#! /usr/bin/env python3 # def triangle_symq_rule_test ( ): #*****************************************************************************80 # ## triangle_symq_rule_test() tests triangle_symq_rule(). # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 10 July 2023 # # Author: # # John Burkardt. # import platform print ( '' ) print ( 'triangle_symq_rule_test():' ) print ( ' Python version: ' + platform.python_version ( ) ) print ( ' Test triangle_symq_rule().' ) p = 5 triangle_symq_rule_test01 ( p ) p = 5 triangle_symq_rule_test02 ( p ) p_lo = 0 p_hi = 50 triangle_symq_rule_test03 ( p_lo, p_hi ) # # Terminate. # print ( '' ) print ( 'triangle_symq_rule_test():' ) print ( ' Normal end of execution.' ) return def triangle_symq_rule_test01 ( p ): #*****************************************************************************80 # ## triangle_symq_rule_test01() computes a quadrature rule of given order. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt. # import numpy as np print ( '' ) print ( 'triangle_symq_rule_test01():' ) print ( ' Quadrature rule for the triangle,' ) print ( ' given in barycentric coordinates.' ) print ( ' Precision p = ', p ) # # Retrieve the rule. # n, a, b, c, w = triangle_symq_rule ( p ) # # Print the rule. # print ( '' ) print ( ' I W A B C' ) print ( '' ) for i in range ( 0, n ): print ( ' %4d %10.6g %10.6g %10.6g %10.6g' \ % ( i, w[i], a[i], b[i], c[i] ) ) # # Verify weights sum to 1. # w_sum = np.sum ( w ) print ( '' ) print ( ' Weight Sum ', w_sum ) return def triangle_symq_rule_test02 ( p ): #*****************************************************************************80 # ## triangle_symq_rule_test02() tests a triangle quadrature rule. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt. # import numpy as np print ( '' ) print ( 'triangle_symq_rule_test02():' ) print ( ' Test the precision of a quadrature rule for the unit triangle.' ) dim_num = 2 # # Retrieve the rule. # n, a, b, c, w = triangle_symq_rule ( p ) # # Pack the x, y, z vectors as rows of an array. # xy = np.transpose ( np.array ( [ a, b ] ) ) 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, xy ) quad = triangle_unit_area ( ) * np.dot ( w, v ) exact = triangle_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 triangle_symq_rule_test03 ( p_lo, p_hi ): #*****************************************************************************80 # ## triangle_symq_rule_test03() tests absolute and relative precision. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 10 July 2023 # # Author: # # John Burkardt. # # Input: # # integer p_lo, p_hi: the lowest and highest rules to check. # import numpy as np print ( '' ) print ( 'triangle_symq_rule_test03():' ) print ( ' Test the precision of quadrature rules for the unit triangle.' ) print ( ' Check rules of precision p =', p_lo, 'through', p_hi ) print ( ' for error in approximating integrals of monomials.' ) dim_num = 2 # # Retrieve the rule. # print ( '' ) print ( ' maximum maximum' ) print ( ' p absolute relative' ) print ( ' error error' ) print ( '' ) for p in range ( p_lo, p_hi + 1 ): n, a, b, c, w = triangle_symq_rule ( p ) # # Pack the x, y, z vectors as rows of an array. # xy = np.transpose ( np.array ( [ a, b ] ) ) 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, xy ) quad = triangle_unit_area ( ) * np.dot ( w, v ) exact = triangle_unit_monomial_integral ( expon ) quad_error = np.abs ( quad - exact ) max_abs = max ( max_abs, quad_error ) max_rel = max ( max_rel, quad_error / 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 = np.array ( []. 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 rule00 ( ): #*****************************************************************************80 # ## rule00() returns the rule of precision 0. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3333333333333333 ] ) b = np.array ( [ \ 0.3333333333333334 ] ) c = np.array ( [ \ 0.3333333333333333 ] ) w = np.array ( [ \ 1.0000000000000000 ] ) return a, b, c, w def rule01 ( ): #*****************************************************************************80 # ## rule01() returns the rule of precision 1. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3333333333333333 ] ) b = np.array ( [ \ 0.3333333333333334 ] ) c = np.array ( [ \ 0.3333333333333333 ] ) w = np.array ( [ \ 1.0000000000000000 ] ) return a, b, c, w def rule02 ( ): #*****************************************************************************80 # ## rule02() returns the rule of precision 2. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1666666666666666, \ 0.6666666666666665, \ 0.1666666666666669 ] ) b = np.array ( [ \ 0.1666666666666668, \ 0.1666666666666667, \ 0.6666666666666667 ] ) c = np.array ( [ \ 0.6666666666666665, \ 0.1666666666666668, \ 0.1666666666666664 ] ) w = np.array ( [ \ 0.3333333333333333, \ 0.3333333333333333, \ 0.3333333333333333 ] ) return a, b, c, w def rule03 ( ): #*****************************************************************************80 # ## rule03() returns the rule of precision 3. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4459484909159648, \ 0.4459484909159649, \ 0.1081030181680702, \ 0.0915762135097707, \ 0.8168475729804584, \ 0.0915762135097710 ] ) b = np.array ( [ \ 0.1081030181680703, \ 0.4459484909159649, \ 0.4459484909159651, \ 0.0915762135097709, \ 0.0915762135097707, \ 0.8168475729804585 ] ) c = np.array ( [ \ 0.4459484909159649, \ 0.1081030181680702, \ 0.4459484909159647, \ 0.8168475729804585, \ 0.0915762135097709, \ 0.0915762135097705 ] ) w = np.array ( [ \ 0.2233815896780115, \ 0.2233815896780115, \ 0.2233815896780115, \ 0.1099517436553219, \ 0.1099517436553219, \ 0.1099517436553219 ] ) return a, b, c, w def rule04 ( ): #*****************************************************************************80 # ## rule04() returns the rule of precision 4. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4459484909159648, \ 0.4459484909159649, \ 0.1081030181680702, \ 0.0915762135097707, \ 0.8168475729804584, \ 0.0915762135097710 ] ) b = np.array ( [ \ 0.1081030181680703, \ 0.4459484909159649, \ 0.4459484909159651, \ 0.0915762135097709, \ 0.0915762135097707, \ 0.8168475729804585 ] ) c = np.array ( [ \ 0.4459484909159649, \ 0.1081030181680702, \ 0.4459484909159647, \ 0.8168475729804585, \ 0.0915762135097709, \ 0.0915762135097705 ] ) w = np.array ( [ \ 0.2233815896780115, \ 0.2233815896780115, \ 0.2233815896780115, \ 0.1099517436553219, \ 0.1099517436553219, \ 0.1099517436553219 ] ) return a, b, c, w def rule05 ( ): #*****************************************************************************80 # ## rule05() returns the rule of precision 5. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1012865073234563, \ 0.7974269853530872, \ 0.1012865073234565, \ 0.4701420641051151, \ 0.4701420641051151, \ 0.0597158717897698, \ 0.3333333333333333 ] ) b = np.array ( [ \ 0.1012865073234565, \ 0.1012865073234562, \ 0.7974269853530874, \ 0.0597158717897699, \ 0.4701420641051151, \ 0.4701420641051153, \ 0.3333333333333334 ] ) c = np.array ( [ \ 0.7974269853530873, \ 0.1012865073234566, \ 0.1012865073234560, \ 0.4701420641051151, \ 0.0597158717897698, \ 0.4701420641051149, \ 0.3333333333333333 ] ) w = np.array ( [ \ 0.1259391805448272, \ 0.1259391805448272, \ 0.1259391805448272, \ 0.1323941527885062, \ 0.1323941527885062, \ 0.1323941527885062, \ 0.2250000000000000 ] ) return a, b, c, w def rule06 ( ): #*****************************************************************************80 # ## rule06() returns the rule of precision 6. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.2194299825497829, \ 0.5611400349004340, \ 0.2194299825497830, \ 0.4801379641122150, \ 0.4801379641122151, \ 0.0397240717755699, \ 0.1416190159239681, \ 0.8390092597147910, \ 0.0193717243612410, \ 0.8390092597147911, \ 0.1416190159239681, \ 0.0193717243612406 ] ) b = np.array ( [ \ 0.2194299825497831, \ 0.2194299825497830, \ 0.5611400349004342, \ 0.0397240717755700, \ 0.4801379641122150, \ 0.4801379641122153, \ 0.0193717243612408, \ 0.1416190159239681, \ 0.8390092597147911, \ 0.0193717243612408, \ 0.8390092597147912, \ 0.1416190159239684 ] ) c = np.array ( [ \ 0.5611400349004340, \ 0.2194299825497831, \ 0.2194299825497829, \ 0.4801379641122150, \ 0.0397240717755699, \ 0.4801379641122148, \ 0.8390092597147911, \ 0.0193717243612409, \ 0.1416190159239679, \ 0.1416190159239681, \ 0.0193717243612407, \ 0.8390092597147910 ] ) w = np.array ( [ \ 0.1713331241529810, \ 0.1713331241529810, \ 0.1713331241529810, \ 0.0807310895930310, \ 0.0807310895930310, \ 0.0807310895930310, \ 0.0406345597936607, \ 0.0406345597936607, \ 0.0406345597936607, \ 0.0406345597936607, \ 0.0406345597936607, \ 0.0406345597936607 ] ) return a, b, c, w def rule07 ( ): #*****************************************************************************80 # ## rule07() returns the rule of precision 7. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4731956536892510, \ 0.4731956536892510, \ 0.0536086926214978, \ 0.0577976400545063, \ 0.8844047198909870, \ 0.0577976400545066, \ 0.2593390118657857, \ 0.6936897820041288, \ 0.0469712061300856, \ 0.6936897820041288, \ 0.2593390118657857, \ 0.0469712061300854, \ 0.2416636063972473, \ 0.5166727872055051, \ 0.2416636063972475 ] ) b = np.array ( [ \ 0.0536086926214979, \ 0.4731956536892511, \ 0.4731956536892513, \ 0.0577976400545066, \ 0.0577976400545063, \ 0.8844047198909872, \ 0.0469712061300856, \ 0.2593390118657857, \ 0.6936897820041289, \ 0.0469712061300856, \ 0.6936897820041289, \ 0.2593390118657859, \ 0.2416636063972475, \ 0.2416636063972474, \ 0.5166727872055052 ] ) c = np.array ( [ \ 0.4731956536892511, \ 0.0536086926214979, \ 0.4731956536892509, \ 0.8844047198909871, \ 0.0577976400545067, \ 0.0577976400545062, \ 0.6936897820041288, \ 0.0469712061300855, \ 0.2593390118657856, \ 0.2593390118657857, \ 0.0469712061300854, \ 0.6936897820041287, \ 0.5166727872055050, \ 0.2416636063972475, \ 0.2416636063972473 ] ) w = np.array ( [ \ 0.0531808332967605, \ 0.0531808332967605, \ 0.0531808332967605, \ 0.0409181703940569, \ 0.0409181703940569, \ 0.0409181703940569, \ 0.0557545405406911, \ 0.0557545405406911, \ 0.0557545405406911, \ 0.0557545405406911, \ 0.0557545405406911, \ 0.0557545405406911, \ 0.1277252485611338, \ 0.1277252485611338, \ 0.1277252485611338 ] ) return a, b, c, w def rule08 ( ): #*****************************************************************************80 # ## rule08() returns the rule of precision 8. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1705693077517601, \ 0.6588613844964795, \ 0.1705693077517604, \ 0.4592925882927231, \ 0.4592925882927231, \ 0.0814148234145537, \ 0.3333333333333333, \ 0.0505472283170309, \ 0.8989055433659379, \ 0.0505472283170313, \ 0.2631128296346381, \ 0.7284923929554042, \ 0.0083947774099577, \ 0.7284923929554042, \ 0.2631128296346381, \ 0.0083947774099575 ] ) b = np.array ( [ \ 0.1705693077517604, \ 0.1705693077517602, \ 0.6588613844964796, \ 0.0814148234145537, \ 0.4592925882927232, \ 0.4592925882927233, \ 0.3333333333333334, \ 0.0505472283170312, \ 0.0505472283170309, \ 0.8989055433659381, \ 0.0083947774099577, \ 0.2631128296346381, \ 0.7284923929554045, \ 0.0083947774099577, \ 0.7284923929554044, \ 0.2631128296346383 ] ) c = np.array ( [ \ 0.6588613844964796, \ 0.1705693077517604, \ 0.1705693077517599, \ 0.4592925882927231, \ 0.0814148234145537, \ 0.4592925882927231, \ 0.3333333333333333, \ 0.8989055433659380, \ 0.0505472283170313, \ 0.0505472283170306, \ 0.7284923929554042, \ 0.0083947774099577, \ 0.2631128296346378, \ 0.2631128296346381, \ 0.0083947774099575, \ 0.7284923929554041 ] ) w = np.array ( [ \ 0.1032173705347182, \ 0.1032173705347182, \ 0.1032173705347182, \ 0.0950916342672846, \ 0.0950916342672846, \ 0.0950916342672846, \ 0.1443156076777872, \ 0.0324584976231981, \ 0.0324584976231981, \ 0.0324584976231981, \ 0.0272303141744350, \ 0.0272303141744350, \ 0.0272303141744350, \ 0.0272303141744350, \ 0.0272303141744350, \ 0.0272303141744350 ] ) return a, b, c, w def rule09 ( ): #*****************************************************************************80 # ## rule09() returns the rule of precision 9. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4896825191987376, \ 0.4896825191987376, \ 0.0206349616025247, \ 0.3333333333333333, \ 0.1882035356190326, \ 0.6235929287619344, \ 0.1882035356190329, \ 0.2219629891607657, \ 0.7411985987844980, \ 0.0368384120547364, \ 0.7411985987844980, \ 0.2219629891607658, \ 0.0368384120547361, \ 0.4370895914929366, \ 0.4370895914929366, \ 0.1258208170141267, \ 0.0447295133944526, \ 0.9105409732110945, \ 0.0447295133944530 ] ) b = np.array ( [ \ 0.0206349616025248, \ 0.4896825191987377, \ 0.4896825191987378, \ 0.3333333333333334, \ 0.1882035356190329, \ 0.1882035356190327, \ 0.6235929287619346, \ 0.0368384120547363, \ 0.2219629891607657, \ 0.7411985987844981, \ 0.0368384120547363, \ 0.7411985987844981, \ 0.2219629891607660, \ 0.1258208170141268, \ 0.4370895914929367, \ 0.4370895914929368, \ 0.0447295133944529, \ 0.0447295133944525, \ 0.9105409732110946 ] ) c = np.array ( [ \ 0.4896825191987376, \ 0.0206349616025246, \ 0.4896825191987374, \ 0.3333333333333333, \ 0.6235929287619345, \ 0.1882035356190329, \ 0.1882035356190325, \ 0.7411985987844980, \ 0.0368384120547363, \ 0.2219629891607655, \ 0.2219629891607657, \ 0.0368384120547361, \ 0.7411985987844979, \ 0.4370895914929366, \ 0.1258208170141267, \ 0.4370895914929366, \ 0.9105409732110946, \ 0.0447295133944530, \ 0.0447295133944524 ] ) w = np.array ( [ \ 0.0313347002271391, \ 0.0313347002271391, \ 0.0313347002271391, \ 0.0971357962827989, \ 0.0796477389272103, \ 0.0796477389272103, \ 0.0796477389272103, \ 0.0432835393772894, \ 0.0432835393772894, \ 0.0432835393772894, \ 0.0432835393772894, \ 0.0432835393772894, \ 0.0432835393772894, \ 0.0778275410047743, \ 0.0778275410047743, \ 0.0778275410047743, \ 0.0255776756586980, \ 0.0255776756586980, \ 0.0255776756586980 ] ) return a, b, c, w def rule10 ( ): #*****************************************************************************80 # ## rule10() returns the rule of precision 10. