#! /usr/bin/env python3 # def pyramid_jaskowiec_rule_test ( ): #*****************************************************************************80 # ## pyramid_jaskowiec_rule_test() tests pyramid_jaskowiec_rule(). # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 12 July 2023 # # Author: # # John Burkardt. # import platform print ( '' ) print ( 'pyramid_jaskowiec_rule_test():' ) print ( ' Python version: ' + platform.python_version ( ) ) print ( ' Test pyramid_jaskowiec_rule().' ) p = 5 pyramid_jaskowiec_rule_test01 ( p ) p = 5 pyramid_jaskowiec_rule_test02 ( p ) p_lo = 0 p_hi = 20 pyramid_jaskowiec_rule_test03 ( p_lo, p_hi ) # # Terminate. # print ( '' ) print ( 'pyramid_jaskowiec_rule_test():' ) print ( ' Normal end of execution.' ) return def pyramid_jaskowiec_rule_test01 ( p ): #*****************************************************************************80 # ## pyramid_jaskowiec_rule_test01() computes a quadrature rule of precision P. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 25 May 2023 # # Author: # # John Burkardt. # import numpy as np print ( '' ) print ( 'pyramid_jaskowiec_rule_test01():' ) print ( ' Quadrature rule for the unit pyramid,' ) print ( ' Precision p = ', p ) # # Retrieve the rule. # n, x, y, z, w = pyramid_jaskowiec_rule ( p ) # # Print the rule. # print ( '' ) print ( ' I W X Y Z' ) print ( '' ) for i in range ( 0, n ): print ( ' %4d %10.6f %10.6f %10.6f %10.6f' \ % ( i, w[i], x[i], y[i], z[i] ) ) # # Verify that weights sum to 1. # w_sum = np.sum ( w ) print ( '' ) print ( ' Weight Sum ', w_sum ) return def pyramid_jaskowiec_rule_test02 ( p ): #*****************************************************************************80 # ## pyramid_jaskowiec_rule_test02() tests a quadrature rule of precision P. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 12 July 2023 # # Author: # # John Burkardt. # import numpy as np print ( '' ) print ( 'pyramid_jaskowiec_rule_test02():' ) print ( ' Test the precision of a quadrature rule for the unit pyramid.' ) dim_num = 3 # # Retrieve the rule. # n, x, y, z, w = pyramid_jaskowiec_rule ( p ) # # Pack the x, y, z vectors as rows of an array. # xyz = np.transpose ( np.array ( [ x, y, z ] ) ) print ( '' ) print ( ' Stated precision of rule = ', p ) print ( ' Number of quadrature points = ', n ) print ( '' ) print ( ' Degree Maximum error' ) print ( '' ) for degree in range ( 0, p + 3 ): expon = np.zeros ( dim_num, dtype = int ) more = False h = 0 t = 0 max_error = 0.0 while ( True ): expon, more, h, t = comp_next ( degree, dim_num, expon, more, h, t ) v = monomial_value ( expon, xyz ) quad = pyramid_unit_volume ( ) * np.dot ( w, v ) exact = pyramid_unit_monomial_integral ( expon ) quad_error = np.abs ( quad - exact ) max_error = max ( max_error, quad_error ) if ( not more ): break print ( ' %2d %24.16g' % ( degree, max_error ) ) return def pyramid_jaskowiec_rule_test03 ( p_lo, p_hi ): #*****************************************************************************80 # ## pyramid_jaskowiec_rule_test03() tests absolute and relative precision. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 12 July 2023 # # Author: # # John Burkardt. # # integer p_lo, p_hi: the lowest and highest rules to check. # import numpy as np print ( '' ) print ( 'pyramid_jaskowiec_rule_test03():' ) print ( ' Test the precision of quadrature rules for the unit pyramid.' ) print ( ' Check rules of precision p =', p_lo, 'through', p_hi ) print ( ' for error in approximating integrals of monomials.' ) dim_num = 3 print ( '' ) print ( ' maximum maximum' ) print ( ' p absolute relative' ) print ( ' error error' ) print ( '' ) for p in range ( p_lo, p_hi + 1 ): n, x, y, z, w = pyramid_jaskowiec_rule ( p ) # # Pack the x, y, z vectors as rows of an array. # xyz = np.transpose ( np.array ( [ x, y, z ] ) ) max_abs = 0.0 max_rel = 0.0 for degree in range ( 0, p + 1 ): expon = np.zeros ( dim_num, dtype = int ) more = False h = 0 t = 0 while ( True ): expon, more, h, t = comp_next ( degree, dim_num, expon, more, h, t ) v = monomial_value ( expon, xyz ) quad = pyramid_unit_volume ( ) * np.dot ( w, v ) exact = pyramid_unit_monomial_integral ( expon ) quad_error = np.abs ( quad - exact ) max_abs = max ( max_abs, quad_error ) if ( exact != 0.0 ): max_rel = max ( max_rel, quad_error / abs ( exact ) ) if ( not more ): break print ( ' %2d %24.16g %24.16g' % ( p, max_abs, max_rel ) ) return def comp_next ( n, k, a, more, h, t ): #*****************************************************************************80 # ## comp_next() computes the compositions of the integer N into K parts. # # Discussion: # # A composition of the integer N into K parts is an ordered sequence # of K nonnegative integers which sum to N. The compositions (1,2,1) # and (1,1,2) are considered to be distinct. # # The routine computes one composition on each call until there are no more. # For instance, one composition of 6 into 3 parts is # 3+2+1, another would be 6+0+0. # # On the first call to this routine, set MORE = FALSE. The routine # will compute the first element in the sequence of compositions, and # return it, as well as setting MORE = TRUE. If more compositions # are desired, call again, and again. Each time, the routine will # return with a new composition. # # However, when the LAST composition in the sequence is computed # and returned, the routine will reset MORE to FALSE, signaling that # the end of the sequence has been reached. # # This routine originally used a SAVE statement to maintain the # variables H and T. I have decided that it is safer # to pass these variables as arguments, even though the user should # never alter them. This allows this routine to safely shuffle # between several ongoing calculations. # # There are 28 compositions of 6 into three parts. This routine will # produce those compositions in the following order: # # I A # - --------- # 1 6 0 0 # 2 5 1 0 # 3 4 2 0 # 4 3 3 0 # 5 2 4 0 # 6 1 5 0 # 7 0 6 0 # 8 5 0 1 # 9 4 1 1 # 10 3 2 1 # 11 2 3 1 # 12 1 4 1 # 13 0 5 1 # 14 4 0 2 # 15 3 1 2 # 16 2 2 2 # 17 1 3 2 # 18 0 4 2 # 19 3 0 3 # 20 2 1 3 # 21 1 2 3 # 22 0 3 3 # 23 2 0 4 # 24 1 1 4 # 25 0 2 4 # 26 1 0 5 # 27 0 1 5 # 28 0 0 6 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 20 May 2015 # # Author: # # John Burkardt. # # Reference: # # Albert Nijenhuis, Herbert Wilf, # Combinatorial Algorithms for Computers and Calculators, # Second Edition, # Academic Press, 1978, # ISBN: 0-12-519260-6, # LC: QA164.N54. # # Input: # # integer N, the integer whose compositions are desired. # # integer K, the number of parts in the composition. # # integer A(K), the previous composition. On the first call, # with MORE = FALSE, set A = []. Thereafter, A should be the # value of A output from the previous call. # # bool MORE. The input value of MORE on the first # call should be FALSE, which tells the program to initialize. # On subsequent calls, MORE should be TRUE, or simply the # output value of MORE from the previous call. # # integer H, T, two internal parameters needed for the # computation. The user may need to initialize these before the # very first call, but these initial values are not important. # The user should not alter these parameters once the computation # begins. # # Output: # # integer A(K), the next composition. # # bool MORE, will be TRUE unless the composition # that is being returned is the final one in the sequence. # # integer H, T, the updated values of the two internal # variables. # if ( k == 0 ): a = [] more = False t = n h = 0 return a, more, h, t if ( not more ): t = n h = 0 a[0] = n for i in range ( 1, k ): a[i] = 0 else: if ( 1 < t ): h = 0 t = a[h] a[h] = 0 a[0] = t - 1 a[h+1] = a[h+1] + 1 h = h + 1 more = ( a[k-1] != n ) return a, more, h, t def monomial_value ( e, x ): #*****************************************************************************80 # ## monomial_value() evaluates a monomial. # # Discussion: # # This routine evaluates a monomial of the form # # product ( 1 <= i <= m ) x(i)^e(i) # # The combination 0.0^0, if encountered, is treated as 1.0. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 15 May 2023 # # Author: # # John Burkardt # # Input: # # integer E(D): the exponents. # # real X(N,D): the point coordinates. # # Output: # # real V(N): the monomial values. # import numpy as np n, d = x.shape v = np.ones ( n ) for j in range ( 0, d ): if ( 0 != e[j] ): v[0:n] = v[0:n] * x[0:n,j] ** e[j] return v def pyramid_jaskowiec_rule ( p ): #*****************************************************************************80 # ## pyramid_jaskowiec_rule() returns a pyramid quadrature rule of given precision. # # Discussion: # # The unit pyramid with square base is the region # # -1 <= X <= 1 # -1 <= Y <= 1 # 0 <= Z <= 1. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 15 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal of Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Input: # # integer p: the precision, 0 <= p <= 20. # # Output: # # integer n: the order of the rule. # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights. # if ( p < 0 ): raise Exception ( 'pyramid_jaskowiec_rule(): Input p < 0.' ) if ( 20 < p ): raise Exception ( 'pyramid_jaskowiec_rule(): Input 20 < p.' ) n = rule_order ( p ) if ( p == 0 ): x, y, z, w = rule00 ( ) elif ( p == 1 ): x, y, z, w = rule01 ( ) elif ( p == 2 ): x, y, z, w = rule02 ( ) elif ( p == 3 ): x, y, z, w = rule03 ( ) elif ( p == 4 ): x, y, z, w = rule04 ( ) elif ( p == 5 ): x, y, z, w = rule05 ( ) elif ( p == 6 ): x, y, z, w = rule06 ( ) elif ( p == 7 ): x, y, z, w = rule07 ( ) elif ( p == 8 ): x, y, z, w = rule08 ( ) elif ( p == 9 ): x, y, z, w = rule09 ( ) elif ( p == 10 ): x, y, z, w = rule10 ( ) elif ( p == 11 ): x, y, z, w = rule11 ( ) elif ( p == 12 ): x, y, z, w = rule12 ( ) elif ( p == 13 ): x, y, z, w = rule13 ( ) elif ( p == 14 ): x, y, z, w = rule14 ( ) elif ( p == 15 ): x, y, z, w = rule15 ( ) elif ( p == 16 ): x, y, z, w = rule16 ( ) elif ( p == 17 ): x, y, z, w = rule17 ( ) elif ( p == 18 ): x, y, z, w = rule18 ( ) elif ( p == 19 ): x, y, z, w = rule19 ( ) elif ( p == 20 ): x, y, z, w = rule20 ( ) return n, x, y, z, w def pyramid_unit_monomial_integral ( expon ): #*****************************************************************************80 # ## pyramid_unit_monomial_integral(): monomial integral in a unit pyramid. # # Discussion: # # This routine returns the integral of # # product ( 1 <= I <= 3 ) X(I)^EXPON(I) # # over the unit pyramid. # # The unit pyramid is defined as: # # - ( 1 - Z ) <= X <= 1 - Z # - ( 1 - Z ) <= Y <= 1 - Z # 0 <= Z <= 1. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 22 June 2015 # # Author: # # John Burkardt # # Reference: # # Arthur Stroud, # Approximate Calculation of Multiple Integrals, # Prentice Hall, 1971, # ISBN: 0130438936, # LC: QA311.S85. # # Input: # # integer EXPON(3): the exponents. # # Output: # # real VALUE: the integral of the monomial. # from scipy.special import comb if ( ( ( expon[0] % 2 ) == 0 ) and ( ( expon[1] % 2 ) == 0 ) ): i_hi = 2 + expon[0] + expon[1] value = 0.0 mop = 1.0 for i in range ( 0, i_hi + 1 ): value = value + mop * comb ( i_hi, i ) / float ( i + expon[2] + 1 ) mop = - mop value = value * 2.0 / float ( expon[0] + 1 ) * 2.0 / float ( expon[1] + 1 ) else: value = 0.0 return value def pyramid_unit_volume ( ): #*****************************************************************************80 # ## pyramid_unit_volume() returns the volume of a unit pyramid. # # Discussion: # # A pyramid with square base can be regarded as the upper half of a # 3D octahedron. # # The integration region: # # - ( 1 - Z ) <= X <= 1 - Z # - ( 1 - Z ) <= Y <= 1 - Z # 0 <= Z <= 1. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 31 March 2008 # # Author: # # John Burkardt # # Output: # # real VALUE, the volume of the pyramid. # value = 4.0 / 3.0 return value def pyramid_volume ( r, h ): #*****************************************************************************80 # ## pyramid_volume() returns the volume of a pyramid with square base in 3D. # # Discussion: # # A pyramid with square base can be regarded as the upper half of a # 3D octahedron. # # Z - R <= X <= R - Z # Z - R <= Y <= R - Z # 0 <= Z <= H. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 31 July 2018 # # Author: # # John Burkardt # # Input: # # real R, the "radius" of the pyramid, that is, half the # length of one of the sides of the square base. # # real H, the height of the pyramid. # # Output: # # real VALUE, the volume of the pyramid. # value = ( 4.0 / 3.0 ) * h * r * r return value def pyramid_volume_test ( ): #*****************************************************************************80 # ## pyramid_volume_test() tests pyramid_volume(). # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # from numpy.random import default_rng rng = default_rng ( ) print ( '' ) print ( 'pyramid_volume_test():' ) print ( ' pyramid_volume() returns the volume of a pyramid.' ) print ( '' ) print ( ' Radius Height Volume' ) print ( '' ) for i in range ( 0, 5 ): r = 1.0 + 9.0 * rng.random ( ) h = 1.0 + 9.0 * rng.random ( ) volume = pyramid_volume ( r, h ) print ( ' %8.4f %8.4f %8.4f' % ( r, h, volume ) ) return def rule_order ( p ): #*****************************************************************************80 # ## rule_order() returns the order of a pyramid quadrature rule of given precision. # # Discussion: # # The "order" of a quadrature rule is the number of points involved. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Input: # # integer p: the precision, 0 <= p <= 20. # # Output: # # integer order: the order of the rule. # if ( p < 0 ): raise Exception ( 'rule_order(): Input p < 0.' ) if ( 20 < p ): raise Exception ( 'rule_order(): Input 20 < p.' ) order_vec = [ \ 1, \ 1, 5, 6, 10, 15, \ 23, 31, 47, 62, 80, \ 103, 127, 152, 184, 234, \ 285, 319, 357, 418, 489 ] order = order_vec[p] return order def rule00 ( ): #*****************************************************************************80 # ## rule00() returns the pyramid quadrature rule of precision 0. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000 ] ) y = np.array ( [ \ 0.00000000000000000000 ] ) z = np.array ( [ \ 0.25000000000000000000 ] ) w= np.array ( [ \ 1.00000000000000000000 ] ) return x, y, z, w def rule01 ( ): #*****************************************************************************80 # ## rule01() returns the pyramid quadrature rule of precision 1. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000 ] ) y = np.array ( [ \ 0.00000000000000000000 ] ) z = np.array ( [ \ 0.25000000000000000000 ] ) w= np.array ( [ \ 1.00000000000000000000 ] ) return x, y, z, w def rule02 ( ): #*****************************************************************************80 # ## rule02() returns the pyramid quadrature rule of precision 2. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.52699748736717488828, \ -0.52699748736717488828, \ 0.52699748736717488828, \ -0.52699748736717488828 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.52699748736717488828, \ 0.52699748736717488828, \ -0.52699748736717488828, \ -0.52699748736717488828 ] ) z = np.array ( [ \ 0.56063221253561712487, \ 0.12927845700902559911, \ 0.12927845700902559911, \ 0.12927845700902559911, \ 0.12927845700902559911 ] ) w= np.array ( [ \ 0.27986667890163369199, \ 0.18003333027459159088, \ 0.18003333027459159088, \ 0.18003333027459159088, \ 0.18003333027459159088 ] ) return x, y, z, w def rule03 ( ): #*****************************************************************************80 # ## rule03() returns the pyramid quadrature rule of precision 3. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.58459636639471157515, \ -0.58459636639471157515, \ 0.58459636639471157515, \ -0.58459636639471157515 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.58459636639471157515, \ 0.58459636639471157515, \ -0.58459636639471157515, \ -0.58459636639471157515 ] ) z = np.array ( [ \ 0.03032132711145601317, \ 0.56560718797897435728, \ 0.16666666666666665741, \ 0.16666666666666665741, \ 0.16666666666666665741, \ 0.16666666666666665741 ] ) w= np.array ( [ \ 0.15345064748545933497, \ 0.26133122207480513621, \ 0.14630453260993386833, \ 0.14630453260993386833, \ 0.14630453260993386833, \ 0.14630453260993386833 ] ) return x, y, z, w def rule04 ( ): #*****************************************************************************80 # ## rule04() returns the pyramid quadrature rule of precision 4. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.65058155639823256333, \ 0.00000000000000000000, \ -0.65058155639823256333, \ 0.00000000000000000000, \ 0.65796699712169004481, \ -0.65796699712169004481, \ 0.65796699712169004481, \ -0.65796699712169004481 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.65058155639823256333, \ 0.00000000000000000000, \ -0.65058155639823256333, \ 0.65796699712169004481, \ 0.65796699712169004481, \ -0.65796699712169004481, \ -0.65796699712169004481 ] ) z = np.array ( [ \ 0.12513695310874645150, \ 0.67723278888613736015, \ 0.32238414957821365237, \ 0.32238414957821365237, \ 0.32238414957821365237, \ 0.32238414957821365237, \ 0.03924828389881535040, \ 0.03924828389881535040, \ 0.03924828389881535040, \ 0.03924828389881535040 ] ) w= np.array ( [ \ 0.20688340258955226214, \ 0.11374188317064193310, \ 0.10632458788932550031, \ 0.10632458788932550031, \ 0.10632458788932550031, \ 0.10632458788932550031, \ 0.06351909067062594394, \ 0.06351909067062594394, \ 0.06351909067062594394, \ 0.06351909067062594394 ] ) return x, y, z, w def rule05 ( ): #*****************************************************************************80 # ## rule05() returns the pyramid quadrature rule of precision 5. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.75344061307932941318, \ 0.00000000000000000000, \ -0.75344061307932941318, \ 0.00000000000000000000, \ 0.41715200242575134482, \ -0.41715200242575134482, \ 0.41715200242575134482, \ -0.41715200242575134482, \ 0.67402251647787037037, \ -0.67402251647787037037, \ 0.67402251647787037037, \ -0.67402251647787037037 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.75344061307932941318, \ 0.00000000000000000000, \ -0.75344061307932941318, \ 0.41715200242575134482, \ 0.41715200242575134482, \ -0.41715200242575134482, \ -0.41715200242575134482, \ 0.67402251647787037037, \ 0.67402251647787037037, \ -0.67402251647787037037, \ -0.67402251647787037037 ] ) z = np.array ( [ \ 0.73070946955479043616, \ 0.00619723285819058847, \ 0.26844580953431373960, \ 0.12500000000000000000, \ 0.12500000000000000000, \ 0.12500000000000000000, \ 0.12500000000000000000, \ 0.42182171100285947851, \ 0.42182171100285947851, \ 0.42182171100285947851, \ 0.42182171100285947851, \ 0.06579572180745926757, \ 0.06579572180745926757, \ 0.06579572180745926757, \ 0.06579572180745926757 ] ) w= np.array ( [ \ 0.06773442693037112772, \ 0.06470893518150579171, \ 0.17727154901514516339, \ 0.05910777216655192096, \ 0.05910777216655192096, \ 0.05910777216655192096, \ 0.05910777216655192096, \ 0.06537546219121122271, \ 0.06537546219121122271, \ 0.06537546219121122271, \ 0.06537546219121122271, \ 0.04808803786048133910, \ 0.04808803786048133910, \ 0.04808803786048133910, \ 0.04808803786048133910 ] ) return x, y, z, w def rule06 ( ): #*****************************************************************************80 # ## rule06() returns the pyramid quadrature rule of precision 6. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.42104595182782333929, \ 0.00000000000000000000, \ -0.42104595182782333929, \ 0.00000000000000000000, \ 0.83584092506524387822, \ 0.00000000000000000000, \ -0.83584092506524387822, \ 0.00000000000000000000, \ 0.51341781341302172859, \ -0.51341781341302172859, \ 0.51341781341302172859, \ -0.51341781341302172859, \ 0.87197953364266822529, \ -0.87197953364266822529, \ 0.87197953364266822529, \ -0.87197953364266822529, \ 0.47733155776773072976, \ -0.47733155776773072976, \ 0.47733155776773072976, \ -0.47733155776773072976 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.42104595182782333929, \ 0.00000000000000000000, \ -0.42104595182782333929, \ 0.00000000000000000000, \ 0.83584092506524387822, \ 0.00000000000000000000, \ -0.83584092506524387822, \ 0.51341781341302172859, \ 0.51341781341302172859, \ -0.51341781341302172859, \ -0.51341781341302172859, \ 0.87197953364266822529, \ 0.87197953364266822529, \ -0.87197953364266822529, \ -0.87197953364266822529, \ 0.47733155776773072976, \ 0.47733155776773072976, \ -0.47733155776773072976, \ -0.47733155776773072976 ] ) z = np.array ( [ \ 0.13353121706321477435, \ 0.80839181878746035892, \ 0.37840352066355309457, \ 0.55635774022808082151, \ 0.55635774022808082151, \ 0.55635774022808082151, \ 0.55635774022808082151, \ 0.09682668434012106640, \ 0.09682668434012106640, \ 0.09682668434012106640, \ 0.09682668434012106640, \ 0.25547807503740499468, \ 0.25547807503740499468, \ 0.25547807503740499468, \ 0.25547807503740499468, \ 0.03348911098405843445, \ 0.03348911098405843445, \ 0.03348911098405843445, \ 0.03348911098405843445, \ 0.02776222122928558023, \ 0.02776222122928558023, \ 0.02776222122928558023, \ 0.02776222122928558023 ] ) w= np.array ( [ \ 0.10236994192337051102, \ 0.02544552509057920395, \ 0.10744358342269332007, \ 0.03715744178992643615, \ 0.03715744178992643615, \ 0.03715744178992643615, \ 0.03715744178992643615, \ 0.03663269740345383857, \ 0.03663269740345383857, \ 0.03663269740345383857, \ 0.03663269740345383857, \ 0.07134885171305939411, \ 0.07134885171305939411, \ 0.07134885171305939411, \ 0.07134885171305939411, \ 0.00865946139444006419, \ 0.00865946139444006419, \ 0.00865946139444006419, \ 0.00865946139444006419, \ 0.03738678508995950389, \ 0.03738678508995950389, \ 0.03738678508995950389, \ 0.03738678508995950389 ] ) return x, y, z, w def rule07 ( ): #*****************************************************************************80 # ## rule07() returns the pyramid quadrature rule of precision 7. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.61721339984836764980, \ 0.00000000000000000000, \ -0.61721339984836764980, \ 0.00000000000000000000, \ 0.86409875978771466531, \ 0.00000000000000000000, \ -0.86409875978771466531, \ 0.00000000000000000000, \ 0.52488756030374572603, \ -0.52488756030374572603, \ 0.52488756030374572603, \ -0.52488756030374572603, \ 0.25419682219463812789, \ -0.25419682219463812789, \ 0.25419682219463812789, \ -0.25419682219463812789, \ 0.35405111881016937403, \ -0.35405111881016937403, \ 0.35405111881016937403, \ -0.35405111881016937403, \ 0.61427194545119712110, \ -0.61427194545119712110, \ 0.61427194545119712110, \ -0.61427194545119712110, \ 0.80282248626994900942, \ -0.80282248626994900942, \ 0.80282248626994900942, \ -0.80282248626994900942 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.61721339984836764980, \ 0.00000000000000000000, \ -0.61721339984836764980, \ 0.00000000000000000000, \ 0.86409875978771466531, \ 0.00000000000000000000, \ -0.86409875978771466531, \ 0.52488756030374572603, \ 0.52488756030374572603, \ -0.52488756030374572603, \ -0.52488756030374572603, \ 0.25419682219463812789, \ 0.25419682219463812789, \ -0.25419682219463812789, \ -0.25419682219463812789, \ 0.35405111881016937403, \ 0.35405111881016937403, \ -0.35405111881016937403, \ -0.35405111881016937403, \ 0.61427194545119712110, \ 0.61427194545119712110, \ -0.61427194545119712110, \ -0.61427194545119712110, \ 0.80282248626994900942, \ 0.80282248626994900942, \ -0.80282248626994900942, \ -0.80282248626994900942 ] ) z = np.array ( [ \ 0.39365048525928414413, \ 0.83863414272299030561, \ 0.00001985131073852604, \ 0.33333333333333331483, \ 0.33333333333333331483, \ 0.33333333333333331483, \ 0.33333333333333331483, \ 0.06666666666666666574, \ 0.06666666666666666574, \ 0.06666666666666666574, \ 0.06666666666666666574, \ 0.29045491084254104752, \ 0.29045491084254104752, \ 0.29045491084254104752, \ 0.29045491084254104752, \ 0.60547835568141594731, \ 0.60547835568141594731, \ 0.60547835568141594731, \ 0.60547835568141594731, \ 0.12931884631055998169, \ 0.12931884631055998169, \ 0.12931884631055998169, \ 0.12931884631055998169, \ 0.00010086339268113571, \ 0.00010086339268113571, \ 0.00010086339268113571, \ 0.00010086339268113571, \ 0.08012951317750569014, \ 0.08012951317750569014, \ 0.08012951317750569014, \ 0.08012951317750569014 ] ) w= np.array ( [ \ 0.10051398177493840735, \ 0.01571901760701541889, \ 0.02499658963028165634, \ 0.02871093749999999861, \ 0.02871093749999999861, \ 0.02871093749999999861, \ 0.02871093749999999861, \ 0.02669175929300291600, \ 0.02669175929300291600, \ 0.02669175929300291600, \ 0.02669175929300291600, \ 0.03572750182264943647, \ 0.03572750182264943647, \ 0.03572750182264943647, \ 0.03572750182264943647, \ 0.02951904528668866309, \ 0.02951904528668866309, \ 0.02951904528668866309, \ 0.02951904528668866309, \ 0.06594160872648228977, \ 0.06594160872648228977, \ 0.06594160872648228977, \ 0.06594160872648228977, \ 0.01333274388639105884, \ 0.01333274388639105884, \ 0.01333274388639105884, \ 0.01333274388639105884, \ 0.01476900623172677438, \ 0.01476900623172677438, \ 0.01476900623172677438, \ 0.01476900623172677438 ] ) return x, y, z, w def rule08 ( ): #*****************************************************************************80 # ## rule08() returns the pyramid quadrature rule of precision 8. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.25367856157821822016, \ 0.00000000000000000000, \ -0.25367856157821822016, \ 0.00000000000000000000, \ 0.71027375776907275551, \ 0.00000000000000000000, \ -0.71027375776907275551, \ 0.00000000000000000000, \ 0.63643362359838895337, \ 0.00000000000000000000, \ -0.63643362359838895337, \ 0.00000000000000000000, \ 0.62337928196226433109, \ 0.00000000000000000000, \ -0.62337928196226433109, \ 0.00000000000000000000, \ 0.51225968171005897833, \ -0.51225968171005897833, \ 0.51225968171005897833, \ -0.51225968171005897833, \ 0.37965901379429650708, \ -0.37965901379429650708, \ 0.37965901379429650708, \ -0.37965901379429650708, \ 0.69140086940529510429, \ -0.69140086940529510429, \ 0.69140086940529510429, \ -0.69140086940529510429, \ 0.86742190798549856368, \ -0.86742190798549856368, \ 0.86742190798549856368, \ -0.86742190798549856368, \ 0.31712322629106232119, \ -0.31712322629106232119, \ 0.31712322629106232119, \ -0.31712322629106232119, \ 0.89374797161835639603, \ 0.40528326346564669258, \ -0.89374797161835639603, \ 0.40528326346564669258, \ 0.89374797161835639603, \ -0.40528326346564669258, \ -0.89374797161835639603, \ -0.40528326346564669258 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.25367856157821822016, \ 0.00000000000000000000, \ -0.25367856157821822016, \ 0.00000000000000000000, \ 0.71027375776907275551, \ 0.00000000000000000000, \ -0.71027375776907275551, \ 0.00000000000000000000, \ 0.63643362359838895337, \ 0.00000000000000000000, \ -0.63643362359838895337, \ 0.00000000000000000000, \ 0.62337928196226433109, \ 0.00000000000000000000, \ -0.62337928196226433109, \ 0.51225968171005897833, \ 0.51225968171005897833, \ -0.51225968171005897833, \ -0.51225968171005897833, \ 0.37965901379429650708, \ 0.37965901379429650708, \ -0.37965901379429650708, \ -0.37965901379429650708, \ 0.69140086940529510429, \ 0.69140086940529510429, \ -0.69140086940529510429, \ -0.69140086940529510429, \ 0.86742190798549856368, \ 0.86742190798549856368, \ -0.86742190798549856368, \ -0.86742190798549856368, \ 0.31712322629106232119, \ 0.31712322629106232119, \ -0.31712322629106232119, \ -0.31712322629106232119, \ 0.40528326346564669258, \ 0.89374797161835639603, \ 0.40528326346564669258, \ -0.89374797161835639603, \ -0.40528326346564669258, \ 0.89374797161835639603, \ -0.40528326346564669258, \ -0.89374797161835639603 ] ) z = np.array ( [ \ 0.07395194949759914538, \ 0.48064180778578036168, \ 0.89787700126494018882, \ 0.70399494392200201442, \ 0.70399494392200201442, \ 0.70399494392200201442, \ 0.70399494392200201442, \ 0.15999762291015326432, \ 0.15999762291015326432, \ 0.15999762291015326432, \ 0.15999762291015326432, \ 0.34740846408160180880, \ 0.34740846408160180880, \ 0.34740846408160180880, \ 0.34740846408160180880, \ 0.01127682420195143774, \ 0.01127682420195143774, \ 0.01127682420195143774, \ 0.01127682420195143774, \ 0.06351022006373874262, \ 0.06351022006373874262, \ 0.06351022006373874262, \ 0.06351022006373874262, \ 0.46284226887006968409, \ 0.46284226887006968409, \ 0.46284226887006968409, \ 0.46284226887006968409, \ 0.19177130509938980496, \ 0.19177130509938980496, \ 0.19177130509938980496, \ 0.19177130509938980496, \ 0.01630913438364359896, \ 0.01630913438364359896, \ 0.01630913438364359896, \ 0.01630913438364359896, \ 0.23681987030130632887, \ 0.23681987030130632887, \ 0.23681987030130632887, \ 0.23681987030130632887, \ 0.05005997974535449785, \ 0.05005997974535449785, \ 0.05005997974535449785, \ 0.05005997974535449785, \ 0.05005997974535449785, \ 0.05005997974535449785, \ 0.05005997974535449785, \ 0.05005997974535449785 ] ) w= np.array ( [ \ 0.05595524252285600381, \ 0.06694668391641565852, \ 0.00475252306983395441, \ 0.01488586682102476834, \ 0.01488586682102476834, \ 0.01488586682102476834, \ 0.01488586682102476834, \ 0.02455698624881830563, \ 0.02455698624881830563, \ 0.02455698624881830563, \ 0.02455698624881830563, \ 0.01608138988371909592, \ 0.01608138988371909592, \ 0.01608138988371909592, \ 0.01608138988371909592, \ 0.01442915622061930955, \ 0.01442915622061930955, \ 0.01442915622061930955, \ 0.01442915622061930955, \ 0.02488836268558412140, \ 0.02488836268558412140, \ 0.02488836268558412140, \ 0.02488836268558412140, \ 0.03016542061786949003, \ 0.03016542061786949003, \ 0.03016542061786949003, \ 0.03016542061786949003, \ 0.01825943823062004326, \ 0.01825943823062004326, \ 0.01825943823062004326, \ 0.01825943823062004326, \ 0.00405270511408486935, \ 0.00405270511408486935, \ 0.00405270511408486935, \ 0.00405270511408486935, \ 0.05109969513593878160, \ 0.05109969513593878160, \ 0.05109969513593878160, \ 0.05109969513593878160, \ 0.00983368333222240688, \ 0.00983368333222240688, \ 0.00983368333222240688, \ 0.00983368333222240688, \ 0.00983368333222240688, \ 0.00983368333222240688, \ 0.00983368333222240688, \ 0.00983368333222240688 ] ) return x, y, z, w def rule09 ( ): #*****************************************************************************80 # ## rule09() returns the pyramid quadrature rule of precision 9. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.21993584526338003093, \ 0.00000000000000000000, \ -0.21993584526338003093, \ 0.00000000000000000000, \ 0.25580155737930071469, \ 0.00000000000000000000, \ -0.25580155737930071469, \ 0.00000000000000000000, \ 0.87392422284165005575, \ 0.00000000000000000000, \ -0.87392422284165005575, \ 0.00000000000000000000, \ 0.62069706482035569284, \ 0.00000000000000000000, \ -0.62069706482035569284, \ 0.00000000000000000000, \ 0.48088720239801563405, \ 0.00000000000000000000, \ -0.48088720239801563405, \ 0.00000000000000000000, \ 0.54766337559892563913, \ 0.00000000000000000000, \ -0.54766337559892563913, \ 0.00000000000000000000, \ 0.31716782120661740629, \ -0.31716782120661740629, \ 0.31716782120661740629, \ -0.31716782120661740629, \ 0.58114214633277661015, \ -0.58114214633277661015, \ 0.58114214633277661015, \ -0.58114214633277661015, \ 0.52308134436113074006, \ -0.52308134436113074006, \ 0.52308134436113074006, \ -0.52308134436113074006, \ 0.87278863855859856180, \ -0.87278863855859856180, \ 0.87278863855859856180, \ -0.87278863855859856180, \ 0.27447830261314615230, \ -0.27447830261314615230, \ 0.27447830261314615230, \ -0.27447830261314615230, \ 0.45787401929460586070, \ 0.76874559686548982196, \ -0.45787401929460586070, \ 0.76874559686548982196, \ 0.45787401929460586070, \ -0.76874559686548982196, \ -0.45787401929460586070, \ -0.76874559686548982196, \ 0.52945920866195028687, \ 0.86516329503292388470, \ -0.52945920866195028687, \ 0.86516329503292388470, \ 0.52945920866195028687, \ -0.86516329503292388470, \ -0.52945920866195028687, \ -0.86516329503292388470 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.21993584526338003093, \ 0.00000000000000000000, \ -0.21993584526338003093, \ 0.00000000000000000000, \ 0.25580155737930071469, \ 0.00000000000000000000, \ -0.25580155737930071469, \ 0.00000000000000000000, \ 0.87392422284165005575, \ 0.00000000000000000000, \ -0.87392422284165005575, \ 0.00000000000000000000, \ 0.62069706482035569284, \ 0.00000000000000000000, \ -0.62069706482035569284, \ 0.00000000000000000000, \ 0.48088720239801563405, \ 0.00000000000000000000, \ -0.48088720239801563405, \ 0.00000000000000000000, \ 0.54766337559892563913, \ 0.00000000000000000000, \ -0.54766337559892563913, \ 0.31716782120661740629, \ 0.31716782120661740629, \ -0.31716782120661740629, \ -0.31716782120661740629, \ 0.58114214633277661015, \ 0.58114214633277661015, \ -0.58114214633277661015, \ -0.58114214633277661015, \ 0.52308134436113074006, \ 0.52308134436113074006, \ -0.52308134436113074006, \ -0.52308134436113074006, \ 0.87278863855859856180, \ 0.87278863855859856180, \ -0.87278863855859856180, \ -0.87278863855859856180, \ 0.27447830261314615230, \ 0.27447830261314615230, \ -0.27447830261314615230, \ -0.27447830261314615230, \ 0.76874559686548982196, \ 0.45787401929460586070, \ 0.76874559686548982196, \ -0.45787401929460586070, \ -0.76874559686548982196, \ 0.45787401929460586070, \ -0.76874559686548982196, \ -0.45787401929460586070, \ 0.86516329503292388470, \ 0.52945920866195028687, \ 0.86516329503292388470, \ -0.52945920866195028687, \ -0.86516329503292388470, \ 0.52945920866195028687, \ -0.86516329503292388470, \ -0.52945920866195028687 ] ) z = np.array ( [ \ 0.90338060334285785746, \ 0.56496444359597119966, \ 0.74856124635194676298, \ 0.74856124635194676298, \ 0.74856124635194676298, \ 0.74856124635194676298, \ 0.13469976629555441283, \ 0.13469976629555441283, \ 0.13469976629555441283, \ 0.13469976629555441283, \ 0.05467616134251215843, \ 0.05467616134251215843, \ 0.05467616134251215843, \ 0.05467616134251215843, \ 0.18946269484050054510, \ 0.18946269484050054510, \ 0.18946269484050054510, \ 0.18946269484050054510, \ 0.02248423582708249449, \ 0.02248423582708249449, \ 0.02248423582708249449, \ 0.02248423582708249449, \ 0.41340822589276282617, \ 0.41340822589276282617, \ 0.41340822589276282617, \ 0.41340822589276282617, \ 0.55077233639120526387, \ 0.55077233639120526387, \ 0.55077233639120526387, \ 0.55077233639120526387, \ 0.31914147555912980581, \ 0.31914147555912980581, \ 0.31914147555912980581, \ 0.31914147555912980581, \ 0.08935238781868591607, \ 0.08935238781868591607, \ 0.08935238781868591607, \ 0.08935238781868591607, \ 0.06151583405729108001, \ 0.06151583405729108001, \ 0.06151583405729108001, \ 0.06151583405729108001, \ 0.32642198515966086569, \ 0.32642198515966086569, \ 0.32642198515966086569, \ 0.32642198515966086569, \ 0.17557242043675652665, \ 0.17557242043675652665, \ 0.17557242043675652665, \ 0.17557242043675652665, \ 0.17557242043675652665, \ 0.17557242043675652665, \ 0.17557242043675652665, \ 0.17557242043675652665, \ 0.01570840570495662947, \ 0.01570840570495662947, \ 0.01570840570495662947, \ 0.01570840570495662947, \ 0.01570840570495662947, \ 0.01570840570495662947, \ 0.01570840570495662947, \ 0.01570840570495662947 ] ) w= np.array ( [ \ 0.00351798245822128233, \ 0.04216520928063208912, \ 0.00852104325745563912, \ 0.00852104325745563912, \ 0.00852104325745563912, \ 0.00852104325745563912, \ 0.02087072229798967934, \ 0.02087072229798967934, \ 0.02087072229798967934, \ 0.02087072229798967934, \ 0.01073969585101612438, \ 0.01073969585101612438, \ 0.01073969585101612438, \ 0.01073969585101612438, \ 0.02521321637389669496, \ 0.02521321637389669496, \ 0.02521321637389669496, \ 0.02521321637389669496, \ 0.01961258547003659133, \ 0.01961258547003659133, \ 0.01961258547003659133, \ 0.01961258547003659133, \ 0.01643323197880764905, \ 0.01643323197880764905, \ 0.01643323197880764905, \ 0.01643323197880764905, \ 0.01830589291063876300, \ 0.01830589291063876300, \ 0.01830589291063876300, \ 0.01830589291063876300, \ 0.01130841811263377274, \ 0.01130841811263377274, \ 0.01130841811263377274, \ 0.01130841811263377274, \ 0.02507245299443831496, \ 0.02507245299443831496, \ 0.02507245299443831496, \ 0.02507245299443831496, \ 0.00441940990434765493, \ 0.00441940990434765493, \ 0.00441940990434765493, \ 0.00441940990434765493, \ 0.04065272607298718588, \ 0.04065272607298718588, \ 0.04065272607298718588, \ 0.04065272607298718588, \ 0.01219793270502279002, \ 0.01219793270502279002, \ 0.01219793270502279002, \ 0.01219793270502279002, \ 0.01219793270502279002, \ 0.01219793270502279002, \ 0.01219793270502279002, \ 0.01219793270502279002, \ 0.00651697071549649839, \ 0.00651697071549649839, \ 0.00651697071549649839, \ 0.00651697071549649839, \ 0.00651697071549649839, \ 0.00651697071549649839, \ 0.00651697071549649839, \ 0.00651697071549649839 ] ) return x, y, z, w def rule10 ( ): #*****************************************************************************80 # ## rule10() returns the pyramid quadrature rule of precision 10. