8.968296850710641E-01, -4.128318260767174E-01, 6.809730423186475E-03, \ -8.963106431292505E-01, 9.531579778618777E-01, 2.914835462196634E-03, \ -8.901833704330284E-01, -8.608019888123171E-01, 5.050561896084555E-03, \ -8.884475404720591E-01, -4.181808934399530E-02, 1.158653342037486E-02, \ -8.859496918290896E-01, -7.137986488176715E-01, 8.297704906842986E-03, \ -8.826270793702349E-01, 8.736037565380022E-01, 4.992525221172924E-03, \ -8.823557325667086E-01, 1.833542443150059E-01, 1.150671440741034E-02, \ -8.803378140572387E-01, -9.483904752475437E-01, 3.713568296274433E-03, \ -8.730496783252757E-01, -2.233431485071996E-01, 9.317119532426758E-03, \ -8.699283953657505E-01, 3.852358620688430E-01, 1.027156006726837E-02, \ -8.698133028410201E-01, 7.486827472812273E-01, 7.596749165870595E-03, \ -8.674834848675760E-01, 5.836354021401285E-01, 9.310768477516692E-03, \ -8.628243813571611E-01, -9.960431212097594E-01, 9.977579306457195E-04, \ -8.624814683206987E-01, 9.841369657891215E-01, 1.842174250748435E-03, \ -8.581906826960382E-01, -5.182071016007672E-01, 9.222800088580358E-03, \ -8.484873092060258E-01, -8.116205306074403E-01, 5.448026047767842E-03, \ -8.375416835189680E-01, 9.244249381249888E-01, 4.359562847763335E-03, \ -8.343496291886240E-01, -3.560928009556643E-01, 1.173308803213457E-02, \ -8.291306871234821E-01, 6.960605157818649E-02, 1.390910739512651E-02, \ -8.281553984054720E-01, -6.382569464166583E-01, 9.693436224505143E-03, \ -8.256425444491163E-01, -9.054076217011587E-01, 5.816411318368521E-03, \ -8.223579984614887E-01, 8.269951489970134E-01, 7.127087970713289E-03, \ -8.215593436322257E-01, 9.981381538674631E-01, 6.329945045794524E-04, \ -8.198483858368308E-01, -1.319278740037157E-01, 1.298320952391481E-02, \ -8.192027189051302E-01, 2.877778785137557E-01, 1.265773788043916E-02, \ -8.172502785117453E-01, -9.750039267897708E-01, 3.134812108850403E-03, \ -8.138299706643672E-01, 4.972544598166810E-01, 1.161528697363953E-02, \ -8.115048842276773E-01, 6.785974006783519E-01, 1.000389489115020E-02, \ -8.033489337701412E-01, -7.623411898836773E-01, 7.618682602864780E-03, \ -7.981451309405014E-01, 9.655610226211084E-01, 3.238149495801071E-03, \ -7.788793515049757E-01, -4.659125664753414E-01, 1.294788836398086E-02, \ -7.676616475483181E-01, 8.903050218772064E-01, 6.412981842164176E-03, \ -7.654405876460623E-01, -2.609719605681909E-01, 1.510691545326006E-02, \ -7.651705117791751E-01, -5.933719404029307E-01, 7.689899801767004E-03, \ -7.610553487070951E-01, -8.537787359055480E-01, 8.005675846962551E-03, \ -7.598494916125437E-01, 1.822273140486022E-01, 1.528388680362909E-02, \ -7.579923742217070E-01, -9.945462254206379E-01, 1.550380002631925E-03, \ -7.554414721363940E-01, 7.704489057786914E-01, 9.613889207061148E-03, \ -7.546303325899156E-01, -2.587451873434423E-02, 1.541716632386868E-02, \ -7.533501105520592E-01, 4.028033457447762E-01, 1.416780003145239E-02, \ -7.512634680369265E-01, -9.427500341739973E-01, 5.278060834005935E-03, \ -7.492677967965817E-01, 9.893278319960217E-01, 1.942720461021166E-03, \ -7.476477835194629E-01, 5.993754192648574E-01, 1.240433786628891E-02, \ -7.384396341741885E-01, -7.049337544138190E-01, 1.019806600177946E-02, \ -7.178686225860993E-01, 9.426175650021613E-01, 5.076879608670298E-03, \ -6.981541470167513E-01, -3.738996976336288E-01, 1.623617174158692E-02, \ -6.930270182761278E-01, -5.503057726865391E-01, 1.252261832635268E-02, \ -6.914007366726129E-01, -1.492403377321120E-01, 1.687175767189600E-02, \ -6.898255514942709E-01, 8.450597437929396E-01, 9.044588739380572E-03, \ -6.878471762364344E-01, -7.980792470880590E-01, 9.683099148036134E-03, \ -6.874914713445559E-01, 9.985765065838036E-01, 5.429828741714135E-04, \ -6.851758646966849E-01, 2.991299533883399E-01, 1.680000628152785E-02, \ -6.841372891501616E-01, -9.759846205669235E-01, 3.792981482377291E-03, \ -6.824533415259976E-01, 7.012478423815675E-01, 1.242282959150627E-02, \ -6.806130791896147E-01, 8.613441527468559E-02, 1.715469593857349E-02, \ -6.782455218903122E-01, 5.106365783701324E-01, 1.495469178663973E-02, \ -6.767016667485439E-01, -9.023128892125745E-01, 7.148516270448834E-03, \ -6.589112285487670E-01, 9.766144758417425E-01, 3.310403467016667E-03, \ -6.511681540558421E-01, -6.631624128792538E-01, 1.080993463231836E-02, \ -6.380516344996316E-01, -9.971292836795032E-01, 1.091941596727160E-03, \ -6.321934701591331E-01, 9.112877114102699E-01, 6.899365963636340E-03, \ -6.189763674514923E-01, -2.549410517879415E-01, 1.680578646075412E-02, \ -6.156902457901138E-01, -4.609743414379315E-01, 1.446782156032898E-02, \ -6.095366081540551E-01, -3.536699015280872E-02, 1.850017035472999E-02, \ -6.064980319841019E-01, 7.855933379724550E-01, 1.191421549804811E-02, \ -6.037838321468384E-01, -8.588880336516307E-01, 7.493653196531501E-03, \ -6.032572636799473E-01, 6.191506051681956E-01, 1.533794488328530E-02, \ -6.029215218823031E-01, 4.121372818661574E-01, 1.746667230493666E-02, \ -6.004670419231046E-01, 2.003417792141365E-01, 1.853576294985650E-02, \ -5.978165937113178E-01, -9.464336654728625E-01, 6.209112452624394E-03, \ -5.973624658830221E-01, -7.522142533728916E-01, 1.070955771848203E-02, \ -5.972383581448467E-01, 9.955134418355728E-01, 1.205515802358963E-03, \ -5.775575710831099E-01, -5.936186239487227E-01, 1.108117334138420E-02, \ -5.716545691484377E-01, 9.586937694828399E-01, 4.477003194366252E-03, \ -5.544501743841143E-01, -9.859194586440739E-01, 2.990668121908608E-03, \ -5.533389067322111E-01, 8.727090179141404E-01, 7.641422231771522E-03, \ -5.508248111710804E-01, -3.360687262652585E-01, 1.326315896795831E-02, \ -5.269836692039951E-01, -1.373273675486175E-01, 1.846993932273529E-02, \ -5.252683048124628E-01, 7.769369828819343E-02, 1.828457505601571E-02, \ -5.232549472077624E-01, -8.262684949558237E-01, 8.105817403692208E-03, \ -5.216149653619029E-01, -4.944286105148744E-01, 1.099366935751496E-02, \ -5.189971990652680E-01, 5.251343160031084E-01, 1.801382551804368E-02, \ -5.187072221708287E-01, 7.127559592388867E-01, 1.475721541133735E-02, \ -5.157523922022348E-01, -6.649848553773774E-01, 1.035112521727110E-02, \ -5.154577487348173E-01, 3.146569819892138E-01, 1.881013777037231E-02, \ -5.121209365416318E-01, 9.881269957126972E-01, 2.581279958818058E-03, \ -5.085478436271724E-01, -9.062214676374273E-01, 7.876549270964693E-03, \ -4.890864408748029E-01, 9.331958642967023E-01, 6.252083630599476E-03, \ -4.830798048819471E-01, 8.307910647681210E-01, 9.069844919775074E-03, \ -4.769568695143335E-01, -7.406437471378572E-01, 9.792607423330369E-03, \ -4.711384868324521E-01, -9.982442886371089E-01, 9.977513750498068E-04, \ -4.670429883275934E-01, -3.837258048261876E-01, 1.481809931562225E-02, \ -4.666978361533338E-01, -9.638780668495475E-01, 5.093634425116185E-03, \ -4.583860333911172E-01, -2.194459707654301E-01, 1.399842259428002E-02, \ -4.488372720482744E-01, 1.852523019019599E-01, 1.562937178489875E-02, \ -4.466182114907417E-01, 1.045052032899272E-02, 9.145117658682660E-03, \ -4.398969646289078E-01, -5.643439180041001E-01, 1.536885553161082E-02, \ -4.286607785443331E-01, 6.284182834880983E-01, 1.704743034990286E-02, \ -4.281803723972377E-01, 4.257307629052356E-01, 1.891821754399137E-02, \ -4.251215127406949E-01, 9.990156228445619E-01, 8.538043330161814E-04, \ -4.118280892991981E-01, 9.714759276031080E-01, 4.880101949369545E-03, \ -4.079009162767762E-01, -8.127761432326117E-01, 9.682944715935253E-03, \ -4.061050423178847E-01, -4.674050637680804E-02, 1.763350006605001E-02, \ -4.056845643788482E-01, -8.739980868114045E-01, 5.900069010534015E-03, \ -4.030307435938099E-01, 7.756488822994984E-01, 1.281187876680621E-02, \ -4.006967431242406E-01, 8.961755809836305E-01, 8.973613291265101E-03, \ -3.916049226821231E-01, -9.273410115124909E-01, 5.297964504333964E-03, \ -3.767714330669960E-01, -6.548167260904730E-01, 9.467239374026879E-03, \ -3.759401992622222E-01, 2.756208903780863E-01, 1.532016187158172E-02, \ -3.755012873186720E-01, -9.871862321784112E-01, 3.250146148554228E-03, \ -3.730541368999579E-01, -7.112556629483213E-01, 7.329934266008029E-03, \ -3.725289366278142E-01, -2.774273474801098E-01, 1.754335020704925E-02, \ -3.672221731554482E-01, -4.498269623849093E-01, 1.635160912830995E-02, \ -3.517016115907431E-01, 5.427475370188103E-01, 1.038435257761881E-02, \ -3.472072906873430E-01, 1.297375715246647E-01, 1.511255362750808E-02, \ -3.288603177035728E-01, 4.816597830509821E-01, 6.559008197617309E-03, \ -3.221265382254779E-01, -1.433656648153948E-01, 1.620111125789070E-02, \ -3.131321362159788E-01, 7.032975112241375E-01, 1.594512703102189E-02, \ -3.082989492612527E-01, -9.578410503896179E-01, 3.982391593695098E-03, \ -3.082247018694904E-01, 9.906739284535425E-01, 2.962374733019264E-03, \ -3.072260057987407E-01, 9.424355086678589E-01, 7.485667285562808E-03, \ -3.062114826214366E-01, -9.347879939525434E-01, 2.589717354994651E-03, \ -3.046631601690127E-01, 8.455016733897478E-01, 1.202814315872106E-02, \ -2.960605213864115E-01, -5.110628541558808E-01, 1.002716095596817E-02, \ -2.917625758358438E-01, 3.593747168154432E-01, 1.837042545246992E-02, \ -2.895557314330913E-01, -6.159501875196743E-01, 1.206000739213904E-02, \ -2.871906599030266E-01, -7.705048149609509E-01, 1.383267273104722E-02, \ -2.859792213471688E-01, -8.714115510524062E-01, 1.038591281351532E-02, \ -2.856503520749610E-01, 5.747007863914991E-02, 1.748058432381039E-02, \ -2.824592805060356E-01, 5.612750161066066E-01, 9.353603746527843E-03, \ -2.728487335032520E-01, -9.975408583725541E-01, 1.264352449742901E-03, \ -2.601809045605671E-01, -3.522853948258879E-01, 2.092850963826799E-02, \ -2.597903214660320E-01, -9.994084053639378E-02, 8.825557728414398E-03, \ -2.256215566562435E-01, 2.283770326898505E-01, 2.160089195520415E-02, \ -2.188098462531380E-01, -2.067500347682650E-01, 1.252332154956301E-02, \ -2.185684926171157E-01, -9.755155987010639E-01, 4.112709587283565E-03, \ -2.053682577466782E-01, 7.806266036689269E-01, 1.501612574781621E-02, \ -2.049162099957439E-01, 6.343543635897640E-01, 1.580531156711188E-02, \ -2.041124215059686E-01, -5.429590922002024E-01, 1.362853247269861E-02, \ -2.002875030215060E-01, 9.009976779341253E-01, 1.031145511059078E-02, \ -1.976029493822827E-01, 9.714461314931776E-01, 5.332016356692966E-03, \ -1.954132400791727E-01, 4.624136298055638E-01, 1.945983666591439E-02, \ -1.879132665032426E-01, -6.925128794555552E-01, 1.703923942906849E-02, \ -1.821951153235339E-01, -1.426582763733243E-02, 1.987409951184996E-02, \ -1.810578998197690E-01, -9.204035043869775E-01, 9.272464757303015E-03, \ -1.774507741267828E-01, 9.978134769969224E-01, 1.228301960791354E-03, \ -1.621404219665848E-01, -8.249452802330807E-01, 1.365662754138641E-02, \ -1.464771076898347E-01, -4.340215233356940E-01, 1.945862436948514E-02, \ -1.460344552467488E-01, -2.429282629387507E-01, 1.565971349603635E-02, \ -1.357303124694478E-01, -9.913278393826657E-01, 2.344766960985844E-03, \ -1.348850451544348E-01, 1.418182577007316E-01, 1.855959179083704E-02, \ -1.178453467617478E-01, 3.462124048386542E-01, 2.128688457301467E-02, \ -1.070963545859648E-01, 5.697167424399421E-01, 1.270219547686097E-02, \ -9.418089864452631E-02, 8.464061176824520E-01, 1.318512157781563E-02, \ -9.284665135473712E-02, 7.115189151497324E-01, 1.693264777896065E-02, \ -8.649884288942110E-02, 9.412721885997597E-01, 7.947036543700148E-03, \ -8.381550837050580E-02, -1.034404718739174E-01, 2.042114347858592E-02, \ -8.132901275144148E-02, -6.047646884556696E-01, 1.901873006719877E-02, \ -7.314393059200233E-02, -9.584726090471121E-01, 6.990580671801756E-03, \ -6.585476015650292E-02, 9.869964307266527E-01, 3.475568911966144E-03, \ -5.940953281811259E-02, -7.531405908206484E-01, 1.610516174433207E-02, \ -5.723571915110250E-02, -3.156995009383814E-01, 1.757545073276317E-02, \ -4.881350872683240E-02, -8.821229556281880E-01, 1.190858000679253E-02, \ -4.623125113800330E-02, -9.984756475663564E-01, 8.661846411096376E-04, \ -4.537127170091439E-02, 5.454245190895872E-01, 7.887365308447648E-03, \ -4.427946025894871E-02, 7.620061393862830E-02, 1.715262718303868E-02, \ -3.652498887773526E-02, -4.854048438229047E-01, 1.164475499560268E-02, \ -2.693515118939117E-02, 4.662758740691014E-01, 1.418575874574526E-02, \ -2.196660636199712E-02, 2.563688847935753E-01, 2.048504486701552E-02, \ 1.684869503861126E-02, 9.985028110516669E-01, 8.343196408295555E-04, \ 1.937078508280643E-02, 7.845643755910120E-01, 1.528657010406891E-02, \ 2.203824694705822E-02, 8.989738024148887E-01, 1.069256626530232E-02, \ 2.241772195214512E-02, -1.754589056829656E-01, 1.981467867657729E-02, \ 2.975250703736150E-02, 1.862596862025734E-03, 1.586261473431975E-02, \ 3.055821004449258E-02, -3.713097808061478E-01, 1.472665339094052E-02, \ 3.289324396609741E-02, 6.432956961893939E-01, 1.864369020889923E-02, \ 3.723492660056246E-02, -9.844719413983402E-01, 4.259554223135243E-03, \ 4.770102526934471E-02, 9.660516213959782E-01, 5.910690727520699E-03, \ 4.835037248406306E-02, -6.721798158089920E-01, 1.837739301039192E-02, \ 5.239032096709587E-02, -5.201345460249732E-01, 1.609773629036364E-02, \ 5.502518798282641E-02, -8.182265682703534E-01, 1.429356112573313E-02, \ 5.830896522283972E-02, 4.016909728418846E-01, 1.831359832124226E-02, \ 6.198731221349852E-02, -9.303653863405975E-01, 9.255582126803446E-03, \ 7.857891643486636E-02, 1.766467214761190E-01, 1.939355213634587E-02, \ 1.208356536244954E-01, 3.216785108904378E-01, 9.071620470626165E-03, \ 1.208368243862543E-01, -2.541561566739803E-01, 2.021580169628961E-02, \ 1.216863587634878E-01, 9.916346904595559E-01, 2.444055246895457E-03, \ 1.232655916759636E-01, 5.414949782908248E-01, 1.986491824292366E-02, \ 1.241778913712552E-01, -4.978636357670361E-02, 1.834144377738077E-02, \ 1.337347631223449E-01, 8.472659711961135E-01, 1.284004194508113E-02, \ 1.466010849626561E-01, 7.236699453278207E-01, 1.678250950273756E-02, \ 1.496400580028691E-01, -9.975365491819376E-01, 1.471039139180874E-03, \ 1.529671602153546E-01, -4.138359329741561E-01, 1.970291306047588E-02, \ 1.553076799904455E-01, 9.825333958721993E-02, 1.331862934874382E-02, \ 1.564393944563869E-01, 9.341317137357775E-01, 8.329285394320438E-03, \ 1.607100339920880E-01, -8.768225824887561E-01, 1.145010706137546E-02, \ 1.633664795918194E-01, -5.876766334680318E-01, 1.831745704958468E-02, \ 1.649345927645013E-01, -7.456333961574857E-01, 1.658594926267819E-02, \ 1.724639115261522E-01, -9.662243526431580E-01, 6.397001220461619E-03, \ 1.856135967174529E-01, 3.019753251009087E-01, 1.604124847134084E-02, \ 2.207568082418493E-01, -1.341768231114187E-01, 2.201353706987977E-02, \ 2.216590623136845E-01, 6.237862843359905E-01, 1.130843281124745E-02, \ 2.222728182351477E-01, 9.767149748533738E-01, 4.270350031153890E-03, \ 2.251913391882167E-01, 4.515133683755246E-01, 1.961372976506132E-02, \ 2.393332091219671E-01, 6.746796047622838E-02, 1.563788629592373E-02, \ 2.454323613661074E-01, 9.987765164968539E-01, 8.734893357177072E-04, \ 2.489948172638105E-01, 2.049235281953148E-01, 1.270930859704317E-02, \ 2.551647790899600E-01, -4.986851928535581E-01, 1.121625142075451E-02, \ 2.569501661619921E-01, 7.948735761125491E-01, 1.372820954751759E-02, \ 2.586452498793473E-01, -9.219424663897881E-01, 8.044149671331794E-03, \ 2.601094175807203E-01, -3.053795751586294E-01, 2.158658189071271E-02, \ 2.633547449910876E-01, 8.921977837870594E-01, 1.019013452355202E-02, \ 2.654090569206588E-01, 6.495375037274833E-01, 8.750452222218987E-03, \ 2.690640635337399E-01, -8.151729320209684E-01, 1.356683615382717E-02, \ 2.728833763425947E-01, -6.617494728362482E-01, 1.691235069293519E-02, \ 2.832389697359580E-01, -4.580344348270283E-01, 7.865208224812631E-03, \ 2.840896766783086E-01, -9.890120421665016E-01, 3.588966784785691E-03, \ 3.151693234434736E-01, 9.534401100755432E-01, 5.557418660257084E-03, \ 3.260081563690662E-01, -1.795252417843553E-02, 2.146401172038991E-02, \ 3.274401122842648E-01, 3.681991260958348E-01, 1.852510306194186E-02, \ 3.284833444644465E-01, 2.189215721397187E-01, 1.439774012533690E-02, \ 3.337782993016923E-01, 5.444183052791469E-01, 1.768422453882693E-02, \ 3.384090593283935E-01, -9.515287291879881E-01, 4.960138634028438E-03, \ 3.438984906707113E-01, -5.371780889807538E-01, 1.068695089769454E-02, \ 3.446230444324452E-01, 7.190351391805496E-01, 1.249860147037258E-02, \ 3.543528388111687E-01, 9.902368488113547E-01, 2.826004111195709E-03, \ 3.602282612815438E-01, -1.947302593649046E-01, 2.173836797361481E-02, \ 3.612552194216351E-01, -7.319208685947469E-01, 1.249441852526187E-02, \ 3.632929794407099E-01, -8.704852750274591E-01, 9.768989552535455E-03, \ 3.744793900580320E-01, 8.286415194062603E-01, 6.671271590709352E-03, \ 3.860890582535335E-01, -3.839824460224215E-01, 2.092918906725470E-02, \ 3.928710017718934E-01, 8.672865777465832E-01, 6.936260220669673E-03, \ 3.931996788966815E-01, 9.279235914180360E-01, 5.272293822412451E-03, \ 4.007261695646738E-01, 1.223557508548206E-01, 1.739277111294605E-02, \ 4.062478163754075E-01, -9.984412635687164E-01, 1.118910221718476E-03, \ 4.106255773005774E-01, -5.988996724168920E-01, 1.562901284122264E-02, \ 4.123501152038699E-01, 7.367091972519042E-01, 4.909337398435131E-03, \ 4.172900522264887E-01, -9.721977396522211E-01, 4.399018232299250E-03, \ 4.314957914891770E-01, 4.647378299513769E-01, 1.657826429386184E-02, \ 4.317959505632551E-01, -7.839966309166440E-01, 1.002961987603591E-02, \ 4.331331185623659E-01, 6.317320218888924E-01, 1.491157542954482E-02, \ 4.400703045168821E-01, -9.090920579494268E-01, 6.758378154370627E-03, \ 4.413453712232151E-01, 3.026452329003297E-01, 1.816222308777934E-02, \ 4.563399517359142E-01, 9.712472856776212E-01, 4.837136504147411E-03, \ 4.566101742568825E-01, -8.299751644192108E-02, 2.070092724204458E-02, \ 4.600940256413679E-01, 7.358720101030228E-02, 9.566565631101559E-03, \ 4.604812529078548E-01, 9.984195308056378E-01, 8.414203442745121E-04, \ 4.808602748352557E-01, 7.905645541015534E-01, 1.052995268205664E-02, \ 4.827694496186490E-01, -2.738930106938465E-01, 2.090057903801916E-02, \ 4.902896825779680E-01, -4.796343698686354E-01, 1.970211671607839E-02, \ 4.980721753534725E-01, 9.157146659597657E-01, 7.088539756844323E-03, \ 4.998104630815455E-01, -6.796065261644658E-01, 1.577525512582634E-02, \ 5.094252232151556E-01, -8.368693540841839E-01, 1.074700155814415E-02, \ 5.192774433643107E-01, -9.883852225797410E-01, 3.036728485600766E-03, \ 5.195781232521763E-01, -9.398491136525347E-01, 6.356409539852770E-03, \ 5.199091809396583E-01, 8.569634476765962E-01, 5.258870099579074E-03, \ 5.229669281084162E-01, 5.594933800929066E-01, 1.395310653595126E-02, \ 5.277471964272620E-01, 2.088203156823199E-01, 1.879162946198670E-02, \ 5.309038668016169E-01, 7.063079812356768E-01, 1.112337221025911E-02, \ 5.382154499373017E-01, 4.065037042579824E-01, 1.597509886966357E-02, \ 5.516901995859222E-01, 2.395725953104485E-02, 1.772537813373606E-02, \ 5.527797967108647E-01, 9.898809035115810E-01, 2.406110601287913E-03, \ 5.750934868747971E-01, -1.608553196274835E-01, 1.999458400282759E-02, \ 5.826416379535926E-01, -5.769647685634977E-01, 1.716174776614503E-02, \ 5.828982582142574E-01, -3.706431888713908E-01, 1.927115149218318E-02, \ 5.850904508510351E-01, 9.536524310311831E-01, 5.849579241942577E-03, \ 5.903129886530973E-01, -7.571779340576262E-01, 1.342299877672259E-02, \ 5.958483435151166E-01, 8.681226767219122E-01, 7.303322832277533E-03, \ 5.993502036615301E-01, -8.879811146186565E-01, 9.100212257108971E-03, \ 6.050183737665353E-01, 6.475724613929950E-01, 1.074862599712923E-02, \ 6.143297462629967E-01, 7.837772856375271E-01, 1.032139260028579E-02, \ 6.153165941746209E-01, -9.665059604638701E-01, 4.843117865525232E-03, \ 6.161439379518383E-01, -9.981214531139727E-01, 9.753216220325940E-04, \ 6.175168884004676E-01, 3.159407352975249E-01, 1.637383804148541E-02, \ 6.217394522871077E-01, 5.078428721394385E-01, 1.362126210274025E-02, \ 6.299826667484392E-01, 1.276627125784212E-01, 1.607743572209873E-02, \ 6.380312602008873E-01, 9.984592465433296E-01, 6.879014666059284E-04, \ 6.619401281471743E-01, -4.910221084647453E-02, 1.800834418028045E-02, \ 6.674023930795736E-01, -4.731419452655840E-01, 1.673528342997327E-02, \ 6.681506875256884E-01, -6.664316392680106E-01, 1.423631431136118E-02, \ 6.699586457560213E-01, -2.582142639784658E-01, 1.831293821635849E-02, \ 6.700629393564212E-01, 9.153625801049049E-01, 7.211301710323832E-03, \ 6.737233221090680E-01, 7.173277865865444E-01, 6.610660635246017E-03, \ 6.745073548792663E-01, 9.808177327151206E-01, 3.335305616421728E-03, \ 6.778146451052540E-01, -8.234922260494466E-01, 1.057682497759063E-02, \ 6.908467734992273E-01, -9.289111905832840E-01, 6.533919963273618E-03, \ 6.953563494538313E-01, 4.185159914801704E-01, 1.411689605267293E-02, \ 6.956622893885850E-01, 5.981008752604229E-01, 1.164860612595941E-02, \ 7.000653188381879E-01, 2.214609724485731E-01, 1.377466770804801E-02, \ 7.037630540132982E-01, -9.876775194786391E-01, 2.680336723639033E-03, \ 7.104138022608364E-01, 8.335936077499366E-01, 9.361402014358680E-03, \ 7.312620222424863E-01, 7.241821704859189E-01, 7.324085688124115E-03, \ 7.377947101997951E-01, 6.019282202794075E-02, 1.545266033002662E-02, \ 7.432626735055564E-01, -5.692902294936619E-01, 1.380983624211225E-02, \ 7.463716527825006E-01, -3.650065781089341E-01, 1.572334278442964E-02, \ 7.473714210847725E-01, -7.438987523094117E-01, 1.119428524509579E-02, \ 7.479060990243412E-01, 9.546404095610349E-01, 4.774712942139564E-03, \ 7.497338213800094E-01, -1.437602092341267E-01, 1.665640989044135E-02, \ 7.551017439728431E-01, 9.959903451333804E-01, 1.228086933220431E-03, \ 7.591482573195993E-01, -8.774194742914248E-01, 7.586269856563272E-03, \ 7.633324906212867E-01, 3.136203740000685E-01, 1.293765982026287E-02, \ 7.650644572872880E-01, 5.091844736715609E-01, 1.189055699839011E-02, \ 7.700358230014746E-01, -9.622554291254800E-01, 4.130632579632251E-03, \ 7.803618979679303E-01, 8.901458109807174E-01, 6.979020029847049E-03, \ 7.864173038832742E-01, -9.978780396924563E-01, 8.523818960483254E-04, \ 7.865539415769538E-01, 6.444528101970656E-01, 9.779082708584302E-03, \ 7.980764438789796E-01, 7.802200932109996E-01, 8.751239749911849E-03, \ 7.998064049263058E-01, 1.573746239393782E-01, 1.153314940800488E-02, \ 8.115339339837927E-01, -6.541157752948943E-01, 1.081501204510849E-02, \ 8.122968512881367E-01, -4.669611624262626E-01, 1.275121734348267E-02, \ 8.172332485051989E-01, -2.537325117758131E-01, 1.424812222167168E-02, \ 8.173520738904602E-01, -8.098997527380203E-01, 8.129789190108278E-03, \ 8.178221088482659E-01, 9.819369149456145E-01, 2.554058729705376E-03, \ 8.203518851901087E-01, -2.848141797141588E-02, 1.462387517662095E-02, \ 8.252880251126054E-01, 4.061913511894648E-01, 1.166744929568591E-02, \ 8.273414827850937E-01, -9.223585802664281E-01, 4.998620758584853E-03, \ 8.407955028132980E-01, -9.831208231993736E-01, 2.226504941332199E-03, \ 8.434816562041050E-01, 9.360798445804146E-01, 4.637841436379602E-03, \ 8.459602643116834E-01, 2.369112261168515E-01, 9.231435360575175E-03, \ 8.471265891317460E-01, 5.607143752033232E-01, 9.370910316615211E-03, \ 8.544039302272810E-01, 8.437316388011586E-01, 6.684546573241642E-03, \ 8.584519706838185E-01, 7.001783215001461E-01, 8.637290041473251E-03, \ 8.691797730219265E-01, -7.293852681306572E-01, 7.916587819483284E-03, \ 8.694955383875622E-01, -5.578683468627721E-01, 9.777395917753213E-03, \ 8.715225068140382E-01, 9.968629229036633E-01, 8.317205346907935E-04, \ 8.737322022500262E-01, -3.624845067925466E-01, 1.142884436428019E-02, \ 8.748455473474397E-01, -8.666688668665444E-01, 5.501879290681462E-03, \ 8.783568279821649E-01, -1.408106351805172E-01, 1.222770107988572E-02, \ 8.807000621010282E-01, 8.577202208035965E-02, 1.208916044443412E-02, \ 8.861191555247315E-01, -9.524587365695271E-01, 2.996809350965912E-03, \ 8.908714545623476E-01, 3.200728941018283E-01, 9.132233939830871E-03, \ 8.918849262329097E-01, -9.953299489673937E-01, 8.349160581858519E-04, \ 8.923957457559257E-01, 4.727862002708382E-01, 7.649082746924224E-03, \ 8.992219867205118E-01, 9.696383870346604E-01, 2.712861853539782E-03, \ 9.037366973903258E-01, 8.982722285187050E-01, 4.553188238165971E-03, \ 9.058049717812220E-01, 7.750612684220821E-01, 6.573933171769569E-03, \ 9.131013487425569E-01, 6.183060481541276E-01, 7.822429485807891E-03, \ 9.152680757385779E-01, -7.967925142545168E-01, 5.472782958925398E-03, \ 9.153194784422245E-01, -6.409066271644237E-01, 7.068811844211731E-03, \ 9.212375062298164E-01, -4.626882296966913E-01, 8.505557437086888E-03, \ 9.241806475212835E-01, -9.073693661022466E-01, 3.491966652690000E-03, \ 9.242655253133358E-01, -2.553881984456130E-01, 9.435712214118857E-03, \ 9.278685381584146E-01, -2.653703926395334E-02, 9.626254172659349E-03, \ 9.292177091225340E-01, 1.981150041249339E-01, 9.120861207209665E-03, \ 9.293709816985555E-01, -9.743419848916115E-01, 1.695761394360294E-03, \ 9.361004878709992E-01, 4.885572309032284E-01, 3.587508119392231E-03, \ 9.386011261575939E-01, 9.923607023625215E-01, 1.027746374416859E-03, \ 9.416316207823281E-01, 3.848246163685812E-01, 5.939044760002660E-03, \ 9.429469392782762E-01, -9.969137251707089E-01, 3.661853125669515E-04, \ 9.451218403684011E-01, 8.425754983796822E-01, 4.380238586156267E-03, \ 9.463230530060351E-01, 9.398320877335458E-01, 2.748352326578851E-03, \ 9.496567334542220E-01, 7.028051861622154E-01, 5.415662354453875E-03, \ 9.504527598249251E-01, -7.179397056605220E-01, 4.858056515732989E-03, \ 9.545502432300008E-01, -8.483672446398389E-01, 3.493614776736699E-03, \ 9.567226666698644E-01, -5.574361090807435E-01, 5.711544750304637E-03, \ 9.604743008370903E-01, -3.634999075225396E-01, 6.518215206604805E-03, \ 9.614350881231609E-01, -9.400793516785635E-01, 2.075637167332280E-03, \ 9.617205731156480E-01, -1.437778684046163E-01, 6.766721124990966E-03, \ 9.627292013618208E-01, 5.526147023410976E-01, 5.203862026907654E-03, \ 9.645339614003799E-01, 8.912679972814096E-02, 6.720220154114170E-03, \ 9.681982898776231E-01, -9.858482988016933E-01, 7.854806252207273E-04, \ 9.684495587062435E-01, 2.941036296126024E-01, 5.195376918064249E-03, \ 9.718043670689287E-01, 9.757438210857030E-01, 1.191159865328584E-03, \ 9.761533852459922E-01, 7.788946250155976E-01, 3.220271808790217E-03, \ 9.766012140635367E-01, 8.955372887998586E-01, 2.409386138666988E-03, \ 9.789182968946982E-01, -7.802922134664675E-01, 2.851798066970247E-03, \ 9.803687856312776E-01, -6.441628855863613E-01, 3.244928766737902E-03, \ 9.822912045411591E-01, 9.984383651196385E-01, 2.341272827142674E-04, \ 9.827025129630593E-01, 4.311771782500267E-01, 3.707882781947956E-03, \ 9.827228609176302E-01, -8.919420074129613E-01, 1.854127115183594E-03, \ 9.832282949134381E-01, -2.444850615823892E-01, 2.565975919898579E-03, \ 9.842695902809974E-01, 6.440248345169696E-01, 3.235673284757067E-03, \ 9.843960342896765E-01, -4.685449063372227E-01, 3.758206611082762E-03, \ 9.863495085969685E-01, -9.979572836369498E-01, 1.885243013566843E-04, \ 9.863894006621330E-01, -3.054206067550260E-02, 4.070957199968271E-03, \ 9.884373933820602E-01, -9.631986863799080E-01, 8.909268125570525E-04, \ 9.889831635646070E-01, 2.001521680789260E-01, 3.415256267259531E-03, \ 9.895486008443393E-01, -2.802400020803678E-01, 1.784951229309678E-03, \ 9.913011952915273E-01, 9.490722861303337E-01, 9.334114310415029E-04, \ 9.939722207265341E-01, 8.378634329981455E-01, 1.348862490324860E-03, \ 9.941405572471773E-01, 5.032506127587780E-01, 1.321839206521580E-03, \ 9.943806852246193E-01, -6.860004265918137E-01, 7.140588378827780E-04, \ 9.957633794231534E-01, -8.360114490592742E-01, 1.041707929268540E-03, \ 9.966883143052717E-01, 7.278496613238243E-01, 1.191792248759857E-03, \ 9.968035955361948E-01, -5.651523666439144E-01, 1.374867996046609E-03, \ 9.968605145969733E-01, -7.336757652882711E-01, 7.990342391998070E-04, \ 9.969384946190634E-01, 9.868433854178995E-01, 2.740236217096047E-04, \ 