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4951734598011704, \ 0.4951734598011704, \ 0.0096530803976590, \ 0.0191394152428411, \ 0.9617211695143175, \ 0.0191394152428416, \ 0.1337347551008691, \ 0.8315416244168033, \ 0.0347236204823275, \ 0.8315416244168033, \ 0.1337347551008692, \ 0.0347236204823273, \ 0.3333333333333333, \ 0.3266931362813369, \ 0.6357241363774715, \ 0.0375827273411917, \ 0.6357241363774714, \ 0.3266931362813369, \ 0.0375827273411916, \ 0.1844850126852464, \ 0.6310299746295069, \ 0.1844850126852466, \ 0.4282348209437188, \ 0.4282348209437188, \ 0.1435303581125623 ] ) b = np.array ( [ \ 0.0096530803976591, \ 0.4951734598011706, \ 0.4951734598011707, \ 0.0191394152428414, \ 0.0191394152428411, \ 0.9617211695143175, \ 0.0347236204823275, \ 0.1337347551008691, \ 0.8315416244168037, \ 0.0347236204823275, \ 0.8315416244168035, \ 0.1337347551008694, \ 0.3333333333333334, \ 0.0375827273411917, \ 0.3266931362813369, \ 0.6357241363774715, \ 0.0375827273411917, \ 0.6357241363774715, \ 0.3266931362813372, \ 0.1844850126852466, \ 0.1844850126852465, \ 0.6310299746295072, \ 0.1435303581125623, \ 0.4282348209437189, \ 0.4282348209437190 ] ) c = np.array ( [ \ 0.4951734598011705, \ 0.0096530803976590, \ 0.4951734598011703, \ 0.9617211695143174, \ 0.0191394152428414, \ 0.0191394152428409, \ 0.8315416244168033, \ 0.0347236204823275, \ 0.1337347551008689, \ 0.1337347551008692, \ 0.0347236204823274, \ 0.8315416244168033, \ 0.3333333333333333, \ 0.6357241363774714, \ 0.0375827273411916, \ 0.3266931362813368, \ 0.3266931362813369, \ 0.0375827273411916, \ 0.6357241363774713, \ 0.6310299746295069, \ 0.1844850126852466, \ 0.1844850126852462, \ 0.4282348209437189, \ 0.1435303581125623, \ 0.4282348209437188 ] ) w = np.array ( [ \ 0.0097925904984183, \ 0.0097925904984183, \ 0.0097925904984183, \ 0.0063853592301187, \ 0.0063853592301187, \ 0.0063853592301187, \ 0.0289622814632563, \ 0.0289622814632563, \ 0.0289622814632563, \ 0.0289622814632563, \ 0.0289622814632563, \ 0.0289622814632563, \ 0.0836148743739739, \ 0.0387390490860189, \ 0.0387390490860189, \ 0.0387390490860189, \ 0.0387390490860189, \ 0.0387390490860189, \ 0.0387390490860189, \ 0.0786337697463773, \ 0.0786337697463773, \ 0.0786337697463773, \ 0.0752473279685440, \ 0.0752473279685440, \ 0.0752473279685440 ] ) return a, b, c, w def rule11 ( ): #*****************************************************************************80 # ## rule11() returns the rule of precision 11. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.0308468956355879, \ 0.9383062087288239, \ 0.0308468956355883, \ 0.4987801651784607, \ 0.4987801651784607, \ 0.0024396696430784, \ 0.1593036198376935, \ 0.8263297175927509, \ 0.0143666625695557, \ 0.8263297175927509, \ 0.1593036198376935, \ 0.0143666625695554, \ 0.3333333333333333, \ 0.1132078272866939, \ 0.7735843454266120, \ 0.1132078272866941, \ 0.4366550163931761, \ 0.4366550163931761, \ 0.1266899672136477, \ 0.2144834586192693, \ 0.5710330827614613, \ 0.2144834586192694, \ 0.3106312163134631, \ 0.6417047167143861, \ 0.0476640669721508, \ 0.6417047167143860, \ 0.3106312163134631, \ 0.0476640669721507 ] ) b = np.array ( [ \ 0.0308468956355882, \ 0.0308468956355879, \ 0.9383062087288241, \ 0.0024396696430785, \ 0.4987801651784608, \ 0.4987801651784610, \ 0.0143666625695556, \ 0.1593036198376935, \ 0.8263297175927511, \ 0.0143666625695556, \ 0.8263297175927511, \ 0.1593036198376938, \ 0.3333333333333334, \ 0.1132078272866941, \ 0.1132078272866939, \ 0.7735843454266123, \ 0.1266899672136478, \ 0.4366550163931761, \ 0.4366550163931763, \ 0.2144834586192694, \ 0.2144834586192693, \ 0.5710330827614615, \ 0.0476640669721508, \ 0.3106312163134631, \ 0.6417047167143863, \ 0.0476640669721508, \ 0.6417047167143861, \ 0.3106312163134634 ] ) c = np.array ( [ \ 0.9383062087288240, \ 0.0308468956355883, \ 0.0308468956355876, \ 0.4987801651784608, \ 0.0024396696430785, \ 0.4987801651784606, \ 0.8263297175927509, \ 0.0143666625695556, \ 0.1593036198376933, \ 0.1593036198376935, \ 0.0143666625695554, \ 0.8263297175927509, \ 0.3333333333333333, \ 0.7735843454266120, \ 0.1132078272866941, \ 0.1132078272866937, \ 0.4366550163931761, \ 0.1266899672136478, \ 0.4366550163931761, \ 0.5710330827614614, \ 0.2144834586192694, \ 0.2144834586192691, \ 0.6417047167143861, \ 0.0476640669721508, \ 0.3106312163134629, \ 0.3106312163134632, \ 0.0476640669721508, \ 0.6417047167143859 ] ) w = np.array ( [ \ 0.0122492969507080, \ 0.0122492969507080, \ 0.0122492969507080, \ 0.0124654918738814, \ 0.0124654918738814, \ 0.0124654918738814, \ 0.0145576233378092, \ 0.0145576233378092, \ 0.0145576233378092, \ 0.0145576233378092, \ 0.0145576233378092, \ 0.0145576233378092, \ 0.0814451347093513, \ 0.0401292423813083, \ 0.0401292423813083, \ 0.0401292423813083, \ 0.0630948721598987, \ 0.0630948721598987, \ 0.0630948721598987, \ 0.0678451077436951, \ 0.0678451077436951, \ 0.0678451077436951, \ 0.0406428486558865, \ 0.0406428486558865, \ 0.0406428486558865, \ 0.0406428486558865, \ 0.0406428486558865, \ 0.0406428486558865 ] ) return a, b, c, w def rule12 ( ): #*****************************************************************************80 # ## rule12() returns the rule of precision 12. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.2714625070149260, \ 0.4570749859701477, \ 0.2714625070149261, \ 0.1092578276593542, \ 0.7814843446812912, \ 0.1092578276593545, \ 0.4401116486585931, \ 0.4401116486585931, \ 0.1197767026828138, \ 0.2554542286385173, \ 0.6282497516835561, \ 0.1162960196779266, \ 0.6282497516835561, \ 0.2554542286385174, \ 0.1162960196779265, \ 0.1272797172335894, \ 0.8513377925102400, \ 0.0213824902561707, \ 0.8513377925102400, \ 0.1272797172335894, \ 0.0213824902561704, \ 0.2916556797383409, \ 0.6853101639063919, \ 0.0230341563552672, \ 0.6853101639063919, \ 0.2916556797383410, \ 0.0230341563552670, \ 0.4882037509455415, \ 0.4882037509455415, \ 0.0235924981089169, \ 0.0246463634363355, \ 0.9507072731273287, \ 0.0246463634363359 ] ) b = np.array ( [ \ 0.2714625070149262, \ 0.2714625070149261, \ 0.4570749859701479, \ 0.1092578276593545, \ 0.1092578276593542, \ 0.7814843446812915, \ 0.1197767026828138, \ 0.4401116486585931, \ 0.4401116486585933, \ 0.1162960196779266, \ 0.2554542286385174, \ 0.6282497516835562, \ 0.1162960196779266, \ 0.6282497516835562, \ 0.2554542286385176, \ 0.0213824902561706, \ 0.1272797172335893, \ 0.8513377925102402, \ 0.0213824902561706, \ 0.8513377925102402, \ 0.1272797172335897, \ 0.0230341563552672, \ 0.2916556797383410, \ 0.6853101639063921, \ 0.0230341563552672, \ 0.6853101639063920, \ 0.2916556797383412, \ 0.0235924981089169, \ 0.4882037509455416, \ 0.4882037509455417, \ 0.0246463634363358, \ 0.0246463634363355, \ 0.9507072731273288 ] ) c = np.array ( [ \ 0.4570749859701478, \ 0.2714625070149261, \ 0.2714625070149260, \ 0.7814843446812914, \ 0.1092578276593545, \ 0.1092578276593540, \ 0.4401116486585931, \ 0.1197767026828138, \ 0.4401116486585929, \ 0.6282497516835560, \ 0.1162960196779265, \ 0.2554542286385172, \ 0.2554542286385172, \ 0.1162960196779265, \ 0.6282497516835559, \ 0.8513377925102400, \ 0.0213824902561707, \ 0.1272797172335890, \ 0.1272797172335894, \ 0.0213824902561704, \ 0.8513377925102400, \ 0.6853101639063919, \ 0.0230341563552671, \ 0.2916556797383407, \ 0.2916556797383409, \ 0.0230341563552671, \ 0.6853101639063917, \ 0.4882037509455416, \ 0.0235924981089169, \ 0.4882037509455414, \ 0.9507072731273288, \ 0.0246463634363358, \ 0.0246463634363353 ] ) w = np.array ( [ \ 0.0625412131959027, \ 0.0625412131959027, \ 0.0625412131959027, \ 0.0284860520688775, \ 0.0284860520688775, \ 0.0284860520688775, \ 0.0499183349280609, \ 0.0499183349280609, \ 0.0499183349280609, \ 0.0432273636594142, \ 0.0432273636594142, \ 0.0432273636594142, \ 0.0432273636594142, \ 0.0432273636594142, \ 0.0432273636594142, \ 0.0150836775765114, \ 0.0150836775765114, \ 0.0150836775765114, \ 0.0150836775765114, \ 0.0150836775765114, \ 0.0150836775765114, \ 0.0217835850386075, \ 0.0217835850386075, \ 0.0217835850386075, \ 0.0217835850386075, \ 0.0217835850386075, \ 0.0217835850386075, \ 0.0242668380814520, \ 0.0242668380814520, \ 0.0242668380814520, \ 0.0079316425099736, \ 0.0079316425099736, \ 0.0079316425099736 ] ) return a, b, c, w def rule13 ( ): #*****************************************************************************80 # ## rule13() returns the rule of precision 13. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4961358947410461, \ 0.4961358947410460, \ 0.0077282105179078, \ 0.4696086896534919, \ 0.4696086896534918, \ 0.0607826206930162, \ 0.2311102849490822, \ 0.5377794301018355, \ 0.2311102849490823, \ 0.2920786885766364, \ 0.6889333070396045, \ 0.0189880043837591, \ 0.6889333070396045, \ 0.2920786885766364, \ 0.0189880043837589, \ 0.3333333333333333, \ 0.2667452533103511, \ 0.6355187156236324, \ 0.0977360310660165, \ 0.6355187156236323, \ 0.2667452533103513, \ 0.0977360310660164, \ 0.4144775702790545, \ 0.4144775702790545, \ 0.1710448594418908, \ 0.1135599125721331, \ 0.7728801748557336, \ 0.1135599125721334, \ 0.1267997757838373, \ 0.8512338800096334, \ 0.0219663442065294, \ 0.8512338800096334, \ 0.1267997757838374, \ 0.0219663442065290, \ 0.0248959314912162, \ 0.9502081370175671, \ 0.0248959314912167 ] ) b = np.array ( [ \ 0.0077282105179079, \ 0.4961358947410461, \ 0.4961358947410462, \ 0.0607826206930162, \ 0.4696086896534920, \ 0.4696086896534921, \ 0.2311102849490824, \ 0.2311102849490823, \ 0.5377794301018356, \ 0.0189880043837590, \ 0.2920786885766364, \ 0.6889333070396048, \ 0.0189880043837590, \ 0.6889333070396046, \ 0.2920786885766367, \ 0.3333333333333334, \ 0.0977360310660166, \ 0.2667452533103512, \ 0.6355187156236326, \ 0.0977360310660166, \ 0.6355187156236323, \ 0.2667452533103514, \ 0.1710448594418909, \ 0.4144775702790546, \ 0.4144775702790547, \ 0.1135599125721333, \ 0.1135599125721331, \ 0.7728801748557337, \ 0.0219663442065293, \ 0.1267997757838373, \ 0.8512338800096335, \ 0.0219663442065293, \ 0.8512338800096335, \ 0.1267997757838377, \ 0.0248959314912165, \ 0.0248959314912162, \ 0.9502081370175673 ] ) c = np.array ( [ \ 0.4961358947410460, \ 0.0077282105179078, \ 0.4961358947410459, \ 0.4696086896534919, \ 0.0607826206930161, \ 0.4696086896534917, \ 0.5377794301018354, \ 0.2311102849490823, \ 0.2311102849490821, \ 0.6889333070396045, \ 0.0189880043837590, \ 0.2920786885766361, \ 0.2920786885766364, \ 0.0189880043837589, \ 0.6889333070396044, \ 0.3333333333333333, \ 0.6355187156236323, \ 0.0977360310660164, \ 0.2667452533103509, \ 0.2667452533103511, \ 0.0977360310660164, \ 0.6355187156236322, \ 0.4144775702790546, \ 0.1710448594418909, \ 0.4144775702790545, \ 0.7728801748557337, \ 0.1135599125721334, \ 0.1135599125721329, \ 0.8512338800096335, \ 0.0219663442065293, \ 0.1267997757838371, \ 0.1267997757838373, \ 0.0219663442065291, \ 0.8512338800096333, \ 0.9502081370175672, \ 0.0248959314912166, \ 0.0248959314912159 ] ) w = np.array ( [ \ 0.0099414763610726, \ 0.0099414763610726, \ 0.0099414763610726, \ 0.0327812416037230, \ 0.0327812416037230, \ 0.0327812416037230, \ 0.0460624095927782, \ 0.0460624095927782, \ 0.0460624095927782, \ 0.0181254986462009, \ 0.0181254986462009, \ 0.0181254986462009, \ 0.0181254986462009, \ 0.0181254986462009, \ 0.0181254986462009, \ 0.0516226466642908, \ 0.0372119604572615, \ 0.0372119604572615, \ 0.0372119604572615, \ 0.0372119604572615, \ 0.0372119604572615, \ 0.0372119604572615, \ 0.0469470955421552, \ 0.0469470955421552, \ 0.0469470955421552, \ 0.0309030979757598, \ 0.0309030979757598, \ 0.0309030979757598, \ 0.0153930726837822, \ 0.0153930726837822, \ 0.0153930726837822, \ 0.0153930726837822, \ 0.0153930726837822, \ 0.0153930726837822, \ 0.0080293997952584, \ 0.0080293997952584, \ 0.0080293997952584 ] ) return a, b, c, w def rule14 ( ): #*****************************************************************************80 # ## rule14() returns the rule of precision 14. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4176447193404539, \ 0.4176447193404539, \ 0.1647105613190921, \ 0.2983728821362577, \ 0.6869801678080878, \ 0.0146469500556545, \ 0.6869801678080878, \ 0.2983728821362577, \ 0.0146469500556543, \ 0.0617998830908725, \ 0.8764002338182547, \ 0.0617998830908729, \ 0.3368614597963450, \ 0.5702222908466831, \ 0.0929162493569718, \ 0.5702222908466831, \ 0.3368614597963450, \ 0.0929162493569718, \ 0.2734775283088386, \ 0.4530449433823227, \ 0.2734775283088388, \ 0.1772055324125434, \ 0.6455889351749130, \ 0.1772055324125437, \ 0.0193909612487009, \ 0.9612180775025979, \ 0.0193909612487014, \ 0.4889639103621786, \ 0.4889639103621787, \ 0.0220721792756427, \ 0.1722666878213555, \ 0.7706085547749963, \ 0.0571247574036480, \ 0.7706085547749965, \ 0.1722666878213556, \ 0.0571247574036478, \ 0.1189744976969568, \ 0.8797571713701711, \ 0.0012683309328722, \ 0.8797571713701712, \ 0.1189744976969569, \ 0.0012683309328719 ] ) b = np.array ( [ \ 0.1647105613190922, \ 0.4176447193404541, \ 0.4176447193404541, \ 0.0146469500556545, \ 0.2983728821362578, \ 0.6869801678080880, \ 0.0146469500556545, \ 0.6869801678080880, \ 0.2983728821362580, \ 0.0617998830908728, \ 0.0617998830908724, \ 0.8764002338182548, \ 0.0929162493569719, \ 0.3368614597963451, \ 0.5702222908466833, \ 0.0929162493569719, \ 0.5702222908466833, \ 0.3368614597963452, \ 0.2734775283088388, \ 0.2734775283088387, \ 0.4530449433823228, \ 0.1772055324125436, \ 0.1772055324125434, \ 0.6455889351749131, \ 0.0193909612487012, \ 0.0193909612487009, \ 0.9612180775025979, \ 0.0220721792756428, \ 0.4889639103621786, \ 0.4889639103621788, \ 0.0571247574036480, \ 0.1722666878213556, \ 0.7706085547749967, \ 0.0571247574036480, \ 0.7706085547749966, \ 0.1722666878213558, \ 0.0012683309328721, \ 0.1189744976969568, \ 0.8797571713701712, \ 0.0012683309328721, \ 0.8797571713701712, \ 0.1189744976969572 ] ) c = np.array ( [ \ 0.4176447193404539, \ 0.1647105613190921, \ 0.4176447193404539, \ 0.6869801678080878, \ 0.0146469500556544, \ 0.2983728821362575, \ 0.2983728821362577, \ 0.0146469500556543, \ 0.6869801678080877, \ 0.8764002338182547, \ 0.0617998830908728, \ 0.0617998830908723, \ 0.5702222908466831, \ 0.0929162493569718, \ 0.3368614597963449, \ 0.3368614597963450, \ 0.0929162493569716, \ 0.5702222908466831, \ 0.4530449433823226, \ 0.2734775283088386, \ 0.2734775283088385, \ 0.6455889351749130, \ 0.1772055324125436, \ 0.1772055324125432, \ 0.9612180775025979, \ 0.0193909612487012, \ 0.0193909612487008, \ 0.4889639103621786, \ 0.0220721792756427, \ 0.4889639103621784, \ 0.7706085547749965, \ 0.0571247574036481, \ 0.1722666878213553, \ 0.1722666878213555, \ 0.0571247574036479, \ 0.7706085547749963, \ 0.8797571713701712, \ 0.0012683309328721, \ 0.1189744976969566, \ 0.1189744976969567, \ 0.0012683309328719, \ 0.8797571713701708 ] ) w = np.array ( [ \ 0.0327883535441254, \ 0.0327883535441254, \ 0.0327883535441254, \ 0.0144363081135338, \ 0.0144363081135338, \ 0.0144363081135338, \ 0.0144363081135338, \ 0.0144363081135338, \ 0.0144363081135338, \ 0.0144336996697767, \ 0.0144336996697767, \ 0.0144336996697767, \ 0.0385715107870607, \ 0.0385715107870607, \ 0.0385715107870607, \ 0.0385715107870607, \ 0.0385715107870607, \ 0.0385715107870607, \ 0.0517741045072916, \ 0.0517741045072916, \ 0.0517741045072916, \ 0.0421625887369930, \ 0.0421625887369930, \ 0.0421625887369930, \ 0.0049234036024001, \ 0.0049234036024001, \ 0.0049234036024001, \ 0.0218835813694289, \ 0.0218835813694289, \ 0.0218835813694289, \ 0.0246657532125637, \ 0.0246657532125637, \ 0.0246657532125637, \ 0.0246657532125637, \ 0.0246657532125637, \ 0.0246657532125637, \ 0.0050102288385007, \ 0.0050102288385007, \ 0.0050102288385007, \ 0.0050102288385007, \ 0.0050102288385007, \ 0.0050102288385007 ] ) return a, b, c, w def rule15 ( ): #*****************************************************************************80 # ## rule15() returns the rule of precision 15. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1299782299330778, \ 0.7400435401338442, \ 0.1299782299330779, \ 0.3333333333333333, \ 0.4600769492970597, \ 0.4600769492970597, \ 0.0798461014058805, \ 0.1823217834071913, \ 0.7330839951106168, \ 0.0845942214821919, \ 0.7330839951106169, \ 0.1823217834071914, \ 0.0845942214821916, \ 0.1502003840652387, \ 0.8337725261484157, \ 0.0160270897863456, \ 0.8337725261484158, \ 0.1502003840652388, \ 0.0160270897863453, \ 0.3231113151637127, \ 0.5792382424060449, \ 0.0976504424302423, \ 0.5792382424060449, \ 0.3231113151637127, \ 0.0976504424302423, \ 0.4916858166302972, \ 0.4916858166302972, \ 0.0166283667394055, \ 0.2215323407951419, \ 0.5569353184097160, \ 0.2215323407951421, \ 0.3969337374090606, \ 0.3969337374090606, \ 0.2061325251818788, \ 0.3079476814836729, \ 0.6735980666116939, \ 0.0184542519046332, \ 0.6735980666116940, \ 0.3079476814836729, \ 0.0184542519046331, \ 0.0563419176961000, \ 0.8873161646077997, \ 0.0563419176961004, \ 0.0380352293011093, \ 0.9608512354248769, \ 0.0011135352740139, \ 0.9608512354248770, \ 0.0380352293011093, \ 0.0011135352740135 ] ) b = np.array ( [ \ 0.1299782299330780, \ 0.1299782299330778, \ 0.7400435401338445, \ 0.3333333333333334, \ 0.0798461014058806, \ 0.4600769492970598, \ 0.4600769492970599, \ 0.0845942214821918, \ 0.1823217834071913, \ 0.7330839951106169, \ 0.0845942214821918, \ 0.7330839951106171, \ 0.1823217834071916, \ 0.0160270897863455, \ 0.1502003840652387, \ 0.8337725261484159, \ 0.0160270897863455, \ 0.8337725261484159, \ 0.1502003840652391, \ 0.0976504424302424, \ 0.3231113151637127, \ 0.5792382424060452, \ 0.0976504424302424, \ 0.5792382424060450, \ 0.3231113151637129, \ 0.0166283667394056, \ 0.4916858166302973, \ 0.4916858166302975, \ 0.2215323407951421, \ 0.2215323407951420, \ 0.5569353184097161, \ 0.2061325251818789, \ 0.3969337374090606, \ 0.3969337374090607, \ 0.0184542519046332, \ 0.3079476814836729, \ 0.6735980666116942, \ 0.0184542519046332, \ 0.6735980666116941, \ 0.3079476814836731, \ 0.0563419176961003, \ 0.0563419176960999, \ 0.8873161646077998, \ 0.0011135352740137, \ 0.0380352293011093, \ 0.9608512354248772, \ 0.0011135352740137, \ 0.9608512354248772, \ 0.0380352293011096 ] ) c = np.array ( [ \ 0.7400435401338443, \ 0.1299782299330780, \ 0.1299782299330775, \ 0.3333333333333333, \ 0.4600769492970597, \ 0.0798461014058806, \ 0.4600769492970595, \ 0.7330839951106168, \ 0.0845942214821918, \ 0.1823217834071911, \ 0.1823217834071912, \ 0.0845942214821916, \ 0.7330839951106169, \ 0.8337725261484158, \ 0.0160270897863456, \ 0.1502003840652385, \ 0.1502003840652387, \ 0.0160270897863453, \ 0.8337725261484157, \ 0.5792382424060450, \ 0.0976504424302423, \ 0.3231113151637125, \ 0.3231113151637127, \ 0.0976504424302423, \ 0.5792382424060449, \ 0.4916858166302972, \ 0.0166283667394055, \ 0.4916858166302970, \ 0.5569353184097159, \ 0.2215323407951420, \ 0.2215323407951418, \ 0.3969337374090605, \ 0.2061325251818788, \ 0.3969337374090605, \ 0.6735980666116940, \ 0.0184542519046332, \ 0.3079476814836727, \ 0.3079476814836729, \ 0.0184542519046330, \ 0.6735980666116937, \ 0.8873161646077997, \ 0.0563419176961003, \ 0.0563419176960998, \ 0.9608512354248770, \ 0.0011135352740138, \ 0.0380352293011089, \ 0.0380352293011092, \ 0.0011135352740136, \ 0.9608512354248769 ] ) w = np.array ( [ \ 0.0073975040670461, \ 0.0073975040670461, \ 0.0073975040670461, \ 0.0297304197480713, \ 0.0215940879364384, \ 0.0215940879364384, \ 0.0215940879364384, \ 0.0242300087831256, \ 0.0242300087831256, \ 0.0242300087831256, \ 0.0242300087831256, \ 0.0242300087831256, \ 0.0242300087831256, \ 0.0112285042988781, \ 0.0112285042988781, \ 0.0112285042988781, \ 0.0112285042988781, \ 0.0112285042988781, \ 0.0112285042988781, \ 0.0310752204705109, \ 0.0310752204705109, \ 0.0310752204705109, \ 0.0310752204705109, \ 0.0310752204705109, \ 0.0310752204705109, \ 0.0158322763500218, \ 0.0158322763500218, \ 0.0158322763500218, \ 0.0462872861051981, \ 0.0462872861051981, \ 0.0462872861051981, \ 0.0463360413912072, \ 0.0463360413912072, \ 0.0463360413912072, \ 0.0164367620928279, \ 0.0164367620928279, \ 0.0164367620928279, \ 0.0164367620928279, \ 0.0164367620928279, \ 0.0164367620928279, \ 0.0150844742475971, \ 0.0150844742475971, \ 0.0150844742475971, \ 0.0024752660145579, \ 0.0024752660145579, \ 0.0024752660145579, \ 0.0024752660145579, \ 0.0024752660145579, \ 0.0024752660145579 ] ) return a, b, c, w def rule16 ( ): #*****************************************************************************80 # ## rule16() returns the rule of precision 16. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4137694858270852, \ 0.5765655597692547, \ 0.0096649544036603, \ 0.5765655597692546, \ 0.4137694858270852, \ 0.0096649544036602, \ 0.3041794482294797, \ 0.6655146084153339, \ 0.0303059433551864, \ 0.6655146084153339, \ 0.3041794482294798, \ 0.0303059433551863, \ 0.0666744722402382, \ 0.8666510555195234, \ 0.0666744722402385, \ 0.0896090890227058, \ 0.8995779382011904, \ 0.0108129727761038, \ 0.8995779382011904, \ 0.0896090890227059, \ 0.0108129727761035, \ 0.2966153724003829, \ 0.5967314670634685, \ 0.1066531605361485, \ 0.5967314670634686, \ 0.2966153724003830, \ 0.1066531605361483, \ 0.2413216807013783, \ 0.5173566385972432, \ 0.2413216807013784, \ 0.4127980959552237, \ 0.4127980959552237, \ 0.1744038080895526, \ 0.1697633551502897, \ 0.7788823295056971, \ 0.0513543153440132, \ 0.7788823295056972, \ 0.1697633551502898, \ 0.0513543153440130, \ 0.1500637365870350, \ 0.6998725268259297, \ 0.1500637365870353, \ 0.2140487799258473, \ 0.7822542773667971, \ 0.0036969427073556, \ 0.7822542773667971, \ 0.2140487799258473, \ 0.0036969427073554, \ 0.4695480309966850, \ 0.4695480309966850, \ 0.0609039380066300, \ 0.3333333333333333, \ 0.0170416294057183, \ 0.9659167411885631, \ 0.0170416294057187 ] ) b = np.array ( [ \ 0.0096649544036603, \ 0.4137694858270852, \ 0.5765655597692547, \ 0.0096649544036603, \ 0.5765655597692547, \ 0.4137694858270854, \ 0.0303059433551864, \ 0.3041794482294797, \ 0.6655146084153342, \ 0.0303059433551864, \ 0.6655146084153339, \ 0.3041794482294800, \ 0.0666744722402385, \ 0.0666744722402381, \ 0.8666510555195236, \ 0.0108129727761038, \ 0.0896090890227058, \ 0.8995779382011906, \ 0.0108129727761038, \ 0.8995779382011906, \ 0.0896090890227062, \ 0.1066531605361485, \ 0.2966153724003830, \ 0.5967314670634687, \ 0.1066531605361485, \ 0.5967314670634686, \ 0.2966153724003832, \ 0.2413216807013785, \ 0.2413216807013784, \ 0.5173566385972433, \ 0.1744038080895527, \ 0.4127980959552238, \ 0.4127980959552238, \ 0.0513543153440131, \ 0.1697633551502898, \ 0.7788823295056972, \ 0.0513543153440131, \ 0.7788823295056971, \ 0.1697633551502900, \ 0.1500637365870353, \ 0.1500637365870350, \ 0.6998725268259298, \ 0.0036969427073556, \ 0.2140487799258473, \ 0.7822542773667974, \ 0.0036969427073556, \ 0.7822542773667972, \ 0.2140487799258476, \ 0.0609039380066301, \ 0.4695480309966850, \ 0.4695480309966852, \ 0.3333333333333334, \ 0.0170416294057186, \ 0.0170416294057182, \ 0.9659167411885633 ] ) c = np.array ( [ \ 0.5765655597692546, \ 0.0096649544036601, \ 0.4137694858270851, \ 0.4137694858270851, \ 0.0096649544036601, \ 0.5765655597692544, \ 0.6655146084153339, \ 0.0303059433551863, \ 0.3041794482294794, \ 0.3041794482294797, \ 0.0303059433551863, \ 0.6655146084153338, \ 0.8666510555195234, \ 0.0666744722402385, \ 0.0666744722402378, \ 0.8995779382011905, \ 0.0108129727761038, \ 0.0896090890227056, \ 0.0896090890227059, \ 0.0108129727761035, \ 0.8995779382011904, \ 0.5967314670634686, \ 0.1066531605361485, \ 0.2966153724003828, \ 0.2966153724003829, \ 0.1066531605361484, \ 0.5967314670634685, \ 0.5173566385972432, \ 0.2413216807013784, \ 0.2413216807013782, \ 0.4127980959552237, \ 0.1744038080895526, \ 0.4127980959552236, \ 0.7788823295056971, \ 0.0513543153440131, \ 0.1697633551502895, \ 0.1697633551502896, \ 0.0513543153440131, \ 0.7788823295056969, \ 0.6998725268259297, \ 0.1500637365870353, \ 0.1500637365870349, \ 0.7822542773667971, \ 0.0036969427073556, \ 0.2140487799258469, \ 0.2140487799258473, \ 0.0036969427073555, \ 0.7822542773667970, \ 0.4695480309966850, \ 0.0609039380066300, \ 0.4695480309966847, \ 0.3333333333333333, \ 0.9659167411885632, \ 0.0170416294057187, \ 0.0170416294057180 ] ) w = np.array ( [ \ 0.0081822105532221, \ 0.0081822105532221, \ 0.0081822105532221, \ 0.0081822105532221, \ 0.0081822105532221, \ 0.0081822105532221, \ 0.0139836071246536, \ 0.0139836071246536, \ 0.0139836071246536, \ 0.0139836071246536, \ 0.0139836071246536, \ 0.0139836071246536, \ 0.0124254255955610, \ 0.0124254255955610, \ 0.0124254255955610, \ 0.0057518699704972, \ 0.0057518699704972, \ 0.0057518699704972, \ 0.0057518699704972, \ 0.0057518699704972, \ 0.0057518699704972, \ 0.0316460616819832, \ 0.0316460616819832, \ 0.0316460616819832, \ 0.0316460616819832, \ 0.0316460616819832, \ 0.0316460616819832, \ 0.0411840410697925, \ 0.0411840410697925, \ 0.0411840410697925, \ 0.0409852197868154, \ 0.0409852197868154, \ 0.0409852197868154, \ 0.0176530810471033, \ 0.0176530810471033, \ 0.0176530810471033, \ 0.0176530810471033, \ 0.0176530810471033, \ 0.0176530810471033, \ 0.0287834967027489, \ 0.0287834967027489, \ 0.0287834967027489, \ 0.0046146906397291, \ 0.0046146906397291, \ 0.0046146906397291, \ 0.0046146906397291, \ 0.0046146906397291, \ 0.0046146906397291, \ 0.0270936694677105, \ 0.0270936694677105, \ 0.0270936694677105, \ 0.0462279103141913, \ 0.0037891352382642, \ 0.0037891352382642, \ 0.0037891352382642 ] ) return a, b, c, w def rule17 ( ): #*****************************************************************************80 # ## rule17() returns the rule of precision 17. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4171034443615992, \ 0.4171034443615992, \ 0.1657931112768016, \ 0.0725054707990024, \ 0.9159193532978169, \ 0.0115751759031809, \ 0.9159193532978169, \ 0.0725054707990024, \ 0.0115751759031804, \ 0.1803581162663705, \ 0.6392837674672587, \ 0.1803581162663708, \ 0.4154754592952291, \ 0.5712948679446841, \ 0.0132296727600869, \ 0.5712948679446841, \ 0.4154754592952290, \ 0.0132296727600868, \ 0.2717918700553548, \ 0.7150722591106424, \ 0.0131358708340029, \ 0.7150722591106424, \ 0.2717918700553550, \ 0.0131358708340026, \ 0.2992189424769703, \ 0.5432755795961597, \ 0.1575054779268699, \ 0.5432755795961597, \ 0.2992189424769702, \ 0.1575054779268698, \ 0.2857065024365866, \ 0.4285869951268267, \ 0.2857065024365867, \ 0.3062815917461865, \ 0.6263690303864522, \ 0.0673493778673613, \ 0.6263690303864522, \ 0.3062815917461865, \ 0.0673493778673612, \ 0.1687225134952594, \ 0.7532351459364581, \ 0.0780423405682825, \ 0.7532351459364581, \ 0.1687225134952594, \ 0.0780423405682823, \ 0.0666540634795968, \ 0.8666918730408060, \ 0.0666540634795971, \ 0.1591922874727927, \ 0.8247900701650880, \ 0.0160176423621194, \ 0.8247900701650880, \ 0.1591922874727927, \ 0.0160176423621192, \ 0.0147554916607538, \ 0.9704890166784920, \ 0.0147554916607542, \ 0.4655978716188903, \ 0.4655978716188902, \ 0.0688042567622194 ] ) b = np.array ( [ \ 0.1657931112768017, \ 0.4171034443615993, \ 0.4171034443615994, \ 0.0115751759031807, \ 0.0725054707990024, \ 0.9159193532978170, \ 0.0115751759031807, \ 0.9159193532978170, \ 0.0725054707990027, \ 0.1803581162663707, \ 0.1803581162663706, \ 0.6392837674672588, \ 0.0132296727600870, \ 0.4154754592952291, \ 0.5712948679446843, \ 0.0132296727600870, \ 0.5712948679446841, \ 0.4154754592952293, \ 0.0131358708340028, \ 0.2717918700553549, \ 0.7150722591106425, \ 0.0131358708340028, \ 0.7150722591106424, \ 0.2717918700553552, \ 0.1575054779268700, \ 0.2992189424769703, \ 0.5432755795961599, \ 0.1575054779268700, \ 0.5432755795961599, \ 0.2992189424769705, \ 0.2857065024365867, \ 0.2857065024365867, \ 0.4285869951268269, \ 0.0673493778673613, \ 0.3062815917461865, \ 0.6263690303864524, \ 0.0673493778673613, \ 0.6263690303864524, \ 0.3062815917461867, \ 0.0780423405682825, \ 0.1687225134952594, \ 0.7532351459364584, \ 0.0780423405682825, \ 0.7532351459364582, \ 0.1687225134952597, \ 0.0666540634795971, \ 0.0666540634795968, \ 0.8666918730408062, \ 0.0160176423621193, \ 0.1591922874727927, \ 