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 14 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.65420170176119341043, \ 0.00000000000000000000, \ -0.65420170176119341043, \ 0.00000000000000000000, \ 0.76633927991746164654, \ 0.00000000000000000000, \ -0.76633927991746164654, \ 0.00000000000000000000, \ 0.80421056101815546757, \ 0.00000000000000000000, \ -0.80421056101815546757, \ 0.00000000000000000000, \ 0.21719757883626783501, \ 0.00000000000000000000, \ -0.21719757883626783501, \ 0.00000000000000000000, \ 0.20937347351036650345, \ 0.00000000000000000000, \ -0.20937347351036650345, \ 0.00000000000000000000, \ 0.52830709053289259813, \ 0.00000000000000000000, \ -0.52830709053289259813, \ 0.00000000000000000000, \ 0.34681490190497532566, \ -0.34681490190497532566, \ 0.34681490190497532566, \ -0.34681490190497532566, \ 0.54234774233239257946, \ -0.54234774233239257946, \ 0.54234774233239257946, \ -0.54234774233239257946, \ 0.42965769544556714488, \ -0.42965769544556714488, \ 0.42965769544556714488, \ -0.42965769544556714488, \ 0.71871414601724947779, \ -0.71871414601724947779, \ 0.71871414601724947779, \ -0.71871414601724947779, \ 0.76244008578748778682, \ -0.76244008578748778682, \ 0.76244008578748778682, \ -0.76244008578748778682, \ 0.96427350086319296718, \ -0.96427350086319296718, \ 0.96427350086319296718, \ -0.96427350086319296718, \ 0.27897388698743774693, \ -0.27897388698743774693, \ 0.27897388698743774693, \ -0.27897388698743774693, \ 0.73124529835235163588, \ 0.37115067890003261564, \ -0.73124529835235163588, \ 0.37115067890003261564, \ 0.73124529835235163588, \ -0.37115067890003261564, \ -0.73124529835235163588, \ -0.37115067890003261564, \ 0.92194807057971739361, \ 0.41966522833393532510, \ -0.92194807057971739361, \ 0.41966522833393532510, \ 0.92194807057971739361, \ -0.41966522833393532510, \ -0.92194807057971739361, \ -0.41966522833393532510, \ 0.19954261519157223681, \ 0.44340097447242488027, \ -0.19954261519157223681, \ 0.44340097447242488027, \ 0.19954261519157223681, \ -0.44340097447242488027, \ -0.19954261519157223681, \ -0.44340097447242488027 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.65420170176119341043, \ 0.00000000000000000000, \ -0.65420170176119341043, \ 0.00000000000000000000, \ 0.76633927991746164654, \ 0.00000000000000000000, \ -0.76633927991746164654, \ 0.00000000000000000000, \ 0.80421056101815546757, \ 0.00000000000000000000, \ -0.80421056101815546757, \ 0.00000000000000000000, \ 0.21719757883626783501, \ 0.00000000000000000000, \ -0.21719757883626783501, \ 0.00000000000000000000, \ 0.20937347351036650345, \ 0.00000000000000000000, \ -0.20937347351036650345, \ 0.00000000000000000000, \ 0.52830709053289259813, \ 0.00000000000000000000, \ -0.52830709053289259813, \ 0.34681490190497532566, \ 0.34681490190497532566, \ -0.34681490190497532566, \ -0.34681490190497532566, \ 0.54234774233239257946, \ 0.54234774233239257946, \ -0.54234774233239257946, \ -0.54234774233239257946, \ 0.42965769544556714488, \ 0.42965769544556714488, \ -0.42965769544556714488, \ -0.42965769544556714488, \ 0.71871414601724947779, \ 0.71871414601724947779, \ -0.71871414601724947779, \ -0.71871414601724947779, \ 0.76244008578748778682, \ 0.76244008578748778682, \ -0.76244008578748778682, \ -0.76244008578748778682, \ 0.96427350086319296718, \ 0.96427350086319296718, \ -0.96427350086319296718, \ -0.96427350086319296718, \ 0.27897388698743774693, \ 0.27897388698743774693, \ -0.27897388698743774693, \ -0.27897388698743774693, \ 0.37115067890003261564, \ 0.73124529835235163588, \ 0.37115067890003261564, \ -0.73124529835235163588, \ -0.37115067890003261564, \ 0.73124529835235163588, \ -0.37115067890003261564, \ -0.73124529835235163588, \ 0.41966522833393532510, \ 0.92194807057971739361, \ 0.41966522833393532510, \ -0.92194807057971739361, \ -0.41966522833393532510, \ 0.92194807057971739361, \ -0.41966522833393532510, \ -0.92194807057971739361, \ 0.44340097447242488027, \ 0.19954261519157223681, \ 0.44340097447242488027, \ -0.19954261519157223681, \ -0.44340097447242488027, \ 0.19954261519157223681, \ -0.44340097447242488027, \ -0.19954261519157223681 ] ) z = np.array ( [ \ 0.91766654896784238815, \ 0.70900937404687269794, \ 0.22713967401042231553, \ 0.06874011069480644165, \ 0.12392544997399050632, \ 0.12392544997399050632, \ 0.12392544997399050632, \ 0.12392544997399050632, \ 0.02096299791450871586, \ 0.02096299791450871586, \ 0.02096299791450871586, \ 0.02096299791450871586, \ 0.16577313546766450636, \ 0.16577313546766450636, \ 0.16577313546766450636, \ 0.16577313546766450636, \ 0.49340520933953563310, \ 0.49340520933953563310, \ 0.49340520933953563310, \ 0.49340520933953563310, \ 0.78969767134839341516, \ 0.78969767134839341516, \ 0.78969767134839341516, \ 0.78969767134839341516, \ 0.47169288904858786005, \ 0.47169288904858786005, \ 0.47169288904858786005, \ 0.47169288904858786005, \ 0.02011394567580290782, \ 0.02011394567580290782, \ 0.02011394567580290782, \ 0.02011394567580290782, \ 0.36822101998927786459, \ 0.36822101998927786459, \ 0.36822101998927786459, \ 0.36822101998927786459, \ 0.12661594867701117528, \ 0.12661594867701117528, \ 0.12661594867701117528, \ 0.12661594867701117528, \ 0.02433819982878694319, \ 0.02433819982878694319, \ 0.02433819982878694319, \ 0.02433819982878694319, \ 0.12701442502569038062, \ 0.12701442502569038062, \ 0.12701442502569038062, \ 0.12701442502569038062, \ 0.01067692573406054529, \ 0.01067692573406054529, \ 0.01067692573406054529, \ 0.01067692573406054529, \ 0.59704297313030385563, \ 0.59704297313030385563, \ 0.59704297313030385563, \ 0.59704297313030385563, \ 0.21756166315495037433, \ 0.21756166315495037433, \ 0.21756166315495037433, \ 0.21756166315495037433, \ 0.21756166315495037433, \ 0.21756166315495037433, \ 0.21756166315495037433, \ 0.21756166315495037433, \ 0.04137857207280886546, \ 0.04137857207280886546, \ 0.04137857207280886546, \ 0.04137857207280886546, \ 0.04137857207280886546, \ 0.04137857207280886546, \ 0.04137857207280886546, \ 0.04137857207280886546, \ 0.32615365723990619173, \ 0.32615365723990619173, \ 0.32615365723990619173, \ 0.32615365723990619173, \ 0.32615365723990619173, \ 0.32615365723990619173, \ 0.32615365723990619173, \ 0.32615365723990619173 ] ) w= np.array ( [ \ 0.00222688724675269151, \ 0.01676862119517166794, \ 0.05218524659101939772, \ 0.02912684113372536118, \ 0.02061250827144200243, \ 0.02061250827144200243, \ 0.02061250827144200243, \ 0.02061250827144200243, \ 0.01001318317045431922, \ 0.01001318317045431922, \ 0.01001318317045431922, \ 0.01001318317045431922, \ 0.00380589471978953851, \ 0.00380589471978953851, \ 0.00380589471978953851, \ 0.00380589471978953851, \ 0.01603356460939567643, \ 0.01603356460939567643, \ 0.01603356460939567643, \ 0.01603356460939567643, \ 0.00421057398582402181, \ 0.00421057398582402181, \ 0.00421057398582402181, \ 0.00421057398582402181, \ 0.00812973230941097316, \ 0.00812973230941097316, \ 0.00812973230941097316, \ 0.00812973230941097316, \ 0.01345646795638386767, \ 0.01345646795638386767, \ 0.01345646795638386767, \ 0.01345646795638386767, \ 0.01016376299548378027, \ 0.01016376299548378027, \ 0.01016376299548378027, \ 0.01016376299548378027, \ 0.02981645762492043245, \ 0.02981645762492043245, \ 0.02981645762492043245, \ 0.02981645762492043245, \ 0.00865712783423741410, \ 0.00865712783423741410, \ 0.00865712783423741410, \ 0.00865712783423741410, \ 0.00953199916493123987, \ 0.00953199916493123987, \ 0.00953199916493123987, \ 0.00953199916493123987, \ 0.00071395826747580517, \ 0.00071395826747580517, \ 0.00071395826747580517, \ 0.00071395826747580517, \ 0.01519293397619959039, \ 0.01519293397619959039, \ 0.01519293397619959039, \ 0.01519293397619959039, \ 0.01008533639437561233, \ 0.01008533639437561233, \ 0.01008533639437561233, \ 0.01008533639437561233, \ 0.01008533639437561233, \ 0.01008533639437561233, \ 0.01008533639437561233, \ 0.01008533639437561233, \ 0.00585933822996072967, \ 0.00585933822996072967, \ 0.00585933822996072967, \ 0.00585933822996072967, \ 0.00585933822996072967, \ 0.00585933822996072967, \ 0.00585933822996072967, \ 0.00585933822996072967, \ 0.02134779341185568530, \ 0.02134779341185568530, \ 0.02134779341185568530, \ 0.02134779341185568530, \ 0.02134779341185568530, \ 0.02134779341185568530, \ 0.02134779341185568530, \ 0.02134779341185568530 ] ) return x, y, z, w def rule11 ( ): #*****************************************************************************80 # ## rule11() returns the pyramid quadrature rule of precision 11. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.30959144111215058937, \ 0.00000000000000000000, \ -0.30959144111215058937, \ 0.00000000000000000000, \ 0.76993922081029786408, \ 0.00000000000000000000, \ -0.76993922081029786408, \ 0.00000000000000000000, \ 0.70027038117446127607, \ 0.00000000000000000000, \ -0.70027038117446127607, \ 0.00000000000000000000, \ 0.46095035429072822586, \ 0.00000000000000000000, \ -0.46095035429072822586, \ 0.00000000000000000000, \ 0.29928938216959510843, \ 0.00000000000000000000, \ -0.29928938216959510843, \ 0.00000000000000000000, \ 0.59114943757155702375, \ 0.00000000000000000000, \ -0.59114943757155702375, \ 0.00000000000000000000, \ 0.01861308147704909821, \ 0.00000000000000000000, \ -0.01861308147704909821, \ 0.00000000000000000000, \ 0.16034290975464657314, \ 0.00000000000000000000, \ -0.16034290975464657314, \ 0.00000000000000000000, \ 0.14450753554447465232, \ -0.14450753554447465232, \ 0.14450753554447465232, \ -0.14450753554447465232, \ 0.59369450979675508773, \ -0.59369450979675508773, \ 0.59369450979675508773, \ -0.59369450979675508773, \ 0.27490141802950085470, \ -0.27490141802950085470, \ 0.27490141802950085470, \ -0.27490141802950085470, \ 0.29680077247241393179, \ -0.29680077247241393179, \ 0.29680077247241393179, \ -0.29680077247241393179, \ 0.59849263706569033605, \ -0.59849263706569033605, \ 0.59849263706569033605, \ -0.59849263706569033605, \ 0.61031415307328662490, \ -0.61031415307328662490, \ 0.61031415307328662490, \ -0.61031415307328662490, \ 0.37345023081856359992, \ -0.37345023081856359992, \ 0.37345023081856359992, \ -0.37345023081856359992, \ 0.26245991463277401623, \ -0.26245991463277401623, \ 0.26245991463277401623, \ -0.26245991463277401623, \ 0.36860635719790568743, \ -0.36860635719790568743, \ 0.36860635719790568743, \ -0.36860635719790568743, \ 0.87026293442361135622, \ -0.87026293442361135622, \ 0.87026293442361135622, \ -0.87026293442361135622, \ 0.81025745002423155139, \ -0.81025745002423155139, \ 0.81025745002423155139, \ -0.81025745002423155139, \ 0.78967657467472973654, \ 0.35527213835047594115, \ -0.78967657467472973654, \ 0.35527213835047594115, \ 0.78967657467472973654, \ -0.35527213835047594115, \ -0.78967657467472973654, \ -0.35527213835047594115, \ 0.92805034944130604391, \ 0.41484210234755791724, \ -0.92805034944130604391, \ 0.41484210234755791724, \ 0.92805034944130604391, \ -0.41484210234755791724, \ -0.92805034944130604391, \ -0.41484210234755791724, \ 0.23313789083599262275, \ 0.55628779191329114084, \ -0.23313789083599262275, \ 0.55628779191329114084, \ 0.23313789083599262275, \ -0.55628779191329114084, \ -0.23313789083599262275, \ -0.55628779191329114084 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.30959144111215058937, \ 0.00000000000000000000, \ -0.30959144111215058937, \ 0.00000000000000000000, \ 0.76993922081029786408, \ 0.00000000000000000000, \ -0.76993922081029786408, \ 0.00000000000000000000, \ 0.70027038117446127607, \ 0.00000000000000000000, \ -0.70027038117446127607, \ 0.00000000000000000000, \ 0.46095035429072822586, \ 0.00000000000000000000, \ -0.46095035429072822586, \ 0.00000000000000000000, \ 0.29928938216959510843, \ 0.00000000000000000000, \ -0.29928938216959510843, \ 0.00000000000000000000, \ 0.59114943757155702375, \ 0.00000000000000000000, \ -0.59114943757155702375, \ 0.00000000000000000000, \ 0.01861308147704909821, \ 0.00000000000000000000, \ -0.01861308147704909821, \ 0.00000000000000000000, \ 0.16034290975464657314, \ 0.00000000000000000000, \ -0.16034290975464657314, \ 0.14450753554447465232, \ 0.14450753554447465232, \ -0.14450753554447465232, \ -0.14450753554447465232, \ 0.59369450979675508773, \ 0.59369450979675508773, \ -0.59369450979675508773, \ -0.59369450979675508773, \ 0.27490141802950085470, \ 0.27490141802950085470, \ -0.27490141802950085470, \ -0.27490141802950085470, \ 0.29680077247241393179, \ 0.29680077247241393179, \ -0.29680077247241393179, \ -0.29680077247241393179, \ 0.59849263706569033605, \ 0.59849263706569033605, \ -0.59849263706569033605, \ -0.59849263706569033605, \ 0.61031415307328662490, \ 0.61031415307328662490, \ -0.61031415307328662490, \ -0.61031415307328662490, \ 0.37345023081856359992, \ 0.37345023081856359992, \ -0.37345023081856359992, \ -0.37345023081856359992, \ 0.26245991463277401623, \ 0.26245991463277401623, \ -0.26245991463277401623, \ -0.26245991463277401623, \ 0.36860635719790568743, \ 0.36860635719790568743, \ -0.36860635719790568743, \ -0.36860635719790568743, \ 0.87026293442361135622, \ 0.87026293442361135622, \ -0.87026293442361135622, \ -0.87026293442361135622, \ 0.81025745002423155139, \ 0.81025745002423155139, \ -0.81025745002423155139, \ -0.81025745002423155139, \ 0.35527213835047594115, \ 0.78967657467472973654, \ 0.35527213835047594115, \ -0.78967657467472973654, \ -0.35527213835047594115, \ 0.78967657467472973654, \ -0.35527213835047594115, \ -0.78967657467472973654, \ 0.41484210234755791724, \ 0.92805034944130604391, \ 0.41484210234755791724, \ -0.92805034944130604391, \ -0.41484210234755791724, \ 0.92805034944130604391, \ -0.41484210234755791724, \ -0.92805034944130604391, \ 0.55628779191329114084, \ 0.23313789083599262275, \ 0.55628779191329114084, \ -0.23313789083599262275, \ -0.55628779191329114084, \ 0.23313789083599262275, \ -0.55628779191329114084, \ -0.23313789083599262275 ] ) z = np.array ( [ \ 0.69295639647508833203, \ 0.91101523446275922691, \ 0.25032929072548470995, \ 0.05040798390564713710, \ 0.05040798390564713710, \ 0.05040798390564713710, \ 0.05040798390564713710, \ 0.01178348626907169128, \ 0.01178348626907169128, \ 0.01178348626907169128, \ 0.01178348626907169128, \ 0.10103940902556154957, \ 0.10103940902556154957, \ 0.10103940902556154957, \ 0.10103940902556154957, \ 0.34272757605804599068, \ 0.34272757605804599068, \ 0.34272757605804599068, \ 0.34272757605804599068, \ 0.62869898216776509692, \ 0.62869898216776509692, \ 0.62869898216776509692, \ 0.62869898216776509692, \ 0.25822848523085090156, \ 0.25822848523085090156, \ 0.25822848523085090156, \ 0.25822848523085090156, \ 0.43583449548328001555, \ 0.43583449548328001555, \ 0.43583449548328001555, \ 0.43583449548328001555, \ 0.21928319414297889334, \ 0.21928319414297889334, \ 0.21928319414297889334, \ 0.21928319414297889334, \ 0.78797433053468768360, \ 0.78797433053468768360, \ 0.78797433053468768360, \ 0.78797433053468768360, \ 0.30892958869107134401, \ 0.30892958869107134401, \ 0.30892958869107134401, \ 0.30892958869107134401, \ 0.01781185684646453826, \ 0.01781185684646453826, \ 0.01781185684646453826, \ 0.01781185684646453826, \ 0.11127033608982600521, \ 0.11127033608982600521, \ 0.11127033608982600521, \ 0.11127033608982600521, \ 0.02444716310077480956, \ 0.02444716310077480956, \ 0.02444716310077480956, \ 0.02444716310077480956, \ 0.12041875519309763742, \ 0.12041875519309763742, \ 0.12041875519309763742, \ 0.12041875519309763742, \ 0.57752532555241498091, \ 0.57752532555241498091, \ 0.57752532555241498091, \ 0.57752532555241498091, \ 0.49169801908816329616, \ 0.49169801908816329616, \ 0.49169801908816329616, \ 0.49169801908816329616, \ 0.26311325712772259955, \ 0.26311325712772259955, \ 0.26311325712772259955, \ 0.26311325712772259955, \ 0.01908681361607608359, \ 0.01908681361607608359, \ 0.01908681361607608359, \ 0.01908681361607608359, \ 0.11692619926762114202, \ 0.11692619926762114202, \ 0.11692619926762114202, \ 0.11692619926762114202, \ 0.17968095390177224457, \ 0.17968095390177224457, \ 0.17968095390177224457, \ 0.17968095390177224457, \ 0.17968095390177224457, \ 0.17968095390177224457, \ 0.17968095390177224457, \ 0.17968095390177224457, \ 0.03535559961728908934, \ 0.03535559961728908934, \ 0.03535559961728908934, \ 0.03535559961728908934, \ 0.03535559961728908934, \ 0.03535559961728908934, \ 0.03535559961728908934, \ 0.03535559961728908934, \ 0.41464402024224555898, \ 0.41464402024224555898, \ 0.41464402024224555898, \ 0.41464402024224555898, \ 0.41464402024224555898, \ 0.41464402024224555898, \ 0.41464402024224555898, \ 0.41464402024224555898 ] ) w= np.array ( [ \ 0.01286363653695535118, \ 0.00259572122542773513, \ 0.00817638570047552610, \ 0.00511941439804289126, \ 0.00511941439804289126, \ 0.00511941439804289126, \ 0.00511941439804289126, \ 0.00684699666646234988, \ 0.00684699666646234988, \ 0.00684699666646234988, \ 0.00684699666646234988, \ 0.02021405278036775971, \ 0.02021405278036775971, \ 0.02021405278036775971, \ 0.02021405278036775971, \ 0.01240017518258633086, \ 0.01240017518258633086, \ 0.01240017518258633086, \ 0.01240017518258633086, \ 0.01050060859922616330, \ 0.01050060859922616330, \ 0.01050060859922616330, \ 0.01050060859922616330, \ 0.01207523991498536502, \ 0.01207523991498536502, \ 0.01207523991498536502, \ 0.01207523991498536502, \ 0.00794549439937168242, \ 0.00794549439937168242, \ 0.00794549439937168242, \ 0.00794549439937168242, \ 0.00897930801963979161, \ 0.00897930801963979161, \ 0.00897930801963979161, \ 0.00897930801963979161, \ 0.00432861007717266853, \ 0.00432861007717266853, \ 0.00432861007717266853, \ 0.00432861007717266853, \ 0.00959150593850333251, \ 0.00959150593850333251, \ 0.00959150593850333251, \ 0.00959150593850333251, \ 0.00845889607542490291, \ 0.00845889607542490291, \ 0.00845889607542490291, \ 0.00845889607542490291, \ 0.02093917618186586990, \ 0.02093917618186586990, \ 0.02093917618186586990, \ 0.02093917618186586990, \ 0.01007335618421271312, \ 0.01007335618421271312, \ 0.01007335618421271312, \ 0.01007335618421271312, \ 0.01474935950898293054, \ 0.01474935950898293054, \ 0.01474935950898293054, \ 0.01474935950898293054, \ 0.00405432020025909591, \ 0.00405432020025909591, \ 0.00405432020025909591, \ 0.00405432020025909591, \ 0.01768012056788626288, \ 0.01768012056788626288, \ 0.01768012056788626288, \ 0.01768012056788626288, \ 0.02349367280688881635, \ 0.02349367280688881635, \ 0.02349367280688881635, \ 0.02349367280688881635, \ 0.00300355345952720053, \ 0.00300355345952720053, \ 0.00300355345952720053, \ 0.00300355345952720053, \ 0.00433057971890565482, \ 0.00433057971890565482, \ 0.00433057971890565482, \ 0.00433057971890565482, \ 0.00788297764391489818, \ 0.00788297764391489818, \ 0.00788297764391489818, \ 0.00788297764391489818, \ 0.00788297764391489818, \ 0.00788297764391489818, \ 0.00788297764391489818, \ 0.00788297764391489818, \ 0.00509491185532656536, \ 0.00509491185532656536, \ 0.00509491185532656536, \ 0.00509491185532656536, \ 0.00509491185532656536, \ 0.00509491185532656536, \ 0.00509491185532656536, \ 0.00509491185532656536, \ 0.00667542222774531943, \ 0.00667542222774531943, \ 0.00667542222774531943, \ 0.00667542222774531943, \ 0.00667542222774531943, \ 0.00667542222774531943, \ 0.00667542222774531943, \ 0.00667542222774531943 ] ) return x, y, z, w def rule12 ( ): #*****************************************************************************80 # ## rule12() returns the pyramid quadrature rule of precision 12. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.61752408228797095457, \ 0.00000000000000000000, \ -0.61752408228797095457, \ 0.00000000000000000000, \ 0.95383417813475923630, \ 0.00000000000000000000, \ -0.95383417813475923630, \ 0.00000000000000000000, \ 0.59503005801385822071, \ 0.00000000000000000000, \ -0.59503005801385822071, \ 0.00000000000000000000, \ 0.43539359820232903520, \ 0.00000000000000000000, \ -0.43539359820232903520, \ 0.00000000000000000000, \ 0.13291355561208040292, \ 0.00000000000000000000, \ -0.13291355561208040292, \ 0.00000000000000000000, \ 0.79714363482446959353, \ 0.00000000000000000000, \ -0.79714363482446959353, \ 0.00000000000000000000, \ 0.31078295049399401462, \ 0.00000000000000000000, \ -0.31078295049399401462, \ 0.00000000000000000000, \ 0.46896896703369211901, \ 0.00000000000000000000, \ -0.46896896703369211901, \ 0.00000000000000000000, \ 0.06329314929065793516, \ 0.00000000000000000000, \ -0.06329314929065793516, \ 0.00000000000000000000, \ 0.11694124473665239161, \ -0.11694124473665239161, \ 0.11694124473665239161, \ -0.11694124473665239161, \ 0.47710850655214198657, \ -0.47710850655214198657, \ 0.47710850655214198657, \ -0.47710850655214198657, \ 0.34796735400888462175, \ -0.34796735400888462175, \ 0.34796735400888462175, \ -0.34796735400888462175, \ 0.21748093989891267852, \ -0.21748093989891267852, \ 0.21748093989891267852, \ -0.21748093989891267852, \ 0.67426207541025851011, \ -0.67426207541025851011, \ 0.67426207541025851011, \ -0.67426207541025851011, \ 0.65415312577816908668, \ -0.65415312577816908668, \ 0.65415312577816908668, \ -0.65415312577816908668, \ 0.26043868995957136780, \ -0.26043868995957136780, \ 0.26043868995957136780, \ -0.26043868995957136780, \ 0.27442107868377230151, \ -0.27442107868377230151, \ 0.27442107868377230151, \ -0.27442107868377230151, \ 0.51259022737109982693, \ -0.51259022737109982693, \ 0.51259022737109982693, \ -0.51259022737109982693, \ 0.86878873539049084052, \ -0.86878873539049084052, \ 0.86878873539049084052, \ -0.86878873539049084052, \ 0.71181681800308360675, \ -0.71181681800308360675, \ 0.71181681800308360675, \ -0.71181681800308360675, \ 0.36754569532388259301, \ -0.36754569532388259301, \ 0.36754569532388259301, \ -0.36754569532388259301, \ 0.84896937482456835689, \ 0.51203646317203110883, \ -0.84896937482456835689, \ 0.51203646317203110883, \ 0.84896937482456835689, \ -0.51203646317203110883, \ -0.84896937482456835689, \ -0.51203646317203110883, \ 0.97385403135997028468, \ 0.74670340940557777820, \ -0.97385403135997028468, \ 0.74670340940557777820, \ 0.97385403135997028468, \ -0.74670340940557777820, \ -0.97385403135997028468, \ -0.74670340940557777820, \ 0.32302405518012644592, \ 0.62555613253804132068, \ -0.32302405518012644592, \ 0.62555613253804132068, \ 0.32302405518012644592, \ -0.62555613253804132068, \ -0.32302405518012644592, \ -0.62555613253804132068, \ 0.19450076345283720536, \ 0.69805959364273262313, \ -0.19450076345283720536, \ 0.69805959364273262313, \ 0.19450076345283720536, \ -0.69805959364273262313, \ -0.19450076345283720536, \ -0.69805959364273262313, \ 0.32894885387189143344, \ 0.85383152896625225114, \ -0.32894885387189143344, \ 0.85383152896625225114, \ 0.32894885387189143344, \ -0.85383152896625225114, \ -0.32894885387189143344, \ -0.85383152896625225114 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.61752408228797095457, \ 0.00000000000000000000, \ -0.61752408228797095457, \ 0.00000000000000000000, \ 0.95383417813475923630, \ 0.00000000000000000000, \ -0.95383417813475923630, \ 0.00000000000000000000, \ 0.59503005801385822071, \ 0.00000000000000000000, \ -0.59503005801385822071, \ 0.00000000000000000000, \ 0.43539359820232903520, \ 0.00000000000000000000, \ -0.43539359820232903520, \ 0.00000000000000000000, \ 0.13291355561208040292, \ 0.00000000000000000000, \ -0.13291355561208040292, \ 0.00000000000000000000, \ 0.79714363482446959353, \ 0.00000000000000000000, \ -0.79714363482446959353, \ 0.00000000000000000000, \ 0.31078295049399401462, \ 0.00000000000000000000, \ -0.31078295049399401462, \ 0.00000000000000000000, \ 0.46896896703369211901, \ 0.00000000000000000000, \ -0.46896896703369211901, \ 0.00000000000000000000, \ 0.06329314929065793516, \ 0.00000000000000000000, \ -0.06329314929065793516, \ 0.11694124473665239161, \ 0.11694124473665239161, \ -0.11694124473665239161, \ -0.11694124473665239161, \ 0.47710850655214198657, \ 0.47710850655214198657, \ -0.47710850655214198657, \ -0.47710850655214198657, \ 0.34796735400888462175, \ 0.34796735400888462175, \ -0.34796735400888462175, \ -0.34796735400888462175, \ 0.21748093989891267852, \ 0.21748093989891267852, \ -0.21748093989891267852, \ -0.21748093989891267852, \ 0.67426207541025851011, \ 0.67426207541025851011, \ -0.67426207541025851011, \ -0.67426207541025851011, \ 0.65415312577816908668, \ 0.65415312577816908668, \ -0.65415312577816908668, \ -0.65415312577816908668, \ 0.26043868995957136780, \ 0.26043868995957136780, \ -0.26043868995957136780, \ -0.26043868995957136780, \ 0.27442107868377230151, \ 0.27442107868377230151, \ -0.27442107868377230151, \ -0.27442107868377230151, \ 0.51259022737109982693, \ 0.51259022737109982693, \ -0.51259022737109982693, \ -0.51259022737109982693, \ 0.86878873539049084052, \ 0.86878873539049084052, \ -0.86878873539049084052, \ -0.86878873539049084052, \ 0.71181681800308360675, \ 0.71181681800308360675, \ -0.71181681800308360675, \ -0.71181681800308360675, \ 0.36754569532388259301, \ 0.36754569532388259301, \ -0.36754569532388259301, \ -0.36754569532388259301, \ 0.51203646317203110883, \ 0.84896937482456835689, \ 0.51203646317203110883, \ -0.84896937482456835689, \ -0.51203646317203110883, \ 0.84896937482456835689, \ -0.51203646317203110883, \ -0.84896937482456835689, \ 0.74670340940557777820, \ 0.97385403135997028468, \ 0.74670340940557777820, \ -0.97385403135997028468, \ -0.74670340940557777820, \ 0.97385403135997028468, \ -0.74670340940557777820, \ -0.97385403135997028468, \ 0.62555613253804132068, \ 0.32302405518012644592, \ 0.62555613253804132068, \ -0.32302405518012644592, \ -0.62555613253804132068, \ 0.32302405518012644592, \ -0.62555613253804132068, \ -0.32302405518012644592, \ 0.69805959364273262313, \ 0.19450076345283720536, \ 0.69805959364273262313, \ -0.19450076345283720536, \ -0.69805959364273262313, \ 0.19450076345283720536, \ -0.69805959364273262313, \ -0.19450076345283720536, \ 0.85383152896625225114, \ 0.32894885387189143344, \ 0.85383152896625225114, \ -0.32894885387189143344, \ -0.85383152896625225114, \ 0.32894885387189143344, \ -0.85383152896625225114, \ -0.32894885387189143344 ] ) z = np.array ( [ \ 0.45700700424071905026, \ 0.96248480104808953328, \ 0.02656531684537740551, \ 0.00537472082577391923, \ 0.00537472082577391923, \ 0.00537472082577391923, \ 0.00537472082577391923, \ 0.03942123626649530338, \ 0.03942123626649530338, \ 0.03942123626649530338, \ 0.03942123626649530338, \ 0.07619184421748394220, \ 0.07619184421748394220, \ 0.07619184421748394220, \ 0.07619184421748394220, \ 0.52461875533620183631, \ 0.52461875533620183631, \ 0.52461875533620183631, \ 0.52461875533620183631, \ 0.83871994031142604875, \ 0.83871994031142604875, \ 0.83871994031142604875, \ 0.83871994031142604875, \ 0.20075189777897944898, \ 0.20075189777897944898, \ 0.20075189777897944898, \ 0.20075189777897944898, \ 0.68265469105314702247, \ 0.68265469105314702247, \ 0.68265469105314702247, \ 0.68265469105314702247, \ 0.31713382467521444852, \ 0.31713382467521444852, \ 0.31713382467521444852, \ 0.31713382467521444852, \ 0.12709629034671870995, \ 0.12709629034671870995, \ 0.12709629034671870995, \ 0.12709629034671870995, \ 0.67124174294922867023, \ 0.67124174294922867023, \ 0.67124174294922867023, \ 0.67124174294922867023, \ 0.45862802718642248223, \ 0.45862802718642248223, \ 0.45862802718642248223, \ 0.45862802718642248223, \ 0.11938890613701966248, \ 0.11938890613701966248, \ 0.11938890613701966248, \ 0.11938890613701966248, \ 0.25741784866521960629, \ 0.25741784866521960629, \ 0.25741784866521960629, \ 0.25741784866521960629, \ 0.02260502558938975656, \ 0.02260502558938975656, \ 0.02260502558938975656, \ 0.02260502558938975656, \ 0.08746307755558260788, \ 0.08746307755558260788, \ 0.08746307755558260788, \ 0.08746307755558260788, \ 0.67140164127972612462, \ 0.67140164127972612462, \ 0.67140164127972612462, \ 0.67140164127972612462, \ 0.47604255048878973966, \ 0.47604255048878973966, \ 0.47604255048878973966, \ 0.47604255048878973966, \ 0.22777955815540271156, \ 0.22777955815540271156, \ 0.22777955815540271156, \ 0.22777955815540271156, \ 0.05850272176027389998, \ 0.05850272176027389998, \ 0.05850272176027389998, \ 0.05850272176027389998, \ 0.22053995731942055425, \ 0.22053995731942055425, \ 0.22053995731942055425, \ 0.22053995731942055425, \ 0.02548724290196442005, \ 0.02548724290196442005, \ 0.02548724290196442005, \ 0.02548724290196442005, \ 0.11145836537804799937, \ 0.11145836537804799937, \ 0.11145836537804799937, \ 0.11145836537804799937, \ 0.11145836537804799937, \ 0.11145836537804799937, \ 0.11145836537804799937, \ 0.11145836537804799937, \ 0.00339220824679912656, \ 0.00339220824679912656, \ 0.00339220824679912656, \ 0.00339220824679912656, \ 0.00339220824679912656, \ 0.00339220824679912656, \ 0.00339220824679912656, \ 0.00339220824679912656, \ 0.32725151644051669875, \ 0.32725151644051669875, \ 0.32725151644051669875, \ 0.32725151644051669875, \ 0.32725151644051669875, \ 0.32725151644051669875, \ 0.32725151644051669875, \ 0.32725151644051669875, \ 0.14805166861898322317, \ 0.14805166861898322317, \ 0.14805166861898322317, \ 0.14805166861898322317, \ 0.14805166861898322317, \ 0.14805166861898322317, \ 0.14805166861898322317, \ 0.14805166861898322317, \ 0.02487563023274973195, \ 0.02487563023274973195, \ 0.02487563023274973195, \ 0.02487563023274973195, \ 0.02487563023274973195, \ 0.02487563023274973195, \ 0.02487563023274973195, \ 0.02487563023274973195 ] ) w= np.array ( [ \ 0.02715854620871203245, \ 0.00043531424244899530, \ 0.01391222140872406220, \ 0.00387288146649252939, \ 0.00387288146649252939, \ 0.00387288146649252939, \ 0.00387288146649252939, \ 0.00217967971593618394, \ 0.00217967971593618394, \ 0.00217967971593618394, \ 0.00217967971593618394, \ 0.01267133485574918096, \ 0.01267133485574918096, \ 0.01267133485574918096, \ 0.01267133485574918096, \ 0.00873464163035380693, \ 0.00873464163035380693, \ 0.00873464163035380693, \ 0.00873464163035380693, \ 0.00289146731615850605, \ 0.00289146731615850605, \ 0.00289146731615850605, \ 0.00289146731615850605, \ 0.00336686848511522736, \ 0.00336686848511522736, \ 0.00336686848511522736, \ 0.00336686848511522736, \ 0.00147603803134411875, \ 0.00147603803134411875, \ 0.00147603803134411875, \ 0.00147603803134411875, \ 0.01998444773599242219, \ 0.01998444773599242219, \ 0.01998444773599242219, \ 0.01998444773599242219, \ 0.00618927170644437228, \ 0.00618927170644437228, \ 0.00618927170644437228, \ 0.00618927170644437228, \ 0.00820078705478863301, \ 0.00820078705478863301, \ 0.00820078705478863301, \ 0.00820078705478863301, \ 0.00509651546458162342, \ 0.00509651546458162342, \ 0.00509651546458162342, \ 0.00509651546458162342, \ 0.01739298850473944280, \ 0.01739298850473944280, \ 0.01739298850473944280, \ 0.01739298850473944280, \ 0.01948797782027694020, \ 0.01948797782027694020, \ 0.01948797782027694020, \ 0.01948797782027694020, \ 0.00538896243467025700, \ 0.00538896243467025700, \ 0.00538896243467025700, \ 0.00538896243467025700, \ 0.00676911731451347500, \ 0.00676911731451347500, \ 0.00676911731451347500, \ 0.00676911731451347500, \ 0.00467587609366508332, \ 0.00467587609366508332, \ 0.00467587609366508332, \ 0.00467587609366508332, \ 0.01838172037009152757, \ 0.01838172037009152757, \ 0.01838172037009152757, \ 0.01838172037009152757, \ 0.01407964506457294943, \ 0.01407964506457294943, \ 0.01407964506457294943, \ 0.01407964506457294943, \ 0.00283370063460703292, \ 0.00283370063460703292, \ 0.00283370063460703292, \ 0.00283370063460703292, \ 0.00479137222817773486, \ 0.00479137222817773486, \ 0.00479137222817773486, \ 0.00479137222817773486, \ 0.00990680633819146332, \ 0.00990680633819146332, \ 0.00990680633819146332, \ 0.00990680633819146332, \ 0.00535574363023301383, \ 0.00535574363023301383, \ 0.00535574363023301383, \ 0.00535574363023301383, \ 0.00535574363023301383, \ 0.00535574363023301383, \ 0.00535574363023301383, \ 0.00535574363023301383, \ 0.00081681851071822213, \ 0.00081681851071822213, \ 0.00081681851071822213, \ 0.00081681851071822213, \ 0.00081681851071822213, \ 0.00081681851071822213, \ 0.00081681851071822213, \ 0.00081681851071822213, \ 0.00854175372189276694, \ 0.00854175372189276694, \ 0.00854175372189276694, \ 0.00854175372189276694, \ 0.00854175372189276694, \ 0.00854175372189276694, \ 0.00854175372189276694, \ 0.00854175372189276694, \ 0.01018769584471248754, \ 0.01018769584471248754, \ 0.01018769584471248754, \ 0.01018769584471248754, \ 0.01018769584471248754, \ 0.01018769584471248754, \ 0.01018769584471248754, \ 0.01018769584471248754, \ 0.00572367792672661812, \ 0.00572367792672661812, \ 0.00572367792672661812, \ 0.00572367792672661812, \ 0.00572367792672661812, \ 0.00572367792672661812, \ 0.00572367792672661812, \ 0.00572367792672661812 ] ) return x, y, z, w def rule13 ( ): #*****************************************************************************80 # ## rule13() returns the pyramid quadrature rule of precision 13. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.41223892088328983885, \ 0.00000000000000000000, \ -0.41223892088328983885, \ 0.00000000000000000000, \ 0.94482408797958883362, \ 0.00000000000000000000, \ -0.94482408797958883362, \ 0.00000000000000000000, \ 0.15012306550295120844, \ 0.00000000000000000000, \ -0.15012306550295120844, \ 0.00000000000000000000, \ 0.36338283577562219273, \ 0.00000000000000000000, \ -0.36338283577562219273, \ 0.00000000000000000000, \ 0.32897122373450704558, \ 0.00000000000000000000, \ -0.32897122373450704558, \ 0.00000000000000000000, \ 0.55704935891608620135, \ 0.00000000000000000000, \ -0.55704935891608620135, \ 0.00000000000000000000, \ 0.71060354437421247020, \ 0.00000000000000000000, \ -0.71060354437421247020, \ 0.00000000000000000000, \ 0.88531748708681257121, \ 0.00000000000000000000, \ -0.88531748708681257121, \ 0.00000000000000000000, \ 0.48884754503841615358, \ -0.48884754503841615358, \ 0.48884754503841615358, \ -0.48884754503841615358, \ 0.45031772456672747307, \ -0.45031772456672747307, \ 0.45031772456672747307, \ -0.45031772456672747307, \ 0.65872956915547864476, \ -0.65872956915547864476, \ 0.65872956915547864476, \ -0.65872956915547864476, \ 0.62588271911798842861, \ -0.62588271911798842861, \ 0.62588271911798842861, \ -0.62588271911798842861, \ 0.25178960033193620305, \ -0.25178960033193620305, \ 0.25178960033193620305, \ -0.25178960033193620305, \ 0.91338191280449132492, \ -0.91338191280449132492, \ 0.91338191280449132492, \ -0.91338191280449132492, \ 0.11117861641720541699, \ -0.11117861641720541699, \ 0.11117861641720541699, \ -0.11117861641720541699, \ 0.37814924987375336807, \ -0.37814924987375336807, \ 0.37814924987375336807, \ -0.37814924987375336807, \ 0.23146195691577758913, \ -0.23146195691577758913, \ 0.23146195691577758913, \ -0.23146195691577758913, \ 0.18598667282576661353, \ -0.18598667282576661353, \ 0.18598667282576661353, \ -0.18598667282576661353, \ 0.72941490542892961635, \ -0.72941490542892961635, \ 0.72941490542892961635, \ -0.72941490542892961635, \ 0.80419241777926819825, \ -0.80419241777926819825, \ 0.80419241777926819825, \ -0.80419241777926819825, \ 0.47036082838417470064, \ -0.47036082838417470064, \ 0.47036082838417470064, \ -0.47036082838417470064, \ 0.27535657520011547206, \ -0.27535657520011547206, \ 0.27535657520011547206, \ -0.27535657520011547206, \ 0.25840443662578793660, \ -0.25840443662578793660, \ 0.25840443662578793660, \ -0.25840443662578793660, \ 0.77456301686419115615, \ 0.43978938971942055369, \ -0.77456301686419115615, \ 0.43978938971942055369, \ 0.77456301686419115615, \ -0.43978938971942055369, \ -0.77456301686419115615, \ -0.43978938971942055369, \ 0.72014146551340840752, \ 0.22174790443082656455, \ -0.72014146551340840752, \ 0.22174790443082656455, \ 0.72014146551340840752, \ -0.22174790443082656455, \ -0.72014146551340840752, \ -0.22174790443082656455, \ 0.17509849556381359981, \ 0.58560797514860796209, \ -0.17509849556381359981, \ 0.58560797514860796209, \ 0.17509849556381359981, \ -0.58560797514860796209, \ -0.17509849556381359981, \ -0.58560797514860796209, \ 0.93762547318055500245, \ 0.73982675325131319610, \ -0.93762547318055500245, \ 0.73982675325131319610, \ 0.93762547318055500245, \ -0.73982675325131319610, \ -0.93762547318055500245, \ -0.73982675325131319610, \ 0.92588822421370353677, \ 0.50002093145521131490, \ -0.92588822421370353677, \ 0.50002093145521131490, \ 0.92588822421370353677, \ -0.50002093145521131490, \ -0.92588822421370353677, \ -0.50002093145521131490, \ 0.26820739210416322251, \ 0.56185198689199644662, \ -0.26820739210416322251, \ 0.56185198689199644662, \ 0.26820739210416322251, \ -0.56185198689199644662, \ -0.26820739210416322251, \ -0.56185198689199644662, \ 0.36207959439737902319, \ 0.79245628070986395830, \ -0.36207959439737902319, \ 0.79245628070986395830, \ 0.36207959439737902319, \ -0.79245628070986395830, \ -0.36207959439737902319, \ -0.79245628070986395830 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.41223892088328983885, \ 0.00000000000000000000, \ -0.41223892088328983885, \ 0.00000000000000000000, \ 0.94482408797958883362, \ 0.00000000000000000000, \ -0.94482408797958883362, \ 0.00000000000000000000, \ 0.15012306550295120844, \ 0.00000000000000000000, \ -0.15012306550295120844, \ 0.00000000000000000000, \ 0.36338283577562219273, \ 0.00000000000000000000, \ -0.36338283577562219273, \ 0.00000000000000000000, \ 0.32897122373450704558, \ 0.00000000000000000000, \ -0.32897122373450704558, \ 0.00000000000000000000, \ 0.55704935891608620135, \ 0.00000000000000000000, \ -0.55704935891608620135, \ 0.00000000000000000000, \ 0.71060354437421247020, \ 0.00000000000000000000, \ -0.71060354437421247020, \ 0.00000000000000000000, \ 0.88531748708681257121, \ 0.00000000000000000000, \ -0.88531748708681257121, \ 0.48884754503841615358, \ 0.48884754503841615358, \ -0.48884754503841615358, \ -0.48884754503841615358, \ 0.45031772456672747307, \ 0.45031772456672747307, \ -0.45031772456672747307, \ -0.45031772456672747307, \ 0.65872956915547864476, \ 0.65872956915547864476, \ -0.65872956915547864476, \ -0.65872956915547864476, \ 0.62588271911798842861, \ 0.62588271911798842861, \ -0.62588271911798842861, \ -0.62588271911798842861, \ 0.25178960033193620305, \ 0.25178960033193620305, \ -0.25178960033193620305, \ -0.25178960033193620305, \ 0.91338191280449132492, \ 0.91338191280449132492, \ -0.91338191280449132492, \ -0.91338191280449132492, \ 0.11117861641720541699, \ 0.11117861641720541699, \ -0.11117861641720541699, \ -0.11117861641720541699, \ 0.37814924987375336807, \ 0.37814924987375336807, \ -0.37814924987375336807, \ -0.37814924987375336807, \ 0.23146195691577758913, \ 0.23146195691577758913, \ -0.23146195691577758913, \ -0.23146195691577758913, \ 0.18598667282576661353, \ 0.18598667282576661353, \ -0.18598667282576661353, \ -0.18598667282576661353, \ 0.72941490542892961635, \ 0.72941490542892961635, \ -0.72941490542892961635, \ -0.72941490542892961635, \ 0.80419241777926819825, \ 0.80419241777926819825, \ -0.80419241777926819825, \ -0.80419241777926819825, \ 0.47036082838417470064, \ 0.47036082838417470064, \ -0.47036082838417470064, \ -0.47036082838417470064, \ 0.27535657520011547206, \ 0.27535657520011547206, \ -0.27535657520011547206, \ -0.27535657520011547206, \ 0.25840443662578793660, \ 0.25840443662578793660, \ -0.25840443662578793660, \ -0.25840443662578793660, \ 0.43978938971942055369, \ 0.77456301686419115615, \ 0.43978938971942055369, \ -0.77456301686419115615, \ -0.43978938971942055369, \ 0.77456301686419115615, \ -0.43978938971942055369, \ -0.77456301686419115615, \ 0.22174790443082656455, \ 0.72014146551340840752, \ 0.22174790443082656455, \ -0.72014146551340840752, \ -0.22174790443082656455, \ 0.72014146551340840752, \ -0.22174790443082656455, \ -0.72014146551340840752, \ 0.58560797514860796209, \ 0.17509849556381359981, \ 0.58560797514860796209, \ -0.17509849556381359981, \ -0.58560797514860796209, \ 0.17509849556381359981, \ -0.58560797514860796209, \ -0.17509849556381359981, \ 0.73982675325131319610, \ 0.93762547318055500245, \ 0.73982675325131319610, \ -0.93762547318055500245, \ -0.73982675325131319610, \ 0.93762547318055500245, \ -0.73982675325131319610, \ -0.93762547318055500245, \ 0.50002093145521131490, \ 0.92588822421370353677, \ 0.50002093145521131490, \ -0.92588822421370353677, \ -0.50002093145521131490, \ 0.92588822421370353677, \ -0.50002093145521131490, \ -0.92588822421370353677, \ 0.56185198689199644662, \ 0.26820739210416322251, \ 0.56185198689199644662, \ -0.26820739210416322251, \ -0.56185198689199644662, \ 0.26820739210416322251, \ -0.56185198689199644662, \ -0.26820739210416322251, \ 0.79245628070986395830, \ 0.36207959439737902319, \ 0.79245628070986395830, \ -0.36207959439737902319, \ -0.79245628070986395830, \ 0.36207959439737902319, \ -0.79245628070986395830, \ -0.36207959439737902319 ] ) z = np.array ( [ \ 0.92974005864256004106, \ 0.58387036044479012631, \ 0.10942458150673148309, \ 0.30043598129646631456, \ 0.40351765144169587929, \ 0.40351765144169587929, \ 0.40351765144169587929, \ 0.40351765144169587929, \ 0.00554139647030791119, \ 0.00554139647030791119, \ 0.00554139647030791119, \ 0.00554139647030791119, \ 0.84979294403286831372, \ 0.84979294403286831372, \ 0.84979294403286831372, \ 0.84979294403286831372, \ 0.60719504362173426504, \ 0.60719504362173426504, \ 0.60719504362173426504, \ 0.60719504362173426504, \ 0.02033792783786766978, \ 0.02033792783786766978, \ 0.02033792783786766978, \ 0.02033792783786766978, \ 0.10601199873730246526, \ 0.10601199873730246526, \ 0.10601199873730246526, \ 0.10601199873730246526, \ 0.24910419915320258788, \ 0.24910419915320258788, \ 0.24910419915320258788, \ 0.24910419915320258788, \ 0.08107956240970674855, \ 0.08107956240970674855, \ 0.08107956240970674855, \ 0.08107956240970674855, \ 0.00950815168106079051, \ 0.00950815168106079051, \ 0.00950815168106079051, \ 0.00950815168106079051, \ 0.48819360509214093646, \ 0.48819360509214093646, \ 0.48819360509214093646, \ 0.48819360509214093646, \ 0.27690831156608641805, \ 0.27690831156608641805, \ 0.27690831156608641805, \ 0.27690831156608641805, \ 0.12248093820428122835, \ 0.12248093820428122835, \ 0.12248093820428122835, \ 0.12248093820428122835, \ 0.22323057279864513824, \ 0.22323057279864513824, \ 0.22323057279864513824, \ 0.22323057279864513824, \ 0.01207165002118426068, \ 0.01207165002118426068, \ 0.01207165002118426068, \ 0.01207165002118426068, \ 0.75518724716690510679, \ 0.75518724716690510679, \ 0.75518724716690510679, \ 0.75518724716690510679, \ 0.08424825204838617965, \ 0.08424825204838617965, \ 0.08424825204838617965, \ 0.08424825204838617965, \ 0.63188577231776799081, \ 0.63188577231776799081, \ 0.63188577231776799081, \ 0.63188577231776799081, \ 0.39892977659234107879, \ 0.39892977659234107879, \ 0.39892977659234107879, \ 0.39892977659234107879, \ 0.02502635713295603415, \ 0.02502635713295603415, \ 0.02502635713295603415, \ 0.02502635713295603415, \ 0.12038000765135539738, \ 0.12038000765135539738, \ 0.12038000765135539738, \ 0.12038000765135539738, \ 0.29270359357039776871, \ 0.29270359357039776871, \ 0.29270359357039776871, \ 0.29270359357039776871, \ 0.70742748921558806785, \ 0.70742748921558806785, \ 0.70742748921558806785, \ 0.70742748921558806785, \ 0.52832746509410000169, \ 0.52832746509410000169, \ 0.52832746509410000169, \ 0.52832746509410000169, \ 0.19538409012904675577, \ 0.19538409012904675577, \ 0.19538409012904675577, \ 0.19538409012904675577, \ 0.19538409012904675577, \ 0.19538409012904675577, \ 0.19538409012904675577, \ 0.19538409012904675577, \ 0.02260035188498128386, \ 0.02260035188498128386, \ 0.02260035188498128386, \ 0.02260035188498128386, \ 0.02260035188498128386, \ 0.02260035188498128386, \ 0.02260035188498128386, \ 0.02260035188498128386, \ 0.21608520533637087802, \ 0.21608520533637087802, \ 0.21608520533637087802, \ 0.21608520533637087802, \ 0.21608520533637087802, \ 0.21608520533637087802, \ 0.21608520533637087802, \ 0.21608520533637087802, \ 0.06232437306564607427, \ 0.06232437306564607427, \ 0.06232437306564607427, \ 0.06232437306564607427, \ 0.06232437306564607427, \ 0.06232437306564607427, \ 0.06232437306564607427, \ 0.06232437306564607427, \ 0.01929314718254383776, \ 0.01929314718254383776, \ 0.01929314718254383776, \ 0.01929314718254383776, \ 0.01929314718254383776, \ 0.01929314718254383776, \ 0.01929314718254383776, \ 0.01929314718254383776, \ 0.40102466550487736452, \ 0.40102466550487736452, \ 0.40102466550487736452, \ 0.40102466550487736452, \ 0.40102466550487736452, \ 0.40102466550487736452, \ 0.40102466550487736452, \ 0.40102466550487736452, \ 0.09200529105614789482, \ 0.09200529105614789482, \ 0.09200529105614789482, \ 0.09200529105614789482, \ 0.09200529105614789482, \ 0.09200529105614789482, \ 0.09200529105614789482, \ 0.09200529105614789482 ] ) w= np.array ( [ \ 0.00120366956557754735, \ 0.01890734566258640142, \ 0.02412883548353303431, \ 0.01430958560741040810, \ 0.01462233467606358257, \ 0.01462233467606358257, \ 0.01462233467606358257, \ 0.01462233467606358257, \ 0.00131047133506746131, \ 0.00131047133506746131, \ 0.00131047133506746131, \ 0.00131047133506746131, \ 0.00131534859459711507, \ 0.00131534859459711507, \ 0.00131534859459711507, \ 0.00131534859459711507, \ 0.00604172938779333306, \ 0.00604172938779333306, \ 0.00604172938779333306, \ 0.00604172938779333306, \ 0.00828934369195859742, \ 0.00828934369195859742, \ 0.00828934369195859742, \ 0.00828934369195859742, \ 0.01293341373858935758, \ 0.01293341373858935758, \ 0.01293341373858935758, \ 0.01293341373858935758, \ 0.00563885419154383245, \ 0.00563885419154383245, \ 0.00563885419154383245, \ 0.00563885419154383245, \ 0.00450499139881360439, \ 0.00450499139881360439, \ 0.00450499139881360439, \ 0.00450499139881360439, \ 0.00363618420610894565, \ 0.00363618420610894565, \ 0.00363618420610894565, \ 0.00363618420610894565, \ 0.00388842116802182820, \ 0.00388842116802182820, \ 0.00388842116802182820, \ 0.00388842116802182820, \ 0.00402365320826360111, \ 0.00402365320826360111, \ 0.00402365320826360111, \ 0.00402365320826360111, \ 0.00955901949244871221, \ 0.00955901949244871221, \ 0.00955901949244871221, \ 0.00955901949244871221, \ 0.01938656716858040696, \ 0.01938656716858040696, \ 0.01938656716858040696, \ 0.01938656716858040696, \ 0.00096875488373819618, \ 0.00096875488373819618, \ 0.00096875488373819618, \ 0.00096875488373819618, \ 0.00502214350286199571, \ 0.00502214350286199571, \ 0.00502214350286199571, \ 0.00502214350286199571, \ 0.01448769412031481602, \ 0.01448769412031481602, \ 0.01448769412031481602, \ 0.01448769412031481602, \ 0.00459976431383042356, \ 0.00459976431383042356, \ 0.00459976431383042356, \ 0.00459976431383042356, \ 0.01107636061349879207, \ 0.01107636061349879207, \ 0.01107636061349879207, \ 0.01107636061349879207, \ 0.00469260200432727610, \ 0.00469260200432727610, \ 0.00469260200432727610, \ 0.00469260200432727610, \ 0.00285194982449880072, \ 0.00285194982449880072, \ 0.00285194982449880072, \ 0.00285194982449880072, \ 0.01323033835935080553, \ 0.01323033835935080553, \ 0.01323033835935080553, \ 0.01323033835935080553, \ 0.00111972343972882474, \ 0.00111972343972882474, \ 0.00111972343972882474, \ 0.00111972343972882474, \ 0.00918246462138119605, \ 0.00918246462138119605, \ 0.00918246462138119605, \ 0.00918246462138119605, \ 0.00456490653701050169, \ 0.00456490653701050169, \ 0.00456490653701050169, \ 0.00456490653701050169, \ 0.00456490653701050169, \ 0.00456490653701050169, \ 0.00456490653701050169, \ 0.00456490653701050169, \ 0.00547503483442879964, \ 0.00547503483442879964, \ 0.00547503483442879964, \ 0.00547503483442879964, \ 0.00547503483442879964, \ 0.00547503483442879964, \ 0.00547503483442879964, \ 0.00547503483442879964, \ 0.00992261207645742799, \ 0.00992261207645742799, \ 0.00992261207645742799, \ 0.00992261207645742799, \ 0.00992261207645742799, \ 0.00992261207645742799, \ 0.00992261207645742799, \ 0.00992261207645742799, \ 0.00110382912156457261, \ 0.00110382912156457261, \ 0.00110382912156457261, \ 0.00110382912156457261, \ 0.00110382912156457261, \ 0.00110382912156457261, \ 0.00110382912156457261, \ 0.00110382912156457261, \ 0.00236228293958670472, \ 0.00236228293958670472, \ 0.00236228293958670472, \ 0.00236228293958670472, \ 0.00236228293958670472, \ 0.00236228293958670472, \ 0.00236228293958670472, \ 0.00236228293958670472, \ 0.00630666584934871672, \ 0.00630666584934871672, \ 0.00630666584934871672, \ 0.00630666584934871672, \ 0.00630666584934871672, \ 0.00630666584934871672, \ 0.00630666584934871672, \ 0.00630666584934871672, \ 0.00675492513102409885, \ 0.00675492513102409885, \ 0.00675492513102409885, \ 0.00675492513102409885, \ 0.00675492513102409885, \ 0.00675492513102409885, \ 0.00675492513102409885, \ 0.00675492513102409885 ] ) return x, y, z, w def rule14 ( ): #*****************************************************************************80 # ## rule14() returns the pyramid quadrature rule of precision 14. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.42182613673485974681, \ 0.00000000000000000000, \ -0.42182613673485974681, \ 0.00000000000000000000, \ 0.08465613435886885918, \ 0.00000000000000000000, \ -0.08465613435886885918, \ 0.00000000000000000000, \ 0.95167131965923157377, \ 0.00000000000000000000, \ -0.95167131965923157377, \ 0.00000000000000000000, \ 0.12212881781145627780, \ 0.00000000000000000000, \ -0.12212881781145627780, \ 0.00000000000000000000, \ 0.34597557868730360875, \ 0.00000000000000000000, \ -0.34597557868730360875, \ 0.00000000000000000000, \ 0.32500209212470398956, \ 0.00000000000000000000, \ -0.32500209212470398956, \ 0.00000000000000000000, \ 0.85274656175184737616, \ 0.00000000000000000000, \ -0.85274656175184737616, \ 0.00000000000000000000, \ 0.63827756477152641779, \ 0.00000000000000000000, \ -0.63827756477152641779, \ 0.00000000000000000000, \ 0.67231147414585012978, \ 0.00000000000000000000, \ -0.67231147414585012978, \ 0.00000000000000000000, \ 0.85374960595109017358, \ 0.00000000000000000000, \ -0.85374960595109017358, \ 0.00000000000000000000, \ 0.32351828528149095821, \ 0.00000000000000000000, \ -0.32351828528149095821, \ 0.00000000000000000000, \ 0.49697514832376565863, \ 0.00000000000000000000, \ -0.49697514832376565863, \ 0.00000000000000000000, \ 0.50417062955844949013, \ -0.50417062955844949013, \ 0.50417062955844949013, \ -0.50417062955844949013, \ 0.63853202881303905425, \ -0.63853202881303905425, \ 0.63853202881303905425, \ -0.63853202881303905425, \ 0.76432244824860651189, \ -0.76432244824860651189, \ 0.76432244824860651189, \ -0.76432244824860651189, \ 0.56133306193833287789, \ -0.56133306193833287789, \ 0.56133306193833287789, \ -0.56133306193833287789, \ 0.28786805395155073972, \ -0.28786805395155073972, \ 0.28786805395155073972, \ -0.28786805395155073972, \ 0.90163083827576329110, \ -0.90163083827576329110, \ 0.90163083827576329110, \ -0.90163083827576329110, \ 0.09459747575878657555, \ -0.09459747575878657555, \ 0.09459747575878657555, \ -0.09459747575878657555, \ 0.26275744057316757774, \ -0.26275744057316757774, \ 0.26275744057316757774, \ -0.26275744057316757774, \ 0.38640915363814193340, \ -0.38640915363814193340, \ 0.38640915363814193340, \ -0.38640915363814193340, \ 0.22823005779855418118, \ -0.22823005779855418118, \ 0.22823005779855418118, \ -0.22823005779855418118, \ 0.70578722692835427210, \ -0.70578722692835427210, \ 0.70578722692835427210, \ -0.70578722692835427210, \ 0.91478755244276455105, \ -0.91478755244276455105, \ 0.91478755244276455105, \ -0.91478755244276455105, \ 0.50883064513682729757, \ -0.50883064513682729757, \ 0.50883064513682729757, \ -0.50883064513682729757, \ 0.21833905510549736495, \ -0.21833905510549736495, \ 0.21833905510549736495, \ -0.21833905510549736495, \ 0.20524210043072979581, \ -0.20524210043072979581, \ 0.20524210043072979581, \ -0.20524210043072979581, \ 0.29109013901653718603, \ -0.29109013901653718603, \ 0.29109013901653718603, \ -0.29109013901653718603, \ 0.74865402480464293689, \ -0.74865402480464293689, \ 0.74865402480464293689, \ -0.74865402480464293689, \ 0.73782464660583058080, \ 0.49284956480916058963, \ -0.73782464660583058080, \ 0.49284956480916058963, \ 0.73782464660583058080, \ -0.49284956480916058963, \ -0.73782464660583058080, \ -0.49284956480916058963, \ 0.85890606200982022589, \ 0.37381968226304934655, \ -0.85890606200982022589, \ 0.37381968226304934655, \ 0.85890606200982022589, \ -0.37381968226304934655, \ -0.85890606200982022589, \ -0.37381968226304934655, \ 0.22436150649227576404, \ 0.63179494567048766207, \ -0.22436150649227576404, \ 0.63179494567048766207, \ 0.22436150649227576404, \ -0.63179494567048766207, \ -0.22436150649227576404, \ -0.63179494567048766207, \ 0.90017577589364738966, \ 0.62618678850176523465, \ -0.90017577589364738966, \ 0.62618678850176523465, \ 0.90017577589364738966, \ -0.62618678850176523465, \ -0.90017577589364738966, \ -0.62618678850176523465, \ 0.97895018498408203911, \ 0.62565783993238355265, \ -0.97895018498408203911, \ 0.62565783993238355265, \ 0.97895018498408203911, \ -0.62565783993238355265, \ -0.97895018498408203911, \ -0.62565783993238355265, \ 0.25607583733637889756, \ 0.51194810665765877467, \ -0.25607583733637889756, \ 0.51194810665765877467, \ 0.25607583733637889756, \ -0.51194810665765877467, \ -0.25607583733637889756, \ -0.51194810665765877467, \ 0.29741762068713811784, \ 0.77553958650832321986, \ -0.29741762068713811784, \ 0.77553958650832321986, \ 0.29741762068713811784, \ -0.77553958650832321986, \ -0.29741762068713811784, \ -0.77553958650832321986, \ 0.29079659566096877077, \ 0.61926152278826551711, \ -0.29079659566096877077, \ 0.61926152278826551711, \ 0.29079659566096877077, \ -0.61926152278826551711, \ -0.29079659566096877077, \ -0.61926152278826551711 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.42182613673485974681, \ 0.00000000000000000000, \ -0.42182613673485974681, \ 0.00000000000000000000, \ 0.08465613435886885918, \ 0.00000000000000000000, \ -0.08465613435886885918, \ 0.00000000000000000000, \ 0.95167131965923157377, \ 0.00000000000000000000, \ -0.95167131965923157377, \ 0.00000000000000000000, \ 0.12212881781145627780, \ 0.00000000000000000000, \ -0.12212881781145627780, \ 0.00000000000000000000, \ 0.34597557868730360875, \ 0.00000000000000000000, \ -0.34597557868730360875, \ 0.00000000000000000000, \ 0.32500209212470398956, \ 0.00000000000000000000, \ -0.32500209212470398956, \ 0.00000000000000000000, \ 0.85274656175184737616, \ 0.00000000000000000000, \ -0.85274656175184737616, \ 0.00000000000000000000, \ 0.63827756477152641779, \ 0.00000000000000000000, \ -0.63827756477152641779, \ 0.00000000000000000000, \ 0.67231147414585012978, \ 0.00000000000000000000, \ -0.67231147414585012978, \ 0.00000000000000000000, \ 0.85374960595109017358, \ 0.00000000000000000000, \ -0.85374960595109017358, \ 0.00000000000000000000, \ 0.32351828528149095821, \ 0.00000000000000000000, \ -0.32351828528149095821, \ 0.00000000000000000000, \ 0.49697514832376565863, \ 0.00000000000000000000, \ -0.49697514832376565863, \ 0.50417062955844949013, \ 0.50417062955844949013, \ -0.50417062955844949013, \ -0.50417062955844949013, \ 0.63853202881303905425, \ 0.63853202881303905425, \ -0.63853202881303905425, \ -0.63853202881303905425, \ 0.76432244824860651189, \ 0.76432244824860651189, \ -0.76432244824860651189, \ -0.76432244824860651189, \ 0.56133306193833287789, \ 0.56133306193833287789, \ -0.56133306193833287789, \ -0.56133306193833287789, \ 0.28786805395155073972, \ 0.28786805395155073972, \ -0.28786805395155073972, \ -0.28786805395155073972, \ 0.90163083827576329110, \ 0.90163083827576329110, \ -0.90163083827576329110, \ -0.90163083827576329110, \ 0.09459747575878657555, \ 0.09459747575878657555, \ -0.09459747575878657555, \ -0.09459747575878657555, \ 0.26275744057316757774, \ 0.26275744057316757774, \ -0.26275744057316757774, \ -0.26275744057316757774, \ 0.38640915363814193340, \ 0.38640915363814193340, \ -0.38640915363814193340, \ -0.38640915363814193340, \ 0.22823005779855418118, \ 0.22823005779855418118, \ -0.22823005779855418118, \ -0.22823005779855418118, \ 0.70578722692835427210, \ 0.70578722692835427210, \ -0.70578722692835427210, \ -0.70578722692835427210, \ 0.91478755244276455105, \ 0.91478755244276455105, \ -0.91478755244276455105, \ -0.91478755244276455105, \ 0.50883064513682729757, \ 0.50883064513682729757, \ -0.50883064513682729757, \ -0.50883064513682729757, \ 0.21833905510549736495, \ 0.21833905510549736495, \ -0.21833905510549736495, \ -0.21833905510549736495, \ 0.20524210043072979581, \ 0.20524210043072979581, \ -0.20524210043072979581, \ -0.20524210043072979581, \ 0.29109013901653718603, \ 0.29109013901653718603, \ -0.29109013901653718603, \ -0.29109013901653718603, \ 0.74865402480464293689, \ 0.74865402480464293689, \ -0.74865402480464293689, \ -0.74865402480464293689, \ 0.49284956480916058963, \ 0.73782464660583058080, \ 0.49284956480916058963, \ -0.73782464660583058080, \ -0.49284956480916058963, \ 0.73782464660583058080, \ -0.49284956480916058963, \ -0.73782464660583058080, \ 0.37381968226304934655, \ 0.85890606200982022589, \ 0.37381968226304934655, \ -0.85890606200982022589, \ -0.37381968226304934655, \ 0.85890606200982022589, \ -0.37381968226304934655, \ -0.85890606200982022589, \ 0.63179494567048766207, \ 0.22436150649227576404, \ 0.63179494567048766207, \ -0.22436150649227576404, \ -0.63179494567048766207, \ 0.22436150649227576404, \ -0.63179494567048766207, \ -0.22436150649227576404, \ 0.62618678850176523465, \ 0.90017577589364738966, \ 0.62618678850176523465, \ -0.90017577589364738966, \ -0.62618678850176523465, \ 0.90017577589364738966, \ -0.62618678850176523465, \ -0.90017577589364738966, \ 0.62565783993238355265, \ 0.97895018498408203911, \ 0.62565783993238355265, \ -0.97895018498408203911, \ -0.62565783993238355265, \ 0.97895018498408203911, \ -0.62565783993238355265, \ -0.97895018498408203911, \ 0.51194810665765877467, \ 0.25607583733637889756, \ 0.51194810665765877467, \ -0.25607583733637889756, \ -0.51194810665765877467, \ 0.25607583733637889756, \ -0.51194810665765877467, \ -0.25607583733637889756, \ 0.77553958650832321986, \ 0.29741762068713811784, \ 0.77553958650832321986, \ -0.29741762068713811784, \ -0.77553958650832321986, \ 0.29741762068713811784, \ -0.77553958650832321986, \ -0.29741762068713811784, \ 0.61926152278826551711, \ 0.29079659566096877077, \ 0.61926152278826551711, \ -0.29079659566096877077, \ -0.61926152278826551711, \ 0.29079659566096877077, \ -0.61926152278826551711, \ -0.29079659566096877077 ] ) z = np.array ( [ \ 0.94550960783801574205, \ 0.61382435648399280570, \ 0.24540497180596210214, \ 0.41832825390859845749, \ 0.40175363160567706400, \ 0.40175363160567706400, \ 0.40175363160567706400, \ 0.40175363160567706400, \ 0.08958821481037450296, \ 0.08958821481037450296, \ 0.08958821481037450296, \ 0.08958821481037450296, \ 0.03128290548598175458, \ 0.03128290548598175458, \ 0.03128290548598175458, \ 0.03128290548598175458, \ 0.86562635222401107526, \ 0.86562635222401107526, \ 0.86562635222401107526, \ 0.86562635222401107526, \ 0.56154915636029745230, \ 0.56154915636029745230, \ 0.56154915636029745230, \ 0.56154915636029745230, \ 0.01398939848661482320, \ 0.01398939848661482320, \ 0.01398939848661482320, \ 0.01398939848661482320, \ 0.00165571829628404746, \ 0.00165571829628404746, \ 0.00165571829628404746, \ 0.00165571829628404746, \ 0.06493816225859559699, \ 0.06493816225859559699, \ 0.06493816225859559699, \ 0.06493816225859559699, \ 0.32265244995852410126, \ 0.32265244995852410126, \ 0.32265244995852410126, \ 0.32265244995852410126, \ 0.14284602353229125526, \ 0.14284602353229125526, \ 0.14284602353229125526, \ 0.14284602353229125526, \ 0.66509821819012426847, \ 0.66509821819012426847, \ 0.66509821819012426847, \ 0.66509821819012426847, \ 0.19278467665636450645, \ 0.19278467665636450645, \ 0.19278467665636450645, \ 0.19278467665636450645, \ 0.05324772752904030626, \ 0.05324772752904030626, \ 0.05324772752904030626, \ 0.05324772752904030626, \ 0.34999224799132661046, \ 0.34999224799132661046, \ 0.34999224799132661046, \ 0.34999224799132661046, \ 0.16096112315804175785, \ 0.16096112315804175785, \ 0.16096112315804175785, \ 0.16096112315804175785, \ 0.16039988924094228384, \ 0.16039988924094228384, \ 0.16039988924094228384, \ 0.16039988924094228384, \ 0.13732763905737063737, \ 0.13732763905737063737, \ 0.13732763905737063737, \ 0.13732763905737063737, \ 0.01032358209500776509, \ 0.01032358209500776509, \ 0.01032358209500776509, \ 0.01032358209500776509, \ 0.76779179416407739023, \ 0.76779179416407739023, \ 0.76779179416407739023, \ 0.76779179416407739023, \ 0.04943554173327800727, \ 0.04943554173327800727, \ 0.04943554173327800727, \ 0.04943554173327800727, \ 0.55602661412166731747, \ 0.55602661412166731747, \ 0.55602661412166731747, \ 0.55602661412166731747, \ 0.49627919975552486909, \ 0.49627919975552486909, \ 0.49627919975552486909, \ 0.49627919975552486909, \ 0.00200880715410161345, \ 0.00200880715410161345, \ 0.00200880715410161345, \ 0.00200880715410161345, \ 0.04956231677804342345, \ 0.04956231677804342345, \ 0.04956231677804342345, \ 0.04956231677804342345, \ 0.34635586968731740809, \ 0.34635586968731740809, \ 0.34635586968731740809, \ 0.34635586968731740809, \ 0.74542883631057244020, \ 0.74542883631057244020, \ 0.74542883631057244020, \ 0.74542883631057244020, \ 0.64153164712892607469, \ 0.64153164712892607469, \ 0.64153164712892607469, \ 0.64153164712892607469, \ 0.30622738335271937338, \ 0.30622738335271937338, \ 0.30622738335271937338, \ 0.30622738335271937338, \ 0.04936880562940795109, \ 0.04936880562940795109, \ 0.04936880562940795109, \ 0.04936880562940795109, \ 0.23699400699902964385, \ 0.23699400699902964385, \ 0.23699400699902964385, \ 0.23699400699902964385, \ 0.23699400699902964385, \ 0.23699400699902964385, \ 0.23699400699902964385, \ 0.23699400699902964385, \ 0.02776225858911670133, \ 0.02776225858911670133, \ 0.02776225858911670133, \ 0.02776225858911670133, \ 0.02776225858911670133, \ 0.02776225858911670133, \ 0.02776225858911670133, \ 0.02776225858911670133, \ 0.25928305502878512545, \ 0.25928305502878512545, \ 0.25928305502878512545, \ 0.25928305502878512545, \ 0.25928305502878512545, \ 0.25928305502878512545, \ 0.25928305502878512545, \ 0.25928305502878512545, \ 0.07806621986847779582, \ 0.07806621986847779582, \ 0.07806621986847779582, \ 0.07806621986847779582, \ 0.07806621986847779582, \ 0.07806621986847779582, \ 0.07806621986847779582, \ 0.07806621986847779582, \ 0.00443001451925785755, \ 0.00443001451925785755, \ 0.00443001451925785755, \ 0.00443001451925785755, \ 0.00443001451925785755, \ 0.00443001451925785755, \ 0.00443001451925785755, \ 0.00443001451925785755, \ 0.45428572768859826203, \ 0.45428572768859826203, \ 0.45428572768859826203, \ 0.45428572768859826203, \ 0.45428572768859826203, \ 0.45428572768859826203, \ 0.45428572768859826203, \ 0.45428572768859826203, \ 0.11761104673332581361, \ 0.11761104673332581361, \ 0.11761104673332581361, \ 0.11761104673332581361, \ 0.11761104673332581361, \ 0.11761104673332581361, \ 0.11761104673332581361, \ 0.11761104673332581361, \ 0.00783483739567485994, \ 0.00783483739567485994, \ 0.00783483739567485994, \ 0.00783483739567485994, \ 0.00783483739567485994, \ 0.00783483739567485994, \ 0.00783483739567485994, \ 0.00783483739567485994 ] ) w= np.array ( [ \ 0.00060098284109148011, \ 0.01255487583666288487, \ 0.02319377258130698310, \ 0.01905556551345680832, \ 0.01191795956205729361, \ 0.01191795956205729361, \ 0.01191795956205729361, \ 0.01191795956205729361, \ 0.00386718441233280599, \ 0.00386718441233280599, \ 0.00386718441233280599, \ 0.00386718441233280599, \ 0.00192376309517474221, \ 0.00192376309517474221, \ 0.00192376309517474221, \ 0.00192376309517474221, \ 0.00123417980449306002, \ 0.00123417980449306002, \ 0.00123417980449306002, \ 0.00123417980449306002, \ 0.00471664803911589926, \ 0.00471664803911589926, \ 0.00471664803911589926, \ 0.00471664803911589926, \ 0.00513404497338453437, \ 0.00513404497338453437, \ 0.00513404497338453437, \ 0.00513404497338453437, \ 0.00115456474640818034, \ 0.00115456474640818034, \ 0.00115456474640818034, \ 0.00115456474640818034, \ 0.01181264118995303640, \ 0.01181264118995303640, \ 0.01181264118995303640, \ 0.01181264118995303640, \ 0.00243693783463101070, \ 0.00243693783463101070, \ 0.00243693783463101070, \ 0.00243693783463101070, \ 0.00244218039395145909, \ 0.00244218039395145909, \ 0.00244218039395145909, \ 0.00244218039395145909, \ 0.00276027206518877129, \ 0.00276027206518877129, \ 0.00276027206518877129, \ 0.00276027206518877129, \ 0.01491875937488000743, \ 0.01491875937488000743, \ 0.01491875937488000743, \ 0.01491875937488000743, \ 0.00860788548052002223, \ 0.00860788548052002223, \ 0.00860788548052002223, \ 0.00860788548052002223, \ 0.00092010540262242146, \ 0.00092010540262242146, \ 0.00092010540262242146, \ 0.00092010540262242146, \ 0.00350658071335885509, \ 0.00350658071335885509, \ 0.00350658071335885509, \ 0.00350658071335885509, \ 0.01184517921997258437, \ 0.01184517921997258437, \ 0.01184517921997258437, \ 0.01184517921997258437, \ 0.01517200950119655840, \ 0.01517200950119655840, \ 0.01517200950119655840, \ 0.01517200950119655840, \ 0.00079885709646654790, \ 0.00079885709646654790, \ 0.00079885709646654790, \ 0.00079885709646654790, \ 0.00346532205672137571, \ 0.00346532205672137571, \ 0.00346532205672137571, \ 0.00346532205672137571, \ 0.00564901752891650531, \ 0.00564901752891650531, \ 0.00564901752891650531, \ 0.00564901752891650531, \ 0.00314499257654337911, \ 0.00314499257654337911, \ 0.00314499257654337911, \ 0.00314499257654337911, \ 0.01042467052306092316, \ 0.01042467052306092316, \ 0.01042467052306092316, \ 0.01042467052306092316, \ 0.00135335334419937545, \ 0.00135335334419937545, \ 0.00135335334419937545, \ 0.00135335334419937545, \ 0.00068639460491782677, \ 0.00068639460491782677, \ 0.00068639460491782677, \ 0.00068639460491782677, \ 0.00848846646315219895, \ 0.00848846646315219895, \ 0.00848846646315219895, \ 0.00848846646315219895, \ 0.00138976471399791693, \ 0.00138976471399791693, \ 0.00138976471399791693, \ 0.00138976471399791693, \ 0.00564687172166134736, \ 0.00564687172166134736, \ 0.00564687172166134736, \ 0.00564687172166134736, \ 0.01822286920356053219, \ 0.01822286920356053219, \ 0.01822286920356053219, \ 0.01822286920356053219, \ 0.00475553584446375757, \ 0.00475553584446375757, \ 0.00475553584446375757, \ 0.00475553584446375757, \ 0.00330839378673254258, \ 0.00330839378673254258, \ 0.00330839378673254258, \ 0.00330839378673254258, \ 0.00330839378673254258, \ 0.00330839378673254258, \ 0.00330839378673254258, \ 0.00330839378673254258, \ 0.00407004510316002176, \ 0.00407004510316002176, \ 0.00407004510316002176, \ 0.00407004510316002176, \ 0.00407004510316002176, \ 0.00407004510316002176, \ 0.00407004510316002176, \ 0.00407004510316002176, \ 0.00826848930450256592, \ 0.00826848930450256592, \ 0.00826848930450256592, \ 0.00826848930450256592, \ 0.00826848930450256592, \ 0.00826848930450256592, \ 0.00826848930450256592, \ 0.00826848930450256592, \ 0.00222137881102773540, \ 0.00222137881102773540, \ 0.00222137881102773540, \ 0.00222137881102773540, \ 0.00222137881102773540, \ 0.00222137881102773540, \ 0.00222137881102773540, \ 0.00222137881102773540, \ 0.00053414917220099471, \ 0.00053414917220099471, \ 0.00053414917220099471, \ 0.00053414917220099471, \ 0.00053414917220099471, \ 0.00053414917220099471, \ 0.00053414917220099471, \ 0.00053414917220099471, \ 0.00487946234737815943, \ 0.00487946234737815943, \ 0.00487946234737815943, \ 0.00487946234737815943, \ 0.00487946234737815943, \ 0.00487946234737815943, \ 0.00487946234737815943, \ 0.00487946234737815943, \ 0.00789729756886463005, \ 0.00789729756886463005, \ 0.00789729756886463005, \ 0.00789729756886463005, \ 0.00789729756886463005, \ 0.00789729756886463005, \ 0.00789729756886463005, \ 0.00789729756886463005, \ 0.00269662856611711495, \ 0.00269662856611711495, \ 0.00269662856611711495, \ 0.00269662856611711495, \ 0.00269662856611711495, \ 0.00269662856611711495, \ 0.00269662856611711495, \ 0.00269662856611711495 ] ) return x, y, z, w def rule15 ( ): #*****************************************************************************80 # ## rule15() returns the pyramid quadrature rule of precision 15. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.70014035742397184858, \ 0.00000000000000000000, \ -0.70014035742397184858, \ 0.00000000000000000000, \ 0.91936314848339839578, \ 0.00000000000000000000, \ -0.91936314848339839578, \ 0.00000000000000000000, \ 0.11013348894423610758, \ 0.00000000000000000000, \ -0.11013348894423610758, \ 0.00000000000000000000, \ 0.44650085670154981976, \ 0.00000000000000000000, \ -0.44650085670154981976, \ 0.00000000000000000000, \ 0.80205385758014868802, \ 0.00000000000000000000, \ -0.80205385758014868802, \ 0.00000000000000000000, \ 0.53015124527324641868, \ 0.00000000000000000000, \ -0.53015124527324641868, \ 0.00000000000000000000, \ 0.97322734428927526462, \ 0.00000000000000000000, \ -0.97322734428927526462, \ 0.00000000000000000000, \ 0.50557186634064188446, \ 0.00000000000000000000, \ -0.50557186634064188446, \ 0.00000000000000000000, \ 0.04618938260051261985, \ 0.00000000000000000000, \ -0.04618938260051261985, \ 0.00000000000000000000, \ 0.62301364063828001960, \ 0.00000000000000000000, \ -0.62301364063828001960, \ 0.00000000000000000000, \ 0.29509310458272342004, \ 0.00000000000000000000, \ -0.29509310458272342004, \ 0.00000000000000000000, \ 0.47760058576112396356, \ 0.00000000000000000000, \ -0.47760058576112396356, \ 0.00000000000000000000, \ 0.36898015805621120489, \ 0.00000000000000000000, \ -0.36898015805621120489, \ 0.00000000000000000000, \ 0.37237829048305948199, \ -0.37237829048305948199, \ 0.37237829048305948199, \ -0.37237829048305948199, \ 0.53419020022883723087, \ -0.53419020022883723087, \ 0.53419020022883723087, \ -0.53419020022883723087, \ 0.06063808134784291065, \ -0.06063808134784291065, \ 0.06063808134784291065, \ -0.06063808134784291065, \ 0.47770687706587527943, \ -0.47770687706587527943, \ 0.47770687706587527943, \ -0.47770687706587527943, \ 0.19875431205737298379, \ -0.19875431205737298379, \ 0.19875431205737298379, \ -0.19875431205737298379, \ 0.75996956110375202265, \ -0.75996956110375202265, \ 0.75996956110375202265, \ -0.75996956110375202265, \ 0.50554584202664287762, \ -0.50554584202664287762, \ 0.50554584202664287762, \ -0.50554584202664287762, \ 0.22064824236265745405, \ -0.22064824236265745405, \ 0.22064824236265745405, \ -0.22064824236265745405, \ 0.34405034181784766023, \ -0.34405034181784766023, \ 0.34405034181784766023, \ -0.34405034181784766023, \ 0.19624129641007534430, \ -0.19624129641007534430, \ 0.19624129641007534430, \ -0.19624129641007534430, \ 0.91947901583738034237, \ -0.91947901583738034237, \ 0.91947901583738034237, \ -0.91947901583738034237, \ 0.26209258399888046842, \ -0.26209258399888046842, \ 0.26209258399888046842, \ -0.26209258399888046842, \ 0.17448879428144709047, \ -0.17448879428144709047, \ 0.17448879428144709047, \ -0.17448879428144709047, \ 0.13256324285803838814, \ -0.13256324285803838814, \ 0.13256324285803838814, \ -0.13256324285803838814, \ 0.30777107074463094794, \ -0.30777107074463094794, \ 0.30777107074463094794, \ -0.30777107074463094794, \ 0.45437881454568046502, \ -0.45437881454568046502, \ 0.45437881454568046502, \ -0.45437881454568046502, \ 0.18203893212319594008, \ -0.18203893212319594008, \ 0.18203893212319594008, \ -0.18203893212319594008, \ 0.18804430068288069400, \ -0.18804430068288069400, \ 0.18804430068288069400, \ -0.18804430068288069400, \ 0.85285866036694601977, \ -0.85285866036694601977, \ 0.85285866036694601977, \ -0.85285866036694601977, \ 0.19395358431436507396, \ -0.19395358431436507396, \ 0.19395358431436507396, \ -0.19395358431436507396, \ 0.63620569449244868121, \ -0.63620569449244868121, \ 0.63620569449244868121, \ -0.63620569449244868121, \ 0.71609629503236627013, \ -0.71609629503236627013, \ 0.71609629503236627013, \ -0.71609629503236627013, \ 0.72970588623268628492, \ -0.72970588623268628492, \ 0.72970588623268628492, \ -0.72970588623268628492, \ 0.85828508770542477624, \ 0.57684038354992128728, \ -0.85828508770542477624, \ 0.57684038354992128728, \ 0.85828508770542477624, \ -0.57684038354992128728, \ -0.85828508770542477624, \ -0.57684038354992128728, \ 0.76336766190340221705, \ 0.21167809325271402798, \ -0.76336766190340221705, \ 0.21167809325271402798, \ 0.76336766190340221705, \ -0.21167809325271402798, \ -0.76336766190340221705, \ -0.21167809325271402798, \ 0.21613035096350702302, \ 0.58392235225835387169, \ -0.21613035096350702302, \ 0.58392235225835387169, \ 0.21613035096350702302, \ -0.58392235225835387169, \ -0.21613035096350702302, \ -0.58392235225835387169, \ 0.95615842996744093707, \ 0.64241827941687201786, \ -0.95615842996744093707, \ 0.64241827941687201786, \ 0.95615842996744093707, \ -0.64241827941687201786, \ -0.95615842996744093707, \ -0.64241827941687201786, \ 0.87592219252594005763, \ 0.37797565831285062643, \ -0.87592219252594005763, \ 0.37797565831285062643, \ 0.87592219252594005763, \ -0.37797565831285062643, \ -0.87592219252594005763, \ -0.37797565831285062643, \ 0.24453940621889402873, \ 0.46719416054032014696, \ -0.24453940621889402873, \ 0.46719416054032014696, \ 0.24453940621889402873, \ -0.46719416054032014696, \ -0.24453940621889402873, \ -0.46719416054032014696, \ 0.37060589700094320742, \ 0.54852690614804233693, \ -0.37060589700094320742, \ 0.54852690614804233693, \ 0.37060589700094320742, \ -0.54852690614804233693, \ -0.37060589700094320742, \ -0.54852690614804233693, \ 0.61567982840573709513, \ 0.00714017158789090767, \ -0.61567982840573709513, \ 0.00714017158789090767, \ 0.61567982840573709513, \ -0.00714017158789090767, \ -0.61567982840573709513, \ -0.00714017158789090767, \ 0.71013273965512191399, \ 0.27918941987191842058, \ -0.71013273965512191399, \ 0.27918941987191842058, \ 0.71013273965512191399, \ -0.27918941987191842058, \ -0.71013273965512191399, \ -0.27918941987191842058, \ 0.82587110596774426785, \ 0.35683026213317575737, \ -0.82587110596774426785, \ 0.35683026213317575737, \ 0.82587110596774426785, \ -0.35683026213317575737, \ -0.82587110596774426785, \ -0.35683026213317575737, \ 0.47557663390649029811, \ 0.69286495782397328203, \ -0.47557663390649029811, \ 0.69286495782397328203, \ 0.47557663390649029811, \ -0.69286495782397328203, \ -0.47557663390649029811, \ -0.69286495782397328203 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.70014035742397184858, \ 0.00000000000000000000, \ -0.70014035742397184858, \ 0.00000000000000000000, \ 0.91936314848339839578, \ 0.00000000000000000000, \ -0.91936314848339839578, \ 0.00000000000000000000, \ 0.11013348894423610758, \ 0.00000000000000000000, \ -0.11013348894423610758, \ 0.00000000000000000000, \ 0.44650085670154981976, \ 0.00000000000000000000, \ -0.44650085670154981976, \ 0.00000000000000000000, \ 0.80205385758014868802, \ 0.00000000000000000000, \ -0.80205385758014868802, \ 0.00000000000000000000, \ 0.53015124527324641868, \ 0.00000000000000000000, \ -0.53015124527324641868, \ 0.00000000000000000000, \ 0.97322734428927526462, \ 0.00000000000000000000, \ -0.97322734428927526462, \ 0.00000000000000000000, \ 0.50557186634064188446, \ 0.00000000000000000000, \ -0.50557186634064188446, \ 0.00000000000000000000, \ 0.04618938260051261985, \ 0.00000000000000000000, \ -0.04618938260051261985, \ 0.00000000000000000000, \ 0.62301364063828001960, \ 0.00000000000000000000, \ -0.62301364063828001960, \ 0.00000000000000000000, \ 0.29509310458272342004, \ 0.00000000000000000000, \ -0.29509310458272342004, \ 0.00000000000000000000, \ 0.47760058576112396356, \ 0.00000000000000000000, \ -0.47760058576112396356, \ 0.00000000000000000000, \ 0.36898015805621120489, \ 0.00000000000000000000, \ -0.36898015805621120489, \ 0.37237829048305948199, \ 0.37237829048305948199, \ -0.37237829048305948199, \ -0.37237829048305948199, \ 0.53419020022883723087, \ 0.53419020022883723087, \ -0.53419020022883723087, \ -0.53419020022883723087, \ 0.06063808134784291065, \ 0.06063808134784291065, \ -0.06063808134784291065, \ -0.06063808134784291065, \ 0.47770687706587527943, \ 0.47770687706587527943, \ -0.47770687706587527943, \ -0.47770687706587527943, \ 0.19875431205737298379, \ 0.19875431205737298379, \ -0.19875431205737298379, \ -0.19875431205737298379, \ 0.75996956110375202265, \ 0.75996956110375202265, \ -0.75996956110375202265, \ -0.75996956110375202265, \ 0.50554584202664287762, \ 0.50554584202664287762, \ -0.50554584202664287762, \ -0.50554584202664287762, \ 0.22064824236265745405, \ 0.22064824236265745405, \ -0.22064824236265745405, \ -0.22064824236265745405, \ 0.34405034181784766023, \ 0.34405034181784766023, \ -0.34405034181784766023, \ -0.34405034181784766023, \ 0.19624129641007534430, \ 0.19624129641007534430, \ -0.19624129641007534430, \ -0.19624129641007534430, \ 0.91947901583738034237, \ 0.91947901583738034237, \ -0.91947901583738034237, \ -0.91947901583738034237, \ 0.26209258399888046842, \ 0.26209258399888046842, \ -0.26209258399888046842, \ -0.26209258399888046842, \ 0.17448879428144709047, \ 0.17448879428144709047, \ -0.17448879428144709047, \ -0.17448879428144709047, \ 0.13256324285803838814, \ 0.13256324285803838814, \ -0.13256324285803838814, \ -0.13256324285803838814, \ 0.30777107074463094794, \ 0.30777107074463094794, \ -0.30777107074463094794, \ -0.30777107074463094794, \ 0.45437881454568046502, \ 0.45437881454568046502, \ -0.45437881454568046502, \ -0.45437881454568046502, \ 0.18203893212319594008, \ 0.18203893212319594008, \ -0.18203893212319594008, \ -0.18203893212319594008, \ 0.18804430068288069400, \ 0.18804430068288069400, \ -0.18804430068288069400, \ -0.18804430068288069400, \ 0.85285866036694601977, \ 0.85285866036694601977, \ -0.85285866036694601977, \ -0.85285866036694601977, \ 0.19395358431436507396, \ 0.19395358431436507396, \ -0.19395358431436507396, \ -0.19395358431436507396, \ 0.63620569449244868121, \ 0.63620569449244868121, \ -0.63620569449244868121, \ -0.63620569449244868121, \ 0.71609629503236627013, \ 0.71609629503236627013, \ -0.71609629503236627013, \ -0.71609629503236627013, \ 0.72970588623268628492, \ 0.72970588623268628492, \ -0.72970588623268628492, \ -0.72970588623268628492, \ 0.57684038354992128728, \ 0.85828508770542477624, \ 0.57684038354992128728, \ -0.85828508770542477624, \ -0.57684038354992128728, \ 0.85828508770542477624, \ -0.57684038354992128728, \ -0.85828508770542477624, \ 0.21167809325271402798, \ 0.76336766190340221705, \ 0.21167809325271402798, \ -0.76336766190340221705, \ -0.21167809325271402798, \ 0.76336766190340221705, \ -0.21167809325271402798, \ -0.76336766190340221705, \ 0.58392235225835387169, \ 0.21613035096350702302, \ 0.58392235225835387169, \ -0.21613035096350702302, \ -0.58392235225835387169, \ 0.21613035096350702302, \ -0.58392235225835387169, \ -0.21613035096350702302, \ 0.64241827941687201786, \ 0.95615842996744093707, \ 0.64241827941687201786, \ -0.95615842996744093707, \ -0.64241827941687201786, \ 0.95615842996744093707, \ -0.64241827941687201786, \ -0.95615842996744093707, \ 0.37797565831285062643, \ 0.87592219252594005763, \ 0.37797565831285062643, \ -0.87592219252594005763, \ -0.37797565831285062643, \ 0.87592219252594005763, \ -0.37797565831285062643, \ -0.87592219252594005763, \ 0.46719416054032014696, \ 0.24453940621889402873, \ 0.46719416054032014696, \ -0.24453940621889402873, \ -0.46719416054032014696, \ 0.24453940621889402873, \ -0.46719416054032014696, \ -0.24453940621889402873, \ 0.54852690614804233693, \ 0.37060589700094320742, \ 0.54852690614804233693, \ -0.37060589700094320742, \ -0.54852690614804233693, \ 0.37060589700094320742, \ -0.54852690614804233693, \ -0.37060589700094320742, \ 0.00714017158789090767, \ 0.61567982840573709513, \ 0.00714017158789090767, \ -0.61567982840573709513, \ -0.00714017158789090767, \ 0.61567982840573709513, \ -0.00714017158789090767, \ -0.61567982840573709513, \ 0.27918941987191842058, \ 0.71013273965512191399, \ 0.27918941987191842058, \ -0.71013273965512191399, \ -0.27918941987191842058, \ 0.71013273965512191399, \ -0.27918941987191842058, \ -0.71013273965512191399, \ 0.35683026213317575737, \ 0.82587110596774426785, \ 0.35683026213317575737, \ -0.82587110596774426785, \ -0.35683026213317575737, \ 0.82587110596774426785, \ -0.35683026213317575737, \ -0.82587110596774426785, \ 0.69286495782397328203, \ 0.47557663390649029811, \ 0.69286495782397328203, \ -0.47557663390649029811, \ -0.69286495782397328203, \ 0.47557663390649029811, \ -0.69286495782397328203, \ -0.47557663390649029811 ] ) z = np.array ( [ \ 0.95167840606392661851, \ 0.29890092144247565331, \ 0.10372522326204723642, \ 0.10372522326204723642, \ 0.10372522326204723642, \ 0.10372522326204723642, \ 0.06052669044962753070, \ 0.06052669044962753070, \ 0.06052669044962753070, \ 0.06052669044962753070, \ 0.87767072134508183900, \ 0.87767072134508183900, \ 0.87767072134508183900, \ 0.87767072134508183900, \ 0.33061431908844512995, \ 0.33061431908844512995, \ 0.33061431908844512995, \ 0.33061431908844512995, \ 0.18913057164406818500, \ 0.18913057164406818500, \ 0.18913057164406818500, \ 0.18913057164406818500, \ 0.15549793195551472880, \ 0.15549793195551472880, \ 0.15549793195551472880, \ 0.15549793195551472880, \ 0.00490511032939973824, \ 0.00490511032939973824, \ 0.00490511032939973824, \ 0.00490511032939973824, \ 0.06238803484862592841, \ 0.06238803484862592841, \ 0.06238803484862592841, \ 0.06238803484862592841, \ 0.53284146417918532013, \ 0.53284146417918532013, \ 0.53284146417918532013, \ 0.53284146417918532013, \ 0.37695593807084121218, \ 0.37695593807084121218, \ 0.37695593807084121218, \ 0.37695593807084121218, \ 0.68148251405524751245, \ 0.68148251405524751245, \ 0.68148251405524751245, \ 0.68148251405524751245, \ 0.23097535663334242684, \ 0.23097535663334242684, \ 0.23097535663334242684, \ 0.23097535663334242684, \ 0.50335666905043052743, \ 0.50335666905043052743, \ 0.50335666905043052743, \ 0.50335666905043052743, \ 0.42353675293216364039, \ 0.42353675293216364039, \ 0.42353675293216364039, \ 0.42353675293216364039, \ 0.41296679793793455993, \ 0.41296679793793455993, \ 0.41296679793793455993, \ 0.41296679793793455993, \ 0.78640579578998992538, \ 0.78640579578998992538, \ 0.78640579578998992538, \ 0.78640579578998992538, \ 0.32653775213007651956, \ 0.32653775213007651956, \ 0.32653775213007651956, \ 0.32653775213007651956, \ 0.05291423306214974864, \ 0.05291423306214974864, \ 0.05291423306214974864, \ 0.05291423306214974864, \ 0.00693099618919339969, \ 0.00693099618919339969, \ 0.00693099618919339969, \ 0.00693099618919339969, \ 0.01799129130112891647, \ 0.01799129130112891647, \ 0.01799129130112891647, \ 0.01799129130112891647, \ 0.00830477370838420340, \ 0.00830477370838420340, \ 0.00830477370838420340, \ 0.00830477370838420340, \ 0.61788739915987689333, \ 0.61788739915987689333, \ 0.61788739915987689333, \ 0.61788739915987689333, \ 0.19265498366863681445, \ 0.19265498366863681445, \ 0.19265498366863681445, \ 0.19265498366863681445, \ 0.01617257265834035757, \ 0.01617257265834035757, \ 0.01617257265834035757, \ 0.01617257265834035757, \ 0.59548810603233670591, \ 0.59548810603233670591, \ 0.59548810603233670591, \ 0.59548810603233670591, \ 0.76735204589989336466, \ 0.76735204589989336466, \ 0.76735204589989336466, \ 0.76735204589989336466, \ 0.64457148839122024864, \ 0.64457148839122024864, \ 0.64457148839122024864, \ 0.64457148839122024864, \ 0.26823389272477243805, \ 0.26823389272477243805, \ 0.26823389272477243805, \ 0.26823389272477243805, \ 0.19249663769902353172, \ 0.19249663769902353172, \ 0.19249663769902353172, \ 0.19249663769902353172, \ 0.35451205561493442930, \ 0.35451205561493442930, \ 0.35451205561493442930, \ 0.35451205561493442930, \ 0.13784397009929885702, \ 0.13784397009929885702, \ 0.13784397009929885702, \ 0.13784397009929885702, \ 0.08819642588395044946, \ 0.08819642588395044946, \ 0.08819642588395044946, \ 0.08819642588395044946, \ 0.44126341704052479686, \ 0.44126341704052479686, \ 0.44126341704052479686, \ 0.44126341704052479686, \ 0.18126706536632553046, \ 0.18126706536632553046, \ 0.18126706536632553046, \ 0.18126706536632553046, \ 0.06273138420630826328, \ 0.06273138420630826328, \ 0.06273138420630826328, \ 0.06273138420630826328, \ 0.22238800479499257201, \ 0.22238800479499257201, \ 0.22238800479499257201, \ 0.22238800479499257201, \ 0.12311329897268918909, \ 0.12311329897268918909, \ 0.12311329897268918909, \ 0.12311329897268918909, \ 0.12311329897268918909, \ 0.12311329897268918909, \ 0.12311329897268918909, \ 0.12311329897268918909, \ 0.02653658688975024313, \ 0.02653658688975024313, \ 0.02653658688975024313, \ 0.02653658688975024313, \ 0.02653658688975024313, \ 0.02653658688975024313, \ 0.02653658688975024313, \ 0.02653658688975024313, \ 0.32949702529445068500, \ 0.32949702529445068500, \ 0.32949702529445068500, \ 0.32949702529445068500, \ 0.32949702529445068500, \ 0.32949702529445068500, \ 0.32949702529445068500, \ 0.32949702529445068500, \ 0.02375108271645150898, \ 0.02375108271645150898, \ 0.02375108271645150898, \ 0.02375108271645150898, \ 0.02375108271645150898, \ 0.02375108271645150898, \ 0.02375108271645150898, \ 0.02375108271645150898, \ 0.01156156746353601689, \ 0.01156156746353601689, \ 0.01156156746353601689, \ 0.01156156746353601689, \ 0.01156156746353601689, \ 0.01156156746353601689, \ 0.01156156746353601689, \ 0.01156156746353601689, \ 0.50478124488277686943, \ 0.50478124488277686943, \ 0.50478124488277686943, \ 0.50478124488277686943, \ 0.50478124488277686943, \ 0.50478124488277686943, \ 0.50478124488277686943, \ 0.50478124488277686943, \ 0.09182493970820698737, \ 0.09182493970820698737, \ 