9.975593611800366E-01, 3.360863758987011E-01, 1.454585250009066E-03, \ 9.978110877289340E-01, -1.465750773024727E-01, 1.377030312298262E-03, \ 9.979325714446113E-01, -9.249224066288942E-01, 4.777113521207585E-04, \ 9.979765814666188E-01, -3.775646733998311E-01, 1.202710471482889E-03, \ 9.980898127659592E-01, -9.874218489978037E-01, 1.849225119026519E-04, \ 9.981040178114964E-01, 8.280125816480956E-02, 1.248796781507533E-03, \ 9.982820382418868E-01, 5.769543802463517E-01, 7.519588496094478E-04, \ 9.990895206748026E-01, 9.085198717249964E-01, 3.348164725496207E-04 ] ) return xyw def smr51 ( ): #*****************************************************************************80 # ## smr51 returns the SMR rule of degree 51. # # Discussion: # # DEGREE: 51 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 462 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*462), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.984626432301655E-01, 7.731810731373280E-01, 2.930667077040843E-04, \ -9.982950612817629E-01, -8.809790422529455E-01, 5.868976563494200E-04, \ -9.982657143502113E-01, -5.472808378415216E-01, 8.825961580004602E-04, \ -9.982465196344393E-01, -5.720585061776626E-02, 1.187360397727577E-03, \ -9.980752383111224E-01, 9.895590629954322E-01, 1.605142582803498E-04, \ -9.980563050335864E-01, 4.026468127795991E-01, 1.133746118823456E-03, \ -9.980560915023025E-01, 9.316458011937399E-01, 4.410107005989047E-04, \ -9.979331148437312E-01, -7.218491788727829E-01, 9.165568347185002E-04, \ -9.978969853829365E-01, 1.744352247684945E-01, 1.316676065658554E-03, \ -9.976266468967849E-01, -3.120694338997498E-01, 1.417265243059842E-03, \ -9.967076640629561E-01, 5.825966069019469E-01, 1.351054193096153E-03, \ -9.966756982844908E-01, -9.646209210318417E-01, 4.673464325522125E-04, \ -9.958487588813290E-01, 8.454813315395656E-01, 9.269269947395651E-04, \ -9.958386434423615E-01, -9.967140264655182E-01, 1.294234585034121E-04, \ -9.947687668481154E-01, 7.122817636688038E-01, 1.297939923938297E-03, \ -9.931482649594923E-01, -4.688097799928717E-01, 1.263445560038073E-03, \ -9.899762961164086E-01, -8.107546466202721E-01, 1.978506208627187E-03, \ -9.894541209227824E-01, -1.743999916176229E-01, 3.272756891802527E-03, \ -9.894046340107479E-01, 3.041157495057775E-01, 2.220343118583675E-03, \ -9.885082901085881E-01, 9.678446822025472E-01, 8.290334262139013E-04, \ -9.872610044005977E-01, -6.363286357326429E-01, 2.912531649448298E-03, \ -9.871440151549654E-01, 5.740263552332389E-02, 3.880572488162640E-03, \ -9.855704338257310E-01, 9.982037827098472E-01, 1.679707148208503E-04, \ -9.855018569701638E-01, -9.249596493833102E-01, 1.577833631361155E-03, \ -9.843630383600804E-01, 4.886238428735122E-01, 3.617312818445750E-03, \ -9.839061975006608E-01, 8.975109105786676E-01, 1.696426511535707E-03, \ -9.834620733084443E-01, -4.095317899088909E-01, 3.294182229441701E-03, \ -9.819763154480772E-01, 2.606278193971512E-01, 2.140965174384009E-03, \ -9.801554723479408E-01, -9.863754508076430E-01, 7.682431569634297E-04, \ -9.796226493234478E-01, 7.887535957547051E-01, 2.729782607675046E-03, \ -9.788073039622869E-01, 6.519818446915956E-01, 3.314343051454497E-03, \ -9.706604253083109E-01, -2.692976728099303E-01, 4.748645217638728E-03, \ -9.705718320763341E-01, -7.396086944705653E-01, 3.749135556172170E-03, \ -9.674102004473606E-01, -5.434109773347497E-01, 4.913196335695364E-03, \ -9.668019398584777E-01, -8.667816625365619E-01, 3.131430980170647E-03, \ -9.665514792427918E-01, 9.883256946409834E-01, 7.290779022650052E-04, \ -9.662771630324206E-01, -6.217984707467629E-02, 6.426823016887218E-03, \ -9.635050607978470E-01, 9.431294630830762E-01, 1.956380667434553E-03, \ -9.627844810540420E-01, 1.672694103301844E-01, 6.389370066661570E-03, \ -9.610263909737414E-01, 3.856673360143000E-01, 6.245421895915378E-03, \ -9.580781208653250E-01, -9.589071798906652E-01, 1.967241617526768E-03, \ -9.561574884827165E-01, 8.545038074891833E-01, 3.350951463581097E-03, \ -9.549317791767546E-01, 5.686259325313919E-01, 5.498722518704855E-03, \ -9.508617818904216E-01, -9.981801380774861E-01, 4.122462038678519E-04, \ -9.503534180334950E-01, 7.288766888422127E-01, 4.767863642349979E-03, \ -9.498352776387182E-01, -3.600313059077714E-01, 4.618417760022735E-03, \ -9.438088288340477E-01, -6.623911600100255E-01, 5.441477466246755E-03, \ -9.383440437473887E-01, -4.677837297857259E-01, 5.286783724635598E-03, \ -9.378343978313476E-01, 9.979840227602486E-01, 2.886874404933051E-04, \ -9.347835826828178E-01, -8.032727461306876E-01, 5.101386107167580E-03, \ -9.335259963058073E-01, -1.741913013268586E-01, 8.674585526845215E-03, \ -9.316426596133324E-01, 9.753406841125737E-01, 1.609586813812562E-03, \ -9.309296248560257E-01, -9.140613176099411E-01, 3.495989691744833E-03, \ -9.305488551107037E-01, 5.136546721748054E-02, 9.197493230088536E-03, \ -9.263857355252882E-01, 2.779326048975370E-01, 9.028086779958895E-03, \ -9.263239701445769E-01, 9.107049422584537E-01, 3.371000191307030E-03, \ -9.205673142765751E-01, 4.776877088663017E-01, 8.065709176393822E-03, \ -9.174707990058046E-01, -9.831219824223332E-01, 1.793027637558652E-03, \ -9.157242077150120E-01, 8.048621575323117E-01, 5.331392481303393E-03, \ -9.146615254968106E-01, 6.525583504423961E-01, 6.930392199976675E-03, \ -9.089721587302551E-01, -5.857463675029180E-01, 7.267970782315043E-03, \ -9.080065935974906E-01, -3.164859240152895E-01, 6.837639413127251E-03, \ -8.947437970286245E-01, -7.322325765211256E-01, 6.893118586976826E-03, \ -8.919221754192620E-01, 9.949598324120587E-01, 8.127871134893036E-04, \ -8.895890260377957E-01, -8.637277108491151E-01, 5.232804117494899E-03, \ -8.886655773400590E-01, 9.537789903620841E-01, 2.876082206616951E-03, \ -8.885392464038627E-01, -4.435272092291309E-01, 7.568949220120856E-03, \ -8.866202065469098E-01, -6.348808497993091E-02, 1.154404882651323E-02, \ -8.824241243616843E-01, 1.639785341465538E-01, 1.169349797338188E-02, \ -8.809708780612643E-01, -9.497050899975726E-01, 3.553886416146671E-03, \ -8.760350227104163E-01, 8.717500400436297E-01, 5.259870620154938E-03, \ -8.754979784047946E-01, 3.798655264692855E-01, 1.081669329181522E-02, \ -8.692675323873814E-01, 5.704948013117649E-01, 9.415315641120716E-03, \ -8.690861109568938E-01, 7.385216965817932E-01, 7.679645948063224E-03, \ -8.682723849317826E-01, -2.413725440218638E-01, 9.253909164096906E-03, \ -8.642150696852295E-01, -9.960092787039047E-01, 1.003841753738079E-03, \ -8.498643855720464E-01, -6.649755550632316E-01, 7.597610473619992E-03, \ -8.467214017035217E-01, -5.362390367615976E-01, 8.895976060123083E-03, \ -8.436301872985277E-01, 9.832315944888775E-01, 2.074514135087015E-03, \ -8.422060631929207E-01, -8.074677442695858E-01, 6.683571843601402E-03, \ -8.299696186499533E-01, 9.252056406107587E-01, 4.686829064201373E-03, \ -8.282749185054267E-01, 4.933486591871209E-02, 1.397066501428090E-02, \ -8.269765469411963E-01, -9.080859052720072E-01, 5.544241952351055E-03, \ -8.257297950277435E-01, -3.708722000140850E-01, 1.212267988934058E-02, \ -8.219455142773742E-01, 2.731244055602917E-01, 1.349903286379663E-02, \ -8.186687694116527E-01, 8.169654336809941E-01, 7.724614247165545E-03, \ -8.177674865173270E-01, -9.751105570722036E-01, 3.104258903016394E-03, \ -8.168195553880896E-01, -1.491433592951066E-01, 1.263065366829014E-02, \ -8.143075811610117E-01, 4.808919934779660E-01, 1.211587707934682E-02, \ -8.122235222464764E-01, 6.645693263356235E-01, 1.034590169853937E-02, \ -7.924551682337602E-01, 9.979434118184467E-01, 7.996645031474067E-04, \ -7.911850724888906E-01, -7.506825569200485E-01, 7.941591929716212E-03, \ -7.837299301003484E-01, -6.221133816449059E-01, 9.355464426914692E-03, \ -7.749274054206045E-01, 9.636900992554140E-01, 3.821815982327952E-03, \ -7.691224233934532E-01, -4.797259824277350E-01, 1.254447144435524E-02, \ -7.648340229962162E-01, -8.581827935318574E-01, 7.491144670441934E-03, \ -7.627844940764947E-01, 8.826229759338237E-01, 7.074367688839350E-03, \ -7.592567621031157E-01, 1.621753494096360E-01, 1.582235203050707E-02, \ -7.592537632153245E-01, -9.944779325803701E-01, 1.562546451718628E-03, \ -7.590915957882161E-01, -2.690284231981802E-01, 1.472349868949412E-02, \ -7.522143486281416E-01, -4.420957762341238E-02, 1.533410434098432E-02, \ -7.517728783471738E-01, 3.808909146571708E-01, 1.484618411110594E-02, \ -7.502398495650368E-01, 7.529941361384164E-01, 1.058551634212385E-02, \ -7.501867381740732E-01, -9.428041484167984E-01, 5.372797181130857E-03, \ -7.465512348230974E-01, 5.812636029728919E-01, 1.308836850969356E-02, \ -7.215017997406428E-01, -7.029762664554089E-01, 8.951206614074616E-03, \ -7.117204454198214E-01, 9.882619725048780E-01, 2.485303732104740E-03, \ -6.985970094666423E-01, -8.050208586687611E-01, 8.605257870218163E-03, \ -6.974082194827886E-01, 9.323769900190633E-01, 6.036713475981832E-03, \ -6.968216588357791E-01, -5.685630259242790E-01, 1.270493967976205E-02, \ -6.965278443683667E-01, -3.813019527700768E-01, 1.500927174360908E-02, \ -6.843613518240634E-01, -1.595802737672721E-01, 1.661539044799480E-02, \ -6.837395418610350E-01, 8.311442230210669E-01, 9.863681583277186E-03, \ -6.834535427418744E-01, -9.760799862104438E-01, 3.846584874829861E-03, \ -6.810744539515917E-01, 2.740932444646828E-01, 1.725213516752411E-02, \ -6.768663568972961E-01, 6.600586241345030E-02, 1.734826728379393E-02, \ -6.745224370419017E-01, 4.870189903811539E-01, 1.578358047019544E-02, \ -6.739684725259000E-01, 6.773736800515929E-01, 1.345027777804938E-02, \ -6.727321115145797E-01, -9.007641976237168E-01, 7.583356682716259E-03, \ -6.450460332339586E-01, -6.757412229808869E-01, 7.508776080828879E-03, \ -6.389939293530692E-01, -9.973854338568079E-01, 1.063420084490733E-03, \ -6.262273709687267E-01, 9.982013719921785E-01, 9.099112612198464E-04, \ -6.247537179451397E-01, 9.683796791313465E-01, 4.469874771751688E-03, \ -6.220861512524035E-01, -4.697281748057330E-01, 1.438590125499024E-02, \ -6.156820155086310E-01, -2.709084325931711E-01, 1.688158496630053E-02, \ -6.129302881959240E-01, -7.641285676915613E-01, 9.495321490596256E-03, \ -6.084927218969570E-01, 8.936876664228429E-01, 8.406065647319754E-03, \ -6.039369653473292E-01, -8.553105132198990E-01, 5.992514339035710E-03, \ -6.024059992622410E-01, -4.938164236519791E-02, 1.789883159375976E-02, \ -5.996089026350557E-01, 7.672038662942753E-01, 1.255110376162054E-02, \ -5.962301970690166E-01, -6.095934069736669E-01, 9.465990926377369E-03, \ -5.961040200801679E-01, 3.848010075739488E-01, 1.817040820422673E-02, \ -5.952839737903306E-01, -9.461274496340163E-01, 6.416292856646743E-03, \ -5.926997294875127E-01, 1.776082891969388E-01, 1.866120408927115E-02, \ -5.923843694597760E-01, 5.896493007707313E-01, 1.621562787972456E-02, \ -5.527846142946271E-01, -9.861830959616884E-01, 3.099780098793835E-03, \ -5.459986569191559E-01, -8.375938371742565E-01, 6.050055084086778E-03, \ -5.388169516109163E-01, -3.607537832967127E-01, 1.609524415648660E-02, \ -5.312450979752437E-01, 9.432008243433877E-01, 5.898171201208263E-03, \ -5.310856361451403E-01, -6.813014817383491E-01, 1.027869913918279E-02, \ -5.304327612566657E-01, 9.890527261919566E-01, 2.827063130099349E-03, \ -5.268264010539805E-01, -5.252722734230787E-01, 1.359552165919798E-02, \ -5.244630726975610E-01, -1.577626633034953E-01, 1.882044362224186E-02, \ -5.224669683154261E-01, 6.130399485027747E-02, 1.507572575361228E-02, \ -5.217650146651664E-01, 8.449124099305068E-01, 1.001711474683906E-02, \ -5.132250082992501E-01, 6.918190741864376E-01, 1.482210020758091E-02, \ -5.059023911245950E-01, 4.925206672723313E-01, 1.868221045034610E-02, \ -5.046922823409280E-01, -9.035785351511306E-01, 8.414747616632558E-03, \ -5.026640169457263E-01, 2.885178419959957E-01, 1.960777274062006E-02, \ -4.917682812876415E-01, -7.568554964536706E-01, 9.839983273859529E-03, \ -4.637181860680785E-01, -9.054278376743077E-04, 9.310011516460947E-03, \ -4.628745793832066E-01, -9.980775898655661E-01, 1.085007318378005E-03, \ -4.612328243535970E-01, -9.636523905629031E-01, 5.391019613357756E-03, \ -4.521990532828559E-01, 9.132454907960982E-01, 6.548142672947493E-03, \ -4.452822066090281E-01, 7.925031022467097E-01, 1.000481753825504E-02, \ -4.434508659987488E-01, -4.254148994030716E-01, 1.620216257327421E-02, \ -4.426248172627640E-01, -2.509072334899481E-01, 1.793705768294306E-02, \ -4.404692204242281E-01, -6.030105930154493E-01, 1.529211567826421E-02, \ -4.402029273535364E-01, 1.500200794764788E-01, 1.542342490182974E-02, \ -4.347931405390690E-01, -8.230011687029393E-01, 8.429370045209109E-03, \ -4.297409120893627E-01, 9.734301034170465E-01, 4.194517995438787E-03, \ -4.280793712750670E-01, 6.111370786685761E-01, 1.539138011397148E-02, \ -4.190565853462007E-01, 9.985365756542770E-01, 1.043658595167089E-03, \ -4.087838261055447E-01, 3.960341312468386E-01, 1.965538234308296E-02, \ -4.013358778023735E-01, -6.857748024247086E-02, 1.914789477071623E-02, \ -3.908325740224702E-01, -9.235350202575059E-01, 5.809955546559159E-03, \ -3.832064070624976E-01, -6.989145768785087E-01, 1.037562767669162E-02, \ -3.758321036768930E-01, 8.749564346095232E-01, 9.283988967311280E-03, \ -3.742272834656374E-01, 7.386438108932267E-01, 1.206959551802083E-02, \ -3.734439819891471E-01, -7.600731641857339E-01, 4.571534994749117E-03, \ -3.686176671629213E-01, -8.637636801184702E-01, 7.881047457319663E-03, \ -3.649610153286265E-01, 2.347382351652932E-01, 1.685485671337773E-02, \ -3.634966464384106E-01, -9.868648166528062E-01, 3.442228582990279E-03, \ -3.600054767607526E-01, 5.420299693619358E-01, 1.119360645451427E-02, \ -3.505957261026271E-01, -5.039294885140760E-01, 1.713918706362200E-02, \ -3.501126585283145E-01, 9.528774489514406E-01, 4.781907234841134E-03, \ -3.431840305246549E-01, -3.234632166086708E-01, 1.841998237556686E-02, \ -3.249814204509735E-01, 7.805883807339332E-02, 2.000458123624601E-02, \ -3.238200997259933E-01, -1.646986314843889E-01, 1.453038910021411E-02, \ -3.071870647501693E-01, 4.525937353623032E-01, 7.042710134632947E-03, \ -3.062952672101842E-01, -6.627772715600880E-01, 9.909474136448071E-03, \ -3.050091209118546E-01, -9.543052172408368E-01, 4.342402989401129E-03, \ -2.996824040276308E-01, 9.893886367263438E-01, 3.372729439255868E-03, \ -2.921284081754466E-01, -9.294730734165612E-01, 2.665965363398914E-03, \ -2.914965364345655E-01, 6.692685855887550E-01, 1.582542223968635E-02, \ -2.849688540703927E-01, 8.208871837516990E-01, 1.282912704147129E-02, \ -2.775942437207699E-01, -7.860689613395975E-01, 1.360434664922907E-02, \ -2.774362772023182E-01, 5.115990505348308E-01, 1.098897677957239E-02, \ -2.755992085208109E-01, 3.254136406036551E-01, 1.925748460208263E-02, \ -2.730189749816505E-01, -5.730141929391641E-01, 8.984924690945310E-03, \ -2.726652774174905E-01, 9.242598423864574E-01, 7.499462320384355E-03, \ -2.634405915779047E-01, -1.587836571409323E-01, 9.151050686680885E-03, \ -2.581490524350047E-01, -9.976246277074098E-01, 1.288369519072761E-03, \ -2.490613945225850E-01, -4.306131655168830E-03, 1.532382255249465E-02, \ -2.481031816687010E-01, -8.793359713116025E-01, 9.514481983528278E-03, \ -2.422113837712834E-01, -4.067758048281825E-01, 2.014440359087718E-02, \ -2.142982700599490E-01, -5.985373158690191E-01, 1.073521366680798E-02, \ -2.135636186828752E-01, -9.733501320280229E-01, 4.395976260430139E-03, \ -2.120981534047442E-01, -2.428876390935836E-01, 1.362392033623074E-02, \ -2.113005630523961E-01, 1.863808573678246E-01, 2.256933019148822E-02, \ -1.895873328892071E-01, 9.674135332629907E-01, 6.051240317593347E-03, \ -1.887919907489533E-01, 5.980986332057304E-01, 1.682881188451604E-02, \ -1.857949999128354E-01, 7.522305689580321E-01, 1.584160022074351E-02, \ -1.785159586757167E-01, 8.807216617533518E-01, 1.082011427084735E-02, \ -1.761916572679682E-01, 4.332093347373318E-01, 1.838648906261771E-02, \ -1.742977443345394E-01, -7.112509510911679E-01, 1.631426543009215E-02, \ -1.702885707912656E-01, 9.976789076998883E-01, 1.351463488000147E-03, \ -1.691543181894413E-01, -6.151605950205655E-02, 1.668922632214760E-02, \ -1.512139533768488E-01, -9.260205563520960E-01, 8.640465753043138E-03, \ -1.429635335922110E-01, -2.866349030383558E-01, 1.453893632844844E-02, \ -1.375607617049847E-01, -4.955879381687505E-01, 2.007831161324815E-02, \ -1.363419810781558E-01, -8.281488459378050E-01, 1.334923028506015E-02, \ -1.250921268079241E-01, -9.903984650569976E-01, 2.682247880612530E-03, \ -1.125935592224152E-01, 3.114936705323088E-01, 2.026270260609158E-02, \ -1.120779617378507E-01, 9.019594046827543E-02, 2.123405804160869E-02, \ -8.562789192900672E-02, 5.348790809658290E-01, 1.342143700870946E-02, \ -8.108140369770123E-02, 9.326400187377183E-01, 8.842669360811586E-03, \ -8.047112887577813E-02, -1.412185710601948E-01, 1.994097452113148E-02, \ -7.703715921083283E-02, 8.232440020795283E-01, 1.369548566612555E-02, \ -7.440127659045481E-02, 6.789581696580780E-01, 1.764482626920084E-02, \ -6.880848892096898E-02, -6.277692461838515E-01, 1.711869621320623E-02, \ -6.244277913125515E-02, -3.629270311886996E-01, 1.813298184989576E-02, \ -6.005252974695677E-02, 9.855825278690261E-01, 3.918915934867240E-03, \ -4.739084718649585E-02, -9.614605234215312E-01, 6.465138335746558E-03, \ -3.228486396950021E-02, -7.582958812442467E-01, 1.552477272766300E-02, \ -2.853961004873518E-02, -9.985342967589811E-01, 9.129413317439405E-04, \ -2.709739827138708E-02, -8.853879813981095E-01, 1.151661207322516E-02, \ -2.187534604509761E-02, 4.331482264797441E-01, 1.526409630067874E-02, \ -1.949843130353365E-02, 2.223381624896826E-01, 2.052030171197288E-02, \ -1.664223141068962E-02, 2.434035865751951E-02, 1.253941316760429E-02, \ -5.632469283442591E-03, -5.482248741666836E-01, 1.007056710865806E-02, \ 5.632469283442591E-03, 5.482248741666836E-01, 1.007056710865806E-02, \ 1.664223141068962E-02, -2.434035865751951E-02, 1.253941316760429E-02, \ 1.949843130353365E-02, -2.223381624896826E-01, 2.052030171197288E-02, \ 2.187534604509761E-02, -4.331482264797441E-01, 1.526409630067874E-02, \ 2.709739827138708E-02, 8.853879813981095E-01, 1.151661207322516E-02, \ 2.853961004873518E-02, 9.985342967589811E-01, 9.129413317439405E-04, \ 3.228486396950021E-02, 7.582958812442467E-01, 1.552477272766300E-02, \ 4.739084718649585E-02, 9.614605234215312E-01, 6.465138335746558E-03, \ 6.005252974695677E-02, -9.855825278690261E-01, 3.918915934867240E-03, \ 6.244277913125515E-02, 3.629270311886996E-01, 1.813298184989576E-02, \ 6.880848892096898E-02, 6.277692461838515E-01, 1.711869621320623E-02, \ 7.440127659045481E-02, -6.789581696580780E-01, 1.764482626920084E-02, \ 7.703715921083283E-02, -8.232440020795283E-01, 1.369548566612555E-02, \ 8.047112887577813E-02, 1.412185710601948E-01, 1.994097452113148E-02, \ 8.108140369770123E-02, -9.326400187377183E-01, 8.842669360811586E-03, \ 8.562789192900672E-02, -5.348790809658290E-01, 1.342143700870946E-02, \ 1.120779617378507E-01, -9.019594046827543E-02, 2.123405804160869E-02, \ 1.125935592224152E-01, -3.114936705323088E-01, 2.026270260609158E-02, \ 1.250921268079241E-01, 9.903984650569976E-01, 2.682247880612530E-03, \ 1.363419810781558E-01, 8.281488459378050E-01, 1.334923028506015E-02, \ 1.375607617049847E-01, 4.955879381687505E-01, 2.007831161324815E-02, \ 1.429635335922110E-01, 2.866349030383558E-01, 1.453893632844844E-02, \ 1.512139533768488E-01, 9.260205563520960E-01, 8.640465753043138E-03, \ 1.691543181894413E-01, 6.151605950205655E-02, 1.668922632214760E-02, \ 1.702885707912656E-01, -9.976789076998883E-01, 1.351463488000147E-03, \ 1.742977443345394E-01, 7.112509510911679E-01, 1.631426543009215E-02, \ 1.761916572679682E-01, -4.332093347373318E-01, 1.838648906261771E-02, \ 1.785159586757167E-01, -8.807216617533518E-01, 1.082011427084735E-02, \ 1.857949999128354E-01, -7.522305689580321E-01, 1.584160022074351E-02, \ 1.887919907489533E-01, -5.980986332057304E-01, 1.682881188451604E-02, \ 1.895873328892071E-01, -9.674135332629907E-01, 6.051240317593347E-03, \ 2.113005630523961E-01, -1.863808573678246E-01, 2.256933019148822E-02, \ 2.120981534047442E-01, 2.428876390935836E-01, 1.362392033623074E-02, \ 2.135636186828752E-01, 9.733501320280229E-01, 4.395976260430139E-03, \ 2.142982700599490E-01, 5.985373158690191E-01, 1.073521366680798E-02, \ 2.422113837712834E-01, 4.067758048281825E-01, 2.014440359087718E-02, \ 2.481031816687010E-01, 8.793359713116025E-01, 9.514481983528278E-03, \ 2.490613945225850E-01, 4.306131655168830E-03, 1.532382255249465E-02, \ 2.581490524350047E-01, 9.976246277074098E-01, 1.288369519072761E-03, \ 2.634405915779047E-01, 1.587836571409323E-01, 9.151050686680885E-03, \ 2.726652774174905E-01, -9.242598423864574E-01, 7.499462320384355E-03, \ 2.730189749816505E-01, 5.730141929391641E-01, 8.984924690945310E-03, \ 2.755992085208109E-01, -3.254136406036551E-01, 1.925748460208263E-02, \ 2.774362772023182E-01, -5.115990505348308E-01, 1.098897677957239E-02, \ 2.775942437207699E-01, 7.860689613395975E-01, 1.360434664922907E-02, \ 2.849688540703927E-01, -8.208871837516990E-01, 1.282912704147129E-02, \ 2.914965364345655E-01, -6.692685855887550E-01, 1.582542223968635E-02, \ 2.921284081754466E-01, 9.294730734165612E-01, 2.665965363398914E-03, \ 2.996824040276308E-01, -9.893886367263438E-01, 3.372729439255868E-03, \ 3.050091209118546E-01, 9.543052172408368E-01, 4.342402989401129E-03, \ 3.062952672101842E-01, 6.627772715600880E-01, 9.909474136448071E-03, \ 3.071870647501693E-01, -4.525937353623032E-01, 7.042710134632947E-03, \ 3.238200997259933E-01, 1.646986314843889E-01, 1.453038910021411E-02, \ 3.249814204509735E-01, -7.805883807339332E-02, 2.000458123624601E-02, \ 3.431840305246549E-01, 3.234632166086708E-01, 1.841998237556686E-02, \ 3.501126585283145E-01, -9.528774489514406E-01, 4.781907234841134E-03, \ 3.505957261026271E-01, 5.039294885140760E-01, 1.713918706362200E-02, \ 3.600054767607526E-01, -5.420299693619358E-01, 1.119360645451427E-02, \ 3.634966464384106E-01, 9.868648166528062E-01, 3.442228582990279E-03, \ 3.649610153286265E-01, -2.347382351652932E-01, 1.685485671337773E-02, \ 3.686176671629213E-01, 8.637636801184702E-01, 7.881047457319663E-03, \ 3.734439819891471E-01, 7.600731641857339E-01, 4.571534994749117E-03, \ 3.742272834656374E-01, -7.386438108932267E-01, 1.206959551802083E-02, \ 3.758321036768930E-01, -8.749564346095232E-01, 9.283988967311280E-03, \ 3.832064070624976E-01, 6.989145768785087E-01, 1.037562767669162E-02, \ 3.908325740224702E-01, 9.235350202575059E-01, 5.809955546559159E-03, \ 4.013358778023735E-01, 6.857748024247086E-02, 1.914789477071623E-02, \ 4.087838261055447E-01, -3.960341312468386E-01, 1.965538234308296E-02, \ 4.190565853462007E-01, -9.985365756542770E-01, 1.043658595167089E-03, \ 4.280793712750670E-01, -6.111370786685761E-01, 1.539138011397148E-02, \ 4.297409120893627E-01, -9.734301034170465E-01, 4.194517995438787E-03, \ 4.347931405390690E-01, 8.230011687029393E-01, 8.429370045209109E-03, \ 4.402029273535364E-01, -1.500200794764788E-01, 1.542342490182974E-02, \ 4.404692204242281E-01, 6.030105930154493E-01, 1.529211567826421E-02, \ 4.426248172627640E-01, 2.509072334899481E-01, 1.793705768294306E-02, \ 4.434508659987488E-01, 4.254148994030716E-01, 1.620216257327421E-02, \ 4.452822066090281E-01, -7.925031022467097E-01, 1.000481753825504E-02, \ 4.521990532828559E-01, -9.132454907960982E-01, 6.548142672947493E-03, \ 4.612328243535970E-01, 9.636523905629031E-01, 5.391019613357756E-03, \ 4.628745793832066E-01, 9.980775898655661E-01, 1.085007318378005E-03, \ 4.637181860680785E-01, 9.054278376743077E-04, 9.310011516460947E-03, \ 4.917682812876415E-01, 7.568554964536706E-01, 9.839983273859529E-03, \ 5.026640169457263E-01, -2.885178419959957E-01, 1.960777274062006E-02, \ 5.046922823409280E-01, 9.035785351511306E-01, 8.414747616632558E-03, \ 5.059023911245950E-01, -4.925206672723313E-01, 1.868221045034610E-02, \ 5.132250082992501E-01, -6.918190741864376E-01, 1.482210020758091E-02, \ 5.217650146651664E-01, -8.449124099305068E-01, 1.001711474683906E-02, \ 5.224669683154261E-01, -6.130399485027747E-02, 1.507572575361228E-02, \ 5.244630726975610E-01, 1.577626633034953E-01, 1.882044362224186E-02, \ 5.268264010539805E-01, 5.252722734230787E-01, 1.359552165919798E-02, \ 5.304327612566657E-01, -9.890527261919566E-01, 2.827063130099349E-03, \ 5.310856361451403E-01, 6.813014817383491E-01, 1.027869913918279E-02, \ 5.312450979752437E-01, -9.432008243433877E-01, 5.898171201208263E-03, \ 5.388169516109163E-01, 3.607537832967127E-01, 1.609524415648660E-02, \ 5.459986569191559E-01, 8.375938371742565E-01, 6.050055084086778E-03, \ 5.527846142946271E-01, 9.861830959616884E-01, 3.099780098793835E-03, \ 5.923843694597760E-01, -5.896493007707313E-01, 1.621562787972456E-02, \ 5.926997294875127E-01, -1.776082891969388E-01, 1.866120408927115E-02, \ 5.952839737903306E-01, 9.461274496340163E-01, 6.416292856646743E-03, \ 5.961040200801679E-01, -3.848010075739488E-01, 1.817040820422673E-02, \ 5.962301970690166E-01, 6.095934069736669E-01, 9.465990926377369E-03, \ 5.996089026350557E-01, -7.672038662942753E-01, 1.255110376162054E-02, \ 6.024059992622410E-01, 4.938164236519791E-02, 1.789883159375976E-02, \ 6.039369653473292E-01, 8.553105132198990E-01, 5.992514339035710E-03, \ 6.084927218969570E-01, -8.936876664228429E-01, 8.406065647319754E-03, \ 6.129302881959240E-01, 7.641285676915613E-01, 9.495321490596256E-03, \ 6.156820155086310E-01, 2.709084325931711E-01, 1.688158496630053E-02, \ 6.220861512524035E-01, 4.697281748057330E-01, 1.438590125499024E-02, \ 6.247537179451397E-01, -9.683796791313465E-01, 4.469874771751688E-03, \ 6.262273709687267E-01, -9.982013719921785E-01, 9.099112612198464E-04, \ 6.389939293530692E-01, 9.973854338568079E-01, 1.063420084490733E-03, \ 6.450460332339586E-01, 6.757412229808869E-01, 7.508776080828879E-03, \ 6.727321115145797E-01, 9.007641976237168E-01, 7.583356682716259E-03, \ 6.739684725259000E-01, -6.773736800515929E-01, 1.345027777804938E-02, \ 6.745224370419017E-01, -4.870189903811539E-01, 1.578358047019544E-02, \ 6.768663568972961E-01, -6.600586241345030E-02, 1.734826728379393E-02, \ 6.810744539515917E-01, -2.740932444646828E-01, 1.725213516752411E-02, \ 6.834535427418744E-01, 9.760799862104438E-01, 3.846584874829861E-03, \ 6.837395418610350E-01, -8.311442230210669E-01, 9.863681583277186E-03, \ 6.843613518240634E-01, 1.595802737672721E-01, 1.661539044799480E-02, \ 6.965278443683667E-01, 3.813019527700768E-01, 1.500927174360908E-02, \ 6.968216588357791E-01, 5.685630259242790E-01, 1.270493967976205E-02, \ 6.974082194827886E-01, -9.323769900190633E-01, 6.036713475981832E-03, \ 6.985970094666423E-01, 8.050208586687611E-01, 8.605257870218163E-03, \ 7.117204454198214E-01, -9.882619725048780E-01, 2.485303732104740E-03, \ 7.215017997406428E-01, 7.029762664554089E-01, 8.951206614074616E-03, \ 7.465512348230974E-01, -5.812636029728919E-01, 1.308836850969356E-02, \ 7.501867381740732E-01, 9.428041484167984E-01, 5.372797181130857E-03, \ 7.502398495650368E-01, -7.529941361384164E-01, 1.058551634212385E-02, \ 7.517728783471738E-01, -3.808909146571708E-01, 1.484618411110594E-02, \ 7.522143486281416E-01, 4.420957762341238E-02, 1.533410434098432E-02, \ 7.590915957882161E-01, 2.690284231981802E-01, 1.472349868949412E-02, \ 7.592537632153245E-01, 9.944779325803701E-01, 1.562546451718628E-03, \ 7.592567621031157E-01, -1.621753494096360E-01, 1.582235203050707E-02, \ 7.627844940764947E-01, -8.826229759338237E-01, 7.074367688839350E-03, \ 7.648340229962162E-01, 8.581827935318574E-01, 7.491144670441934E-03, \ 7.691224233934532E-01, 4.797259824277350E-01, 1.254447144435524E-02, \ 7.749274054206045E-01, -9.636900992554140E-01, 3.821815982327952E-03, \ 7.837299301003484E-01, 6.221133816449059E-01, 9.355464426914692E-03, \ 7.911850724888906E-01, 7.506825569200485E-01, 7.941591929716212E-03, \ 7.924551682337602E-01, -9.979434118184467E-01, 7.996645031474067E-04, \ 8.122235222464764E-01, -6.645693263356235E-01, 1.034590169853937E-02, \ 