0.8247900701650882, \ 0.0160176423621193, \ 0.8247900701650882, \ 0.1591922874727930, \ 0.0147554916607541, \ 0.0147554916607538, \ 0.9704890166784922, \ 0.0688042567622194, \ 0.4655978716188904, \ 0.4655978716188905 ] ) c = np.array ( [ \ 0.4171034443615991, \ 0.1657931112768015, \ 0.4171034443615990, \ 0.9159193532978169, \ 0.0115751759031807, \ 0.0725054707990022, \ 0.0725054707990024, \ 0.0115751759031805, \ 0.9159193532978168, \ 0.6392837674672587, \ 0.1803581162663707, \ 0.1803581162663704, \ 0.5712948679446841, \ 0.0132296727600869, \ 0.4154754592952288, \ 0.4154754592952289, \ 0.0132296727600869, \ 0.5712948679446839, \ 0.7150722591106424, \ 0.0131358708340027, \ 0.2717918700553547, \ 0.2717918700553548, \ 0.0131358708340026, \ 0.7150722591106422, \ 0.5432755795961598, \ 0.1575054779268700, \ 0.2992189424769702, \ 0.2992189424769703, \ 0.1575054779268699, \ 0.5432755795961597, \ 0.4285869951268267, \ 0.2857065024365867, \ 0.2857065024365865, \ 0.6263690303864522, \ 0.0673493778673613, \ 0.3062815917461863, \ 0.3062815917461865, \ 0.0673493778673611, \ 0.6263690303864521, \ 0.7532351459364580, \ 0.0780423405682825, \ 0.1687225134952591, \ 0.1687225134952594, \ 0.0780423405682823, \ 0.7532351459364579, \ 0.8666918730408061, \ 0.0666540634795972, \ 0.0666540634795967, \ 0.8247900701650880, \ 0.0160176423621193, \ 0.1591922874727923, \ 0.1591922874727927, \ 0.0160176423621191, \ 0.8247900701650878, \ 0.9704890166784921, \ 0.0147554916607542, \ 0.0147554916607536, \ 0.4655978716188903, \ 0.0688042567622194, \ 0.4655978716188902 ] ) w = np.array ( [ \ 0.0273109265281021, \ 0.0273109265281021, \ 0.0273109265281021, \ 0.0045843484017359, \ 0.0045843484017359, \ 0.0045843484017359, \ 0.0045843484017359, \ 0.0045843484017359, \ 0.0045843484017359, \ 0.0263126305880180, \ 0.0263126305880180, \ 0.0263126305880180, \ 0.0103984399558395, \ 0.0103984399558395, \ 0.0103984399558395, \ 0.0103984399558395, \ 0.0103984399558395, \ 0.0103984399558395, \ 0.0086922145010012, \ 0.0086922145010012, \ 0.0086922145010012, \ 0.0086922145010012, \ 0.0086922145010012, \ 0.0086922145010012, \ 0.0261716259353370, \ 0.0261716259353370, \ 0.0261716259353370, \ 0.0261716259353370, \ 0.0261716259353370, \ 0.0261716259353370, \ 0.0377162371527953, \ 0.0377162371527953, \ 0.0377162371527953, \ 0.0224877725466911, \ 0.0224877725466911, \ 0.0224877725466911, \ 0.0224877725466911, \ 0.0224877725466911, \ 0.0224877725466911, \ 0.0205578983204545, \ 0.0205578983204545, \ 0.0205578983204545, \ 0.0205578983204545, \ 0.0205578983204545, \ 0.0205578983204545, \ 0.0124590008023054, \ 0.0124590008023054, \ 0.0124590008023054, \ 0.0079783002059296, \ 0.0079783002059296, \ 0.0079783002059296, \ 0.0079783002059296, \ 0.0079783002059296, \ 0.0079783002059296, \ 0.0027738875776376, \ 0.0027738875776376, \ 0.0027738875776376, \ 0.0250194509504974, \ 0.0250194509504974, \ 0.0250194509504974 ] ) return a, b, c, w def rule18 ( ): #*****************************************************************************80 # ## rule18() returns the rule of precision 18. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3850440344131636, \ 0.5245289252324958, \ 0.0904270403543406, \ 0.5245289252324957, \ 0.3850440344131637, \ 0.0904270403543405, \ 0.4749182113240457, \ 0.4749182113240458, \ 0.0501635773519085, \ 0.1516385069726047, \ 0.6967229860547902, \ 0.1516385069726050, \ 0.0472761418326517, \ 0.9402249256838527, \ 0.0124989324834957, \ 0.9402249256838527, \ 0.0472761418326518, \ 0.0124989324834952, \ 0.3333333333333333, \ 0.3020619577128708, \ 0.6439263069481050, \ 0.0540117353390243, \ 0.6439263069481049, \ 0.3020619577128708, \ 0.0540117353390241, \ 0.2565061597742415, \ 0.7329888214065164, \ 0.0105050188192420, \ 0.7329888214065166, \ 0.2565061597742415, \ 0.0105050188192418, \ 0.4110671018759194, \ 0.4110671018759194, \ 0.1778657962481610, \ 0.1784791255658876, \ 0.7553984164057089, \ 0.0661224580284036, \ 0.7553984164057089, \ 0.1784791255658877, \ 0.0661224580284032, \ 0.2656146099053742, \ 0.4687707801892516, \ 0.2656146099053743, \ 0.0037589443410682, \ 0.9924821113178632, \ 0.0037589443410687, \ 0.2685733063960138, \ 0.5823597834782123, \ 0.1490669101257739, \ 0.5823597834782123, \ 0.2685733063960138, \ 0.1490669101257737, \ 0.4110656686746184, \ 0.5772425066507145, \ 0.0116918246746671, \ 0.5772425066507145, \ 0.4110656686746185, \ 0.0116918246746671, \ 0.1327788302713893, \ 0.8528896449496687, \ 0.0143315247789422, \ 0.8528896449496688, \ 0.1327788302713893, \ 0.0143315247789417, \ 0.0724387055673328, \ 0.8551225888653341, \ 0.0724387055673332 ] ) b = np.array ( [ \ 0.0904270403543407, \ 0.3850440344131637, \ 0.5245289252324959, \ 0.0904270403543407, \ 0.5245289252324958, \ 0.3850440344131639, \ 0.0501635773519086, \ 0.4749182113240458, \ 0.4749182113240459, \ 0.1516385069726050, \ 0.1516385069726048, \ 0.6967229860547904, \ 0.0124989324834955, \ 0.0472761418326518, \ 0.9402249256838529, \ 0.0124989324834955, \ 0.9402249256838529, \ 0.0472761418326521, \ 0.3333333333333334, \ 0.0540117353390243, \ 0.3020619577128708, \ 0.6439263069481052, \ 0.0540117353390243, \ 0.6439263069481049, \ 0.3020619577128710, \ 0.0105050188192420, \ 0.2565061597742415, \ 0.7329888214065168, \ 0.0105050188192420, \ 0.7329888214065168, \ 0.2565061597742418, \ 0.1778657962481611, \ 0.4110671018759195, \ 0.4110671018759197, \ 0.0661224580284034, \ 0.1784791255658876, \ 0.7553984164057090, \ 0.0661224580284034, \ 0.7553984164057090, \ 0.1784791255658879, \ 0.2656146099053743, \ 0.2656146099053742, \ 0.4687707801892517, \ 0.0037589443410685, \ 0.0037589443410682, \ 0.9924821113178633, \ 0.1490669101257739, \ 0.2685733063960138, \ 0.5823597834782125, \ 0.1490669101257739, \ 0.5823597834782125, \ 0.2685733063960140, \ 0.0116918246746672, \ 0.4110656686746184, \ 0.5772425066507147, \ 0.0116918246746672, \ 0.5772425066507145, \ 0.4110656686746186, \ 0.0143315247789420, \ 0.1327788302713893, \ 0.8528896449496687, \ 0.0143315247789420, \ 0.8528896449496690, \ 0.1327788302713896, \ 0.0724387055673330, \ 0.0724387055673327, \ 0.8551225888653343 ] ) c = np.array ( [ \ 0.5245289252324957, \ 0.0904270403543405, \ 0.3850440344131635, \ 0.3850440344131636, \ 0.0904270403543405, \ 0.5245289252324956, \ 0.4749182113240457, \ 0.0501635773519085, \ 0.4749182113240456, \ 0.6967229860547902, \ 0.1516385069726050, \ 0.1516385069726046, \ 0.9402249256838529, \ 0.0124989324834955, \ 0.0472761418326515, \ 0.0472761418326518, \ 0.0124989324834953, \ 0.9402249256838527, \ 0.3333333333333333, \ 0.6439263069481050, \ 0.0540117353390242, \ 0.3020619577128706, \ 0.3020619577128708, \ 0.0540117353390243, \ 0.6439263069481048, \ 0.7329888214065166, \ 0.0105050188192420, \ 0.2565061597742413, \ 0.2565061597742415, \ 0.0105050188192417, \ 0.7329888214065164, \ 0.4110671018759195, \ 0.1778657962481610, \ 0.4110671018759194, \ 0.7553984164057089, \ 0.0661224580284035, \ 0.1784791255658874, \ 0.1784791255658876, \ 0.0661224580284032, \ 0.7553984164057088, \ 0.4687707801892514, \ 0.2656146099053742, \ 0.2656146099053741, \ 0.9924821113178633, \ 0.0037589443410686, \ 0.0037589443410680, \ 0.5823597834782123, \ 0.1490669101257739, \ 0.2685733063960136, \ 0.2685733063960138, \ 0.1490669101257737, \ 0.5823597834782122, \ 0.5772425066507145, \ 0.0116918246746671, \ 0.4110656686746181, \ 0.4110656686746183, \ 0.0116918246746670, \ 0.5772425066507143, \ 0.8528896449496688, \ 0.0143315247789421, \ 0.1327788302713891, \ 0.1327788302713892, \ 0.0143315247789417, \ 0.8528896449496687, \ 0.8551225888653342, \ 0.0724387055673332, \ 0.0724387055673325 ] ) w = np.array ( [ \ 0.0153282581945531, \ 0.0153282581945531, \ 0.0153282581945531, \ 0.0153282581945531, \ 0.0153282581945531, \ 0.0153282581945531, \ 0.0131070274917388, \ 0.0131070274917388, \ 0.0131070274917388, \ 0.0203183388454584, \ 0.0203183388454584, \ 0.0203183388454584, \ 0.0042175167747444, \ 0.0042175167747444, \ 0.0042175167747444, \ 0.0042175167747444, \ 0.0042175167747444, \ 0.0042175167747444, \ 0.0307485212391159, \ 0.0163659084139866, \ 0.0163659084139866, \ 0.0163659084139866, \ 0.0163659084139866, \ 0.0163659084139866, \ 0.0163659084139866, \ 0.0077298352800062, \ 0.0077298352800062, \ 0.0077298352800062, \ 0.0077298352800062, \ 0.0077298352800062, \ 0.0077298352800062, \ 0.0334719940598479, \ 0.0334719940598479, \ 0.0334719940598479, \ 0.0169116539174801, \ 0.0169116539174801, \ 0.0169116539174801, \ 0.0169116539174801, \ 0.0169116539174801, \ 0.0169116539174801, \ 0.0311163966020061, \ 0.0311163966020061, \ 0.0311163966020061, \ 0.0005320056169478, \ 0.0005320056169478, \ 0.0005320056169478, \ 0.0275928864885795, \ 0.0275928864885795, \ 0.0275928864885795, \ 0.0275928864885795, \ 0.0275928864885795, \ 0.0275928864885795, \ 0.0095861244743615, \ 0.0095861244743615, \ 0.0095861244743615, \ 0.0095861244743615, \ 0.0095861244743615, \ 0.0095861244743615, \ 0.0076417049727196, \ 0.0076417049727196, \ 0.0076417049727196, \ 0.0076417049727196, \ 0.0076417049727196, \ 0.0076417049727196, \ 0.0137902866047669, \ 0.0137902866047669, \ 0.0137902866047669 ] ) return a, b, c, w def rule19 ( ): #*****************************************************************************80 # ## rule19() returns the rule of precision 19. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1424222825711269, \ 0.8525725750765226, \ 0.0050051423523504, \ 0.8525725750765226, \ 0.1424222825711269, \ 0.0050051423523502, \ 0.0525262798541034, \ 0.8949474402917929, \ 0.0525262798541039, \ 0.0600838999627024, \ 0.9301390385986208, \ 0.0097770614386771, \ 0.9301390385986208, \ 0.0600838999627025, \ 0.0097770614386767, \ 0.1307006699605345, \ 0.8301568806048565, \ 0.0391424494346090, \ 0.8301568806048566, \ 0.1307006699605346, \ 0.0391424494346087, \ 0.3113183832239869, \ 0.5593688070080342, \ 0.1293128097679790, \ 0.5593688070080342, \ 0.3113183832239869, \ 0.1293128097679789, \ 0.1114480557169985, \ 0.7771038885660025, \ 0.1114480557169988, \ 0.0116390273279224, \ 0.9767219453441548, \ 0.0116390273279229, \ 0.2551621331531247, \ 0.4896757336937503, \ 0.2551621331531249, \ 0.2214339418891134, \ 0.7040048688065315, \ 0.0745611893043552, \ 0.7040048688065313, \ 0.2214339418891134, \ 0.0745611893043550, \ 0.4039697179663860, \ 0.4039697179663860, \ 0.1920605640672278, \ 0.3540259269997119, \ 0.6050857585353100, \ 0.0408883144649781, \ 0.6050857585353100, \ 0.3540259269997119, \ 0.0408883144649780, \ 0.1781710060796274, \ 0.6436579878407451, \ 0.1781710060796276, \ 0.4591943889568276, \ 0.4591943889568276, \ 0.0816112220863447, \ 0.3333333333333333, \ 0.4925124498658742, \ 0.4925124498658742, \ 0.0149751002682516, \ 0.2418941040068926, \ 0.7431822570856689, \ 0.0149236389074385, \ 0.7431822570856689, \ 0.2418941040068927, \ 0.0149236389074383, \ 0.3646204143387100, \ 0.6333104818121875, \ 0.0020691038491024, \ 0.6333104818121876, \ 0.3646204143387101, \ 0.0020691038491022 ] ) b = np.array ( [ \ 0.0050051423523504, \ 0.1424222825711269, \ 0.8525725750765228, \ 0.0050051423523504, \ 0.8525725750765228, \ 0.1424222825711273, \ 0.0525262798541037, \ 0.0525262798541034, \ 0.8949474402917930, \ 0.0097770614386769, \ 0.0600838999627023, \ 0.9301390385986208, \ 0.0097770614386769, \ 0.9301390385986208, \ 0.0600838999627027, \ 0.0391424494346089, \ 0.1307006699605346, \ 0.8301568806048567, \ 0.0391424494346089, \ 0.8301568806048567, \ 0.1307006699605348, \ 0.1293128097679790, \ 0.3113183832239869, \ 0.5593688070080343, \ 0.1293128097679790, \ 0.5593688070080343, \ 0.3113183832239870, \ 0.1114480557169988, \ 0.1114480557169985, \ 0.7771038885660028, \ 0.0116390273279228, \ 0.0116390273279224, \ 0.9767219453441548, \ 0.2551621331531249, \ 0.2551621331531249, \ 0.4896757336937504, \ 0.0745611893043552, \ 0.2214339418891134, \ 0.7040048688065317, \ 0.0745611893043552, \ 0.7040048688065317, \ 0.2214339418891137, \ 0.1920605640672279, \ 0.4039697179663861, \ 0.4039697179663862, \ 0.0408883144649781, \ 0.3540259269997119, \ 0.6050857585353102, \ 0.0408883144649781, \ 0.6050857585353101, \ 0.3540259269997121, \ 0.1781710060796276, \ 0.1781710060796274, \ 0.6436579878407452, \ 0.0816112220863448, \ 0.4591943889568277, \ 0.4591943889568278, \ 0.3333333333333334, \ 0.0149751002682516, \ 0.4925124498658743, \ 0.4925124498658744, \ 0.0149236389074385, \ 0.2418941040068926, \ 0.7431822570856692, \ 0.0149236389074385, \ 0.7431822570856690, \ 0.2418941040068929, \ 0.0020691038491024, \ 0.3646204143387101, \ 0.6333104818121877, \ 0.0020691038491024, \ 0.6333104818121877, \ 0.3646204143387103 ] ) c = np.array ( [ \ 0.8525725750765227, \ 0.0050051423523504, \ 0.1424222825711267, \ 0.1424222825711269, \ 0.0050051423523502, \ 0.8525725750765225, \ 0.8949474402917929, \ 0.0525262798541037, \ 0.0525262798541032, \ 0.9301390385986208, \ 0.0097770614386769, \ 0.0600838999627021, \ 0.0600838999627024, \ 0.0097770614386767, \ 0.9301390385986207, \ 0.8301568806048566, \ 0.0391424494346090, \ 0.1307006699605343, \ 0.1307006699605345, \ 0.0391424494346087, \ 0.8301568806048565, \ 0.5593688070080340, \ 0.1293128097679789, \ 0.3113183832239867, \ 0.3113183832239868, \ 0.1293128097679789, \ 0.5593688070080340, \ 0.7771038885660027, \ 0.1114480557169989, \ 0.1114480557169985, \ 0.9767219453441548, \ 0.0116390273279228, \ 0.0116390273279222, \ 0.4896757336937503, \ 0.2551621331531249, \ 0.2551621331531247, \ 0.7040048688065315, \ 0.0745611893043551, \ 0.2214339418891131, \ 0.2214339418891135, \ 0.0745611893043550, \ 0.7040048688065313, \ 0.4039697179663861, \ 0.1920605640672278, \ 0.4039697179663860, \ 0.6050857585353100, \ 0.0408883144649781, \ 0.3540259269997117, \ 0.3540259269997119, \ 0.0408883144649780, \ 0.6050857585353098, \ 0.6436579878407449, \ 0.1781710060796274, \ 0.1781710060796272, \ 0.4591943889568276, \ 0.0816112220863447, \ 0.4591943889568275, \ 0.3333333333333333, \ 0.4925124498658742, \ 0.0149751002682516, \ 0.4925124498658741, \ 0.7431822570856689, \ 0.0149236389074385, \ 0.2418941040068923, \ 0.2418941040068927, \ 0.0149236389074383, \ 0.7431822570856688, \ 0.6333104818121876, \ 0.0020691038491024, \ 0.3646204143387098, \ 0.3646204143387100, \ 0.0020691038491022, \ 0.6333104818121874 ] ) w = np.array ( [ \ 0.0029256924878801, \ 0.0029256924878801, \ 0.0029256924878801, \ 0.0029256924878801, \ 0.0029256924878801, \ 0.0029256924878801, \ 0.0071093936227949, \ 0.0071093936227949, \ 0.0071093936227949, \ 0.0033273888405939, \ 0.0033273888405939, \ 0.0033273888405939, \ 0.0033273888405939, \ 0.0033273888405939, \ 0.0033273888405939, \ 0.0096955190816242, \ 0.0096955190816242, \ 0.0096955190816242, \ 0.0096955190816242, \ 0.0096955190816242, \ 0.0096955190816242, \ 0.0263462647074454, \ 0.0263462647074454, \ 0.0263462647074454, \ 0.0263462647074454, \ 0.0263462647074454, \ 0.0263462647074454, \ 0.0152349565170048, \ 0.0152349565170048, \ 0.0152349565170048, \ 0.0017651924183085, \ 0.0017651924183085, \ 0.0017651924183085, \ 0.0317528545875300, \ 0.0317528545875300, \ 0.0317528545875300, \ 0.0181080745904305, \ 0.0181080745904305, \ 0.0181080745904305, \ 0.0181080745904305, \ 0.0181080745904305, \ 0.0181080745904305, \ 0.0315373586452396, \ 0.0315373586452396, \ 0.0315373586452396, \ 0.0161022094609394, \ 0.0161022094609394, \ 0.0161022094609394, \ 0.0161022094609394, \ 0.0161022094609394, \ 0.0161022094609394, \ 0.0246519810535848, \ 0.0246519810535848, \ 0.0246519810535848, \ 0.0229835709771232, \ 0.0229835709771232, \ 0.0229835709771232, \ 0.0344691608509053, \ 0.0103218821824189, \ 0.0103218821824189, \ 0.0103218821824189, \ 0.0084559248390935, \ 0.0084559248390935, \ 0.0084559248390935, \ 0.0084559248390935, \ 0.0084559248390935, \ 0.0084559248390935, \ 0.0032821375148397, \ 0.0032821375148397, \ 0.0032821375148397, \ 0.0032821375148397, \ 0.0032821375148397, \ 0.0032821375148397 ] ) return a, b, c, w def rule20 ( ): #*****************************************************************************80 # ## rule20() returns the rule of precision 20. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1862949977445409, \ 0.6274100045109180, \ 0.1862949977445411, \ 0.0373108805988846, \ 0.9253782388022305, \ 0.0373108805988850, \ 0.4762456115404990, \ 0.4762456115404990, \ 0.0475087769190019, \ 0.0640905856084340, \ 0.9310544767839422, \ 0.0048549376076240, \ 0.9310544767839422, \ 0.0640905856084341, \ 0.0048549376076235, \ 0.2156070573900944, \ 0.6781657378896355, \ 0.1062272047202701, \ 0.6781657378896355, \ 0.2156070573900943, \ 0.1062272047202699, \ 0.4455510569559248, \ 0.4455510569559248, \ 0.1088978860881503, \ 0.1591337076570672, \ 0.8332955118382362, \ 0.0075707805046966, \ 0.8332955118382362, \ 0.1591337076570672, \ 0.0075707805046964, \ 0.3178601238357719, \ 0.5423318041724280, \ 0.1398080719918000, \ 0.5423318041724280, \ 0.3178601238357719, \ 0.1398080719917999, \ 0.2545792676733390, \ 0.4908414646533217, \ 0.2545792676733392, \ 0.3333333333333333, \ 0.1985181322287882, \ 0.7549215028635475, \ 0.0465603649076644, \ 0.7549215028635474, \ 0.1985181322287882, \ 0.0465603649076642, \ 0.3934253478170998, \ 0.3934253478170998, \ 0.2131493043658002, \ 0.0999522962881386, \ 0.8616840189364867, \ 0.0383636847753748, \ 0.8616840189364866, \ 0.0999522962881387, \ 0.0383636847753744, \ 0.4200237588162241, \ 0.5701446928909734, \ 0.0098315482928025, \ 0.5701446928909734, \ 0.4200237588162241, \ 0.0098315482928025, \ 0.3331348173095874, \ 0.6118777035474257, \ 0.0549874791429869, \ 0.6118777035474257, \ 0.3331348173095874, \ 0.0549874791429867, \ 0.2805814114236652, \ 0.7086813757203236, \ 0.0107372128560111, \ 0.7086813757203237, \ 0.2805814114236653, \ 0.0107372128560110, \ 0.0109761410283976, \ 0.9780477179432044, \ 0.0109761410283981, \ 0.1093835967117145, \ 0.7812328065765708, \ 0.1093835967117148 ] ) b = np.array ( [ \ 0.1862949977445411, \ 0.1862949977445409, \ 0.6274100045109182, \ 0.0373108805988849, \ 0.0373108805988846, \ 0.9253782388022306, \ 0.0475087769190020, \ 0.4762456115404990, \ 0.4762456115404993, \ 0.0048549376076238, \ 0.0640905856084340, \ 0.9310544767839423, \ 0.0048549376076238, \ 0.9310544767839423, \ 0.0640905856084343, \ 0.1062272047202701, \ 0.2156070573900944, \ 0.6781657378896357, \ 0.1062272047202701, \ 0.6781657378896357, \ 0.2156070573900946, \ 0.1088978860881504, \ 0.4455510569559249, \ 0.4455510569559250, \ 0.0075707805046966, \ 0.1591337076570672, \ 0.8332955118382365, \ 0.0075707805046966, \ 0.8332955118382364, \ 0.1591337076570676, \ 0.1398080719918000, \ 0.3178601238357721, \ 0.5423318041724282, \ 0.1398080719918000, \ 0.5423318041724282, \ 0.3178601238357722, \ 0.2545792676733392, \ 0.2545792676733392, \ 0.4908414646533218, \ 0.3333333333333334, \ 0.0465603649076644, \ 0.1985181322287882, \ 0.7549215028635476, \ 0.0465603649076644, \ 0.7549215028635476, \ 0.1985181322287885, \ 0.2131493043658003, \ 0.3934253478171000, \ 0.3934253478171000, \ 0.0383636847753747, \ 0.0999522962881386, \ 0.8616840189364868, \ 0.0383636847753747, \ 0.8616840189364868, \ 0.0999522962881389, \ 0.0098315482928026, \ 0.4200237588162241, \ 0.5701446928909736, \ 0.0098315482928026, \ 0.5701446928909735, \ 0.4200237588162243, \ 0.0549874791429869, \ 0.3331348173095875, \ 0.6118777035474259, \ 0.0549874791429869, \ 0.6118777035474258, \ 0.3331348173095877, \ 0.0107372128560111, \ 0.2805814114236653, \ 0.7086813757203239, \ 0.0107372128560111, \ 0.7086813757203237, \ 0.2805814114236655, \ 0.0109761410283979, \ 0.0109761410283976, \ 0.9780477179432047, \ 0.1093835967117148, \ 0.1093835967117145, \ 0.7812328065765709 ] ) c = np.array ( [ \ 0.6274100045109180, \ 0.1862949977445411, \ 0.1862949977445406, \ 0.9253782388022306, \ 0.0373108805988850, \ 0.0373108805988843, \ 0.4762456115404990, \ 0.0475087769190020, \ 0.4762456115404988, \ 0.9310544767839422, \ 0.0048549376076238, \ 0.0640905856084338, \ 0.0640905856084340, \ 0.0048549376076236, \ 0.9310544767839422, \ 0.6781657378896355, \ 0.1062272047202700, \ 0.2156070573900941, \ 0.2156070573900944, \ 0.1062272047202699, \ 0.6781657378896354, \ 0.4455510569559248, \ 0.1088978860881503, \ 0.4455510569559247, \ 0.8332955118382361, \ 0.0075707805046965, \ 0.1591337076570670, \ 0.1591337076570672, \ 0.0075707805046964, \ 0.8332955118382360, \ 0.5423318041724281, \ 0.1398080719918000, \ 0.3178601238357718, \ 0.3178601238357720, \ 0.1398080719917999, \ 0.5423318041724279, \ 0.4908414646533217, \ 0.2545792676733392, \ 0.2545792676733390, \ 0.3333333333333333, \ 0.7549215028635475, \ 0.0465603649076643, \ 0.1985181322287879, \ 0.1985181322287882, \ 0.0465603649076641, \ 0.7549215028635474, \ 0.3934253478170998, \ 0.2131493043658002, \ 0.3934253478170998, \ 0.8616840189364867, \ 0.0383636847753747, \ 0.0999522962881384, \ 0.0999522962881387, \ 0.0383636847753744, \ 0.8616840189364866, \ 0.5701446928909732, \ 0.0098315482928025, \ 0.4200237588162239, \ 0.4200237588162241, \ 0.0098315482928024, \ 0.5701446928909732, \ 0.6118777035474258, \ 0.0549874791429869, \ 0.3331348173095873, \ 0.3331348173095875, \ 0.0549874791429869, \ 0.6118777035474255, \ 0.7086813757203236, \ 0.0107372128560111, \ 0.2805814114236650, \ 0.2805814114236652, \ 0.0107372128560109, \ 0.7086813757203236, \ 0.9780477179432044, \ 0.0109761410283980, \ 0.0109761410283972, \ 0.7812328065765708, \ 0.1093835967117147, \ 0.1093835967117144 ] ) w = np.array ( [ \ 0.0183469259485058, \ 0.0183469259485058, \ 0.0183469259485058, \ 0.0043225508213312, \ 0.0043225508213312, \ 0.0043225508213312, \ 0.0142036506068169, \ 0.0142036506068169, \ 0.0142036506068169, \ 0.0022597392042517, \ 0.0022597392042517, \ 0.0022597392042517, \ 0.0022597392042517, \ 0.0022597392042517, \ 0.0022597392042517, \ 0.0154452156441985, \ 0.0154452156441985, \ 0.0154452156441985, \ 0.0154452156441985, \ 0.0154452156441985, \ 0.0154452156441985, \ 0.0189047998664649, \ 0.0189047998664649, \ 0.0189047998664649, \ 0.0044057948371170, \ 0.0044057948371170, \ 0.0044057948371170, \ 0.0044057948371170, \ 0.0044057948371170, \ 0.0044057948371170, \ 0.0233834914636555, \ 0.0233834914636555, \ 0.0233834914636555, \ 0.0233834914636555, \ 0.0233834914636555, \ 0.0233834914636555, \ 0.0281664026150405, \ 0.0281664026150405, \ 0.0281664026150405, \ 0.0278202214029062, \ 0.0119727971579094, \ 0.0119727971579094, \ 0.0119727971579094, \ 0.0119727971579094, \ 0.0119727971579094, \ 0.0119727971579094, \ 0.0275761012581409, \ 0.0275761012581409, \ 0.0275761012581409, \ 0.0082914230552277, \ 0.0082914230552277, \ 0.0082914230552277, \ 0.0082914230552277, \ 0.0082914230552277, \ 0.0082914230552277, \ 0.0073913630005106, \ 0.0073913630005106, \ 0.0073913630005106, \ 0.0073913630005106, \ 0.0073913630005106, \ 0.0073913630005106, \ 0.0173344511344387, \ 0.0173344511344387, \ 0.0173344511344387, \ 0.0173344511344387, \ 0.0173344511344387, \ 0.0173344511344387, \ 0.0071564004769154, \ 0.0071564004769154, \ 0.0071564004769154, \ 0.0071564004769154, \ 0.0071564004769154, \ 0.0071564004769154, \ 0.0015976815821332, \ 0.0015976815821332, \ 0.0015976815821332, \ 0.0156604615521491, \ 0.0156604615521491, \ 0.0156604615521491 ] ) return a, b, c, w def rule21 ( ): #*****************************************************************************80 # ## rule21() returns the rule of precision 21. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.2989362353149825, \ 0.4021275293700348, \ 0.2989362353149825, \ 0.2891894960785947, \ 0.5055149445862437, \ 0.2052955593351616, \ 0.5055149445862437, \ 0.2891894960785947, \ 0.2052955593351615, \ 0.4970078754686856, \ 0.4970078754686856, \ 0.0059842490626288, \ 0.2378733825979940, \ 0.7551948083705379, \ 0.0069318090314683, \ 0.7551948083705379, \ 0.2378733825979941, \ 0.0069318090314680, \ 0.4036175865463851, \ 0.4036175865463851, \ 0.1927648269072297, \ 0.3188653107948282, \ 0.5573552887996790, \ 0.1237794004054928, \ 0.5573552887996790, \ 0.3188653107948283, \ 0.1237794004054926, \ 0.2318736253704010, \ 0.7291350120063786, \ 0.0389913626232204, \ 0.7291350120063788, \ 0.2318736253704010, \ 0.0389913626232202, \ 0.1331671229413703, \ 0.8572966295289191, \ 0.0095362475297107, \ 0.8572966295289192, \ 0.1331671229413703, \ 0.0095362475297104, \ 0.3468079798099110, \ 0.6001398284888722, \ 0.0530521917012168, \ 0.6001398284888722, \ 0.3468079798099111, \ 0.0530521917012167, \ 0.1189885776227193, \ 0.7620228447545612, \ 0.1189885776227196, \ 0.1902887180912784, \ 0.6194225638174430, \ 0.1902887180912786, \ 0.2165996231899825, \ 0.6829423567359030, \ 0.1004580200741146, \ 0.6829423567359030, \ 0.2165996231899825, \ 0.1004580200741143, \ 0.4815978686532166, \ 0.4815978686532166, \ 0.0368042626935668, \ 0.4498127917753624, \ 0.4498127917753624, \ 0.1003744164492752, \ 0.1288298079620515, \ 0.8217191264694078, \ 0.0494510655685407, \ 0.8217191264694079, \ 0.1288298079620517, \ 0.0494510655685403, \ 0.0536275755461449, \ 0.8927448489077100, \ 0.0536275755461453, \ 0.3609534080189222, \ 0.6287919561081534, \ 0.0102546358729245, \ 0.6287919561081533, \ 0.3609534080189222, \ 0.0102546358729244, \ 0.0107424564328283, \ 0.9785150871343431, \ 0.0107424564328287, \ 0.0557195650723719, \ 0.9339785312842042, \ 0.0103019036434240, \ 0.9339785312842040, \ 0.0557195650723720, \ 0.0103019036434236 ] ) b = np.array ( [ \ 0.2989362353149826, \ 0.2989362353149826, \ 0.4021275293700349, \ 0.2052955593351616, \ 0.2891894960785948, \ 0.5055149445862438, \ 0.2052955593351616, \ 0.5055149445862438, \ 0.2891894960785949, \ 0.0059842490626289, \ 0.4970078754686856, \ 0.4970078754686857, \ 0.0069318090314681, \ 0.2378733825979940, \ 0.7551948083705379, \ 0.0069318090314681, \ 0.7551948083705379, \ 0.2378733825979943, \ 0.1927648269072298, \ 0.4036175865463852, \ 0.4036175865463852, \ 0.1237794004054928, \ 0.3188653107948283, \ 0.5573552887996791, \ 0.1237794004054928, \ 0.5573552887996791, \ 0.3188653107948285, \ 0.0389913626232203, \ 0.2318736253704010, \ 0.7291350120063789, \ 0.0389913626232203, \ 0.7291350120063789, \ 0.2318736253704013, \ 0.0095362475297106, \ 0.1331671229413703, \ 0.8572966295289193, \ 0.0095362475297106, \ 0.8572966295289193, \ 0.1331671229413706, \ 0.0530521917012168, \ 0.3468079798099111, \ 0.6001398284888723, \ 0.0530521917012168, \ 0.6001398284888722, \ 0.3468079798099113, \ 0.1189885776227196, \ 0.1189885776227193, \ 0.7620228447545613, \ 0.1902887180912786, \ 0.1902887180912785, \ 0.6194225638174431, \ 0.1004580200741145, \ 0.2165996231899825, \ 0.6829423567359031, \ 0.1004580200741145, \ 0.6829423567359032, \ 0.2165996231899828, \ 0.0368042626935668, \ 0.4815978686532166, \ 0.4815978686532168, \ 0.1003744164492753, \ 0.4498127917753625, \ 0.4498127917753625, \ 0.0494510655685406, \ 0.1288298079620515, \ 0.8217191264694079, \ 0.0494510655685406, \ 0.8217191264694079, \ 0.1288298079620518, \ 0.0536275755461451, \ 0.0536275755461448, \ 0.8927448489077101, \ 0.0102546358729245, \ 0.3609534080189222, \ 0.6287919561081535, \ 0.0102546358729245, \ 0.6287919561081534, \ 0.3609534080189224, \ 0.0107424564328286, \ 0.0107424564328283, \ 0.9785150871343433, \ 0.0103019036434239, \ 0.0557195650723719, \ 0.9339785312842044, \ 0.0103019036434239, \ 0.9339785312842044, \ 0.0557195650723723 ] ) c = np.array ( [ \ 0.4021275293700349, \ 0.2989362353149825, \ 0.2989362353149826, \ 0.5055149445862437, \ 0.2052955593351615, \ 0.2891894960785947, \ 0.2891894960785947, \ 0.2052955593351614, \ 0.5055149445862436, \ 0.4970078754686856, \ 0.0059842490626288, \ 0.4970078754686854, \ 0.7551948083705379, \ 0.0069318090314681, \ 0.2378733825979938, \ 0.2378733825979940, \ 0.0069318090314680, \ 0.7551948083705377, \ 0.4036175865463850, \ 0.1927648269072297, \ 0.4036175865463850, \ 0.5573552887996789, \ 0.1237794004054927, \ 0.3188653107948280, \ 0.3188653107948282, \ 0.1237794004054926, \ 0.5573552887996789, \ 0.7291350120063786, \ 0.0389913626232204, \ 0.2318736253704008, \ 0.2318736253704009, \ 0.0389913626232201, \ 0.7291350120063785, \ 0.8572966295289192, \ 0.0095362475297107, \ 0.1331671229413700, \ 0.1331671229413702, \ 0.0095362475297104, \ 0.8572966295289191, \ 0.6001398284888720, \ 0.0530521917012167, \ 0.3468079798099110, \ 0.3468079798099110, \ 0.0530521917012168, \ 0.6001398284888719, \ 0.7620228447545612, \ 0.1189885776227195, \ 