0.09182493970820698737, \ 0.09182493970820698737, \ 0.09182493970820698737, \ 0.09182493970820698737, \ 0.09182493970820698737, \ 0.09182493970820698737, \ 0.01061641469954416848, \ 0.01061641469954416848, \ 0.01061641469954416848, \ 0.01061641469954416848, \ 0.01061641469954416848, \ 0.01061641469954416848, \ 0.01061641469954416848, \ 0.01061641469954416848, \ 0.18699248305545079774, \ 0.18699248305545079774, \ 0.18699248305545079774, \ 0.18699248305545079774, \ 0.18699248305545079774, \ 0.18699248305545079774, \ 0.18699248305545079774, \ 0.18699248305545079774, \ 0.07551964039133612916, \ 0.07551964039133612916, \ 0.07551964039133612916, \ 0.07551964039133612916, \ 0.07551964039133612916, \ 0.07551964039133612916, \ 0.07551964039133612916, \ 0.07551964039133612916, \ 0.28631001132523614672, \ 0.28631001132523614672, \ 0.28631001132523614672, \ 0.28631001132523614672, \ 0.28631001132523614672, \ 0.28631001132523614672, \ 0.28631001132523614672, \ 0.28631001132523614672 ] ) w= np.array ( [ \ 0.00042533015548600539, \ 0.01525748792328103336, \ 0.00528017662585705642, \ 0.00528017662585705642, \ 0.00528017662585705642, \ 0.00528017662585705642, \ 0.00244639458990403638, \ 0.00244639458990403638, \ 0.00244639458990403638, \ 0.00244639458990403638, \ 0.00097370603129723528, \ 0.00097370603129723528, \ 0.00097370603129723528, \ 0.00097370603129723528, \ 0.00777612495382315819, \ 0.00777612495382315819, \ 0.00777612495382315819, \ 0.00777612495382315819, \ 0.00267697092767919202, \ 0.00267697092767919202, \ 0.00267697092767919202, \ 0.00267697092767919202, \ 0.00619081284266621932, \ 0.00619081284266621932, \ 0.00619081284266621932, \ 0.00619081284266621932, \ 0.00065618656167288063, \ 0.00065618656167288063, \ 0.00065618656167288063, \ 0.00065618656167288063, \ 0.00656994056618269082, \ 0.00656994056618269082, \ 0.00656994056618269082, \ 0.00656994056618269082, \ 0.00267308743214515841, \ 0.00267308743214515841, \ 0.00267308743214515841, \ 0.00267308743214515841, \ 0.00175949530216048481, \ 0.00175949530216048481, \ 0.00175949530216048481, \ 0.00175949530216048481, \ 0.00331285760856183092, \ 0.00331285760856183092, \ 0.00331285760856183092, \ 0.00331285760856183092, \ 0.00751034506572093984, \ 0.00751034506572093984, \ 0.00751034506572093984, \ 0.00751034506572093984, \ 0.00893166529089345351, \ 0.00893166529089345351, \ 0.00893166529089345351, \ 0.00893166529089345351, \ 0.00556841825996671948, \ 0.00556841825996671948, \ 0.00556841825996671948, \ 0.00556841825996671948, \ 0.00264945739278132876, \ 0.00264945739278132876, \ 0.00264945739278132876, \ 0.00264945739278132876, \ 0.00197028999055473379, \ 0.00197028999055473379, \ 0.00197028999055473379, \ 0.00197028999055473379, \ 0.00513483903966016272, \ 0.00513483903966016272, \ 0.00513483903966016272, \ 0.00513483903966016272, \ 0.00742192548155929527, \ 0.00742192548155929527, \ 0.00742192548155929527, \ 0.00742192548155929527, \ 0.00164485721629859362, \ 0.00164485721629859362, \ 0.00164485721629859362, \ 0.00164485721629859362, \ 0.00553453693910099451, \ 0.00553453693910099451, \ 0.00553453693910099451, \ 0.00553453693910099451, \ 0.00325628156420546379, \ 0.00325628156420546379, \ 0.00325628156420546379, \ 0.00325628156420546379, \ 0.00151506082426114191, \ 0.00151506082426114191, \ 0.00151506082426114191, \ 0.00151506082426114191, \ 0.00591126556727756668, \ 0.00591126556727756668, \ 0.00591126556727756668, \ 0.00591126556727756668, \ 0.00083923797814166039, \ 0.00083923797814166039, \ 0.00083923797814166039, \ 0.00083923797814166039, \ 0.00402240401025226024, \ 0.00402240401025226024, \ 0.00402240401025226024, \ 0.00402240401025226024, \ 0.00223169575519892738, \ 0.00223169575519892738, \ 0.00223169575519892738, \ 0.00223169575519892738, \ 0.00615688200816193708, \ 0.00615688200816193708, \ 0.00615688200816193708, \ 0.00615688200816193708, \ 0.00864232058920194786, \ 0.00864232058920194786, \ 0.00864232058920194786, \ 0.00864232058920194786, \ 0.00745270338750553870, \ 0.00745270338750553870, \ 0.00745270338750553870, \ 0.00745270338750553870, \ 0.00502880383507017109, \ 0.00502880383507017109, \ 0.00502880383507017109, \ 0.00502880383507017109, \ 0.00879638512225545434, \ 0.00879638512225545434, \ 0.00879638512225545434, \ 0.00879638512225545434, \ 0.00174781246088704756, \ 0.00174781246088704756, \ 0.00174781246088704756, \ 0.00174781246088704756, \ 0.00918989383822925963, \ 0.00918989383822925963, \ 0.00918989383822925963, \ 0.00918989383822925963, \ 0.00620807391936788796, \ 0.00620807391936788796, \ 0.00620807391936788796, \ 0.00620807391936788796, \ 0.00568398055245949909, \ 0.00568398055245949909, \ 0.00568398055245949909, \ 0.00568398055245949909, \ 0.00183658571623211762, \ 0.00183658571623211762, \ 0.00183658571623211762, \ 0.00183658571623211762, \ 0.00221869264777755162, \ 0.00221869264777755162, \ 0.00221869264777755162, \ 0.00221869264777755162, \ 0.00221869264777755162, \ 0.00221869264777755162, \ 0.00221869264777755162, \ 0.00221869264777755162, \ 0.00260988740586402639, \ 0.00260988740586402639, \ 0.00260988740586402639, \ 0.00260988740586402639, \ 0.00260988740586402639, \ 0.00260988740586402639, \ 0.00260988740586402639, \ 0.00260988740586402639, \ 0.00616875610859360119, \ 0.00616875610859360119, \ 0.00616875610859360119, \ 0.00616875610859360119, \ 0.00616875610859360119, \ 0.00616875610859360119, \ 0.00616875610859360119, \ 0.00616875610859360119, \ 0.00122995761226799547, \ 0.00122995761226799547, \ 0.00122995761226799547, \ 0.00122995761226799547, \ 0.00122995761226799547, \ 0.00122995761226799547, \ 0.00122995761226799547, \ 0.00122995761226799547, \ 0.00195493878423380618, \ 0.00195493878423380618, \ 0.00195493878423380618, \ 0.00195493878423380618, \ 0.00195493878423380618, \ 0.00195493878423380618, \ 0.00195493878423380618, \ 0.00195493878423380618, \ 0.00346763933769407258, \ 0.00346763933769407258, \ 0.00346763933769407258, \ 0.00346763933769407258, \ 0.00346763933769407258, \ 0.00346763933769407258, \ 0.00346763933769407258, \ 0.00346763933769407258, \ 0.00677026604334400768, \ 0.00677026604334400768, \ 0.00677026604334400768, \ 0.00677026604334400768, \ 0.00677026604334400768, \ 0.00677026604334400768, \ 0.00677026604334400768, \ 0.00677026604334400768, \ 0.00167829416355688515, \ 0.00167829416355688515, \ 0.00167829416355688515, \ 0.00167829416355688515, \ 0.00167829416355688515, \ 0.00167829416355688515, \ 0.00167829416355688515, \ 0.00167829416355688515, \ 0.00713079759016688013, \ 0.00713079759016688013, \ 0.00713079759016688013, \ 0.00713079759016688013, \ 0.00713079759016688013, \ 0.00713079759016688013, \ 0.00713079759016688013, \ 0.00713079759016688013, \ 0.00467547289885053390, \ 0.00467547289885053390, \ 0.00467547289885053390, \ 0.00467547289885053390, \ 0.00467547289885053390, \ 0.00467547289885053390, \ 0.00467547289885053390, \ 0.00467547289885053390, \ 0.00253420752420773854, \ 0.00253420752420773854, \ 0.00253420752420773854, \ 0.00253420752420773854, \ 0.00253420752420773854, \ 0.00253420752420773854, \ 0.00253420752420773854, \ 0.00253420752420773854 ] ) return x, y, z, w def rule16 ( ): #*****************************************************************************80 # ## rule16() returns the pyramid quadrature rule of precision 16. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.51870388022974789344, \ 0.00000000000000000000, \ -0.51870388022974789344, \ 0.00000000000000000000, \ 0.91531292456766799592, \ 0.00000000000000000000, \ -0.91531292456766799592, \ 0.00000000000000000000, \ 0.01655472656731888509, \ 0.00000000000000000000, \ -0.01655472656731888509, \ 0.00000000000000000000, \ 0.36912135575078097727, \ 0.00000000000000000000, \ -0.36912135575078097727, \ 0.00000000000000000000, \ 0.02060330211667108294, \ 0.00000000000000000000, \ -0.02060330211667108294, \ 0.00000000000000000000, \ 0.87194193710104261896, \ 0.00000000000000000000, \ -0.87194193710104261896, \ 0.00000000000000000000, \ 0.31538420787936460865, \ 0.00000000000000000000, \ -0.31538420787936460865, \ 0.00000000000000000000, \ 0.61399555563153074278, \ 0.00000000000000000000, \ -0.61399555563153074278, \ 0.00000000000000000000, \ 0.09765007634893953237, \ 0.00000000000000000000, \ -0.09765007634893953237, \ 0.00000000000000000000, \ 0.73176464480784220168, \ 0.00000000000000000000, \ -0.73176464480784220168, \ 0.00000000000000000000, \ 0.84054220943522905962, \ 0.00000000000000000000, \ -0.84054220943522905962, \ 0.00000000000000000000, \ 0.55574609505629035677, \ 0.00000000000000000000, \ -0.55574609505629035677, \ 0.00000000000000000000, \ 0.26438021717351822826, \ 0.00000000000000000000, \ -0.26438021717351822826, \ 0.00000000000000000000, \ 0.13755031468645742554, \ -0.13755031468645742554, \ 0.13755031468645742554, \ -0.13755031468645742554, \ 0.55599929975376194413, \ -0.55599929975376194413, \ 0.55599929975376194413, \ -0.55599929975376194413, \ 0.68037602529077279012, \ -0.68037602529077279012, \ 0.68037602529077279012, \ -0.68037602529077279012, \ 0.68987074662201319786, \ -0.68987074662201319786, \ 0.68987074662201319786, \ -0.68987074662201319786, \ 0.46656016616381063011, \ -0.46656016616381063011, \ 0.46656016616381063011, \ -0.46656016616381063011, \ 0.93657427078716448676, \ -0.93657427078716448676, \ 0.93657427078716448676, \ -0.93657427078716448676, \ 0.10668464068510881415, \ -0.10668464068510881415, \ 0.10668464068510881415, \ -0.10668464068510881415, \ 0.56362866319030435758, \ -0.56362866319030435758, \ 0.56362866319030435758, \ -0.56362866319030435758, \ 0.08721470315267314255, \ -0.08721470315267314255, \ 0.08721470315267314255, \ -0.08721470315267314255, \ 0.28826482911237666373, \ -0.28826482911237666373, \ 0.28826482911237666373, \ -0.28826482911237666373, \ 0.23503249705404929970, \ -0.23503249705404929970, \ 0.23503249705404929970, \ -0.23503249705404929970, \ 0.24508582185951371946, \ -0.24508582185951371946, \ 0.24508582185951371946, \ -0.24508582185951371946, \ 0.50030649786215641850, \ -0.50030649786215641850, \ 0.50030649786215641850, \ -0.50030649786215641850, \ 0.05973130190403576345, \ -0.05973130190403576345, \ 0.05973130190403576345, \ -0.05973130190403576345, \ 0.36285963939710730308, \ -0.36285963939710730308, \ 0.36285963939710730308, \ -0.36285963939710730308, \ 0.83163011923015617288, \ -0.83163011923015617288, \ 0.83163011923015617288, \ -0.83163011923015617288, \ 0.59815151207893801910, \ -0.59815151207893801910, \ 0.59815151207893801910, \ -0.59815151207893801910, \ 0.32452468623385005708, \ -0.32452468623385005708, \ 0.32452468623385005708, \ -0.32452468623385005708, \ 0.18400437828694599096, \ -0.18400437828694599096, \ 0.18400437828694599096, \ -0.18400437828694599096, \ 0.80685585076678034699, \ -0.80685585076678034699, \ 0.80685585076678034699, \ -0.80685585076678034699, \ 0.39038172839426421579, \ -0.39038172839426421579, \ 0.39038172839426421579, \ -0.39038172839426421579, \ 0.16205656720464603482, \ -0.16205656720464603482, \ 0.16205656720464603482, \ -0.16205656720464603482, \ 0.79557791018541468286, \ 0.52651319421754327887, \ -0.79557791018541468286, \ 0.52651319421754327887, \ 0.79557791018541468286, \ -0.52651319421754327887, \ -0.79557791018541468286, \ -0.52651319421754327887, \ 0.82001165757451899285, \ 0.58763897947885146422, \ -0.82001165757451899285, \ 0.58763897947885146422, \ 0.82001165757451899285, \ -0.58763897947885146422, \ -0.82001165757451899285, \ -0.58763897947885146422, \ 0.48106775949054608743, \ 0.14913701615330382522, \ -0.48106775949054608743, \ 0.14913701615330382522, \ 0.48106775949054608743, \ -0.14913701615330382522, \ -0.48106775949054608743, \ -0.14913701615330382522, \ 0.91698017235976392314, \ 0.63033943569284833774, \ -0.91698017235976392314, \ 0.63033943569284833774, \ 0.91698017235976392314, \ -0.63033943569284833774, \ -0.91698017235976392314, \ -0.63033943569284833774, \ 0.95781996021629389748, \ 0.33277831868591489783, \ -0.95781996021629389748, \ 0.33277831868591489783, \ 0.95781996021629389748, \ -0.33277831868591489783, \ -0.95781996021629389748, \ -0.33277831868591489783, \ 0.21226792819096282350, \ 0.42143671745401867224, \ -0.21226792819096282350, \ 0.42143671745401867224, \ 0.21226792819096282350, \ -0.42143671745401867224, \ -0.21226792819096282350, \ -0.42143671745401867224, \ 0.24859573800356360440, \ 0.62623217679932552393, \ -0.24859573800356360440, \ 0.62623217679932552393, \ 0.24859573800356360440, \ -0.62623217679932552393, \ -0.24859573800356360440, \ -0.62623217679932552393, \ 0.55347901385730624568, \ 0.18815805920102898763, \ -0.55347901385730624568, \ 0.18815805920102898763, \ 0.55347901385730624568, \ -0.18815805920102898763, \ -0.55347901385730624568, \ -0.18815805920102898763, \ 0.82422827852456481690, \ 0.36376205736175593053, \ -0.82422827852456481690, \ 0.36376205736175593053, \ 0.82422827852456481690, \ -0.36376205736175593053, \ -0.82422827852456481690, \ -0.36376205736175593053, \ 0.14606542728759722150, \ 0.44268310223761137001, \ -0.14606542728759722150, \ 0.44268310223761137001, \ 0.14606542728759722150, \ -0.44268310223761137001, \ -0.14606542728759722150, \ -0.44268310223761137001, \ 0.38810720735022874450, \ 0.62355125720878634699, \ -0.38810720735022874450, \ 0.62355125720878634699, \ 0.38810720735022874450, \ -0.62355125720878634699, \ -0.38810720735022874450, \ -0.62355125720878634699, \ 0.95674484283290128772, \ 0.79844517503668932523, \ -0.95674484283290128772, \ 0.79844517503668932523, \ 0.95674484283290128772, \ -0.79844517503668932523, \ -0.95674484283290128772, \ -0.79844517503668932523, \ 0.60984849485865177954, \ 0.31205150762818156807, \ -0.60984849485865177954, \ 0.31205150762818156807, \ 0.60984849485865177954, \ -0.31205150762818156807, \ -0.60984849485865177954, \ -0.31205150762818156807, \ 0.24847427215400066935, \ 0.13406531787546346890, \ -0.24847427215400066935, \ 0.13406531787546346890, \ 0.24847427215400066935, \ -0.13406531787546346890, \ -0.24847427215400066935, \ -0.13406531787546346890, \ 0.69918943535356659069, \ 0.17767876450874769967, \ -0.69918943535356659069, \ 0.17767876450874769967, \ 0.69918943535356659069, \ -0.17767876450874769967, \ -0.69918943535356659069, \ -0.17767876450874769967, \ 0.36015415281659141078, \ 0.43011776020837644285, \ -0.36015415281659141078, \ 0.43011776020837644285, \ 0.36015415281659141078, \ -0.43011776020837644285, \ -0.36015415281659141078, \ -0.43011776020837644285, \ 0.73668742050512570074, \ 0.30298735173674529175, \ -0.73668742050512570074, \ 0.30298735173674529175, \ 0.73668742050512570074, \ -0.30298735173674529175, \ -0.73668742050512570074, \ -0.30298735173674529175, \ 0.31424806302114011158, \ 0.02522065148266495332, \ -0.31424806302114011158, \ 0.02522065148266495332, \ 0.31424806302114011158, \ -0.02522065148266495332, \ -0.31424806302114011158, \ -0.02522065148266495332 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.51870388022974789344, \ 0.00000000000000000000, \ -0.51870388022974789344, \ 0.00000000000000000000, \ 0.91531292456766799592, \ 0.00000000000000000000, \ -0.91531292456766799592, \ 0.00000000000000000000, \ 0.01655472656731888509, \ 0.00000000000000000000, \ -0.01655472656731888509, \ 0.00000000000000000000, \ 0.36912135575078097727, \ 0.00000000000000000000, \ -0.36912135575078097727, \ 0.00000000000000000000, \ 0.02060330211667108294, \ 0.00000000000000000000, \ -0.02060330211667108294, \ 0.00000000000000000000, \ 0.87194193710104261896, \ 0.00000000000000000000, \ -0.87194193710104261896, \ 0.00000000000000000000, \ 0.31538420787936460865, \ 0.00000000000000000000, \ -0.31538420787936460865, \ 0.00000000000000000000, \ 0.61399555563153074278, \ 0.00000000000000000000, \ -0.61399555563153074278, \ 0.00000000000000000000, \ 0.09765007634893953237, \ 0.00000000000000000000, \ -0.09765007634893953237, \ 0.00000000000000000000, \ 0.73176464480784220168, \ 0.00000000000000000000, \ -0.73176464480784220168, \ 0.00000000000000000000, \ 0.84054220943522905962, \ 0.00000000000000000000, \ -0.84054220943522905962, \ 0.00000000000000000000, \ 0.55574609505629035677, \ 0.00000000000000000000, \ -0.55574609505629035677, \ 0.00000000000000000000, \ 0.26438021717351822826, \ 0.00000000000000000000, \ -0.26438021717351822826, \ 0.13755031468645742554, \ 0.13755031468645742554, \ -0.13755031468645742554, \ -0.13755031468645742554, \ 0.55599929975376194413, \ 0.55599929975376194413, \ -0.55599929975376194413, \ -0.55599929975376194413, \ 0.68037602529077279012, \ 0.68037602529077279012, \ -0.68037602529077279012, \ -0.68037602529077279012, \ 0.68987074662201319786, \ 0.68987074662201319786, \ -0.68987074662201319786, \ -0.68987074662201319786, \ 0.46656016616381063011, \ 0.46656016616381063011, \ -0.46656016616381063011, \ -0.46656016616381063011, \ 0.93657427078716448676, \ 0.93657427078716448676, \ -0.93657427078716448676, \ -0.93657427078716448676, \ 0.10668464068510881415, \ 0.10668464068510881415, \ -0.10668464068510881415, \ -0.10668464068510881415, \ 0.56362866319030435758, \ 0.56362866319030435758, \ -0.56362866319030435758, \ -0.56362866319030435758, \ 0.08721470315267314255, \ 0.08721470315267314255, \ -0.08721470315267314255, \ -0.08721470315267314255, \ 0.28826482911237666373, \ 0.28826482911237666373, \ -0.28826482911237666373, \ -0.28826482911237666373, \ 0.23503249705404929970, \ 0.23503249705404929970, \ -0.23503249705404929970, \ -0.23503249705404929970, \ 0.24508582185951371946, \ 0.24508582185951371946, \ -0.24508582185951371946, \ -0.24508582185951371946, \ 0.50030649786215641850, \ 0.50030649786215641850, \ -0.50030649786215641850, \ -0.50030649786215641850, \ 0.05973130190403576345, \ 0.05973130190403576345, \ -0.05973130190403576345, \ -0.05973130190403576345, \ 0.36285963939710730308, \ 0.36285963939710730308, \ -0.36285963939710730308, \ -0.36285963939710730308, \ 0.83163011923015617288, \ 0.83163011923015617288, \ -0.83163011923015617288, \ -0.83163011923015617288, \ 0.59815151207893801910, \ 0.59815151207893801910, \ -0.59815151207893801910, \ -0.59815151207893801910, \ 0.32452468623385005708, \ 0.32452468623385005708, \ -0.32452468623385005708, \ -0.32452468623385005708, \ 0.18400437828694599096, \ 0.18400437828694599096, \ -0.18400437828694599096, \ -0.18400437828694599096, \ 0.80685585076678034699, \ 0.80685585076678034699, \ -0.80685585076678034699, \ -0.80685585076678034699, \ 0.39038172839426421579, \ 0.39038172839426421579, \ -0.39038172839426421579, \ -0.39038172839426421579, \ 0.16205656720464603482, \ 0.16205656720464603482, \ -0.16205656720464603482, \ -0.16205656720464603482, \ 0.52651319421754327887, \ 0.79557791018541468286, \ 0.52651319421754327887, \ -0.79557791018541468286, \ -0.52651319421754327887, \ 0.79557791018541468286, \ -0.52651319421754327887, \ -0.79557791018541468286, \ 0.58763897947885146422, \ 0.82001165757451899285, \ 0.58763897947885146422, \ -0.82001165757451899285, \ -0.58763897947885146422, \ 0.82001165757451899285, \ -0.58763897947885146422, \ -0.82001165757451899285, \ 0.14913701615330382522, \ 0.48106775949054608743, \ 0.14913701615330382522, \ -0.48106775949054608743, \ -0.14913701615330382522, \ 0.48106775949054608743, \ -0.14913701615330382522, \ -0.48106775949054608743, \ 0.63033943569284833774, \ 0.91698017235976392314, \ 0.63033943569284833774, \ -0.91698017235976392314, \ -0.63033943569284833774, \ 0.91698017235976392314, \ -0.63033943569284833774, \ -0.91698017235976392314, \ 0.33277831868591489783, \ 0.95781996021629389748, \ 0.33277831868591489783, \ -0.95781996021629389748, \ -0.33277831868591489783, \ 0.95781996021629389748, \ -0.33277831868591489783, \ -0.95781996021629389748, \ 0.42143671745401867224, \ 0.21226792819096282350, \ 0.42143671745401867224, \ -0.21226792819096282350, \ -0.42143671745401867224, \ 0.21226792819096282350, \ -0.42143671745401867224, \ -0.21226792819096282350, \ 0.62623217679932552393, \ 0.24859573800356360440, \ 0.62623217679932552393, \ -0.24859573800356360440, \ -0.62623217679932552393, \ 0.24859573800356360440, \ -0.62623217679932552393, \ -0.24859573800356360440, \ 0.18815805920102898763, \ 0.55347901385730624568, \ 0.18815805920102898763, \ -0.55347901385730624568, \ -0.18815805920102898763, \ 0.55347901385730624568, \ -0.18815805920102898763, \ -0.55347901385730624568, \ 0.36376205736175593053, \ 0.82422827852456481690, \ 0.36376205736175593053, \ -0.82422827852456481690, \ -0.36376205736175593053, \ 0.82422827852456481690, \ -0.36376205736175593053, \ -0.82422827852456481690, \ 0.44268310223761137001, \ 0.14606542728759722150, \ 0.44268310223761137001, \ -0.14606542728759722150, \ -0.44268310223761137001, \ 0.14606542728759722150, \ -0.44268310223761137001, \ -0.14606542728759722150, \ 0.62355125720878634699, \ 0.38810720735022874450, \ 0.62355125720878634699, \ -0.38810720735022874450, \ -0.62355125720878634699, \ 0.38810720735022874450, \ -0.62355125720878634699, \ -0.38810720735022874450, \ 0.79844517503668932523, \ 0.95674484283290128772, \ 0.79844517503668932523, \ -0.95674484283290128772, \ -0.79844517503668932523, \ 0.95674484283290128772, \ -0.79844517503668932523, \ -0.95674484283290128772, \ 0.31205150762818156807, \ 0.60984849485865177954, \ 0.31205150762818156807, \ -0.60984849485865177954, \ -0.31205150762818156807, \ 0.60984849485865177954, \ -0.31205150762818156807, \ -0.60984849485865177954, \ 0.13406531787546346890, \ 0.24847427215400066935, \ 0.13406531787546346890, \ -0.24847427215400066935, \ -0.13406531787546346890, \ 0.24847427215400066935, \ -0.13406531787546346890, \ -0.24847427215400066935, \ 0.17767876450874769967, \ 0.69918943535356659069, \ 0.17767876450874769967, \ -0.69918943535356659069, \ -0.17767876450874769967, \ 0.69918943535356659069, \ -0.17767876450874769967, \ -0.69918943535356659069, \ 0.43011776020837644285, \ 0.36015415281659141078, \ 0.43011776020837644285, \ -0.36015415281659141078, \ -0.43011776020837644285, \ 0.36015415281659141078, \ -0.43011776020837644285, \ -0.36015415281659141078, \ 0.30298735173674529175, \ 0.73668742050512570074, \ 0.30298735173674529175, \ -0.73668742050512570074, \ -0.30298735173674529175, \ 0.73668742050512570074, \ -0.30298735173674529175, \ -0.73668742050512570074, \ 0.02522065148266495332, \ 0.31424806302114011158, \ 0.02522065148266495332, \ -0.31424806302114011158, \ -0.02522065148266495332, \ 0.31424806302114011158, \ -0.02522065148266495332, \ -0.31424806302114011158 ] ) z = np.array ( [ \ 0.95860354636208366941, \ 0.14065559413657438559, \ 0.14065559413657438559, \ 0.14065559413657438559, \ 0.14065559413657438559, \ 0.04316491102619297859, \ 0.04316491102619297859, \ 0.04316491102619297859, \ 0.04316491102619297859, \ 0.39522832646013361657, \ 0.39522832646013361657, \ 0.39522832646013361657, \ 0.39522832646013361657, \ 0.29890125561593927639, \ 0.29890125561593927639, \ 0.29890125561593927639, \ 0.29890125561593927639, \ 0.06870461262955433746, \ 0.06870461262955433746, \ 0.06870461262955433746, \ 0.06870461262955433746, \ 0.11193495967860304929, \ 0.11193495967860304929, \ 0.11193495967860304929, \ 0.11193495967860304929, \ 0.56665435040432854397, \ 0.56665435040432854397, \ 0.56665435040432854397, \ 0.56665435040432854397, \ 0.15957732786354647536, \ 0.15957732786354647536, \ 0.15957732786354647536, \ 0.15957732786354647536, \ 0.89220214923004481644, \ 0.89220214923004481644, \ 0.89220214923004481644, \ 0.89220214923004481644, \ 0.24754993371512326594, \ 0.24754993371512326594, \ 0.24754993371512326594, \ 0.24754993371512326594, \ 0.01014565417563986251, \ 0.01014565417563986251, \ 0.01014565417563986251, \ 0.01014565417563986251, \ 0.42885512420774396514, \ 0.42885512420774396514, \ 0.42885512420774396514, \ 0.42885512420774396514, \ 0.71649796495360695836, \ 0.71649796495360695836, \ 0.71649796495360695836, \ 0.71649796495360695836, \ 0.17877523402579234557, \ 0.17877523402579234557, \ 0.17877523402579234557, \ 0.17877523402579234557, \ 0.29295501084965730465, \ 0.29295501084965730465, \ 0.29295501084965730465, \ 0.29295501084965730465, \ 0.27447523572941867620, \ 0.27447523572941867620, \ 0.27447523572941867620, \ 0.27447523572941867620, \ 0.15714127239405312197, \ 0.15714127239405312197, \ 0.15714127239405312197, \ 0.15714127239405312197, \ 0.25035924766443973244, \ 0.25035924766443973244, \ 0.25035924766443973244, \ 0.25035924766443973244, \ 0.02983913639912040561, \ 0.02983913639912040561, \ 0.02983913639912040561, \ 0.02983913639912040561, \ 0.70189657043113384827, \ 0.70189657043113384827, \ 0.70189657043113384827, \ 0.70189657043113384827, \ 0.05534643995880605266, \ 0.05534643995880605266, \ 0.05534643995880605266, \ 0.05534643995880605266, \ 0.58803180785949038523, \ 0.58803180785949038523, \ 0.58803180785949038523, \ 0.58803180785949038523, \ 0.35760040041294161028, \ 0.35760040041294161028, \ 0.35760040041294161028, \ 0.35760040041294161028, \ 0.63808499834946807994, \ 0.63808499834946807994, \ 0.63808499834946807994, \ 0.63808499834946807994, \ 0.11180046767985268863, \ 0.11180046767985268863, \ 0.11180046767985268863, \ 0.11180046767985268863, \ 0.45799604201643168144, \ 0.45799604201643168144, \ 0.45799604201643168144, \ 0.45799604201643168144, \ 0.81600939659279747573, \ 0.81600939659279747573, \ 0.81600939659279747573, \ 0.81600939659279747573, \ 0.05597294995869231404, \ 0.05597294995869231404, \ 0.05597294995869231404, \ 0.05597294995869231404, \ 0.12573106601315930941, \ 0.12573106601315930941, \ 0.12573106601315930941, \ 0.12573106601315930941, \ 0.10680199134354546875, \ 0.10680199134354546875, \ 0.10680199134354546875, \ 0.10680199134354546875, \ 0.64658620070888050968, \ 0.64658620070888050968, \ 0.64658620070888050968, \ 0.64658620070888050968, \ 0.25409417136336337473, \ 0.25409417136336337473, \ 0.25409417136336337473, \ 0.25409417136336337473, \ 0.05465918013108818363, \ 0.05465918013108818363, \ 0.05465918013108818363, \ 0.05465918013108818363, \ 0.45345939462310336232, \ 0.45345939462310336232, \ 0.45345939462310336232, \ 0.45345939462310336232, \ 0.78917660780490361816, \ 0.78917660780490361816, \ 0.78917660780490361816, \ 0.78917660780490361816, \ 0.18689788541072827055, \ 0.18689788541072827055, \ 0.18689788541072827055, \ 0.18689788541072827055, \ 0.18689788541072827055, \ 0.18689788541072827055, \ 0.18689788541072827055, \ 0.18689788541072827055, \ 0.01494308906905271982, \ 0.01494308906905271982, \ 0.01494308906905271982, \ 0.01494308906905271982, \ 0.01494308906905271982, \ 0.01494308906905271982, \ 0.01494308906905271982, \ 0.01494308906905271982, \ 0.39770246065633879651, \ 0.39770246065633879651, \ 0.39770246065633879651, \ 0.39770246065633879651, \ 0.39770246065633879651, \ 0.39770246065633879651, \ 0.39770246065633879651, \ 0.39770246065633879651, \ 0.06620609897561705037, \ 0.06620609897561705037, \ 0.06620609897561705037, \ 0.06620609897561705037, \ 0.06620609897561705037, \ 0.06620609897561705037, \ 0.06620609897561705037, \ 0.06620609897561705037, \ 0.01432824105432797292, \ 0.01432824105432797292, \ 0.01432824105432797292, \ 0.01432824105432797292, \ 0.01432824105432797292, \ 0.01432824105432797292, \ 0.01432824105432797292, \ 0.01432824105432797292, \ 0.55099638203681522430, \ 0.55099638203681522430, \ 0.55099638203681522430, \ 0.55099638203681522430, \ 0.55099638203681522430, \ 0.55099638203681522430, \ 0.55099638203681522430, \ 0.55099638203681522430, \ 0.28000300498314673048, \ 0.28000300498314673048, \ 0.28000300498314673048, \ 0.28000300498314673048, \ 0.28000300498314673048, \ 0.28000300498314673048, \ 0.28000300498314673048, \ 0.28000300498314673048, \ 0.24363304655846618196, \ 0.24363304655846618196, \ 0.24363304655846618196, \ 0.24363304655846618196, \ 0.24363304655846618196, \ 0.24363304655846618196, \ 0.24363304655846618196, \ 0.24363304655846618196, \ 0.07506931441576017439, \ 0.07506931441576017439, \ 0.07506931441576017439, \ 0.07506931441576017439, \ 0.07506931441576017439, \ 0.07506931441576017439, \ 0.07506931441576017439, \ 0.07506931441576017439, \ 0.05795059845476016602, \ 0.05795059845476016602, \ 0.05795059845476016602, \ 0.05795059845476016602, \ 0.05795059845476016602, \ 0.05795059845476016602, \ 0.05795059845476016602, \ 0.05795059845476016602, \ 0.35631158631326498298, \ 0.35631158631326498298, \ 0.35631158631326498298, \ 0.35631158631326498298, \ 0.35631158631326498298, \ 0.35631158631326498298, \ 0.35631158631326498298, \ 0.35631158631326498298, \ 0.00597525511512164969, \ 0.00597525511512164969, \ 0.00597525511512164969, \ 0.00597525511512164969, \ 0.00597525511512164969, \ 0.00597525511512164969, \ 0.00597525511512164969, \ 0.00597525511512164969, \ 0.01006650964023972882, \ 0.01006650964023972882, \ 0.01006650964023972882, \ 0.01006650964023972882, \ 0.01006650964023972882, \ 0.01006650964023972882, \ 0.01006650964023972882, \ 0.01006650964023972882, \ 0.47619683731341805322, \ 0.47619683731341805322, \ 0.47619683731341805322, \ 0.47619683731341805322, \ 0.47619683731341805322, \ 0.47619683731341805322, \ 0.47619683731341805322, \ 0.47619683731341805322, \ 0.05836635447459245785, \ 0.05836635447459245785, \ 0.05836635447459245785, \ 0.05836635447459245785, \ 0.05836635447459245785, \ 0.05836635447459245785, \ 0.05836635447459245785, \ 0.05836635447459245785, \ 0.16495562918454476087, \ 0.16495562918454476087, \ 0.16495562918454476087, \ 0.16495562918454476087, \ 0.16495562918454476087, \ 0.16495562918454476087, \ 0.16495562918454476087, \ 0.16495562918454476087, \ 0.15963984721353552398, \ 0.15963984721353552398, \ 0.15963984721353552398, \ 0.15963984721353552398, \ 0.15963984721353552398, \ 0.15963984721353552398, \ 0.15963984721353552398, \ 0.15963984721353552398, \ 0.01331460692424766938, \ 0.01331460692424766938, \ 0.01331460692424766938, \ 0.01331460692424766938, \ 0.01331460692424766938, \ 0.01331460692424766938, \ 0.01331460692424766938, \ 0.01331460692424766938 ] ) w= np.array ( [ \ 0.00027672120207682897, \ 0.00734944257707945050, \ 0.00734944257707945050, \ 0.00734944257707945050, \ 0.00734944257707945050, \ 0.00148740437072881278, \ 0.00148740437072881278, \ 0.00148740437072881278, \ 0.00148740437072881278, \ 0.00387693638421187639, \ 0.00387693638421187639, \ 0.00387693638421187639, \ 0.00387693638421187639, \ 0.01030614824039441553, \ 0.01030614824039441553, \ 0.01030614824039441553, \ 0.01030614824039441553, \ 0.00272673198843895789, \ 0.00272673198843895789, \ 0.00272673198843895789, \ 0.00272673198843895789, \ 0.00244629213408558690, \ 0.00244629213408558690, \ 0.00244629213408558690, \ 0.00244629213408558690, \ 0.00554924399761744409, \ 0.00554924399761744409, \ 0.00554924399761744409, \ 0.00554924399761744409, \ 0.00502262417466419701, \ 0.00502262417466419701, \ 0.00502262417466419701, \ 0.00502262417466419701, \ 0.00067111170084793834, \ 0.00067111170084793834, \ 0.00067111170084793834, \ 0.00067111170084793834, \ 0.00316873518673754882, \ 0.00316873518673754882, \ 0.00316873518673754882, \ 0.00316873518673754882, \ 0.00230707268685653678, \ 0.00230707268685653678, \ 0.00230707268685653678, \ 0.00230707268685653678, \ 0.00223355434035575010, \ 0.00223355434035575010, \ 0.00223355434035575010, \ 0.00223355434035575010, \ 0.00228685693132126217, \ 0.00228685693132126217, \ 0.00228685693132126217, \ 0.00228685693132126217, \ 0.00583888699964928409, \ 0.00583888699964928409, \ 0.00583888699964928409, \ 0.00583888699964928409, \ 0.00412038756118528714, \ 0.00412038756118528714, \ 0.00412038756118528714, \ 0.00412038756118528714, \ 0.00173037948168740284, \ 0.00173037948168740284, \ 0.00173037948168740284, \ 0.00173037948168740284, \ 0.00410680906602167630, \ 0.00410680906602167630, \ 0.00410680906602167630, \ 0.00410680906602167630, \ 0.00635438948067259222, \ 0.00635438948067259222, \ 0.00635438948067259222, \ 0.00635438948067259222, \ 0.00043262101844333546, \ 0.00043262101844333546, \ 0.00043262101844333546, \ 0.00043262101844333546, \ 0.00345263292981801964, \ 0.00345263292981801964, \ 0.00345263292981801964, \ 0.00345263292981801964, \ 0.00424071455736505301, \ 0.00424071455736505301, \ 0.00424071455736505301, \ 0.00424071455736505301, \ 0.00340526631678994204, \ 0.00340526631678994204, \ 0.00340526631678994204, \ 0.00340526631678994204, \ 0.00700942929302337137, \ 0.00700942929302337137, \ 0.00700942929302337137, \ 0.00700942929302337137, \ 0.00371184509938299149, \ 0.00371184509938299149, \ 0.00371184509938299149, \ 0.00371184509938299149, \ 0.00655769989421819445, \ 0.00655769989421819445, \ 0.00655769989421819445, \ 0.00655769989421819445, \ 0.00169996297833195664, \ 0.00169996297833195664, \ 0.00169996297833195664, \ 0.00169996297833195664, \ 0.00134740004835729398, \ 0.00134740004835729398, \ 0.00134740004835729398, \ 0.00134740004835729398, \ 0.00363396950461261376, \ 0.00363396950461261376, \ 0.00363396950461261376, \ 0.00363396950461261376, \ 0.00121619462900863910, \ 0.00121619462900863910, \ 0.00121619462900863910, \ 0.00121619462900863910, \ 0.00549579708316756677, \ 0.00549579708316756677, \ 0.00549579708316756677, \ 0.00549579708316756677, \ 0.00097330273562793888, \ 0.00097330273562793888, \ 0.00097330273562793888, \ 0.00097330273562793888, \ 0.00725393003232855348, \ 0.00725393003232855348, \ 0.00725393003232855348, \ 0.00725393003232855348, \ 0.00261600067059077025, \ 0.00261600067059077025, \ 0.00261600067059077025, \ 0.00261600067059077025, \ 0.00548333692337083910, \ 0.00548333692337083910, \ 0.00548333692337083910, \ 0.00548333692337083910, \ 0.00150187064516151079, \ 0.00150187064516151079, \ 0.00150187064516151079, \ 0.00150187064516151079, \ 0.00224211276351870626, \ 0.00224211276351870626, \ 0.00224211276351870626, \ 0.00224211276351870626, \ 0.00224211276351870626, \ 0.00224211276351870626, \ 0.00224211276351870626, \ 0.00224211276351870626, \ 0.00254357012140252583, \ 0.00254357012140252583, \ 0.00254357012140252583, \ 0.00254357012140252583, \ 0.00254357012140252583, \ 0.00254357012140252583, \ 0.00254357012140252583, \ 0.00254357012140252583, \ 0.00536144481406866224, \ 0.00536144481406866224, \ 0.00536144481406866224, \ 0.00536144481406866224, \ 0.00536144481406866224, \ 0.00536144481406866224, \ 0.00536144481406866224, \ 0.00536144481406866224, \ 0.00150566238487620605, \ 0.00150566238487620605, \ 0.00150566238487620605, \ 0.00150566238487620605, \ 0.00150566238487620605, \ 0.00150566238487620605, \ 0.00150566238487620605, \ 0.00150566238487620605, \ 0.00112651998000158019, \ 0.00112651998000158019, \ 0.00112651998000158019, \ 0.00112651998000158019, \ 0.00112651998000158019, \ 0.00112651998000158019, \ 0.00112651998000158019, \ 0.00112651998000158019, \ 0.00283697215367184055, \ 0.00283697215367184055, \ 0.00283697215367184055, \ 0.00283697215367184055, \ 0.00283697215367184055, \ 0.00283697215367184055, \ 0.00283697215367184055, \ 0.00283697215367184055, \ 0.00423443304160556894, \ 0.00423443304160556894, \ 0.00423443304160556894, \ 0.00423443304160556894, \ 0.00423443304160556894, \ 0.00423443304160556894, \ 0.00423443304160556894, \ 0.00423443304160556894, \ 0.00318414785741326324, \ 0.00318414785741326324, \ 0.00318414785741326324, \ 0.00318414785741326324, \ 0.00318414785741326324, \ 0.00318414785741326324, \ 0.00318414785741326324, \ 0.00318414785741326324, \ 0.00402977998773114843, \ 0.00402977998773114843, \ 0.00402977998773114843, \ 0.00402977998773114843, \ 0.00402977998773114843, \ 0.00402977998773114843, \ 0.00402977998773114843, \ 0.00402977998773114843, \ 0.00366973681687540396, \ 0.00366973681687540396, \ 0.00366973681687540396, \ 0.00366973681687540396, \ 0.00366973681687540396, \ 0.00366973681687540396, \ 0.00366973681687540396, \ 0.00366973681687540396, \ 0.00248888728757531682, \ 0.00248888728757531682, \ 0.00248888728757531682, \ 0.00248888728757531682, \ 0.00248888728757531682, \ 0.00248888728757531682, \ 0.00248888728757531682, \ 0.00248888728757531682, \ 0.00048888922605729013, \ 0.00048888922605729013, \ 0.00048888922605729013, \ 0.00048888922605729013, \ 0.00048888922605729013, \ 0.00048888922605729013, \ 0.00048888922605729013, \ 0.00048888922605729013, \ 0.00325264515509947555, \ 0.00325264515509947555, \ 0.00325264515509947555, \ 0.00325264515509947555, \ 0.00325264515509947555, \ 0.00325264515509947555, \ 0.00325264515509947555, \ 0.00325264515509947555, \ 0.00495505909145715732, \ 0.00495505909145715732, \ 0.00495505909145715732, \ 0.00495505909145715732, \ 0.00495505909145715732, \ 0.00495505909145715732, \ 0.00495505909145715732, \ 0.00495505909145715732, \ 0.00457024218025166729, \ 0.00457024218025166729, \ 0.00457024218025166729, \ 0.00457024218025166729, \ 0.00457024218025166729, \ 0.00457024218025166729, \ 0.00457024218025166729, \ 0.00457024218025166729, \ 0.00481061764241353957, \ 0.00481061764241353957, \ 0.00481061764241353957, \ 0.00481061764241353957, \ 0.00481061764241353957, \ 0.00481061764241353957, \ 0.00481061764241353957, \ 0.00481061764241353957, \ 0.00538791794721728626, \ 0.00538791794721728626, \ 0.00538791794721728626, \ 0.00538791794721728626, \ 0.00538791794721728626, \ 0.00538791794721728626, \ 0.00538791794721728626, \ 0.00538791794721728626, \ 0.00246928056742645339, \ 0.00246928056742645339, \ 0.00246928056742645339, \ 0.00246928056742645339, \ 0.00246928056742645339, \ 0.00246928056742645339, \ 0.00246928056742645339, \ 0.00246928056742645339 ] ) return x, y, z, w def rule17 ( ): #*****************************************************************************80 # ## rule17() returns the pyramid quadrature rule of precision 17. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.95241408581244602072, \ 0.00000000000000000000, \ -0.95241408581244602072, \ 0.00000000000000000000, \ 0.08275692125030435775, \ 0.00000000000000000000, \ -0.08275692125030435775, \ 0.00000000000000000000, \ 0.26578545043127727032, \ 0.00000000000000000000, \ -0.26578545043127727032, \ 0.00000000000000000000, \ 0.81155940028479511827, \ 0.00000000000000000000, \ -0.81155940028479511827, \ 0.00000000000000000000, \ 0.35232799954016802424, \ 0.00000000000000000000, \ -0.35232799954016802424, \ 0.00000000000000000000, \ 0.60303771218972423984, \ 0.00000000000000000000, \ -0.60303771218972423984, \ 0.00000000000000000000, \ 0.78402604202159054125, \ 0.00000000000000000000, \ -0.78402604202159054125, \ 0.00000000000000000000, \ 0.49346472198646390561, \ 0.00000000000000000000, \ -0.49346472198646390561, \ 0.00000000000000000000, \ 0.35038751648906635294, \ 0.00000000000000000000, \ -0.35038751648906635294, \ 0.00000000000000000000, \ 0.00336404312107426752, \ 0.00000000000000000000, \ -0.00336404312107426752, \ 0.00000000000000000000, \ 0.43074512679067450405, \ 0.00000000000000000000, \ -0.43074512679067450405, \ 0.00000000000000000000, \ 0.59254801282947688890, \ 0.00000000000000000000, \ -0.59254801282947688890, \ 0.00000000000000000000, \ 0.22550686036585329552, \ 0.00000000000000000000, \ -0.22550686036585329552, \ 0.00000000000000000000, \ 0.63975863740336180729, \ -0.63975863740336180729, \ 0.63975863740336180729, \ -0.63975863740336180729, \ 0.16463474879631256886, \ -0.16463474879631256886, \ 0.16463474879631256886, \ -0.16463474879631256886, \ 0.49303563319629611916, \ -0.49303563319629611916, \ 0.49303563319629611916, \ -0.49303563319629611916, \ 0.74791280396309745004, \ -0.74791280396309745004, \ 0.74791280396309745004, \ -0.74791280396309745004, \ 0.26251317864285966808, \ -0.26251317864285966808, \ 0.26251317864285966808, \ -0.26251317864285966808, \ 0.17484215589868074003, \ -0.17484215589868074003, \ 0.17484215589868074003, \ -0.17484215589868074003, \ 0.27602468785670569718, \ -0.27602468785670569718, \ 0.27602468785670569718, \ -0.27602468785670569718, \ 0.43512552408987620334, \ -0.43512552408987620334, \ 0.43512552408987620334, \ -0.43512552408987620334, \ 0.95307694157738065410, \ -0.95307694157738065410, \ 0.95307694157738065410, \ -0.95307694157738065410, \ 0.48425597905194911474, \ -0.48425597905194911474, \ 0.48425597905194911474, \ -0.48425597905194911474, \ 0.29381061843327571648, \ -0.29381061843327571648, \ 0.29381061843327571648, \ -0.29381061843327571648, \ 0.16057200503692023452, \ -0.16057200503692023452, \ 0.16057200503692023452, \ -0.16057200503692023452, \ 0.81014529214207364749, \ -0.81014529214207364749, \ 0.81014529214207364749, \ -0.81014529214207364749, \ 0.18009325754915589402, \ -0.18009325754915589402, \ 0.18009325754915589402, \ -0.18009325754915589402, \ 0.50136799407459931022, \ -0.50136799407459931022, \ 0.50136799407459931022, \ -0.50136799407459931022, \ 0.92284407855436589863, \ -0.92284407855436589863, \ 0.92284407855436589863, \ -0.92284407855436589863, \ 0.32077249570607596629, \ -0.32077249570607596629, \ 0.32077249570607596629, \ -0.32077249570607596629, \ 0.02145401504974505866, \ -0.02145401504974505866, \ 0.02145401504974505866, \ -0.02145401504974505866, \ 0.65293078741937671250, \ -0.65293078741937671250, \ 0.65293078741937671250, \ -0.65293078741937671250, \ 0.38109206736816036987, \ -0.38109206736816036987, \ 0.38109206736816036987, \ -0.38109206736816036987, \ 0.41413124714030785656, \ -0.41413124714030785656, \ 0.41413124714030785656, \ -0.41413124714030785656, \ 0.14311887945931867083, \ -0.14311887945931867083, \ 0.14311887945931867083, \ -0.14311887945931867083, \ 0.06816745760360433393, \ -0.06816745760360433393, \ 0.06816745760360433393, \ -0.06816745760360433393, \ 0.22977242422012536527, \ -0.22977242422012536527, \ 0.22977242422012536527, \ -0.22977242422012536527, \ 0.78211200270072955831, \ -0.78211200270072955831, \ 0.78211200270072955831, \ -0.78211200270072955831, \ 0.47646421490609353055, \ -0.47646421490609353055, \ 0.47646421490609353055, \ -0.47646421490609353055, \ 0.66550056762002873789, \ -0.66550056762002873789, \ 0.66550056762002873789, \ -0.66550056762002873789, \ 0.15755371600385464914, \ -0.15755371600385464914, \ 0.15755371600385464914, \ -0.15755371600385464914, \ 0.74760255490899130137, \ 0.13357335558335847736, \ -0.74760255490899130137, \ 0.13357335558335847736, \ 0.74760255490899130137, \ -0.13357335558335847736, \ -0.74760255490899130137, \ -0.13357335558335847736, \ 0.64024497237564748087, \ 0.36978998725981265805, \ -0.64024497237564748087, \ 0.36978998725981265805, \ 0.64024497237564748087, \ -0.36978998725981265805, \ -0.64024497237564748087, \ -0.36978998725981265805, \ 0.27725002720745439699, \ 0.65880359279798383909, \ -0.27725002720745439699, \ 0.65880359279798383909, \ 0.27725002720745439699, \ -0.65880359279798383909, \ -0.27725002720745439699, \ -0.65880359279798383909, \ 0.88435969563492811130, \ 0.76901445510268306993, \ -0.88435969563492811130, \ 0.76901445510268306993, \ 0.88435969563492811130, \ -0.76901445510268306993, \ -0.88435969563492811130, \ -0.76901445510268306993, \ 0.95432083454417460100, \ 0.27565292566365701132, \ -0.95432083454417460100, \ 0.27565292566365701132, \ 0.95432083454417460100, \ -0.27565292566365701132, \ -0.95432083454417460100, \ -0.27565292566365701132, \ 0.19610686376179234380, \ 0.48815934289407264535, \ -0.19610686376179234380, \ 0.48815934289407264535, \ 0.19610686376179234380, \ -0.48815934289407264535, \ -0.19610686376179234380, \ -0.48815934289407264535, \ 0.52539286886562275303, \ 0.90365402298313357576, \ -0.52539286886562275303, \ 0.90365402298313357576, \ 0.52539286886562275303, \ -0.90365402298313357576, \ -0.52539286886562275303, \ -0.90365402298313357576, \ 0.78710506457062645591, \ 0.53056669085425134380, \ -0.78710506457062645591, \ 0.53056669085425134380, \ 0.78710506457062645591, \ -0.53056669085425134380, \ -0.78710506457062645591, \ -0.53056669085425134380, \ 0.87305124922384047537, \ 0.58249614598785404151, \ -0.87305124922384047537, \ 0.58249614598785404151, \ 0.87305124922384047537, \ -0.58249614598785404151, \ -0.87305124922384047537, \ -0.58249614598785404151, \ 0.49539855010659772372, \ 0.21910184606142177333, \ -0.49539855010659772372, \ 0.21910184606142177333, \ 0.49539855010659772372, \ -0.21910184606142177333, \ -0.49539855010659772372, \ -0.21910184606142177333, \ 0.86957254282469464979, \ 0.30557223260338794990, \ -0.86957254282469464979, \ 0.30557223260338794990, \ 0.86957254282469464979, \ -0.30557223260338794990, \ -0.86957254282469464979, \ -0.30557223260338794990, \ 0.82556821539161207024, \ 0.18201665219265533713, \ -0.82556821539161207024, \ 0.18201665219265533713, \ 0.82556821539161207024, \ -0.18201665219265533713, \ -0.82556821539161207024, \ -0.18201665219265533713, \ 0.22633675831897015485, \ 0.35538499166679399233, \ -0.22633675831897015485, \ 0.35538499166679399233, \ 0.22633675831897015485, \ -0.35538499166679399233, \ -0.22633675831897015485, \ -0.35538499166679399233, \ 0.55136786560508410648, \ 0.74868759522365924131, \ -0.55136786560508410648, \ 0.74868759522365924131, \ 0.55136786560508410648, \ -0.74868759522365924131, \ -0.55136786560508410648, \ -0.74868759522365924131, \ 0.64168041273857601148, \ 0.25896549169892302267, \ -0.64168041273857601148, \ 0.25896549169892302267, \ 0.64168041273857601148, \ -0.25896549169892302267, \ -0.64168041273857601148, \ -0.25896549169892302267, \ 0.48623936010342988512, \ 0.11286859018565884027, \ -0.48623936010342988512, \ 0.11286859018565884027, \ 0.48623936010342988512, \ -0.11286859018565884027, \ -0.48623936010342988512, \ -0.11286859018565884027, \ 0.42728691837450794022, \ 0.62836164145805561976, \ -0.42728691837450794022, \ 0.62836164145805561976, \ 0.42728691837450794022, \ -0.62836164145805561976, \ -0.42728691837450794022, \ -0.62836164145805561976, \ 0.97870776397134839897, \ 0.73410552715894472620, \ -0.97870776397134839897, \ 0.73410552715894472620, \ 0.97870776397134839897, \ -0.73410552715894472620, \ -0.97870776397134839897, \ -0.73410552715894472620, \ 0.70585052586641572336, \ 0.41358916179473048658, \ -0.70585052586641572336, \ 0.41358916179473048658, \ 0.70585052586641572336, \ -0.41358916179473048658, \ -0.70585052586641572336, \ -0.41358916179473048658 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.95241408581244602072, \ 0.00000000000000000000, \ -0.95241408581244602072, \ 0.00000000000000000000, \ 0.08275692125030435775, \ 0.00000000000000000000, \ -0.08275692125030435775, \ 0.00000000000000000000, \ 0.26578545043127727032, \ 0.00000000000000000000, \ -0.26578545043127727032, \ 0.00000000000000000000, \ 0.81155940028479511827, \ 0.00000000000000000000, \ -0.81155940028479511827, \ 0.00000000000000000000, \ 0.35232799954016802424, \ 0.00000000000000000000, \ -0.35232799954016802424, \ 0.00000000000000000000, \ 0.60303771218972423984, \ 0.00000000000000000000, \ -0.60303771218972423984, \ 0.00000000000000000000, \ 0.78402604202159054125, \ 0.00000000000000000000, \ -0.78402604202159054125, \ 0.00000000000000000000, \ 0.49346472198646390561, \ 0.00000000000000000000, \ -0.49346472198646390561, \ 0.00000000000000000000, \ 0.35038751648906635294, \ 0.00000000000000000000, \ -0.35038751648906635294, \ 0.00000000000000000000, \ 0.00336404312107426752, \ 0.00000000000000000000, \ -0.00336404312107426752, \ 0.00000000000000000000, \ 0.43074512679067450405, \ 0.00000000000000000000, \ -0.43074512679067450405, \ 0.00000000000000000000, \ 0.59254801282947688890, \ 0.00000000000000000000, \ -0.59254801282947688890, \ 0.00000000000000000000, \ 0.22550686036585329552, \ 0.00000000000000000000, \ -0.22550686036585329552, \ 0.63975863740336180729, \ 0.63975863740336180729, \ -0.63975863740336180729, \ -0.63975863740336180729, \ 0.16463474879631256886, \ 0.16463474879631256886, \ -0.16463474879631256886, \ -0.16463474879631256886, \ 0.49303563319629611916, \ 0.49303563319629611916, \ -0.49303563319629611916, \ -0.49303563319629611916, \ 0.74791280396309745004, \ 0.74791280396309745004, \ -0.74791280396309745004, \ -0.74791280396309745004, \ 0.26251317864285966808, \ 0.26251317864285966808, \ -0.26251317864285966808, \ -0.26251317864285966808, \ 0.17484215589868074003, \ 0.17484215589868074003, \ -0.17484215589868074003, \ -0.17484215589868074003, \ 0.27602468785670569718, \ 0.27602468785670569718, \ -0.27602468785670569718, \ -0.27602468785670569718, \ 0.43512552408987620334, \ 0.43512552408987620334, \ -0.43512552408987620334, \ -0.43512552408987620334, \ 0.95307694157738065410, \ 0.95307694157738065410, \ -0.95307694157738065410, \ -0.95307694157738065410, \ 0.48425597905194911474, \ 0.48425597905194911474, \ -0.48425597905194911474, \ -0.48425597905194911474, \ 0.29381061843327571648, \ 0.29381061843327571648, \ -0.29381061843327571648, \ -0.29381061843327571648, \ 0.16057200503692023452, \ 0.16057200503692023452, \ -0.16057200503692023452, \ -0.16057200503692023452, \ 0.81014529214207364749, \ 0.81014529214207364749, \ -0.81014529214207364749, \ -0.81014529214207364749, \ 0.18009325754915589402, \ 0.18009325754915589402, \ -0.18009325754915589402, \ -0.18009325754915589402, \ 0.50136799407459931022, \ 0.50136799407459931022, \ -0.50136799407459931022, \ -0.50136799407459931022, \ 0.92284407855436589863, \ 0.92284407855436589863, \ -0.92284407855436589863, \ -0.92284407855436589863, \ 0.32077249570607596629, \ 0.32077249570607596629, \ -0.32077249570607596629, \ -0.32077249570607596629, \ 0.02145401504974505866, \ 0.02145401504974505866, \ -0.02145401504974505866, \ -0.02145401504974505866, \ 0.65293078741937671250, \ 0.65293078741937671250, \ -0.65293078741937671250, \ -0.65293078741937671250, \ 0.38109206736816036987, \ 0.38109206736816036987, \ -0.38109206736816036987, \ -0.38109206736816036987, \ 0.41413124714030785656, \ 0.41413124714030785656, \ -0.41413124714030785656, \ -0.41413124714030785656, \ 0.14311887945931867083, \ 0.14311887945931867083, \ -0.14311887945931867083, \ -0.14311887945931867083, \ 0.06816745760360433393, \ 0.06816745760360433393, \ -0.06816745760360433393, \ -0.06816745760360433393, \ 0.22977242422012536527, \ 0.22977242422012536527, \ -0.22977242422012536527, \ -0.22977242422012536527, \ 0.78211200270072955831, \ 0.78211200270072955831, \ -0.78211200270072955831, \ -0.78211200270072955831, \ 0.47646421490609353055, \ 0.47646421490609353055, \ -0.47646421490609353055, \ -0.47646421490609353055, \ 0.66550056762002873789, \ 0.66550056762002873789, \ -0.66550056762002873789, \ -0.66550056762002873789, \ 0.15755371600385464914, \ 0.15755371600385464914, \ -0.15755371600385464914, \ -0.15755371600385464914, \ 0.13357335558335847736, \ 0.74760255490899130137, \ 0.13357335558335847736, \ -0.74760255490899130137, \ -0.13357335558335847736, \ 0.74760255490899130137, \ -0.13357335558335847736, \ -0.74760255490899130137, \ 0.36978998725981265805, \ 0.64024497237564748087, \ 0.36978998725981265805, \ -0.64024497237564748087, \ -0.36978998725981265805, \ 0.64024497237564748087, \ -0.36978998725981265805, \ -0.64024497237564748087, \ 0.65880359279798383909, \ 0.27725002720745439699, \ 0.65880359279798383909, \ -0.27725002720745439699, \ -0.65880359279798383909, \ 0.27725002720745439699, \ -0.65880359279798383909, \ -0.27725002720745439699, \ 0.76901445510268306993, \ 0.88435969563492811130, \ 0.76901445510268306993, \ -0.88435969563492811130, \ -0.76901445510268306993, \ 0.88435969563492811130, \ -0.76901445510268306993, \ -0.88435969563492811130, \ 0.27565292566365701132, \ 0.95432083454417460100, \ 0.27565292566365701132, \ -0.95432083454417460100, \ -0.27565292566365701132, \ 0.95432083454417460100, \ -0.27565292566365701132, \ -0.95432083454417460100, \ 0.48815934289407264535, \ 0.19610686376179234380, \ 0.48815934289407264535, \ -0.19610686376179234380, \ -0.48815934289407264535, \ 0.19610686376179234380, \ -0.48815934289407264535, \ -0.19610686376179234380, \ 0.90365402298313357576, \ 0.52539286886562275303, \ 0.90365402298313357576, \ -0.52539286886562275303, \ -0.90365402298313357576, \ 0.52539286886562275303, \ -0.90365402298313357576, \ -0.52539286886562275303, \ 0.53056669085425134380, \ 0.78710506457062645591, \ 0.53056669085425134380, \ -0.78710506457062645591, \ -0.53056669085425134380, \ 0.78710506457062645591, \ -0.53056669085425134380, \ -0.78710506457062645591, \ 0.58249614598785404151, \ 0.87305124922384047537, \ 0.58249614598785404151, \ -0.87305124922384047537, \ -0.58249614598785404151, \ 0.87305124922384047537, \ -0.58249614598785404151, \ -0.87305124922384047537, \ 0.21910184606142177333, \ 0.49539855010659772372, \ 0.21910184606142177333, \ -0.49539855010659772372, \ -0.21910184606142177333, \ 0.49539855010659772372, \ -0.21910184606142177333, \ -0.49539855010659772372, \ 0.30557223260338794990, \ 0.86957254282469464979, \ 0.30557223260338794990, \ -0.86957254282469464979, \ -0.30557223260338794990, \ 0.86957254282469464979, \ -0.30557223260338794990, \ -0.86957254282469464979, \ 0.18201665219265533713, \ 0.82556821539161207024, \ 0.18201665219265533713, \ -0.82556821539161207024, \ -0.18201665219265533713, \ 0.82556821539161207024, \ -0.18201665219265533713, \ -0.82556821539161207024, \ 0.35538499166679399233, \ 0.22633675831897015485, \ 0.35538499166679399233, \ -0.22633675831897015485, \ -0.35538499166679399233, \ 0.22633675831897015485, \ -0.35538499166679399233, \ -0.22633675831897015485, \ 0.74868759522365924131, \ 0.55136786560508410648, \ 0.74868759522365924131, \ -0.55136786560508410648, \ -0.74868759522365924131, \ 0.55136786560508410648, \ -0.74868759522365924131, \ -0.55136786560508410648, \ 0.25896549169892302267, \ 0.64168041273857601148, \ 0.25896549169892302267, \ -0.64168041273857601148, \ -0.25896549169892302267, \ 0.64168041273857601148, \ -0.25896549169892302267, \ -0.64168041273857601148, \ 0.11286859018565884027, \ 0.48623936010342988512, \ 0.11286859018565884027, \ -0.48623936010342988512, \ -0.11286859018565884027, \ 0.48623936010342988512, \ -0.11286859018565884027, \ -0.48623936010342988512, \ 0.62836164145805561976, \ 0.42728691837450794022, \ 0.62836164145805561976, \ -0.42728691837450794022, \ -0.62836164145805561976, \ 0.42728691837450794022, \ -0.62836164145805561976, \ -0.42728691837450794022, \ 0.73410552715894472620, \ 0.97870776397134839897, \ 0.73410552715894472620, \ -0.97870776397134839897, \ -0.73410552715894472620, \ 0.97870776397134839897, \ -0.73410552715894472620, \ -0.97870776397134839897, \ 0.41358916179473048658, \ 0.70585052586641572336, \ 0.41358916179473048658, \ -0.70585052586641572336, \ -0.41358916179473048658, \ 0.70585052586641572336, \ -0.41358916179473048658, \ -0.70585052586641572336 ] ) z = np.array ( [ \ 0.97220323387036922114, \ 0.63870352926681406291, \ 0.68020043208055336326, \ 0.04194980824924493534, \ 0.04194980824924493534, \ 0.04194980824924493534, \ 0.04194980824924493534, \ 0.90141183204156405395, \ 0.90141183204156405395, \ 0.90141183204156405395, \ 0.90141183204156405395, \ 0.68432529322768964608, \ 0.68432529322768964608, \ 0.68432529322768964608, \ 0.68432529322768964608, \ 0.00000008245324867689, \ 0.00000008245324867689, \ 0.00000008245324867689, \ 0.00000008245324867689, \ 0.55417390873649197136, \ 0.55417390873649197136, \ 0.55417390873649197136, \ 0.55417390873649197136, \ 0.36258805988768089135, \ 0.36258805988768089135, \ 0.36258805988768089135, \ 0.36258805988768089135, \ 0.13875708503462674814, \ 0.13875708503462674814, \ 0.13875708503462674814, \ 0.13875708503462674814, \ 0.24260167486456202246, \ 0.24260167486456202246, \ 0.24260167486456202246, \ 0.24260167486456202246, \ 0.40130775806887936108, \ 0.40130775806887936108, \ 0.40130775806887936108, \ 0.40130775806887936108, \ 0.38152973269372325582, \ 0.38152973269372325582, \ 0.38152973269372325582, \ 0.38152973269372325582, \ 0.11901456915448617446, \ 0.11901456915448617446, \ 0.11901456915448617446, \ 0.11901456915448617446, \ 0.04928012549325393871, \ 0.04928012549325393871, \ 0.04928012549325393871, \ 0.04928012549325393871, \ 0.76206391519358240849, \ 0.76206391519358240849, \ 0.76206391519358240849, \ 0.76206391519358240849, \ 0.31153469497121605292, \ 0.31153469497121605292, \ 0.31153469497121605292, \ 0.31153469497121605292, \ 0.25650991726217964306, \ 0.25650991726217964306, \ 0.25650991726217964306, \ 0.25650991726217964306, \ 0.07449733603189459541, \ 0.07449733603189459541, \ 0.07449733603189459541, \ 0.07449733603189459541, \ 0.00130788548084566922, \ 0.00130788548084566922, \ 0.00130788548084566922, \ 0.00130788548084566922, \ 0.52858580218461959088, \ 0.52858580218461959088, \ 0.52858580218461959088, \ 0.52858580218461959088, \ 0.00955221072473505343, \ 0.00955221072473505343, \ 0.00955221072473505343, \ 0.00955221072473505343, \ 0.34142989905969745035, \ 0.34142989905969745035, \ 0.34142989905969745035, \ 0.34142989905969745035, \ 0.00027022925967801637, \ 0.00027022925967801637, \ 0.00027022925967801637, \ 0.00027022925967801637, \ 0.04692242455320395911, \ 0.04692242455320395911, \ 0.04692242455320395911, \ 0.04692242455320395911, \ 0.34449713283505384309, \ 0.34449713283505384309, \ 0.34449713283505384309, \ 0.34449713283505384309, \ 0.66811923014208407512, \ 0.66811923014208407512, \ 0.66811923014208407512, \ 0.66811923014208407512, \ 0.67391287157124502016, \ 0.67391287157124502016, \ 0.67391287157124502016, \ 0.67391287157124502016, \ 0.03437584591482227558, \ 0.03437584591482227558, \ 0.03437584591482227558, \ 0.03437584591482227558, \ 0.15542872578297051156, \ 0.15542872578297051156, \ 0.15542872578297051156, \ 0.15542872578297051156, \ 0.26971828733855934823, \ 0.26971828733855934823, \ 0.26971828733855934823, \ 0.26971828733855934823, \ 0.01181428825288092545, \ 0.01181428825288092545, \ 0.01181428825288092545, \ 0.01181428825288092545, \ 0.06366317285532444026, \ 0.06366317285532444026, \ 0.06366317285532444026, \ 0.06366317285532444026, \ 0.06762724457801919109, \ 0.06762724457801919109, \ 0.06762724457801919109, \ 0.06762724457801919109, \ 0.20149664605408518225, \ 0.20149664605408518225, \ 0.20149664605408518225, \ 0.20149664605408518225, \ 0.48586744666719888786, \ 0.48586744666719888786, \ 0.48586744666719888786, \ 0.48586744666719888786, \ 0.19071052464250978775, \ 0.19071052464250978775, \ 0.19071052464250978775, \ 0.19071052464250978775, \ 0.51037375853206956577, \ 0.51037375853206956577, \ 0.51037375853206956577, \ 0.51037375853206956577, \ 0.80351245513246505325, \ 0.80351245513246505325, \ 0.80351245513246505325, \ 0.80351245513246505325, \ 0.04121355156423638089, \ 0.04121355156423638089, \ 0.04121355156423638089, \ 0.04121355156423638089, \ 0.17760016176122497833, \ 0.17760016176122497833, \ 0.17760016176122497833, \ 0.17760016176122497833, \ 0.48439012439328182902, \ 0.48439012439328182902, \ 0.48439012439328182902, \ 0.48439012439328182902, \ 0.04796979480806326523, \ 0.04796979480806326523, \ 0.04796979480806326523, \ 0.04796979480806326523, \ 0.80108123458344093759, \ 0.80108123458344093759, \ 0.80108123458344093759, \ 0.80108123458344093759, \ 0.24101422703502115019, \ 0.24101422703502115019, \ 0.24101422703502115019, \ 0.24101422703502115019, \ 0.24101422703502115019, \ 0.24101422703502115019, \ 0.24101422703502115019, \ 0.24101422703502115019, \ 0.01069891762813818432, \ 0.01069891762813818432, \ 0.01069891762813818432, \ 0.01069891762813818432, \ 0.01069891762813818432, \ 0.01069891762813818432, \ 0.01069891762813818432, \ 0.01069891762813818432, \ 0.23988631383389671936, \ 0.23988631383389671936, \ 0.23988631383389671936, \ 0.23988631383389671936, \ 0.23988631383389671936, \ 0.23988631383389671936, \ 0.23988631383389671936, \ 0.23988631383389671936, \ 0.08514410320936129095, \ 0.08514410320936129095, \ 0.08514410320936129095, \ 0.08514410320936129095, \ 0.08514410320936129095, \ 0.08514410320936129095, \ 0.08514410320936129095, \ 0.08514410320936129095, \ 0.00847110534891616467, \ 0.00847110534891616467, \ 0.00847110534891616467, \ 0.00847110534891616467, \ 0.00847110534891616467, \ 0.00847110534891616467, \ 0.00847110534891616467, \ 0.00847110534891616467, \ 0.49562245065536153499, \ 0.49562245065536153499, \ 0.49562245065536153499, \ 0.49562245065536153499, \ 0.49562245065536153499, \ 0.49562245065536153499, \ 0.49562245065536153499, \ 0.49562245065536153499, \ 0.04642983560786508729, \ 0.04642983560786508729, \ 0.04642983560786508729, \ 0.04642983560786508729, \ 0.04642983560786508729, \ 0.04642983560786508729, \ 0.04642983560786508729, \ 0.04642983560786508729, \ 0.19656151852896430743, \ 0.19656151852896430743, \ 0.19656151852896430743, \ 0.19656151852896430743, \ 0.19656151852896430743, \ 0.19656151852896430743, \ 0.19656151852896430743, \ 0.19656151852896430743, \ 0.00687572309208568308, \ 0.00687572309208568308, \ 0.00687572309208568308, \ 0.00687572309208568308, \ 0.00687572309208568308, \ 0.00687572309208568308, \ 0.00687572309208568308, \ 0.00687572309208568308, \ 0.38670513013019941484, \ 0.38670513013019941484, \ 0.38670513013019941484, \ 0.38670513013019941484, \ 0.38670513013019941484, \ 0.38670513013019941484, \ 0.38670513013019941484, \ 0.38670513013019941484, \ 0.10896106798490250156, \ 0.10896106798490250156, \ 0.10896106798490250156, \ 0.10896106798490250156, \ 0.10896106798490250156, \ 0.10896106798490250156, \ 0.10896106798490250156, \ 0.10896106798490250156, \ 0.04416884971526349735, \ 0.04416884971526349735, \ 0.04416884971526349735, \ 0.04416884971526349735, \ 0.04416884971526349735, \ 0.04416884971526349735, \ 0.04416884971526349735, \ 0.04416884971526349735, \ 0.62489254847899400325, \ 0.62489254847899400325, \ 0.62489254847899400325, \ 0.62489254847899400325, \ 0.62489254847899400325, \ 0.62489254847899400325, \ 0.62489254847899400325, \ 0.62489254847899400325, \ 0.11727329599993376041, \ 0.11727329599993376041, \ 0.11727329599993376041, \ 0.11727329599993376041, \ 0.11727329599993376041, \ 0.11727329599993376041, \ 0.11727329599993376041, \ 0.11727329599993376041, \ 0.11958436259454885420, \ 0.11958436259454885420, \ 0.11958436259454885420, \ 0.11958436259454885420, \ 0.11958436259454885420, \ 0.11958436259454885420, \ 0.11958436259454885420, \ 0.11958436259454885420, \ 0.01562091696416078104, \ 0.01562091696416078104, \ 0.01562091696416078104, \ 0.01562091696416078104, \ 0.01562091696416078104, \ 0.01562091696416078104, \ 0.01562091696416078104, \ 0.01562091696416078104, \ 0.35132620557004257122, \ 0.35132620557004257122, \ 0.35132620557004257122, \ 0.35132620557004257122, \ 0.35132620557004257122, \ 0.35132620557004257122, \ 0.35132620557004257122, \ 0.35132620557004257122, \ 0.01323405399603627339, \ 0.01323405399603627339, \ 0.01323405399603627339, \ 0.01323405399603627339, \ 0.01323405399603627339, \ 0.01323405399603627339, \ 0.01323405399603627339, \ 0.01323405399603627339, \ 0.02986233869137579211, \ 0.02986233869137579211, \ 0.02986233869137579211, \ 0.02986233869137579211, \ 0.02986233869137579211, \ 0.02986233869137579211, \ 0.02986233869137579211, \ 0.02986233869137579211 ] ) w= np.array ( [ \ 0.00012216821078901854, \ 0.00563943629581533951, \ 0.00187116838043227779, \ 0.00087900554061397717, \ 0.00087900554061397717, \ 0.00087900554061397717, \ 0.00087900554061397717, \ 0.00063973688323901037, \ 0.00063973688323901037, \ 0.00063973688323901037, \ 0.00063973688323901037, \ 0.00191942477958428285, \ 0.00191942477958428285, \ 0.00191942477958428285, \ 0.00191942477958428285, \ 0.00108856800183791767, \ 0.00108856800183791767, \ 0.00108856800183791767, \ 0.00108856800183791767, \ 0.00579178348482820276, \ 0.00579178348482820276, \ 0.00579178348482820276, \ 0.00579178348482820276, \ 0.00333567983247391557, \ 0.00333567983247391557, \ 0.00333567983247391557, \ 0.00333567983247391557, \ 0.00483993401414843216, \ 0.00483993401414843216, \ 0.00483993401414843216, \ 0.00483993401414843216, \ 0.01171223275540323253, \ 0.01171223275540323253, \ 0.01171223275540323253, \ 0.01171223275540323253, \ 0.00781803283741232084, \ 0.00781803283741232084, \ 0.00781803283741232084, \ 0.00781803283741232084, \ 0.00316389891636655388, \ 0.00316389891636655388, \ 0.00316389891636655388, \ 0.00316389891636655388, \ 0.00813627882273969955, \ 0.00813627882273969955, \ 0.00813627882273969955, \ 0.00813627882273969955, \ 0.00471982615752600254, \ 0.00471982615752600254, \ 0.00471982615752600254, \ 0.00471982615752600254, \ 0.00096237134938021330, \ 0.00096237134938021330, \ 0.00096237134938021330, \ 0.00096237134938021330, \ 0.00162378774013503748, \ 0.00162378774013503748, \ 0.00162378774013503748, \ 0.00162378774013503748, \ 0.00871345927599746599, \ 0.00871345927599746599, \ 0.00871345927599746599, \ 0.00871345927599746599, \ 0.00412008618466326321, \ 0.00412008618466326321, \ 0.00412008618466326321, \ 0.00412008618466326321, \ 0.00052206472289359268, \ 0.00052206472289359268, \ 0.00052206472289359268, \ 0.00052206472289359268, \ 0.00389716456343351799, \ 0.00389716456343351799, \ 0.00389716456343351799, \ 0.00389716456343351799, \ 0.00222992187534444422, \ 0.00222992187534444422, \ 0.00222992187534444422, \ 0.00222992187534444422, \ 0.00941806762258396400, \ 0.00941806762258396400, \ 0.00941806762258396400, \ 0.00941806762258396400, \ 0.00066158322303103113, \ 0.00066158322303103113, \ 0.00066158322303103113, \ 0.00066158322303103113, \ 0.00010739422189895962, \ 0.00010739422189895962, \ 0.00010739422189895962, \ 0.00010739422189895962, \ 0.00303147852588211194, \ 0.00303147852588211194, \ 0.00303147852588211194, \ 0.00303147852588211194, \ 0.00081932641066923071, \ 0.00081932641066923071, \ 0.00081932641066923071, \ 0.00081932641066923071, \ 0.00465121449070608067, \ 0.00465121449070608067, \ 0.00465121449070608067, \ 0.00465121449070608067, \ 0.00167606716811515987, \ 0.00167606716811515987, \ 0.00167606716811515987, \ 0.00167606716811515987, \ 0.00825768957465656227, \ 0.00825768957465656227, \ 0.00825768957465656227, \ 0.00825768957465656227, \ 0.00397545859544364086, \ 0.00397545859544364086, \ 0.00397545859544364086, \ 0.00397545859544364086, \ 0.00051722520547986095, \ 0.00051722520547986095, \ 0.00051722520547986095, \ 0.00051722520547986095, \ 0.00624136348038179748, \ 0.00624136348038179748, \ 0.00624136348038179748, \ 0.00624136348038179748, \ 0.00249954122416236671, \ 0.00249954122416236671, \ 0.00249954122416236671, \ 0.00249954122416236671, \ 0.00344134582405346756, \ 0.00344134582405346756, \ 0.00344134582405346756, \ 0.00344134582405346756, \ 0.00373085764189791565, \ 0.00373085764189791565, \ 0.00373085764189791565, \ 0.00373085764189791565, \ 0.00985379501780648571, \ 0.00985379501780648571, \ 0.00985379501780648571, \ 0.00985379501780648571, \ 0.00736757952028449341, \ 0.00736757952028449341, \ 0.00736757952028449341, \ 0.00736757952028449341, \ 0.00178048730560625978, \ 0.00178048730560625978, \ 0.00178048730560625978, \ 0.00178048730560625978, \ 0.00242313168519621295, \ 0.00242313168519621295, \ 0.00242313168519621295, \ 0.00242313168519621295, \ 0.00105734008948304265, \ 0.00105734008948304265, \ 0.00105734008948304265, \ 0.00105734008948304265, \ 0.00145036343491798387, \ 0.00145036343491798387, \ 0.00145036343491798387, \ 0.00145036343491798387, \ 0.00271057993574526021, \ 0.00271057993574526021, \ 0.00271057993574526021, \ 0.00271057993574526021, \ 0.00112014566884451267, \ 0.00112014566884451267, \ 0.00112014566884451267, \ 0.00112014566884451267, \ 0.00120917104359697324, \ 0.00120917104359697324, \ 0.00120917104359697324, \ 0.00120917104359697324, \ 0.00120917104359697324, \ 0.00120917104359697324, \ 0.00120917104359697324, \ 0.00120917104359697324, \ 0.00162471395073617649, \ 0.00162471395073617649, \ 0.00162471395073617649, \ 0.00162471395073617649, \ 0.00162471395073617649, \ 0.00162471395073617649, \ 0.00162471395073617649, \ 0.00162471395073617649, \ 0.00620858966914663961, \ 0.00620858966914663961, \ 0.00620858966914663961, \ 0.00620858966914663961, \ 0.00620858966914663961, \ 0.00620858966914663961, \ 0.00620858966914663961, \ 0.00620858966914663961, \ 0.00135724577802302663, \ 0.00135724577802302663, \ 0.00135724577802302663, \ 0.00135724577802302663, \ 0.00135724577802302663, \ 0.00135724577802302663, \ 0.00135724577802302663, \ 0.00135724577802302663, \ 0.00077688230182242947, \ 0.00077688230182242947, \ 0.00077688230182242947, \ 0.00077688230182242947, \ 0.00077688230182242947, \ 0.00077688230182242947, \ 0.00077688230182242947, \ 0.00077688230182242947, \ 0.00190538850038805656, \ 0.00190538850038805656, \ 0.00190538850038805656, \ 0.00190538850038805656, \ 0.00190538850038805656, \ 0.00190538850038805656, \ 0.00190538850038805656, \ 0.00190538850038805656, \ 0.00183635585567423158, \ 0.00183635585567423158, \ 0.00183635585567423158, \ 0.00183635585567423158, \ 0.00183635585567423158, \ 0.00183635585567423158, \ 0.00183635585567423158, \ 0.00183635585567423158, \ 0.00173312265591197071, \ 0.00173312265591197071, \ 0.00173312265591197071, \ 0.00173312265591197071, \ 0.00173312265591197071, \ 0.00173312265591197071, \ 0.00173312265591197071, \ 0.00173312265591197071, \ 0.00087558681440168869, \ 0.00087558681440168869, \ 0.00087558681440168869, \ 0.00087558681440168869, \ 0.00087558681440168869, \ 0.00087558681440168869, \ 0.00087558681440168869, \ 0.00087558681440168869, \ 0.00529919935281060114, \ 0.00529919935281060114, \ 0.00529919935281060114, \ 0.00529919935281060114, \ 0.00529919935281060114, \ 0.00529919935281060114, \ 0.00529919935281060114, \ 0.00529919935281060114, \ 0.00190923140339424222, \ 0.00190923140339424222, \ 0.00190923140339424222, \ 0.00190923140339424222, \ 0.00190923140339424222, \ 0.00190923140339424222, \ 0.00190923140339424222, \ 0.00190923140339424222, \ 0.00333270329648946212, \ 0.00333270329648946212, \ 0.00333270329648946212, \ 0.00333270329648946212, \ 0.00333270329648946212, \ 0.00333270329648946212, \ 0.00333270329648946212, \ 0.00333270329648946212, \ 0.00137258273942558089, \ 0.00137258273942558089, \ 0.00137258273942558089, \ 0.00137258273942558089, \ 0.00137258273942558089, \ 0.00137258273942558089, \ 0.00137258273942558089, \ 0.00137258273942558089, \ 0.00440562895172808174, \ 0.00440562895172808174, \ 0.00440562895172808174, \ 0.00440562895172808174, \ 0.00440562895172808174, \ 0.00440562895172808174, \ 0.00440562895172808174, \ 0.00440562895172808174, \ 0.00690265770456989416, \ 0.00690265770456989416, \ 0.00690265770456989416, \ 0.00690265770456989416, \ 0.00690265770456989416, \ 0.00690265770456989416, \ 0.00690265770456989416, \ 0.00690265770456989416, \ 0.00202734469527626228, \ 0.00202734469527626228, \ 0.00202734469527626228, \ 0.00202734469527626228, \ 0.00202734469527626228, \ 0.00202734469527626228, \ 0.00202734469527626228, \ 0.00202734469527626228, \ 0.00204643595334019031, \ 0.00204643595334019031, \ 0.00204643595334019031, \ 0.00204643595334019031, \ 0.00204643595334019031, \ 0.00204643595334019031, \ 0.00204643595334019031, \ 0.00204643595334019031, \ 0.00034532641662137929, \ 0.00034532641662137929, \ 0.00034532641662137929, \ 0.00034532641662137929, \ 0.00034532641662137929, \ 0.00034532641662137929, \ 0.00034532641662137929, \ 0.00034532641662137929, \ 0.00242508950332979241, \ 0.00242508950332979241, \ 0.00242508950332979241, \ 0.00242508950332979241, \ 0.00242508950332979241, \ 0.00242508950332979241, \ 0.00242508950332979241, \ 0.00242508950332979241 ] ) return x, y, z, w def rule18 ( ): #*****************************************************************************80 # ## rule18() returns the pyramid quadrature rule of precision 18. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.73869275831950009792, \ 0.00000000000000000000, \ -0.73869275831950009792, \ 0.00000000000000000000, \ 0.76806657302952874300, \ 0.00000000000000000000, \ -0.76806657302952874300, \ 0.00000000000000000000, \ 0.31673944809898013641, \ 0.00000000000000000000, \ -0.31673944809898013641, \ 0.00000000000000000000, \ 0.61877572218072185439, \ 0.00000000000000000000, \ -0.61877572218072185439, \ 0.00000000000000000000, \ 0.37235294402955443349, \ 0.00000000000000000000, \ -0.37235294402955443349, \ 0.00000000000000000000, \ 0.50387193570782862206, \ 0.00000000000000000000, \ -0.50387193570782862206, \ 0.00000000000000000000, \ 0.72207836507269651527, \ 0.00000000000000000000, \ -0.72207836507269651527, \ 0.00000000000000000000, \ 0.39403113359582681019, \ 0.00000000000000000000, \ -0.39403113359582681019, \ 0.00000000000000000000, \ 0.11819479806124476295, \ 0.00000000000000000000, \ -0.11819479806124476295, \ 0.00000000000000000000, \ 0.51179862044264223808, \ 0.00000000000000000000, \ -0.51179862044264223808, \ 0.00000000000000000000, \ 0.09344056049843052492, \ 0.00000000000000000000, \ -0.09344056049843052492, \ 0.00000000000000000000, \ 0.97786305288383967849, \ 0.00000000000000000000, \ -0.97786305288383967849, \ 0.00000000000000000000, \ 0.26893118028825491184, \ 0.00000000000000000000, \ -0.26893118028825491184, \ 0.00000000000000000000, \ 0.18588876717193755783, \ 0.00000000000000000000, \ -0.18588876717193755783, \ 0.00000000000000000000, \ 0.88032062123229137818, \ -0.88032062123229137818, \ 0.88032062123229137818, \ -0.88032062123229137818, \ 0.68145212136761557087, \ -0.68145212136761557087, \ 0.68145212136761557087, \ -0.68145212136761557087, \ 0.49699036434274163065, \ -0.49699036434274163065, \ 0.49699036434274163065, \ -0.49699036434274163065, \ 0.30634018082228819946, \ -0.30634018082228819946, \ 0.30634018082228819946, \ -0.30634018082228819946, \ 0.58539966455385050725, \ -0.58539966455385050725, \ 0.58539966455385050725, \ -0.58539966455385050725, \ 0.77694395476943478585, \ -0.77694395476943478585, \ 0.77694395476943478585, \ -0.77694395476943478585, \ 0.18695368401965414829, \ -0.18695368401965414829, \ 0.18695368401965414829, \ -0.18695368401965414829, \ 0.64402844061291575350, \ -0.64402844061291575350, \ 0.64402844061291575350, \ -0.64402844061291575350, \ 0.19939684409397287479, \ -0.19939684409397287479, \ 0.19939684409397287479, \ -0.19939684409397287479, \ 0.49151662722959021945, \ -0.49151662722959021945, \ 0.49151662722959021945, \ -0.49151662722959021945, \ 0.21971883736597888626, \ -0.21971883736597888626, \ 0.21971883736597888626, \ -0.21971883736597888626, \ 0.38181860275292400786, \ -0.38181860275292400786, \ 0.38181860275292400786, \ -0.38181860275292400786, \ 0.13233574436496933768, \ -0.13233574436496933768, \ 0.13233574436496933768, \ -0.13233574436496933768, \ 0.26434906680031583504, \ -0.26434906680031583504, \ 0.26434906680031583504, \ -0.26434906680031583504, \ 0.26259016722585765136, \ -0.26259016722585765136, \ 0.26259016722585765136, \ -0.26259016722585765136, \ 0.63683049968859806178, \ -0.63683049968859806178, \ 0.63683049968859806178, \ -0.63683049968859806178, \ 0.50333230035733345087, \ -0.50333230035733345087, \ 0.50333230035733345087, \ -0.50333230035733345087, \ 0.43053066487698737896, \ -0.43053066487698737896, \ 0.43053066487698737896, \ -0.43053066487698737896, \ 0.44121177996231647489, \ -0.44121177996231647489, \ 0.44121177996231647489, \ -0.44121177996231647489, \ 0.12338526534910826404, \ -0.12338526534910826404, \ 0.12338526534910826404, \ -0.12338526534910826404, \ 0.28196466746787440805, \ -0.28196466746787440805, \ 0.28196466746787440805, \ -0.28196466746787440805, \ 0.12302065942509179952, \ -0.12302065942509179952, \ 0.12302065942509179952, \ -0.12302065942509179952, \ 0.96995340856169265376, \ -0.96995340856169265376, \ 0.96995340856169265376, \ -0.96995340856169265376, \ 0.15367597423015844083, \ -0.15367597423015844083, \ 0.15367597423015844083, \ -0.15367597423015844083, \ 0.32324916002943732130, \ -0.32324916002943732130, \ 0.32324916002943732130, \ -0.32324916002943732130, \ 0.07979061002341172881, \ -0.07979061002341172881, \ 0.07979061002341172881, \ -0.07979061002341172881, \ 0.05572751587573096521, \ -0.05572751587573096521, \ 0.05572751587573096521, \ -0.05572751587573096521, \ 0.80407180079417317486, \ -0.80407180079417317486, \ 0.80407180079417317486, \ -0.80407180079417317486, \ 0.10630794929321137066, \ -0.10630794929321137066, \ 0.10630794929321137066, \ -0.10630794929321137066, \ 0.14968116552008028930, \ -0.14968116552008028930, \ 0.14968116552008028930, \ -0.14968116552008028930, \ 0.72179802358977040999, \ -0.72179802358977040999, \ 0.72179802358977040999, \ -0.72179802358977040999, \ 0.81797170822487763608, \ 0.64320215485058829241, \ -0.81797170822487763608, \ 0.64320215485058829241, \ 0.81797170822487763608, \ -0.64320215485058829241, \ -0.81797170822487763608, \ -0.64320215485058829241, \ 0.45477772302529712034, \ 0.16636418997995866542, \ -0.45477772302529712034, \ 0.16636418997995866542, \ 0.45477772302529712034, \ -0.16636418997995866542, \ -0.45477772302529712034, \ -0.16636418997995866542, \ 0.22077509021471022899, \ 0.64919419286301172090, \ -0.22077509021471022899, \ 0.64919419286301172090, \ 0.22077509021471022899, \ -0.64919419286301172090, \ -0.22077509021471022899, \ -0.64919419286301172090, \ 0.85849144377065222944, \ 0.26442320916257716634, \ -0.85849144377065222944, \ 0.26442320916257716634, \ 0.85849144377065222944, \ -0.26442320916257716634, \ -0.85849144377065222944, \ -0.26442320916257716634, \ 0.19087247051624386951, \ 0.45655985846318541954, \ -0.19087247051624386951, \ 0.45655985846318541954, \ 0.19087247051624386951, \ -0.45655985846318541954, \ -0.19087247051624386951, \ -0.45655985846318541954, \ 0.37787816613860053527, \ 0.66406293254753101518, \ -0.37787816613860053527, \ 0.66406293254753101518, \ 0.37787816613860053527, \ -0.66406293254753101518, \ -0.37787816613860053527, \ -0.66406293254753101518, \ 0.89395556646395457623, \ 0.17283329178347239807, \ -0.89395556646395457623, \ 0.17283329178347239807, \ 0.89395556646395457623, \ -0.17283329178347239807, \ -0.89395556646395457623, \ -0.17283329178347239807, \ 0.40991415053935187363, \ 0.05003413197772252352, \ -0.40991415053935187363, \ 0.05003413197772252352, \ 0.40991415053935187363, \ -0.05003413197772252352, \ -0.40991415053935187363, \ -0.05003413197772252352, \ 0.93198108654420652730, \ 0.10662173986061880548, \ -0.93198108654420652730, \ 0.10662173986061880548, \ 0.93198108654420652730, \ -0.10662173986061880548, \ -0.93198108654420652730, \ -0.10662173986061880548, \ 0.28018220607206512085, \ 0.84993195986801317598, \ -0.28018220607206512085, \ 0.84993195986801317598, \ 0.28018220607206512085, \ -0.84993195986801317598, \ -0.28018220607206512085, \ -0.84993195986801317598, \ 0.57728165413613941048, \ 0.46201429744731292715, \ -0.57728165413613941048, \ 0.46201429744731292715, \ 0.57728165413613941048, \ -0.46201429744731292715, \ -0.57728165413613941048, \ -0.46201429744731292715, \ 0.84451580808527704214, \ 0.61756791755060624904, \ -0.84451580808527704214, \ 0.61756791755060624904, \ 0.84451580808527704214, \ -0.61756791755060624904, \ -0.84451580808527704214, \ -0.61756791755060624904, \ 0.52941572893811861267, \ 0.23348533584682021336, \ -0.52941572893811861267, \ 0.23348533584682021336, \ 0.52941572893811861267, \ -0.23348533584682021336, \ -0.52941572893811861267, \ -0.23348533584682021336, \ 0.92827521801894674613, \ 0.67941786279817284466, \ -0.92827521801894674613, \ 0.67941786279817284466, \ 0.92827521801894674613, \ -0.67941786279817284466, \ -0.92827521801894674613, \ -0.67941786279817284466, \ 0.96836516384095050469, \ 0.46144251438466377113, \ -0.96836516384095050469, \ 0.46144251438466377113, \ 0.96836516384095050469, \ -0.46144251438466377113, \ -0.96836516384095050469, \ -0.46144251438466377113, \ 0.16744571840030086918, \ 0.31430414794159466929, \ -0.16744571840030086918, \ 0.31430414794159466929, \ 0.16744571840030086918, \ -0.31430414794159466929, \ -0.16744571840030086918, \ -0.31430414794159466929, \ 0.49232718454496093852, \ 0.73988842925403419670, \ -0.49232718454496093852, \ 0.73988842925403419670, \ 0.49232718454496093852, \ -0.73988842925403419670, \ -0.49232718454496093852, \ -0.73988842925403419670, \ 0.85659974228270108210, \ 0.54061065617200576572, \ -0.85659974228270108210, \ 0.54061065617200576572, \ 0.85659974228270108210, \ -0.54061065617200576572, \ -0.85659974228270108210, \ -0.54061065617200576572, \ 0.26702277361260906563, \ 0.57531393529153806998, \ -0.26702277361260906563, \ 0.57531393529153806998, \ 0.26702277361260906563, \ -0.57531393529153806998, \ -0.26702277361260906563, \ -0.57531393529153806998, \ 0.41506457665342233465, \ 0.71731018735152574095, \ -0.41506457665342233465, \ 0.71731018735152574095, \ 0.41506457665342233465, \ -0.71731018735152574095, \ -0.41506457665342233465, \ -0.71731018735152574095, \ 0.94466239579161759288, \ 0.81619080186595505122, \ -0.94466239579161759288, \ 0.81619080186595505122, \ 0.94466239579161759288, \ -0.81619080186595505122, \ -0.94466239579161759288, \ -0.81619080186595505122, \ 0.71450522624081691525, \ 0.31179783227055996031, \ -0.71450522624081691525, \ 0.31179783227055996031, \ 0.71450522624081691525, \ -0.31179783227055996031, \ -0.71450522624081691525, \ -0.31179783227055996031 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.73869275831950009792, \ 0.00000000000000000000, \ -0.73869275831950009792, \ 0.00000000000000000000, \ 0.76806657302952874300, \ 0.00000000000000000000, \ -0.76806657302952874300, \ 0.00000000000000000000, \ 0.31673944809898013641, \ 0.00000000000000000000, \ -0.31673944809898013641, \ 0.00000000000000000000, \ 0.61877572218072185439, \ 0.00000000000000000000, \ -0.61877572218072185439, \ 0.00000000000000000000, \ 0.37235294402955443349, \ 0.00000000000000000000, \ -0.37235294402955443349, \ 0.00000000000000000000, \ 0.50387193570782862206, \ 0.00000000000000000000, \ -0.50387193570782862206, \ 0.00000000000000000000, \ 0.72207836507269651527, \ 0.00000000000000000000, \ -0.72207836507269651527, \ 0.00000000000000000000, \ 0.39403113359582681019, \ 0.00000000000000000000, \ -0.39403113359582681019, \ 0.00000000000000000000, \ 0.11819479806124476295, \ 0.00000000000000000000, \ -0.11819479806124476295, \ 0.00000000000000000000, \ 0.51179862044264223808, \ 0.00000000000000000000, \ -0.51179862044264223808, \ 0.00000000000000000000, \ 0.09344056049843052492, \ 0.00000000000000000000, \ -0.09344056049843052492, \ 0.00000000000000000000, \ 0.97786305288383967849, \ 0.00000000000000000000, \ -0.97786305288383967849, \ 0.00000000000000000000, \ 0.26893118028825491184, \ 0.00000000000000000000, \ -0.26893118028825491184, \ 0.00000000000000000000, \ 0.18588876717193755783, \ 