8.143075811610117E-01, -4.808919934779660E-01, 1.211587707934682E-02, \ 8.168195553880896E-01, 1.491433592951066E-01, 1.263065366829014E-02, \ 8.177674865173270E-01, 9.751105570722036E-01, 3.104258903016394E-03, \ 8.186687694116527E-01, -8.169654336809941E-01, 7.724614247165545E-03, \ 8.219455142773742E-01, -2.731244055602917E-01, 1.349903286379663E-02, \ 8.257297950277435E-01, 3.708722000140850E-01, 1.212267988934058E-02, \ 8.269765469411963E-01, 9.080859052720072E-01, 5.544241952351055E-03, \ 8.282749185054267E-01, -4.933486591871209E-02, 1.397066501428090E-02, \ 8.299696186499533E-01, -9.252056406107587E-01, 4.686829064201373E-03, \ 8.422060631929207E-01, 8.074677442695858E-01, 6.683571843601402E-03, \ 8.436301872985277E-01, -9.832315944888775E-01, 2.074514135087015E-03, \ 8.467214017035217E-01, 5.362390367615976E-01, 8.895976060123083E-03, \ 8.498643855720464E-01, 6.649755550632316E-01, 7.597610473619992E-03, \ 8.642150696852295E-01, 9.960092787039047E-01, 1.003841753738079E-03, \ 8.682723849317826E-01, 2.413725440218638E-01, 9.253909164096906E-03, \ 8.690861109568938E-01, -7.385216965817932E-01, 7.679645948063224E-03, \ 8.692675323873814E-01, -5.704948013117649E-01, 9.415315641120716E-03, \ 8.754979784047946E-01, -3.798655264692855E-01, 1.081669329181522E-02, \ 8.760350227104163E-01, -8.717500400436297E-01, 5.259870620154938E-03, \ 8.809708780612643E-01, 9.497050899975726E-01, 3.553886416146671E-03, \ 8.824241243616843E-01, -1.639785341465538E-01, 1.169349797338188E-02, \ 8.866202065469098E-01, 6.348808497993091E-02, 1.154404882651323E-02, \ 8.885392464038627E-01, 4.435272092291309E-01, 7.568949220120856E-03, \ 8.886655773400590E-01, -9.537789903620841E-01, 2.876082206616951E-03, \ 8.895890260377957E-01, 8.637277108491151E-01, 5.232804117494899E-03, \ 8.919221754192620E-01, -9.949598324120587E-01, 8.127871134893036E-04, \ 8.947437970286245E-01, 7.322325765211256E-01, 6.893118586976826E-03, \ 9.080065935974906E-01, 3.164859240152895E-01, 6.837639413127251E-03, \ 9.089721587302551E-01, 5.857463675029180E-01, 7.267970782315043E-03, \ 9.146615254968106E-01, -6.525583504423961E-01, 6.930392199976675E-03, \ 9.157242077150120E-01, -8.048621575323117E-01, 5.331392481303393E-03, \ 9.174707990058046E-01, 9.831219824223332E-01, 1.793027637558652E-03, \ 9.205673142765751E-01, -4.776877088663017E-01, 8.065709176393822E-03, \ 9.263239701445769E-01, -9.107049422584537E-01, 3.371000191307030E-03, \ 9.263857355252882E-01, -2.779326048975370E-01, 9.028086779958895E-03, \ 9.305488551107037E-01, -5.136546721748054E-02, 9.197493230088536E-03, \ 9.309296248560257E-01, 9.140613176099411E-01, 3.495989691744833E-03, \ 9.316426596133324E-01, -9.753406841125737E-01, 1.609586813812562E-03, \ 9.335259963058073E-01, 1.741913013268586E-01, 8.674585526845215E-03, \ 9.347835826828178E-01, 8.032727461306876E-01, 5.101386107167580E-03, \ 9.378343978313476E-01, -9.979840227602486E-01, 2.886874404933051E-04, \ 9.383440437473887E-01, 4.677837297857259E-01, 5.286783724635598E-03, \ 9.438088288340477E-01, 6.623911600100255E-01, 5.441477466246755E-03, \ 9.498352776387182E-01, 3.600313059077714E-01, 4.618417760022735E-03, \ 9.503534180334950E-01, -7.288766888422127E-01, 4.767863642349979E-03, \ 9.508617818904216E-01, 9.981801380774861E-01, 4.122462038678519E-04, \ 9.549317791767546E-01, -5.686259325313919E-01, 5.498722518704855E-03, \ 9.561574884827165E-01, -8.545038074891833E-01, 3.350951463581097E-03, \ 9.580781208653250E-01, 9.589071798906652E-01, 1.967241617526768E-03, \ 9.610263909737414E-01, -3.856673360143000E-01, 6.245421895915378E-03, \ 9.627844810540420E-01, -1.672694103301844E-01, 6.389370066661570E-03, \ 9.635050607978470E-01, -9.431294630830762E-01, 1.956380667434553E-03, \ 9.662771630324206E-01, 6.217984707467629E-02, 6.426823016887218E-03, \ 9.665514792427918E-01, -9.883256946409834E-01, 7.290779022650052E-04, \ 9.668019398584777E-01, 8.667816625365619E-01, 3.131430980170647E-03, \ 9.674102004473606E-01, 5.434109773347497E-01, 4.913196335695364E-03, \ 9.705718320763341E-01, 7.396086944705653E-01, 3.749135556172170E-03, \ 9.706604253083109E-01, 2.692976728099303E-01, 4.748645217638728E-03, \ 9.788073039622869E-01, -6.519818446915956E-01, 3.314343051454497E-03, \ 9.796226493234478E-01, -7.887535957547051E-01, 2.729782607675046E-03, \ 9.801554723479408E-01, 9.863754508076430E-01, 7.682431569634297E-04, \ 9.819763154480772E-01, -2.606278193971512E-01, 2.140965174384009E-03, \ 9.834620733084443E-01, 4.095317899088909E-01, 3.294182229441701E-03, \ 9.839061975006608E-01, -8.975109105786676E-01, 1.696426511535707E-03, \ 9.843630383600804E-01, -4.886238428735122E-01, 3.617312818445750E-03, \ 9.855018569701638E-01, 9.249596493833102E-01, 1.577833631361155E-03, \ 9.855704338257310E-01, -9.982037827098472E-01, 1.679707148208503E-04, \ 9.871440151549654E-01, -5.740263552332389E-02, 3.880572488162640E-03, \ 9.872610044005977E-01, 6.363286357326429E-01, 2.912531649448298E-03, \ 9.885082901085881E-01, -9.678446822025472E-01, 8.290334262139013E-04, \ 9.894046340107479E-01, -3.041157495057775E-01, 2.220343118583675E-03, \ 9.894541209227824E-01, 1.743999916176229E-01, 3.272756891802527E-03, \ 9.899762961164086E-01, 8.107546466202721E-01, 1.978506208627187E-03, \ 9.931482649594923E-01, 4.688097799928717E-01, 1.263445560038073E-03, \ 9.947687668481154E-01, -7.122817636688038E-01, 1.297939923938297E-03, \ 9.958386434423615E-01, 9.967140264655182E-01, 1.294234585034121E-04, \ 9.958487588813290E-01, -8.454813315395656E-01, 9.269269947395651E-04, \ 9.966756982844908E-01, 9.646209210318417E-01, 4.673464325522125E-04, \ 9.967076640629561E-01, -5.825966069019469E-01, 1.351054193096153E-03, \ 9.976266468967849E-01, 3.120694338997498E-01, 1.417265243059842E-03, \ 9.978969853829365E-01, -1.744352247684945E-01, 1.316676065658554E-03, \ 9.979331148437312E-01, 7.218491788727829E-01, 9.165568347185002E-04, \ 9.980560915023025E-01, -9.316458011937399E-01, 4.410107005989047E-04, \ 9.980563050335864E-01, -4.026468127795991E-01, 1.133746118823456E-03, \ 9.980752383111224E-01, -9.895590629954322E-01, 1.605142582803498E-04, \ 9.982465196344393E-01, 5.720585061776626E-02, 1.187360397727577E-03, \ 9.982657143502113E-01, 5.472808378415216E-01, 8.825961580004602E-04, \ 9.982950612817629E-01, 8.809790422529455E-01, 5.868976563494200E-04, \ 9.984626432301655E-01, -7.731810731373280E-01, 2.930667077040843E-04 ] ) return xyw def smr52 ( ): #*****************************************************************************80 # ## smr52 returns the SMR rule of degree 52. # # Discussion: # # DEGREE: 52 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 493 # NORM INF MOMS. RESIDUAL: 1.77636e-15 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*493), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.988127014409341E-01, -9.436524211624828E-01, 2.625526521558170E-04, \ -9.987672107909694E-01, 6.030206237885709E-01, 5.695969962358445E-04, \ -9.985482219550218E-01, -5.039975022757507E-02, 7.711038314291110E-04, \ -9.984716084730251E-01, 1.648465544907188E-01, 9.876559621004946E-04, \ -9.983247427277899E-01, 9.851489095644117E-01, 1.847474866940015E-04, \ -9.981050848344004E-01, -9.897892710317165E-01, 1.455770846634000E-04, \ -9.980702320219238E-01, -8.710220064295600E-01, 3.606265853945270E-04, \ -9.980157290478607E-01, 3.823621895788871E-01, 1.084084984803506E-03, \ -9.979067456855214E-01, -3.075229364789735E-01, 1.191752453605670E-03, \ -9.976530827260541E-01, -4.990560694030991E-01, 1.016394895068514E-03, \ -9.976275687951667E-01, 7.452570753224620E-01, 7.962338632193404E-04, \ -9.975360338995326E-01, 9.261655839467660E-01, 4.882884021026501E-04, \ -9.975285341692078E-01, -6.928059429685538E-01, 9.702964010210698E-04, \ -9.953470417114124E-01, 8.469149414179490E-01, 1.047597310781277E-03, \ -9.949171976648574E-01, -8.070683057038244E-01, 1.108166020112025E-03, \ -9.944164425670770E-01, -5.787407343604202E-01, 7.129063333926422E-04, \ -9.941125375307870E-01, -1.470529960706050E-01, 1.642945733107137E-03, \ -9.940811335498559E-01, 5.262691220462341E-01, 1.362380806792382E-03, \ -9.897485255752738E-01, 5.394829132785462E-02, 2.963671420601588E-03, \ -9.892180378042456E-01, -9.087168466804317E-01, 1.131388755188889E-03, \ -9.889422632399338E-01, 2.713380420380118E-01, 3.125665368172544E-03, \ -9.885261339590784E-01, 6.719762287559811E-01, 2.097374310513504E-03, \ -9.884080307277354E-01, 9.975758923464908E-01, 1.953339748936135E-04, \ -9.882332182747464E-01, -9.695741031299449E-01, 7.675549180338620E-04, \ -9.877426889646129E-01, 9.620340499987866E-01, 8.981773684854589E-04, \ -9.866490694768677E-01, -4.072569387119710E-01, 3.309040261667309E-03, \ -9.862080286100734E-01, -9.979989708388572E-01, 1.771493432242450E-04, \ -9.850029364942529E-01, -6.122812872550168E-01, 2.518297727094817E-03, \ -9.837180977617805E-01, 4.565187303545456E-01, 2.849889245739051E-03, \ -9.828587452609784E-01, -2.237836811810542E-01, 3.333021131510325E-03, \ -9.812038715498557E-01, -7.470892816031330E-01, 2.670944794198278E-03, \ -9.804090236453241E-01, 7.865707923823555E-01, 2.595590100008589E-03, \ -9.803632387653639E-01, 8.971515025804927E-01, 1.885488419687061E-03, \ -9.744321506843910E-01, -8.554737714830845E-01, 2.459646855887305E-03, \ -9.742163651294308E-01, 6.008292093097657E-01, 2.870907182669987E-03, \ -9.729683924479909E-01, -5.587440042487817E-02, 4.917833265113004E-03, \ -9.697112617400576E-01, 1.602542576828755E-01, 5.452176079736804E-03, \ -9.680411604163617E-01, 9.857573537516288E-01, 8.708152215923545E-04, \ -9.671487130651160E-01, -5.124328504244583E-01, 4.833032752395291E-03, \ -9.660915478928949E-01, -9.410399722417206E-01, 1.871973610506917E-03, \ -9.654667822672215E-01, 3.609268066648831E-01, 5.184591828903681E-03, \ -9.639431956447733E-01, -9.879198529552836E-01, 8.794879382184762E-04, \ -9.614660794937132E-01, -3.152384510082097E-01, 5.556266122517595E-03, \ -9.578505518072694E-01, -6.724291809200033E-01, 4.600539485987667E-03, \ -9.577920524303927E-01, 9.419676523596269E-01, 2.067193179306530E-03, \ -9.565901478096345E-01, 7.131943261709114E-01, 4.501746579124314E-03, \ -9.563856659236216E-01, 5.366994723963830E-01, 4.091039972256468E-03, \ -9.547002111419167E-01, 8.456829919243595E-01, 3.449895771139099E-03, \ -9.480347148392301E-01, -7.980108126871678E-01, 4.091232197362770E-03, \ -9.466546601107151E-01, -1.535515771237759E-01, 6.528301611585182E-03, \ -9.407727344940110E-01, 9.974474996682516E-01, 4.106004179329372E-04, \ -9.406336688240443E-01, 4.809416959792988E-02, 7.867342756512173E-03, \ -9.385942706076326E-01, -8.971257377253743E-01, 3.361963450252926E-03, \ -9.374484562304576E-01, -4.280910958367013E-01, 5.268531158388501E-03, \ -9.355541598304502E-01, 2.580629240689983E-01, 7.741872807667612E-03, \ -9.298520361643660E-01, 4.530291593891102E-01, 6.861969988622674E-03, \ -9.288002329410462E-01, -9.982636344108895E-01, 4.247627014166712E-04, \ -9.286076316092796E-01, -9.683702815657360E-01, 2.067880829241110E-03, \ -9.273140499128685E-01, -5.830164942292532E-01, 6.818967325836010E-03, \ -9.241333130400774E-01, 9.730541529028506E-01, 1.883965192232535E-03, \ -9.237428919656653E-01, 9.027306131882519E-01, 3.504902468774958E-03, \ -9.235277754610037E-01, 6.312812357563800E-01, 6.653238342342486E-03, \ -9.201554641362426E-01, 7.828842024684245E-01, 5.399263941930352E-03, \ -9.146048961351547E-01, -3.818203957693841E-01, 3.883204055435776E-03, \ -9.134571331269357E-01, -7.302858649211827E-01, 5.936946390067688E-03, \ -9.127061051003793E-01, -2.440926271600780E-01, 7.778151311059332E-03, \ -9.000460112835083E-01, -5.999759307515896E-02, 1.006988417423119E-02, \ -8.993673287617778E-01, -8.451235123042792E-01, 5.132639563405409E-03, \ -8.951339292576600E-01, 1.501613851250017E-01, 1.029518732475798E-02, \ -8.900418335246519E-01, -9.336515985913562E-01, 3.643970310522402E-03, \ -8.898728450490625E-01, 3.576291382984933E-01, 9.637275856624482E-03, \ -8.857738818343428E-01, 9.936543288762641E-01, 1.022984433880787E-03, \ -8.818416083906041E-01, 9.450853611425074E-01, 3.145523188534807E-03, \ -8.817749203273469E-01, -4.932298853007941E-01, 9.084000283221681E-03, \ -8.814761392195805E-01, 5.416562961189009E-01, 9.072290159833062E-03, \ -8.809406948295482E-01, 8.535407316796645E-01, 5.347074653297229E-03, \ -8.798020856626885E-01, -9.884352690470977E-01, 1.656645365945089E-03, \ -8.768241727520295E-01, 7.105750002763417E-01, 7.595594780779568E-03, \ -8.743313495697173E-01, -6.501013827893755E-01, 7.766100758953991E-03, \ -8.675207720318823E-01, -3.252706153983532E-01, 8.588815830823287E-03, \ -8.531346041372393E-01, -7.827795724666364E-01, 6.991254752878786E-03, \ -8.485014584070562E-01, -1.648574733809313E-01, 1.202856513087624E-02, \ -8.434761432300958E-01, 4.179466117573257E-02, 1.258022009476385E-02, \ -8.393214861404557E-01, -8.894108000250006E-01, 5.524277448717241E-03, \ -8.391818467944713E-01, 2.545179546089011E-01, 1.225926031029606E-02, \ -8.389010580797999E-01, 9.785599021539588E-01, 2.201494437849886E-03, \ -8.333919059785300E-01, 9.103106242715236E-01, 4.477470554220304E-03, \ -8.311563781350246E-01, -9.635256164514960E-01, 3.376010197250481E-03, \ -8.298217920912521E-01, 7.941332222788777E-01, 7.533564430897306E-03, \ -8.290685095371755E-01, 4.482650209711272E-01, 1.149566481976958E-02, \ -8.246295014835788E-01, 6.305997501362324E-01, 1.002133619364441E-02, \ -8.207113611081525E-01, -5.682370182998021E-01, 9.882671274606030E-03, \ -8.184340779238838E-01, -4.076114937064008E-01, 1.051088940238909E-02, \ -8.157166374300039E-01, -9.978562540287571E-01, 7.535666678414864E-04, \ -8.078488627527156E-01, -7.069269989950133E-01, 8.137719625036887E-03, \ -8.030595241917000E-01, 9.978144889761291E-01, 7.398767813052343E-04, \ -7.837853688110477E-01, -2.620814341544582E-01, 1.356775659591216E-02, \ -7.828099445346539E-01, 9.554066491475680E-01, 3.742102504728495E-03, \ -7.821811758153498E-01, -8.335204770344818E-01, 7.560387964952924E-03, \ -7.806111270198954E-01, 8.684234719628749E-01, 6.102001596168975E-03, \ -7.803524467869071E-01, -6.465757120579249E-02, 1.471759892403581E-02, \ -7.781302732885756E-01, 1.478929640026117E-01, 1.455413037861192E-02, \ -7.699048258009954E-01, -9.276274655447458E-01, 5.304525007717353E-03, \ -7.695306270777027E-01, 7.257931943974629E-01, 1.003569188582270E-02, \ -7.682303760797261E-01, 3.499626949711698E-01, 1.375880064922265E-02, \ -7.631751201806299E-01, 5.447749679670292E-01, 1.242753039931487E-02, \ -7.596138287899911E-01, -9.835396090923282E-01, 2.607052889697995E-03, \ -7.538052521221817E-01, -4.841495100795145E-01, 1.150926269265990E-02, \ -7.454457200592598E-01, -6.328463240917150E-01, 1.022935020395876E-02, \ -7.377478072703448E-01, -7.556338792328159E-01, 7.532798021311965E-03, \ -7.352232084975729E-01, 9.868858130897517E-01, 2.411113681116213E-03, \ -7.198141234443793E-01, 8.186185822277544E-01, 8.298549121304033E-03, \ -7.182219035413855E-01, 9.224204584112459E-01, 5.742283577427958E-03, \ -7.128567090368071E-01, -3.559798783186696E-01, 1.405749666059914E-02, \ -7.053617504255151E-01, 4.264400312830402E-02, 1.671342637637877E-02, \ -7.048221835776498E-01, -1.660772434082720E-01, 1.620416954102582E-02, \ -7.028328208733023E-01, -8.796259271763389E-01, 7.428666069379373E-03, \ -7.005292342230423E-01, 2.490631256735430E-01, 1.528459322279345E-02, \ -7.004349479969345E-01, 6.487283853703079E-01, 1.261520225658359E-02, \ -6.939940634234720E-01, 4.522675627245327E-01, 1.477231723739015E-02, \ -6.903338552941003E-01, -9.562199287411650E-01, 4.558348175052095E-03, \ -6.871780610546661E-01, -9.960902675679658E-01, 1.281042369432823E-03, \ -6.751199651659419E-01, -7.954841412473590E-01, 6.801383287420498E-03, \ -6.746711192530436E-01, -5.537611273503755E-01, 1.197946633058212E-02, \ -6.594485902401920E-01, -6.893928585162992E-01, 1.054328271246189E-02, \ -6.589580171205064E-01, 9.979540800990127E-01, 9.138061267054189E-04, \ -6.581546857660769E-01, 9.651549901275206E-01, 4.438106561226704E-03, \ -6.508115469743178E-01, 7.593018044169728E-01, 1.059590935519099E-02, \ -6.442960669971189E-01, 8.800883973543062E-01, 8.056539860531373E-03, \ -6.342911650570392E-01, -4.362965821626758E-01, 1.297306553921443E-02, \ -6.311270608623304E-01, 1.623081864679719E-01, 1.169419850392987E-02, \ -6.236113280952295E-01, 5.626303448491500E-01, 1.512993252997899E-02, \ -6.230699212989589E-01, -2.676031853187564E-01, 1.701679082042949E-02, \ -6.228316359543020E-01, -6.139199670125942E-02, 1.791234833004659E-02, \ -6.180167254452483E-01, 3.536311947236717E-01, 1.688041459255943E-02, \ -6.139917320508425E-01, -9.166124328923988E-01, 6.752267430799639E-03, \ -6.135997420321182E-01, -9.785871069978234E-01, 3.265291929749685E-03, \ -6.049437626707715E-01, -8.348685175419790E-01, 7.920079758120289E-03, \ -5.924156072192565E-01, 1.122151337459072E-01, 9.854536189651026E-03, \ -5.808954536963412E-01, -6.144989257211043E-01, 1.238347439918297E-02, \ -5.771402248064471E-01, 6.916411158262615E-01, 1.234940827737965E-02, \ -5.727489353537671E-01, -7.435597296984338E-01, 1.009808411716704E-02, \ -5.727126755704744E-01, 9.873108745063405E-01, 2.892689438784615E-03, \ -5.726969487730084E-01, 9.340439611874428E-01, 6.716170602729774E-03, \ -5.641880535367902E-01, 8.278878381092918E-01, 1.034186096378337E-02, \ -5.619751160626054E-01, -9.957490800477657E-01, 1.306397050035806E-03, \ -5.595114849904512E-01, -4.950932951701612E-01, 1.012055396521365E-02, \ -5.404408181688395E-01, 4.682798275107506E-01, 1.740850053308458E-02, \ -5.346178912468168E-01, -1.658145193211824E-01, 1.879896919108429E-02, \ -5.316901221553333E-01, 2.545384708233044E-01, 1.840778394220723E-02, \ -5.304417973198247E-01, -3.592809785284879E-01, 1.695143266847294E-02, \ -5.280451477489559E-01, -9.481339086199096E-01, 5.577814969827481E-03, \ -5.221322143523578E-01, 2.800952111551927E-02, 1.767290541941230E-02, \ -5.151186905025813E-01, -8.730519403291820E-01, 8.112883844601817E-03, \ -5.020061912373424E-01, 6.192421120294556E-01, 1.353861723690707E-02, \ -4.903530401754813E-01, -7.931258003876139E-01, 8.399071608732376E-03, \ -4.865831129729520E-01, 9.982345574079382E-01, 8.888257339789671E-04, \ -4.846013662166668E-01, -6.763247187729596E-01, 1.217250051276967E-02, \ -4.839999766820920E-01, 8.928758009749419E-01, 8.937216600833743E-03, \ -4.825855280212472E-01, -5.431509513734653E-01, 1.183707346969829E-02, \ -4.823249529225693E-01, 7.660844388757198E-01, 1.216788713755992E-02, \ -4.796646373118009E-01, -9.806365591887873E-01, 2.997919914508063E-03, \ -4.767777412147164E-01, 9.670704183485596E-01, 5.199287981007803E-03, \ -4.578606953009008E-01, 3.653266008375833E-01, 1.471515179826852E-02, \ -4.457848210286569E-01, 1.456094511265953E-01, 1.865104111169145E-02, \ -4.379382988456925E-01, -2.629650176911282E-01, 1.846921409696814E-02, \ -4.348650881002861E-01, -9.972784483849305E-01, 1.074202056193302E-03, \ -4.322726489605065E-01, -7.297583238110245E-02, 1.906793743471395E-02, \ -4.275919441110620E-01, -4.360820986786115E-01, 1.573633000734291E-02, \ -4.270673912729934E-01, -9.090686566218157E-01, 7.431022374141501E-03, \ -4.254326005730727E-01, 5.424147018907464E-01, 1.524591494142875E-02, \ -4.034134004690716E-01, 4.015985647828361E-01, 8.132984537933393E-03, \ -4.019562701112450E-01, -7.422749928931541E-01, 8.984384832841273E-03, \ -4.007956316021173E-01, 6.977544690649647E-01, 1.324825764743806E-02, \ -3.970394499889119E-01, 8.417028483702832E-01, 1.064019181372773E-02, \ -3.962311519387068E-01, -8.266178179921937E-01, 8.217747940915577E-03, \ -3.925693641275523E-01, -6.062484728313788E-01, 1.307080472085916E-02, \ -3.914186598228789E-01, 9.913544137855500E-01, 2.245607042588322E-03, \ -3.907636956098022E-01, -9.581583494234572E-01, 4.727344394460009E-03, \ -3.802684631916854E-01, 9.356425085799084E-01, 7.546845180916252E-03, \ -3.667235432096608E-01, 2.538377799106385E-01, 1.802700518759309E-02, \ -3.542077324305666E-01, 3.400725316094907E-02, 1.656276879967741E-02, \ -3.382472441767229E-01, -1.769861959933089E-01, 1.695133386076922E-02, \ -3.360507944158749E-01, -9.870600771841807E-01, 2.993500538686252E-03, \ -3.321333158476729E-01, -3.472770242047587E-01, 1.692208839910539E-02, \ -3.283161387055968E-01, -5.022338788020836E-01, 1.384987928124117E-02, \ -3.234470453782608E-01, 4.749702348708390E-01, 1.664727618065397E-02, \ -3.202148987380042E-01, 7.835525766177759E-01, 1.004319161998912E-02, \ -3.190832382601436E-01, 6.269941745416843E-01, 1.454224638443978E-02, \ -3.189860391580026E-01, -8.607035592419185E-01, 8.155361325578816E-03, \ -3.171223960288885E-01, 9.776396030267889E-01, 3.392812344765450E-03, \ -3.152599194498346E-01, -6.813908984973552E-01, 1.112163469352541E-02, \ -3.048189974393888E-01, -7.518549520866326E-01, 5.276819552431108E-03, \ -3.010266238384297E-01, 1.148836153616587E-01, 1.208064328383956E-02, \ -2.975203773505370E-01, -9.264620147915089E-01, 6.591008941421552E-03, \ -2.866843597937876E-01, 8.916357142521784E-01, 9.722680920609808E-03, \ -2.778520292008587E-01, 3.379398856834260E-01, 1.660452875526483E-02, \ -2.744543978372941E-01, -9.801898430305439E-02, 1.247830609628909E-02, \ -2.587845000315547E-01, -9.987548667843699E-01, 8.603127328776212E-04, \ -2.544608894429891E-01, 9.979361786556559E-01, 1.252512834658488E-03, \ -2.535888618284378E-01, -5.699260916663523E-01, 1.192322325012015E-02, \ -2.516174268783917E-01, 7.330785425737227E-01, 8.853857957147779E-03, \ -2.417076375974273E-01, -7.891442960379055E-01, 1.102295327385847E-02, \ -2.413622675326031E-01, -2.767284930209392E-01, 1.077421913186015E-02, \ -2.328396638924550E-01, -9.660240239613915E-01, 5.265050387190376E-03, \ -2.312798916515771E-01, 8.188743812299971E-01, 4.930961548632319E-03, \ -2.306624795927337E-01, 9.461369824834985E-01, 3.182424510285970E-03, \ -2.303709121443397E-01, 9.629630229642722E-01, 3.441645956712537E-03, \ -2.267984183900834E-01, -4.153651530633773E-01, 1.478553509404215E-02, \ -2.256135494476024E-01, 1.919211927874176E-01, 1.887063394340442E-02, \ -2.179557409452807E-01, 5.651427172988402E-01, 1.620039755630136E-02, \ -2.168766477790742E-01, -1.012612126707933E-02, 1.760999731931498E-02, \ -2.016684978642726E-01, -8.842464367674409E-01, 8.512644523701873E-03, \ -1.993535882469331E-01, -6.338481461271839E-01, 9.730410168975228E-03, \ -1.913491324242725E-01, -2.232354009324879E-01, 1.422718417945826E-02, \ -1.890072860808679E-01, 4.247570907504695E-01, 1.695426438700273E-02, \ -1.862712620524861E-01, 6.913654513337745E-01, 1.082745299386850E-02, \ -1.746191018373572E-01, 8.480550307741350E-01, 8.886868262309344E-03, \ -1.675200684369691E-01, -7.047430234854786E-01, 1.094270966276307E-02, \ -1.555836887665503E-01, -4.800663622673465E-01, 1.256149504580157E-02, \ -1.539778628553684E-01, -9.901542147304263E-01, 2.778842341022969E-03, \ -1.428714573350953E-01, 9.873473637042918E-01, 3.649388897241209E-03, \ -1.384698657127528E-01, 9.205163602534699E-01, 7.904116666380833E-03, \ -1.280453089534869E-01, -8.261529284212121E-01, 1.003683355115124E-02, \ -1.269663966462650E-01, -9.340066191936205E-01, 7.536775230064883E-03, \ -1.262851022233290E-01, 9.368263634475028E-02, 1.974459832420309E-02, \ -1.259733133156085E-01, 2.934330084484927E-01, 2.074833465157029E-02, \ -1.215370941220813E-01, -1.129536910574994E-01, 1.891311893739475E-02, \ -1.063702041365650E-01, 7.792027274018843E-01, 1.191220588531841E-02, \ -1.040885518460405E-01, -3.345081265086896E-01, 1.973449969826947E-02, \ -9.605998455844682E-02, 6.444074525536151E-01, 1.345070861908871E-02, \ -9.279166418896197E-02, 5.146935916151650E-01, 1.655226263892481E-02, \ -9.125555597164577E-02, -5.450318588034616E-01, 1.217992697790634E-02, \ -8.532044687750825E-02, -7.537009739836885E-01, 6.788672864407014E-03, \ -6.799112688359676E-02, -6.229899588936270E-01, 1.080161967200763E-02, \ -6.241140417558962E-02, -9.744491489990948E-01, 3.566539673859765E-03, \ -5.161370829018064E-02, 9.610809656564491E-01, 6.005594200474568E-03, \ -4.538160583172780E-02, 1.675029579312542E-02, 1.139804373859566E-02, \ -4.097385567264155E-02, 8.800609612527350E-01, 8.815909757700713E-03, \ -3.655935033800797E-02, -1.968615631298038E-01, 1.402267657973052E-02, \ -3.473806771275045E-02, -8.898414026442482E-01, 8.163797867856551E-03, \ -3.115326906841854E-02, -7.299617142501118E-01, 8.753969855827624E-03, \ -2.664715561157583E-02, -9.979756016894712E-01, 1.223714150081927E-03, \ -2.609621149728821E-02, 9.978312276054969E-01, 1.321094043330279E-03, \ -2.462169196136119E-02, 4.000170187213391E-01, 1.964525457913152E-02, \ -1.904435752714274E-02, 7.360687696712604E-01, 8.550678949429199E-03, \ -1.889566824340530E-02, 1.984890570456425E-01, 2.186008310624084E-02, \ -9.785690785648083E-03, -8.389279715572893E-01, 6.367637566748681E-03, \ -9.157810803927260E-03, -4.247277120525336E-01, 1.808897606828866E-02, \ 3.179810404505250E-03, 8.314617064208917E-01, 7.240482363634763E-03, \ 8.164449639995641E-03, -3.602121469951976E-02, 1.507784539606016E-02, \ 8.914821501355173E-03, -9.569660527272593E-01, 4.452800904218950E-03, \ 1.397375150217838E-02, 6.074602279060227E-01, 1.339941447663378E-02, \ 2.177165943291160E-02, -2.514057561092151E-01, 1.257069649597742E-02, \ 4.345656816980569E-02, -6.515535698280098E-01, 1.376520145235682E-02, \ 4.780837263094481E-02, -5.293455201419695E-01, 1.433806151954274E-02, \ 5.126722291181950E-02, 7.136184270678109E-01, 9.059040654245952E-03, \ 5.384128121275275E-02, 5.215281819965334E-01, 1.026521104059108E-02, \ 5.402250856984708E-02, 9.276694371633791E-01, 7.888401157883149E-03, \ 5.581143910668790E-02, 9.821386878503260E-01, 3.771203907120499E-03, \ 6.627333635862039E-02, -7.885663982200815E-01, 1.217604845925398E-02, \ 7.206636203593361E-02, -9.211241316961639E-01, 6.736415177465982E-03, \ 7.992668048420556E-02, 3.134386785203354E-01, 2.055572742606252E-02, \ 8.448805256391662E-02, 9.712957741353333E-02, 2.128227886088045E-02, \ 8.463750249088479E-02, -9.874388870838863E-01, 3.523234483327328E-03, \ 9.799267198568701E-02, -1.212891339515704E-01, 1.949535188292260E-02, \ 9.827877674637196E-02, -3.251986289297008E-01, 1.749435408326382E-02, \ 9.985235399264410E-02, 8.076435842941359E-01, 1.073632596606910E-02, \ 1.057705156820273E-01, 4.793866965123078E-01, 1.166074198719580E-02, \ 1.278018204573015E-01, -8.673024017686580E-01, 8.130060280452144E-03, \ 1.364747655580873E-01, 8.824534837148562E-01, 8.631223960740082E-03, \ 1.418802082443522E-01, 6.877615804223791E-01, 1.036232616585965E-02, \ 1.441395429362260E-01, -7.037951529711909E-01, 1.188979856915669E-02, \ 1.469434540715263E-01, -4.441704987291489E-01, 1.490787435959768E-02, \ 1.506185900581580E-01, 9.946720380541423E-01, 1.885774991512346E-03, \ 1.560960715550660E-01, -9.625915789870874E-01, 3.201097878674840E-03, \ 1.604800952783144E-01, 6.059469388605253E-01, 1.251646880334661E-02, \ 1.635825517653865E-01, -5.753866291936182E-01, 1.530295086183503E-02, \ 1.655478645083420E-01, 9.589555963365791E-01, 5.804218295769638E-03, \ 1.726856195129373E-01, 2.122274920034202E-01, 1.881284565328789E-02, \ 1.789604491789879E-01, -9.402742786279485E-01, 3.866866604734349E-03, \ 1.830770810490266E-01, -7.917068664553941E-03, 1.896081259105628E-02, \ 1.917045789075228E-01, -8.352790590418837E-01, 6.668422594982694E-03, \ 1.919614057410328E-01, 4.159468317764071E-01, 1.803709701284910E-02, \ 1.934907380358813E-01, -2.169747177608121E-01, 1.856246659829771E-02, \ 1.969572179795044E-01, -9.977527139562596E-01, 1.300798686497381E-03, \ 2.107123929928807E-01, -7.484424229574373E-01, 8.397883820247469E-03, \ 2.151288514233329E-01, 7.680354518275807E-01, 1.267367187142015E-02, \ 2.377269840756392E-01, -3.593587047461513E-01, 1.531855347072487E-02, \ 2.449798765113445E-01, 8.561714185289828E-01, 8.384247794169401E-03, \ 2.461530653627976E-01, 9.236449528059149E-01, 6.701681191198367E-03, \ 2.486966580905335E-01, 