0.1189885776227192, \ 0.6194225638174429, \ 0.1902887180912785, \ 0.1902887180912783, \ 0.6829423567359030, \ 0.1004580200741145, \ 0.2165996231899824, \ 0.2165996231899825, \ 0.1004580200741143, \ 0.6829423567359030, \ 0.4815978686532166, \ 0.0368042626935668, \ 0.4815978686532165, \ 0.4498127917753624, \ 0.1003744164492751, \ 0.4498127917753622, \ 0.8217191264694078, \ 0.0494510655685407, \ 0.1288298079620513, \ 0.1288298079620515, \ 0.0494510655685404, \ 0.8217191264694079, \ 0.8927448489077100, \ 0.0536275755461452, \ 0.0536275755461446, \ 0.6287919561081533, \ 0.0102546358729244, \ 0.3609534080189220, \ 0.3609534080189222, \ 0.0102546358729244, \ 0.6287919561081532, \ 0.9785150871343432, \ 0.0107424564328287, \ 0.0107424564328280, \ 0.9339785312842042, \ 0.0103019036434239, \ 0.0557195650723716, \ 0.0557195650723720, \ 0.0103019036434236, \ 0.9339785312842040 ] ) w = np.array ( [ \ 0.0214511219291323, \ 0.0214511219291323, \ 0.0214511219291323, \ 0.0174954161557631, \ 0.0174954161557631, \ 0.0174954161557631, \ 0.0174954161557631, \ 0.0174954161557631, \ 0.0174954161557631, \ 0.0044378296970659, \ 0.0044378296970659, \ 0.0044378296970659, \ 0.0042061202881497, \ 0.0042061202881497, \ 0.0042061202881497, \ 0.0042061202881497, \ 0.0042061202881497, \ 0.0042061202881497, \ 0.0230007046532839, \ 0.0230007046532839, \ 0.0230007046532839, \ 0.0184474848479328, \ 0.0184474848479328, \ 0.0184474848479328, \ 0.0184474848479328, \ 0.0184474848479328, \ 0.0184474848479328, \ 0.0104699041853248, \ 0.0104699041853248, \ 0.0104699041853248, \ 0.0104699041853248, \ 0.0104699041853248, \ 0.0104699041853248, \ 0.0044808131219015, \ 0.0044808131219015, \ 0.0044808131219015, \ 0.0044808131219015, \ 0.0044808131219015, \ 0.0044808131219015, \ 0.0145003059189710, \ 0.0145003059189710, \ 0.0145003059189710, \ 0.0145003059189710, \ 0.0145003059189710, \ 0.0145003059189710, \ 0.0136560324522302, \ 0.0136560324522302, \ 0.0136560324522302, \ 0.0194552418607507, \ 0.0194552418607507, \ 0.0194552418607507, \ 0.0159040367054280, \ 0.0159040367054280, \ 0.0159040367054280, \ 0.0159040367054280, \ 0.0159040367054280, \ 0.0159040367054280, \ 0.0122144101633844, \ 0.0122144101633844, \ 0.0122144101633844, \ 0.0196144752278240, \ 0.0196144752278240, \ 0.0196144752278240, \ 0.0098119718225504, \ 0.0098119718225504, \ 0.0098119718225504, \ 0.0098119718225504, \ 0.0098119718225504, \ 0.0098119718225504, \ 0.0071520851012837, \ 0.0071520851012837, \ 0.0071520851012837, \ 0.0068398848579343, \ 0.0068398848579343, \ 0.0068398848579343, \ 0.0068398848579343, \ 0.0068398848579343, \ 0.0068398848579343, \ 0.0015086992723787, \ 0.0015086992723787, \ 0.0015086992723787, \ 0.0032654285840441, \ 0.0032654285840441, \ 0.0032654285840441, \ 0.0032654285840441, \ 0.0032654285840441, \ 0.0032654285840441 ] ) return a, b, c, w def rule22 ( ): #*****************************************************************************80 # ## rule22() returns the rule of precision 22. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3851845246273021, \ 0.3851845246273021, \ 0.2296309507453957, \ 0.4577694113676721, \ 0.4577694113676721, \ 0.0844611772646559, \ 0.0698421694674436, \ 0.9222815483109740, \ 0.0078762822215824, \ 0.9222815483109740, \ 0.0698421694674436, \ 0.0078762822215821, \ 0.2945582590299500, \ 0.4108834819400997, \ 0.2945582590299501, \ 0.1885105236302838, \ 0.6229789527394320, \ 0.1885105236302841, \ 0.4219818887935349, \ 0.4219818887935349, \ 0.1560362224129301, \ 0.0903988311664077, \ 0.8648488844852564, \ 0.0447522843483360, \ 0.8648488844852564, \ 0.0903988311664079, \ 0.0447522843483357, \ 0.4113417640205587, \ 0.5503830012785774, \ 0.0382752347008638, \ 0.5503830012785774, \ 0.4113417640205588, \ 0.0382752347008637, \ 0.3321061050074464, \ 0.5651468190056221, \ 0.1027470759869314, \ 0.5651468190056222, \ 0.3321061050074463, \ 0.1027470759869313, \ 0.3625762804324673, \ 0.6300234783328220, \ 0.0074002412347108, \ 0.6300234783328220, \ 0.3625762804324673, \ 0.0074002412347107, \ 0.2900668241166688, \ 0.5188518779166110, \ 0.1910812979667201, \ 0.5188518779166110, \ 0.2900668241166688, \ 0.1910812979667200, \ 0.4961611784097086, \ 0.4961611784097086, \ 0.0076776431805827, \ 0.2879318028241718, \ 0.6680765517823724, \ 0.0439916453934559, \ 0.6680765517823722, \ 0.2879318028241718, \ 0.0439916453934557, \ 0.2167869333649411, \ 0.6745231247723867, \ 0.1086899418626721, \ 0.6745231247723867, \ 0.2167869333649412, \ 0.1086899418626718, \ 0.1458737198735252, \ 0.8449815687515108, \ 0.0091447113749641, \ 0.8449815687515108, \ 0.1458737198735252, \ 0.0091447113749638, \ 0.1762974348245001, \ 0.7754476410608585, \ 0.0482549241146414, \ 0.7754476410608585, \ 0.1762974348245001, \ 0.0482549241146412, \ 0.2439906460394931, \ 0.7468454447123216, \ 0.0091639092481853, \ 0.7468454447123217, \ 0.2439906460394931, \ 0.0091639092481851, \ 0.0291084706708074, \ 0.9417830586583850, \ 0.0291084706708079, \ 0.1154315382192049, \ 0.7691369235615900, \ 0.1154315382192052, \ 0.0179343210529390, \ 0.9802672139581126, \ 0.0017984649889486, \ 0.9802672139581127, \ 0.0179343210529391, \ 0.0017984649889481 ] ) b = np.array ( [ \ 0.2296309507453958, \ 0.3851845246273022, \ 0.3851845246273022, \ 0.0844611772646559, \ 0.4577694113676721, \ 0.4577694113676722, \ 0.0078762822215824, \ 0.0698421694674436, \ 0.9222815483109743, \ 0.0078762822215824, \ 0.9222815483109743, \ 0.0698421694674439, \ 0.2945582590299502, \ 0.2945582590299502, \ 0.4108834819400998, \ 0.1885105236302840, \ 0.1885105236302839, \ 0.6229789527394323, \ 0.1560362224129302, \ 0.4219818887935350, \ 0.4219818887935351, \ 0.0447522843483359, \ 0.0903988311664078, \ 0.8648488844852564, \ 0.0447522843483359, \ 0.8648488844852564, \ 0.0903988311664081, \ 0.0382752347008638, \ 0.4113417640205588, \ 0.5503830012785776, \ 0.0382752347008638, \ 0.5503830012785775, \ 0.4113417640205590, \ 0.1027470759869314, \ 0.3321061050074464, \ 0.5651468190056224, \ 0.1027470759869314, \ 0.5651468190056224, \ 0.3321061050074466, \ 0.0074002412347108, \ 0.3625762804324673, \ 0.6300234783328221, \ 0.0074002412347108, \ 0.6300234783328221, \ 0.3625762804324675, \ 0.1910812979667202, \ 0.2900668241166688, \ 0.5188518779166111, \ 0.1910812979667202, \ 0.5188518779166111, \ 0.2900668241166690, \ 0.0076776431805828, \ 0.4961611784097087, \ 0.4961611784097089, \ 0.0439916453934559, \ 0.2879318028241719, \ 0.6680765517823725, \ 0.0439916453934559, \ 0.6680765517823725, \ 0.2879318028241721, \ 0.1086899418626720, \ 0.2167869333649412, \ 0.6745231247723870, \ 0.1086899418626720, \ 0.6745231247723870, \ 0.2167869333649414, \ 0.0091447113749641, \ 0.1458737198735252, \ 0.8449815687515109, \ 0.0091447113749641, \ 0.8449815687515109, \ 0.1458737198735255, \ 0.0482549241146414, \ 0.1762974348245001, \ 0.7754476410608587, \ 0.0482549241146414, \ 0.7754476410608587, \ 0.1762974348245004, \ 0.0091639092481852, \ 0.2439906460394931, \ 0.7468454447123218, \ 0.0091639092481852, \ 0.7468454447123218, \ 0.2439906460394934, \ 0.0291084706708077, \ 0.0291084706708073, \ 0.9417830586583850, \ 0.1154315382192051, \ 0.1154315382192049, \ 0.7691369235615901, \ 0.0017984649889484, \ 0.0179343210529390, \ 0.9802672139581127, \ 0.0017984649889484, \ 0.9802672139581129, \ 0.0179343210529393 ] ) c = np.array ( [ \ 0.3851845246273021, \ 0.2296309507453957, \ 0.3851845246273020, \ 0.4577694113676721, \ 0.0844611772646559, \ 0.4577694113676719, \ 0.9222815483109740, \ 0.0078762822215824, \ 0.0698421694674433, \ 0.0698421694674436, \ 0.0078762822215821, \ 0.9222815483109740, \ 0.4108834819400998, \ 0.2945582590299501, \ 0.2945582590299501, \ 0.6229789527394320, \ 0.1885105236302841, \ 0.1885105236302836, \ 0.4219818887935349, \ 0.1560362224129300, \ 0.4219818887935349, \ 0.8648488844852564, \ 0.0447522843483358, \ 0.0903988311664076, \ 0.0903988311664077, \ 0.0447522843483357, \ 0.8648488844852562, \ 0.5503830012785774, \ 0.0382752347008638, \ 0.4113417640205586, \ 0.4113417640205587, \ 0.0382752347008637, \ 0.5503830012785773, \ 0.5651468190056222, \ 0.1027470759869314, \ 0.3321061050074462, \ 0.3321061050074463, \ 0.1027470759869313, \ 0.5651468190056220, \ 0.6300234783328220, \ 0.0074002412347107, \ 0.3625762804324671, \ 0.3625762804324672, \ 0.0074002412347106, \ 0.6300234783328218, \ 0.5188518779166110, \ 0.1910812979667201, \ 0.2900668241166687, \ 0.2900668241166688, \ 0.1910812979667200, \ 0.5188518779166110, \ 0.4961611784097086, \ 0.0076776431805827, \ 0.4961611784097084, \ 0.6680765517823724, \ 0.0439916453934558, \ 0.2879318028241716, \ 0.2879318028241719, \ 0.0439916453934558, \ 0.6680765517823722, \ 0.6745231247723869, \ 0.1086899418626721, \ 0.2167869333649409, \ 0.2167869333649412, \ 0.1086899418626718, \ 0.6745231247723867, \ 0.8449815687515108, \ 0.0091447113749641, \ 0.1458737198735250, \ 0.1458737198735252, \ 0.0091447113749640, \ 0.8449815687515108, \ 0.7754476410608585, \ 0.0482549241146414, \ 0.1762974348244998, \ 0.1762974348245001, \ 0.0482549241146412, \ 0.7754476410608585, \ 0.7468454447123217, \ 0.0091639092481853, \ 0.2439906460394928, \ 0.2439906460394931, \ 0.0091639092481851, \ 0.7468454447123216, \ 0.9417830586583850, \ 0.0291084706708077, \ 0.0291084706708072, \ 0.7691369235615899, \ 0.1154315382192051, \ 0.1154315382192047, \ 0.9802672139581126, \ 0.0017984649889485, \ 0.0179343210529387, \ 0.0179343210529390, \ 0.0017984649889481, \ 0.9802672139581127 ] ) w = np.array ( [ \ 0.0134930838836107, \ 0.0134930838836107, \ 0.0134930838836107, \ 0.0138613995242342, \ 0.0138613995242342, \ 0.0138613995242342, \ 0.0025954384742313, \ 0.0025954384742313, \ 0.0025954384742313, \ 0.0025954384742313, \ 0.0025954384742313, \ 0.0025954384742313, \ 0.0210757639574522, \ 0.0210757639574522, \ 0.0210757639574522, \ 0.0160212991251489, \ 0.0160212991251489, \ 0.0160212991251489, \ 0.0188530925538413, \ 0.0188530925538413, \ 0.0188530925538413, \ 0.0075175778177884, \ 0.0075175778177884, \ 0.0075175778177884, \ 0.0075175778177884, \ 0.0075175778177884, \ 0.0075175778177884, \ 0.0111973134719628, \ 0.0111973134719628, \ 0.0111973134719628, \ 0.0111973134719628, \ 0.0111973134719628, \ 0.0111973134719628, \ 0.0177190934895102, \ 0.0177190934895102, \ 0.0177190934895102, \ 0.0177190934895102, \ 0.0177190934895102, \ 0.0177190934895102, \ 0.0049042603975570, \ 0.0049042603975570, \ 0.0049042603975570, \ 0.0049042603975570, \ 0.0049042603975570, \ 0.0049042603975570, \ 0.0217064195555090, \ 0.0217064195555090, \ 0.0217064195555090, \ 0.0217064195555090, \ 0.0217064195555090, \ 0.0217064195555090, \ 0.0052893396659844, \ 0.0052893396659844, \ 0.0052893396659844, \ 0.0116622228673430, \ 0.0116622228673430, \ 0.0116622228673430, \ 0.0116622228673430, \ 0.0116622228673430, \ 0.0116622228673430, \ 0.0157101626225703, \ 0.0157101626225703, \ 0.0157101626225703, \ 0.0157101626225703, \ 0.0157101626225703, \ 0.0157101626225703, \ 0.0041066870715756, \ 0.0041066870715756, \ 0.0041066870715756, \ 0.0041066870715756, \ 0.0041066870715756, \ 0.0041066870715756, \ 0.0105635849677469, \ 0.0105635849677469, \ 0.0105635849677469, \ 0.0105635849677469, \ 0.0105635849677469, \ 0.0105635849677469, \ 0.0050540768975846, \ 0.0050540768975846, \ 0.0050540768975846, \ 0.0050540768975846, \ 0.0050540768975846, \ 0.0050540768975846, \ 0.0035691091658564, \ 0.0035691091658564, \ 0.0035691091658564, \ 0.0144157131281046, \ 0.0144157131281046, \ 0.0144157131281046, \ 0.0006404285311714, \ 0.0006404285311714, \ 0.0006404285311714, \ 0.0006404285311714, \ 0.0006404285311714, \ 0.0006404285311714 ] ) return a, b, c, w def rule23 ( ): #*****************************************************************************80 # ## rule23() returns the rule of precision 23. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1595037989247572, \ 0.8166259474208891, \ 0.0238702536543537, \ 0.8166259474208892, \ 0.1595037989247573, \ 0.0238702536543534, \ 0.1141013603223645, \ 0.8807088179167908, \ 0.0051898217608446, \ 0.8807088179167909, \ 0.1141013603223646, \ 0.0051898217608443, \ 0.0390072687570320, \ 0.9219854624859357, \ 0.0390072687570324, \ 0.0955398781717349, \ 0.8717190926395586, \ 0.0327410291887065, \ 0.8717190926395587, \ 0.0955398781717349, \ 0.0327410291887062, \ 0.3111622680517019, \ 0.6863901320923316, \ 0.0024475998559664, \ 0.6863901320923317, \ 0.3111622680517019, \ 0.0024475998559662, \ 0.2056172320580521, \ 0.7856574783566395, \ 0.0087252895853085, \ 0.7856574783566393, \ 0.2056172320580521, \ 0.0087252895853083, \ 0.0472616294497253, \ 0.9455758306400303, \ 0.0071625399102447, \ 0.9455758306400303, \ 0.0472616294497255, \ 0.0071625399102442, \ 0.3585095935696251, \ 0.5729634522431619, \ 0.0685269541872131, \ 0.5729634522431619, \ 0.3585095935696250, \ 0.0685269541872129, \ 0.4803288773373085, \ 0.4803288773373085, \ 0.0393422453253830, \ 0.2404827720350127, \ 0.6577888986377031, \ 0.1017283293272843, \ 0.6577888986377032, \ 0.2404827720350126, \ 0.1017283293272841, \ 0.0868410482076331, \ 0.8263179035847337, \ 0.0868410482076334, \ 0.3943235060115415, \ 0.3943235060115415, \ 0.2113529879769169, \ 0.2662513178772472, \ 0.4674973642455053, \ 0.2662513178772474, \ 0.1729323031292240, \ 0.7687161216332605, \ 0.0583515752375156, \ 0.7687161216332605, \ 0.1729323031292240, \ 0.0583515752375153, \ 0.3163043076538381, \ 0.5288655369406456, \ 0.1548301554055163, \ 0.5288655369406456, \ 0.3163043076538382, \ 0.1548301554055161, \ 0.1371293873116475, \ 0.7257412253767047, \ 0.1371293873116478, \ 0.4989594312095863, \ 0.4989594312095863, \ 0.0020811375808273, \ 0.3977585768030076, \ 0.5874824534670471, \ 0.0147589697299451, \ 0.5874824534670471, \ 0.3977585768030076, \ 0.0147589697299450, \ 0.4446924421277275, \ 0.4446924421277275, \ 0.1106151157445449, \ 0.1987498063965361, \ 0.6025003872069274, \ 0.1987498063965363, \ 0.2787941698141023, \ 0.6882121219933649, \ 0.0329937081925328, \ 0.6882121219933649, \ 0.2787941698141023, \ 0.0329937081925327, \ 0.0090164402055982, \ 0.9819671195888033, \ 0.0090164402055986, \ 0.3333333333333333 ] ) b = np.array ( [ \ 