0.00000000000000000000, \ -0.18588876717193755783, \ 0.88032062123229137818, \ 0.88032062123229137818, \ -0.88032062123229137818, \ -0.88032062123229137818, \ 0.68145212136761557087, \ 0.68145212136761557087, \ -0.68145212136761557087, \ -0.68145212136761557087, \ 0.49699036434274163065, \ 0.49699036434274163065, \ -0.49699036434274163065, \ -0.49699036434274163065, \ 0.30634018082228819946, \ 0.30634018082228819946, \ -0.30634018082228819946, \ -0.30634018082228819946, \ 0.58539966455385050725, \ 0.58539966455385050725, \ -0.58539966455385050725, \ -0.58539966455385050725, \ 0.77694395476943478585, \ 0.77694395476943478585, \ -0.77694395476943478585, \ -0.77694395476943478585, \ 0.18695368401965414829, \ 0.18695368401965414829, \ -0.18695368401965414829, \ -0.18695368401965414829, \ 0.64402844061291575350, \ 0.64402844061291575350, \ -0.64402844061291575350, \ -0.64402844061291575350, \ 0.19939684409397287479, \ 0.19939684409397287479, \ -0.19939684409397287479, \ -0.19939684409397287479, \ 0.49151662722959021945, \ 0.49151662722959021945, \ -0.49151662722959021945, \ -0.49151662722959021945, \ 0.21971883736597888626, \ 0.21971883736597888626, \ -0.21971883736597888626, \ -0.21971883736597888626, \ 0.38181860275292400786, \ 0.38181860275292400786, \ -0.38181860275292400786, \ -0.38181860275292400786, \ 0.13233574436496933768, \ 0.13233574436496933768, \ -0.13233574436496933768, \ -0.13233574436496933768, \ 0.26434906680031583504, \ 0.26434906680031583504, \ -0.26434906680031583504, \ -0.26434906680031583504, \ 0.26259016722585765136, \ 0.26259016722585765136, \ -0.26259016722585765136, \ -0.26259016722585765136, \ 0.63683049968859806178, \ 0.63683049968859806178, \ -0.63683049968859806178, \ -0.63683049968859806178, \ 0.50333230035733345087, \ 0.50333230035733345087, \ -0.50333230035733345087, \ -0.50333230035733345087, \ 0.43053066487698737896, \ 0.43053066487698737896, \ -0.43053066487698737896, \ -0.43053066487698737896, \ 0.44121177996231647489, \ 0.44121177996231647489, \ -0.44121177996231647489, \ -0.44121177996231647489, \ 0.12338526534910826404, \ 0.12338526534910826404, \ -0.12338526534910826404, \ -0.12338526534910826404, \ 0.28196466746787440805, \ 0.28196466746787440805, \ -0.28196466746787440805, \ -0.28196466746787440805, \ 0.12302065942509179952, \ 0.12302065942509179952, \ -0.12302065942509179952, \ -0.12302065942509179952, \ 0.96995340856169265376, \ 0.96995340856169265376, \ -0.96995340856169265376, \ -0.96995340856169265376, \ 0.15367597423015844083, \ 0.15367597423015844083, \ -0.15367597423015844083, \ -0.15367597423015844083, \ 0.32324916002943732130, \ 0.32324916002943732130, \ -0.32324916002943732130, \ -0.32324916002943732130, \ 0.07979061002341172881, \ 0.07979061002341172881, \ -0.07979061002341172881, \ -0.07979061002341172881, \ 0.05572751587573096521, \ 0.05572751587573096521, \ -0.05572751587573096521, \ -0.05572751587573096521, \ 0.80407180079417317486, \ 0.80407180079417317486, \ -0.80407180079417317486, \ -0.80407180079417317486, \ 0.10630794929321137066, \ 0.10630794929321137066, \ -0.10630794929321137066, \ -0.10630794929321137066, \ 0.14968116552008028930, \ 0.14968116552008028930, \ -0.14968116552008028930, \ -0.14968116552008028930, \ 0.72179802358977040999, \ 0.72179802358977040999, \ -0.72179802358977040999, \ -0.72179802358977040999, \ 0.64320215485058829241, \ 0.81797170822487763608, \ 0.64320215485058829241, \ -0.81797170822487763608, \ -0.64320215485058829241, \ 0.81797170822487763608, \ -0.64320215485058829241, \ -0.81797170822487763608, \ 0.16636418997995866542, \ 0.45477772302529712034, \ 0.16636418997995866542, \ -0.45477772302529712034, \ -0.16636418997995866542, \ 0.45477772302529712034, \ -0.16636418997995866542, \ -0.45477772302529712034, \ 0.64919419286301172090, \ 0.22077509021471022899, \ 0.64919419286301172090, \ -0.22077509021471022899, \ -0.64919419286301172090, \ 0.22077509021471022899, \ -0.64919419286301172090, \ -0.22077509021471022899, \ 0.26442320916257716634, \ 0.85849144377065222944, \ 0.26442320916257716634, \ -0.85849144377065222944, \ -0.26442320916257716634, \ 0.85849144377065222944, \ -0.26442320916257716634, \ -0.85849144377065222944, \ 0.45655985846318541954, \ 0.19087247051624386951, \ 0.45655985846318541954, \ -0.19087247051624386951, \ -0.45655985846318541954, \ 0.19087247051624386951, \ -0.45655985846318541954, \ -0.19087247051624386951, \ 0.66406293254753101518, \ 0.37787816613860053527, \ 0.66406293254753101518, \ -0.37787816613860053527, \ -0.66406293254753101518, \ 0.37787816613860053527, \ -0.66406293254753101518, \ -0.37787816613860053527, \ 0.17283329178347239807, \ 0.89395556646395457623, \ 0.17283329178347239807, \ -0.89395556646395457623, \ -0.17283329178347239807, \ 0.89395556646395457623, \ -0.17283329178347239807, \ -0.89395556646395457623, \ 0.05003413197772252352, \ 0.40991415053935187363, \ 0.05003413197772252352, \ -0.40991415053935187363, \ -0.05003413197772252352, \ 0.40991415053935187363, \ -0.05003413197772252352, \ -0.40991415053935187363, \ 0.10662173986061880548, \ 0.93198108654420652730, \ 0.10662173986061880548, \ -0.93198108654420652730, \ -0.10662173986061880548, \ 0.93198108654420652730, \ -0.10662173986061880548, \ -0.93198108654420652730, \ 0.84993195986801317598, \ 0.28018220607206512085, \ 0.84993195986801317598, \ -0.28018220607206512085, \ -0.84993195986801317598, \ 0.28018220607206512085, \ -0.84993195986801317598, \ -0.28018220607206512085, \ 0.46201429744731292715, \ 0.57728165413613941048, \ 0.46201429744731292715, \ -0.57728165413613941048, \ -0.46201429744731292715, \ 0.57728165413613941048, \ -0.46201429744731292715, \ -0.57728165413613941048, \ 0.61756791755060624904, \ 0.84451580808527704214, \ 0.61756791755060624904, \ -0.84451580808527704214, \ -0.61756791755060624904, \ 0.84451580808527704214, \ -0.61756791755060624904, \ -0.84451580808527704214, \ 0.23348533584682021336, \ 0.52941572893811861267, \ 0.23348533584682021336, \ -0.52941572893811861267, \ -0.23348533584682021336, \ 0.52941572893811861267, \ -0.23348533584682021336, \ -0.52941572893811861267, \ 0.67941786279817284466, \ 0.92827521801894674613, \ 0.67941786279817284466, \ -0.92827521801894674613, \ -0.67941786279817284466, \ 0.92827521801894674613, \ -0.67941786279817284466, \ -0.92827521801894674613, \ 0.46144251438466377113, \ 0.96836516384095050469, \ 0.46144251438466377113, \ -0.96836516384095050469, \ -0.46144251438466377113, \ 0.96836516384095050469, \ -0.46144251438466377113, \ -0.96836516384095050469, \ 0.31430414794159466929, \ 0.16744571840030086918, \ 0.31430414794159466929, \ -0.16744571840030086918, \ -0.31430414794159466929, \ 0.16744571840030086918, \ -0.31430414794159466929, \ -0.16744571840030086918, \ 0.73988842925403419670, \ 0.49232718454496093852, \ 0.73988842925403419670, \ -0.49232718454496093852, \ -0.73988842925403419670, \ 0.49232718454496093852, \ -0.73988842925403419670, \ -0.49232718454496093852, \ 0.54061065617200576572, \ 0.85659974228270108210, \ 0.54061065617200576572, \ -0.85659974228270108210, \ -0.54061065617200576572, \ 0.85659974228270108210, \ -0.54061065617200576572, \ -0.85659974228270108210, \ 0.57531393529153806998, \ 0.26702277361260906563, \ 0.57531393529153806998, \ -0.26702277361260906563, \ -0.57531393529153806998, \ 0.26702277361260906563, \ -0.57531393529153806998, \ -0.26702277361260906563, \ 0.71731018735152574095, \ 0.41506457665342233465, \ 0.71731018735152574095, \ -0.41506457665342233465, \ -0.71731018735152574095, \ 0.41506457665342233465, \ -0.71731018735152574095, \ -0.41506457665342233465, \ 0.81619080186595505122, \ 0.94466239579161759288, \ 0.81619080186595505122, \ -0.94466239579161759288, \ -0.81619080186595505122, \ 0.94466239579161759288, \ -0.81619080186595505122, \ -0.94466239579161759288, \ 0.31179783227055996031, \ 0.71450522624081691525, \ 0.31179783227055996031, \ -0.71450522624081691525, \ -0.31179783227055996031, \ 0.71450522624081691525, \ -0.31179783227055996031, \ -0.71450522624081691525 ] ) z = np.array ( [ \ 0.96891318773147550036, \ 0.11218085315386774892, \ 0.11218085315386774892, \ 0.11218085315386774892, \ 0.11218085315386774892, \ 0.20952037314221555464, \ 0.20952037314221555464, \ 0.20952037314221555464, \ 0.20952037314221555464, \ 0.45043339209409832824, \ 0.45043339209409832824, \ 0.45043339209409832824, \ 0.45043339209409832824, \ 0.36713809241502448621, \ 0.36713809241502448621, \ 0.36713809241502448621, \ 0.36713809241502448621, \ 0.51496945555138884387, \ 0.51496945555138884387, \ 0.51496945555138884387, \ 0.51496945555138884387, \ 0.24658740648660407158, \ 0.24658740648660407158, \ 0.24658740648660407158, \ 0.24658740648660407158, \ 0.03347288009925680763, \ 0.03347288009925680763, \ 0.03347288009925680763, \ 0.03347288009925680763, \ 0.17604915946010571415, \ 0.17604915946010571415, \ 0.17604915946010571415, \ 0.17604915946010571415, \ 0.12627670900302459533, \ 0.12627670900302459533, \ 0.12627670900302459533, \ 0.12627670900302459533, \ 0.01146186842907397259, \ 0.01146186842907397259, \ 0.01146186842907397259, \ 0.01146186842907397259, \ 0.82865571811563620841, \ 0.82865571811563620841, \ 0.82865571811563620841, \ 0.82865571811563620841, \ 0.00411477663570613411, \ 0.00411477663570613411, \ 0.00411477663570613411, \ 0.00411477663570613411, \ 0.66431760085930258164, \ 0.66431760085930258164, \ 0.66431760085930258164, \ 0.66431760085930258164, \ 0.80714531646844267510, \ 0.80714531646844267510, \ 0.80714531646844267510, \ 0.80714531646844267510, \ 0.06759778909905436728, \ 0.06759778909905436728, \ 0.06759778909905436728, \ 0.06759778909905436728, \ 0.29403431132680074578, \ 0.29403431132680074578, \ 0.29403431132680074578, \ 0.29403431132680074578, \ 0.49665508093160370962, \ 0.49665508093160370962, \ 0.49665508093160370962, \ 0.49665508093160370962, \ 0.27911320549015106174, \ 0.27911320549015106174, \ 0.27911320549015106174, \ 0.27911320549015106174, \ 0.07876704807666434771, \ 0.07876704807666434771, \ 0.07876704807666434771, \ 0.07876704807666434771, \ 0.04825635484814582571, \ 0.04825635484814582571, \ 0.04825635484814582571, \ 0.04825635484814582571, \ 0.00881247486166711683, \ 0.00881247486166711683, \ 0.00881247486166711683, \ 0.00881247486166711683, \ 0.02005872107121197886, \ 0.02005872107121197886, \ 0.02005872107121197886, \ 0.02005872107121197886, \ 0.75639094968056375112, \ 0.75639094968056375112, \ 0.75639094968056375112, \ 0.75639094968056375112, \ 0.15155505938254110188, \ 0.15155505938254110188, \ 0.15155505938254110188, \ 0.15155505938254110188, \ 0.60842758819371955958, \ 0.60842758819371955958, \ 0.60842758819371955958, \ 0.60842758819371955958, \ 0.52569545459372502005, \ 0.52569545459372502005, \ 0.52569545459372502005, \ 0.52569545459372502005, \ 0.40281226004252063122, \ 0.40281226004252063122, \ 0.40281226004252063122, \ 0.40281226004252063122, \ 0.04148931197347632133, \ 0.04148931197347632133, \ 0.04148931197347632133, \ 0.04148931197347632133, \ 0.14661700764838450639, \ 0.14661700764838450639, \ 0.14661700764838450639, \ 0.14661700764838450639, \ 0.25661597420550030790, \ 0.25661597420550030790, \ 0.25661597420550030790, \ 0.25661597420550030790, \ 0.25552367243392443141, \ 0.25552367243392443141, \ 0.25552367243392443141, \ 0.25552367243392443141, \ 0.36981856719481731588, \ 0.36981856719481731588, \ 0.36981856719481731588, \ 0.36981856719481731588, \ 0.01554708555805913925, \ 0.01554708555805913925, \ 0.01554708555805913925, \ 0.01554708555805913925, \ 0.04951092940950102550, \ 0.04951092940950102550, \ 0.04951092940950102550, \ 0.04951092940950102550, \ 0.45729924127195364925, \ 0.45729924127195364925, \ 0.45729924127195364925, \ 0.45729924127195364925, \ 0.25865392811548787444, \ 0.25865392811548787444, \ 0.25865392811548787444, \ 0.25865392811548787444, \ 0.01471561063742727986, \ 0.01471561063742727986, \ 0.01471561063742727986, \ 0.01471561063742727986, \ 0.84302938509543134948, \ 0.84302938509543134948, \ 0.84302938509543134948, \ 0.84302938509543134948, \ 0.64221316316195331542, \ 0.64221316316195331542, \ 0.64221316316195331542, \ 0.64221316316195331542, \ 0.70815468949755844275, \ 0.70815468949755844275, \ 0.70815468949755844275, \ 0.70815468949755844275, \ 0.90756616766447684164, \ 0.90756616766447684164, \ 0.90756616766447684164, \ 0.90756616766447684164, \ 0.15801098912608321778, \ 0.15801098912608321778, \ 0.15801098912608321778, \ 0.15801098912608321778, \ 0.55864014423757180072, \ 0.55864014423757180072, \ 0.55864014423757180072, \ 0.55864014423757180072, \ 0.76553411212536370822, \ 0.76553411212536370822, \ 0.76553411212536370822, \ 0.76553411212536370822, \ 0.12038628177040819334, \ 0.12038628177040819334, \ 0.12038628177040819334, \ 0.12038628177040819334, \ 0.16540042455816997280, \ 0.16540042455816997280, \ 0.16540042455816997280, \ 0.16540042455816997280, \ 0.16540042455816997280, \ 0.16540042455816997280, \ 0.16540042455816997280, \ 0.16540042455816997280, \ 0.07191647566286844817, \ 0.07191647566286844817, \ 0.07191647566286844817, \ 0.07191647566286844817, \ 0.07191647566286844817, \ 0.07191647566286844817, \ 0.07191647566286844817, \ 0.07191647566286844817, \ 0.24369366228681560438, \ 0.24369366228681560438, \ 0.24369366228681560438, \ 0.24369366228681560438, \ 0.24369366228681560438, \ 0.24369366228681560438, \ 0.24369366228681560438, \ 0.24369366228681560438, \ 0.03997911405124788403, \ 0.03997911405124788403, \ 0.03997911405124788403, \ 0.03997911405124788403, \ 0.03997911405124788403, \ 0.03997911405124788403, \ 0.03997911405124788403, \ 0.03997911405124788403, \ 0.52403522696450499652, \ 0.52403522696450499652, \ 0.52403522696450499652, \ 0.52403522696450499652, \ 0.52403522696450499652, \ 0.52403522696450499652, \ 0.52403522696450499652, \ 0.52403522696450499652, \ 0.06332251756914623886, \ 0.06332251756914623886, \ 0.06332251756914623886, \ 0.06332251756914623886, \ 0.06332251756914623886, \ 0.06332251756914623886, \ 0.06332251756914623886, \ 0.06332251756914623886, \ 0.00627167365301165187, \ 0.00627167365301165187, \ 0.00627167365301165187, \ 0.00627167365301165187, \ 0.00627167365301165187, \ 0.00627167365301165187, \ 0.00627167365301165187, \ 0.00627167365301165187, \ 0.34612550470442166040, \ 0.34612550470442166040, \ 0.34612550470442166040, \ 0.34612550470442166040, \ 0.34612550470442166040, \ 0.34612550470442166040, \ 0.34612550470442166040, \ 0.34612550470442166040, \ 0.04934944134498662344, \ 0.04934944134498662344, \ 0.04934944134498662344, \ 0.04934944134498662344, \ 0.04934944134498662344, \ 0.04934944134498662344, \ 0.04934944134498662344, \ 0.04934944134498662344, \ 0.12050259192784877615, \ 0.12050259192784877615, \ 0.12050259192784877615, \ 0.12050259192784877615, \ 0.12050259192784877615, \ 0.12050259192784877615, \ 0.12050259192784877615, \ 0.12050259192784877615, \ 0.39428120571642771841, \ 0.39428120571642771841, \ 0.39428120571642771841, \ 0.39428120571642771841, \ 0.39428120571642771841, \ 0.39428120571642771841, \ 0.39428120571642771841, \ 0.39428120571642771841, \ 0.00838019453790634500, \ 0.00838019453790634500, \ 0.00838019453790634500, \ 0.00838019453790634500, \ 0.00838019453790634500, \ 0.00838019453790634500, \ 0.00838019453790634500, \ 0.00838019453790634500, \ 0.37991521751516699190, \ 0.37991521751516699190, \ 0.37991521751516699190, \ 0.37991521751516699190, \ 0.37991521751516699190, \ 0.37991521751516699190, \ 0.37991521751516699190, \ 0.37991521751516699190, \ 0.06658426856019065976, \ 0.06658426856019065976, \ 0.06658426856019065976, \ 0.06658426856019065976, \ 0.06658426856019065976, \ 0.06658426856019065976, \ 0.06658426856019065976, \ 0.06658426856019065976, \ 0.01360996700708025364, \ 0.01360996700708025364, \ 0.01360996700708025364, \ 0.01360996700708025364, \ 0.01360996700708025364, \ 0.01360996700708025364, \ 0.01360996700708025364, \ 0.01360996700708025364, \ 0.67377911630059594827, \ 0.67377911630059594827, \ 0.67377911630059594827, \ 0.67377911630059594827, \ 0.67377911630059594827, \ 0.67377911630059594827, \ 0.67377911630059594827, \ 0.67377911630059594827, \ 0.15122396864513820702, \ 0.15122396864513820702, \ 0.15122396864513820702, \ 0.15122396864513820702, \ 0.15122396864513820702, \ 0.15122396864513820702, \ 0.15122396864513820702, \ 0.15122396864513820702, \ 0.05960704457999711076, \ 0.05960704457999711076, \ 0.05960704457999711076, \ 0.05960704457999711076, \ 0.05960704457999711076, \ 0.05960704457999711076, \ 0.05960704457999711076, \ 0.05960704457999711076, \ 0.15557252093495238521, \ 0.15557252093495238521, \ 0.15557252093495238521, \ 0.15557252093495238521, \ 0.15557252093495238521, \ 0.15557252093495238521, \ 0.15557252093495238521, \ 0.15557252093495238521, \ 0.26467312835339185106, \ 0.26467312835339185106, \ 0.26467312835339185106, \ 0.26467312835339185106, \ 0.26467312835339185106, \ 0.26467312835339185106, \ 0.26467312835339185106, \ 0.26467312835339185106, \ 0.01193065095103094247, \ 0.01193065095103094247, \ 0.01193065095103094247, \ 0.01193065095103094247, \ 0.01193065095103094247, \ 0.01193065095103094247, \ 0.01193065095103094247, \ 0.01193065095103094247, \ 0.00729413025649284976, \ 0.00729413025649284976, \ 0.00729413025649284976, \ 0.00729413025649284976, \ 0.00729413025649284976, \ 0.00729413025649284976, \ 0.00729413025649284976, \ 0.00729413025649284976 ] ) w= np.array ( [ \ 0.00013400520132544013, \ 0.00653282923653435328, \ 0.00653282923653435328, \ 0.00653282923653435328, \ 0.00653282923653435328, \ 0.00246267782986044981, \ 0.00246267782986044981, \ 0.00246267782986044981, \ 0.00246267782986044981, \ 0.00236266319877590381, \ 0.00236266319877590381, \ 0.00236266319877590381, \ 0.00236266319877590381, \ 0.00241284626019594179, \ 0.00241284626019594179, \ 0.00241284626019594179, \ 0.00241284626019594179, \ 0.00563939918988414120, \ 0.00563939918988414120, \ 0.00563939918988414120, \ 0.00563939918988414120, \ 0.00530879464537392220, \ 0.00530879464537392220, \ 0.00530879464537392220, \ 0.00530879464537392220, \ 0.00330320967760970065, \ 0.00330320967760970065, \ 0.00330320967760970065, \ 0.00330320967760970065, \ 0.00715709687293028703, \ 0.00715709687293028703, \ 0.00715709687293028703, \ 0.00715709687293028703, \ 0.00356020900079922868, \ 0.00356020900079922868, \ 0.00356020900079922868, \ 0.00356020900079922868, \ 0.00286908910615377545, \ 0.00286908910615377545, \ 0.00286908910615377545, \ 0.00286908910615377545, \ 0.00119238795542696220, \ 0.00119238795542696220, \ 0.00119238795542696220, \ 0.00119238795542696220, \ 0.00023570897730274608, \ 0.00023570897730274608, \ 0.00023570897730274608, \ 0.00023570897730274608, \ 0.00332415202652309181, \ 0.00332415202652309181, \ 0.00332415202652309181, \ 0.00332415202652309181, \ 0.00064424498387906620, \ 0.00064424498387906620, \ 0.00064424498387906620, \ 0.00064424498387906620, \ 0.00093040828397316332, \ 0.00093040828397316332, \ 0.00093040828397316332, \ 0.00093040828397316332, \ 0.00061531263855177734, \ 0.00061531263855177734, \ 0.00061531263855177734, \ 0.00061531263855177734, \ 0.00028907482286127771, \ 0.00028907482286127771, \ 0.00028907482286127771, \ 0.00028907482286127771, \ 0.00957928057788382838, \ 0.00957928057788382838, \ 0.00957928057788382838, \ 0.00957928057788382838, \ 0.00256243378291242307, \ 0.00256243378291242307, \ 0.00256243378291242307, \ 0.00256243378291242307, \ 0.00197009710848232650, \ 0.00197009710848232650, \ 0.00197009710848232650, \ 0.00197009710848232650, \ 0.00224853801623185919, \ 0.00224853801623185919, \ 0.00224853801623185919, \ 0.00224853801623185919, \ 0.00178378503667077598, \ 0.00178378503667077598, \ 0.00178378503667077598, \ 0.00178378503667077598, \ 0.00046154884778758861, \ 0.00046154884778758861, \ 0.00046154884778758861, \ 0.00046154884778758861, \ 0.00383567352584877853, \ 0.00383567352584877853, \ 0.00383567352584877853, \ 0.00383567352584877853, \ 0.00424323389268952030, \ 0.00424323389268952030, \ 0.00424323389268952030, \ 0.00424323389268952030, \ 0.00297709850925886605, \ 0.00297709850925886605, \ 0.00297709850925886605, \ 0.00297709850925886605, \ 0.00750097658421174009, \ 0.00750097658421174009, \ 0.00750097658421174009, \ 0.00750097658421174009, \ 0.00208064231905125911, \ 0.00208064231905125911, \ 0.00208064231905125911, \ 0.00208064231905125911, \ 0.00676296550091519920, \ 0.00676296550091519920, \ 0.00676296550091519920, \ 0.00676296550091519920, \ 0.00300587484767854103, \ 0.00300587484767854103, \ 0.00300587484767854103, \ 0.00300587484767854103, \ 0.00569473175276393340, \ 0.00569473175276393340, \ 0.00569473175276393340, \ 0.00569473175276393340, \ 0.00329345228074993208, \ 0.00329345228074993208, \ 0.00329345228074993208, \ 0.00329345228074993208, \ 0.00319343074693561636, \ 0.00319343074693561636, \ 0.00319343074693561636, \ 0.00319343074693561636, \ 0.00300785963957934336, \ 0.00300785963957934336, \ 0.00300785963957934336, \ 0.00300785963957934336, \ 0.00621018081426024000, \ 0.00621018081426024000, \ 0.00621018081426024000, \ 0.00621018081426024000, \ 0.00690380129393601029, \ 0.00690380129393601029, \ 0.00690380129393601029, \ 0.00690380129393601029, \ 0.00010061838637633462, \ 0.00010061838637633462, \ 0.00010061838637633462, \ 0.00010061838637633462, \ 0.00013563078282338245, \ 0.00013563078282338245, \ 0.00013563078282338245, \ 0.00013563078282338245, \ 0.00077893767219553941, \ 0.00077893767219553941, \ 0.00077893767219553941, \ 0.00077893767219553941, \ 0.00267441470336475876, \ 0.00267441470336475876, \ 0.00267441470336475876, \ 0.00267441470336475876, \ 0.00047754594130653132, \ 0.00047754594130653132, \ 0.00047754594130653132, \ 0.00047754594130653132, \ 0.00074066104011807129, \ 0.00074066104011807129, \ 0.00074066104011807129, \ 0.00074066104011807129, \ 0.00529137043945265752, \ 0.00529137043945265752, \ 0.00529137043945265752, \ 0.00529137043945265752, \ 0.00150066461105524858, \ 0.00150066461105524858, \ 0.00150066461105524858, \ 0.00150066461105524858, \ 0.00262627399936291505, \ 0.00262627399936291505, \ 0.00262627399936291505, \ 0.00262627399936291505, \ 0.00106543689917693658, \ 0.00106543689917693658, \ 0.00106543689917693658, \ 0.00106543689917693658, \ 0.00106543689917693658, \ 0.00106543689917693658, \ 0.00106543689917693658, \ 0.00106543689917693658, \ 0.00608072256149797419, \ 0.00608072256149797419, \ 0.00608072256149797419, \ 0.00608072256149797419, \ 0.00608072256149797419, \ 0.00608072256149797419, \ 0.00608072256149797419, \ 0.00608072256149797419, \ 0.00531002301058563358, \ 0.00531002301058563358, \ 0.00531002301058563358, \ 0.00531002301058563358, \ 0.00531002301058563358, \ 0.00531002301058563358, \ 0.00531002301058563358, \ 0.00531002301058563358, \ 0.00202003342483236250, \ 0.00202003342483236250, \ 0.00202003342483236250, \ 0.00202003342483236250, \ 0.00202003342483236250, \ 0.00202003342483236250, \ 0.00202003342483236250, \ 0.00202003342483236250, \ 0.00216470393083745358, \ 0.00216470393083745358, \ 0.00216470393083745358, \ 0.00216470393083745358, \ 0.00216470393083745358, \ 0.00216470393083745358, \ 0.00216470393083745358, \ 0.00216470393083745358, \ 0.00435330698915271062, \ 0.00435330698915271062, \ 0.00435330698915271062, \ 0.00435330698915271062, \ 0.00435330698915271062, \ 0.00435330698915271062, \ 0.00435330698915271062, \ 0.00435330698915271062, \ 0.00068634034778216149, \ 0.00068634034778216149, \ 0.00068634034778216149, \ 0.00068634034778216149, \ 0.00068634034778216149, \ 0.00068634034778216149, \ 0.00068634034778216149, \ 0.00068634034778216149, \ 0.00401906783115373901, \ 0.00401906783115373901, \ 0.00401906783115373901, \ 0.00401906783115373901, \ 0.00401906783115373901, \ 0.00401906783115373901, \ 0.00401906783115373901, \ 0.00401906783115373901, \ 0.00079127284739705225, \ 0.00079127284739705225, \ 0.00079127284739705225, \ 0.00079127284739705225, \ 0.00079127284739705225, \ 0.00079127284739705225, \ 0.00079127284739705225, \ 0.00079127284739705225, \ 0.00244671052896765998, \ 0.00244671052896765998, \ 0.00244671052896765998, \ 0.00244671052896765998, \ 0.00244671052896765998, \ 0.00244671052896765998, \ 0.00244671052896765998, \ 0.00244671052896765998, \ 0.00195038190205695967, \ 0.00195038190205695967, \ 0.00195038190205695967, \ 0.00195038190205695967, \ 0.00195038190205695967, \ 0.00195038190205695967, \ 0.00195038190205695967, \ 0.00195038190205695967, \ 0.00110591593882085814, \ 0.00110591593882085814, \ 0.00110591593882085814, \ 0.00110591593882085814, \ 0.00110591593882085814, \ 0.00110591593882085814, \ 0.00110591593882085814, \ 0.00110591593882085814, \ 0.00503011482374766256, \ 0.00503011482374766256, \ 0.00503011482374766256, \ 0.00503011482374766256, \ 0.00503011482374766256, \ 0.00503011482374766256, \ 0.00503011482374766256, \ 0.00503011482374766256, \ 0.00065967081570031318, \ 0.00065967081570031318, \ 0.00065967081570031318, \ 0.00065967081570031318, \ 0.00065967081570031318, \ 0.00065967081570031318, \ 0.00065967081570031318, \ 0.00065967081570031318, \ 0.00061321639781390126, \ 0.00061321639781390126, \ 0.00061321639781390126, \ 0.00061321639781390126, \ 0.00061321639781390126, \ 0.00061321639781390126, \ 0.00061321639781390126, \ 0.00061321639781390126, \ 0.00089657142446607598, \ 0.00089657142446607598, \ 0.00089657142446607598, \ 0.00089657142446607598, \ 0.00089657142446607598, \ 0.00089657142446607598, \ 0.00089657142446607598, \ 0.00089657142446607598, \ 0.00363983560477118984, \ 0.00363983560477118984, \ 0.00363983560477118984, \ 0.00363983560477118984, \ 0.00363983560477118984, \ 0.00363983560477118984, \ 0.00363983560477118984, \ 0.00363983560477118984, \ 0.00211128919028042220, \ 0.00211128919028042220, \ 0.00211128919028042220, \ 0.00211128919028042220, \ 0.00211128919028042220, \ 0.00211128919028042220, \ 0.00211128919028042220, \ 0.00211128919028042220, \ 0.00570062224543081177, \ 0.00570062224543081177, \ 0.00570062224543081177, \ 0.00570062224543081177, \ 0.00570062224543081177, \ 0.00570062224543081177, \ 0.00570062224543081177, \ 0.00570062224543081177, \ 0.00195532776601042716, \ 0.00195532776601042716, \ 0.00195532776601042716, \ 0.00195532776601042716, \ 0.00195532776601042716, \ 0.00195532776601042716, \ 0.00195532776601042716, \ 0.00195532776601042716, \ 0.00062384953506176009, \ 0.00062384953506176009, \ 0.00062384953506176009, \ 0.00062384953506176009, \ 0.00062384953506176009, \ 0.00062384953506176009, \ 0.00062384953506176009, \ 0.00062384953506176009, \ 0.00151792165402074965, \ 0.00151792165402074965, \ 0.00151792165402074965, \ 0.00151792165402074965, \ 0.00151792165402074965, \ 0.00151792165402074965, \ 0.00151792165402074965, \ 0.00151792165402074965 ] ) return x, y, z, w def rule19 ( ): #*****************************************************************************80 # ## rule19() returns the pyramid quadrature rule of precision 19. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.37365721634528792361, \ 0.00000000000000000000, \ -0.37365721634528792361, \ 0.00000000000000000000, \ 0.43752827030428453892, \ 0.00000000000000000000, \ -0.43752827030428453892, \ 0.00000000000000000000, \ 0.55782756293242685697, \ 0.00000000000000000000, \ -0.55782756293242685697, \ 0.00000000000000000000, \ 0.27275879229149846417, \ 0.00000000000000000000, \ -0.27275879229149846417, \ 0.00000000000000000000, \ 0.28872411753825932834, \ 0.00000000000000000000, \ -0.28872411753825932834, \ 0.00000000000000000000, \ 0.11277465623250763904, \ 0.00000000000000000000, \ -0.11277465623250763904, \ 0.00000000000000000000, \ 0.65470230415224206499, \ 0.00000000000000000000, \ -0.65470230415224206499, \ 0.00000000000000000000, \ 0.22295101282662088682, \ 0.00000000000000000000, \ -0.22295101282662088682, \ 0.00000000000000000000, \ 0.35176689121153298379, \ 0.00000000000000000000, \ -0.35176689121153298379, \ 0.00000000000000000000, \ 0.20697735413665671600, \ 0.00000000000000000000, \ -0.20697735413665671600, \ 0.00000000000000000000, \ 0.93111189027726670719, \ 0.00000000000000000000, \ -0.93111189027726670719, \ 0.00000000000000000000, \ 0.84303358445951348532, \ 0.00000000000000000000, \ -0.84303358445951348532, \ 0.00000000000000000000, \ 0.07303948013428374075, \ 0.00000000000000000000, \ -0.07303948013428374075, \ 0.00000000000000000000, \ 0.67807351338628540915, \ 0.00000000000000000000, \ -0.67807351338628540915, \ 0.00000000000000000000, \ 0.88198482628664209848, \ 0.00000000000000000000, \ -0.88198482628664209848, \ 0.00000000000000000000, \ 0.38587811686103651310, \ 0.00000000000000000000, \ -0.38587811686103651310, \ 0.00000000000000000000, \ 0.13708884737518356456, \ 0.00000000000000000000, \ -0.13708884737518356456, \ 0.00000000000000000000, \ 0.52558521108268729805, \ -0.52558521108268729805, \ 0.52558521108268729805, \ -0.52558521108268729805, \ 0.45301642570589800707, \ -0.45301642570589800707, \ 0.45301642570589800707, \ -0.45301642570589800707, \ 0.67125116320175959306, \ -0.67125116320175959306, \ 0.67125116320175959306, \ -0.67125116320175959306, \ 0.36951418649168821240, \ -0.36951418649168821240, \ 0.36951418649168821240, \ -0.36951418649168821240, \ 0.28838223435586252119, \ -0.28838223435586252119, \ 0.28838223435586252119, \ -0.28838223435586252119, \ 0.82857238389465803774, \ -0.82857238389465803774, \ 0.82857238389465803774, \ -0.82857238389465803774, \ 0.67246070085447195996, \ -0.67246070085447195996, \ 0.67246070085447195996, \ -0.67246070085447195996, \ 0.48736689338962557727, \ -0.48736689338962557727, \ 0.48736689338962557727, \ -0.48736689338962557727, \ 0.95036644315079843448, \ -0.95036644315079843448, \ 0.95036644315079843448, \ -0.95036644315079843448, \ 0.09132353058612172059, \ -0.09132353058612172059, \ 0.09132353058612172059, \ -0.09132353058612172059, \ 0.15520695551416591185, \ -0.15520695551416591185, \ 0.15520695551416591185, \ -0.15520695551416591185, \ 0.05052806321356113906, \ -0.05052806321356113906, \ 0.05052806321356113906, \ -0.05052806321356113906, \ 0.39781392804166187949, \ -0.39781392804166187949, \ 0.39781392804166187949, \ -0.39781392804166187949, \ 0.37607913140641990868, \ -0.37607913140641990868, \ 0.37607913140641990868, \ -0.37607913140641990868, \ 0.16436382679828262510, \ -0.16436382679828262510, \ 0.16436382679828262510, \ -0.16436382679828262510, \ 0.34688925556861166521, \ -0.34688925556861166521, \ 0.34688925556861166521, \ -0.34688925556861166521, \ 0.11913325793719439782, \ -0.11913325793719439782, \ 0.11913325793719439782, \ -0.11913325793719439782, \ 0.74545838141881970440, \ -0.74545838141881970440, \ 0.74545838141881970440, \ -0.74545838141881970440, \ 0.76104952097303479874, \ -0.76104952097303479874, \ 0.76104952097303479874, \ -0.76104952097303479874, \ 0.24208120588771878112, \ -0.24208120588771878112, \ 0.24208120588771878112, \ -0.24208120588771878112, \ 0.84457983815668913330, \ -0.84457983815668913330, \ 0.84457983815668913330, \ -0.84457983815668913330, \ 0.16456465781662479864, \ -0.16456465781662479864, \ 0.16456465781662479864, \ -0.16456465781662479864, \ 0.27478423472388602278, \ -0.27478423472388602278, \ 0.27478423472388602278, \ -0.27478423472388602278, \ 0.58499194505600049521, \ -0.58499194505600049521, \ 0.58499194505600049521, \ -0.58499194505600049521, \ 0.14897381246033866709, \ -0.14897381246033866709, \ 0.14897381246033866709, \ -0.14897381246033866709, \ 0.43892903976173064384, \ -0.43892903976173064384, \ 0.43892903976173064384, \ -0.43892903976173064384, \ 0.87981971200037256686, \ -0.87981971200037256686, \ 0.87981971200037256686, \ -0.87981971200037256686, \ 0.11685331930792351718, \ -0.11685331930792351718, \ 0.11685331930792351718, \ -0.11685331930792351718, \ 0.34287164858560836844, \ -0.34287164858560836844, \ 0.34287164858560836844, \ -0.34287164858560836844, \ 0.86433279841860011228, \ 0.64222367435367522237, \ -0.86433279841860011228, \ 0.64222367435367522237, \ 0.86433279841860011228, \ -0.64222367435367522237, \ -0.86433279841860011228, \ -0.64222367435367522237, \ 0.57840479596659710726, \ 0.15700371479211361336, \ -0.57840479596659710726, \ 0.15700371479211361336, \ 0.57840479596659710726, \ -0.15700371479211361336, \ -0.57840479596659710726, \ -0.15700371479211361336, \ 0.31087991149352928177, \ 0.53916009809927645247, \ -0.31087991149352928177, \ 0.53916009809927645247, \ 0.31087991149352928177, \ -0.53916009809927645247, \ -0.31087991149352928177, \ -0.53916009809927645247, \ 0.20472565121250529963, \ 0.56505069862686030380, \ -0.20472565121250529963, \ 0.56505069862686030380, \ 0.20472565121250529963, \ -0.56505069862686030380, \ -0.20472565121250529963, \ -0.56505069862686030380, \ 0.15477148314547456431, \ 0.80087300859132681818, \ -0.15477148314547456431, \ 0.80087300859132681818, \ 0.15477148314547456431, \ -0.80087300859132681818, \ -0.15477148314547456431, \ -0.80087300859132681818, \ 0.91122224850183075606, \ 0.36196927102445491942, \ -0.91122224850183075606, \ 0.36196927102445491942, \ 0.91122224850183075606, \ -0.36196927102445491942, \ -0.91122224850183075606, \ -0.36196927102445491942, \ 0.23763934442358639054, \ 0.46054474775257370212, \ -0.23763934442358639054, \ 0.46054474775257370212, \ 0.23763934442358639054, \ -0.46054474775257370212, \ -0.23763934442358639054, \ -0.46054474775257370212, \ 0.93026675012099768747, \ 0.32159807642681254025, \ -0.93026675012099768747, \ 0.32159807642681254025, \ 0.93026675012099768747, \ -0.32159807642681254025, \ -0.93026675012099768747, \ -0.32159807642681254025, \ 0.27330670991417554960, \ 0.75417578802823215245, \ -0.27330670991417554960, \ 0.75417578802823215245, \ 0.27330670991417554960, \ -0.75417578802823215245, \ -0.27330670991417554960, \ -0.75417578802823215245, \ 0.61977908311233775862, \ 0.40094999523846291956, \ -0.61977908311233775862, \ 0.40094999523846291956, \ 0.61977908311233775862, \ -0.40094999523846291956, \ -0.61977908311233775862, \ -0.40094999523846291956, \ 0.96731797310728928618, \ 0.71750306782387462956, \ -0.96731797310728928618, \ 0.71750306782387462956, \ 0.96731797310728928618, \ -0.71750306782387462956, \ -0.96731797310728928618, \ -0.71750306782387462956, \ 0.28107596241726462427, \ 0.14469640753388121612, \ -0.28107596241726462427, \ 0.14469640753388121612, \ 0.28107596241726462427, \ -0.14469640753388121612, \ -0.28107596241726462427, \ -0.14469640753388121612, \ 0.95723494789717944453, \ 0.80544313431837344375, \ -0.95723494789717944453, \ 0.80544313431837344375, \ 0.95723494789717944453, \ -0.80544313431837344375, \ -0.95723494789717944453, \ -0.80544313431837344375, \ 0.93415043892659577196, \ 0.56426321835446102693, \ -0.93415043892659577196, \ 0.56426321835446102693, \ 0.93415043892659577196, \ -0.56426321835446102693, \ -0.93415043892659577196, \ -0.56426321835446102693, \ 0.22124438393817494330, \ 0.27637233377156195102, \ -0.22124438393817494330, \ 0.27637233377156195102, \ 0.22124438393817494330, \ -0.27637233377156195102, \ -0.22124438393817494330, \ -0.27637233377156195102, \ 0.51440860154860901243, \ 0.67110969363741279636, \ -0.51440860154860901243, \ 0.67110969363741279636, \ 0.51440860154860901243, \ -0.67110969363741279636, \ -0.51440860154860901243, \ -0.67110969363741279636, \ 0.84669681763194848401, \ 0.64763095243614277052, \ -0.84669681763194848401, \ 0.64763095243614277052, \ 0.84669681763194848401, \ -0.64763095243614277052, \ -0.84669681763194848401, \ -0.64763095243614277052, \ 0.58372340157348212575, \ 0.75878491584810681125, \ -0.58372340157348212575, \ 0.75878491584810681125, \ 0.58372340157348212575, \ -0.75878491584810681125, \ -0.58372340157348212575, \ -0.75878491584810681125, \ 0.23125484278203506383, \ 0.75795786639659157302, \ -0.23125484278203506383, \ 0.75795786639659157302, \ 0.23125484278203506383, \ -0.75795786639659157302, \ -0.23125484278203506383, \ -0.75795786639659157302, \ 0.65351981646876278198, \ 0.21186490812432900999, \ -0.65351981646876278198, \ 0.21186490812432900999, \ 0.65351981646876278198, \ -0.21186490812432900999, \ -0.65351981646876278198, \ -0.21186490812432900999, \ 0.69534501524896896729, \ 0.18605131637198926708, \ -0.69534501524896896729, \ 0.18605131637198926708, \ 0.69534501524896896729, \ -0.18605131637198926708, \ -0.69534501524896896729, \ -0.18605131637198926708, \ 0.08127234831798690884, \ 0.52410330742380673019, \ -0.08127234831798690884, \ 0.52410330742380673019, \ 0.08127234831798690884, \ -0.52410330742380673019, \ -0.08127234831798690884, \ -0.52410330742380673019, \ 0.67316244188134488624, \ 0.47074593361034250405, \ -0.67316244188134488624, \ 0.47074593361034250405, \ 0.67316244188134488624, \ -0.47074593361034250405, \ -0.67316244188134488624, \ -0.47074593361034250405, \ 0.82977152170712553669, \ 0.38456345752643983360, \ -0.82977152170712553669, \ 0.38456345752643983360, \ 0.82977152170712553669, \ -0.38456345752643983360, \ -0.82977152170712553669, \ -0.38456345752643983360, \ 0.85308428733291663537, \ 0.48551299054356161777, \ -0.85308428733291663537, \ 0.48551299054356161777, \ 0.85308428733291663537, \ -0.48551299054356161777, \ -0.85308428733291663537, \ -0.48551299054356161777, \ 0.44670731850691264286, \ 0.17757095991022572856, \ -0.44670731850691264286, \ 0.17757095991022572856, \ 0.44670731850691264286, \ -0.17757095991022572856, \ -0.44670731850691264286, \ -0.17757095991022572856, \ 0.67009672120301455589, \ 0.46199941611318601220, \ -0.67009672120301455589, \ 0.46199941611318601220, \ 0.67009672120301455589, \ -0.46199941611318601220, \ -0.67009672120301455589, \ -0.46199941611318601220, \ 0.97673360371074724462, \ 0.26790019276269744219, \ -0.97673360371074724462, \ 0.26790019276269744219, \ 0.97673360371074724462, \ -0.26790019276269744219, \ -0.97673360371074724462, \ -0.26790019276269744219, \ 0.31887900072125263673, \ 0.45381764631367643714, \ -0.31887900072125263673, \ 0.45381764631367643714, \ 0.31887900072125263673, \ -0.45381764631367643714, \ -0.31887900072125263673, \ -0.45381764631367643714 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.37365721634528792361, \ 0.00000000000000000000, \ -0.37365721634528792361, \ 0.00000000000000000000, \ 0.43752827030428453892, \ 0.00000000000000000000, \ -0.43752827030428453892, \ 0.00000000000000000000, \ 0.55782756293242685697, \ 0.00000000000000000000, \ -0.55782756293242685697, \ 0.00000000000000000000, \ 0.27275879229149846417, \ 0.00000000000000000000, \ -0.27275879229149846417, \ 0.00000000000000000000, \ 0.28872411753825932834, \ 0.00000000000000000000, \ -0.28872411753825932834, \ 0.00000000000000000000, \ 0.11277465623250763904, \ 0.00000000000000000000, \ -0.11277465623250763904, \ 0.00000000000000000000, \ 0.65470230415224206499, \ 0.00000000000000000000, \ -0.65470230415224206499, \ 0.00000000000000000000, \ 0.22295101282662088682, \ 0.00000000000000000000, \ -0.22295101282662088682, \ 0.00000000000000000000, \ 0.35176689121153298379, \ 0.00000000000000000000, \ -0.35176689121153298379, \ 0.00000000000000000000, \ 0.20697735413665671600, \ 0.00000000000000000000, \ -0.20697735413665671600, \ 0.00000000000000000000, \ 0.93111189027726670719, \ 0.00000000000000000000, \ -0.93111189027726670719, \ 0.00000000000000000000, \ 0.84303358445951348532, \ 0.00000000000000000000, \ -0.84303358445951348532, \ 0.00000000000000000000, \ 0.07303948013428374075, \ 0.00000000000000000000, \ -0.07303948013428374075, \ 0.00000000000000000000, \ 0.67807351338628540915, \ 0.00000000000000000000, \ -0.67807351338628540915, \ 0.00000000000000000000, \ 0.88198482628664209848, \ 0.00000000000000000000, \ -0.88198482628664209848, \ 0.00000000000000000000, \ 0.38587811686103651310, \ 0.00000000000000000000, \ -0.38587811686103651310, \ 0.00000000000000000000, \ 0.13708884737518356456, \ 0.00000000000000000000, \ -0.13708884737518356456, \ 0.52558521108268729805, \ 0.52558521108268729805, \ -0.52558521108268729805, \ -0.52558521108268729805, \ 0.45301642570589800707, \ 0.45301642570589800707, \ -0.45301642570589800707, \ -0.45301642570589800707, \ 0.67125116320175959306, \ 0.67125116320175959306, \ -0.67125116320175959306, \ -0.67125116320175959306, \ 0.36951418649168821240, \ 0.36951418649168821240, \ -0.36951418649168821240, \ -0.36951418649168821240, \ 0.28838223435586252119, \ 0.28838223435586252119, \ -0.28838223435586252119, \ -0.28838223435586252119, \ 0.82857238389465803774, \ 0.82857238389465803774, \ -0.82857238389465803774, \ -0.82857238389465803774, \ 0.67246070085447195996, \ 0.67246070085447195996, \ -0.67246070085447195996, \ -0.67246070085447195996, \ 0.48736689338962557727, \ 0.48736689338962557727, \ -0.48736689338962557727, \ -0.48736689338962557727, \ 0.95036644315079843448, \ 0.95036644315079843448, \ -0.95036644315079843448, \ -0.95036644315079843448, \ 0.09132353058612172059, \ 0.09132353058612172059, \ -0.09132353058612172059, \ -0.09132353058612172059, \ 0.15520695551416591185, \ 0.15520695551416591185, \ -0.15520695551416591185, \ -0.15520695551416591185, \ 0.05052806321356113906, \ 0.05052806321356113906, \ -0.05052806321356113906, \ -0.05052806321356113906, \ 0.39781392804166187949, \ 