3.008228521374701E-01, 1.106325734333346E-02, \ 2.499701593513872E-01, -9.752017232492153E-01, 3.850329050405175E-03, \ 2.501058258824206E-01, 5.509389569101368E-01, 1.475977026196545E-02, \ 2.528611993268930E-01, 9.351675397537039E-02, 1.449585921909408E-02, \ 2.568949734863621E-01, -9.022348356156346E-01, 8.940909487499378E-03, \ 2.683426686375737E-01, 9.991154086591990E-01, 5.889345360874240E-04, \ 2.685503151871029E-01, -6.356230295277764E-01, 1.517335754148565E-02, \ 2.697644015612075E-01, 9.815789636486361E-01, 3.726914126330296E-03, \ 2.709381851134464E-01, -1.244795386325534E-01, 1.382732736695818E-02, \ 2.737056179114525E-01, -4.896517471925337E-01, 1.596973556497186E-02, \ 2.841153891916503E-01, -7.963610419905591E-01, 1.018240390326565E-02, \ 2.887360776877746E-01, 6.760513756029857E-01, 1.358604251351786E-02, \ 3.149795837868063E-01, 1.767826719425314E-01, 1.445177151533629E-02, \ 3.165712280980518E-01, 3.479571606636541E-01, 1.397116071739750E-02, \ 3.233387951857696E-01, -3.964021294199390E-02, 1.467594281112195E-02, \ 3.268920397235026E-01, -2.731725775852362E-01, 1.771570545449453E-02, \ 3.326248311408019E-01, 4.836740826389543E-01, 1.486343284668958E-02, \ 3.335126221786843E-01, -9.908899215613953E-01, 2.568858034338105E-03, \ 3.408563759162994E-01, 7.550164756697521E-01, 6.822413031377531E-03, \ 3.443109876462521E-01, 8.290574313399783E-01, 9.197826117265570E-03, \ 3.486450229035982E-01, -9.439378779811103E-01, 6.983226832200802E-03, \ 3.518759527448840E-01, 9.560724389841232E-01, 4.965627623349140E-03, \ 3.524828322454360E-01, -7.050052060893320E-01, 1.197554054145159E-02, \ 3.590126501200323E-01, 9.063249825645421E-01, 6.542367126762410E-03, \ 3.633899545054107E-01, -4.158806284730630E-01, 1.021934848164813E-02, \ 3.656349853648961E-01, -8.551125998661749E-01, 1.062020373233702E-02, \ 3.807891001192470E-01, 6.253125077526936E-01, 1.119123494000414E-02, \ 3.808423427288536E-01, 9.944730583867565E-01, 1.632382643499531E-03, \ 3.809375504826950E-01, -5.546294515204083E-01, 1.615046394684124E-02, \ 3.945468502595033E-01, 6.752821319401937E-02, 1.729957749916545E-02, \ 4.037326882224722E-01, -7.443269137253894E-01, 5.244741835639755E-03, \ 4.039759465731999E-01, -1.584043966963531E-01, 1.831424532905047E-02, \ 4.104920535739149E-01, 2.529785766209403E-01, 1.814309214474618E-02, \ 4.222816582184452E-01, 7.408148672071336E-01, 7.766759229688390E-03, \ 4.224134639390744E-01, -3.745372912517947E-01, 1.317478594938575E-02, \ 4.277143244118732E-01, 4.170215562701938E-01, 1.538057245965674E-02, \ 4.333717867425739E-01, 5.690603581255754E-01, 1.115237702189693E-02, \ 4.349755932480709E-01, -9.985636264967975E-01, 8.821277372105579E-04, \ 4.398941633478518E-01, 9.803729409712968E-01, 2.765623301727146E-03, \ 4.441324812379997E-01, -9.722660935224676E-01, 4.719463795528141E-03, \ 4.543070171443870E-01, 8.838298014870239E-01, 7.433086897010635E-03, \ 4.552061144607135E-01, 8.130123814788113E-01, 6.665811090423725E-03, \ 4.563764124987013E-01, -9.047285344881011E-01, 8.712285205058833E-03, \ 4.605130146464505E-01, -7.890667787179867E-01, 1.104769785347448E-02, \ 4.650767440674204E-01, -6.345308909000896E-01, 1.471818226211541E-02, \ 4.674115659846697E-01, -2.156835684881248E-02, 1.289379103218861E-02, \ 4.773494044297329E-01, 9.456346888484196E-01, 5.554333960414898E-03, \ 4.810795638831788E-01, 7.045677590620393E-01, 8.378675676746713E-03, \ 4.883109086023527E-01, -2.624666533620124E-01, 1.805604188701234E-02, \ 4.989586416584096E-01, -4.789926304087422E-01, 1.768874128800384E-02, \ 5.035782169093800E-01, 1.523921509996070E-01, 1.912436354376622E-02, \ 5.136924925920076E-01, 9.970688163327739E-01, 1.172939498317349E-03, \ 5.169947058579401E-01, 3.370225548177525E-01, 1.637088692250307E-02, \ 5.191129921767861E-01, -8.134646960530036E-02, 1.194181152772743E-02, \ 5.204183249331878E-01, 5.085175426873372E-01, 1.466908354875696E-02, \ 5.393484610466828E-01, 6.440810813198078E-01, 1.182257049730026E-02, \ 5.409261529913778E-01, -9.899204841179033E-01, 2.610777565683107E-03, \ 5.436431320060356E-01, -8.462212203410651E-01, 1.007390508879517E-02, \ 5.451712421766679E-01, 8.553559399904247E-01, 5.821377493347785E-03, \ 5.478116255118839E-01, -9.433804473799871E-01, 6.399987549895861E-03, \ 5.478642383937216E-01, -7.090052412035255E-01, 1.297516415531765E-02, \ 5.564069189295534E-01, 7.864423641670446E-01, 9.321003881444800E-03, \ 5.624905637364527E-01, 9.770501107487227E-01, 3.623905342788340E-03, \ 5.756133273548432E-01, 9.199072591365679E-01, 6.781383669452935E-03, \ 5.767931202505592E-01, -3.594698820499517E-01, 1.753399004685696E-02, \ 5.847884341379717E-01, -5.712950409715517E-01, 1.571578525431043E-02, \ 5.874943626825653E-01, -1.671372439879485E-01, 1.698143276407778E-02, \ 5.907655121511671E-01, 4.660979703031718E-02, 1.844804672503901E-02, \ 6.025450669838789E-01, 2.467984537567849E-01, 1.677462288624064E-02, \ 6.090800603255943E-01, 4.286875996929576E-01, 1.513541325944424E-02, \ 6.258710710954998E-01, 7.165277069854407E-01, 1.099701682736415E-02, \ 6.266701063249871E-01, 5.769310800380454E-01, 1.308931762513766E-02, \ 6.270265093488953E-01, -8.955278457672096E-01, 7.880275838227896E-03, \ 6.270791988555975E-01, -7.761774347112587E-01, 1.090179865169966E-02, \ 6.345595645944537E-01, -9.984595226960734E-01, 7.958742560860689E-04, \ 6.370082702111213E-01, -9.713020953178747E-01, 4.152547195517621E-03, \ 6.401569547703443E-01, 9.938746764274359E-01, 1.693532564574805E-03, \ 6.497075309477621E-01, 8.190875365131459E-01, 4.464599165971847E-03, \ 6.531764939123219E-01, 8.722128479560702E-01, 7.098779024952168E-03, \ 6.562818147683037E-01, -4.576915030242588E-01, 1.578169238311144E-02, \ 6.591132614876472E-01, 9.562877989480233E-01, 4.990862456559823E-03, \ 6.665524280175228E-01, -6.564174347015698E-01, 1.340898468809120E-02, \ 6.700483215827622E-01, -2.620296401455633E-01, 1.661493024207803E-02, \ 6.739087687271405E-01, -5.912298687650318E-02, 1.738774404391026E-02, \ 6.804263668179958E-01, 1.460527560676405E-01, 1.628317266757141E-02, \ 6.912597270988795E-01, 3.404614930979913E-01, 1.475743069354967E-02, \ 7.014060026242689E-01, -8.344065963965686E-01, 8.628757323236287E-03, \ 7.058713078417868E-01, -9.347792116756997E-01, 5.591815013522645E-03, \ 7.079262640927377E-01, 7.724165756101982E-01, 8.029293398342626E-03, \ 7.088857312664080E-01, 4.967023279703596E-01, 1.280511610828170E-02, \ 7.101371621418650E-01, 6.457186195302522E-01, 1.105714695286113E-02, \ 7.202725263717996E-01, 9.994335364106648E-01, 3.332183106806338E-04, \ 7.207000082772794E-01, -9.895454215133570E-01, 2.196061699346258E-03, \ 7.292419930403204E-01, 9.157811426160827E-01, 6.384383783991632E-03, \ 7.313037161184995E-01, -5.505073556267344E-01, 1.356179225976500E-02, \ 7.360379569189480E-01, 9.821653512788314E-01, 2.896207033581717E-03, \ 7.420779913438207E-01, -7.334083762452253E-01, 1.091197483582354E-02, \ 7.426392282312145E-01, -3.645617372015513E-01, 1.485653149831074E-02, \ 7.528875171829301E-01, -1.601913784019904E-01, 1.550841643509901E-02, \ 7.554705394085318E-01, 4.459678870394624E-02, 1.525675110217471E-02, \ 7.615088314802664E-01, 8.361789767059251E-01, 7.437033911513647E-03, \ 7.616191329271083E-01, 2.428806469892401E-01, 1.393414245795238E-02, \ 7.690623514791849E-01, -8.832140323355561E-01, 6.416243610572680E-03, \ 7.769110395657105E-01, -9.640621745534697E-01, 3.536472011287542E-03, \ 7.791327107486173E-01, 7.076456730403544E-01, 8.608254113024549E-03, \ 7.829433189081187E-01, 4.115102550571496E-01, 1.200809373544269E-02, \ 7.868440926994443E-01, 5.651491336107541E-01, 1.060866196158618E-02, \ 7.972018338130737E-01, -9.982656120587307E-01, 6.617532655225795E-04, \ 7.992533072865277E-01, 9.540895776450939E-01, 4.268074259130473E-03, \ 7.997458930401107E-01, -6.367603626594224E-01, 1.111474927165712E-02, \ 8.081744777455525E-01, 9.960702140107771E-01, 1.017600517226123E-03, \ 8.089591973706927E-01, -4.632652606248073E-01, 1.251849428515888E-02, \ 8.099291035161289E-01, -8.014389840867161E-01, 8.342550278485161E-03, \ 8.178497193943023E-01, -2.666599682868107E-01, 1.332265855465428E-02, \ 8.217550355721945E-01, 8.852380807000872E-01, 5.823149693854945E-03, \ 8.248245538809940E-01, -5.566567666688539E-02, 1.345955258709000E-02, \ 8.273765716391087E-01, 1.453558810621134E-01, 1.259780460396138E-02, \ 8.290016229908019E-01, -9.229141926989057E-01, 4.488946673444931E-03, \ 8.312137267728380E-01, 7.737766398959207E-01, 7.517252141547089E-03, \ 8.388984040766698E-01, -9.832445987611033E-01, 1.929266776470329E-03, \ 8.403266531241620E-01, 3.204495146952222E-01, 1.029684622414818E-02, \ 8.460597215913815E-01, 6.338027356985795E-01, 8.416485697270661E-03, \ 8.568044167409157E-01, 4.819269934220108E-01, 1.007395289111620E-02, \ 8.594761322839366E-01, -7.158610827355618E-01, 8.544219655885121E-03, \ 8.596747778040242E-01, 9.812814052217911E-01, 2.240512756664986E-03, \ 8.673861033254269E-01, -5.560970888453474E-01, 9.984840676923732E-03, \ 8.687781521055384E-01, -8.598267927850410E-01, 5.909994487514023E-03, \ 8.736670048192481E-01, -3.696430123878972E-01, 1.076394694975309E-02, \ 8.755805123744724E-01, 9.286193847818732E-01, 4.104689783978988E-03, \ 8.802236992100727E-01, -1.636568935863089E-01, 1.134645488289895E-02, \ 8.818997102528549E-01, -9.534487417523689E-01, 2.910586840863237E-03, \ 8.822967422821377E-01, 8.327421092911165E-01, 5.857534910892974E-03, \ 8.855982125406932E-01, 4.859209760326954E-02, 1.081167505168916E-02, \ 8.890374543692038E-01, -9.948464939801149E-01, 8.623364516957774E-04, \ 8.910752241508448E-01, 2.326161934300192E-01, 8.657918564170076E-03, \ 8.924589745638828E-01, 7.060431740562146E-01, 7.042076085079714E-03, \ 9.038398251450660E-01, 3.788269004577886E-01, 7.187646339123819E-03, \ 9.047525315555535E-01, 9.968725405524917E-01, 6.949154523896342E-04, \ 9.073202051898728E-01, 5.601382603883635E-01, 7.436779820469599E-03, \ 9.094763644040651E-01, -7.866497708112262E-01, 6.068502473389529E-03, \ 9.156228827733042E-01, -6.431201317749281E-01, 7.377455744161945E-03, \ 9.180472655171079E-01, -9.072540984216338E-01, 3.786751966998675E-03, \ 9.201626776981597E-01, -4.661265100590501E-01, 8.127631621548038E-03, \ 9.203986204520849E-01, 9.637153195221804E-01, 2.417737344163030E-03, \ 9.253660941390490E-01, -2.716337337205402E-01, 8.801548207513724E-03, \ 9.261353319076545E-01, 8.862669995455879E-01, 4.060802203561684E-03, \ 9.267589978677341E-01, -9.763906164865308E-01, 1.670956060135679E-03, \ 9.296045895443023E-01, -5.692925807559270E-02, 8.746043891267270E-03, \ 9.333076832759312E-01, 7.750586963210155E-01, 5.218813242315273E-03, \ 9.349472019768319E-01, 1.484963626935633E-01, 7.389237501576750E-03, \ 9.374075610340270E-01, 4.399432525590961E-01, 5.306731082295346E-03, \ 9.400580998441358E-01, 2.800423571899046E-01, 2.918608608301983E-03, \ 9.427005957607336E-01, -9.981293404387946E-01, 3.121604460197559E-04, \ 9.429072476811193E-01, 6.363767343005619E-01, 5.407112479875284E-03, \ 9.493669863964902E-01, -8.473200668433625E-01, 3.846633887541680E-03, \ 9.531421892703198E-01, 9.886504733043840E-01, 1.059870260157853E-03, \ 9.531523577846154E-01, -7.227080846477228E-01, 4.913934090239149E-03, \ 9.551294253765648E-01, -5.565381013465578E-01, 5.502249381020629E-03, \ 9.565005297414140E-01, -9.442027533788165E-01, 2.096401005441424E-03, \ 9.593664858716742E-01, 3.053899240329821E-01, 4.414651034089092E-03, \ 9.596171541726947E-01, 9.321549520212439E-01, 2.376782646049461E-03, \ 9.608407654147756E-01, -3.746593104351715E-01, 6.173923907524476E-03, \ 9.621733022265412E-01, -1.656432296827873E-01, 6.194664026342116E-03, \ 9.653886055298680E-01, 5.150967645436137E-01, 4.919715066546461E-03, \ 9.657457263464734E-01, 8.382246690529398E-01, 3.337986835409403E-03, \ 9.659619334304088E-01, 5.177847935345642E-02, 5.910264564840144E-03, \ 9.680706602854513E-01, -9.879517363794693E-01, 7.458697645747395E-04, \ 9.699041735219510E-01, 7.091732174417210E-01, 3.716606593077174E-03, \ 9.780789408497448E-01, -8.978740559477660E-01, 2.027198167864543E-03, \ 9.785773409931260E-01, 3.759248114479532E-01, 2.296845005889542E-03, \ 9.787987362927277E-01, -6.363450519845599E-01, 3.147711109744902E-03, \ 9.798364272746407E-01, -7.938445879710778E-01, 2.695483313991862E-03, \ 9.808577769253177E-01, 9.991060454256292E-01, 1.898396166637044E-04, \ 9.809404950148999E-01, 2.027338094714153E-01, 3.990737313161254E-03, \ 9.816961339717497E-01, 9.686754967649751E-01, 1.091492569688088E-03, \ 9.840712745111234E-01, -2.626430872984131E-01, 3.097193509559313E-03, \ 9.843743224238546E-01, -4.750390603479636E-01, 3.584637477381167E-03, \ 9.862128026721591E-01, -9.654567087398049E-01, 8.890511587785677E-04, \ 9.863734263187778E-01, -5.930270513959802E-02, 3.688256991164665E-03, \ 9.865546785141253E-01, 6.035001549964859E-01, 3.023283764277423E-03, \ 9.869243250476414E-01, 8.947234846399443E-01, 1.668881526792388E-03, \ 9.893166095732513E-01, 7.775602858535637E-01, 2.064175704304855E-03, \ 9.894504025423468E-01, 4.193743047955185E-01, 2.246763513509927E-03, \ 9.896385884303135E-01, -9.973923443405563E-01, 1.851291041947312E-04, \ 9.901336007320924E-01, -7.114773894581000E-01, 1.034175772851253E-03, \ 9.919851856512742E-01, -3.114226899156755E-01, 1.170994569732132E-03, \ 9.940232288498372E-01, 1.283386128570500E-01, 1.603565228346927E-03, \ 9.953349820305321E-01, -8.536885202268084E-01, 1.025029596972725E-03, \ 9.959554742671337E-01, -6.783893531292533E-01, 6.259052194003695E-04, \ 9.962560319135685E-01, 9.890105787700981E-01, 2.669967855812931E-04, \ 9.964245305056454E-01, -9.302976837204511E-01, 6.033448523675142E-04, \ 9.967719421795390E-01, -5.665750992594114E-01, 1.303580233612213E-03, \ 9.972052149065609E-01, 9.417145950405990E-01, 5.101220212030444E-04, \ 9.973430748397051E-01, 2.936231135628724E-01, 1.457376036828792E-03, \ 9.977062733384420E-01, 3.661565190365799E-02, 9.783420284466598E-04, \ 9.978229005821968E-01, 6.875780893713088E-01, 9.676594371466553E-04, \ 9.978827039187840E-01, -1.661072510068121E-01, 1.283088734138761E-03, \ 9.979604058269933E-01, 5.108799809982550E-01, 1.066411053654888E-03, \ 9.980979734268004E-01, -3.916679884444568E-01, 1.034466005643900E-03, \ 9.983096397698943E-01, -7.631969332836371E-01, 5.325513292549041E-04, \ 9.985301658336433E-01, 8.440237285924725E-01, 5.771277489702493E-04, \ 9.987276765293339E-01, -9.843837655020101E-01, 1.687416201363766E-04 ] ) return xyw def smr53 ( ): #*****************************************************************************80 # ## smr53 returns the SMR rule of degree 53. # # Discussion: # # DEGREE: 53 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 498 # NORM INF MOMS. RESIDUAL: 8.88178e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*498), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.985928023604709E-01, 9.844383621232889E-01, 1.770821645368481E-04, \ -9.985845745857554E-01, -8.445726670375774E-01, 5.544684199320334E-04, \ -9.983624118051736E-01, 7.608024429037672E-01, 5.224452130672093E-04, \ -9.981572755902530E-01, 3.878455559966326E-01, 9.745188221536845E-04, \ -9.979563603675163E-01, 1.627643560997576E-01, 1.227147024948174E-03, \ -9.979346610008943E-01, -5.127640690222413E-01, 1.033714442116006E-03, \ -9.979107729485314E-01, 6.529159127971879E-01, 3.633867657362896E-04, \ -9.978751297025205E-01, -6.879180639452499E-01, 9.450952193083518E-04, \ -9.974464559033922E-01, -2.966888554053162E-01, 1.397441303354461E-03, \ -9.973454309733404E-01, -9.423377622335455E-01, 4.836806630189215E-04, \ -9.972986691166712E-01, -2.707798066058207E-02, 8.893716616277809E-04, \ -9.965532592866511E-01, 9.290044070830288E-01, 6.034648824689160E-04, \ -9.964624830190837E-01, 5.570787045642487E-01, 1.303165763686854E-03, \ -9.964167588339662E-01, -9.892036664406441E-01, 2.516135591721077E-04, \ -9.954005028570233E-01, -1.203116337354302E-01, 1.443569885953676E-03, \ -9.953468235808713E-01, 8.508120228627952E-01, 1.028310207063733E-03, \ -9.933660348449341E-01, 3.161717536031352E-01, 8.387713122106447E-04, \ -9.914304305563754E-01, -4.291601514462605E-01, 1.270285302858647E-03, \ -9.914052559973405E-01, 7.023250519059472E-01, 1.361348704496822E-03, \ -9.896982696240531E-01, -7.781770875290389E-01, 1.992196225105480E-03, \ -9.891720527404116E-01, 9.974135252406250E-01, 1.922590066403422E-04, \ -9.875040522290420E-01, -8.954189297031747E-01, 1.599426753793162E-03, \ -9.867187183083578E-01, -6.036002868761330E-01, 2.989922308625185E-03, \ -9.865979212862428E-01, 5.871716068212986E-02, 3.448498853249387E-03, \ -9.861629614331282E-01, 9.648994574590848E-01, 9.190271035579097E-04, \ -9.853079288654077E-01, 2.623064638103086E-01, 3.238657892966299E-03, \ -9.844227148004673E-01, 4.680325982952541E-01, 3.466798907655683E-03, \ -9.831116643490232E-01, -3.932597865155385E-01, 2.757351758467422E-03, \ -9.826130188082844E-01, -2.018533291539324E-01, 3.940386018971356E-03, \ -9.825204731628883E-01, -9.691072435867270E-01, 1.033098155222703E-03, \ -9.815923254661588E-01, -9.991082969355470E-01, 1.800328977889874E-04, \ -9.799368890832454E-01, 7.898861275347491E-01, 2.697855299373055E-03, \ -9.789828886434943E-01, 6.301653850940090E-01, 3.120578758401599E-03, \ -9.785540980020077E-01, 8.955915042635302E-01, 2.022068123378164E-03, \ -9.708143762319804E-01, -7.098339240446494E-01, 3.611310052438938E-03, \ -9.679069092640856E-01, -5.291894734981822E-02, 5.483965867735776E-03, \ -9.669765353727785E-01, -8.388123877959717E-01, 3.240365622776667E-03, \ -9.666680119711900E-01, 9.879489037902746E-01, 8.035625344075275E-04, \ -9.651954595073776E-01, -5.128458551084091E-01, 5.121256639651095E-03, \ -9.634120661314701E-01, 1.626856446045910E-01, 5.991502859241982E-03, \ -9.617304012154808E-01, 3.684756255396696E-01, 5.961021756038116E-03, \ -9.614256374444105E-01, -9.328771743819428E-01, 2.264842731050030E-03, \ -9.606958049220916E-01, -3.081366550020263E-01, 5.455334451053538E-03, \ -9.572708860210799E-01, 9.424725960383203E-01, 2.087979607175203E-03, \ -9.558923457352529E-01, 5.499187290928166E-01, 5.368921482058166E-03, \ -9.549989203380340E-01, -9.887724667769165E-01, 1.007773895019914E-03, \ -9.539639220051850E-01, 7.173033838147738E-01, 4.862799620669253E-03, \ -9.502192536056790E-01, 8.439252795287028E-01, 3.825522511161339E-03, \ -9.443304774038754E-01, -6.368742088572625E-01, 5.273401811778445E-03, \ -9.395231994348571E-01, -1.457862489409124E-01, 6.657538796439106E-03, \ -9.389178998337855E-01, 9.983688364336674E-01, 3.205800161394826E-04, \ -9.350865783178156E-01, -7.749842255798853E-01, 5.158635670181725E-03, \ -9.343242796602114E-01, -4.294254268855136E-01, 6.109989073144874E-03, \ -9.338088134935508E-01, -2.598456851976017E-01, 2.595536800191603E-03, \ -9.320728477635706E-01, 5.264490338972241E-02, 8.452404593360153E-03, \ -9.290856294325159E-01, -8.871608380321619E-01, 3.918401242147426E-03, \ -9.273226373183119E-01, 2.659618987488091E-01, 8.495674903422557E-03, \ -9.261329198739888E-01, 9.746027153962696E-01, 1.776302974763280E-03, \ -9.235763538947596E-01, -9.640444233499114E-01, 2.312159206833450E-03, \ -9.220086198065640E-01, 4.592930118785874E-01, 7.896825458118423E-03, \ -9.202380773523146E-01, 9.050386110265841E-01, 3.683312035807689E-03, \ -9.172703778429636E-01, 6.365672819732232E-01, 7.262815260314241E-03, \ -9.111951012665040E-01, 7.814905098540573E-01, 6.041492892648836E-03, \ -9.096781399489776E-01, -5.604773052603598E-01, 7.205603970066971E-03, \ -9.087015117883152E-01, -9.969915072869269E-01, 6.470318411854381E-04, \ -9.013251796383466E-01, -3.666844788249730E-01, 6.151586476003017E-03, \ -8.969710028279102E-01, -2.256802214985589E-01, 7.410425347310207E-03, \ -8.940375402275955E-01, -7.041313708313275E-01, 7.142826419236804E-03, \ -8.895672957850502E-01, -5.293510599726065E-02, 1.040987558289029E-02, \ -8.866199302094060E-01, 9.938258930614400E-01, 9.839665860219130E-04, \ -8.860972589276557E-01, -8.331612020727454E-01, 5.781048219808546E-03, \ -8.837148490953154E-01, 1.576361975891787E-01, 1.099997902023932E-02, \ -8.811873265749205E-01, 9.497474912342982E-01, 3.085534283412631E-03, \ -8.801258841317081E-01, -9.290747990279913E-01, 3.975614899427044E-03, \ -8.768491423274493E-01, 3.627381824235000E-01, 1.044386961685712E-02, \ -8.732550362347075E-01, 8.574796771270368E-01, 5.681748093343370E-03, \ -8.702282345000577E-01, 5.484829121208596E-01, 9.793908671588478E-03, \ -8.659273047100809E-01, -9.818377837992252E-01, 2.087386821145729E-03, \ -8.621111168073954E-01, 7.090421883632249E-01, 8.492263963507059E-03, \ -8.619939023548052E-01, -4.806373416483297E-01, 9.672951472047629E-03, \ -8.480068796648080E-01, -3.119740973719929E-01, 9.321790315925496E-03, \ -8.467158604246162E-01, -6.289407999349215E-01, 8.567266871139807E-03, \ -8.371745526664012E-01, 9.808931214242823E-01, 2.050522723814058E-03, \ -8.345679943920669E-01, -7.722499650445845E-01, 7.694139784998021E-03, \ -8.333486955686686E-01, -1.495187297327515E-01, 1.195411188321836E-02, \ -8.298817228165417E-01, 4.932544049099609E-02, 1.308861281523968E-02, \ -8.279841059514953E-01, 9.168099196511450E-01, 4.729333631541270E-03, \ -8.271269848617255E-01, -8.851367103086550E-01, 5.783392447697547E-03, \ -8.226990779980473E-01, 2.594419621957182E-01, 1.295208242924248E-02, \ -8.174915256392483E-01, 7.995012686440126E-01, 7.949359593998170E-03, \ -8.152897321117292E-01, -9.960859909883866E-01, 9.730665170684366E-04, \ -8.132142904625197E-01, 4.548944220943146E-01, 1.223637699266143E-02, \ -8.087394328827582E-01, -9.556037745856076E-01, 3.933758242891774E-03, \ -8.034618006847678E-01, 6.281857009049345E-01, 1.103532286602404E-02, \ -8.009671113820225E-01, 9.981533390719061E-01, 6.852854862182664E-04, \ -7.947551849888224E-01, -4.052480669355576E-01, 1.157650073560808E-02, \ -7.898299665920954E-01, -5.577510224714766E-01, 1.013316669078794E-02, \ -7.803754591141053E-01, -7.029689837797256E-01, 8.961843744448235E-03, \ -7.774912262938560E-01, 9.604818908070105E-01, 3.634588036562608E-03, \ -7.686352988370738E-01, -2.446641549937693E-01, 1.323529815530171E-02, \ -7.677740322724570E-01, 8.743907671109992E-01, 6.716521459650556E-03, \ -7.660500336383849E-01, -8.342336877874392E-01, 7.639362847929806E-03, \ -7.626828581715114E-01, -5.217879939928463E-02, 1.481683281953144E-02, \ -7.594734183304540E-01, 1.526746736533888E-01, 1.510577254629861E-02, \ -7.533200770053481E-01, 7.322571707312160E-01, 1.036649979314898E-02, \ -7.486275502230029E-01, 3.557473677134377E-01, 1.447118457086799E-02, \ -7.453991512679197E-01, -9.822746950042834E-01, 2.777507829800740E-03, \ -7.437035450232024E-01, -9.192149785074237E-01, 5.716340360168384E-03, \ -7.360777363538358E-01, 5.402149274576373E-01, 1.345453771968750E-02, \ -7.329540430986968E-01, -9.994520361414482E-01, 3.041538127530700E-04, \ -7.269321822743222E-01, 9.887675638640850E-01, 2.273665309343846E-03, \ -7.196190732492783E-01, -4.882248666799530E-01, 1.197379647349226E-02, \ -7.140404207255062E-01, -6.371246573044332E-01, 1.070392459478854E-02, \ -7.086337444142102E-01, -7.695704670416541E-01, 8.641963674824546E-03, \ -7.084219401683487E-01, 9.298201384783297E-01, 5.716321197953060E-03, \ -7.024233424547481E-01, -3.412634918186152E-01, 1.381334136967731E-02, \ -7.000574548967922E-01, 8.225599957784430E-01, 8.956533081134005E-03, \ -6.875688691464135E-01, -1.523532795702211E-01, 1.589039314041529E-02, \ -6.831396553262982E-01, 5.025358955518219E-02, 1.692483716041910E-02, \ -6.816715380174886E-01, 6.562333074021302E-01, 1.277287173246379E-02, \ -6.782866455285573E-01, 2.534754008840426E-01, 1.602307855437726E-02, \ -6.743483706032866E-01, -8.786507719647361E-01, 6.600160557324268E-03, \ -6.712488971549284E-01, -9.564498500229109E-01, 4.776110132553591E-03, \ -6.620238508003119E-01, 4.457520355368754E-01, 1.565706421137813E-02, \ -6.547035795617938E-01, -9.940970172871774E-01, 1.595895622818180E-03, \ -6.450215203909843E-01, 9.694287012984952E-01, 4.254123969191675E-03, \ -6.435026336621807E-01, 9.983082528329512E-01, 8.406070876814557E-04, \ -6.410984836103271E-01, -8.238821673751913E-01, 5.824601846420805E-03, \ -6.379215112130751E-01, -5.670614401267176E-01, 1.233100287824145E-02, \ -6.326491461674595E-01, -7.087147856504342E-01, 1.065338418396687E-02, \ -6.312112678821253E-01, 8.887426834499652E-01, 8.035436464026399E-03, \ -6.261412120185321E-01, 7.612964882114873E-01, 1.115166684172651E-02, \ -6.218404535164949E-01, -4.260251807764488E-01, 1.409803518042624E-02, \ -6.122357177770217E-01, -2.548990689966739E-01, 1.629549089611943E-02, \ -6.033379016027892E-01, 5.719396137245076E-01, 1.508372611713938E-02, \ -6.007203269774244E-01, 1.597960513238969E-01, 1.570057785252238E-02, \ -6.002219783980102E-01, -5.403874585262955E-02, 1.797054198971408E-02, \ -5.890404501501693E-01, -9.206940307202106E-01, 6.572394666527264E-03, \ -5.835973374377773E-01, 3.461086614433988E-01, 1.732203682677555E-02, \ -5.799634263647828E-01, -9.772590728941044E-01, 3.449436790328003E-03, \ -5.625099260935547E-01, -7.778619069194846E-01, 8.878902849634178E-03, \ -5.587300450136236E-01, -8.583430849979702E-01, 5.927281418798553E-03, \ -5.576025578329094E-01, 9.401328137991951E-01, 6.500514236109148E-03, \ -5.528541698467803E-01, -6.361229352805877E-01, 1.171212237998683E-02, \ -5.519019991796891E-01, 9.890368385507939E-01, 2.732564982558912E-03, \ -5.492720320374657E-01, 8.373014762031777E-01, 1.023676166331683E-02, \ -5.487723900103840E-01, 6.920470750806444E-01, 1.280023752030945E-02, \ -5.371325089697084E-01, 8.011203379709990E-02, 1.181135941584131E-02, \ -5.343185807415033E-01, -5.029270269025070E-01, 1.396353037202522E-02, \ -5.331665865462701E-01, -9.970597494728978E-01, 1.110041538717393E-03, \ -5.262824452533256E-01, -3.433052927748735E-01, 1.581695407925873E-02, \ -5.196722725049188E-01, 4.801432725924391E-01, 1.725926992286396E-02, \ -5.157073778702320E-01, -1.609863620383591E-01, 1.879587748844137E-02, \ -4.969937503660588E-01, 2.466042915149466E-01, 1.784450657561326E-02, \ -4.936443037514611E-01, -9.465513055935159E-01, 5.403406971553440E-03, \ -4.845997407738473E-01, -7.035482990021875E-01, 1.037135994169719E-02, \ -4.758233967224794E-01, 9.499700014764531E-03, 1.501969591730733E-02, \ -4.731977818372050E-01, -8.122514030227285E-01, 6.930386109087627E-03, \ -4.709097305697209E-01, 6.192328037671802E-01, 1.353895520891179E-02, \ -4.688360336456553E-01, -8.843163742148189E-01, 7.157111782324953E-03, \ -4.681987676963164E-01, 9.000816415421663E-01, 8.752217670591854E-03, \ -4.671044062418229E-01, 7.773382366003790E-01, 1.148882380125715E-02, \ -4.632227635675115E-01, -9.814205193370379E-01, 2.613335253646615E-03, \ -4.561007226835129E-01, 9.700945862732528E-01, 4.912897122852274E-03, \ -4.519080731349339E-01, 9.984396765695470E-01, 9.104456319465278E-04, \ -4.472892660613361E-01, -5.690445212955879E-01, 1.221020583633636E-02, \ -4.441617460367955E-01, 3.742961592477722E-01, 1.369039678808185E-02, \ -4.362577546949490E-01, -4.202960350604942E-01, 1.486935839319106E-02, \ -4.218638446966653E-01, -2.592840266301589E-01, 1.805298724340071E-02, \ -4.145077201239032E-01, 1.434465664707271E-01, 1.725622426589416E-02, \ -4.108551792292466E-01, 7.261324870817387E-01, 4.306155002341567E-03, \ -4.077259796016033E-01, -7.492102429229035E-01, 8.694161987156229E-03, \ -3.994375393561766E-01, -8.413566670896548E-02, 1.767270854523918E-02, \ -3.989722688095441E-01, -9.952608430268175E-01, 1.546205690889865E-03, \ -3.955046992121652E-01, 5.474259893157579E-01, 1.426771157675970E-02, \ -3.864577517310250E-01, -6.299902317618596E-01, 1.049642638160978E-02, \ -3.849225170655068E-01, 4.169734666972951E-01, 9.724255552168744E-03, \ -3.802442553217521E-01, 8.493133552804323E-01, 1.051968675909273E-02, \ -3.796487515464433E-01, -9.092228699079343E-01, 6.356176322652544E-03, \ -3.737267040247370E-01, -9.590954871481244E-01, 4.640668672343144E-03, \ -3.680086351266054E-01, 6.979889582949302E-01, 1.081487021761422E-02, \ -3.617280769528435E-01, 9.401480659088486E-01, 7.154768091047104E-03, \ -3.610877408616728E-01, -8.297008620205625E-01, 9.406051770632176E-03, \ -3.522240818473209E-01, 9.904239151356983E-01, 2.630094662997393E-03, \ -3.486739568508627E-01, 2.706799453032748E-01, 1.790534599137358E-02, \ -3.459056603672409E-01, -4.880157144461191E-01, 1.427913060937561E-02, \ -3.274412213828406E-01, 2.260401457313204E-02, 1.328209466144314E-02, \ -3.211239215007341E-01, -3.481155947386593E-01, 1.639976888297377E-02, \ -3.164232593211551E-01, -7.429261686367324E-01, 5.976361940569912E-03, \ -3.145433255025609E-01, -1.887048598242300E-01, 1.548218828411259E-02, \ -3.098139879229698E-01, 1.066163988920963E-01, 1.095431624202562E-02, \ -3.093324993446162E-01, 7.866827669318777E-01, 8.507371224954144E-03, \ -3.012423936798629E-01, -6.693885031733898E-01, 1.126757188865965E-02, \ -2.957526162080209E-01, 4.876169383565411E-01, 1.534619575085735E-02, \ -2.954492755010769E-01, -9.834117127161082E-01, 3.379925266369860E-03, \ -2.898542188079066E-01, 6.330069652325342E-01, 1.412145798182586E-02, \ -2.722006540631997E-01, -9.272099993727561E-01, 6.281659290118641E-03, \ -2.721846392481617E-01, 8.970549509207049E-01, 9.025150443164945E-03, \ -2.702194513535268E-01, -8.611546877103153E-01, 7.548029223327319E-03, \ -2.701666789762488E-01, 9.741038333559231E-01, 3.879006409933471E-03, \ -2.633486798231064E-01, -5.531499703542735E-01, 1.398453718361448E-02, \ -2.602577385956935E-01, 3.559789948391511E-01, 1.590809902210510E-02, \ -2.539085167701460E-01, -9.992367354749008E-01, 7.362226870467214E-04, \ -2.528734987524705E-01, -1.000864569130400E-01, 1.372369295593181E-02, \ -2.418266355083030E-01, 8.155977304752622E-01, 5.639586061670630E-03, \ -2.299925708319869E-01, -7.766849935728968E-01, 1.162319829976198E-02, \ -2.281975753978523E-01, -2.933251049638128E-01, 1.039571151862245E-02, \ -2.264962677001022E-01, 7.406196628504332E-01, 9.018221989261329E-03, \ -2.254137995022369E-01, 1.945262619590385E-01, 2.032600241526465E-02, \ -2.202097667160187E-01, 9.977429662985270E-01, 1.303069934955326E-03, \ -2.115604600690373E-01, -4.206501628650725E-01, 1.622528102872075E-02, \ -2.042331092646998E-01, 1.225948074751524E-02, 1.663069524482181E-02, \ -1.950313398093114E-01, 9.390444256419040E-01, 4.129734438091659E-03, \ -1.946536814154290E-01, -9.612563295817905E-01, 5.490013367391810E-03, \ -1.910999388491465E-01, 5.748539496478213E-01, 1.509977429582099E-02, \ -1.816716354061224E-01, 9.615618491387735E-01, 2.978742099030132E-03, \ -1.726116714065732E-01, -2.174974452316975E-01, 1.590035665116296E-02, \ -1.725147740607741E-01, -5.976020811915204E-01, 1.140314608712299E-02, \ -1.722055467782442E-01, -6.873345735469495E-01, 1.133583684301726E-02, \ -1.706449838302763E-01, -8.836551802782431E-01, 8.038658519121712E-03, \ -1.679988089754341E-01, 4.388106052157863E-01, 1.571275386456942E-02, \ -1.602837781659527E-01, 8.546895483149928E-01, 9.885073478511747E-03, \ -1.570373933725618E-01, 6.978163142964436E-01, 1.148876151378708E-02, \ -1.442219587876548E-01, -9.917004260484690E-01, 2.527011807500108E-03, \ -1.276588070261918E-01, 3.027418975026165E-01, 1.880072826559714E-02, \ -1.231008517680125E-01, -4.753879650258501E-01, 1.324596293468438E-02, \ -1.151860373260542E-01, -8.151600041578237E-01, 1.116067302973472E-02, \ -1.128965150592470E-01, -8.839516814078634E-02, 1.821643608834104E-02, \ -1.123053787507008E-01, 1.095876693506785E-01, 1.978565819024786E-02, \ -1.100537548339115E-01, 9.869592350981791E-01, 3.620908902716640E-03, \ -9.648898098941808E-02, 9.150132212119572E-01, 7.261424197102146E-03, \ -9.000801156431583E-02, -9.281582931717732E-01, 7.762421934834004E-03, \ -8.755571046923658E-02, -3.265338207762313E-01, 1.966893754969280E-02, \ -8.676802116466929E-02, 7.890938948277969E-01, 1.182634147172253E-02, \ -7.982169502523445E-02, -7.229964637208218E-01, 8.885119945778230E-03, \ -7.533277250983217E-02, 5.253341801281358E-01, 1.477352957389778E-02, \ -6.228882188644439E-02, 6.470376895730875E-01, 1.366136970817887E-02, \ -5.300829581300114E-02, -9.768027160770031E-01, 3.724202248380016E-03, \ -5.089861416336603E-02, -5.276784631402766E-01, 1.097680016715092E-02, \ -4.834001433988518E-02, -6.180420749231472E-01, 1.165892332494916E-02, \ -3.421706220224403E-02, 2.365146730869494E-01, 1.410226757763090E-02, \ -3.231589699057937E-02, 9.563884909129237E-01, 5.327701488888538E-03, \ -3.123410684940927E-02, -1.756994941404730E-01, 1.459727035314452E-02, \ -2.386449228293084E-02, 2.645142455623201E-02, 1.287803629578976E-02, \ -1.944503626409501E-02, 4.054741591181015E-01, 1.890683720388499E-02, \ -8.808200593649371E-03, -8.379258906397793E-01, 5.653566114720740E-03, \ -3.602758322849902E-03, -7.412893889188407E-01, 9.311057693238088E-03, \ -1.793626428337108E-03, -8.801377765241419E-01, 7.932756458617183E-03, \ -8.655140792606699E-04, -9.978429364835631E-01, 1.282195110221903E-03, \ 8.655140792606699E-04, 9.978429364835631E-01, 1.282195110221903E-03, \ 1.793626428337108E-03, 8.801377765241419E-01, 7.932756458617183E-03, \ 3.602758322849902E-03, 7.412893889188407E-01, 9.311057693238088E-03, \ 8.808200593649371E-03, 8.379258906397793E-01, 5.653566114720740E-03, \ 1.944503626409501E-02, -4.054741591181015E-01, 1.890683720388499E-02, \ 2.386449228293084E-02, -2.645142455623201E-02, 1.287803629578976E-02, \ 3.123410684940927E-02, 1.756994941404730E-01, 1.459727035314452E-02, \ 3.231589699057937E-02, -9.563884909129237E-01, 5.327701488888538E-03, \ 3.421706220224403E-02, -2.365146730869494E-01, 1.410226757763090E-02, \ 4.834001433988518E-02, 6.180420749231472E-01, 1.165892332494916E-02, \ 5.089861416336603E-02, 5.276784631402766E-01, 1.097680016715092E-02, \ 5.300829581300114E-02, 9.768027160770031E-01, 3.724202248380016E-03, \ 6.228882188644439E-02, -6.470376895730875E-01, 1.366136970817887E-02, \ 7.533277250983217E-02, -5.253341801281358E-01, 1.477352957389778E-02, \ 7.982169502523445E-02, 7.229964637208218E-01, 8.885119945778230E-03, \ 8.676802116466929E-02, -7.890938948277969E-01, 1.182634147172253E-02, \ 8.755571046923658E-02, 3.265338207762313E-01, 1.966893754969280E-02, \ 9.000801156431583E-02, 9.281582931717732E-01, 7.762421934834004E-03, \ 9.648898098941808E-02, -9.150132212119572E-01, 7.261424197102146E-03, \ 1.100537548339115E-01, -9.869592350981791E-01, 3.620908902716640E-03, \ 1.123053787507008E-01, -1.095876693506785E-01, 1.978565819024786E-02, \ 1.128965150592470E-01, 8.839516814078634E-02, 1.821643608834104E-02, \ 1.151860373260542E-01, 8.151600041578237E-01, 1.116067302973472E-02, \ 1.231008517680125E-01, 4.753879650258501E-01, 1.324596293468438E-02, \ 1.276588070261918E-01, -3.027418975026165E-01, 1.880072826559714E-02, \ 1.442219587876548E-01, 9.917004260484690E-01, 2.527011807500108E-03, \ 1.570373933725618E-01, -6.978163142964436E-01, 1.148876151378708E-02, \ 1.602837781659527E-01, -8.546895483149928E-01, 9.885073478511747E-03, \ 1.679988089754341E-01, -4.388106052157863E-01, 1.571275386456942E-02, \ 1.706449838302763E-01, 8.836551802782431E-01, 8.038658519121712E-03, \ 1.722055467782442E-01, 6.873345735469495E-01, 1.133583684301726E-02, \ 1.725147740607741E-01, 5.976020811915204E-01, 1.140314608712299E-02, \ 1.726116714065732E-01, 2.174974452316975E-01, 1.590035665116296E-02, \ 1.816716354061224E-01, -9.615618491387735E-01, 2.978742099030132E-03, \ 1.910999388491465E-01, -5.748539496478213E-01, 1.509977429582099E-02, \ 1.946536814154290E-01, 9.612563295817905E-01, 5.490013367391810E-03, \ 1.950313398093114E-01, -9.390444256419040E-01, 4.129734438091659E-03, \ 2.042331092646998E-01, -1.225948074751524E-02, 1.663069524482181E-02, \ 2.115604600690373E-01, 4.206501628650725E-01, 1.622528102872075E-02, \ 2.202097667160187E-01, -9.977429662985270E-01, 1.303069934955326E-03, \ 2.254137995022369E-01, -1.945262619590385E-01, 2.032600241526465E-02, \ 2.264962677001022E-01, -7.406196628504332E-01, 9.018221989261329E-03, \ 2.281975753978523E-01, 2.933251049638128E-01, 1.039571151862245E-02, \ 2.299925708319869E-01, 7.766849935728968E-01, 1.162319829976198E-02, \ 2.418266355083030E-01, -8.155977304752622E-01, 5.639586061670630E-03, \ 2.528734987524705E-01, 1.000864569130400E-01, 1.372369295593181E-02, \ 2.539085167701460E-01, 9.992367354749008E-01, 7.362226870467214E-04, \ 2.602577385956935E-01, -3.559789948391511E-01, 1.590809902210510E-02, \ 2.633486798231064E-01, 5.531499703542735E-01, 1.398453718361448E-02, \ 2.701666789762488E-01, -9.741038333559231E-01, 3.879006409933471E-03, \ 2.702194513535268E-01, 8.611546877103153E-01, 7.548029223327319E-03, \ 2.721846392481617E-01, -8.970549509207049E-01, 9.025150443164945E-03, \ 2.722006540631997E-01, 9.272099993727561E-01, 6.281659290118641E-03, \ 2.898542188079066E-01, -6.330069652325342E-01, 1.412145798182586E-02, \ 2.954492755010769E-01, 9.834117127161082E-01, 3.379925266369860E-03, \ 2.957526162080209E-01, -4.876169383565411E-01, 1.534619575085735E-02, \ 3.012423936798629E-01, 6.693885031733898E-01, 1.126757188865965E-02, \ 3.093324993446162E-01, -7.866827669318777E-01, 8.507371224954144E-03, \ 3.098139879229698E-01, -1.066163988920963E-01, 1.095431624202562E-02, \ 3.145433255025609E-01, 1.887048598242300E-01, 1.548218828411259E-02, \ 3.164232593211551E-01, 7.429261686367324E-01, 5.976361940569912E-03, \ 3.211239215007341E-01, 3.481155947386593E-01, 1.639976888297377E-02, \ 3.274412213828406E-01, -2.260401457313204E-02, 1.328209466144314E-02, \ 3.459056603672409E-01, 4.880157144461191E-01, 1.427913060937561E-02, \ 3.486739568508627E-01, -2.706799453032748E-01, 1.790534599137358E-02, \ 3.522240818473209E-01, -9.904239151356983E-01, 2.630094662997393E-03, \ 3.610877408616728E-01, 8.297008620205625E-01, 9.406051770632176E-03, \ 3.617280769528435E-01, -9.401480659088486E-01, 7.154768091047104E-03, \ 3.680086351266054E-01, -6.979889582949302E-01, 1.081487021761422E-02, \ 3.737267040247370E-01, 9.590954871481244E-01, 4.640668672343144E-03, \ 3.796487515464433E-01, 9.092228699079343E-01, 6.356176322652544E-03, \ 3.802442553217521E-01, -8.493133552804323E-01, 1.051968675909273E-02, \ 3.849225170655068E-01, -4.169734666972951E-01, 9.724255552168744E-03, \ 3.864577517310250E-01, 6.299902317618596E-01, 1.049642638160978E-02, \ 3.955046992121652E-01, -5.474259893157579E-01, 1.426771157675970E-02, \ 3.989722688095441E-01, 9.952608430268175E-01, 1.546205690889865E-03, \ 3.994375393561766E-01, 8.413566670896548E-02, 1.767270854523918E-02, \ 4.077259796016033E-01, 7.492102429229035E-01, 8.694161987156229E-03, \ 4.108551792292466E-01, -7.261324870817387E-01, 4.306155002341567E-03, \ 4.145077201239032E-01, -1.434465664707271E-01, 1.725622426589416E-02, \ 4.218638446966653E-01, 2.592840266301589E-01, 1.805298724340071E-02, \ 4.362577546949490E-01, 4.202960350604942E-01, 1.486935839319106E-02, \ 4.441617460367955E-01, -3.742961592477722E-01, 1.369039678808185E-02, \ 4.472892660613361E-01, 5.690445212955879E-01, 1.221020583633636E-02, \ 4.519080731349339E-01, -9.984396765695470E-01, 9.104456319465278E-04, \ 4.561007226835129E-01, -9.700945862732528E-01, 4.912897122852274E-03, \ 4.632227635675115E-01, 9.814205193370379E-01, 2.613335253646615E-03, \ 4.671044062418229E-01, -7.773382366003790E-01, 1.148882380125715E-02, \ 4.681987676963164E-01, -9.000816415421663E-01, 8.752217670591854E-03, \ 4.688360336456553E-01, 8.843163742148189E-01, 7.157111782324953E-03, \ 4.709097305697209E-01, -6.192328037671802E-01, 1.353895520891179E-02, \ 4.731977818372050E-01, 8.122514030227285E-01, 6.930386109087627E-03, \ 4.758233967224794E-01, -9.499700014764531E-03, 1.501969591730733E-02, \ 4.845997407738473E-01, 7.035482990021875E-01, 1.037135994169719E-02, \ 4.936443037514611E-01, 9.465513055935159E-01, 5.403406971553440E-03, \ 4.969937503660588E-01, -2.466042915149466E-01, 1.784450657561326E-02, \ 5.157073778702320E-01, 1.609863620383591E-01, 1.879587748844137E-02, \ 5.196722725049188E-01, -4.801432725924391E-01, 1.725926992286396E-02, \ 5.262824452533256E-01, 3.433052927748735E-01, 1.581695407925873E-02, \ 5.331665865462701E-01, 9.970597494728978E-01, 1.110041538717393E-03, \ 5.343185807415033E-01, 5.029270269025070E-01, 1.396353037202522E-02, \ 5.371325089697084E-01, -8.011203379709990E-02, 1.181135941584131E-02, \ 5.487723900103840E-01, -6.920470750806444E-01, 1.280023752030945E-02, \ 5.492720320374657E-01, -8.373014762031777E-01, 1.023676166331683E-02, \ 5.519019991796891E-01, -9.890368385507939E-01, 2.732564982558912E-03, \ 5.528541698467803E-01, 6.361229352805877E-01, 1.171212237998683E-02, \ 5.576025578329094E-01, -9.401328137991951E-01, 6.500514236109148E-03, \ 5.587300450136236E-01, 8.583430849979702E-01, 5.927281418798553E-03, \ 5.625099260935547E-01, 7.778619069194846E-01, 8.878902849634178E-03, \ 5.799634263647828E-01, 9.772590728941044E-01, 3.449436790328003E-03, \ 5.835973374377773E-01, -3.461086614433988E-01, 1.732203682677555E-02, \ 5.890404501501693E-01, 9.206940307202106E-01, 6.572394666527264E-03, \ 6.002219783980102E-01, 5.403874585262955E-02, 1.797054198971408E-02, \ 6.007203269774244E-01, -1.597960513238969E-01, 1.570057785252238E-02, \ 6.033379016027892E-01, -5.719396137245076E-01, 1.508372611713938E-02, \ 6.122357177770217E-01, 2.548990689966739E-01, 1.629549089611943E-02, \ 6.218404535164949E-01, 4.260251807764488E-01, 1.409803518042624E-02, \ 6.261412120185321E-01, -7.612964882114873E-01, 1.115166684172651E-02, \ 6.312112678821253E-01, -8.887426834499652E-01, 8.035436464026399E-03, \ 6.326491461674595E-01, 7.087147856504342E-01, 1.065338418396687E-02, \ 6.379215112130751E-01, 5.670614401267176E-01, 1.233100287824145E-02, \ 6.410984836103271E-01, 8.238821673751913E-01, 5.824601846420805E-03, \ 6.435026336621807E-01, -9.983082528329512E-01, 8.406070876814557E-04, \ 6.450215203909843E-01, -9.694287012984952E-01, 4.254123969191675E-03, \ 6.547035795617938E-01, 9.940970172871774E-01, 1.595895622818180E-03, \ 6.620238508003119E-01, -4.457520355368754E-01, 1.565706421137813E-02, \ 6.712488971549284E-01, 9.564498500229109E-01, 4.776110132553591E-03, \ 6.743483706032866E-01, 8.786507719647361E-01, 6.600160557324268E-03, \ 6.782866455285573E-01, -2.534754008840426E-01, 1.602307855437726E-02, \ 6.816715380174886E-01, -6.562333074021302E-01, 1.277287173246379E-02, \ 6.831396553262982E-01, -5.025358955518219E-02, 1.692483716041910E-02, \ 6.875688691464135E-01, 1.523532795702211E-01, 1.589039314041529E-02, \ 7.000574548967922E-01, -8.225599957784430E-01, 8.956533081134005E-03, \ 7.024233424547481E-01, 3.412634918186152E-01, 1.381334136967731E-02, \ 7.084219401683487E-01, -9.298201384783297E-01, 5.716321197953060E-03, \ 7.086337444142102E-01, 7.695704670416541E-01, 8.641963674824546E-03, \ 7.140404207255062E-01, 6.371246573044332E-01, 1.070392459478854E-02, \ 7.196190732492783E-01, 4.882248666799530E-01, 1.197379647349226E-02, \ 7.269321822743222E-01, -9.887675638640850E-01, 2.273665309343846E-03, \ 7.329540430986968E-01, 9.994520361414482E-01, 3.041538127530700E-04, \ 7.360777363538358E-01, -5.402149274576373E-01, 1.345453771968750E-02, \ 7.437035450232024E-01, 9.192149785074237E-01, 5.716340360168384E-03, \ 7.453991512679197E-01, 9.822746950042834E-01, 2.777507829800740E-03, \ 7.486275502230029E-01, -3.557473677134377E-01, 1.447118457086799E-02, \ 7.533200770053481E-01, -7.322571707312160E-01, 1.036649979314898E-02, \ 7.594734183304540E-01, -1.526746736533888E-01, 1.510577254629861E-02, \ 7.626828581715114E-01, 5.217879939928463E-02, 1.481683281953144E-02, \ 7.660500336383849E-01, 8.342336877874392E-01, 7.639362847929806E-03, \ 7.677740322724570E-01, -8.743907671109992E-01, 6.716521459650556E-03, \ 7.686352988370738E-01, 2.446641549937693E-01, 1.323529815530171E-02, \ 7.774912262938560E-01, -9.604818908070105E-01, 3.634588036562608E-03, \ 7.803754591141053E-01, 7.029689837797256E-01, 8.961843744448235E-03, \ 7.898299665920954E-01, 5.577510224714766E-01, 1.013316669078794E-02, \ 7.947551849888224E-01, 4.052480669355576E-01, 1.157650073560808E-02, \ 8.009671113820225E-01, -9.981533390719061E-01, 6.852854862182664E-04, \ 8.034618006847678E-01, -6.281857009049345E-01, 1.103532286602404E-02, \ 8.087394328827582E-01, 9.556037745856076E-01, 3.933758242891774E-03, \ 8.132142904625197E-01, -4.548944220943146E-01, 1.223637699266143E-02, \ 8.152897321117292E-01, 9.960859909883866E-01, 9.730665170684366E-04, \ 8.174915256392483E-01, -7.995012686440126E-01, 7.949359593998170E-03, \ 8.226990779980473E-01, -2.594419621957182E-01, 1.295208242924248E-02, \ 8.271269848617255E-01, 8.851367103086550E-01, 5.783392447697547E-03, \ 8.279841059514953E-01, -9.168099196511450E-01, 4.729333631541270E-03, \ 8.298817228165417E-01, -4.932544049099609E-02, 1.308861281523968E-02, \ 8.333486955686686E-01, 1.495187297327515E-01, 1.195411188321836E-02, \ 8.345679943920669E-01, 7.722499650445845E-01, 7.694139784998021E-03, \ 8.371745526664012E-01, -9.808931214242823E-01, 2.050522723814058E-03, \ 8.467158604246162E-01, 6.289407999349215E-01, 8.567266871139807E-03, \ 8.480068796648080E-01, 3.119740973719929E-01, 9.321790315925496E-03, \ 8.619939023548052E-01, 4.806373416483297E-01, 9.672951472047629E-03, \ 8.621111168073954E-01, -7.090421883632249E-01, 8.492263963507059E-03, \ 8.659273047100809E-01, 9.818377837992252E-01, 2.087386821145729E-03, \ 8.702282345000577E-01, -5.484829121208596E-01, 9.793908671588478E-03, \ 8.732550362347075E-01, -8.574796771270368E-01, 5.681748093343370E-03, \ 8.768491423274493E-01, -3.627381824235000E-01, 1.044386961685712E-02, \ 8.801258841317081E-01, 9.290747990279913E-01, 3.975614899427044E-03, \ 8.811873265749205E-01, -9.497474912342982E-01, 3.085534283412631E-03, \ 8.837148490953154E-01, -1.576361975891787E-01, 1.099997902023932E-02, \ 8.860972589276557E-01, 8.331612020727454E-01, 5.781048219808546E-03, \ 8.866199302094060E-01, -9.938258930614400E-01, 9.839665860219130E-04, \ 8.895672957850502E-01, 5.293510599726065E-02, 1.040987558289029E-02, \ 8.940375402275955E-01, 7.041313708313275E-01, 7.142826419236804E-03, \ 8.969710028279102E-01, 2.256802214985589E-01, 7.410425347310207E-03, \ 9.013251796383466E-01, 3.666844788249730E-01, 6.151586476003017E-03, \ 9.087015117883152E-01, 9.969915072869269E-01, 6.470318411854381E-04, \ 9.096781399489776E-01, 5.604773052603598E-01, 7.205603970066971E-03, \ 9.111951012665040E-01, -7.814905098540573E-01, 6.041492892648836E-03, \ 9.172703778429636E-01, -6.365672819732232E-01, 7.262815260314241E-03, \ 9.202380773523146E-01, -9.050386110265841E-01, 3.683312035807689E-03, \ 9.220086198065640E-01, -4.592930118785874E-01, 7.896825458118423E-03, \ 9.235763538947596E-01, 9.640444233499114E-01, 2.312159206833450E-03, \ 9.261329198739888E-01, -9.746027153962696E-01, 1.776302974763280E-03, \ 9.273226373183119E-01, -2.659618987488091E-01, 8.495674903422557E-03, \ 9.290856294325159E-01, 8.871608380321619E-01, 3.918401242147426E-03, \ 9.320728477635706E-01, -5.264490338972241E-02, 8.452404593360153E-03, \ 9.338088134935508E-01, 2.598456851976017E-01, 2.595536800191603E-03, \ 9.343242796602114E-01, 4.294254268855136E-01, 6.109989073144874E-03, \ 9.350865783178156E-01, 7.749842255798853E-01, 5.158635670181725E-03, \ 9.389178998337855E-01, -9.983688364336674E-01, 3.205800161394826E-04, \ 9.395231994348571E-01, 1.457862489409124E-01, 6.657538796439106E-03, \ 9.443304774038754E-01, 6.368742088572625E-01, 5.273401811778445E-03, \ 9.502192536056790E-01, -8.439252795287028E-01, 3.825522511161339E-03, \ 9.539639220051850E-01, -7.173033838147738E-01, 4.862799620669253E-03, \ 9.549989203380340E-01, 9.887724667769165E-01, 1.007773895019914E-03, \ 9.558923457352529E-01, -5.499187290928166E-01, 5.368921482058166E-03, \ 9.572708860210799E-01, -9.424725960383203E-01, 2.087979607175203E-03, \ 9.606958049220916E-01, 3.081366550020263E-01, 5.455334451053538E-03, \ 9.614256374444105E-01, 9.328771743819428E-01, 2.264842731050030E-03, \ 9.617304012154808E-01, -3.684756255396696E-01, 5.961021756038116E-03, \ 9.634120661314701E-01, -1.626856446045910E-01, 5.991502859241982E-03, \ 9.651954595073776E-01, 5.128458551084091E-01, 5.121256639651095E-03, \ 9.666680119711900E-01, -9.879489037902746E-01, 8.035625344075275E-04, \ 9.669765353727785E-01, 8.388123877959717E-01, 3.240365622776667E-03, \ 9.679069092640856E-01, 5.291894734981822E-02, 5.483965867735776E-03, \ 9.708143762319804E-01, 7.098339240446494E-01, 3.611310052438938E-03, \ 9.785540980020077E-01, -8.955915042635302E-01, 2.022068123378164E-03, \ 9.789828886434943E-01, -6.301653850940090E-01, 3.120578758401599E-03, \ 9.799368890832454E-01, -7.898861275347491E-01, 2.697855299373055E-03, \ 9.815923254661588E-01, 9.991082969355470E-01, 1.800328977889874E-04, \ 9.825204731628883E-01, 9.691072435867270E-01, 1.033098155222703E-03, \ 9.826130188082844E-01, 2.018533291539324E-01, 3.940386018971356E-03, \ 9.831116643490232E-01, 3.932597865155385E-01, 2.757351758467422E-03, \ 9.844227148004673E-01, -4.680325982952541E-01, 3.466798907655683E-03, \ 9.853079288654077E-01, -2.623064638103086E-01, 3.238657892966299E-03, \ 9.861629614331282E-01, -9.648994574590848E-01, 9.190271035579097E-04, \ 9.865979212862428E-01, -5.871716068212986E-02, 3.448498853249387E-03, \ 9.867187183083578E-01, 6.036002868761330E-01, 2.989922308625185E-03, \ 9.875040522290420E-01, 8.954189297031747E-01, 1.599426753793162E-03, \ 9.891720527404116E-01, -9.974135252406250E-01, 1.922590066403422E-04, \ 9.896982696240531E-01, 7.781770875290389E-01, 1.992196225105480E-03, \ 9.914052559973405E-01, -7.023250519059472E-01, 1.361348704496822E-03, \ 9.914304305563754E-01, 4.291601514462605E-01, 1.270285302858647E-03, \ 9.933660348449341E-01, -3.161717536031352E-01, 8.387713122106447E-04, \ 9.953468235808713E-01, -8.508120228627952E-01, 1.028310207063733E-03, \ 9.954005028570233E-01, 1.203116337354302E-01, 1.443569885953676E-03, \ 9.964167588339662E-01, 9.892036664406441E-01, 2.516135591721077E-04, \ 9.964624830190837E-01, -5.570787045642487E-01, 1.303165763686854E-03, \ 9.965532592866511E-01, -9.290044070830288E-01, 6.034648824689160E-04, \ 9.972986691166712E-01, 2.707798066058207E-02, 8.893716616277809E-04, \ 9.973454309733404E-01, 9.423377622335455E-01, 4.836806630189215E-04, \ 9.974464559033922E-01, 2.966888554053162E-01, 1.397441303354461E-03, \ 9.978751297025205E-01, 6.879180639452499E-01, 9.450952193083518E-04, \ 9.979107729485314E-01, -6.529159127971879E-01, 3.633867657362896E-04, \ 9.979346610008943E-01, 5.127640690222413E-01, 1.033714442116006E-03, \ 9.979563603675163E-01, -1.627643560997576E-01, 1.227147024948174E-03, \ 9.981572755902530E-01, -3.878455559966326E-01, 9.745188221536845E-04, \ 9.983624118051736E-01, -7.608024429037672E-01, 5.224452130672093E-04, \ 9.985845745857554E-01, 8.445726670375774E-01, 5.544684199320334E-04, \ 9.985928023604709E-01, -9.844383621232889E-01, 1.770821645368481E-04 ] ) return xyw def smr54 ( ): #*****************************************************************************80 # ## smr54 returns the SMR rule of degree 54. # # Discussion: # # DEGREE: 54 # POINTS CARDINALITY: 530 # NORM INF MOMS. RESIDUAL: 5.39824e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*530), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.989817717908982E-01, 5.919272627455578E-01, 4.192164731453299E-04, \ -9.987404572465737E-01, 1.308084790329531E-01, 1.021852171532156E-03, \ -9.986234267784356E-01, -4.263738548438438E-01, 8.092096026376365E-04, \ -9.981931054807527E-01, 3.646305906433953E-01, 9.508207239229283E-04, \ -9.981856973324568E-01, 7.272619710460589E-01, 6.106524315481551E-04, \ -9.980709749587124E-01, -6.001863748613854E-01, 8.126915872357096E-04, \ -9.980413923840483E-01, -8.914269607610811E-01, 4.682310231840477E-04, \ -9.979705384624564E-01, -7.412992362417765E-01, 7.151087866573973E-04, \ -9.978690979638140E-01, 9.663123578468790E-01, 3.202153175837222E-04, \ -9.977258243819628E-01, -9.652827050987313E-01, 3.283439367940058E-04, \ -9.971716111831748E-01, -9.974268956785031E-01, 8.241300038356087E-05, \ -9.970352418855494E-01, 9.974255320425583E-01, 8.212998926647490E-05, \ -9.969224314551484E-01, -9.393125488685919E-02, 1.504803327632492E-03, \ -9.960677559421486E-01, -2.647274988430133E-01, 1.572549858547515E-03, \ -9.960215426387498E-01, 8.267393820611655E-01, 9.559033420839447E-04, \ -9.948684167675756E-01, 9.071416133542933E-01, 8.949139768864249E-04, \ -9.947720129850103E-01, 5.104011858905396E-01, 1.494625194595164E-03, \ -9.928183610027883E-01, -8.240968026714828E-01, 1.339991144849752E-03, \ -9.913254503184387E-01, 2.674834631813928E-01, 2.106476272485075E-03, \ -9.904625945177303E-01, 6.584559213904446E-01, 1.813259044357879E-03, \ -9.890383005625215E-01, -5.149553957207894E-01, 2.455252158291572E-03, \ -9.881194568841846E-01, 2.614827265266613E-02, 3.325719901930421E-03, \ -9.879408478281920E-01, -9.291292547818254E-01, 1.147091172840035E-03, \ -9.875251490473347E-01, -6.727745764892368E-01, 2.262078818748468E-03, \ -9.858527951227277E-01, -9.864963721615293E-01, 5.725658200176546E-04, \ -9.854338631227043E-01, 9.874105156506667E-01, 5.586886490640081E-04, \ -9.852263671099249E-01, -3.625385392177216E-01, 2.857661335439080E-03, \ -9.825593639450432E-01, 1.995031163134125E-01, 2.367547927531011E-03, \ -9.824114240376021E-01, 4.281675290505715E-01, 3.355872483204902E-03, \ -9.817256672127911E-01, 7.647122894159171E-01, 2.575116468351886E-03, \ -9.805318040753007E-01, -1.804457704525198E-01, 4.118289237515360E-03, \ -9.805039503463728E-01, 9.466567028850934E-01, 1.325628488583474E-03, \ -9.756665239670562E-01, 8.635894110547788E-01, 2.435706692004165E-03, \ -9.752755423873182E-01, 5.832180325449532E-01, 3.514659543525947E-03, \ -9.750402397814284E-01, -7.646880569660038E-01, 2.888748522483849E-03, \ -9.735468564559212E-01, -8.717051891324532E-01, 2.366889660470246E-03, \ -9.679592288793518E-01, -5.935816838222202E-01, 3.995306431519523E-03, \ -9.677571838023695E-01, -9.595967788974593E-01, 1.428616809901578E-03, \ -9.658639079002952E-01, -4.432770743101457E-01, 3.839496537131441E-03, \ -9.650415941859795E-01, 1.236248887610379E-01, 4.840226470267086E-03, \ -9.631290872983891E-01, -5.876034750881315E-02, 5.470783159765819E-03, \ -9.631034141806328E-01, -9.976850977314620E-01, 3.419776280288853E-04, \ -9.625553199946670E-01, 3.295323982859324E-01, 5.459065077538461E-03, \ -9.612827522133878E-01, 9.981364356409019E-01, 3.166348923351850E-04, \ -9.580877877056461E-01, -2.969810053181347E-01, 5.220897083430127E-03, \ -9.571485087500350E-01, 6.922808060935507E-01, 4.586679952432644E-03, \ -9.535301324509948E-01, 9.746155590088402E-01, 1.418913803798055E-03, \ -9.524379004857232E-01, 9.162146344965918E-01, 2.407729567382604E-03, \ -9.505895051965978E-01, 5.014963263274375E-01, 5.575945233813663E-03, \ -9.478749822163210E-01, -6.944812783499223E-01, 4.655155635074236E-03, \ -9.455021911300354E-01, 8.056725087594965E-01, 4.359359472393902E-03, \ -9.447465384828663E-01, -9.154409664580865E-01, 2.795239997076277E-03, \ -9.433146066792609E-01, -8.168805299510518E-01, 4.028643084029805E-03, \ -9.387233616656319E-01, -5.109006904129239E-01, 4.894958084076135E-03, \ -9.384629482238540E-01, -9.818626877894082E-01, 1.310428168181814E-03, \ -9.381114810015984E-01, 2.185836698314924E-01, 4.884732944819899E-03, \ -9.358560535321955E-01, -2.315428002863897E-01, 3.316562519259470E-03, \ -9.308010611209707E-01, -1.424231144558627E-01, 5.747390039768777E-03, \ -9.297630644633869E-01, 4.416527314167950E-02, 7.517898257378467E-03, \ -9.233227723178385E-01, 4.023719757646702E-01, 5.284707530975812E-03, \ -9.224542858756197E-01, 6.127728993680069E-01, 6.776489078687089E-03, \ -9.196650460217998E-01, -3.918897734223120E-01, 7.307992712751874E-03, \ -9.194831397810722E-01, 8.782442449140750E-01, 3.380706025809833E-03, \ -9.150738342453455E-01, 2.565854509614714E-01, 4.607153630685746E-03, \ -9.145318414055876E-01, -6.141747725191304E-01, 