0.0238702536543536, \ 0.1595037989247572, \ 0.8166259474208892, \ 0.0238702536543536, \ 0.8166259474208892, \ 0.1595037989247576, \ 0.0051898217608445, \ 0.1141013603223645, \ 0.8807088179167911, \ 0.0051898217608445, \ 0.8807088179167911, \ 0.1141013603223648, \ 0.0390072687570323, \ 0.0390072687570320, \ 0.9219854624859359, \ 0.0327410291887064, \ 0.0955398781717349, \ 0.8717190926395588, \ 0.0327410291887064, \ 0.8717190926395588, \ 0.0955398781717352, \ 0.0024475998559664, \ 0.3111622680517020, \ 0.6863901320923319, \ 0.0024475998559664, \ 0.6863901320923319, \ 0.3111622680517022, \ 0.0087252895853085, \ 0.2056172320580521, \ 0.7856574783566396, \ 0.0087252895853085, \ 0.7856574783566396, \ 0.2056172320580524, \ 0.0071625399102445, \ 0.0472616294497253, \ 0.9455758306400303, \ 0.0071625399102445, \ 0.9455758306400303, \ 0.0472616294497257, \ 0.0685269541872130, \ 0.3585095935696251, \ 0.5729634522431620, \ 0.0685269541872130, \ 0.5729634522431620, \ 0.3585095935696253, \ 0.0393422453253830, \ 0.4803288773373086, \ 0.4803288773373087, \ 0.1017283293272843, \ 0.2404827720350127, \ 0.6577888986377033, \ 0.1017283293272843, \ 0.6577888986377033, \ 0.2404827720350129, \ 0.0868410482076333, \ 0.0868410482076330, \ 0.8263179035847338, \ 0.2113529879769170, \ 0.3943235060115416, \ 0.3943235060115416, \ 0.2662513178772474, \ 0.2662513178772473, \ 0.4674973642455055, \ 0.0583515752375155, \ 0.1729323031292239, \ 0.7687161216332608, \ 0.0583515752375155, \ 0.7687161216332608, \ 0.1729323031292242, \ 0.1548301554055163, \ 0.3163043076538382, \ 0.5288655369406458, \ 0.1548301554055163, \ 0.5288655369406458, \ 0.3163043076538383, \ 0.1371293873116478, \ 0.1371293873116475, \ 0.7257412253767048, \ 0.0020811375808274, \ 0.4989594312095864, \ 0.4989594312095865, \ 0.0147589697299452, \ 0.3977585768030077, \ 0.5874824534670474, \ 0.0147589697299452, \ 0.5874824534670473, \ 0.3977585768030079, \ 0.1106151157445450, \ 0.4446924421277276, \ 0.4446924421277277, \ 0.1987498063965364, \ 0.1987498063965362, \ 0.6025003872069277, \ 0.0329937081925328, \ 0.2787941698141023, \ 0.6882121219933651, \ 0.0329937081925328, \ 0.6882121219933650, \ 0.2787941698141025, \ 0.0090164402055985, \ 0.0090164402055982, \ 0.9819671195888034, \ 0.3333333333333334 ] ) c = np.array ( [ \ 0.8166259474208892, \ 0.0238702536543536, \ 0.1595037989247570, \ 0.1595037989247572, \ 0.0238702536543535, \ 0.8166259474208891, \ 0.8807088179167910, \ 0.0051898217608447, \ 0.1141013603223643, \ 0.1141013603223646, \ 0.0051898217608443, \ 0.8807088179167908, \ 0.9219854624859357, \ 0.0390072687570323, \ 0.0390072687570316, \ 0.8717190926395586, \ 0.0327410291887065, \ 0.0955398781717347, \ 0.0955398781717349, \ 0.0327410291887062, \ 0.8717190926395585, \ 0.6863901320923317, \ 0.0024475998559664, \ 0.3111622680517018, \ 0.3111622680517019, \ 0.0024475998559662, \ 0.6863901320923316, \ 0.7856574783566395, \ 0.0087252895853084, \ 0.2056172320580519, \ 0.2056172320580521, \ 0.0087252895853084, \ 0.7856574783566393, \ 0.9455758306400301, \ 0.0071625399102445, \ 0.0472616294497251, \ 0.0472616294497253, \ 0.0071625399102443, \ 0.9455758306400301, \ 0.5729634522431619, \ 0.0685269541872129, \ 0.3585095935696249, \ 0.3585095935696251, \ 0.0685269541872130, \ 0.5729634522431618, \ 0.4803288773373085, \ 0.0393422453253830, \ 0.4803288773373083, \ 0.6577888986377031, \ 0.1017283293272842, \ 0.2404827720350124, \ 0.2404827720350126, \ 0.1017283293272840, \ 0.6577888986377031, \ 0.8263179035847337, \ 0.0868410482076333, \ 0.0868410482076328, \ 0.3943235060115415, \ 0.2113529879769168, \ 0.3943235060115414, \ 0.4674973642455054, \ 0.2662513178772473, \ 0.2662513178772471, \ 0.7687161216332605, \ 0.0583515752375155, \ 0.1729323031292237, \ 0.1729323031292240, \ 0.0583515752375152, \ 0.7687161216332604, \ 0.5288655369406456, \ 0.1548301554055162, \ 0.3163043076538380, \ 0.3163043076538381, \ 0.1548301554055161, \ 0.5288655369406455, \ 0.7257412253767047, \ 0.1371293873116478, \ 0.1371293873116474, \ 0.4989594312095863, \ 0.0020811375808273, \ 0.4989594312095861, \ 0.5874824534670472, \ 0.0147589697299452, \ 0.3977585768030075, \ 0.3977585768030077, \ 0.0147589697299451, \ 0.5874824534670471, \ 0.4446924421277275, \ 0.1106151157445449, \ 0.4446924421277273, \ 0.6025003872069276, \ 0.1987498063965363, \ 0.1987498063965361, \ 0.6882121219933649, \ 0.0329937081925328, \ 0.2787941698141020, \ 0.2787941698141023, \ 0.0329937081925327, \ 0.6882121219933648, \ 0.9819671195888033, \ 0.0090164402055985, \ 0.0090164402055980, \ 0.3333333333333333 ] ) w = np.array ( [ \ 0.0025281660553823, \ 0.0025281660553823, \ 0.0025281660553823, \ 0.0025281660553823, \ 0.0025281660553823, \ 0.0025281660553823, \ 0.0022250197297245, \ 0.0022250197297245, \ 0.0022250197297245, \ 0.0022250197297245, \ 0.0022250197297245, \ 0.0022250197297245, \ 0.0039157402590329, \ 0.0039157402590329, \ 0.0039157402590329, \ 0.0053280304311948, \ 0.0053280304311948, \ 0.0053280304311948, \ 0.0053280304311948, \ 0.0053280304311948, \ 0.0053280304311948, \ 0.0022811036762558, \ 0.0022811036762558, \ 0.0022811036762558, \ 0.0022811036762558, \ 0.0022811036762558, \ 0.0022811036762558, \ 0.0041147503444161, \ 0.0041147503444161, \ 0.0041147503444161, \ 0.0041147503444161, \ 0.0041147503444161, \ 0.0041147503444161, \ 0.0019525913278907, \ 0.0019525913278907, \ 0.0019525913278907, \ 0.0019525913278907, \ 0.0019525913278907, \ 0.0019525913278907, \ 0.0149811133931992, \ 0.0149811133931992, \ 0.0149811133931992, \ 0.0149811133931992, \ 0.0149811133931992, \ 0.0149811133931992, \ 0.0113978892678008, \ 0.0113978892678008, \ 0.0113978892678008, \ 0.0161212416370172, \ 0.0161212416370172, \ 0.0161212416370172, \ 0.0161212416370172, \ 0.0161212416370172, \ 0.0161212416370172, \ 0.0089599170255135, \ 0.0089599170255135, \ 0.0089599170255135, \ 0.0236746084631280, \ 0.0236746084631280, \ 0.0236746084631280, \ 0.0238078628874998, \ 0.0238078628874998, \ 0.0238078628874998, \ 0.0104702564931301, \ 0.0104702564931301, \ 0.0104702564931301, \ 0.0104702564931301, \ 0.0104702564931301, \ 0.0104702564931301, \ 0.0208443958589688, \ 0.0208443958589688, \ 0.0208443958589688, \ 0.0208443958589688, \ 0.0208443958589688, \ 0.0208443958589688, \ 0.0145594493927417, \ 0.0145594493927417, \ 0.0145594493927417, \ 0.0024075446041814, \ 0.0024075446041814, \ 0.0024075446041814, \ 0.0070977788345218, \ 0.0070977788345218, \ 0.0070977788345218, \ 0.0070977788345218, \ 0.0070977788345218, \ 0.0070977788345218, \ 0.0189519506693389, \ 0.0189519506693389, \ 0.0189519506693389, \ 0.0199352778801050, \ 0.0199352778801050, \ 0.0199352778801050, \ 0.0101755746567070, \ 0.0101755746567070, \ 0.0101755746567070, \ 0.0101755746567070, \ 0.0101755746567070, \ 0.0101755746567070, \ 0.0010653612328293, \ 0.0010653612328293, \ 0.0010653612328293, \ 0.0252530603230362 ] ) return a, b, c, w def rule24 ( ): #*****************************************************************************80 # ## rule24() returns the rule of precision 24. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3333333333333333, \ 0.4188909749106027, \ 0.4188909749106027, \ 0.1622180501787944, \ 0.1623606337169263, \ 0.6752787325661472, \ 0.1623606337169265, \ 0.2414797600735940, \ 0.5881529574639622, \ 0.1703672824624437, \ 0.5881529574639622, \ 0.2414797600735940, \ 0.1703672824624436, \ 0.3289758089242263, \ 0.5012643952150375, \ 0.1697597958607360, \ 0.5012643952150376, \ 0.3289758089242264, \ 0.1697597958607359, \ 0.0409856290011169, \ 0.9180287419977657, \ 0.0409856290011174, \ 0.0067312708878883, \ 0.9865374582242232, \ 0.0067312708878887, \ 0.0931674097798811, \ 0.8685143643990995, \ 0.0383182258210195, \ 0.8685143643990995, \ 0.0931674097798812, \ 0.0383182258210191, \ 0.3945202798001943, \ 0.5128232386790481, \ 0.0926564815207574, \ 0.5128232386790481, \ 0.3945202798001944, \ 0.0926564815207574, \ 0.1626774163944774, \ 0.7961338693570472, \ 0.0411887142484756, \ 0.7961338693570472, \ 0.1626774163944775, \ 0.0411887142484752, \ 0.2535890142188795, \ 0.7068400808109625, \ 0.0395709049701581, \ 0.7068400808109625, \ 0.2535890142188795, \ 0.0395709049701579, \ 0.3622522413177913, \ 0.5991550585073127, \ 0.0385927001748961, \ 0.5991550585073125, \ 0.3622522413177913, \ 0.0385927001748960, \ 0.2816225777061608, \ 0.6238424605572400, \ 0.0945349617365990, \ 0.6238424605572401, \ 0.2816225777061608, \ 0.0945349617365988, \ 0.3832726649926592, \ 0.6093393403750466, \ 0.0073879946322942, \ 0.6093393403750464, \ 0.3832726649926592, \ 0.0073879946322941, \ 0.2737503525162605, \ 0.7187036443214266, \ 0.0075460031623129, \ 0.7187036443214266, \ 0.2737503525162606, \ 0.0075460031623126, \ 0.4962552776757351, \ 0.4962552776757351, \ 0.0074894446485297, \ 0.0941213427973660, \ 0.8986440987448518, \ 0.0072345584577822, \ 0.8986440987448518, \ 0.0941213427973661, \ 0.0072345584577819, \ 0.2642313154382725, \ 0.4715373691234548, \ 0.2642313154382727, \ 0.1803961518867657, \ 0.7240375785858689, \ 0.0955662695273654, \ 0.7240375785858689, \ 0.1803961518867657, \ 0.0955662695273650, \ 0.4806125617925032, \ 0.4806125617925033, \ 0.0387748764149934, \ 0.1747373462828057, \ 0.8172747318363464, \ 0.0079879218808480, \ 0.8172747318363462, \ 0.1747373462828057, \ 0.0079879218808478, \ 0.0963284955992151, \ 0.8073430088015696, \ 0.0963284955992154, \ 0.0372914720512912, \ 0.9546336170785000, \ 0.0080749108702090, \ 0.9546336170785000, \ 0.0372914720512914, \ 0.0080749108702085, \ 0.3753529267020863, \ 0.3753529267020863, \ 0.2492941465958274 ] ) b = np.array ( [ \ 0.3333333333333334, \ 0.1622180501787945, \ 0.4188909749106028, \ 0.4188909749106029, \ 0.1623606337169265, \ 0.1623606337169263, \ 0.6752787325661475, \ 0.1703672824624437, \ 0.2414797600735941, \ 0.5881529574639625, \ 0.1703672824624437, \ 0.5881529574639625, \ 0.2414797600735942, \ 0.1697597958607361, \ 0.3289758089242264, \ 0.5012643952150377, \ 0.1697597958607361, \ 0.5012643952150377, \ 0.3289758089242266, \ 0.0409856290011173, \ 0.0409856290011169, \ 0.9180287419977659, \ 0.0067312708878885, \ 0.0067312708878882, \ 0.9865374582242232, \ 0.0383182258210194, \ 0.0931674097798812, \ 0.8685143643990996, \ 0.0383182258210194, \ 0.8685143643990996, \ 0.0931674097798815, \ 0.0926564815207575, \ 0.3945202798001944, \ 0.5128232386790483, \ 0.0926564815207575, \ 0.5128232386790482, \ 0.3945202798001946, \ 0.0411887142484754, \ 0.1626774163944774, \ 0.7961338693570472, \ 0.0411887142484754, \ 0.7961338693570472, \ 0.1626774163944777, \ 0.0395709049701581, \ 0.2535890142188795, \ 0.7068400808109626, \ 0.0395709049701581, \ 0.7068400808109626, \ 0.2535890142188797, \ 0.0385927001748961, \ 0.3622522413177914, \ 0.5991550585073128, \ 0.0385927001748961, \ 0.5991550585073127, \ 0.3622522413177915, \ 0.0945349617365990, \ 0.2816225777061609, \ 0.6238424605572404, \ 0.0945349617365990, \ 0.6238424605572404, \ 0.2816225777061611, \ 0.0073879946322942, \ 0.3832726649926593, \ 0.6093393403750468, \ 0.0073879946322942, \ 0.6093393403750467, \ 0.3832726649926595, \ 0.0075460031623128, \ 0.2737503525162605, \ 0.7187036443214270, \ 0.0075460031623128, \ 0.7187036443214267, \ 0.2737503525162608, \ 0.0074894446485298, \ 0.4962552776757352, \ 0.4962552776757354, \ 0.0072345584577821, \ 0.0941213427973660, \ 0.8986440987448521, \ 0.0072345584577821, \ 0.8986440987448520, \ 0.0941213427973664, \ 0.2642313154382727, \ 0.2642313154382726, \ 0.4715373691234549, \ 0.0955662695273653, \ 0.1803961518867657, \ 0.7240375785858691, \ 0.0955662695273653, \ 0.7240375785858693, \ 0.1803961518867660, \ 0.0387748764149935, \ 0.4806125617925033, \ 0.4806125617925034, \ 0.0079879218808480, \ 0.1747373462828057, \ 0.8172747318363466, \ 0.0079879218808480, \ 0.8172747318363466, \ 0.1747373462828060, \ 0.0963284955992153, \ 0.0963284955992151, \ 0.8073430088015697, \ 0.0080749108702088, \ 0.0372914720512912, \ 0.9546336170785000, \ 0.0080749108702088, \ 0.9546336170785000, \ 0.0372914720512916, \ 0.2492941465958275, \ 0.3753529267020864, \ 0.3753529267020864 ] ) c = np.array ( [ \ 0.3333333333333333, \ 0.4188909749106028, \ 0.1622180501787945, \ 0.4188909749106027, \ 0.6752787325661472, \ 0.1623606337169265, \ 0.1623606337169260, \ 0.5881529574639622, \ 0.1703672824624437, \ 0.2414797600735938, \ 0.2414797600735940, \ 0.1703672824624435, \ 0.5881529574639621, \ 0.5012643952150376, \ 0.1697597958607361, \ 0.3289758089242263, \ 0.3289758089242263, \ 0.1697597958607359, \ 0.5012643952150375, \ 0.9180287419977659, \ 0.0409856290011173, \ 0.0409856290011167, \ 0.9865374582242232, \ 0.0067312708878886, \ 0.0067312708878881, \ 0.8685143643990995, \ 0.0383182258210194, \ 0.0931674097798809, \ 0.0931674097798811, \ 0.0383182258210192, \ 0.8685143643990995, \ 0.5128232386790481, \ 0.0926564815207574, \ 0.3945202798001942, \ 0.3945202798001943, \ 0.0926564815207574, \ 0.5128232386790480, \ 0.7961338693570472, \ 0.0411887142484754, \ 0.1626774163944772, \ 0.1626774163944774, \ 0.0411887142484753, \ 0.7961338693570471, \ 0.7068400808109625, \ 0.0395709049701580, \ 0.2535890142188794, \ 0.2535890142188795, \ 0.0395709049701579, \ 0.7068400808109623, \ 0.5991550585073125, \ 0.0385927001748960, \ 0.3622522413177912, \ 0.3622522413177913, \ 0.0385927001748960, \ 0.5991550585073124, \ 0.6238424605572401, \ 0.0945349617365990, \ 0.2816225777061607, \ 0.2816225777061608, \ 0.0945349617365988, \ 0.6238424605572401, \ 0.6093393403750466, \ 0.0073879946322942, \ 0.3832726649926591, \ 0.3832726649926593, \ 0.0073879946322941, \ 0.6093393403750464, \ 0.7187036443214266, \ 0.0075460031623129, \ 0.2737503525162601, \ 0.2737503525162606, \ 0.0075460031623127, \ 0.7187036443214266, \ 0.4962552776757350, \ 0.0074894446485297, \ 0.4962552776757349, \ 0.8986440987448518, \ 0.0072345584577821, \ 0.0941213427973657, \ 0.0941213427973660, \ 0.0072345584577819, \ 0.8986440987448517, \ 0.4715373691234548, \ 0.2642313154382726, \ 0.2642313154382724, \ 0.7240375785858690, \ 0.0955662695273653, \ 0.1803961518867655, \ 0.1803961518867658, \ 0.0955662695273650, \ 0.7240375785858690, \ 0.4806125617925033, \ 