0.39781392804166187949, \ -0.39781392804166187949, \ -0.39781392804166187949, \ 0.37607913140641990868, \ 0.37607913140641990868, \ -0.37607913140641990868, \ -0.37607913140641990868, \ 0.16436382679828262510, \ 0.16436382679828262510, \ -0.16436382679828262510, \ -0.16436382679828262510, \ 0.34688925556861166521, \ 0.34688925556861166521, \ -0.34688925556861166521, \ -0.34688925556861166521, \ 0.11913325793719439782, \ 0.11913325793719439782, \ -0.11913325793719439782, \ -0.11913325793719439782, \ 0.74545838141881970440, \ 0.74545838141881970440, \ -0.74545838141881970440, \ -0.74545838141881970440, \ 0.76104952097303479874, \ 0.76104952097303479874, \ -0.76104952097303479874, \ -0.76104952097303479874, \ 0.24208120588771878112, \ 0.24208120588771878112, \ -0.24208120588771878112, \ -0.24208120588771878112, \ 0.84457983815668913330, \ 0.84457983815668913330, \ -0.84457983815668913330, \ -0.84457983815668913330, \ 0.16456465781662479864, \ 0.16456465781662479864, \ -0.16456465781662479864, \ -0.16456465781662479864, \ 0.27478423472388602278, \ 0.27478423472388602278, \ -0.27478423472388602278, \ -0.27478423472388602278, \ 0.58499194505600049521, \ 0.58499194505600049521, \ -0.58499194505600049521, \ -0.58499194505600049521, \ 0.14897381246033866709, \ 0.14897381246033866709, \ -0.14897381246033866709, \ -0.14897381246033866709, \ 0.43892903976173064384, \ 0.43892903976173064384, \ -0.43892903976173064384, \ -0.43892903976173064384, \ 0.87981971200037256686, \ 0.87981971200037256686, \ -0.87981971200037256686, \ -0.87981971200037256686, \ 0.11685331930792351718, \ 0.11685331930792351718, \ -0.11685331930792351718, \ -0.11685331930792351718, \ 0.34287164858560836844, \ 0.34287164858560836844, \ -0.34287164858560836844, \ -0.34287164858560836844, \ 0.64222367435367522237, \ 0.86433279841860011228, \ 0.64222367435367522237, \ -0.86433279841860011228, \ -0.64222367435367522237, \ 0.86433279841860011228, \ -0.64222367435367522237, \ -0.86433279841860011228, \ 0.15700371479211361336, \ 0.57840479596659710726, \ 0.15700371479211361336, \ -0.57840479596659710726, \ -0.15700371479211361336, \ 0.57840479596659710726, \ -0.15700371479211361336, \ -0.57840479596659710726, \ 0.53916009809927645247, \ 0.31087991149352928177, \ 0.53916009809927645247, \ -0.31087991149352928177, \ -0.53916009809927645247, \ 0.31087991149352928177, \ -0.53916009809927645247, \ -0.31087991149352928177, \ 0.56505069862686030380, \ 0.20472565121250529963, \ 0.56505069862686030380, \ -0.20472565121250529963, \ -0.56505069862686030380, \ 0.20472565121250529963, \ -0.56505069862686030380, \ -0.20472565121250529963, \ 0.80087300859132681818, \ 0.15477148314547456431, \ 0.80087300859132681818, \ -0.15477148314547456431, \ -0.80087300859132681818, \ 0.15477148314547456431, \ -0.80087300859132681818, \ -0.15477148314547456431, \ 0.36196927102445491942, \ 0.91122224850183075606, \ 0.36196927102445491942, \ -0.91122224850183075606, \ -0.36196927102445491942, \ 0.91122224850183075606, \ -0.36196927102445491942, \ -0.91122224850183075606, \ 0.46054474775257370212, \ 0.23763934442358639054, \ 0.46054474775257370212, \ -0.23763934442358639054, \ -0.46054474775257370212, \ 0.23763934442358639054, \ -0.46054474775257370212, \ -0.23763934442358639054, \ 0.32159807642681254025, \ 0.93026675012099768747, \ 0.32159807642681254025, \ -0.93026675012099768747, \ -0.32159807642681254025, \ 0.93026675012099768747, \ -0.32159807642681254025, \ -0.93026675012099768747, \ 0.75417578802823215245, \ 0.27330670991417554960, \ 0.75417578802823215245, \ -0.27330670991417554960, \ -0.75417578802823215245, \ 0.27330670991417554960, \ -0.75417578802823215245, \ -0.27330670991417554960, \ 0.40094999523846291956, \ 0.61977908311233775862, \ 0.40094999523846291956, \ -0.61977908311233775862, \ -0.40094999523846291956, \ 0.61977908311233775862, \ -0.40094999523846291956, \ -0.61977908311233775862, \ 0.71750306782387462956, \ 0.96731797310728928618, \ 0.71750306782387462956, \ -0.96731797310728928618, \ -0.71750306782387462956, \ 0.96731797310728928618, \ -0.71750306782387462956, \ -0.96731797310728928618, \ 0.14469640753388121612, \ 0.28107596241726462427, \ 0.14469640753388121612, \ -0.28107596241726462427, \ -0.14469640753388121612, \ 0.28107596241726462427, \ -0.14469640753388121612, \ -0.28107596241726462427, \ 0.80544313431837344375, \ 0.95723494789717944453, \ 0.80544313431837344375, \ -0.95723494789717944453, \ -0.80544313431837344375, \ 0.95723494789717944453, \ -0.80544313431837344375, \ -0.95723494789717944453, \ 0.56426321835446102693, \ 0.93415043892659577196, \ 0.56426321835446102693, \ -0.93415043892659577196, \ -0.56426321835446102693, \ 0.93415043892659577196, \ -0.56426321835446102693, \ -0.93415043892659577196, \ 0.27637233377156195102, \ 0.22124438393817494330, \ 0.27637233377156195102, \ -0.22124438393817494330, \ -0.27637233377156195102, \ 0.22124438393817494330, \ -0.27637233377156195102, \ -0.22124438393817494330, \ 0.67110969363741279636, \ 0.51440860154860901243, \ 0.67110969363741279636, \ -0.51440860154860901243, \ -0.67110969363741279636, \ 0.51440860154860901243, \ -0.67110969363741279636, \ -0.51440860154860901243, \ 0.64763095243614277052, \ 0.84669681763194848401, \ 0.64763095243614277052, \ -0.84669681763194848401, \ -0.64763095243614277052, \ 0.84669681763194848401, \ -0.64763095243614277052, \ -0.84669681763194848401, \ 0.75878491584810681125, \ 0.58372340157348212575, \ 0.75878491584810681125, \ -0.58372340157348212575, \ -0.75878491584810681125, \ 0.58372340157348212575, \ -0.75878491584810681125, \ -0.58372340157348212575, \ 0.75795786639659157302, \ 0.23125484278203506383, \ 0.75795786639659157302, \ -0.23125484278203506383, \ -0.75795786639659157302, \ 0.23125484278203506383, \ -0.75795786639659157302, \ -0.23125484278203506383, \ 0.21186490812432900999, \ 0.65351981646876278198, \ 0.21186490812432900999, \ -0.65351981646876278198, \ -0.21186490812432900999, \ 0.65351981646876278198, \ -0.21186490812432900999, \ -0.65351981646876278198, \ 0.18605131637198926708, \ 0.69534501524896896729, \ 0.18605131637198926708, \ -0.69534501524896896729, \ -0.18605131637198926708, \ 0.69534501524896896729, \ -0.18605131637198926708, \ -0.69534501524896896729, \ 0.52410330742380673019, \ 0.08127234831798690884, \ 0.52410330742380673019, \ -0.08127234831798690884, \ -0.52410330742380673019, \ 0.08127234831798690884, \ -0.52410330742380673019, \ -0.08127234831798690884, \ 0.47074593361034250405, \ 0.67316244188134488624, \ 0.47074593361034250405, \ -0.67316244188134488624, \ -0.47074593361034250405, \ 0.67316244188134488624, \ -0.47074593361034250405, \ -0.67316244188134488624, \ 0.38456345752643983360, \ 0.82977152170712553669, \ 0.38456345752643983360, \ -0.82977152170712553669, \ -0.38456345752643983360, \ 0.82977152170712553669, \ -0.38456345752643983360, \ -0.82977152170712553669, \ 0.48551299054356161777, \ 0.85308428733291663537, \ 0.48551299054356161777, \ -0.85308428733291663537, \ -0.48551299054356161777, \ 0.85308428733291663537, \ -0.48551299054356161777, \ -0.85308428733291663537, \ 0.17757095991022572856, \ 0.44670731850691264286, \ 0.17757095991022572856, \ -0.44670731850691264286, \ -0.17757095991022572856, \ 0.44670731850691264286, \ -0.17757095991022572856, \ -0.44670731850691264286, \ 0.46199941611318601220, \ 0.67009672120301455589, \ 0.46199941611318601220, \ -0.67009672120301455589, \ -0.46199941611318601220, \ 0.67009672120301455589, \ -0.46199941611318601220, \ -0.67009672120301455589, \ 0.26790019276269744219, \ 0.97673360371074724462, \ 0.26790019276269744219, \ -0.97673360371074724462, \ -0.26790019276269744219, \ 0.97673360371074724462, \ -0.26790019276269744219, \ -0.97673360371074724462, \ 0.45381764631367643714, \ 0.31887900072125263673, \ 0.45381764631367643714, \ -0.31887900072125263673, \ -0.45381764631367643714, \ 0.31887900072125263673, \ -0.45381764631367643714, \ -0.31887900072125263673 ] ) z = np.array ( [ \ 0.96739133523703502160, \ 0.54366532464638728239, \ 0.41887560622759456574, \ 0.41887560622759456574, \ 0.41887560622759456574, \ 0.41887560622759456574, \ 0.29774894445685839983, \ 0.29774894445685839983, \ 0.29774894445685839983, \ 0.29774894445685839983, \ 0.43632558904359264318, \ 0.43632558904359264318, \ 0.43632558904359264318, \ 0.43632558904359264318, \ 0.13123475865230219140, \ 0.13123475865230219140, \ 0.13123475865230219140, \ 0.13123475865230219140, \ 0.56882169546815719574, \ 0.56882169546815719574, \ 0.56882169546815719574, \ 0.56882169546815719574, \ 0.66230573631886058283, \ 0.66230573631886058283, \ 0.66230573631886058283, \ 0.66230573631886058283, \ 0.21963789124598576130, \ 0.21963789124598576130, \ 0.21963789124598576130, \ 0.21963789124598576130, \ 0.22732696332834559372, \ 0.22732696332834559372, \ 0.22732696332834559372, \ 0.22732696332834559372, \ 0.00541751512625303269, \ 0.00541751512625303269, \ 0.00541751512625303269, \ 0.00541751512625303269, \ 0.79294906136483345183, \ 0.79294906136483345183, \ 0.79294906136483345183, \ 0.79294906136483345183, \ 0.04180662980331771583, \ 0.04180662980331771583, \ 0.04180662980331771583, \ 0.04180662980331771583, \ 0.13615518064579532065, \ 0.13615518064579532065, \ 0.13615518064579532065, \ 0.13615518064579532065, \ 0.91875475602806166986, \ 0.91875475602806166986, \ 0.91875475602806166986, \ 0.91875475602806166986, \ 0.30191905621780101843, \ 0.30191905621780101843, \ 0.30191905621780101843, \ 0.30191905621780101843, \ 0.00938749984908901144, \ 0.00938749984908901144, \ 0.00938749984908901144, \ 0.00938749984908901144, \ 0.60658598457462375997, \ 0.60658598457462375997, \ 0.60658598457462375997, \ 0.60658598457462375997, \ 0.75353482202105526166, \ 0.75353482202105526166, \ 0.75353482202105526166, \ 0.75353482202105526166, \ 0.44086853690608979184, \ 0.44086853690608979184, \ 0.44086853690608979184, \ 0.44086853690608979184, \ 0.41889775081556313019, \ 0.41889775081556313019, \ 0.41889775081556313019, \ 0.41889775081556313019, \ 0.01251810432139164979, \ 0.01251810432139164979, \ 0.01251810432139164979, \ 0.01251810432139164979, \ 0.62460148383811031625, \ 0.62460148383811031625, \ 0.62460148383811031625, \ 0.62460148383811031625, \ 0.05439973273857341696, \ 0.05439973273857341696, \ 0.05439973273857341696, \ 0.05439973273857341696, \ 0.16191862193166678408, \ 0.16191862193166678408, \ 0.16191862193166678408, \ 0.16191862193166678408, \ 0.29300331383428240839, \ 0.29300331383428240839, \ 0.29300331383428240839, \ 0.29300331383428240839, \ 0.26342658893870185555, \ 0.26342658893870185555, \ 0.26342658893870185555, \ 0.26342658893870185555, \ 0.01127614473867753070, \ 0.01127614473867753070, \ 0.01127614473867753070, \ 0.01127614473867753070, \ 0.35807984614999605055, \ 0.35807984614999605055, \ 0.35807984614999605055, \ 0.35807984614999605055, \ 0.47141886716708586436, \ 0.47141886716708586436, \ 0.47141886716708586436, \ 0.47141886716708586436, \ 0.85446407112095401626, \ 0.85446407112095401626, \ 0.85446407112095401626, \ 0.85446407112095401626, \ 0.12930311691456014556, \ 0.12930311691456014556, \ 0.12930311691456014556, \ 0.12930311691456014556, \ 0.07899233073306564934, \ 0.07899233073306564934, \ 0.07899233073306564934, \ 0.07899233073306564934, \ 0.01672886065733771022, \ 0.01672886065733771022, \ 0.01672886065733771022, \ 0.01672886065733771022, \ 0.38850504372376110096, \ 0.38850504372376110096, \ 0.38850504372376110096, \ 0.38850504372376110096, \ 0.84754739757493258168, \ 0.84754739757493258168, \ 0.84754739757493258168, \ 0.84754739757493258168, \ 0.16263602800181631292, \ 0.16263602800181631292, \ 0.16263602800181631292, \ 0.16263602800181631292, \ 0.07862268330374026781, \ 0.07862268330374026781, \ 0.07862268330374026781, \ 0.07862268330374026781, \ 0.32028064376194109730, \ 0.32028064376194109730, \ 0.32028064376194109730, \ 0.32028064376194109730, \ 0.01382133423647079022, \ 0.01382133423647079022, \ 0.01382133423647079022, \ 0.01382133423647079022, \ 0.76877522504357953537, \ 0.76877522504357953537, \ 0.76877522504357953537, \ 0.76877522504357953537, \ 0.53014024087305255950, \ 0.53014024087305255950, \ 0.53014024087305255950, \ 0.53014024087305255950, \ 0.30089238244412036538, \ 0.30089238244412036538, \ 0.30089238244412036538, \ 0.30089238244412036538, \ 0.61673192700785928189, \ 0.61673192700785928189, \ 0.61673192700785928189, \ 0.61673192700785928189, \ 0.01376377254881575897, \ 0.01376377254881575897, \ 0.01376377254881575897, \ 0.01376377254881575897, \ 0.07210305012229555055, \ 0.07210305012229555055, \ 0.07210305012229555055, \ 0.07210305012229555055, \ 0.06238118616203952582, \ 0.06238118616203952582, \ 0.06238118616203952582, \ 0.06238118616203952582, \ 0.58557953491658876199, \ 0.58557953491658876199, \ 0.58557953491658876199, \ 0.58557953491658876199, \ 0.11791920647798490029, \ 0.11791920647798490029, \ 0.11791920647798490029, \ 0.11791920647798490029, \ 0.11791920647798490029, \ 0.11791920647798490029, \ 0.11791920647798490029, \ 0.11791920647798490029, \ 0.11142523412928505289, \ 0.11142523412928505289, \ 0.11142523412928505289, \ 0.11142523412928505289, \ 0.11142523412928505289, \ 0.11142523412928505289, \ 0.11142523412928505289, \ 0.11142523412928505289, \ 0.27502672812187933804, \ 0.27502672812187933804, \ 0.27502672812187933804, \ 0.27502672812187933804, \ 0.27502672812187933804, \ 0.27502672812187933804, \ 0.27502672812187933804, \ 0.27502672812187933804, \ 0.34728469726559213493, \ 0.34728469726559213493, \ 0.34728469726559213493, \ 0.34728469726559213493, \ 0.34728469726559213493, \ 0.34728469726559213493, \ 0.34728469726559213493, \ 0.34728469726559213493, \ 0.07549551730236130076, \ 0.07549551730236130076, \ 0.07549551730236130076, \ 0.07549551730236130076, \ 0.07549551730236130076, \ 0.07549551730236130076, \ 0.07549551730236130076, \ 0.07549551730236130076, \ 0.03464296962031117311, \ 0.03464296962031117311, \ 0.03464296962031117311, \ 0.03464296962031117311, \ 0.03464296962031117311, \ 0.03464296962031117311, \ 0.03464296962031117311, \ 0.03464296962031117311, \ 0.20441529779235670383, \ 0.20441529779235670383, \ 0.20441529779235670383, \ 0.20441529779235670383, \ 0.20441529779235670383, \ 0.20441529779235670383, \ 0.20441529779235670383, \ 0.20441529779235670383, \ 0.06972695561067981940, \ 0.06972695561067981940, \ 0.06972695561067981940, \ 0.06972695561067981940, \ 0.06972695561067981940, \ 0.06972695561067981940, \ 0.06972695561067981940, \ 0.06972695561067981940, \ 0.21998980465815576313, \ 0.21998980465815576313, \ 0.21998980465815576313, \ 0.21998980465815576313, \ 0.21998980465815576313, \ 0.21998980465815576313, \ 0.21998980465815576313, \ 0.21998980465815576313, \ 0.36462254947959177320, \ 0.36462254947959177320, \ 0.36462254947959177320, \ 0.36462254947959177320, \ 0.36462254947959177320, \ 0.36462254947959177320, \ 0.36462254947959177320, \ 0.36462254947959177320, \ 0.00458633496122378467, \ 0.00458633496122378467, \ 0.00458633496122378467, \ 0.00458633496122378467, \ 0.00458633496122378467, \ 0.00458633496122378467, \ 0.00458633496122378467, \ 0.00458633496122378467, \ 0.66642300488713057671, \ 0.66642300488713057671, \ 0.66642300488713057671, \ 0.66642300488713057671, \ 0.66642300488713057671, \ 0.66642300488713057671, \ 0.66642300488713057671, \ 0.66642300488713057671, \ 0.03975302308577006311, \ 0.03975302308577006311, \ 0.03975302308577006311, \ 0.03975302308577006311, \ 0.03975302308577006311, \ 0.03975302308577006311, \ 0.03975302308577006311, \ 0.03975302308577006311, \ 0.03073598825835915579, \ 0.03073598825835915579, \ 0.03073598825835915579, \ 0.03073598825835915579, \ 0.03073598825835915579, \ 0.03073598825835915579, \ 0.03073598825835915579, \ 0.03073598825835915579, \ 0.72077351789673316240, \ 0.72077351789673316240, \ 0.72077351789673316240, \ 0.72077351789673316240, \ 0.72077351789673316240, \ 0.72077351789673316240, \ 0.72077351789673316240, \ 0.72077351789673316240, \ 0.14036094696120685055, \ 0.14036094696120685055, \ 0.14036094696120685055, \ 0.14036094696120685055, \ 0.14036094696120685055, \ 0.14036094696120685055, \ 0.14036094696120685055, \ 0.14036094696120685055, \ 0.05264191965632582237, \ 0.05264191965632582237, \ 0.05264191965632582237, \ 0.05264191965632582237, \ 0.05264191965632582237, \ 0.05264191965632582237, \ 0.05264191965632582237, \ 0.05264191965632582237, \ 0.22702332489421667150, \ 0.22702332489421667150, \ 0.22702332489421667150, \ 0.22702332489421667150, \ 0.22702332489421667150, \ 0.22702332489421667150, \ 0.22702332489421667150, \ 0.22702332489421667150, \ 0.02881326163838642679, \ 0.02881326163838642679, \ 0.02881326163838642679, \ 0.02881326163838642679, \ 0.02881326163838642679, \ 0.02881326163838642679, \ 0.02881326163838642679, \ 0.02881326163838642679, \ 0.00532138936818496097, \ 0.00532138936818496097, \ 0.00532138936818496097, \ 0.00532138936818496097, \ 0.00532138936818496097, \ 0.00532138936818496097, \ 0.00532138936818496097, \ 0.00532138936818496097, \ 0.15917093130673495849, \ 0.15917093130673495849, \ 0.15917093130673495849, \ 0.15917093130673495849, \ 0.15917093130673495849, \ 0.15917093130673495849, \ 0.15917093130673495849, \ 0.15917093130673495849, \ 0.04286780869626788393, \ 0.04286780869626788393, \ 0.04286780869626788393, \ 0.04286780869626788393, \ 0.04286780869626788393, \ 0.04286780869626788393, \ 0.04286780869626788393, \ 0.04286780869626788393, \ 0.22819215603891684907, \ 0.22819215603891684907, \ 0.22819215603891684907, \ 0.22819215603891684907, \ 0.22819215603891684907, \ 0.22819215603891684907, \ 0.22819215603891684907, \ 0.22819215603891684907, \ 0.11497584756253050042, \ 0.11497584756253050042, \ 0.11497584756253050042, \ 0.11497584756253050042, \ 0.11497584756253050042, \ 0.11497584756253050042, \ 0.11497584756253050042, \ 0.11497584756253050042, \ 0.00654660357363916808, \ 0.00654660357363916808, \ 0.00654660357363916808, \ 0.00654660357363916808, \ 0.00654660357363916808, \ 0.00654660357363916808, \ 0.00654660357363916808, \ 0.00654660357363916808, \ 0.48896580613114126734, \ 0.48896580613114126734, \ 0.48896580613114126734, \ 0.48896580613114126734, \ 0.48896580613114126734, \ 0.48896580613114126734, \ 0.48896580613114126734, \ 0.48896580613114126734, \ 0.05843691849737928795, \ 0.05843691849737928795, \ 0.05843691849737928795, \ 0.05843691849737928795, \ 0.05843691849737928795, \ 0.05843691849737928795, \ 0.05843691849737928795, \ 0.05843691849737928795, \ 0.00610498541327420680, \ 0.00610498541327420680, \ 0.00610498541327420680, \ 0.00610498541327420680, \ 0.00610498541327420680, \ 0.00610498541327420680, \ 0.00610498541327420680, \ 0.00610498541327420680, \ 0.53408664015576723383, \ 0.53408664015576723383, \ 0.53408664015576723383, \ 0.53408664015576723383, \ 0.53408664015576723383, \ 0.53408664015576723383, \ 0.53408664015576723383, \ 0.53408664015576723383 ] ) w= np.array ( [ \ 0.00012870022397472401, \ 0.00539076125430030910, \ 0.00666687105780559754, \ 0.00666687105780559754, \ 0.00666687105780559754, \ 0.00666687105780559754, \ 0.00619801121379879964, \ 0.00619801121379879964, \ 0.00619801121379879964, \ 0.00619801121379879964, \ 0.00119690394217259041, \ 0.00119690394217259041, \ 0.00119690394217259041, \ 0.00119690394217259041, \ 0.00900035197624313339, \ 0.00900035197624313339, \ 0.00900035197624313339, \ 0.00900035197624313339, \ 0.00416463710538401977, \ 0.00416463710538401977, \ 0.00416463710538401977, \ 0.00416463710538401977, \ 0.00182449720872727593, \ 0.00182449720872727593, \ 0.00182449720872727593, \ 0.00182449720872727593, \ 0.00452371868333050885, \ 0.00452371868333050885, \ 0.00452371868333050885, \ 0.00452371868333050885, \ 0.00816111606481412406, \ 0.00816111606481412406, \ 0.00816111606481412406, \ 0.00816111606481412406, \ 0.00164832682863707940, \ 0.00164832682863707940, \ 0.00164832682863707940, \ 0.00164832682863707940, \ 0.00055714923095003237, \ 0.00055714923095003237, \ 0.00055714923095003237, \ 0.00055714923095003237, \ 0.00111821525219482697, \ 0.00111821525219482697, \ 0.00111821525219482697, \ 0.00111821525219482697, \ 0.00188581015876115280, \ 0.00188581015876115280, \ 0.00188581015876115280, \ 0.00188581015876115280, \ 0.00028281012262636759, \ 0.00028281012262636759, \ 0.00028281012262636759, \ 0.00028281012262636759, \ 0.00181586354615248828, \ 0.00181586354615248828, \ 0.00181586354615248828, \ 0.00181586354615248828, \ 0.00124708244822032614, \ 0.00124708244822032614, \ 0.00124708244822032614, \ 0.00124708244822032614, \ 0.00107416255302727809, \ 0.00107416255302727809, \ 0.00107416255302727809, \ 0.00107416255302727809, \ 0.00257977077737831396, \ 0.00257977077737831396, \ 0.00257977077737831396, \ 0.00257977077737831396, \ 0.00091701544972603221, \ 0.00091701544972603221, \ 0.00091701544972603221, \ 0.00091701544972603221, \ 0.00306877872117356605, \ 0.00306877872117356605, \ 0.00306877872117356605, \ 0.00306877872117356605, \ 0.00187105817191728823, \ 0.00187105817191728823, \ 0.00187105817191728823, \ 0.00187105817191728823, \ 0.00015369093908062739, \ 0.00015369093908062739, \ 0.00015369093908062739, \ 0.00015369093908062739, \ 0.00384529073211040779, \ 0.00384529073211040779, \ 0.00384529073211040779, \ 0.00384529073211040779, \ 0.00022431161642440681, \ 0.00022431161642440681, \ 0.00022431161642440681, \ 0.00022431161642440681, \ 0.00084020876261339610, \ 0.00084020876261339610, \ 0.00084020876261339610, \ 0.00084020876261339610, \ 0.00304195767454043140, \ 0.00304195767454043140, \ 0.00304195767454043140, \ 0.00304195767454043140, \ 0.00022948417669879317, \ 0.00022948417669879317, \ 0.00022948417669879317, \ 0.00022948417669879317, \ 0.00418242059186963843, \ 0.00418242059186963843, \ 0.00418242059186963843, \ 0.00418242059186963843, \ 0.00632709108150545339, \ 0.00632709108150545339, \ 0.00632709108150545339, \ 0.00632709108150545339, \ 0.00075928340059512709, \ 0.00075928340059512709, \ 0.00075928340059512709, \ 0.00075928340059512709, \ 0.00459683666227672476, \ 0.00459683666227672476, \ 0.00459683666227672476, \ 0.00459683666227672476, \ 0.00276636427423579932, \ 0.00276636427423579932, \ 0.00276636427423579932, \ 0.00276636427423579932, \ 0.00214485080151055087, \ 0.00214485080151055087, \ 0.00214485080151055087, \ 0.00214485080151055087, \ 0.00528314448618283795, \ 0.00528314448618283795, \ 0.00528314448618283795, \ 0.00528314448618283795, \ 0.00048810523226141780, \ 0.00048810523226141780, \ 0.00048810523226141780, \ 0.00048810523226141780, \ 0.00212069545834849948, \ 0.00212069545834849948, \ 0.00212069545834849948, \ 0.00212069545834849948, \ 0.00161506019948201812, \ 0.00161506019948201812, \ 0.00161506019948201812, \ 0.00161506019948201812, \ 0.00694225709294844437, \ 0.00694225709294844437, \ 0.00694225709294844437, \ 0.00694225709294844437, \ 0.00100268302008121369, \ 0.00100268302008121369, \ 0.00100268302008121369, \ 0.00100268302008121369, \ 0.00092077531674916973, \ 0.00092077531674916973, \ 0.00092077531674916973, \ 0.00092077531674916973, \ 0.00355616947744542573, \ 0.00355616947744542573, \ 0.00355616947744542573, \ 0.00355616947744542573, \ 0.00218617871329652470, \ 0.00218617871329652470, \ 0.00218617871329652470, \ 0.00218617871329652470, \ 0.00269165166203209818, \ 0.00269165166203209818, \ 0.00269165166203209818, \ 0.00269165166203209818, \ 0.00301674010475732127, \ 0.00301674010475732127, \ 0.00301674010475732127, \ 0.00301674010475732127, \ 0.00074666452415505266, \ 0.00074666452415505266, \ 0.00074666452415505266, \ 0.00074666452415505266, \ 0.00299748233690233252, \ 0.00299748233690233252, \ 0.00299748233690233252, \ 0.00299748233690233252, \ 0.00144784702606324633, \ 0.00144784702606324633, \ 0.00144784702606324633, \ 0.00144784702606324633, \ 0.00107280962935336075, \ 0.00107280962935336075, \ 0.00107280962935336075, \ 0.00107280962935336075, \ 0.00107280962935336075, \ 0.00107280962935336075, \ 0.00107280962935336075, \ 0.00107280962935336075, \ 0.00483903734837801830, \ 0.00483903734837801830, \ 0.00483903734837801830, \ 0.00483903734837801830, \ 0.00483903734837801830, \ 0.00483903734837801830, \ 0.00483903734837801830, \ 0.00483903734837801830, \ 0.00274709905982003805, \ 0.00274709905982003805, \ 0.00274709905982003805, \ 0.00274709905982003805, \ 0.00274709905982003805, \ 0.00274709905982003805, \ 0.00274709905982003805, \ 0.00274709905982003805, \ 0.00433501688902940795, \ 0.00433501688902940795, \ 0.00433501688902940795, \ 0.00433501688902940795, \ 0.00433501688902940795, \ 0.00433501688902940795, \ 0.00433501688902940795, \ 0.00433501688902940795, \ 0.00271810015984954700, \ 0.00271810015984954700, \ 0.00271810015984954700, \ 0.00271810015984954700, \ 0.00271810015984954700, \ 0.00271810015984954700, \ 0.00271810015984954700, \ 0.00271810015984954700, \ 0.00091685473986105473, \ 0.00091685473986105473, \ 0.00091685473986105473, \ 0.00091685473986105473, \ 0.00091685473986105473, \ 0.00091685473986105473, \ 0.00091685473986105473, \ 0.00091685473986105473, \ 0.00680895101968847279, \ 0.00680895101968847279, \ 0.00680895101968847279, \ 0.00680895101968847279, \ 0.00680895101968847279, \ 0.00680895101968847279, \ 0.00680895101968847279, \ 0.00680895101968847279, \ 0.00040138568966109102, \ 0.00040138568966109102, \ 0.00040138568966109102, \ 0.00040138568966109102, \ 0.00040138568966109102, \ 0.00040138568966109102, \ 0.00040138568966109102, \ 0.00040138568966109102, \ 0.00215500289545228485, \ 0.00215500289545228485, \ 0.00215500289545228485, \ 0.00215500289545228485, \ 0.00215500289545228485, \ 0.00215500289545228485, \ 0.00215500289545228485, \ 0.00215500289545228485, \ 0.00161154257302305293, \ 0.00161154257302305293, \ 0.00161154257302305293, \ 0.00161154257302305293, \ 0.00161154257302305293, \ 0.00161154257302305293, \ 0.00161154257302305293, \ 0.00161154257302305293, \ 0.00027434552667444364, \ 0.00027434552667444364, \ 0.00027434552667444364, \ 0.00027434552667444364, \ 0.00027434552667444364, \ 0.00027434552667444364, \ 0.00027434552667444364, \ 0.00027434552667444364, \ 0.00230008297506218524, \ 0.00230008297506218524, \ 0.00230008297506218524, \ 0.00230008297506218524, \ 0.00230008297506218524, \ 0.00230008297506218524, \ 0.00230008297506218524, \ 0.00230008297506218524, \ 0.00029458357590517713, \ 0.00029458357590517713, \ 0.00029458357590517713, \ 0.00029458357590517713, \ 0.00029458357590517713, \ 0.00029458357590517713, \ 0.00029458357590517713, \ 0.00029458357590517713, \ 0.00060073122167725204, \ 0.00060073122167725204, \ 0.00060073122167725204, \ 0.00060073122167725204, \ 0.00060073122167725204, \ 0.00060073122167725204, \ 0.00060073122167725204, \ 0.00060073122167725204, \ 0.00026201750375773298, \ 0.00026201750375773298, \ 0.00026201750375773298, \ 0.00026201750375773298, \ 0.00026201750375773298, \ 0.00026201750375773298, \ 0.00026201750375773298, \ 0.00026201750375773298, \ 0.00419283249870963659, \ 0.00419283249870963659, \ 0.00419283249870963659, \ 0.00419283249870963659, \ 0.00419283249870963659, \ 0.00419283249870963659, \ 0.00419283249870963659, \ 0.00419283249870963659, \ 0.00173629430868813472, \ 0.00173629430868813472, \ 0.00173629430868813472, \ 0.00173629430868813472, \ 0.00173629430868813472, \ 0.00173629430868813472, \ 0.00173629430868813472, \ 0.00173629430868813472, \ 0.00094391016694345316, \ 0.00094391016694345316, \ 0.00094391016694345316, \ 0.00094391016694345316, \ 0.00094391016694345316, \ 0.00094391016694345316, \ 0.00094391016694345316, \ 0.00094391016694345316, \ 0.00217551360850374046, \ 0.00217551360850374046, \ 0.00217551360850374046, \ 0.00217551360850374046, \ 0.00217551360850374046, \ 0.00217551360850374046, \ 0.00217551360850374046, \ 0.00217551360850374046, \ 0.00128339469018335490, \ 0.00128339469018335490, \ 0.00128339469018335490, \ 0.00128339469018335490, \ 0.00128339469018335490, \ 0.00128339469018335490, \ 0.00128339469018335490, \ 0.00128339469018335490, \ 0.00272615049960569979, \ 0.00272615049960569979, \ 0.00272615049960569979, \ 0.00272615049960569979, \ 0.00272615049960569979, \ 0.00272615049960569979, \ 0.00272615049960569979, \ 0.00272615049960569979, \ 0.00318533960385062025, \ 0.00318533960385062025, \ 0.00318533960385062025, \ 0.00318533960385062025, \ 0.00318533960385062025, \ 0.00318533960385062025, \ 0.00318533960385062025, \ 0.00318533960385062025, \ 0.00266309286664456963, \ 0.00266309286664456963, \ 0.00266309286664456963, \ 0.00266309286664456963, \ 0.00266309286664456963, \ 0.00266309286664456963, \ 0.00266309286664456963, \ 0.00266309286664456963, \ 0.00232666846528824418, \ 0.00232666846528824418, \ 0.00232666846528824418, \ 0.00232666846528824418, \ 0.00232666846528824418, \ 0.00232666846528824418, \ 0.00232666846528824418, \ 0.00232666846528824418, \ 0.00097346311519703153, \ 0.00097346311519703153, \ 0.00097346311519703153, \ 0.00097346311519703153, \ 0.00097346311519703153, \ 0.00097346311519703153, \ 0.00097346311519703153, \ 0.00097346311519703153, \ 0.00348345685139948022, \ 0.00348345685139948022, \ 0.00348345685139948022, \ 0.00348345685139948022, \ 0.00348345685139948022, \ 0.00348345685139948022, \ 0.00348345685139948022, \ 0.00348345685139948022, \ 0.00406195421696304172, \ 0.00406195421696304172, \ 0.00406195421696304172, \ 0.00406195421696304172, \ 0.00406195421696304172, \ 0.00406195421696304172, \ 0.00406195421696304172, \ 0.00406195421696304172, \ 0.00033245593568842263, \ 0.00033245593568842263, \ 0.00033245593568842263, \ 0.00033245593568842263, \ 0.00033245593568842263, \ 0.00033245593568842263, \ 0.00033245593568842263, \ 0.00033245593568842263, \ 0.00092328174175319150, \ 0.00092328174175319150, \ 0.00092328174175319150, \ 0.00092328174175319150, \ 0.00092328174175319150, \ 0.00092328174175319150, \ 0.00092328174175319150, \ 0.00092328174175319150 ] ) return x, y, z, w def rule20 ( ): #*****************************************************************************80 # ## rule20() returns the pyramid quadrature rule of precision 20. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 16 April 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # x(n), y(n), z(n): the coordinates of quadrature points. # # w(n): the quadrature weights. # import numpy as np x = np.array ( [ \ 0.00000000000000000000, \ 0.48169354344312520499, \ 0.00000000000000000000, \ -0.48169354344312520499, \ 0.00000000000000000000, \ 0.69858038869870031640, \ 0.00000000000000000000, \ -0.69858038869870031640, \ 0.00000000000000000000, \ 0.53468657951770970360, \ 0.00000000000000000000, \ -0.53468657951770970360, \ 0.00000000000000000000, \ 0.42228380878442672852, \ 0.00000000000000000000, \ -0.42228380878442672852, \ 0.00000000000000000000, \ 0.30680451888779119995, \ 0.00000000000000000000, \ -0.30680451888779119995, \ 0.00000000000000000000, \ 0.22877498497689821577, \ 0.00000000000000000000, \ -0.22877498497689821577, \ 0.00000000000000000000, \ 0.55389687412807175892, \ 0.00000000000000000000, \ -0.55389687412807175892, \ 0.00000000000000000000, \ 0.38489228042331330437, \ 0.00000000000000000000, \ -0.38489228042331330437, \ 0.00000000000000000000, \ 0.25711056873844140291, \ 0.00000000000000000000, \ -0.25711056873844140291, \ 0.00000000000000000000, \ 0.94954208334711565076, \ 0.00000000000000000000, \ -0.94954208334711565076, \ 0.00000000000000000000, \ 0.09635090648066924057, \ 0.00000000000000000000, \ -0.09635090648066924057, \ 0.00000000000000000000, \ 0.91044931261818451418, \ 0.00000000000000000000, \ -0.91044931261818451418, \ 0.00000000000000000000, \ 0.26830824357428106897, \ 0.00000000000000000000, \ -0.26830824357428106897, \ 0.00000000000000000000, \ 0.82744656686299722370, \ 0.00000000000000000000, \ -0.82744656686299722370, \ 0.00000000000000000000, \ 0.03789270083108932374, \ 0.00000000000000000000, \ -0.03789270083108932374, \ 0.00000000000000000000, \ 0.57352052408158127328, \ 0.00000000000000000000, \ -0.57352052408158127328, \ 0.00000000000000000000, \ 0.74231157227003041754, \ 0.00000000000000000000, \ -0.74231157227003041754, \ 0.00000000000000000000, \ 0.28469096413200573048, \ 0.00000000000000000000, \ -0.28469096413200573048, \ 0.00000000000000000000, \ 0.11281627950690893691, \ 0.00000000000000000000, \ -0.11281627950690893691, \ 0.00000000000000000000, \ 0.45356762399670425001, \ -0.45356762399670425001, \ 0.45356762399670425001, \ -0.45356762399670425001, \ 0.33361103852611595499, \ -0.33361103852611595499, \ 0.33361103852611595499, \ -0.33361103852611595499, \ 0.37733375278222114346, \ -0.37733375278222114346, \ 0.37733375278222114346, \ -0.37733375278222114346, \ 0.30611174916927796907, \ -0.30611174916927796907, \ 0.30611174916927796907, \ -0.30611174916927796907, \ 0.29044600765245415230, \ -0.29044600765245415230, \ 0.29044600765245415230, \ -0.29044600765245415230, \ 0.59141068840923671779, \ -0.59141068840923671779, \ 0.59141068840923671779, \ -0.59141068840923671779, \ 0.76605496491352953470, \ -0.76605496491352953470, \ 0.76605496491352953470, \ -0.76605496491352953470, \ 0.44962169263179840861, \ -0.44962169263179840861, \ 0.44962169263179840861, \ -0.44962169263179840861, \ 0.61256910754587590162, \ -0.61256910754587590162, \ 0.61256910754587590162, \ -0.61256910754587590162, \ 0.96517775637880776074, \ -0.96517775637880776074, \ 0.96517775637880776074, \ -0.96517775637880776074, \ 0.18509443085238544424, \ -0.18509443085238544424, \ 0.18509443085238544424, \ -0.18509443085238544424, \ 0.13053399140728452754, \ -0.13053399140728452754, \ 0.13053399140728452754, \ -0.13053399140728452754, \ 0.08713330755302489683, \ -0.08713330755302489683, \ 0.08713330755302489683, \ -0.08713330755302489683, \ 0.11626579551616780805, \ -0.11626579551616780805, \ 0.11626579551616780805, \ -0.11626579551616780805, \ 0.03353132384174680597, \ -0.03353132384174680597, \ 0.03353132384174680597, \ -0.03353132384174680597, \ 0.63007044649757071308, \ -0.63007044649757071308, \ 0.63007044649757071308, \ -0.63007044649757071308, \ 0.10081553511278160129, \ -0.10081553511278160129, \ 0.10081553511278160129, \ -0.10081553511278160129, \ 0.09712721271803037570, \ -0.09712721271803037570, \ 0.09712721271803037570, \ -0.09712721271803037570, \ 0.65036744612024988133, \ -0.65036744612024988133, \ 0.65036744612024988133, \ -0.65036744612024988133, \ 0.78816705553909693904, \ -0.78816705553909693904, \ 0.78816705553909693904, \ -0.78816705553909693904, \ 0.46326102535176988395, \ -0.46326102535176988395, \ 0.46326102535176988395, \ -0.46326102535176988395, \ 0.87426225625453524160, \ -0.87426225625453524160, \ 0.87426225625453524160, \ -0.87426225625453524160, \ 0.09693365579654888986, \ -0.09693365579654888986, \ 0.09693365579654888986, \ -0.09693365579654888986, \ 0.52651234369915456135, \ -0.52651234369915456135, \ 0.52651234369915456135, \ -0.52651234369915456135, \ 0.21058018350559978837, \ -0.21058018350559978837, \ 0.21058018350559978837, \ -0.21058018350559978837, \ 0.48341786018142590686, \ -0.48341786018142590686, \ 0.48341786018142590686, \ -0.48341786018142590686, \ 0.27232398053992901144, \ -0.27232398053992901144, \ 0.27232398053992901144, \ -0.27232398053992901144, \ 0.88748390701146573356, \ -0.88748390701146573356, \ 0.88748390701146573356, \ -0.88748390701146573356, \ 0.34004340177081920915, \ -0.34004340177081920915, \ 0.34004340177081920915, \ -0.34004340177081920915, \ 0.24657134521158877161, \ -0.24657134521158877161, \ 0.24657134521158877161, \ -0.24657134521158877161, \ 0.72032611852462202773, \ -0.72032611852462202773, \ 0.72032611852462202773, \ -0.72032611852462202773, \ 0.86934672471843543740, \ 0.66053776743762293577, \ -0.86934672471843543740, \ 0.66053776743762293577, \ 0.86934672471843543740, \ -0.66053776743762293577, \ -0.86934672471843543740, \ -0.66053776743762293577, \ 0.51657003644145271792, \ 0.12681144322431647797, \ -0.51657003644145271792, \ 0.12681144322431647797, \ 0.51657003644145271792, \ -0.12681144322431647797, \ -0.51657003644145271792, \ -0.12681144322431647797, \ 0.21419492835914627493, \ 0.53514205206517340141, \ -0.21419492835914627493, \ 0.53514205206517340141, \ 0.21419492835914627493, \ -0.53514205206517340141, \ -0.21419492835914627493, \ -0.53514205206517340141, \ 0.38606155250360069120, \ 0.14309874624364349316, \ -0.38606155250360069120, \ 0.14309874624364349316, \ 0.38606155250360069120, \ -0.14309874624364349316, \ -0.38606155250360069120, \ -0.14309874624364349316, \ 0.31482652231165053625, \ 0.57887349054423364869, \ -0.31482652231165053625, \ 0.57887349054423364869, \ 0.31482652231165053625, \ -0.57887349054423364869, \ -0.31482652231165053625, \ -0.57887349054423364869, \ 0.13337762200744199270, \ 0.86857348087766383937, \ -0.13337762200744199270, \ 0.86857348087766383937, \ 0.13337762200744199270, \ -0.86857348087766383937, \ -0.13337762200744199270, \ -0.86857348087766383937, \ 0.89334514265657827270, \ 0.29700939611864535239, \ -0.89334514265657827270, \ 0.29700939611864535239, \ 0.89334514265657827270, \ -0.29700939611864535239, \ -0.89334514265657827270, \ -0.29700939611864535239, \ 0.64207321281802853807, \ 0.21859043909362887992, \ -0.64207321281802853807, \ 0.21859043909362887992, \ 0.64207321281802853807, \ -0.21859043909362887992, \ -0.64207321281802853807, \ -0.21859043909362887992, \ 0.90155669259026749440, \ 0.28504501057958070431, \ -0.90155669259026749440, \ 0.28504501057958070431, \ 0.90155669259026749440, \ -0.28504501057958070431, \ -0.90155669259026749440, \ -0.28504501057958070431, \ 0.17950781738619853156, \ 0.67966060973500286302, \ -0.17950781738619853156, \ 0.67966060973500286302, \ 0.17950781738619853156, \ -0.67966060973500286302, \ -0.17950781738619853156, \ -0.67966060973500286302, \ 0.52877164545115751260, \ 0.37525379145011561466, \ -0.52877164545115751260, \ 0.37525379145011561466, \ 0.52877164545115751260, \ -0.37525379145011561466, \ -0.52877164545115751260, \ -0.37525379145011561466, \ 0.85684776838109344421, \ 0.70614261226539476457, \ -0.85684776838109344421, \ 0.70614261226539476457, \ 0.85684776838109344421, \ -0.70614261226539476457, \ -0.85684776838109344421, \ -0.70614261226539476457, \ 0.23744649710478388238, \ 0.09039264484495425356, \ -0.23744649710478388238, \ 0.09039264484495425356, \ 0.23744649710478388238, \ -0.09039264484495425356, \ -0.23744649710478388238, \ -0.09039264484495425356, \ 0.94065987701065645332, \ 0.74375119609914763785, \ -0.94065987701065645332, \ 0.74375119609914763785, \ 0.94065987701065645332, \ -0.74375119609914763785, \ -0.94065987701065645332, \ -0.74375119609914763785, \ 0.96544985579484265958, \ 0.55816486672448317741, \ -0.96544985579484265958, \ 0.55816486672448317741, \ 0.96544985579484265958, \ -0.55816486672448317741, \ -0.96544985579484265958, \ -0.55816486672448317741, \ 0.11859977159394578805, \ 0.19730553454891092136, \ -0.11859977159394578805, \ 0.19730553454891092136, \ 0.11859977159394578805, \ -0.19730553454891092136, \ -0.11859977159394578805, \ -0.19730553454891092136, \ 0.43836828746731176798, \ 0.68010534456895455069, \ -0.43836828746731176798, \ 0.68010534456895455069, \ 0.43836828746731176798, \ -0.68010534456895455069, \ -0.43836828746731176798, \ -0.68010534456895455069, \ 0.85015015838954666183, \ 0.57767859879985306026, \ -0.85015015838954666183, \ 0.57767859879985306026, \ 0.85015015838954666183, \ -0.57767859879985306026, \ -0.85015015838954666183, \ -0.57767859879985306026, \ 0.40977883537749759668, \ 0.59926491678603310831, \ -0.40977883537749759668, \ 0.59926491678603310831, \ 0.40977883537749759668, \ -0.59926491678603310831, \ -0.40977883537749759668, \ -0.59926491678603310831, \ 0.62540250575452105419, \ 0.77938113963987465382, \ -0.62540250575452105419, \ 0.77938113963987465382, \ 0.62540250575452105419, \ -0.77938113963987465382, \ -0.62540250575452105419, \ -0.77938113963987465382, \ 0.16587947711557049502, \ 0.65137881658599783297, \ -0.16587947711557049502, \ 0.65137881658599783297, \ 0.16587947711557049502, \ -0.65137881658599783297, \ -0.16587947711557049502, \ -0.65137881658599783297, \ 0.50625591443667894431, \ 0.24708268775667227568, \ -0.50625591443667894431, \ 0.24708268775667227568, \ 0.50625591443667894431, \ -0.24708268775667227568, \ -0.50625591443667894431, \ -0.24708268775667227568, \ 0.74292936328073289065, \ 0.16823593457058672040, \ -0.74292936328073289065, \ 0.16823593457058672040, \ 0.74292936328073289065, \ -0.16823593457058672040, \ -0.74292936328073289065, \ -0.16823593457058672040, \ 0.01867609649526593210, \ 0.25362045997818172260, \ -0.01867609649526593210, \ 0.25362045997818172260, \ 0.01867609649526593210, \ -0.25362045997818172260, \ -0.01867609649526593210, \ -0.25362045997818172260, \ 0.26086005279281720970, \ 0.40946055588941798753, \ -0.26086005279281720970, \ 0.40946055588941798753, \ 0.26086005279281720970, \ -0.40946055588941798753, \ -0.26086005279281720970, \ -0.40946055588941798753, \ 0.79388083129835063101, \ 0.46918818998244915530, \ -0.79388083129835063101, \ 0.46918818998244915530, \ 0.79388083129835063101, \ -0.46918818998244915530, \ -0.79388083129835063101, \ -0.46918818998244915530, \ 