6.046283805446541E-03, \ -9.139502328154178E-01, 9.519560268303220E-01, 2.502572477084220E-03, \ -9.134793665954337E-01, 9.919095371825775E-01, 1.124626818044628E-03, \ -9.060090402237246E-01, -9.506888110190086E-01, 2.778798298294591E-03, \ -9.053928987959834E-01, 4.255816005703235E-01, 3.224317780033523E-03, \ -9.044639609806726E-01, 7.378720657330040E-01, 6.636831081783288E-03, \ -9.041783402072592E-01, -8.694205435587335E-01, 4.455650498659537E-03, \ -9.040300328146645E-01, -7.515160741939899E-01, 5.918295079633594E-03, \ -9.017899755155315E-01, -9.954102906217157E-01, 7.928254709759700E-04, \ -8.897004636163042E-01, -2.191520488598997E-01, 5.655997887446038E-03, \ -8.877453802381129E-01, -5.477593167943130E-02, 9.196179323015951E-03, \ -8.840808803351360E-01, 1.391072028749891E-01, 9.640533450227940E-03, \ -8.828518434418928E-01, -3.121002666602964E-01, 6.236556130589060E-03, \ -8.818476420260746E-01, 8.364954439794862E-01, 4.678268202212999E-03, \ -8.816605510809139E-01, -5.252727670887154E-01, 6.613415579576893E-03, \ -8.785653704569504E-01, 5.278061262141955E-01, 8.847143039918376E-03, \ -8.699871131424373E-01, 9.213357639099106E-01, 3.632006018382626E-03, \ -8.683297949701945E-01, 3.231905589440098E-01, 9.593963354545314E-03, \ -8.604990767543338E-01, -6.723649810540170E-01, 7.844257742747529E-03, \ -8.592897950466277E-01, 9.761958158048712E-01, 2.408602549499724E-03, \ -8.585649827583716E-01, -9.769138516545594E-01, 2.321654990097349E-03, \ -8.555827158290819E-01, -4.472850328113563E-01, 7.381515678371422E-03, \ -8.554969798794826E-01, -9.140049134243882E-01, 4.445756671413822E-03, \ -8.549727674964507E-01, -8.129934326041193E-01, 6.375752094967673E-03, \ -8.537907187771469E-01, 9.988992207578934E-01, 4.358179382894343E-04, \ -8.531681357690770E-01, 6.611164416907961E-01, 9.119660780491236E-03, \ -8.350636199588630E-01, 7.852767143246269E-01, 6.889525487372896E-03, \ -8.349595897816755E-01, -1.520071332967412E-01, 1.065179565209894E-02, \ -8.320657289288327E-01, 3.716906860716102E-02, 1.146602495213217E-02, \ -8.268341463810431E-01, -2.968395593787465E-01, 6.862218866630454E-03, \ -8.246596591114025E-01, -9.965096629638894E-01, 8.191929500848176E-04, \ -8.245747953184245E-01, 4.399187035083351E-01, 1.074447207779778E-02, \ -8.205544234046400E-01, 8.852149825875817E-01, 5.035650441337556E-03, \ -8.201077685552812E-01, 2.167941468653240E-01, 1.120664310470067E-02, \ -8.133180823505128E-01, -5.827868689492453E-01, 1.020050720602399E-02, \ -8.039514840518650E-01, -3.887612693005317E-01, 8.156471508075192E-03, \ -8.020182152432404E-01, -7.434295570675248E-01, 8.516722515686231E-03, \ -7.993113635576975E-01, 9.508317269117940E-01, 3.951550791219958E-03, \ -7.977917653551984E-01, -9.498027641226449E-01, 4.046020691573701E-03, \ -7.966018517884945E-01, -8.670707527670807E-01, 6.396726072271494E-03, \ -7.931825421678735E-01, 5.760232971144895E-01, 1.150512626594489E-02, \ -7.926266834000572E-01, 9.921891129165684E-01, 1.367686056645448E-03, \ -7.771396199978947E-01, 7.224416691496910E-01, 9.346300134052963E-03, \ -7.734124506696661E-01, 3.227290869794067E-01, 8.975472976200140E-03, \ -7.703196567703094E-01, -6.166649668685752E-02, 1.296602865392240E-02, \ -7.639145055393257E-01, -9.849091728353774E-01, 2.189782887003045E-03, \ -7.629322821804013E-01, 8.407308321500763E-01, 7.120214624978285E-03, \ -7.626926298628909E-01, -2.351311412555938E-01, 1.196574993978526E-02, \ -7.595961758924654E-01, -4.888664940264281E-01, 1.136013589405564E-02, \ -7.583264577383526E-01, 1.203418784123442E-01, 1.319999781535264E-02, \ -7.534370979577448E-01, 3.876976391386210E-01, 5.897710869634649E-03, \ -7.446105000480632E-01, -6.652463657026361E-01, 1.063122807861948E-02, \ -7.403189886112194E-01, 9.802339164748645E-01, 2.050796688775679E-03, \ -7.335598541855958E-01, -8.081850052797745E-01, 8.660179094542753E-03, \ -7.323073282715993E-01, 9.179212596057432E-01, 5.596503741402021E-03, \ -7.283214984315893E-01, -9.121288534905104E-01, 6.106288648057536E-03, \ -7.205165128910833E-01, 4.912094353971421E-01, 1.322119178401210E-02, \ -7.202928498310126E-01, -9.987309089969828E-01, 5.258054963828562E-04, \ -7.140760443768659E-01, -3.530100176005496E-01, 1.329784234525705E-02, \ -7.124579482134324E-01, 6.494569766773742E-01, 1.132420139371352E-02, \ -7.046398991051476E-01, 2.461557767190701E-01, 1.316382807437570E-02, \ -6.965139599435282E-01, 9.980269396597710E-01, 8.468443147483151E-04, \ -6.955976699513159E-01, 7.858134610190387E-01, 9.483582940511751E-03, \ -6.933698254139239E-01, -9.638333240537718E-01, 3.924272626110384E-03, \ -6.916049886292619E-01, -1.473824067364324E-01, 1.379946652263615E-02, \ -6.900647649939231E-01, -5.756250123370613E-01, 1.131366317435485E-02, \ -6.896395099305572E-01, 2.450716766496345E-02, 1.433783710214306E-02, \ -6.791067170899857E-01, 9.629073491101878E-01, 3.765624216430676E-03, \ -6.665583661377872E-01, -7.396479470660201E-01, 1.078002527678657E-02, \ -6.617665117353752E-01, 8.782682043901964E-01, 7.160836419170941E-03, \ -6.547645869221170E-01, -4.567828647957672E-01, 1.235987868867504E-02, \ -6.534762438686446E-01, -8.630076300534779E-01, 8.538047957473528E-03, \ -6.520027037508170E-01, 3.735882243699723E-01, 1.516020774574135E-02, \ -6.517784533911791E-01, -9.917908605039587E-01, 1.649695282763077E-03, \ -6.392095883446625E-01, 5.800402186061466E-01, 1.161152099493760E-02, \ -6.376246103269898E-01, 1.586423655659965E-01, 1.380903763545163E-02, \ -6.327846798140507E-01, -2.616795092165446E-01, 1.537715962316561E-02, \ -6.240350274451502E-01, 7.202357912728578E-01, 1.128423081027187E-02, \ -6.149539141562774E-01, -9.331114005968212E-01, 5.973942783567584E-03, \ -6.122194846749883E-01, -6.515331165545560E-01, 1.111044461856676E-02, \ -6.109552256753611E-01, 9.882437872281699E-01, 2.667119864257815E-03, \ -6.075850901806646E-01, -6.310115283305893E-02, 1.462210878363727E-02, \ -6.072861502023867E-01, 4.905670021193503E-01, 8.470043747920344E-03, \ -6.015220267548393E-01, 9.349603376928803E-01, 6.061794422141538E-03, \ -5.905725005438208E-01, 8.331968654144224E-01, 8.330672895641352E-03, \ -5.805512578578408E-01, -9.781724160170889E-01, 3.002089846665531E-03, \ -5.766322657231936E-01, -8.019456106219724E-01, 1.071573135474418E-02, \ -5.758873833179518E-01, -3.797930059724561E-01, 1.410780437411866E-02, \ -5.758044628531556E-01, -5.431666836509476E-01, 1.250321425804641E-02, \ -5.701897881977539E-01, 7.196089886371619E-02, 1.340015602318261E-02, \ -5.675904138396737E-01, 2.751253062951665E-01, 1.737410839787904E-02, \ -5.553792678938588E-01, -9.985017652958537E-01, 7.085987040688918E-04, \ -5.456087648129923E-01, 6.599941556879438E-01, 1.081777781980287E-02, \ -5.428550764673452E-01, -1.681164911727584E-01, 1.620487411044344E-02, \ -5.392986597197948E-01, 4.382461398474867E-01, 1.322051456706655E-02, \ -5.333581011400846E-01, -8.924070574982715E-01, 8.096515253402553E-03, \ -5.293207101815004E-01, -7.129696889928183E-01, 1.046695608551654E-02, \ -5.290868756599331E-01, 7.840020586708457E-01, 8.165858398272986E-03, \ -5.276014126395560E-01, 5.734029485384756E-01, 8.947303079726300E-03, \ -5.208347199729565E-01, 9.983223158535289E-01, 9.204125169539234E-04, \ -5.167452045861149E-01, 9.688882331602159E-01, 4.810895911417227E-03, \ -5.152624846429958E-01, 8.963754564805726E-01, 8.321128511156680E-03, \ -5.002251071203062E-01, -9.570565024360769E-01, 4.944271560105734E-03, \ -4.932266910589403E-01, -4.711107586002372E-01, 1.392484590851878E-02, \ -4.921580787739357E-01, -2.932163995933711E-01, 1.583029572106085E-02, \ -4.879008547264502E-01, -6.201644318968081E-03, 1.496619326816272E-02, \ -4.852163690035972E-01, 1.624165605662743E-01, 1.717478193204391E-02, \ -4.823665194042128E-01, -6.169799586006250E-01, 1.293927977760325E-02, \ -4.703674730266642E-01, -9.914498714302058E-01, 2.012990135531071E-03, \ -4.636605522134049E-01, 3.574499996088237E-01, 1.446178985104287E-02, \ -4.635626709780222E-01, -8.379512800964518E-01, 8.670390056290013E-03, \ -4.616882999336276E-01, 7.441874849999627E-01, 9.278333622213229E-03, \ -4.428826220830571E-01, 5.242412903345882E-01, 1.401423158385144E-02, \ -4.375574474750148E-01, -7.560923913938994E-01, 1.060832188420960E-02, \ -4.373507999119863E-01, 2.790611242916685E-01, 5.124081896234384E-03, \ -4.360016080614369E-01, -9.911845198571319E-02, 1.336294282347855E-02, \ -4.318212671580576E-01, 6.490625104897801E-01, 1.048403694888664E-02, \ -4.312768828083386E-01, 8.458926838617457E-01, 1.005241229734938E-02, \ -4.195936220368654E-01, 9.896332053755005E-01, 2.832340745872356E-03, \ -4.195035071205845E-01, 9.391789505533757E-01, 7.087287993156248E-03, \ -4.158372945781164E-01, -9.247166955115301E-01, 7.200678481835746E-03, \ -4.082322252181940E-01, -3.895067692217146E-01, 1.571591993987856E-02, \ -3.945619771869534E-01, -2.102382908787201E-01, 1.645442705259772E-02, \ -3.927191939155762E-01, -5.456985704133576E-01, 1.387951318062375E-02, \ -3.871818805737522E-01, -9.785560486250816E-01, 3.357590491647819E-03, \ -3.777405489965089E-01, 2.271876155103771E-01, 1.464444862096865E-02, \ -3.759119908505304E-01, 6.749055163565303E-02, 1.970543400262736E-02, \ -3.723355165014207E-01, -6.701266603185027E-01, 1.262000893299485E-02, \ -3.676289846847610E-01, -8.661368970945535E-01, 7.011405339219392E-03, \ -3.664037660595558E-01, 4.496056266935061E-01, 1.177520117108604E-02, \ -3.644175466900805E-01, -9.988404483094074E-01, 6.861446217182368E-04, \ -3.612218369591753E-01, 7.139281737711283E-01, 8.660409393382987E-03, \ -3.533163408214845E-01, 3.703602260250929E-01, 7.687812735908846E-03, \ -3.390251629862523E-01, 7.979819236131581E-01, 1.008487673748482E-02, \ -3.345649108519196E-01, 9.723276852657335E-01, 2.678299050653827E-03, \ -3.293646261299018E-01, 5.938175713548932E-01, 1.490674822227216E-02, \ -3.289203518655379E-01, 8.957126445136651E-01, 8.989588878027095E-03, \ -3.243047057088739E-01, -7.936980547794279E-01, 1.075979049243002E-02, \ -3.129605000582947E-01, -6.643571783650405E-02, 1.856839158447809E-02, \ -3.117073855253361E-01, -3.093183812990403E-01, 1.656632086288442E-02, \ -3.072762353389070E-01, -9.564548826763054E-01, 5.369964649875180E-03, \ -3.061436378051206E-01, -4.704135840359435E-01, 1.475623099958883E-02, \ -3.021913077128562E-01, 9.981390270674768E-01, 1.131666739617315E-03, \ -2.949530243768917E-01, 9.686835034877084E-01, 2.797024137967235E-03, \ -2.924635827539191E-01, -7.047858510122733E-01, 6.851571387118350E-03, \ -2.812350771273387E-01, -8.980684313341059E-01, 7.363138635454566E-03, \ -2.806273605262599E-01, 3.029645468518594E-01, 1.520110596476129E-02, \ -2.745982375561375E-01, -9.934986711091262E-01, 1.673742994343650E-03, \ -2.710331296874568E-01, 4.652469064012115E-01, 1.090810494083061E-02, \ -2.635463086619279E-01, 1.586055674415278E-01, 1.746954739472360E-02, \ -2.625382248376168E-01, -5.932891429782097E-01, 1.529823413526504E-02, \ -2.590525077776922E-01, -1.823032100069667E-01, 1.460011251776361E-02, \ -2.581989912968990E-01, 6.927205540494286E-01, 1.020066380845207E-02, \ -2.411331427499952E-01, 9.344875760714670E-01, 5.158877832261257E-03, \ -2.406223697257603E-01, 7.735613151103899E-01, 6.930533482154789E-03, \ -2.306207507959519E-01, 4.834271168445705E-02, 1.167695287885717E-02, \ -2.256547660822549E-01, -8.303251302805508E-01, 5.969813944396011E-03, \ -2.233405416434596E-01, 8.513588948939629E-01, 1.041708126169881E-02, \ -2.200209241310239E-01, 5.418414720955490E-01, 1.204616875868074E-02, \ -2.140824323336795E-01, -3.999817827003599E-01, 1.469205327663902E-02, \ -2.099887189967384E-01, -7.385652177919024E-01, 1.102272008220242E-02, \ -2.055981693756977E-01, -9.815381529846507E-01, 3.208405941212317E-03, \ -1.907642188897441E-01, 9.883341858044101E-01, 3.400965087265759E-03, \ -1.897223918835828E-01, -9.336864994968639E-01, 6.598813190376643E-03, \ -1.856872749545497E-01, 3.807518860810150E-01, 1.626600502334043E-02, \ -1.856560896180115E-01, 6.458143580207676E-01, 9.595353199870314E-03, \ -1.771535862151187E-01, -8.502150916777047E-01, 6.882856119388930E-03, \ -1.761506840632638E-01, -2.849688737894649E-01, 1.376397443479240E-02, \ -1.760694512771735E-01, 9.487132134491084E-01, 3.463137052103194E-03, \ -1.759090616673586E-01, -1.668583040865908E-02, 1.494943461671058E-02, \ -1.743545387314084E-01, -6.480592314695985E-01, 8.068616752476498E-03, \ -1.646646667032431E-01, -1.549382245795711E-01, 1.229946774808041E-02, \ -1.564278540839040E-01, -5.099794466889294E-01, 1.583679910644951E-02, \ -1.476250668191063E-01, 2.508400888737863E-01, 1.598240477070294E-02, \ -1.378533885088872E-01, 7.470167466939204E-01, 1.025090566987707E-02, \ -1.339102361885577E-01, 1.587463638591125E-01, 1.042002071483287E-02, \ -1.253458474656329E-01, 9.016084675302966E-01, 8.382092697242076E-03, \ -1.242718966113707E-01, -9.975311977305669E-01, 1.307493707247085E-03, \ -1.149177253012365E-01, 5.015141775843105E-01, 1.335216066856519E-02, \ -1.062013123816681E-01, 8.113862649434280E-01, 8.240179055283665E-03, \ -1.005242315957304E-01, -6.768307306217036E-01, 9.892753624061720E-03, \ -9.910296904870308E-02, -9.655033098878887E-01, 4.971432564142077E-03, \ -9.822456345521705E-02, 6.182616980114717E-01, 1.154982585129897E-02, \ -9.094894553724515E-02, -7.832264404807726E-01, 1.272153770310018E-02, \ -8.951973571157114E-02, -8.934469335864712E-01, 9.040121806196625E-03, \ -8.864913498943343E-02, -5.752029154809029E-01, 7.696987946647426E-03, \ -7.813610453536655E-02, -3.824731713047965E-01, 1.595389785417394E-02, \ -7.808279619773810E-02, 9.678657629328651E-01, 5.348961931934154E-03, \ -7.518429220875299E-02, -9.501265478490149E-02, 1.603342783311217E-02, \ -7.256720788480295E-02, 9.980188020733000E-01, 1.239829395370563E-03, \ -7.160051871827056E-02, 7.964916268348117E-02, 1.747639962808621E-02, \ -6.658775866489877E-02, -2.544806391357054E-01, 1.439738622078677E-02, \ -5.912591896874869E-02, 4.086931280855817E-01, 1.434397636411426E-02, \ -3.003234825592526E-02, 8.585057270530800E-01, 8.172528647752865E-03, \ -2.645953523971930E-02, 7.046260937171298E-01, 1.344291776488621E-02, \ -2.534886371863461E-02, 2.933719416861227E-01, 1.759197717607860E-02, \ -1.323065725566219E-02, -4.759685548931392E-01, 1.437852891867941E-02, \ -1.108857312313384E-02, -6.086185473503245E-01, 1.096431541959337E-02, \ -9.767336568716133E-03, -9.880188324263295E-01, 3.240769608183762E-03, \ 2.472574608889389E-03, 9.298777848313345E-01, 7.408272240383237E-03, \ 3.476131508526145E-03, 5.622804755214021E-01, 1.417273440946883E-02, \ 5.102825364173400E-03, -9.360854000426274E-01, 7.306890259002694E-03, \ 7.481806578463433E-03, -4.304909728461822E-03, 9.644021597489717E-03, \ 1.083187044442501E-02, -8.405067439387872E-01, 1.139227327264933E-02, \ 2.078810983363222E-02, -7.184977995593806E-01, 1.419275964745119E-02, \ 2.352332931112040E-02, -1.777262641278441E-01, 1.513652886721543E-02, \ 2.605792957621816E-02, 1.714141618252540E-01, 1.746784365412643E-02, \ 3.419270449758923E-02, 7.926923352194076E-01, 1.114588247114633E-02, \ 3.689227013453180E-02, 9.869329842141271E-01, 3.587800597955966E-03, \ 5.231331279344743E-02, -2.983724214658152E-01, 1.282800566620749E-02, \ 5.333417882238150E-02, -3.150790865005272E-02, 1.067689529371097E-02, \ 5.515446270123405E-02, 4.640348051148255E-01, 1.483471286370125E-02, \ 7.326926690316637E-02, -3.859166123826371E-01, 1.317399038328787E-02, \ 7.896436713254719E-02, 6.515068803712124E-01, 1.175778018467305E-02, \ 8.106589543358063E-02, -5.455789831489050E-01, 1.257961431518928E-02, \ 9.143189128962997E-02, 8.849636002129454E-01, 7.995804990083446E-03, \ 9.183620472220967E-02, -9.982620877010548E-01, 1.071611175557207E-03, \ 1.020899734795291E-01, -9.680677235297332E-01, 5.359511511849509E-03, \ 1.032064648808839E-01, 3.508166883429220E-01, 1.821445820076782E-02, \ 1.055465484669112E-01, -8.936553035854308E-01, 9.364571370580868E-03, \ 1.116319040200762E-01, 9.569683551028125E-01, 5.799167128957759E-03, \ 1.184093061912173E-01, 6.460797547191485E-02, 1.538648042988892E-02, \ 1.211496833043070E-01, -7.832288499871760E-01, 1.305125306673873E-02, \ 1.222296761980543E-01, -6.414978463247534E-01, 1.274307450341386E-02, \ 1.268780973858983E-01, 2.124489885142361E-01, 1.303843019488049E-02, \ 1.334028983920185E-01, 7.430849024557798E-01, 1.170710723942358E-02, \ 1.377561712790752E-01, -1.149141127497300E-01, 1.518998754371716E-02, \ 1.443645551391211E-01, 5.914798921541217E-01, 9.267995494968094E-03, \ 1.464713397158526E-01, 9.975108317870389E-01, 1.344221020630127E-03, \ 1.471243438702994E-01, 8.406549255746518E-01, 6.868706503673577E-03, \ 1.539021244046412E-01, -2.177903033576761E-01, 1.189096266115889E-02, \ 1.645948745810365E-01, -4.622499482006776E-01, 1.598264890363537E-02, \ 1.737606299255193E-01, 5.108712579502437E-01, 1.343700851176021E-02, \ 1.960337529226180E-01, -3.160892037041645E-01, 1.517528874189867E-02, \ 1.996879640965994E-01, -6.932804184761608E-01, 1.065797263441093E-02, \ 2.020074577970664E-01, -9.886491220693521E-01, 3.111072986126015E-03, \ 2.033963003224787E-01, -9.351529309857213E-01, 7.383713855162398E-03, \ 2.050316445884164E-01, 9.183031846509473E-01, 7.915254944655616E-03, \ 2.133741088627701E-01, -8.457977005703088E-01, 1.089663499513872E-02, \ 2.141494782415598E-01, 9.779765604905496E-01, 4.137849906961731E-03, \ 2.177197497330517E-01, 2.653968084572469E-01, 1.606441497945596E-02, \ 2.182669785207582E-01, 1.002641349031797E-01, 1.470303701111106E-02, \ 2.208729153200149E-01, -3.179321251109352E-02, 1.319786624286162E-02, \ 2.223340049334479E-01, 6.699405548173695E-01, 1.117930035973834E-02, \ 2.292846440205571E-01, 4.151794226086859E-01, 1.606327398417143E-02, \ 2.309770714797946E-01, 8.143538927981072E-01, 8.974695973354508E-03, \ 2.394458713565459E-01, -5.651074560068458E-01, 1.649544265573178E-02, \ 2.617303912242682E-01, 7.450665189174808E-01, 6.665865551621909E-03, \ 2.691992761760191E-01, -7.480558691506524E-01, 1.062817914743759E-02, \ 2.801184378515139E-01, -8.648253256664529E-02, 1.029103279941478E-02, \ 2.802549482883130E-01, -3.882923892722029E-01, 1.369193939295842E-02, \ 2.839000603830919E-01, -2.046740542904322E-01, 1.736776423460412E-02, \ 2.887898581531176E-01, 5.814667573861627E-01, 1.465252164582414E-02, \ 2.943230313566177E-01, 8.763787360351365E-01, 7.624320350783295E-03, \ 2.984713532756781E-01, -9.662504924043853E-01, 5.098404762337242E-03, \ 3.006596174432872E-01, 9.936320220137688E-01, 2.068083074134366E-03, \ 3.050565768027433E-01, -9.982304187004531E-01, 1.009394886038144E-03, \ 3.085263100239341E-01, -7.996443277472217E-01, 3.534840513865065E-03, \ 3.116498242262688E-01, -8.955597721317096E-01, 9.093317546816406E-03, \ 3.117692757107713E-01, 1.675250048357164E-01, 1.698233278167723E-02, \ 3.159624611068410E-01, 9.489971508109396E-01, 6.529106763034471E-03, \ 3.197420491834217E-01, -4.656026992118575E-01, 1.003556952514073E-02, \ 3.267298270221274E-01, 3.348095746744744E-01, 1.595497306519906E-02, \ 3.309355307192962E-01, 7.014929727551507E-01, 6.957256742470056E-03, \ 3.342067700349441E-01, -6.419472908347359E-01, 1.483566807534002E-02, \ 3.430031057615673E-01, 4.809677053778840E-01, 1.448748066501445E-02, \ 3.497052562336275E-01, 1.998383478506136E-02, 1.800443798157775E-02, \ 3.644044878216754E-01, 7.810190581938899E-01, 1.024800809296951E-02, \ 3.661215757514518E-01, 8.526602936761131E-01, 4.944710357542757E-03, \ 3.672978740253939E-01, -8.151652782533108E-01, 8.850306571457656E-03, \ 3.728404816069009E-01, -2.931068378076280E-01, 1.638751096673266E-02, \ 3.898390476140786E-01, -9.858802308984792E-01, 2.780360483093786E-03, \ 3.909041204424732E-01, -5.186781535306678E-01, 1.326546194250014E-02, \ 3.968946098564246E-01, 9.780951815512755E-01, 3.201595614419611E-03, \ 4.004938098642667E-01, -7.280056190997359E-01, 7.945101887599497E-03, \ 4.022693250846630E-01, 6.492118066390665E-01, 1.299783839137487E-02, \ 4.046537911668389E-01, -9.367754362358695E-01, 6.856064424860622E-03, \ 4.069866793578729E-01, -1.279310253654376E-01, 1.953042326766891E-02, \ 4.136981826382187E-01, 2.469380555174871E-01, 1.590510409056284E-02, \ 4.155832387933074E-01, 9.987480710406026E-01, 7.122111647233873E-04, \ 4.163004497201460E-01, 9.096099007093472E-01, 7.935410861629728E-03, \ 4.170780839937515E-01, -3.956847909278206E-01, 6.071769193397902E-03, \ 4.358054536464377E-01, 5.406610991088344E-01, 1.142900377925798E-02, \ 4.402901712712737E-01, 1.068482982519669E-01, 1.483195555696222E-02, \ 4.415350462115391E-01, 3.998613126727678E-01, 1.544068952195007E-02, \ 4.424667710350890E-01, 9.683394190344123E-01, 1.611489458792926E-03, \ 4.438046510707432E-01, -6.946709046201798E-01, 6.566325499215901E-03, \ 4.460211421946402E-01, -8.651830868268215E-01, 8.948003496330081E-03, \ 4.538136212528461E-01, -9.949158557964749E-01, 9.385320236765432E-04, \ 4.539118311079229E-01, -3.619729438336315E-01, 7.295767791185555E-03, \ 4.640451021391556E-01, -5.874486068652885E-01, 1.173519860285180E-02, \ 4.730268087671548E-01, 8.312799295231539E-01, 9.822207517714310E-03, \ 4.758178764632183E-01, 7.358820987969293E-01, 1.092908968471396E-02, \ 4.903555614512899E-01, -1.585768379668491E-02, 1.599968590908050E-02, \ 4.941909567997217E-01, -7.741409899278064E-01, 9.298225635133817E-03, \ 4.963751357099565E-01, -9.672078799697353E-01, 4.661655661126369E-03, \ 4.967756100113436E-01, -4.362959868721491E-01, 1.193356100090212E-02, \ 5.000706488516046E-01, -2.331541719563617E-01, 1.856492166793463E-02, \ 5.046834517044907E-01, 9.440657290862045E-01, 5.549588703986526E-03, \ 5.082232650322930E-01, 9.906467286106726E-01, 2.226696053003991E-03, \ 5.160453615337504E-01, 5.957388605223901E-01, 1.121045861005303E-02, \ 5.174302117309763E-01, -9.984556911044671E-01, 6.178035235308593E-04, \ 5.242858161358990E-01, -6.284397942390747E-01, 6.102441007443274E-03, \ 5.256042669730074E-01, 3.069119064348889E-01, 1.440185388865715E-02, \ 5.269880492231742E-01, 1.756864225241269E-01, 1.321861287755303E-02, \ 5.270935009054812E-01, -9.093268419114411E-01, 7.024404856386155E-03, \ 5.351103385815182E-01, 4.676099826976436E-01, 1.240897009695142E-02, \ 5.522815966751274E-01, 6.908618824073344E-01, 8.695368896060368E-03, \ 5.538334779895970E-01, -8.184578724868724E-01, 6.919587428835741E-03, \ 5.538529139427266E-01, 8.832881173595583E-01, 8.500683283786904E-03, \ 5.632577394770644E-01, -1.008778811503898E-01, 1.434254071405664E-02, \ 5.636677818818019E-01, -6.847919323382405E-01, 9.749954332983632E-03, \ 5.639706182528545E-01, -5.072914896235071E-01, 1.248972405626944E-02, \ 5.855037849088083E-01, -9.870796028611907E-01, 2.635159595180530E-03, \ 5.871939805088643E-01, -3.393304454099807E-01, 1.722776519999956E-02, \ 5.873693348599127E-01, 9.705200439306851E-01, 3.780770676414746E-03, \ 5.906291713968752E-01, 7.237558809133927E-02, 1.587807859048982E-02, \ 5.925278367683712E-01, 7.893333499850927E-01, 1.138048852557252E-02, \ 5.953381157637589E-01, 9.983578941888753E-01, 7.034511014927064E-04, \ 6.048511251578461E-01, -9.438915264002324E-01, 5.098619467503369E-03, \ 6.096234974510961E-01, 3.718408906537116E-01, 1.196081090276131E-02, \ 6.109255118670557E-01, 5.230124092297559E-01, 1.003484742952671E-02, \ 6.137767907325069E-01, -8.605257481153944E-01, 7.236718965777555E-03, \ 6.217826405123270E-01, -5.581746176691810E-01, 4.316164008023176E-03, \ 6.246099189559922E-01, 6.358877552910304E-01, 1.025865841557620E-02, \ 6.284044434870041E-01, -7.434235031370082E-01, 9.441418508366915E-03, \ 6.310832515721740E-01, -1.878541135764036E-01, 1.431221258093288E-02, \ 6.345735406340975E-01, 2.275406791927811E-01, 1.538937487698498E-02, \ 6.360661118767135E-01, 9.263313590847803E-01, 6.260040454883993E-03, \ 6.398284843293994E-01, -5.970215524417410E-01, 8.476553668468471E-03, \ 6.649793750204779E-01, 9.883407907673419E-01, 2.094151290945697E-03, \ 6.654072620160371E-01, -2.363946414555849E-02, 1.496699675280598E-02, \ 6.659574757730714E-01, -9.976555625653712E-01, 8.961864501173595E-04, \ 6.691783842005241E-01, -4.395721919427361E-01, 1.512613718261678E-02, \ 6.721936512472663E-01, 8.515744193688413E-01, 8.861042223773296E-03, \ 6.777928890916691E-01, 4.328419152202564E-01, 9.776985446244503E-03, \ 6.782432986711542E-01, -9.696626891387243E-01, 3.431665660167878E-03, \ 6.812902581446887E-01, 7.225085203170045E-01, 1.117216385145412E-02, \ 6.834490098708866E-01, -9.033281433037320E-01, 6.317527410068836E-03, \ 6.924893003140195E-01, -8.005420801936927E-01, 8.320626487524666E-03, \ 6.983314069183064E-01, -6.580165170885999E-01, 9.761529855522378E-03, \ 6.985277688751799E-01, -2.783908913323763E-01, 1.342822159901166E-02, \ 7.008430500305758E-01, 5.594372141944102E-01, 1.072177885303342E-02, \ 7.068216200939229E-01, 1.246262362418973E-01, 1.472068962752201E-02, \ 7.126940396729210E-01, 9.599964346557995E-01, 4.096951260374946E-03, \ 7.178748920387166E-01, 3.138413638113185E-01, 1.320209574966812E-02, \ 7.341287552219317E-01, 9.979860760796205E-01, 6.952108677952970E-04, \ 7.342099274750985E-01, -1.209563345827185E-01, 1.379890445331191E-02, \ 7.423415965113581E-01, -5.379109496936945E-01, 1.292345963370039E-02, \ 7.444692651522274E-01, -9.882712947131560E-01, 1.957053218307852E-03, \ 7.453095007801902E-01, 9.038501012536742E-01, 6.328045119260687E-03, \ 7.494521020396612E-01, 7.927256925287816E-01, 8.961091095120005E-03, \ 7.528242556745927E-01, -9.406599209068169E-01, 4.646624808921421E-03, \ 7.547920587433695E-01, -3.572335113090026E-01, 7.889039673801524E-03, \ 7.566797098881304E-01, -8.534641077327416E-01, 6.970605288870389E-03, \ 7.576126656619195E-01, 6.437458483576055E-01, 1.076928925040325E-02, \ 7.581112942065328E-01, -7.245614233244616E-01, 9.029141466832830E-03, \ 7.628918949884904E-01, 4.623403366366171E-01, 1.090159565188403E-02, \ 7.766396378745131E-01, 2.261756565641802E-02, 1.348877811014296E-02, \ 7.810744268992557E-01, 2.131893811715405E-01, 1.210095928415743E-02, \ 7.812685180469271E-01, 9.836432079909175E-01, 2.255486894669111E-03, \ 7.833445634886622E-01, -4.071221655913209E-01, 7.458693727198815E-03, \ 7.964722407123696E-01, -2.187772943009381E-01, 1.222549520115298E-02, \ 8.020186660324402E-01, -9.983065602932809E-01, 5.862836379827036E-04, \ 8.041315522722302E-01, 3.586679600337050E-01, 8.633096906834895E-03, \ 8.090967096294495E-01, -6.272230964719828E-01, 1.054178563124901E-02, \ 8.108485375531935E-01, 9.451998657334438E-01, 4.141165511985786E-03, \ 8.109640154941112E-01, 8.551876501059489E-01, 6.621506960771783E-03, \ 8.151954694973160E-01, 7.229674728378743E-01, 8.717208142352892E-03, \ 8.153549506988876E-01, -9.703796385813469E-01, 2.953498033751418E-03, \ 8.172395811056902E-01, -7.891470762601582E-01, 7.528638399462986E-03, \ 8.177798317131469E-01, -9.009186885288820E-01, 5.272832904013914E-03, \ 8.208257565286451E-01, 5.503592548730148E-01, 1.054494230976308E-02, \ 8.329246417765747E-01, -4.845120828987132E-01, 9.960600804233005E-03, \ 8.375428168005339E-01, -8.162809594255294E-02, 1.178121026024084E-02, \ 8.386131595480735E-01, 9.965580003832177E-01, 8.087443020783061E-04, \ 8.415522987753493E-01, 1.153254562596080E-01, 1.088575597786116E-02, \ 8.503864327379893E-01, -3.173993641314918E-01, 1.038483762724286E-02, \ 8.531522884093242E-01, 4.035736040841352E-01, 6.302313466112946E-03, \ 8.541610211751280E-01, 2.680874670901057E-01, 7.527298628284477E-03, \ 8.657666650779589E-01, 9.068436211751228E-01, 4.549038886289249E-03, \ 8.664555255514452E-01, -7.090083499012046E-01, 8.071696882394806E-03, \ 8.664770965796653E-01, 7.958591698926688E-01, 6.538372590971846E-03, \ 8.677306492980269E-01, -9.908410519990466E-01, 1.416231188437276E-03, \ 8.684658881444902E-01, 9.747744029833587E-01, 2.379114842060784E-03, \ 8.691737799892778E-01, 6.418561562064864E-01, 8.197723506703251E-03, \ 8.711421380941257E-01, -8.482965458047063E-01, 5.636974183261061E-03, \ 8.717470929454793E-01, -9.410134880535705E-01, 3.553458092063557E-03, \ 8.842658311334305E-01, -5.712045519918001E-01, 8.457837440018774E-03, \ 8.858918774596265E-01, 4.761224644485181E-01, 7.791095831926886E-03, \ 8.887874898320439E-01, -4.134188226282018E-01, 4.059336672999811E-03, \ 8.888733039484702E-01, -1.867627150101622E-01, 9.832441758484581E-03, \ 8.924277378906769E-01, 1.414711422648437E-02, 9.363946896165124E-03, \ 9.009124683482767E-01, 2.977042992859208E-01, 4.958146707886305E-03, \ 9.010130683954759E-01, 1.826981564981862E-01, 6.492822410153440E-03, \ 9.072024742810378E-01, -4.184292901501477E-01, 4.774740801925348E-03, \ 9.111065823100322E-01, 9.944171031036695E-01, 8.780207710373898E-04, \ 9.114979269985268E-01, 8.578389833509421E-01, 4.544508627245127E-03, \ 9.115732033892179E-01, 7.257086927558489E-01, 6.103200593411189E-03, \ 9.131615645699338E-01, 9.465673322575073E-01, 2.807911611163054E-03, \ 9.141377233271082E-01, -7.823208061882461E-01, 5.719546762015152E-03, \ 9.154133627565975E-01, -9.723972924107900E-01, 2.022847142178555E-03, \ 9.167586103246737E-01, -8.996397400727117E-01, 3.801697006719042E-03, \ 9.185218417882126E-01, -3.128496473837001E-01, 3.188755821162131E-03, \ 9.195615536817429E-01, 5.722168961060426E-01, 6.380773543501595E-03, \ 9.224781848073185E-01, -9.985982423657683E-01, 3.867061146665929E-04, \ 9.267209776934766E-01, -6.555982315165978E-01, 6.278150490060387E-03, \ 9.287273685779625E-01, 3.701731556290727E-01, 6.625786458114385E-03, \ 9.335598233788510E-01, -8.772263219538960E-02, 7.531298731793813E-03, \ 9.372373370259899E-01, 1.003699940791335E-01, 5.803669510571517E-03, \ 9.381596020314867E-01, -2.714682784663502E-01, 5.599760135209719E-03, \ 9.392008661159771E-01, -5.070230655068764E-01, 6.382320939876130E-03, \ 9.458552781613642E-01, 9.787913214594990E-01, 1.364728190261521E-03, \ 9.467118325180552E-01, 2.073531201970276E-01, 3.340176953373344E-03, \ 9.474307117494180E-01, 7.982968423254421E-01, 4.139255006817926E-03, \ 9.488517823808786E-01, 9.079595933711595E-01, 2.809691915547652E-03, \ 9.500559469496047E-01, 4.843282580769499E-01, 4.555672065182541E-03, \ 9.514139598012699E-01, 6.593996703812790E-01, 4.775414025344274E-03, \ 9.515054065604527E-01, -8.462535973926137E-01, 3.659192971392661E-03, \ 9.518829254547306E-01, -9.423704869562158E-01, 2.246099949633720E-03, \ 9.577559031192738E-01, -9.884414315999143E-01, 9.138432349434030E-04, \ 9.597823200164480E-01, -7.333102517228226E-01, 4.172167786588739E-03, \ 9.632858025253836E-01, 2.676516560448716E-01, 4.435731025511098E-03, \ 9.633285939046516E-01, -3.830059130508450E-01, 5.251904961064754E-03, \ 9.659428214621411E-01, -1.681070365939437E-01, 3.910206880549662E-03, \ 9.662259959061779E-01, 9.975594517947205E-01, 3.405077457162791E-04, \ 9.667240278631448E-01, 1.427934466963100E-02, 5.159593067194380E-03, \ 9.682866853444982E-01, -5.956513635056965E-01, 4.355417541710161E-03, \ 9.710401795521018E-01, 4.115441754007046E-01, 3.080413657595975E-03, \ 9.723123261969079E-01, 9.532023404173199E-01, 1.437187961183978E-03, \ 9.749343472618806E-01, 5.694643711049896E-01, 3.514758009687542E-03, \ 9.750107495446679E-01, 8.593595879607496E-01, 2.404761206356202E-03, \ 9.755637104115001E-01, -2.162755744715040E-01, 2.069281536160542E-03, \ 9.761350537022933E-01, 7.378942771881075E-01, 2.990197999475044E-03, \ 9.778730077694230E-01, -9.006863126694932E-01, 2.019519731278123E-03, \ 9.822797218536741E-01, -9.673403735244110E-01, 1.011623047148952E-03, \ 9.828503527488298E-01, -9.972100487317516E-01, 2.034653337738994E-04, \ 9.828700260178675E-01, 1.402696637585946E-01, 3.875549745497106E-03, \ 9.829328496130976E-01, -8.027321126645347E-01, 2.328452025760749E-03, \ 9.830518093779190E-01, -4.725198861348646E-01, 2.884600800613669E-03, \ 9.865083692792747E-01, 3.318292049120302E-01, 2.535389452668076E-03, \ 9.870651427476129E-01, 9.851097580641042E-01, 5.787962104520319E-04, \ 9.878909985266884E-01, -6.792964437614948E-01, 2.397415128865462E-03, \ 9.890599145180482E-01, -3.004235153742925E-01, 2.952394914871963E-03, \ 9.891268190165852E-01, -7.461522335461102E-02, 3.147967359176418E-03, \ 9.900018031563753E-01, 9.183273178173896E-01, 1.129303662157627E-03, \ 9.906700419592033E-01, 6.532346934319574E-01, 1.929434615425692E-03, \ 9.912596163219474E-01, 4.801078529393079E-01, 2.082572420594760E-03, \ 9.924744721609760E-01, 8.057094807256353E-01, 1.431280556327198E-03, \ 9.936122984604325E-01, -5.399266031918037E-01, 1.361643312207529E-03, \ 9.945101783976882E-01, -9.964564449204121E-01, 6.738824280797225E-05, \ 9.959237770580724E-01, -9.356939566617255E-01, 6.409569163115698E-04, \ 9.960185717579940E-01, -8.614455712828953E-01, 8.970688263528367E-04, \ 9.963549802489995E-01, 2.297860268936834E-01, 1.493840185718328E-03, \ 9.974280487247386E-01, 9.970685285995574E-01, 8.386486527342163E-05, \ 9.974477484292649E-01, 4.872754674637698E-02, 1.368835501840511E-03, \ 9.974884982557854E-01, -9.835909301201050E-01, 2.155878200460052E-04, \ 9.979151073110650E-01, 9.613613215256067E-01, 3.343893771661675E-04, \ 9.979318948645635E-01, -7.553329869388302E-01, 7.631344418442518E-04, \ 9.981736018665053E-01, -4.034601085328000E-01, 1.016793649077959E-03, \ 9.983952046173069E-01, -1.854951369598807E-01, 1.067126311051324E-03, \ 9.985153359170394E-01, 5.693738362511860E-01, 6.823019963489656E-04, \ 9.985841032168380E-01, 8.747010290291490E-01, 4.298394507636698E-04, \ 9.986616936036532E-01, 7.274743018665757E-01, 5.666609989068298E-04, \ 9.986723383294596E-01, -6.114560344532366E-01, 5.878791899273640E-04, \ 9.988762864534128E-01, 3.869508160326630E-01, 6.702204214070438E-04 ] ) return xyw def smr55 ( ): #*****************************************************************************80 # ## smr55 returns the SMR rule of degree 55. # # Discussion: # # DEGREE: 55 # SYMMETRY: (X, Y), (-X, -Y). # POINTS CARDINALITY: 536 # NORM INF MOMS. RESIDUAL: 2.29858e-16 # SUM NEGATIVE WEIGHTS: 0.00000E+00 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # Original MATLAB version by Mattia Festa, Alvise Sommariva, # Python version by John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # real XYW(3*536), the requested rule. # import numpy as np xyw = np.array ( [ \ -9.988024883360008E-01, -4.104312670989267E-01, 7.247738364520382E-04, \ -9.986637711500016E-01, 5.835721439184322E-01, 6.485919247428450E-04, \ -9.985517638075939E-01, 1.568937801098068E-01, 1.047965997616771E-03, \ -9.983624199159088E-01, -7.311569400195331E-01, 6.234634259867621E-04, \ -9.982698924284638E-01, -5.843339960398285E-01, 7.392815641484668E-04, \ -9.982434766908749E-01, 3.819333028903024E-01, 9.500630778549490E-04, \ -9.982097416579526E-01, -8.832442641091779E-01, 4.604405106623550E-04, \ -9.978286522784937E-01, -9.628763075615144E-01, 3.344694660648939E-04, \ -9.976963561372271E-01, 9.678687355428703E-01, 3.138082077303478E-04, \ -9.976125620794032E-01, 7.261201764578525E-01, 8.279866159627213E-04, \ -9.973396392196245E-01, -9.972222237164891E-01, 8.333752929282447E-05, \ -9.972455951936153E-01, -7.187156081293171E-02, 1.410032513903549E-03, \ -9.971099785500591E-01, 9.975224120853297E-01, 7.798442798007867E-05, \ -9.963480933133427E-01, -2.479538638037798E-01, 1.491315677106339E-03, \ -9.958519119176469E-01, 9.077787403602237E-01, 7.431854366720857E-04, \ -9.952342237683616E-01, 8.286466960550624E-01, 1.082707396932906E-03, \ -9.929995253631880E-01, -8.129871703624600E-01, 1.347117277977657E-03, \ -9.920960970276202E-01, 5.044070130004836E-01, 1.824136223192767E-03, \ -9.906699598276788E-01, 2.862146444653838E-01, 2.228303203490404E-03, \ -9.900482572019094E-01, -4.985621080229760E-01, 2.242724334598082E-03, \ -9.892479265001065E-01, -6.612276378064350E-01, 2.043285817276434E-03, \ -9.888908697853098E-01, -9.233667636095402E-01, 1.140018239107126E-03, \ -9.885804018012844E-01, 4.855418553020024E-02, 3.260277409726965E-03, \ -9.872410998898277E-01, 6.516124343282037E-01, 2.451688694670727E-03, \ -9.865494934684096E-01, -9.856652402947823E-01, 5.802863637376822E-04, \ -9.864237410369340E-01, -3.474984134057699E-01, 2.626333169195453E-03, \ -9.854696330893135E-01, 9.878927125972993E-01, 5.302485898777602E-04, \ -9.823718529863428E-01, 9.448695023246775E-01, 1.256965089029987E-03, \ -9.820307319973294E-01, -1.607872100549523E-01, 3.959806596474525E-03, \ -9.817367673963038E-01, 2.211661902207940E-01, 2.176154471489884E-03, \ -9.798298883847092E-01, 7.687042632123031E-01, 2.691125475983456E-03, \ -9.794817550638735E-01, 4.308079229171551E-01, 3.138802635622372E-03, \ -9.760951773774511E-01, -7.497184921929896E-01, 2.895893718670046E-03, \ -9.756611980550673E-01, 8.717067247715160E-01, 2.345719243525908E-03, \ -9.748150682339674E-01, -8.630701855337108E-01, 2.379490945836736E-03, \ -9.716942423922518E-01, -5.810982845814314E-01, 3.659348716877558E-03, \ -9.702051269912042E-01, -9.560511844190226E-01, 1.434791120385777E-03, \ -9.688706334298569E-01, -4.266194891481059E-01, 3.409732775774852E-03, \ -9.675772091594030E-01, 5.706238471045659E-01, 4.319580505788219E-03, \ -9.654793296651025E-01, 1.449151374798731E-01, 4.901363403832491E-03, \ -9.648815628338514E-01, -9.976194228266280E-01, 3.422316968868938E-04, \ -9.644011406655369E-01, -3.955662605890648E-02, 5.487620385431768E-03, \ -9.621685673801630E-01, 9.981498616350863E-01, 2.983264390605248E-04, \ -9.618072357953964E-01, -2.840075572844367E-01, 4.584997220482829E-03, \ -9.603547491901058E-01, 3.444098104140523E-01, 5.192860463827343E-03, \ -9.572722322598644E-01, 9.727383585296555E-01, 1.371820477478312E-03, \ -9.543120615194950E-01, 6.978166939707769E-01, 4.657220418242932E-03, \ -9.502228126713501E-01, -6.756755603285315E-01, 4.638832336370128E-03, \ -9.497373302590694E-01, 9.198416005546896E-01, 2.489219831374708E-03, \ -9.477372910934111E-01, -9.097890847623551E-01, 2.819888629654258E-03, \ -9.461037891822155E-01, 8.162510788029149E-01, 4.131502513773345E-03, \ -9.459596501532294E-01, -8.050199903923727E-01, 4.077330276254603E-03, \ -9.454153692097916E-01, -4.969416983931578E-01, 4.614178689184361E-03, \ -9.435279532066055E-01, -2.221999393850942E-01, 3.479548412810748E-03, \ -9.426467016723202E-01, -9.801477693736759E-01, 1.345953538075658E-03, \ -9.392911967713488E-01, 4.855179051814372E-01, 6.174008549382279E-03, \ -9.351449029460894E-01, 2.406511548034665E-01, 5.779691515292159E-03, \ -9.316323693555080E-01, -1.260692370780684E-01, 6.144629409760324E-03, \ -9.303888378867309E-01, 6.224958329536455E-02, 7.669256083745869E-03, \ -9.252698678871364E-01, -3.816000875630634E-01, 6.720562662548456E-03, \ -9.211332348776220E-01, 9.906945704103310E-01, 1.078080942745430E-03, \ -9.188758666484276E-01, 6.191245374224351E-01, 6.822998261844405E-03, \ -9.180486167649172E-01, -5.920245031381465E-01, 6.069384535392124E-03, \ -9.147536811475745E-01, 8.800465507878222E-01, 3.625599405917247E-03, \ -9.116846414755537E-01, 3.946552397032295E-01, 4.799510717398269E-03, \ -9.109269835273496E-01, -9.474408959785233E-01, 2.828303409790731E-03, \ -9.107962036779229E-01, 9.546466357227235E-01, 2.504361618864681E-03, \ -9.097119148344930E-01, 2.791721791436264E-01, 3.325039377988705E-03, \ -9.088140552343917E-01, -8.613880826568586E-01, 4.524206023005564E-03, \ -9.085091703518080E-01, -7.357866023957996E-01, 5.980225096092428E-03, \ -9.069440260746182E-01, -9.948615423994508E-01, 8.460206194961731E-04, \ -9.060257668239784E-01, 7.510933281143483E-01, 6.285183519604021E-03, \ -8.966458818425863E-01, -3.077535071435578E-01, 5.074492497678043E-03, \ -8.914497061411687E-01, -2.063254399354762E-01, 6.379677376597891E-03, \ -8.886925006776532E-01, 4.029207162992898E-01, 3.953122632176603E-03, \ -8.877478758386065E-01, -3.703102823746122E-02, 9.391237982629010E-03, \ -8.863873331866154E-01, -5.014911962761207E-01, 6.732637721829442E-03, \ -8.840931476725340E-01, 1.591395148790940E-01, 9.725396029596314E-03, \ -8.750871750612564E-01, 8.371208783269141E-01, 4.667481132791865E-03, \ -8.746997180248225E-01, 5.337452183276610E-01, 8.969697082860535E-03, \ -8.738193544174702E-01, 9.987050363801271E-01, 4.029777384147725E-04, \ -8.656342986234824E-01, -6.539955758641589E-01, 8.007673011011452E-03, \ -8.653144381651936E-01, 9.229713406820786E-01, 3.786147464455085E-03, \ -8.649186611907598E-01, -9.752422585287235E-01, 2.397696219433860E-03, \ -8.620920815291837E-01, -9.088307352715838E-01, 4.535170978475270E-03, \ -8.618783040518693E-01, -8.015653601725335E-01, 6.476664260979469E-03, \ -8.591213496900382E-01, 9.789218555148047E-01, 2.183949091910629E-03, \ -8.580096391046452E-01, -4.289163888579028E-01, 7.032590377677609E-03, \ -8.561231024886632E-01, 6.768698449375528E-01, 8.653374792867137E-03, \ -8.531080996665429E-01, 3.100864425712632E-01, 9.462959763014268E-03, \ -8.445552751701417E-01, -2.869258517851172E-01, 7.087178777230579E-03, \ -8.345746770920350E-01, -1.348195251852799E-01, 1.086669255897672E-02, \ -8.323840732904080E-01, 5.770931774582546E-02, 1.157981674113329E-02, \ -8.316280572729237E-01, -9.963536786620084E-01, 8.601012497443448E-04, \ -8.302233642792779E-01, 7.887974291015537E-01, 6.403870452065013E-03, \ -8.198903592035567E-01, 4.474759410866835E-01, 1.039723732697557E-02, \ -8.179555207385244E-01, -5.630877825822931E-01, 1.038670426889326E-02, \ -8.131642862712356E-01, 8.855936518041989E-01, 5.172308318006293E-03, \ -8.095710479011895E-01, -7.299545306893604E-01, 8.640988335276857E-03, \ -8.060880027952726E-01, -9.464168885010812E-01, 4.138102993626548E-03, \ -8.055768707550288E-01, -8.588418294042808E-01, 6.546425691890088E-03, \ -8.052848747707124E-01, 2.154694645963307E-01, 1.115929240605312E-02, \ -8.048061510789419E-01, -3.718357650456645E-01, 8.637973753390449E-03, \ -8.013660329335811E-01, 9.549385718300994E-01, 3.667653054187556E-03, \ -7.996575186605993E-01, 9.945437983737444E-01, 1.170500089565615E-03, \ -7.978946443412313E-01, 5.940088162963154E-01, 1.102206312002593E-02, \ -7.753719582521668E-01, 7.296837750586209E-01, 8.830371768634843E-03, \ -7.728941799568024E-01, -9.834791267225803E-01, 2.318079830785805E-03, \ -7.713573933240646E-01, -2.292623609101414E-01, 1.222664318821314E-02, \ -7.703655439710254E-01, -4.177172398061163E-02, 1.320655645297225E-02, \ -7.696542328903390E-01, 3.800140053796911E-01, 5.896276097702543E-03, \ -7.613061970586104E-01, -4.720892602078328E-01, 1.121593897330926E-02, \ -7.555601563064301E-01, 8.414687309753481E-01, 6.891618536870428E-03, \ -7.520357832344026E-01, -6.508886285165648E-01, 1.070105581225020E-02, \ -7.490155562917605E-01, 3.252336868606283E-01, 9.351093216509690E-03, \ -7.459343555200221E-01, 1.236717037454283E-01, 1.296776589532101E-02, \ -7.431555210822531E-01, -7.977482842071556E-01, 8.833161716226669E-03, \ -7.403849867503648E-01, 9.819171911401473E-01, 2.337724717192945E-03, \ -7.391722285237710E-01, -9.062068947141577E-01, 6.258431339300329E-03, \ -7.351348537506192E-01, 9.235000024040693E-01, 5.339474521352486E-03, \ -7.281406688886811E-01, 5.071254424742396E-01, 1.331196820325115E-02, \ -7.243383015839274E-01, -9.980207065293273E-01, 7.199560063855860E-04, \ -7.131083800360229E-01, -3.348252722558369E-01, 1.317500343117314E-02, \ -7.125260040531168E-01, 6.588957967703316E-01, 1.101941046086741E-02, \ -7.032675418563811E-01, -9.600474050632336E-01, 4.157108404417536E-03, \ -6.986567532110330E-01, -1.382567167908484E-01, 1.442120114433883E-02, \ -6.958360474648256E-01, -5.644565737670422E-01, 1.103743316814278E-02, \ -6.909159146496135E-01, 7.887887571343239E-01, 8.977062336109128E-03, \ -6.906859319625951E-01, 9.979604128976195E-01, 8.435777152586793E-04, \ -6.849076257411216E-01, 2.427166387314666E-01, 1.397568311805146E-02, \ -6.779414345191699E-01, 3.063740688329146E-02, 1.447701175069298E-02, \ -6.754749986154636E-01, -7.281422316126919E-01, 1.097118103052011E-02, \ -6.718973107043948E-01, 9.628615704165838E-01, 3.868709630540442E-03, \ -6.652837909761897E-01, -8.550121217464759E-01, 8.720558763742966E-03, \ -6.641092110776139E-01, 8.842872475223941E-01, 7.073002093332755E-03, \ -6.638595707485085E-01, -4.439193977915850E-01, 1.102925103533717E-02, \ -6.582656205134384E-01, 4.038261118251286E-01, 1.497892745877775E-02, \ -6.531607555762389E-01, -9.883039600294047E-01, 2.166784944891255E-03, \ -6.403455995923052E-01, 5.867373929097057E-01, 1.193450620498925E-02, \ -6.314704538659979E-01, -2.446105067220338E-01, 1.537286390141198E-02, \ -6.254538870491240E-01, -9.264854004436116E-01, 6.307266862024064E-03, \ -6.226576289009583E-01, 7.259246555573967E-01, 1.069584666724211E-02, \ -6.191838769193574E-01, -6.420040583801523E-01, 1.067988406928965E-02, \ -6.149834556692348E-01, 1.527830270721475E-01, 1.405889213374533E-02, \ -6.058697705151179E-01, 9.883839405182854E-01, 2.594759629417247E-03, \ -6.031110203472072E-01, 5.107400343109616E-01, 6.474717016434753E-03, \ -6.014430739812223E-01, -6.305652605767732E-02, 1.564707540156174E-02, \ -5.949690407134853E-01, 9.351174758101611E-01, 5.854723529644378E-03, \ -5.939522570295417E-01, -5.310108582117370E-01, 1.096129405119757E-02, \ -5.910214836343624E-01, 8.384444159782082E-01, 8.418868716555618E-03, \ -5.881718967548081E-01, -3.744506110517851E-01, 1.307998578130345E-02, \ -5.864634403080233E-01, -7.932418330534410E-01, 1.112227385834183E-02, \ -5.811601592234984E-01, -9.983496902489798E-01, 7.104280334676121E-04, \ -5.757548043279564E-01, -9.703367418123594E-01, 3.757168119063795E-03, \ -5.748025638560177E-01, 3.067973240959255E-01, 1.707935332348776E-02, \ -5.497845124077343E-01, 7.333202414867040E-02, 1.235895418614051E-02, \ -5.484074961393921E-01, 6.660476228238359E-01, 1.048532964530446E-02, \ -5.467362660936782E-01, 4.682073286935134E-01, 1.236063811528119E-02, \ -5.421728509707354E-01, -8.831112721261267E-01, 8.569226685725167E-03, \ -5.413187638370147E-01, -7.008354250408056E-01, 9.314699663035950E-03, \ -5.351205786493067E-01, -1.662338233527932E-01, 1.523192606517475E-02, \ -5.291031884464018E-01, 7.888885157981417E-01, 7.737672122912299E-03, \ -5.186382422892405E-01, 5.909018703387654E-01, 8.134241234233111E-03, \ -5.176647451047708E-01, 9.983923444453340E-01, 8.821790616867712E-04, \ -5.132865237464714E-01, -4.688970718806879E-01, 1.282967010005945E-02, \ -5.131329313010590E-01, 9.693478795578427E-01, 4.668299073616817E-03, \ -5.113306771546843E-01, 8.975233040638488E-01, 8.023411794220729E-03, \ -5.043040025277375E-01, -6.040349373214349E-01, 1.160242726756205E-02, \ -5.035820355440569E-01, -2.986926997353190E-01, 1.507793601848234E-02, \ -4.965158961324884E-01, -9.906821956576266E-01, 2.159685403265884E-03, \ -4.961172566625360E-01, -9.440998487019658E-01, 5.059202691726304E-03, \ -4.886505110046377E-01, 2.014030458083448E-01, 1.779060966900524E-02, \ -4.814712707153859E-01, 1.018471840513952E-03, 1.494149892965163E-02, \ -4.724465250882208E-01, 3.901946239850855E-01, 1.407056045257186E-02, \ -4.673690443814725E-01, 7.510905791040010E-01, 8.653955385139918E-03, \ -4.643134260679443E-01, -8.291696117863686E-01, 9.380625377758188E-03, \ -4.620662895796879E-01, -7.420575670812756E-01, 1.005785415907135E-02, \ -4.544968567562652E-01, -9.637138942504565E-01, 1.122463533992389E-03, \ -4.392936416624263E-01, 5.418537987967835E-01, 1.354180192499032E-02, \ -4.360207998774642E-01, 3.149360384017255E-01, 5.844690041934657E-03, \ -4.337443890556876E-01, 6.598862990786999E-01, 8.546812451435981E-03, \ -4.331554234268176E-01, -1.092637162347169E-01, 1.439377035472382E-02, \ -4.291577428294838E-01, 8.476059832446078E-01, 9.902296083341852E-03, \ -4.229143668793170E-01, -3.960647752213135E-01, 1.549781901257185E-02, \ -4.187017631471830E-01, -5.436803325150400E-01, 1.209743843849932E-02, \ -4.183500029509192E-01, 9.898883598570750E-01, 2.709117739353572E-03, \ -4.173246329940232E-01, 9.401616974636222E-01, 6.891766839873124E-03, \ -4.112319822368788E-01, -9.120363501798638E-01, 7.424471893404875E-03, \ -4.048315435775057E-01, -9.987956142180350E-01, 6.718324805703920E-04, \ -3.980418991846619E-01, -2.327471046963004E-01, 1.625275270500379E-02, \ -3.953464161989157E-01, -9.776274329999616E-01, 3.590227670893820E-03, \ -3.927964120379244E-01, -6.567324722323492E-01, 1.286468850270801E-02, \ -3.908992398262501E-01, 1.029204492534816E-01, 1.923372019735730E-02, \ -3.783036687069794E-01, 7.129987503369131E-01, 8.163366302461943E-03, \ -3.709983918669602E-01, 3.878951046903481E-01, 5.919722230014070E-03, \ -3.686946309484030E-01, 2.658237229153717E-01, 1.502100476996729E-02, \ -3.670884151507721E-01, -8.541749683199031E-01, 5.997903388653519E-03, \ -3.597392305547168E-01, 4.702440999029917E-01, 1.222936506074443E-02, \ -3.456801320384574E-01, -7.767804274879180E-01, 1.064901135031854E-02, \ -3.354206745206995E-01, 7.970083033314623E-01, 1.098275538515688E-02, \ -3.349659026157715E-01, 9.738986981710231E-01, 2.585251695131729E-03, \ -3.317394233870357E-01, -3.629784813923093E-02, 1.817689182146082E-02, \ -3.292032308163682E-01, 8.969852827615720E-01, 8.651055110598674E-03, \ -3.270737918480568E-01, -4.795137218921213E-01, 1.439474911975008E-02, \ -3.252517001548298E-01, 6.111780771310250E-01, 1.471608963923809E-02, \ -3.127045248917160E-01, -9.507593463893184E-01, 6.165042832173903E-03, \ -3.122739080164743E-01, -7.037282845144895E-01, 6.502793402916389E-03, \ -3.121872182700364E-01, -3.284494967900573E-01, 1.665094260609503E-02, \ -3.021802314007289E-01, 9.981802915822515E-01, 1.089216259085527E-03, \ -2.961390561335081E-01, -9.938134682747217E-01, 1.955987410825677E-03, \ -2.929939168803610E-01, 9.675850235289137E-01, 2.923308696330317E-03, \ -2.870583486247197E-01, -1.684615473834412E-01, 1.611587845368105E-02, \ -2.869268892504222E-01, -8.836970380549014E-01, 7.313309499881776E-03, \ -2.824132709710231E-01, -5.861790192624122E-01, 1.402973677831503E-02, \ -2.801601822730441E-01, 4.674597814398905E-01, 7.723487106141499E-03, \ -2.735536542584517E-01, 1.882929761148383E-01, 1.635032477992683E-02, \ -2.681837896607717E-01, 3.462108439336833E-01, 1.561212360653534E-02, \ -2.638750753550576E-01, 7.175917772976728E-01, 9.196701513559774E-03, \ -2.562280695633936E-01, 7.536618699046908E-02, 1.159566375455242E-02, \ -2.449718364656067E-01, 9.329876539574047E-01, 4.442995362383195E-03, \ -2.367076649306707E-01, -8.164340093215012E-01, 8.859159397898358E-03, \ -2.263564338237641E-01, 8.525868904257583E-01, 1.025853294633492E-02, \ -2.233777787601983E-01, -6.690920935223389E-01, 8.457199667884932E-03, \ -2.225881310352093E-01, 5.464598853057760E-01, 1.451315283307596E-02, \ -2.172243346336479E-01, 7.779346875182629E-01, 5.453876637219251E-03, \ -2.167851796507998E-01, -7.340009575500001E-01, 7.704445266317693E-03, \ -2.156912547618889E-01, -4.159114007166079E-01, 1.600761576189837E-02, \ -2.126675089250964E-01, -9.790313276822009E-01, 3.898756652243800E-03, \ -2.057013987550619E-01, 6.714574222473618E-01, 8.548373971133082E-03, \ -2.001222956524658E-01, -9.229708435499334E-01, 7.317697261380912E-03, \ -1.968485732716530E-01, -2.684443696987204E-01, 1.551989981674327E-02, \ -1.952851800362058E-01, -1.181886347339289E-01, 1.249411507302537E-02, \ -1.930088850045736E-01, 1.067037967524868E-02, 1.502128981902244E-02, \ -1.927893567464448E-01, 9.885913799935848E-01, 3.285042178348613E-03, \ -1.843627359591440E-01, 9.475189594826643E-01, 3.879323024081221E-03, \ -1.721744096018839E-01, -5.142401574740272E-01, 1.164304712326221E-02, \ -1.700184298252278E-01, 4.192688036006606E-01, 1.408971892461283E-02, \ -1.624664921006047E-01, 2.057032829234850E-01, 1.045498739102006E-02, \ -1.559859159591793E-01, 2.894304583316343E-01, 1.306941393934462E-02, \ -1.518484005740585E-01, -8.477732470072303E-01, 7.414729733024272E-03, \ -1.476070990486803E-01, -5.880708608342150E-01, 9.069852257674605E-03, \ -1.416105434314038E-01, -9.974967466477315E-01, 1.331241793936731E-03, \ -1.264308798345233E-01, 9.023791087885762E-01, 8.220753803377345E-03, \ -1.229412724709716E-01, 7.559125625986661E-01, 9.067738186701686E-03, \ -1.211233536563693E-01, 6.333611074991552E-01, 1.314389634964796E-02, \ -1.171435843878661E-01, -7.589099321895559E-01, 1.034402317344686E-02, \ -1.142916155264042E-01, 8.134828246262563E-01, 6.912585182173686E-03, \ -1.091562261809793E-01, -9.593556005291021E-01, 5.529710901059238E-03, \ -1.050166495242263E-01, -2.262609218574975E-01, 1.163508798500837E-02, \ -1.039822454676996E-01, 1.147960727732085E-01, 1.726822277670347E-02, \ -9.753315478770204E-02, 5.156121655539427E-01, 1.303842924168740E-02, \ -9.563339138231701E-02, -8.253348748785061E-02, 1.590204206847470E-02, \ -9.364067514936512E-02, -6.600655556642241E-01, 1.223016394781105E-02, \ -8.965966879899780E-02, -3.586799588937428E-01, 1.756886760866844E-02, \ -8.551197009473779E-02, -8.901928888130525E-01, 7.846676697391447E-03, \ -8.365029898380197E-02, 9.685292909194466E-01, 5.214647863353589E-03, \ -7.568647243766341E-02, 9.980944345717083E-01, 1.190071691701019E-03, \ -5.482069463596000E-02, -4.814553453340769E-01, 1.503245155554792E-02, \ -4.844652587154250E-02, 4.108333656727153E-01, 1.342616839842313E-02, \ -3.841094055935779E-02, 2.983156459040408E-01, 1.541784656069183E-02, \ -3.632741707588952E-02, 8.600961271871967E-01, 8.090610682724464E-03, \ -3.153704671275477E-02, -9.872255003269456E-01, 3.471711085681394E-03, \ -3.056480134457628E-02, 2.747004986895673E-02, 1.221572001121651E-02, \ -2.872714752032467E-02, -8.038829114783085E-01, 9.938639300940503E-03, \ -2.162030480223479E-02, 7.100363302853934E-01, 1.355512556979677E-02, \ -7.873257230365114E-03, -1.856407375954660E-01, 1.627356809068969E-02, \ -1.536827915034127E-03, 9.326306951328229E-01, 7.198183297047558E-03, \ -2.078796471167668E-05, -5.847656060556753E-01, 1.411565553024802E-02, \ 2.078796471167668E-05, 5.847656060556753E-01, 1.411565553024802E-02, \ 1.536827915034127E-03, -9.326306951328229E-01, 7.198183297047558E-03, \ 7.873257230365114E-03, 1.856407375954660E-01, 1.627356809068969E-02, \ 2.162030480223479E-02, -7.100363302853934E-01, 1.355512556979677E-02, \ 2.872714752032467E-02, 8.038829114783085E-01, 9.938639300940503E-03, \ 3.056480134457628E-02, -2.747004986895673E-02, 1.221572001121651E-02, \ 3.153704671275477E-02, 9.872255003269456E-01, 3.471711085681394E-03, \ 3.632741707588952E-02, -8.600961271871967E-01, 8.090610682724464E-03, \ 3.841094055935779E-02, -2.983156459040408E-01, 1.541784656069183E-02, \ 4.844652587154250E-02, -4.108333656727153E-01, 1.342616839842313E-02, \ 5.482069463596000E-02, 4.814553453340769E-01, 1.503245155554792E-02, \ 7.568647243766341E-02, -9.980944345717083E-01, 1.190071691701019E-03, \ 8.365029898380197E-02, -9.685292909194466E-01, 5.214647863353589E-03, \ 8.551197009473779E-02, 8.901928888130525E-01, 7.846676697391447E-03, \ 8.965966879899780E-02, 3.586799588937428E-01, 1.756886760866844E-02, \ 9.364067514936512E-02, 6.600655556642241E-01, 1.223016394781105E-02, \ 9.563339138231701E-02, 8.253348748785061E-02, 1.590204206847470E-02, \ 9.753315478770204E-02, -5.156121655539427E-01, 1.303842924168740E-02, \ 1.039822454676996E-01, -1.147960727732085E-01, 1.726822277670347E-02, \ 1.050166495242263E-01, 2.262609218574975E-01, 1.163508798500837E-02, \ 1.091562261809793E-01, 9.593556005291021E-01, 5.529710901059238E-03, \ 1.142916155264042E-01, -8.134828246262563E-01, 6.912585182173686E-03, \ 1.171435843878661E-01, 7.589099321895559E-01, 1.034402317344686E-02, \ 1.211233536563693E-01, -6.333611074991552E-01, 1.314389634964796E-02, \ 1.229412724709716E-01, -7.559125625986661E-01, 9.067738186701686E-03, \ 1.264308798345233E-01, -9.023791087885762E-01, 8.220753803377345E-03, \ 1.416105434314038E-01, 9.974967466477315E-01, 1.331241793936731E-03, \ 1.476070990486803E-01, 5.880708608342150E-01, 9.069852257674605E-03, \ 1.518484005740585E-01, 8.477732470072303E-01, 7.414729733024272E-03, \ 1.559859159591793E-01, -2.894304583316343E-01, 1.306941393934462E-02, \ 1.624664921006047E-01, -2.057032829234850E-01, 