0.79301165544060303603, \ 0.29864577765030031475, \ -0.79301165544060303603, \ 0.29864577765030031475, \ 0.79301165544060303603, \ -0.29864577765030031475, \ -0.79301165544060303603, \ -0.29864577765030031475, \ 0.44929996069833155747, \ 0.16967965727402492537, \ -0.44929996069833155747, \ 0.16967965727402492537, \ 0.44929996069833155747, \ -0.16967965727402492537, \ -0.44929996069833155747, \ -0.16967965727402492537, \ 0.76873831458793862037, \ 0.39677450550481596636, \ -0.76873831458793862037, \ 0.39677450550481596636, \ 0.76873831458793862037, \ -0.39677450550481596636, \ -0.76873831458793862037, \ -0.39677450550481596636, \ 0.97859975977571478367, \ 0.19094705775922465874, \ -0.97859975977571478367, \ 0.19094705775922465874, \ 0.97859975977571478367, \ -0.19094705775922465874, \ -0.97859975977571478367, \ -0.19094705775922465874, \ 0.21358909276843840441, \ 0.36041615296155676829, \ -0.21358909276843840441, \ 0.36041615296155676829, \ 0.21358909276843840441, \ -0.36041615296155676829, \ -0.21358909276843840441, \ -0.36041615296155676829, \ 0.79625257738750132575, \ 0.15628526976368214974, \ -0.79625257738750132575, \ 0.15628526976368214974, \ 0.79625257738750132575, \ -0.15628526976368214974, \ -0.79625257738750132575, \ -0.15628526976368214974, \ 0.91939856562697519493, \ 0.41486074510619452838, \ -0.91939856562697519493, \ 0.41486074510619452838, \ 0.91939856562697519493, \ -0.41486074510619452838, \ -0.91939856562697519493, \ -0.41486074510619452838, \ 0.51507330251609151350, \ 0.68962930070823635909, \ -0.51507330251609151350, \ 0.68962930070823635909, \ 0.51507330251609151350, \ -0.68962930070823635909, \ -0.51507330251609151350, \ -0.68962930070823635909, \ 0.96361213891168562284, \ 0.85957679427925348659, \ -0.96361213891168562284, \ 0.85957679427925348659, \ 0.96361213891168562284, \ -0.85957679427925348659, \ -0.96361213891168562284, \ -0.85957679427925348659, \ 0.72140711490936071382, \ 0.49209543700208141503, \ -0.72140711490936071382, \ 0.49209543700208141503, \ 0.72140711490936071382, \ -0.49209543700208141503, \ -0.72140711490936071382, \ -0.49209543700208141503 ] ) y = np.array ( [ \ 0.00000000000000000000, \ 0.00000000000000000000, \ 0.48169354344312520499, \ 0.00000000000000000000, \ -0.48169354344312520499, \ 0.00000000000000000000, \ 0.69858038869870031640, \ 0.00000000000000000000, \ -0.69858038869870031640, \ 0.00000000000000000000, \ 0.53468657951770970360, \ 0.00000000000000000000, \ -0.53468657951770970360, \ 0.00000000000000000000, \ 0.42228380878442672852, \ 0.00000000000000000000, \ -0.42228380878442672852, \ 0.00000000000000000000, \ 0.30680451888779119995, \ 0.00000000000000000000, \ -0.30680451888779119995, \ 0.00000000000000000000, \ 0.22877498497689821577, \ 0.00000000000000000000, \ -0.22877498497689821577, \ 0.00000000000000000000, \ 0.55389687412807175892, \ 0.00000000000000000000, \ -0.55389687412807175892, \ 0.00000000000000000000, \ 0.38489228042331330437, \ 0.00000000000000000000, \ -0.38489228042331330437, \ 0.00000000000000000000, \ 0.25711056873844140291, \ 0.00000000000000000000, \ -0.25711056873844140291, \ 0.00000000000000000000, \ 0.94954208334711565076, \ 0.00000000000000000000, \ -0.94954208334711565076, \ 0.00000000000000000000, \ 0.09635090648066924057, \ 0.00000000000000000000, \ -0.09635090648066924057, \ 0.00000000000000000000, \ 0.91044931261818451418, \ 0.00000000000000000000, \ -0.91044931261818451418, \ 0.00000000000000000000, \ 0.26830824357428106897, \ 0.00000000000000000000, \ -0.26830824357428106897, \ 0.00000000000000000000, \ 0.82744656686299722370, \ 0.00000000000000000000, \ -0.82744656686299722370, \ 0.00000000000000000000, \ 0.03789270083108932374, \ 0.00000000000000000000, \ -0.03789270083108932374, \ 0.00000000000000000000, \ 0.57352052408158127328, \ 0.00000000000000000000, \ -0.57352052408158127328, \ 0.00000000000000000000, \ 0.74231157227003041754, \ 0.00000000000000000000, \ -0.74231157227003041754, \ 0.00000000000000000000, \ 0.28469096413200573048, \ 0.00000000000000000000, \ -0.28469096413200573048, \ 0.00000000000000000000, \ 0.11281627950690893691, \ 0.00000000000000000000, \ -0.11281627950690893691, \ 0.45356762399670425001, \ 0.45356762399670425001, \ -0.45356762399670425001, \ -0.45356762399670425001, \ 0.33361103852611595499, \ 0.33361103852611595499, \ -0.33361103852611595499, \ -0.33361103852611595499, \ 0.37733375278222114346, \ 0.37733375278222114346, \ -0.37733375278222114346, \ -0.37733375278222114346, \ 0.30611174916927796907, \ 0.30611174916927796907, \ -0.30611174916927796907, \ -0.30611174916927796907, \ 0.29044600765245415230, \ 0.29044600765245415230, \ -0.29044600765245415230, \ -0.29044600765245415230, \ 0.59141068840923671779, \ 0.59141068840923671779, \ -0.59141068840923671779, \ -0.59141068840923671779, \ 0.76605496491352953470, \ 0.76605496491352953470, \ -0.76605496491352953470, \ -0.76605496491352953470, \ 0.44962169263179840861, \ 0.44962169263179840861, \ -0.44962169263179840861, \ -0.44962169263179840861, \ 0.61256910754587590162, \ 0.61256910754587590162, \ -0.61256910754587590162, \ -0.61256910754587590162, \ 0.96517775637880776074, \ 0.96517775637880776074, \ -0.96517775637880776074, \ -0.96517775637880776074, \ 0.18509443085238544424, \ 0.18509443085238544424, \ -0.18509443085238544424, \ -0.18509443085238544424, \ 0.13053399140728452754, \ 0.13053399140728452754, \ -0.13053399140728452754, \ -0.13053399140728452754, \ 0.08713330755302489683, \ 0.08713330755302489683, \ -0.08713330755302489683, \ -0.08713330755302489683, \ 0.11626579551616780805, \ 0.11626579551616780805, \ -0.11626579551616780805, \ -0.11626579551616780805, \ 0.03353132384174680597, \ 0.03353132384174680597, \ -0.03353132384174680597, \ -0.03353132384174680597, \ 0.63007044649757071308, \ 0.63007044649757071308, \ -0.63007044649757071308, \ -0.63007044649757071308, \ 0.10081553511278160129, \ 0.10081553511278160129, \ -0.10081553511278160129, \ -0.10081553511278160129, \ 0.09712721271803037570, \ 0.09712721271803037570, \ -0.09712721271803037570, \ -0.09712721271803037570, \ 0.65036744612024988133, \ 0.65036744612024988133, \ -0.65036744612024988133, \ -0.65036744612024988133, \ 0.78816705553909693904, \ 0.78816705553909693904, \ -0.78816705553909693904, \ -0.78816705553909693904, \ 0.46326102535176988395, \ 0.46326102535176988395, \ -0.46326102535176988395, \ -0.46326102535176988395, \ 0.87426225625453524160, \ 0.87426225625453524160, \ -0.87426225625453524160, \ -0.87426225625453524160, \ 0.09693365579654888986, \ 0.09693365579654888986, \ -0.09693365579654888986, \ -0.09693365579654888986, \ 0.52651234369915456135, \ 0.52651234369915456135, \ -0.52651234369915456135, \ -0.52651234369915456135, \ 0.21058018350559978837, \ 0.21058018350559978837, \ -0.21058018350559978837, \ -0.21058018350559978837, \ 0.48341786018142590686, \ 0.48341786018142590686, \ -0.48341786018142590686, \ -0.48341786018142590686, \ 0.27232398053992901144, \ 0.27232398053992901144, \ -0.27232398053992901144, \ -0.27232398053992901144, \ 0.88748390701146573356, \ 0.88748390701146573356, \ -0.88748390701146573356, \ -0.88748390701146573356, \ 0.34004340177081920915, \ 0.34004340177081920915, \ -0.34004340177081920915, \ -0.34004340177081920915, \ 0.24657134521158877161, \ 0.24657134521158877161, \ -0.24657134521158877161, \ -0.24657134521158877161, \ 0.72032611852462202773, \ 0.72032611852462202773, \ -0.72032611852462202773, \ -0.72032611852462202773, \ 0.66053776743762293577, \ 0.86934672471843543740, \ 0.66053776743762293577, \ -0.86934672471843543740, \ -0.66053776743762293577, \ 0.86934672471843543740, \ -0.66053776743762293577, \ -0.86934672471843543740, \ 0.12681144322431647797, \ 0.51657003644145271792, \ 0.12681144322431647797, \ -0.51657003644145271792, \ -0.12681144322431647797, \ 0.51657003644145271792, \ -0.12681144322431647797, \ -0.51657003644145271792, \ 0.53514205206517340141, \ 0.21419492835914627493, \ 0.53514205206517340141, \ -0.21419492835914627493, \ -0.53514205206517340141, \ 0.21419492835914627493, \ -0.53514205206517340141, \ -0.21419492835914627493, \ 0.14309874624364349316, \ 0.38606155250360069120, \ 0.14309874624364349316, \ -0.38606155250360069120, \ -0.14309874624364349316, \ 0.38606155250360069120, \ -0.14309874624364349316, \ -0.38606155250360069120, \ 0.57887349054423364869, \ 0.31482652231165053625, \ 0.57887349054423364869, \ -0.31482652231165053625, \ -0.57887349054423364869, \ 0.31482652231165053625, \ -0.57887349054423364869, \ -0.31482652231165053625, \ 0.86857348087766383937, \ 0.13337762200744199270, \ 0.86857348087766383937, \ -0.13337762200744199270, \ -0.86857348087766383937, \ 0.13337762200744199270, \ -0.86857348087766383937, \ -0.13337762200744199270, \ 0.29700939611864535239, \ 0.89334514265657827270, \ 0.29700939611864535239, \ -0.89334514265657827270, \ -0.29700939611864535239, \ 0.89334514265657827270, \ -0.29700939611864535239, \ -0.89334514265657827270, \ 0.21859043909362887992, \ 0.64207321281802853807, \ 0.21859043909362887992, \ -0.64207321281802853807, \ -0.21859043909362887992, \ 0.64207321281802853807, \ -0.21859043909362887992, \ -0.64207321281802853807, \ 0.28504501057958070431, \ 0.90155669259026749440, \ 0.28504501057958070431, \ -0.90155669259026749440, \ -0.28504501057958070431, \ 0.90155669259026749440, \ -0.28504501057958070431, \ -0.90155669259026749440, \ 0.67966060973500286302, \ 0.17950781738619853156, \ 0.67966060973500286302, \ -0.17950781738619853156, \ -0.67966060973500286302, \ 0.17950781738619853156, \ -0.67966060973500286302, \ -0.17950781738619853156, \ 0.37525379145011561466, \ 0.52877164545115751260, \ 0.37525379145011561466, \ -0.52877164545115751260, \ -0.37525379145011561466, \ 0.52877164545115751260, \ -0.37525379145011561466, \ -0.52877164545115751260, \ 0.70614261226539476457, \ 0.85684776838109344421, \ 0.70614261226539476457, \ -0.85684776838109344421, \ -0.70614261226539476457, \ 0.85684776838109344421, \ -0.70614261226539476457, \ -0.85684776838109344421, \ 0.09039264484495425356, \ 0.23744649710478388238, \ 0.09039264484495425356, \ -0.23744649710478388238, \ -0.09039264484495425356, \ 0.23744649710478388238, \ -0.09039264484495425356, \ -0.23744649710478388238, \ 0.74375119609914763785, \ 0.94065987701065645332, \ 0.74375119609914763785, \ -0.94065987701065645332, \ -0.74375119609914763785, \ 0.94065987701065645332, \ -0.74375119609914763785, \ -0.94065987701065645332, \ 0.55816486672448317741, \ 0.96544985579484265958, \ 0.55816486672448317741, \ -0.96544985579484265958, \ -0.55816486672448317741, \ 0.96544985579484265958, \ -0.55816486672448317741, \ -0.96544985579484265958, \ 0.19730553454891092136, \ 0.11859977159394578805, \ 0.19730553454891092136, \ -0.11859977159394578805, \ -0.19730553454891092136, \ 0.11859977159394578805, \ -0.19730553454891092136, \ -0.11859977159394578805, \ 0.68010534456895455069, \ 0.43836828746731176798, \ 0.68010534456895455069, \ -0.43836828746731176798, \ -0.68010534456895455069, \ 0.43836828746731176798, \ -0.68010534456895455069, \ -0.43836828746731176798, \ 0.57767859879985306026, \ 0.85015015838954666183, \ 0.57767859879985306026, \ -0.85015015838954666183, \ -0.57767859879985306026, \ 0.85015015838954666183, \ -0.57767859879985306026, \ -0.85015015838954666183, \ 0.59926491678603310831, \ 0.40977883537749759668, \ 0.59926491678603310831, \ -0.40977883537749759668, \ -0.59926491678603310831, \ 0.40977883537749759668, \ -0.59926491678603310831, \ -0.40977883537749759668, \ 0.77938113963987465382, \ 0.62540250575452105419, \ 0.77938113963987465382, \ -0.62540250575452105419, \ -0.77938113963987465382, \ 0.62540250575452105419, \ -0.77938113963987465382, \ -0.62540250575452105419, \ 0.65137881658599783297, \ 0.16587947711557049502, \ 0.65137881658599783297, \ -0.16587947711557049502, \ -0.65137881658599783297, \ 0.16587947711557049502, \ -0.65137881658599783297, \ -0.16587947711557049502, \ 0.24708268775667227568, \ 0.50625591443667894431, \ 0.24708268775667227568, \ -0.50625591443667894431, \ -0.24708268775667227568, \ 0.50625591443667894431, \ -0.24708268775667227568, \ -0.50625591443667894431, \ 0.16823593457058672040, \ 0.74292936328073289065, \ 0.16823593457058672040, \ -0.74292936328073289065, \ -0.16823593457058672040, \ 0.74292936328073289065, \ -0.16823593457058672040, \ -0.74292936328073289065, \ 0.25362045997818172260, \ 0.01867609649526593210, \ 0.25362045997818172260, \ -0.01867609649526593210, \ -0.25362045997818172260, \ 0.01867609649526593210, \ -0.25362045997818172260, \ -0.01867609649526593210, \ 0.40946055588941798753, \ 0.26086005279281720970, \ 0.40946055588941798753, \ -0.26086005279281720970, \ -0.40946055588941798753, \ 0.26086005279281720970, \ -0.40946055588941798753, \ -0.26086005279281720970, \ 0.46918818998244915530, \ 0.79388083129835063101, \ 0.46918818998244915530, \ -0.79388083129835063101, \ -0.46918818998244915530, \ 0.79388083129835063101, \ -0.46918818998244915530, \ -0.79388083129835063101, \ 0.29864577765030031475, \ 0.79301165544060303603, \ 0.29864577765030031475, \ -0.79301165544060303603, \ -0.29864577765030031475, \ 0.79301165544060303603, \ -0.29864577765030031475, \ -0.79301165544060303603, \ 0.16967965727402492537, \ 0.44929996069833155747, \ 0.16967965727402492537, \ -0.44929996069833155747, \ -0.16967965727402492537, \ 0.44929996069833155747, \ -0.16967965727402492537, \ -0.44929996069833155747, \ 0.39677450550481596636, \ 0.76873831458793862037, \ 0.39677450550481596636, \ -0.76873831458793862037, \ -0.39677450550481596636, \ 0.76873831458793862037, \ -0.39677450550481596636, \ -0.76873831458793862037, \ 0.19094705775922465874, \ 0.97859975977571478367, \ 0.19094705775922465874, \ -0.97859975977571478367, \ -0.19094705775922465874, \ 0.97859975977571478367, \ -0.19094705775922465874, \ -0.97859975977571478367, \ 0.36041615296155676829, \ 0.21358909276843840441, \ 0.36041615296155676829, \ -0.21358909276843840441, \ -0.36041615296155676829, \ 0.21358909276843840441, \ -0.36041615296155676829, \ -0.21358909276843840441, \ 0.15628526976368214974, \ 0.79625257738750132575, \ 0.15628526976368214974, \ -0.79625257738750132575, \ -0.15628526976368214974, \ 0.79625257738750132575, \ -0.15628526976368214974, \ -0.79625257738750132575, \ 0.41486074510619452838, \ 0.91939856562697519493, \ 0.41486074510619452838, \ -0.91939856562697519493, \ -0.41486074510619452838, \ 0.91939856562697519493, \ -0.41486074510619452838, \ -0.91939856562697519493, \ 0.68962930070823635909, \ 0.51507330251609151350, \ 0.68962930070823635909, \ -0.51507330251609151350, \ -0.68962930070823635909, \ 0.51507330251609151350, \ -0.68962930070823635909, \ -0.51507330251609151350, \ 0.85957679427925348659, \ 0.96361213891168562284, \ 0.85957679427925348659, \ -0.96361213891168562284, \ -0.85957679427925348659, \ 0.96361213891168562284, \ -0.85957679427925348659, \ -0.96361213891168562284, \ 0.49209543700208141503, \ 0.72140711490936071382, \ 0.49209543700208141503, \ -0.72140711490936071382, \ -0.49209543700208141503, \ 0.72140711490936071382, \ -0.49209543700208141503, \ -0.72140711490936071382 ] ) z = np.array ( [ \ 0.60412613281560589851, \ 0.12832541213701875726, \ 0.12832541213701875726, \ 0.12832541213701875726, \ 0.12832541213701875726, \ 0.23636452793876766565, \ 0.23636452793876766565, \ 0.23636452793876766565, \ 0.23636452793876766565, \ 0.36948143968736257836, \ 0.36948143968736257836, \ 0.36948143968736257836, \ 0.36948143968736257836, \ 0.57413522292238361455, \ 0.57413522292238361455, \ 0.57413522292238361455, \ 0.57413522292238361455, \ 0.57097027691958568418, \ 0.57097027691958568418, \ 0.57097027691958568418, \ 0.57097027691958568418, \ 0.44532726334384131750, \ 0.44532726334384131750, \ 0.44532726334384131750, \ 0.44532726334384131750, \ 0.18507199264697138386, \ 0.18507199264697138386, \ 0.18507199264697138386, \ 0.18507199264697138386, \ 0.28281898722495468768, \ 0.28281898722495468768, \ 0.28281898722495468768, \ 0.28281898722495468768, \ 0.00745381355051214466, \ 0.00745381355051214466, \ 0.00745381355051214466, \ 0.00745381355051214466, \ 0.00273060888853154026, \ 0.00273060888853154026, \ 0.00273060888853154026, \ 0.00273060888853154026, \ 0.89474683073191085825, \ 0.89474683073191085825, \ 0.89474683073191085825, \ 0.89474683073191085825, \ 0.05489260378459437373, \ 0.05489260378459437373, \ 0.05489260378459437373, \ 0.05489260378459437373, \ 0.17890547617113325418, \ 0.17890547617113325418, \ 0.17890547617113325418, \ 0.17890547617113325418, \ 0.14438727929533640149, \ 0.14438727929533640149, \ 0.14438727929533640149, \ 0.14438727929533640149, \ 0.96005329029751285130, \ 0.96005329029751285130, \ 0.96005329029751285130, \ 0.96005329029751285130, \ 0.42262373956574911249, \ 0.42262373956574911249, \ 0.42262373956574911249, \ 0.42262373956574911249, \ 0.00937341178432237430, \ 0.00937341178432237430, \ 0.00937341178432237430, \ 0.00937341178432237430, \ 0.70511644808626805503, \ 0.70511644808626805503, \ 0.70511644808626805503, \ 0.70511644808626805503, \ 0.80976037637526798729, \ 0.80976037637526798729, \ 0.80976037637526798729, \ 0.80976037637526798729, \ 0.52107002257796464217, \ 0.52107002257796464217, \ 0.52107002257796464217, \ 0.52107002257796464217, \ 0.47622191262040014514, \ 0.47622191262040014514, \ 0.47622191262040014514, \ 0.47622191262040014514, \ 0.04553198949867700435, \ 0.04553198949867700435, \ 0.04553198949867700435, \ 0.04553198949867700435, \ 0.68236516778452971366, \ 0.68236516778452971366, \ 0.68236516778452971366, \ 0.68236516778452971366, \ 0.36766518307523687881, \ 0.36766518307523687881, \ 0.36766518307523687881, \ 0.36766518307523687881, \ 0.03140155892114703667, \ 0.03140155892114703667, \ 0.03140155892114703667, \ 0.03140155892114703667, \ 0.20854763179877680579, \ 0.20854763179877680579, \ 0.20854763179877680579, \ 0.20854763179877680579, \ 0.32095943995186076991, \ 0.32095943995186076991, \ 0.32095943995186076991, \ 0.32095943995186076991, \ 0.35590541054356356065, \ 0.35590541054356356065, \ 0.35590541054356356065, \ 0.35590541054356356065, \ 0.01963481046583391565, \ 0.01963481046583391565, \ 0.01963481046583391565, \ 0.01963481046583391565, \ 0.58110848325376152079, \ 0.58110848325376152079, \ 0.58110848325376152079, \ 0.58110848325376152079, \ 0.22030183551151610866, \ 0.22030183551151610866, \ 0.22030183551151610866, \ 0.22030183551151610866, \ 0.70743374610149956094, \ 0.70743374610149956094, \ 0.70743374610149956094, \ 0.70743374610149956094, \ 0.49754618392934674143, \ 0.49754618392934674143, \ 0.49754618392934674143, \ 0.49754618392934674143, \ 0.90197994879909670907, \ 0.90197994879909670907, \ 0.90197994879909670907, \ 0.90197994879909670907, \ 0.15830174812382535876, \ 0.15830174812382535876, \ 0.15830174812382535876, \ 0.15830174812382535876, \ 0.34703489296133355202, \ 0.34703489296133355202, \ 0.34703489296133355202, \ 0.34703489296133355202, \ 0.87727590777505048969, \ 0.87727590777505048969, \ 0.87727590777505048969, \ 0.87727590777505048969, \ 0.25098088788741812483, \ 0.25098088788741812483, \ 0.25098088788741812483, \ 0.25098088788741812483, \ 0.12287487061124809096, \ 0.12287487061124809096, \ 0.12287487061124809096, \ 0.12287487061124809096, \ 0.21569557215246823456, \ 0.21569557215246823456, \ 0.21569557215246823456, \ 0.21569557215246823456, \ 0.04316688220319717106, \ 0.04316688220319717106, \ 0.04316688220319717106, \ 0.04316688220319717106, \ 0.10724275430905566564, \ 0.10724275430905566564, \ 0.10724275430905566564, \ 0.10724275430905566564, \ 0.32964277824701476716, \ 0.32964277824701476716, \ 0.32964277824701476716, \ 0.32964277824701476716, \ 0.71600680775916891729, \ 0.71600680775916891729, \ 0.71600680775916891729, \ 0.71600680775916891729, \ 0.41973631072686923282, \ 0.41973631072686923282, \ 0.41973631072686923282, \ 0.41973631072686923282, \ 0.10771970940234577852, \ 0.10771970940234577852, \ 0.10771970940234577852, \ 0.10771970940234577852, \ 0.09137076099343852120, \ 0.09137076099343852120, \ 0.09137076099343852120, \ 0.09137076099343852120, \ 0.57433224555240058873, \ 0.57433224555240058873, \ 0.57433224555240058873, \ 0.57433224555240058873, \ 0.29652789568067272619, \ 0.29652789568067272619, \ 0.29652789568067272619, \ 0.29652789568067272619, \ 0.06861567128774997970, \ 0.06861567128774997970, \ 0.06861567128774997970, \ 0.06861567128774997970, \ 0.12112687504129497629, \ 0.12112687504129497629, \ 0.12112687504129497629, \ 0.12112687504129497629, \ 0.12112687504129497629, \ 0.12112687504129497629, \ 0.12112687504129497629, \ 0.12112687504129497629, \ 0.06232922095164156878, \ 0.06232922095164156878, \ 0.06232922095164156878, \ 0.06232922095164156878, \ 0.06232922095164156878, \ 0.06232922095164156878, \ 0.06232922095164156878, \ 0.06232922095164156878, \ 0.28878375602826145130, \ 0.28878375602826145130, \ 0.28878375602826145130, \ 0.28878375602826145130, \ 0.28878375602826145130, \ 0.28878375602826145130, \ 0.28878375602826145130, \ 0.28878375602826145130, \ 0.41981996327982368244, \ 0.41981996327982368244, \ 0.41981996327982368244, \ 0.41981996327982368244, \ 0.41981996327982368244, \ 0.41981996327982368244, \ 0.41981996327982368244, \ 0.41981996327982368244, \ 0.36719716335126328932, \ 0.36719716335126328932, \ 0.36719716335126328932, \ 0.36719716335126328932, \ 0.36719716335126328932, \ 0.36719716335126328932, \ 0.36719716335126328932, \ 0.36719716335126328932, \ 0.03539982573087990109, \ 0.03539982573087990109, \ 0.03539982573087990109, \ 0.03539982573087990109, \ 0.03539982573087990109, \ 0.03539982573087990109, \ 0.03539982573087990109, \ 0.03539982573087990109, \ 0.00689409549706292753, \ 0.00689409549706292753, \ 0.00689409549706292753, \ 0.00689409549706292753, \ 0.00689409549706292753, \ 0.00689409549706292753, \ 0.00689409549706292753, \ 0.00689409549706292753, \ 0.18034097822548403323, \ 0.18034097822548403323, \ 0.18034097822548403323, \ 0.18034097822548403323, \ 0.18034097822548403323, \ 0.18034097822548403323, \ 0.18034097822548403323, \ 0.18034097822548403323, \ 0.08701177937660883877, \ 0.08701177937660883877, \ 0.08701177937660883877, \ 0.08701177937660883877, \ 0.08701177937660883877, \ 0.08701177937660883877, \ 0.08701177937660883877, \ 0.08701177937660883877, \ 0.30184034189885056154, \ 0.30184034189885056154, \ 0.30184034189885056154, \ 0.30184034189885056154, \ 0.30184034189885056154, \ 0.30184034189885056154, \ 0.30184034189885056154, \ 0.30184034189885056154, \ 0.46375316476153072287, \ 0.46375316476153072287, \ 0.46375316476153072287, \ 0.46375316476153072287, \ 0.46375316476153072287, \ 0.46375316476153072287, \ 0.46375316476153072287, \ 0.46375316476153072287, \ 0.01259447070049873885, \ 0.01259447070049873885, \ 0.01259447070049873885, \ 0.01259447070049873885, \ 0.01259447070049873885, \ 0.01259447070049873885, \ 0.01259447070049873885, \ 0.01259447070049873885, \ 0.68464554842762070930, \ 0.68464554842762070930, \ 0.68464554842762070930, \ 0.68464554842762070930, \ 0.68464554842762070930, \ 0.68464554842762070930, \ 0.68464554842762070930, \ 0.68464554842762070930, \ 0.04669618994654996941, \ 0.04669618994654996941, \ 0.04669618994654996941, \ 0.04669618994654996941, \ 0.04669618994654996941, \ 0.04669618994654996941, \ 0.04669618994654996941, \ 0.04669618994654996941, \ 0.00997909979720432855, \ 0.00997909979720432855, \ 0.00997909979720432855, \ 0.00997909979720432855, \ 0.00997909979720432855, \ 0.00997909979720432855, \ 0.00997909979720432855, \ 0.00997909979720432855, \ 0.79170760938063011736, \ 0.79170760938063011736, \ 0.79170760938063011736, \ 0.79170760938063011736, \ 0.79170760938063011736, \ 0.79170760938063011736, \ 0.79170760938063011736, \ 0.79170760938063011736, \ 0.23239746807120234551, \ 0.23239746807120234551, \ 0.23239746807120234551, \ 0.23239746807120234551, \ 0.23239746807120234551, \ 0.23239746807120234551, \ 0.23239746807120234551, \ 0.23239746807120234551, \ 0.06212941698545271230, \ 0.06212941698545271230, \ 0.06212941698545271230, \ 0.06212941698545271230, \ 0.06212941698545271230, \ 0.06212941698545271230, \ 0.06212941698545271230, \ 0.06212941698545271230, \ 0.10250007471008426574, \ 0.10250007471008426574, \ 0.10250007471008426574, \ 0.10250007471008426574, \ 0.10250007471008426574, \ 0.10250007471008426574, \ 0.10250007471008426574, \ 0.10250007471008426574, \ 0.19638105364011448906, \ 0.19638105364011448906, \ 0.19638105364011448906, \ 0.19638105364011448906, \ 0.19638105364011448906, \ 0.19638105364011448906, \ 0.19638105364011448906, \ 0.19638105364011448906, \ 0.03807225396126873163, \ 0.03807225396126873163, \ 0.03807225396126873163, \ 0.03807225396126873163, \ 0.03807225396126873163, \ 0.03807225396126873163, \ 0.03807225396126873163, \ 0.03807225396126873163, \ 0.00969993829969578725, \ 0.00969993829969578725, \ 0.00969993829969578725, \ 0.00969993829969578725, \ 0.00969993829969578725, \ 0.00969993829969578725, \ 0.00969993829969578725, \ 0.00969993829969578725, \ 0.08712730173221996943, \ 0.08712730173221996943, \ 0.08712730173221996943, \ 0.08712730173221996943, \ 0.08712730173221996943, \ 0.08712730173221996943, \ 0.08712730173221996943, \ 0.08712730173221996943, \ 0.04169093747605617795, \ 0.04169093747605617795, \ 0.04169093747605617795, \ 0.04169093747605617795, \ 0.04169093747605617795, \ 0.04169093747605617795, \ 0.04169093747605617795, \ 0.04169093747605617795, \ 0.18982222362689099571, \ 0.18982222362689099571, \ 0.18982222362689099571, \ 0.18982222362689099571, \ 0.18982222362689099571, \ 0.18982222362689099571, \ 0.18982222362689099571, \ 0.18982222362689099571, \ 0.12762173979455287975, \ 0.12762173979455287975, \ 0.12762173979455287975, \ 0.12762173979455287975, \ 0.12762173979455287975, \ 0.12762173979455287975, \ 0.12762173979455287975, \ 0.12762173979455287975, \ 0.19550632719707150553, \ 0.19550632719707150553, \ 0.19550632719707150553, \ 0.19550632719707150553, \ 0.19550632719707150553, \ 0.19550632719707150553, \ 0.19550632719707150553, \ 0.19550632719707150553, \ 0.49356773754307026181, \ 0.49356773754307026181, \ 0.49356773754307026181, \ 0.49356773754307026181, \ 0.49356773754307026181, \ 0.49356773754307026181, \ 0.49356773754307026181, \ 0.49356773754307026181, \ 0.03472481178210238412, \ 0.03472481178210238412, \ 0.03472481178210238412, \ 0.03472481178210238412, \ 0.03472481178210238412, \ 0.03472481178210238412, \ 0.03472481178210238412, \ 0.03472481178210238412, \ 0.01518094278770998860, \ 0.01518094278770998860, \ 0.01518094278770998860, \ 0.01518094278770998860, \ 0.01518094278770998860, \ 0.01518094278770998860, \ 0.01518094278770998860, \ 0.01518094278770998860, \ 0.61542031522620999073, \ 0.61542031522620999073, \ 0.61542031522620999073, \ 0.61542031522620999073, \ 0.61542031522620999073, \ 0.61542031522620999073, \ 0.61542031522620999073, \ 0.61542031522620999073, \ 0.12575204752531654595, \ 0.12575204752531654595, \ 0.12575204752531654595, \ 0.12575204752531654595, \ 0.12575204752531654595, \ 0.12575204752531654595, \ 0.12575204752531654595, \ 0.12575204752531654595, \ 0.04457888016467764086, \ 0.04457888016467764086, \ 0.04457888016467764086, \ 0.04457888016467764086, \ 0.04457888016467764086, \ 0.04457888016467764086, \ 0.04457888016467764086, \ 0.04457888016467764086, \ 0.30170781950633751567, \ 0.30170781950633751567, \ 0.30170781950633751567, \ 0.30170781950633751567, \ 0.30170781950633751567, \ 0.30170781950633751567, \ 0.30170781950633751567, \ 0.30170781950633751567, \ 0.00577128438055363874, \ 0.00577128438055363874, \ 0.00577128438055363874, \ 0.00577128438055363874, \ 0.00577128438055363874, \ 0.00577128438055363874, \ 0.00577128438055363874, \ 0.00577128438055363874, \ 0.00239530919218184334, \ 0.00239530919218184334, \ 0.00239530919218184334, \ 0.00239530919218184334, \ 0.00239530919218184334, \ 0.00239530919218184334, \ 0.00239530919218184334, \ 0.00239530919218184334 ] ) w= np.array ( [ \ 0.00537430973147919565, \ 0.00567173429377825552, \ 0.00567173429377825552, \ 0.00567173429377825552, \ 0.00567173429377825552, \ 0.00324886088172405109, \ 0.00324886088172405109, \ 0.00324886088172405109, \ 0.00324886088172405109, \ 0.00345209452668273666, \ 0.00345209452668273666, \ 0.00345209452668273666, \ 0.00345209452668273666, \ 0.00066660334447695205, \ 0.00066660334447695205, \ 0.00066660334447695205, \ 0.00066660334447695205, \ 0.00399579246038160064, \ 0.00399579246038160064, \ 0.00399579246038160064, \ 0.00399579246038160064, \ 0.00499277895953007846, \ 0.00499277895953007846, \ 0.00499277895953007846, \ 0.00499277895953007846, \ 0.00246962297642099688, \ 0.00246962297642099688, \ 0.00246962297642099688, \ 0.00246962297642099688, \ 0.00706615575413061577, \ 0.00706615575413061577, \ 0.00706615575413061577, \ 0.00706615575413061577, \ 0.00191698003537197552, \ 0.00191698003537197552, \ 0.00191698003537197552, \ 0.00191698003537197552, \ 0.00023875415581936437, \ 0.00023875415581936437, \ 0.00023875415581936437, \ 0.00023875415581936437, \ 0.00016802396701300472, \ 0.00016802396701300472, \ 0.00016802396701300472, \ 0.00016802396701300472, \ 0.00099443273732332323, \ 0.00099443273732332323, \ 0.00099443273732332323, \ 0.00099443273732332323, \ 0.00345494167713882722, \ 0.00345494167713882722, \ 0.00345494167713882722, \ 0.00345494167713882722, \ 0.00137778065777168987, \ 0.00137778065777168987, \ 0.00137778065777168987, \ 0.00137778065777168987, \ 0.00006135678341459227, \ 0.00006135678341459227, \ 0.00006135678341459227, \ 0.00006135678341459227, \ 0.00099615960761120759, \ 0.00099615960761120759, \ 0.00099615960761120759, \ 0.00099615960761120759, \ 0.00173468884468413759, \ 0.00173468884468413759, \ 0.00173468884468413759, \ 0.00173468884468413759, \ 0.00064089052901790020, \ 0.00064089052901790020, \ 0.00064089052901790020, \ 0.00064089052901790020, \ 0.00174770174992903656, \ 0.00174770174992903656, \ 0.00174770174992903656, \ 0.00174770174992903656, \ 0.00053561830982834806, \ 0.00053561830982834806, \ 0.00053561830982834806, \ 0.00053561830982834806, \ 0.00374412815566966747, \ 0.00374412815566966747, \ 0.00374412815566966747, \ 0.00374412815566966747, \ 0.00364849854393893731, \ 0.00364849854393893731, \ 0.00364849854393893731, \ 0.00364849854393893731, \ 0.00027221046304926988, \ 0.00027221046304926988, \ 0.00027221046304926988, \ 0.00027221046304926988, \ 0.00403805862793428852, \ 0.00403805862793428852, \ 0.00403805862793428852, \ 0.00403805862793428852, \ 0.00284945501315263380, \ 0.00284945501315263380, \ 0.00284945501315263380, \ 0.00284945501315263380, \ 0.00049463185151189392, \ 0.00049463185151189392, \ 0.00049463185151189392, \ 0.00049463185151189392, \ 0.00343575024351558140, \ 0.00343575024351558140, \ 0.00343575024351558140, \ 0.00343575024351558140, \ 0.00076547936426975662, \ 0.00076547936426975662, \ 0.00076547936426975662, \ 0.00076547936426975662, \ 0.00009270297025443059, \ 0.00009270297025443059, \ 0.00009270297025443059, \ 0.00009270297025443059, \ 0.00444044740059815115, \ 0.00444044740059815115, \ 0.00444044740059815115, \ 0.00444044740059815115, \ 0.00499528418027490092, \ 0.00499528418027490092, \ 0.00499528418027490092, \ 0.00499528418027490092, \ 0.00232760564344115621, \ 0.00232760564344115621, \ 0.00232760564344115621, \ 0.00232760564344115621, \ 0.00305846111057695401, \ 0.00305846111057695401, \ 0.00305846111057695401, \ 0.00305846111057695401, \ 0.00027167033342833963, \ 0.00027167033342833963, \ 0.00027167033342833963, \ 0.00027167033342833963, \ 0.00359204041455288758, \ 0.00359204041455288758, \ 0.00359204041455288758, \ 0.00359204041455288758, \ 0.00450623232462683300, \ 0.00450623232462683300, \ 0.00450623232462683300, \ 0.00450623232462683300, \ 0.00026620595222711166, \ 0.00026620595222711166, \ 0.00026620595222711166, \ 0.00026620595222711166, \ 0.00172242225189580926, \ 0.00172242225189580926, \ 0.00172242225189580926, \ 0.00172242225189580926, \ 0.00152990216308249529, \ 0.00152990216308249529, \ 0.00152990216308249529, \ 0.00152990216308249529, \ 0.00433172345565203346, \ 0.00433172345565203346, \ 0.00433172345565203346, \ 0.00433172345565203346, \ 0.00086984955905943873, \ 0.00086984955905943873, \ 0.00086984955905943873, \ 0.00086984955905943873, \ 0.00316655761594148268, \ 0.00316655761594148268, \ 0.00316655761594148268, \ 0.00316655761594148268, \ 0.00145516775846500309, \ 0.00145516775846500309, \ 0.00145516775846500309, \ 0.00145516775846500309, \ 0.00113761603493167554, \ 0.00113761603493167554, \ 0.00113761603493167554, \ 0.00113761603493167554, \ 0.00188490438846629360, \ 0.00188490438846629360, \ 0.00188490438846629360, \ 0.00188490438846629360, \ 0.00604980306252401318, \ 0.00604980306252401318, \ 0.00604980306252401318, \ 0.00604980306252401318, \ 0.00027850531603908424, \ 0.00027850531603908424, \ 0.00027850531603908424, \ 0.00027850531603908424, \ 0.00164429091495763209, \ 0.00164429091495763209, \ 0.00164429091495763209, \ 0.00164429091495763209, \ 0.00438466987463943282, \ 0.00438466987463943282, \ 0.00438466987463943282, \ 0.00438466987463943282, \ 0.00250821736032557372, \ 0.00250821736032557372, \ 0.00250821736032557372, \ 0.00250821736032557372, \ 0.00064031929971637594, \ 0.00064031929971637594, \ 0.00064031929971637594, \ 0.00064031929971637594, \ 0.00064031929971637594, \ 0.00064031929971637594, \ 0.00064031929971637594, \ 0.00064031929971637594, \ 0.00274360981913367684, \ 0.00274360981913367684, \ 0.00274360981913367684, \ 0.00274360981913367684, \ 0.00274360981913367684, \ 0.00274360981913367684, \ 0.00274360981913367684, \ 0.00274360981913367684, \ 0.00442513215733170758, \ 0.00442513215733170758, \ 0.00442513215733170758, \ 0.00442513215733170758, \ 0.00442513215733170758, \ 0.00442513215733170758, \ 0.00442513215733170758, \ 0.00442513215733170758, \ 0.00379353354761960502, \ 0.00379353354761960502, \ 0.00379353354761960502, \ 0.00379353354761960502, \ 0.00379353354761960502, \ 0.00379353354761960502, \ 0.00379353354761960502, \ 0.00379353354761960502, \ 0.00259873188089142833, \ 0.00259873188089142833, \ 0.00259873188089142833, \ 0.00259873188089142833, \ 0.00259873188089142833, \ 0.00259873188089142833, \ 0.00259873188089142833, \ 0.00259873188089142833, \ 0.00110056207140428312, \ 0.00110056207140428312, \ 0.00110056207140428312, \ 0.00110056207140428312, \ 0.00110056207140428312, \ 0.00110056207140428312, \ 0.00110056207140428312, \ 0.00110056207140428312, \ 0.00075594512745462764, \ 0.00075594512745462764, \ 0.00075594512745462764, \ 0.00075594512745462764, \ 0.00075594512745462764, \ 0.00075594512745462764, \ 0.00075594512745462764, \ 0.00075594512745462764, \ 0.00416443295717523060, \ 0.00416443295717523060, \ 0.00416443295717523060, \ 0.00416443295717523060, \ 0.00416443295717523060, \ 0.00416443295717523060, \ 0.00416443295717523060, \ 0.00416443295717523060, \ 0.00079864720063192577, \ 0.00079864720063192577, \ 0.00079864720063192577, \ 0.00079864720063192577, \ 0.00079864720063192577, \ 0.00079864720063192577, \ 0.00079864720063192577, \ 0.00079864720063192577, \ 0.00127477283170923661, \ 0.00127477283170923661, \ 0.00127477283170923661, \ 0.00127477283170923661, \ 0.00127477283170923661, \ 0.00127477283170923661, \ 0.00127477283170923661, \ 0.00127477283170923661, \ 0.00077420720151948649, \ 0.00077420720151948649, \ 0.00077420720151948649, \ 0.00077420720151948649, \ 0.00077420720151948649, \ 0.00077420720151948649, \ 0.00077420720151948649, \ 0.00077420720151948649, \ 0.00107986786877537822, \ 0.00107986786877537822, \ 0.00107986786877537822, \ 0.00107986786877537822, \ 0.00107986786877537822, \ 0.00107986786877537822, \ 0.00107986786877537822, \ 0.00107986786877537822, \ 0.00155093578240393421, \ 0.00155093578240393421, \ 0.00155093578240393421, \ 0.00155093578240393421, \ 0.00155093578240393421, \ 0.00155093578240393421, \ 0.00155093578240393421, \ 0.00155093578240393421, \ 0.00049937862088166734, \ 0.00049937862088166734, \ 0.00049937862088166734, \ 0.00049937862088166734, \ 0.00049937862088166734, \ 0.00049937862088166734, \ 0.00049937862088166734, \ 0.00049937862088166734, \ 0.00042623664206464421, \ 0.00042623664206464421, \ 0.00042623664206464421, \ 0.00042623664206464421, \ 0.00042623664206464421, \ 0.00042623664206464421, \ 0.00042623664206464421, \ 0.00042623664206464421, \ 0.00052445285235233835, \ 0.00052445285235233835, \ 0.00052445285235233835, \ 0.00052445285235233835, \ 0.00052445285235233835, \ 0.00052445285235233835, \ 0.00052445285235233835, \ 0.00052445285235233835, \ 0.00295483873714207741, \ 0.00295483873714207741, \ 0.00295483873714207741, \ 0.00295483873714207741, \ 0.00295483873714207741, \ 0.00295483873714207741, \ 0.00295483873714207741, \ 0.00295483873714207741, \ 0.00154064844826157059, \ 0.00154064844826157059, \ 0.00154064844826157059, \ 0.00154064844826157059, \ 0.00154064844826157059, \ 0.00154064844826157059, \ 0.00154064844826157059, \ 0.00154064844826157059, \ 0.00484986123625866239, \ 0.00484986123625866239, \ 0.00484986123625866239, \ 0.00484986123625866239, \ 0.00484986123625866239, \ 0.00484986123625866239, \ 0.00484986123625866239, \ 0.00484986123625866239, \ 0.00074953722109848120, \ 0.00074953722109848120, \ 0.00074953722109848120, \ 0.00074953722109848120, \ 0.00074953722109848120, \ 0.00074953722109848120, \ 0.00074953722109848120, \ 0.00074953722109848120, \ 0.00167732903590775981, \ 0.00167732903590775981, \ 0.00167732903590775981, \ 0.00167732903590775981, \ 0.00167732903590775981, \ 0.00167732903590775981, \ 0.00167732903590775981, \ 0.00167732903590775981, \ 0.00224204091471395155, \ 0.00224204091471395155, \ 0.00224204091471395155, \ 0.00224204091471395155, \ 0.00224204091471395155, \ 0.00224204091471395155, \ 0.00224204091471395155, \ 0.00224204091471395155, \ 0.00305423895198708934, \ 0.00305423895198708934, \ 0.00305423895198708934, \ 0.00305423895198708934, \ 0.00305423895198708934, \ 0.00305423895198708934, \ 0.00305423895198708934, \ 0.00305423895198708934, \ 0.00236370915044872495, \ 0.00236370915044872495, \ 0.00236370915044872495, \ 0.00236370915044872495, \ 0.00236370915044872495, \ 0.00236370915044872495, \ 0.00236370915044872495, \ 0.00236370915044872495, \ 0.00412477376791669549, \ 0.00412477376791669549, \ 0.00412477376791669549, \ 0.00412477376791669549, \ 0.00412477376791669549, \ 0.00412477376791669549, \ 0.00412477376791669549, \ 0.00412477376791669549, \ 0.00252281437387082835, \ 0.00252281437387082835, \ 0.00252281437387082835, \ 0.00252281437387082835, \ 0.00252281437387082835, \ 0.00252281437387082835, \ 0.00252281437387082835, \ 0.00252281437387082835, \ 0.00114336403720023422, \ 0.00114336403720023422, \ 0.00114336403720023422, \ 0.00114336403720023422, \ 0.00114336403720023422, \ 0.00114336403720023422, \ 0.00114336403720023422, \ 0.00114336403720023422, \ 0.00278500419257705868, \ 0.00278500419257705868, \ 0.00278500419257705868, \ 0.00278500419257705868, \ 0.00278500419257705868, \ 0.00278500419257705868, \ 0.00278500419257705868, \ 0.00278500419257705868, \ 0.00222262578256617873, \ 0.00222262578256617873, \ 0.00222262578256617873, \ 0.00222262578256617873, \ 0.00222262578256617873, \ 0.00222262578256617873, \ 0.00222262578256617873, \ 0.00222262578256617873, \ 0.00026099460442016807, \ 0.00026099460442016807, \ 0.00026099460442016807, \ 0.00026099460442016807, \ 0.00026099460442016807, \ 0.00026099460442016807, \ 0.00026099460442016807, \ 0.00026099460442016807, \ 0.00125217421068957169, \ 0.00125217421068957169, \ 0.00125217421068957169, \ 0.00125217421068957169, \ 0.00125217421068957169, \ 0.00125217421068957169, \ 0.00125217421068957169, \ 0.00125217421068957169, \ 0.00127967033864278819, \ 0.00127967033864278819, \ 0.00127967033864278819, \ 0.00127967033864278819, \ 0.00127967033864278819, \ 0.00127967033864278819, \ 0.00127967033864278819, \ 0.00127967033864278819, \ 0.00079904956567299025, \ 0.00079904956567299025, \ 0.00079904956567299025, \ 0.00079904956567299025, \ 0.00079904956567299025, \ 0.00079904956567299025, \ 0.00079904956567299025, \ 0.00079904956567299025, \ 0.00078122198597418405, \ 0.00078122198597418405, \ 0.00078122198597418405, \ 0.00078122198597418405, \ 0.00078122198597418405, \ 0.00078122198597418405, \ 0.00078122198597418405, \ 0.00078122198597418405, \ 0.00021725880518099310, \ 0.00021725880518099310, \ 0.00021725880518099310, \ 0.00021725880518099310, \ 0.00021725880518099310, \ 0.00021725880518099310, \ 0.00021725880518099310, \ 0.00021725880518099310, \ 0.00075955776144381827, \ 0.00075955776144381827, \ 0.00075955776144381827, \ 0.00075955776144381827, \ 0.00075955776144381827, \ 0.00075955776144381827, \ 0.00075955776144381827, \ 0.00075955776144381827 ] ) return x, y, z, w def timestamp ( ): #*****************************************************************************80 # ## timestamp() prints the date as a timestamp. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 21 August 2019 # # Author: # # John Burkardt # import time t = time.time ( ) print ( time.ctime ( t ) ) return if ( __name__ == "__main__" ): timestamp ( ) pyramid_jaskowiec_rule_test ( ) timestamp ( )