1.045498739102006E-02, \ 1.700184298252278E-01, -4.192688036006606E-01, 1.408971892461283E-02, \ 1.721744096018839E-01, 5.142401574740272E-01, 1.164304712326221E-02, \ 1.843627359591440E-01, -9.475189594826643E-01, 3.879323024081221E-03, \ 1.927893567464448E-01, -9.885913799935848E-01, 3.285042178348613E-03, \ 1.930088850045736E-01, -1.067037967524868E-02, 1.502128981902244E-02, \ 1.952851800362058E-01, 1.181886347339289E-01, 1.249411507302537E-02, \ 1.968485732716530E-01, 2.684443696987204E-01, 1.551989981674327E-02, \ 2.001222956524658E-01, 9.229708435499334E-01, 7.317697261380912E-03, \ 2.057013987550619E-01, -6.714574222473618E-01, 8.548373971133082E-03, \ 2.126675089250964E-01, 9.790313276822009E-01, 3.898756652243800E-03, \ 2.156912547618889E-01, 4.159114007166079E-01, 1.600761576189837E-02, \ 2.167851796507998E-01, 7.340009575500001E-01, 7.704445266317693E-03, \ 2.172243346336479E-01, -7.779346875182629E-01, 5.453876637219251E-03, \ 2.225881310352093E-01, -5.464598853057760E-01, 1.451315283307596E-02, \ 2.233777787601983E-01, 6.690920935223389E-01, 8.457199667884932E-03, \ 2.263564338237641E-01, -8.525868904257583E-01, 1.025853294633492E-02, \ 2.367076649306707E-01, 8.164340093215012E-01, 8.859159397898358E-03, \ 2.449718364656067E-01, -9.329876539574047E-01, 4.442995362383195E-03, \ 2.562280695633936E-01, -7.536618699046908E-02, 1.159566375455242E-02, \ 2.638750753550576E-01, -7.175917772976728E-01, 9.196701513559774E-03, \ 2.681837896607717E-01, -3.462108439336833E-01, 1.561212360653534E-02, \ 2.735536542584517E-01, -1.882929761148383E-01, 1.635032477992683E-02, \ 2.801601822730441E-01, -4.674597814398905E-01, 7.723487106141499E-03, \ 2.824132709710231E-01, 5.861790192624122E-01, 1.402973677831503E-02, \ 2.869268892504222E-01, 8.836970380549014E-01, 7.313309499881776E-03, \ 2.870583486247197E-01, 1.684615473834412E-01, 1.611587845368105E-02, \ 2.929939168803610E-01, -9.675850235289137E-01, 2.923308696330317E-03, \ 2.961390561335081E-01, 9.938134682747217E-01, 1.955987410825677E-03, \ 3.021802314007289E-01, -9.981802915822515E-01, 1.089216259085527E-03, \ 3.121872182700364E-01, 3.284494967900573E-01, 1.665094260609503E-02, \ 3.122739080164743E-01, 7.037282845144895E-01, 6.502793402916389E-03, \ 3.127045248917160E-01, 9.507593463893184E-01, 6.165042832173903E-03, \ 3.252517001548298E-01, -6.111780771310250E-01, 1.471608963923809E-02, \ 3.270737918480568E-01, 4.795137218921213E-01, 1.439474911975008E-02, \ 3.292032308163682E-01, -8.969852827615720E-01, 8.651055110598674E-03, \ 3.317394233870357E-01, 3.629784813923093E-02, 1.817689182146082E-02, \ 3.349659026157715E-01, -9.738986981710231E-01, 2.585251695131729E-03, \ 3.354206745206995E-01, -7.970083033314623E-01, 1.098275538515688E-02, \ 3.456801320384574E-01, 7.767804274879180E-01, 1.064901135031854E-02, \ 3.597392305547168E-01, -4.702440999029917E-01, 1.222936506074443E-02, \ 3.670884151507721E-01, 8.541749683199031E-01, 5.997903388653519E-03, \ 3.686946309484030E-01, -2.658237229153717E-01, 1.502100476996729E-02, \ 3.709983918669602E-01, -3.878951046903481E-01, 5.919722230014070E-03, \ 3.783036687069794E-01, -7.129987503369131E-01, 8.163366302461943E-03, \ 3.908992398262501E-01, -1.029204492534816E-01, 1.923372019735730E-02, \ 3.927964120379244E-01, 6.567324722323492E-01, 1.286468850270801E-02, \ 3.953464161989157E-01, 9.776274329999616E-01, 3.590227670893820E-03, \ 3.980418991846619E-01, 2.327471046963004E-01, 1.625275270500379E-02, \ 4.048315435775057E-01, 9.987956142180350E-01, 6.718324805703920E-04, \ 4.112319822368788E-01, 9.120363501798638E-01, 7.424471893404875E-03, \ 4.173246329940232E-01, -9.401616974636222E-01, 6.891766839873124E-03, \ 4.183500029509192E-01, -9.898883598570750E-01, 2.709117739353572E-03, \ 4.187017631471830E-01, 5.436803325150400E-01, 1.209743843849932E-02, \ 4.229143668793170E-01, 3.960647752213135E-01, 1.549781901257185E-02, \ 4.291577428294838E-01, -8.476059832446078E-01, 9.902296083341852E-03, \ 4.331554234268176E-01, 1.092637162347169E-01, 1.439377035472382E-02, \ 4.337443890556876E-01, -6.598862990786999E-01, 8.546812451435981E-03, \ 4.360207998774642E-01, -3.149360384017255E-01, 5.844690041934657E-03, \ 4.392936416624263E-01, -5.418537987967835E-01, 1.354180192499032E-02, \ 4.544968567562652E-01, 9.637138942504565E-01, 1.122463533992389E-03, \ 4.620662895796879E-01, 7.420575670812756E-01, 1.005785415907135E-02, \ 4.643134260679443E-01, 8.291696117863686E-01, 9.380625377758188E-03, \ 4.673690443814725E-01, -7.510905791040010E-01, 8.653955385139918E-03, \ 4.724465250882208E-01, -3.901946239850855E-01, 1.407056045257186E-02, \ 4.814712707153859E-01, -1.018471840513952E-03, 1.494149892965163E-02, \ 4.886505110046377E-01, -2.014030458083448E-01, 1.779060966900524E-02, \ 4.961172566625360E-01, 9.440998487019658E-01, 5.059202691726304E-03, \ 4.965158961324884E-01, 9.906821956576266E-01, 2.159685403265884E-03, \ 5.035820355440569E-01, 2.986926997353190E-01, 1.507793601848234E-02, \ 5.043040025277375E-01, 6.040349373214349E-01, 1.160242726756205E-02, \ 5.113306771546843E-01, -8.975233040638488E-01, 8.023411794220729E-03, \ 5.131329313010590E-01, -9.693478795578427E-01, 4.668299073616817E-03, \ 5.132865237464714E-01, 4.688970718806879E-01, 1.282967010005945E-02, \ 5.176647451047708E-01, -9.983923444453340E-01, 8.821790616867712E-04, \ 5.186382422892405E-01, -5.909018703387654E-01, 8.134241234233111E-03, \ 5.291031884464018E-01, -7.888885157981417E-01, 7.737672122912299E-03, \ 5.351205786493067E-01, 1.662338233527932E-01, 1.523192606517475E-02, \ 5.413187638370147E-01, 7.008354250408056E-01, 9.314699663035950E-03, \ 5.421728509707354E-01, 8.831112721261267E-01, 8.569226685725167E-03, \ 5.467362660936782E-01, -4.682073286935134E-01, 1.236063811528119E-02, \ 5.484074961393921E-01, -6.660476228238359E-01, 1.048532964530446E-02, \ 5.497845124077343E-01, -7.333202414867040E-02, 1.235895418614051E-02, \ 5.748025638560177E-01, -3.067973240959255E-01, 1.707935332348776E-02, \ 5.757548043279564E-01, 9.703367418123594E-01, 3.757168119063795E-03, \ 5.811601592234984E-01, 9.983496902489798E-01, 7.104280334676121E-04, \ 5.864634403080233E-01, 7.932418330534410E-01, 1.112227385834183E-02, \ 5.881718967548081E-01, 3.744506110517851E-01, 1.307998578130345E-02, \ 5.910214836343624E-01, -8.384444159782082E-01, 8.418868716555618E-03, \ 5.939522570295417E-01, 5.310108582117370E-01, 1.096129405119757E-02, \ 5.949690407134853E-01, -9.351174758101611E-01, 5.854723529644378E-03, \ 6.014430739812223E-01, 6.305652605767732E-02, 1.564707540156174E-02, \ 6.031110203472072E-01, -5.107400343109616E-01, 6.474717016434753E-03, \ 6.058697705151179E-01, -9.883839405182854E-01, 2.594759629417247E-03, \ 6.149834556692348E-01, -1.527830270721475E-01, 1.405889213374533E-02, \ 6.191838769193574E-01, 6.420040583801523E-01, 1.067988406928965E-02, \ 6.226576289009583E-01, -7.259246555573967E-01, 1.069584666724211E-02, \ 6.254538870491240E-01, 9.264854004436116E-01, 6.307266862024064E-03, \ 6.314704538659979E-01, 2.446105067220338E-01, 1.537286390141198E-02, \ 6.403455995923052E-01, -5.867373929097057E-01, 1.193450620498925E-02, \ 6.531607555762389E-01, 9.883039600294047E-01, 2.166784944891255E-03, \ 6.582656205134384E-01, -4.038261118251286E-01, 1.497892745877775E-02, \ 6.638595707485085E-01, 4.439193977915850E-01, 1.102925103533717E-02, \ 6.641092110776139E-01, -8.842872475223941E-01, 7.073002093332755E-03, \ 6.652837909761897E-01, 8.550121217464759E-01, 8.720558763742966E-03, \ 6.718973107043948E-01, -9.628615704165838E-01, 3.868709630540442E-03, \ 6.754749986154636E-01, 7.281422316126919E-01, 1.097118103052011E-02, \ 6.779414345191699E-01, -3.063740688329146E-02, 1.447701175069298E-02, \ 6.849076257411216E-01, -2.427166387314666E-01, 1.397568311805146E-02, \ 6.906859319625951E-01, -9.979604128976195E-01, 8.435777152586793E-04, \ 6.909159146496135E-01, -7.887887571343239E-01, 8.977062336109128E-03, \ 6.958360474648256E-01, 5.644565737670422E-01, 1.103743316814278E-02, \ 6.986567532110330E-01, 1.382567167908484E-01, 1.442120114433883E-02, \ 7.032675418563811E-01, 9.600474050632336E-01, 4.157108404417536E-03, \ 7.125260040531168E-01, -6.588957967703316E-01, 1.101941046086741E-02, \ 7.131083800360229E-01, 3.348252722558369E-01, 1.317500343117314E-02, \ 7.243383015839274E-01, 9.980207065293273E-01, 7.199560063855860E-04, \ 7.281406688886811E-01, -5.071254424742396E-01, 1.331196820325115E-02, \ 7.351348537506192E-01, -9.235000024040693E-01, 5.339474521352486E-03, \ 7.391722285237710E-01, 9.062068947141577E-01, 6.258431339300329E-03, \ 7.403849867503648E-01, -9.819171911401473E-01, 2.337724717192945E-03, \ 7.431555210822531E-01, 7.977482842071556E-01, 8.833161716226669E-03, \ 7.459343555200221E-01, -1.236717037454283E-01, 1.296776589532101E-02, \ 7.490155562917605E-01, -3.252336868606283E-01, 9.351093216509690E-03, \ 7.520357832344026E-01, 6.508886285165648E-01, 1.070105581225020E-02, \ 7.555601563064301E-01, -8.414687309753481E-01, 6.891618536870428E-03, \ 7.613061970586104E-01, 4.720892602078328E-01, 1.121593897330926E-02, \ 7.696542328903390E-01, -3.800140053796911E-01, 5.896276097702543E-03, \ 7.703655439710254E-01, 4.177172398061163E-02, 1.320655645297225E-02, \ 7.713573933240646E-01, 2.292623609101414E-01, 1.222664318821314E-02, \ 7.728941799568024E-01, 9.834791267225803E-01, 2.318079830785805E-03, \ 7.753719582521668E-01, -7.296837750586209E-01, 8.830371768634843E-03, \ 7.978946443412313E-01, -5.940088162963154E-01, 1.102206312002593E-02, \ 7.996575186605993E-01, -9.945437983737444E-01, 1.170500089565615E-03, \ 8.013660329335811E-01, -9.549385718300994E-01, 3.667653054187556E-03, \ 8.048061510789419E-01, 3.718357650456645E-01, 8.637973753390449E-03, \ 8.052848747707124E-01, -2.154694645963307E-01, 1.115929240605312E-02, \ 8.055768707550288E-01, 8.588418294042808E-01, 6.546425691890088E-03, \ 8.060880027952726E-01, 9.464168885010812E-01, 4.138102993626548E-03, \ 8.095710479011895E-01, 7.299545306893604E-01, 8.640988335276857E-03, \ 8.131642862712356E-01, -8.855936518041989E-01, 5.172308318006293E-03, \ 8.179555207385244E-01, 5.630877825822931E-01, 1.038670426889326E-02, \ 8.198903592035567E-01, -4.474759410866835E-01, 1.039723732697557E-02, \ 8.302233642792779E-01, -7.887974291015537E-01, 6.403870452065013E-03, \ 8.316280572729237E-01, 9.963536786620084E-01, 8.601012497443448E-04, \ 8.323840732904080E-01, -5.770931774582546E-02, 1.157981674113329E-02, \ 8.345746770920350E-01, 1.348195251852799E-01, 1.086669255897672E-02, \ 8.445552751701417E-01, 2.869258517851172E-01, 7.087178777230579E-03, \ 8.531080996665429E-01, -3.100864425712632E-01, 9.462959763014268E-03, \ 8.561231024886632E-01, -6.768698449375528E-01, 8.653374792867137E-03, \ 8.580096391046452E-01, 4.289163888579028E-01, 7.032590377677609E-03, \ 8.591213496900382E-01, -9.789218555148047E-01, 2.183949091910629E-03, \ 8.618783040518693E-01, 8.015653601725335E-01, 6.476664260979469E-03, \ 8.620920815291837E-01, 9.088307352715838E-01, 4.535170978475270E-03, \ 8.649186611907598E-01, 9.752422585287235E-01, 2.397696219433860E-03, \ 8.653144381651936E-01, -9.229713406820786E-01, 3.786147464455085E-03, \ 8.656342986234824E-01, 6.539955758641589E-01, 8.007673011011452E-03, \ 8.738193544174702E-01, -9.987050363801271E-01, 4.029777384147725E-04, \ 8.746997180248225E-01, -5.337452183276610E-01, 8.969697082860535E-03, \ 8.750871750612564E-01, -8.371208783269141E-01, 4.667481132791865E-03, \ 8.840931476725340E-01, -1.591395148790940E-01, 9.725396029596314E-03, \ 8.863873331866154E-01, 5.014911962761207E-01, 6.732637721829442E-03, \ 8.877478758386065E-01, 3.703102823746122E-02, 9.391237982629010E-03, \ 8.886925006776532E-01, -4.029207162992898E-01, 3.953122632176603E-03, \ 8.914497061411687E-01, 2.063254399354762E-01, 6.379677376597891E-03, \ 8.966458818425863E-01, 3.077535071435578E-01, 5.074492497678043E-03, \ 9.060257668239784E-01, -7.510933281143483E-01, 6.285183519604021E-03, \ 9.069440260746182E-01, 9.948615423994508E-01, 8.460206194961731E-04, \ 9.085091703518080E-01, 7.357866023957996E-01, 5.980225096092428E-03, \ 9.088140552343917E-01, 8.613880826568586E-01, 4.524206023005564E-03, \ 9.097119148344930E-01, -2.791721791436264E-01, 3.325039377988705E-03, \ 9.107962036779229E-01, -9.546466357227235E-01, 2.504361618864681E-03, \ 9.109269835273496E-01, 9.474408959785233E-01, 2.828303409790731E-03, \ 9.116846414755537E-01, -3.946552397032295E-01, 4.799510717398269E-03, \ 9.147536811475745E-01, -8.800465507878222E-01, 3.625599405917247E-03, \ 9.180486167649172E-01, 5.920245031381465E-01, 6.069384535392124E-03, \ 9.188758666484276E-01, -6.191245374224351E-01, 6.822998261844405E-03, \ 9.211332348776220E-01, -9.906945704103310E-01, 1.078080942745430E-03, \ 9.252698678871364E-01, 3.816000875630634E-01, 6.720562662548456E-03, \ 9.303888378867309E-01, -6.224958329536455E-02, 7.669256083745869E-03, \ 9.316323693555080E-01, 1.260692370780684E-01, 6.144629409760324E-03, \ 9.351449029460894E-01, -2.406511548034665E-01, 5.779691515292159E-03, \ 9.392911967713488E-01, -4.855179051814372E-01, 6.174008549382279E-03, \ 9.426467016723202E-01, 9.801477693736759E-01, 1.345953538075658E-03, \ 9.435279532066055E-01, 2.221999393850942E-01, 3.479548412810748E-03, \ 9.454153692097916E-01, 4.969416983931578E-01, 4.614178689184361E-03, \ 9.459596501532294E-01, 8.050199903923727E-01, 4.077330276254603E-03, \ 9.461037891822155E-01, -8.162510788029149E-01, 4.131502513773345E-03, \ 9.477372910934111E-01, 9.097890847623551E-01, 2.819888629654258E-03, \ 9.497373302590694E-01, -9.198416005546896E-01, 2.489219831374708E-03, \ 9.502228126713501E-01, 6.756755603285315E-01, 4.638832336370128E-03, \ 9.543120615194950E-01, -6.978166939707769E-01, 4.657220418242932E-03, \ 9.572722322598644E-01, -9.727383585296555E-01, 1.371820477478312E-03, \ 9.603547491901058E-01, -3.444098104140523E-01, 5.192860463827343E-03, \ 9.618072357953964E-01, 2.840075572844367E-01, 4.584997220482829E-03, \ 9.621685673801630E-01, -9.981498616350863E-01, 2.983264390605248E-04, \ 9.644011406655369E-01, 3.955662605890648E-02, 5.487620385431768E-03, \ 9.648815628338514E-01, 9.976194228266280E-01, 3.422316968868938E-04, \ 9.654793296651025E-01, -1.449151374798731E-01, 4.901363403832491E-03, \ 9.675772091594030E-01, -5.706238471045659E-01, 4.319580505788219E-03, \ 9.688706334298569E-01, 4.266194891481059E-01, 3.409732775774852E-03, \ 9.702051269912042E-01, 9.560511844190226E-01, 1.434791120385777E-03, \ 9.716942423922518E-01, 5.810982845814314E-01, 3.659348716877558E-03, \ 9.748150682339674E-01, 8.630701855337108E-01, 2.379490945836736E-03, \ 9.756611980550673E-01, -8.717067247715160E-01, 2.345719243525908E-03, \ 9.760951773774511E-01, 7.497184921929896E-01, 2.895893718670046E-03, \ 9.794817550638735E-01, -4.308079229171551E-01, 3.138802635622372E-03, \ 9.798298883847092E-01, -7.687042632123031E-01, 2.691125475983456E-03, \ 9.817367673963038E-01, -2.211661902207940E-01, 2.176154471489884E-03, \ 9.820307319973294E-01, 1.607872100549523E-01, 3.959806596474525E-03, \ 9.823718529863428E-01, -9.448695023246775E-01, 1.256965089029987E-03, \ 9.854696330893135E-01, -9.878927125972993E-01, 5.302485898777602E-04, \ 9.864237410369340E-01, 3.474984134057699E-01, 2.626333169195453E-03, \ 9.865494934684096E-01, 9.856652402947823E-01, 5.802863637376822E-04, \ 9.872410998898277E-01, -6.516124343282037E-01, 2.451688694670727E-03, \ 9.885804018012844E-01, -4.855418553020024E-02, 3.260277409726965E-03, \ 9.888908697853098E-01, 9.233667636095402E-01, 1.140018239107126E-03, \ 9.892479265001065E-01, 6.612276378064350E-01, 2.043285817276434E-03, \ 9.900482572019094E-01, 4.985621080229760E-01, 2.242724334598082E-03, \ 9.906699598276788E-01, -2.862146444653838E-01, 2.228303203490404E-03, \ 9.920960970276202E-01, -5.044070130004836E-01, 1.824136223192767E-03, \ 9.929995253631880E-01, 8.129871703624600E-01, 1.347117277977657E-03, \ 9.952342237683616E-01, -8.286466960550624E-01, 1.082707396932906E-03, \ 9.958519119176469E-01, -9.077787403602237E-01, 7.431854366720857E-04, \ 9.963480933133427E-01, 2.479538638037798E-01, 1.491315677106339E-03, \ 9.971099785500591E-01, -9.975224120853297E-01, 7.798442798007867E-05, \ 9.972455951936153E-01, 7.187156081293171E-02, 1.410032513903549E-03, \ 9.973396392196245E-01, 9.972222237164891E-01, 8.333752929282447E-05, \ 9.976125620794032E-01, -7.261201764578525E-01, 8.279866159627213E-04, \ 9.976963561372271E-01, -9.678687355428703E-01, 3.138082077303478E-04, \ 9.978286522784937E-01, 9.628763075615144E-01, 3.344694660648939E-04, \ 9.982097416579526E-01, 8.832442641091779E-01, 4.604405106623550E-04, \ 9.982434766908749E-01, -3.819333028903024E-01, 9.500630778549490E-04, \ 9.982698924284638E-01, 5.843339960398285E-01, 7.392815641484668E-04, \ 9.983624199159088E-01, 7.311569400195331E-01, 6.234634259867621E-04, \ 9.985517638075939E-01, -1.568937801098068E-01, 1.047965997616771E-03, \ 9.986637711500016E-01, -5.835721439184322E-01, 6.485919247428450E-04, \ 9.988024883360008E-01, 4.104312670989267E-01, 7.247738364520382E-04 ] ) return xyw def square_minimal_rule ( degree ): #*****************************************************************************80 # ## square_minimal_rule() returns a minimal rule for the square. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 24 February 2018 # # Author: # # John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Input: # # integer DEGREE, the degree, between 0 and 55. # # Output: # # real XYW(3*ORDER), the rule. # if ( degree == 0 ): xyw = smr00 ( ) elif ( degree == 1 ): xyw = smr01 ( ) elif ( degree == 2 ): xyw = smr02 ( ) elif ( degree == 3 ): xyw = smr03 ( ) elif ( degree == 4 ): xyw = smr04 ( ) elif ( degree == 5 ): xyw = smr05 ( ) elif ( degree == 6 ): xyw = smr06 ( ) elif ( degree == 7 ): xyw = smr07 ( ) elif ( degree == 8 ): xyw = smr08 ( ) elif ( degree == 9 ): xyw = smr09 ( ) elif ( degree == 10 ): xyw = smr10 ( ) elif ( degree == 11 ): xyw = smr11 ( ) elif ( degree == 12 ): xyw = smr12 ( ) elif ( degree == 13 ): xyw = smr13 ( ) elif ( degree == 14 ): xyw = smr14 ( ) elif ( degree == 15 ): xyw = smr15 ( ) elif ( degree == 16 ): xyw = smr16 ( ) elif ( degree == 17 ): xyw = smr17 ( ) elif ( degree == 18 ): xyw = smr18 ( ) elif ( degree == 19 ): xyw = smr19 ( ) elif ( degree == 20 ): xyw = smr20 ( ) elif ( degree == 21 ): xyw = smr21 ( ) elif ( degree == 22 ): xyw = smr22 ( ) elif ( degree == 23 ): xyw = smr23 ( ) elif ( degree == 24 ): xyw = smr24 ( ) elif ( degree == 25 ): xyw = smr25 ( ) elif ( degree == 26 ): xyw = smr26 ( ) elif ( degree == 27 ): xyw = smr27 ( ) elif ( degree == 28 ): xyw = smr28 ( ) elif ( degree == 29 ): xyw = smr29 ( ) elif ( degree == 30 ): xyw = smr30 ( ) elif ( degree == 31 ): xyw = smr31 ( ) elif ( degree == 32 ): xyw = smr32 ( ) elif ( degree == 33 ): xyw = smr33 ( ) elif ( degree == 34 ): xyw = smr34 ( ) elif ( degree == 35 ): xyw = smr35 ( ) elif ( degree == 36 ): xyw = smr36 ( ) elif ( degree == 37 ): xyw = smr37 ( ) elif ( degree == 38 ): xyw = smr38 ( ) elif ( degree == 39 ): xyw = smr39 ( ) elif ( degree == 40 ): xyw = smr40 ( ) elif ( degree == 41 ): xyw = smr41 ( ) elif ( degree == 42 ): xyw = smr42 ( ) elif ( degree == 43 ): xyw = smr43 ( ) elif ( degree == 44 ): xyw = smr44 ( ) elif ( degree == 45 ): xyw = smr45 ( ) elif ( degree == 46 ): xyw = smr46 ( ) elif ( degree == 47 ): xyw = smr47 ( ) elif ( degree == 48 ): xyw = smr48 ( ) elif ( degree == 49 ): xyw = smr49 ( ) elif ( degree == 50 ): xyw = smr50 ( ) elif ( degree == 51 ): xyw = smr51 ( ) elif ( degree == 52 ): xyw = smr52 ( ) elif ( degree == 53 ): xyw = smr53 ( ) elif ( degree == 54 ): xyw = smr54 ( ) elif ( degree == 55 ): xyw = smr55 ( ) else: print ( '' ) print ( 'square_minimal_rule - Fatal error!' ) print ( ' 0 <= DEGREE <= 55 is required.' ) raise Exception ( 'square_minimal_rule - Fatal error!' ) return xyw def square_minimal_rule_degree_max ( ): #*****************************************************************************80 # ## square_minimal_rule_degree_max returns the maximum rule degree. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 24 February 2018 # # Author: # # John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Output: # # integer degree_max, the maximum degree of the minimal # rules for the square. # degree_max = 55 return degree_max def square_minimal_rule_error_max ( degree ): #*****************************************************************************80 # ## square_minimal_rule_error_max returns the maximum error. # # Discussion: # # The rule of given DEGREE should theoretically have zero error # for all monomials of degrees 0 <= D <= DEGREE. This function # checks every such monomial and reports the maximum error. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 24 February 2018 # # Author: # # John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Input: # # integer DEGREE, the desired total polynomial degree exactness # of the quadrature rule. # # Output: # # real square_minimal_rule_error_max, the maximum error observed # when using the rule to compute the integrals of all monomials of degree # between 0 and DEGREE. # import numpy as np order = square_minimal_rule_order ( degree ) xyw = square_minimal_rule ( degree ) error_max = 0.0 for d in range ( 0, degree + 1 ): for i in range ( 0, d + 1 ): j = d - i e = np.array ( [ i, j ] ) exact = squaresym_monomial_integral ( e ) s = 0.0 for k in range ( 0, order ): s = s + xyw[2+k*3] * xyw[0+k*3] ** i * xyw[1+k*3] ** j error = abs ( exact - s ) error_max = max ( error_max, error ) return error_max def square_minimal_rule_error_max_test ( ): #*****************************************************************************80 # ## square_minimal_rule_error_max_test tests square_minimal_rule_error_max. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 24 February 2018 # # Author: # # John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # print ( '' ) print ( 'square_minimal_rule_error_max_test' ) print ( ' square_minimal_rule_error_max computes the maximum' ) print ( ' error for a rule that should be exact for all monomials' ) print ( ' up to a given value of DEGREE.' ) degree_max = square_minimal_rule_degree_max ( ) print ( '' ) print ( ' Degree Monomials Error Max' ) print ( '' ) for degree in range ( 0, degree_max + 1 ): error_max = square_minimal_rule_error_max ( degree ) m_num = ( ( degree + 1 ) * ( degree + 2 ) ) / 2 print ( ' %4d %4d %14.6g' \ % ( degree, m_num, error_max ) ) return def square_minimal_rule_order ( degree ): #*****************************************************************************80 # ## square_minimal_rule_order returns the order of a minimal square rule. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 24 February 2018 # # Author: # # John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # # Input: # # integer DEGREE, the degree of the rule, # between 0 and 55. # # Output: # # integer ORDER, the order of the rule. # import numpy as np order_list = np.array ( [ \ 1, 1, 3, 4, 6, \ 7, 10, 12, 16, 17, \ 22, 24, 31, 33, 40, \ 43, 52, 54, 64, 67, \ 78, 81, 93, 96, 109, \ 113, 127, 132, 146, 153, \ 167, 172, 189, 197, 211, \ 220, 238, 245, 265, 274, \ 296, 303, 326, 331, 353, \ 359, 387, 396, 417, 427, \ 454, 462, 493, 498, 530, \ 536 ] ) degree_max = square_minimal_rule_degree_max ( ) if ( degree < 0 ): order = 0 elif ( degree_max < degree ): order = 0 else: order = order_list[degree] return order def square_minimal_rule_order_test ( ): #*****************************************************************************80 # ## square_minimal_rule_order_test tests square_minimal_rule_order. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 24 February 2018 # # Author: # # John Burkardt. # # Reference: # # Mattia Festa, Alvise Sommariva, # Computing almost minimal formulas on the square, # Journal of Computational and Applied Mathematics, # Volume 17, Number 236, November 2012, pages 4296-4302. # print ( '' ) print ( 'square_minimal_rule_order_test' ) print ( ' Print the order (number of points) for each' ) print ( ' minimal square rule.' ) degree_max = square_minimal_rule_degree_max ( ) print ( '' ) print ( ' Degree Order' ) print ( '' ) for degree in range ( 0, degree_max + 1 ): order = square_minimal_rule_order ( degree ) print ( ' %4d %4d' % ( degree, order ) ) return def square_minimal_rule_print_test ( degree ): #*****************************************************************************80 # ## square_minimal_rule_print_test tests square_minimal_rule_print. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # John Burkardt # print ( '' ) print ( 'square_minimal_rule_print_test' ) print ( ' square_minimal_rule_print prints a quadrature rule' ) print ( ' for the symmetric unit square.' ) print ( ' Minimal quadrature rule for a square.' ) print ( ' Polynomial exactness degree DEGREE = %d' % ( degree ) ) # # Retrieve and print a symmetric quadrature rule. # order = square_minimal_rule_order ( degree ) xyw = square_minimal_rule ( degree ) print ( '' ) print ( ' Number of nodes N = %d' % ( order ) ) print ( '' ) print ( ' J X Y W' ) print ( '' ) for j in range ( 0, order ): print ( ' %4d %14.6g %14.6g %14.6g' \ % ( j, xyw[0+j*3], xyw[1+j*3], xyw[2+j*3] ) ) d = 0.0 for j in range ( 0, order ): d = d + xyw[2+j*3] print ( '' ) print ( ' Sum %g' % ( d ) ) area = squaresym_area ( ) print ( ' Area %g' % ( area ) ) return def squaresym_area ( ): #*****************************************************************************80 # ## squaresym_area returns the area of the symmetric unit square in 2D. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 20 February 2018 # # Author: # # John Burkardt # # Output: # # real VALUE, the area. # value = 4.0 return value def squaresym_monomial_integral ( e ): #*****************************************************************************80 # ## squaresym_monomial_integral: integrals over the symmetric unit square in 2D. # # Discussion: # # The integration region is # # -1 <= X <= 1, # -1 <= Y <= 1. # # The monomial is F(X,Y) = X^E(1) * Y^E(2). # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 20 February 2018 # # Author: # # John Burkardt # # Reference: # # Philip Davis, Philip Rabinowitz, # Methods of Numerical Integration, # Second Edition, # Academic Press, 1984, page 263. # # Input: # # integer E(2), the exponents. Each exponent must be nonnegative. # # Output: # # real INTEGRAL, the integral. # if ( e[0] < 0 or e[1] < 0 ): print ( '' ) print ( 'squaresym_monomial_integral - Fatal error!' ) print ( ' All exponents must be nonnegative.' ) raise Exception ( 'squaresym_monomial_integral - Fatal error!' ) if ( e[0] % 2 == 1 or e[1] % 2 == 1 ): integral = 0.0 else: integral = 4.0 / float ( e[0] + 1 ) / float ( e[1] + 1 ) return integral def square_minimal_rule_test ( ): #*****************************************************************************80 # ## square_minimal_rule_test tests square_minimal_rule(). # # Discussion: # # square_minimal_rule_test tests the square_minimal_rule library. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 24 February 2018 # # Author: # # John Burkardt # print ( '' ) print ( 'square_minimal_rule_test' ) print ( ' Python version' ) print ( ' Test the square_minimal_rule library.' ) degree = 8 square_minimal_rule_print_test ( degree ) square_minimal_rule_order_test ( ) square_minimal_rule_error_max_test ( ) # # Terminate. # print ( '' ) print ( 'square_minimal_rule_test' ) print ( ' Normal end of execution.' ) print ( '' ) return def timestamp ( ): #*****************************************************************************80 # ## timestamp() prints the date as a timestamp. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 06 April 2013 # # Author: # # John Burkardt # import time t = time.time ( ) print ( time.ctime ( t ) ) return None if ( __name__ == '__main__' ): timestamp ( ) square_minimal_rule_test ( ) timestamp ( )