0.0387748764149934, \ 0.4806125617925031, \ 0.8172747318363464, \ 0.0079879218808480, \ 0.1747373462828054, \ 0.1747373462828058, \ 0.0079879218808477, \ 0.8172747318363462, \ 0.8073430088015696, \ 0.0963284955992153, \ 0.0963284955992149, \ 0.9546336170785000, \ 0.0080749108702088, \ 0.0372914720512910, \ 0.0372914720512912, \ 0.0080749108702086, \ 0.9546336170784999, \ 0.3753529267020862, \ 0.2492941465958273, \ 0.3753529267020862 ] ) w = np.array ( [ \ 0.0125456898456003, \ 0.0131105327018852, \ 0.0131105327018852, \ 0.0131105327018852, \ 0.0103790160564002, \ 0.0103790160564002, \ 0.0103790160564002, \ 0.0141450458064848, \ 0.0141450458064848, \ 0.0141450458064848, \ 0.0141450458064848, \ 0.0141450458064848, \ 0.0141450458064848, \ 0.0152744426013246, \ 0.0152744426013246, \ 0.0152744426013246, \ 0.0152744426013246, \ 0.0152744426013246, \ 0.0152744426013246, \ 0.0038336997309292, \ 0.0038336997309292, \ 0.0038336997309292, \ 0.0006172545054966, \ 0.0006172545054966, \ 0.0006172545054966, \ 0.0053662714541678, \ 0.0053662714541678, \ 0.0053662714541678, \ 0.0053662714541678, \ 0.0053662714541678, \ 0.0053662714541678, \ 0.0150318543497413, \ 0.0150318543497413, \ 0.0150318543497413, \ 0.0150318543497413, \ 0.0150318543497413, \ 0.0150318543497413, \ 0.0072041341747974, \ 0.0072041341747974, \ 0.0072041341747974, \ 0.0072041341747974, \ 0.0072041341747974, \ 0.0072041341747974, \ 0.0089048769281636, \ 0.0089048769281636, \ 0.0089048769281636, \ 0.0089048769281636, \ 0.0089048769281636, \ 0.0089048769281636, \ 0.0099472518756824, \ 0.0099472518756824, \ 0.0099472518756824, \ 0.0099472518756824, \ 0.0099472518756824, \ 0.0099472518756824, \ 0.0143523515781575, \ 0.0143523515781575, \ 0.0143523515781575, \ 0.0143523515781575, \ 0.0143523515781575, \ 0.0143523515781575, \ 0.0042421492668038, \ 0.0042421492668038, \ 0.0042421492668038, \ 0.0042421492668038, \ 0.0042421492668038, \ 0.0042421492668038, \ 0.0040812750771165, \ 0.0040812750771165, \ 0.0040812750771165, \ 0.0040812750771165, \ 0.0040812750771165, \ 0.0040812750771165, \ 0.0043432467221707, \ 0.0043432467221707, \ 0.0043432467221707, \ 0.0025892123823980, \ 0.0025892123823980, \ 0.0025892123823980, \ 0.0025892123823980, \ 0.0025892123823980, \ 0.0025892123823980, \ 0.0205200086715098, \ 0.0205200086715098, \ 0.0205200086715098, \ 0.0118435621425431, \ 0.0118435621425431, \ 0.0118435621425431, \ 0.0118435621425431, \ 0.0118435621425431, \ 0.0118435621425431, \ 0.0103524947708526, \ 0.0103524947708526, \ 0.0103524947708526, \ 0.0037072267642463, \ 0.0037072267642463, \ 0.0037072267642463, \ 0.0037072267642463, \ 0.0037072267642463, \ 0.0037072267642463, \ 0.0100273930673889, \ 0.0100273930673889, \ 0.0100273930673889, \ 0.0017969475854466, \ 0.0017969475854466, \ 0.0017969475854466, \ 0.0017969475854466, \ 0.0017969475854466, \ 0.0017969475854466, \ 0.0189945865173527, \ 0.0189945865173527, \ 0.0189945865173527 ] ) return a, b, c, w def rule25 ( ): #*****************************************************************************80 # ## rule25() returns the rule of precision 25. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3876420304045634, \ 0.3876420304045634, \ 0.2247159391908731, \ 0.2110045080614966, \ 0.5779909838770066, \ 0.2110045080614967, \ 0.4404169274793433, \ 0.5577642058863823, \ 0.0018188666342743, \ 0.5577642058863823, \ 0.4404169274793434, \ 0.0018188666342743, \ 0.2994923158045084, \ 0.4010153683909830, \ 0.2994923158045084, \ 0.1590079061973279, \ 0.8040319522230005, \ 0.0369601415796716, \ 0.8040319522230007, \ 0.1590079061973279, \ 0.0369601415796713, \ 0.0372229259924406, \ 0.9255541480151184, \ 0.0372229259924410, \ 0.1773537967572529, \ 0.7437881352371117, \ 0.0788580680056354, \ 0.7437881352371118, \ 0.1773537967572530, \ 0.0788580680056351, \ 0.1451092435745002, \ 0.7097815128509992, \ 0.1451092435745006, \ 0.2700667358209594, \ 0.6610857347475426, \ 0.0688475294314979, \ 0.6610857347475427, \ 0.2700667358209594, \ 0.0688475294314977, \ 0.3413910330211499, \ 0.5426091593378899, \ 0.1159998076409602, \ 0.5426091593378899, \ 0.3413910330211499, \ 0.1159998076409601, \ 0.3739379797195844, \ 0.5777445859930386, \ 0.0483174342873769, \ 0.5777445859930387, \ 0.3739379797195845, \ 0.0483174342873768, \ 0.0991330633416822, \ 0.8937386221570603, \ 0.0071283145012576, \ 0.8937386221570603, \ 0.0991330633416823, \ 0.0071283145012572, \ 0.2995064186296745, \ 0.4968006707860745, \ 0.2036929105842510, \ 0.4968006707860745, \ 0.2995064186296745, \ 0.2036929105842509, \ 0.4247593045405747, \ 0.4247593045405746, \ 0.1504813909188505, \ 0.1786298486036162, \ 0.8141339896484356, \ 0.0072361617479482, \ 0.8141339896484356, \ 0.1786298486036164, \ 0.0072361617479479, \ 0.3620688018959720, \ 0.6250173148539955, \ 0.0129138832500325, \ 0.6250173148539954, \ 0.3620688018959721, \ 0.0129138832500325, \ 0.0887929154893665, \ 0.8735191347263743, \ 0.0376879497842592, \ 0.8735191347263743, \ 0.0887929154893666, \ 0.0376879497842588, \ 0.2336228101417152, \ 0.6293704957712137, \ 0.1370066940870710, \ 0.6293704957712138, \ 0.2336228101417152, \ 0.1370066940870708, \ 0.4622087087487061, \ 0.4622087087487061, \ 0.0755825825025877, \ 0.2565954097090198, \ 0.7188645300434557, \ 0.0245400602475245, \ 0.7188645300434559, \ 0.2565954097090199, \ 0.0245400602475242, \ 0.0929497017007698, \ 0.8141005965984600, \ 0.0929497017007701, \ 0.0410688191117846, \ 0.9517423526265223, \ 0.0071888282616933, \ 0.9517423526265224, \ 0.0410688191117848, \ 0.0071888282616928, \ 0.0078353442826036, \ 0.9843293114347924, \ 0.0078353442826041, \ 0.4890393696603955, \ 0.4890393696603955, \ 0.0219212606792090, \ 0.2794161886492607, \ 0.7196923470332411, \ 0.0008914643174981, \ 0.7196923470332411, \ 0.2794161886492608, \ 0.0008914643174980 ] ) b = np.array ( [ \ 0.2247159391908732, \ 0.3876420304045635, \ 0.3876420304045636, \ 0.2110045080614968, \ 0.2110045080614966, \ 0.5779909838770069, \ 0.0018188666342744, \ 0.4404169274793434, \ 0.5577642058863825, \ 0.0018188666342744, \ 0.5577642058863823, \ 0.4404169274793436, \ 0.2994923158045086, \ 0.2994923158045085, \ 0.4010153683909831, \ 0.0369601415796715, \ 0.1590079061973279, \ 0.8040319522230007, \ 0.0369601415796715, \ 0.8040319522230007, \ 0.1590079061973282, \ 0.0372229259924409, \ 0.0372229259924406, \ 0.9255541480151186, \ 0.0788580680056353, \ 0.1773537967572529, \ 0.7437881352371120, \ 0.0788580680056353, \ 0.7437881352371120, \ 0.1773537967572532, \ 0.1451092435745005, \ 0.1451092435745003, \ 0.7097815128509993, \ 0.0688475294314979, \ 0.2700667358209594, \ 0.6610857347475428, \ 0.0688475294314979, \ 0.6610857347475428, \ 0.2700667358209596, \ 0.1159998076409602, \ 0.3413910330211499, \ 0.5426091593378901, \ 0.1159998076409602, \ 0.5426091593378900, \ 0.3413910330211500, \ 0.0483174342873770, \ 0.3739379797195844, \ 0.5777445859930388, \ 0.0483174342873770, \ 0.5777445859930387, \ 0.3739379797195846, \ 0.0071283145012574, \ 0.0991330633416822, \ 0.8937386221570605, \ 0.0071283145012574, \ 0.8937386221570605, \ 0.0991330633416825, \ 0.2036929105842510, \ 0.2995064186296746, \ 0.4968006707860746, \ 0.2036929105842510, \ 0.4968006707860746, \ 0.2995064186296747, \ 0.1504813909188506, \ 0.4247593045405748, \ 0.4247593045405749, \ 0.0072361617479482, \ 0.1786298486036162, \ 0.8141339896484358, \ 0.0072361617479482, \ 0.8141339896484358, \ 0.1786298486036166, \ 0.0129138832500325, \ 0.3620688018959721, \ 0.6250173148539957, \ 0.0129138832500325, \ 0.6250173148539956, \ 0.3620688018959722, \ 0.0376879497842591, \ 0.0887929154893666, \ 0.8735191347263744, \ 0.0376879497842591, \ 0.8735191347263744, \ 0.0887929154893669, \ 0.1370066940870710, \ 0.2336228101417153, \ 0.6293704957712140, \ 0.1370066940870710, \ 0.6293704957712140, \ 0.2336228101417155, \ 0.0755825825025878, \ 0.4622087087487062, \ 0.4622087087487063, \ 0.0245400602475244, \ 0.2565954097090198, \ 0.7188645300434559, \ 0.0245400602475244, \ 0.7188645300434559, \ 0.2565954097090201, \ 0.0929497017007700, \ 0.0929497017007698, \ 0.8141005965984602, \ 0.0071888282616930, \ 0.0410688191117846, \ 0.9517423526265224, \ 0.0071888282616930, \ 0.9517423526265224, \ 0.0410688191117850, \ 0.0078353442826039, \ 0.0078353442826036, \ 0.9843293114347926, \ 0.0219212606792091, \ 0.4890393696603955, \ 0.4890393696603957, \ 0.0008914643174981, \ 0.2794161886492607, \ 0.7196923470332415, \ 0.0008914643174981, \ 0.7196923470332413, \ 0.2794161886492610 ] ) c = np.array ( [ \ 0.3876420304045634, \ 0.2247159391908732, \ 0.3876420304045634, \ 0.5779909838770066, \ 0.2110045080614967, \ 0.2110045080614965, \ 0.5577642058863823, \ 0.0018188666342743, \ 0.4404169274793431, \ 0.4404169274793433, \ 0.0018188666342743, \ 0.5577642058863822, \ 0.4010153683909830, \ 0.2994923158045085, \ 0.2994923158045085, \ 0.8040319522230006, \ 0.0369601415796716, \ 0.1590079061973276, \ 0.1590079061973278, \ 0.0369601415796713, \ 0.8040319522230005, \ 0.9255541480151185, \ 0.0372229259924410, \ 0.0372229259924404, \ 0.7437881352371117, \ 0.0788580680056354, \ 0.1773537967572526, \ 0.1773537967572529, \ 0.0788580680056351, \ 0.7437881352371117, \ 0.7097815128509992, \ 0.1451092435745005, \ 0.1451092435745002, \ 0.6610857347475426, \ 0.0688475294314980, \ 0.2700667358209593, \ 0.2700667358209593, \ 0.0688475294314977, \ 0.6610857347475426, \ 0.5426091593378900, \ 0.1159998076409602, \ 0.3413910330211497, \ 0.3413910330211499, \ 0.1159998076409602, \ 0.5426091593378899, \ 0.5777445859930387, \ 0.0483174342873770, \ 0.3739379797195843, \ 0.3739379797195844, \ 0.0483174342873768, \ 0.5777445859930385, \ 0.8937386221570605, \ 0.0071283145012575, \ 0.0991330633416820, \ 0.0991330633416822, \ 0.0071283145012573, \ 0.8937386221570603, \ 0.4968006707860744, \ 0.2036929105842509, \ 0.2995064186296744, \ 0.2995064186296745, \ 0.2036929105842509, \ 0.4968006707860744, \ 0.4247593045405748, \ 0.1504813909188505, \ 0.4247593045405746, \ 0.8141339896484356, \ 0.0072361617479481, \ 0.1786298486036161, \ 0.1786298486036162, \ 0.0072361617479478, \ 0.8141339896484355, \ 0.6250173148539955, \ 0.0129138832500325, \ 0.3620688018959718, \ 0.3620688018959721, \ 0.0129138832500323, \ 0.6250173148539954, \ 0.8735191347263744, \ 0.0376879497842591, \ 0.0887929154893663, \ 0.0887929154893666, \ 0.0376879497842589, \ 0.8735191347263743, \ 0.6293704957712137, \ 0.1370066940870710, \ 0.2336228101417150, \ 0.2336228101417152, \ 0.1370066940870708, \ 0.6293704957712137, \ 0.4622087087487061, \ 0.0755825825025877, \ 0.4622087087487059, \ 0.7188645300434559, \ 0.0245400602475244, \ 0.2565954097090196, \ 0.2565954097090197, \ 0.0245400602475242, \ 0.7188645300434557, \ 0.8141005965984602, \ 0.0929497017007702, \ 0.0929497017007697, \ 0.9517423526265223, \ 0.0071888282616931, \ 0.0410688191117844, \ 0.0410688191117846, \ 0.0071888282616929, \ 0.9517423526265223, \ 0.9843293114347924, \ 0.0078353442826040, \ 0.0078353442826032, \ 0.4890393696603955, \ 0.0219212606792091, \ 0.4890393696603952, \ 0.7196923470332411, \ 0.0008914643174981, \ 0.2794161886492604, \ 0.2794161886492607, \ 0.0008914643174980, \ 0.7196923470332410 ] ) w = np.array ( [ \ 0.0136898515482722, \ 0.0136898515482722, \ 0.0136898515482722, \ 0.0115872632360106, \ 0.0115872632360106, \ 0.0115872632360106, \ 0.0016748178319347, \ 0.0016748178319347, \ 0.0016748178319347, \ 0.0016748178319347, \ 0.0016748178319347, \ 0.0016748178319347, \ 0.0180176407017015, \ 0.0180176407017015, \ 0.0180176407017015, \ 0.0063114780247593, \ 0.0063114780247593, \ 0.0063114780247593, \ 0.0063114780247593, \ 0.0063114780247593, \ 0.0063114780247593, \ 0.0033972977219047, \ 0.0033972977219047, \ 0.0033972977219047, \ 0.0095150215674558, \ 0.0095150215674558, \ 0.0095150215674558, \ 0.0095150215674558, \ 0.0095150215674558, \ 0.0095150215674558, \ 0.0114915258625648, \ 0.0114915258625648, \ 0.0114915258625648, \ 0.0108843936124369, \ 0.0108843936124369, \ 0.0108843936124369, \ 0.0108843936124369, \ 0.0108843936124369, \ 0.0108843936124369, \ 0.0158403522878984, \ 0.0158403522878984, \ 0.0158403522878984, \ 0.0158403522878984, \ 0.0158403522878984, \ 0.0158403522878984, \ 0.0106401706955088, \ 0.0106401706955088, \ 0.0106401706955088, \ 0.0106401706955088, \ 0.0106401706955088, \ 0.0106401706955088, \ 0.0025452716253490, \ 0.0025452716253490, \ 0.0025452716253490, \ 0.0025452716253490, \ 0.0025452716253490, \ 0.0025452716253490, \ 0.0179138208922761, \ 0.0179138208922761, \ 0.0179138208922761, \ 0.0179138208922761, \ 0.0179138208922761, \ 0.0179138208922761, \ 0.0159113101374584, \ 0.0159113101374584, \ 0.0159113101374584, \ 0.0032637396820492, \ 0.0032637396820492, \ 0.0032637396820492, \ 0.0032637396820492, \ 0.0032637396820492, \ 0.0032637396820492, \ 0.0054546383679744, \ 0.0054546383679744, \ 0.0054546383679744, \ 0.0054546383679744, \ 0.0054546383679744, \ 0.0054546383679744, \ 0.0052725619214294, \ 0.0052725619214294, \ 0.0052725619214294, \ 0.0052725619214294, \ 0.0052725619214294, \ 0.0052725619214294, \ 0.0137400825920226, \ 0.0137400825920226, \ 0.0137400825920226, \ 0.0137400825920226, \ 0.0137400825920226, \ 0.0137400825920226, \ 0.0136542751875280, \ 0.0136542751875280, \ 0.0136542751875280, \ 0.0073143409079328, \ 0.0073143409079328, \ 0.0073143409079328, \ 0.0073143409079328, \ 0.0073143409079328, \ 0.0073143409079328, \ 0.0091828212598200, \ 0.0091828212598200, \ 0.0091828212598200, \ 0.0016929836341273, \ 0.0016929836341273, \ 0.0016929836341273, \ 0.0016929836341273, \ 0.0016929836341273, \ 0.0016929836341273, \ 0.0008065102883246, \ 0.0008065102883246, \ 0.0008065102883246, \ 0.0084440859465211, \ 0.0084440859465211, \ 0.0084440859465211, \ 0.0015117020784589, \ 0.0015117020784589, \ 0.0015117020784589, \ 0.0015117020784589, \ 0.0015117020784589, \ 0.0015117020784589 ] ) return a, b, c, w def rule26 ( ): #*****************************************************************************80 # ## rule26() returns the rule of precision 26. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 July 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.0800716549403165, \ 0.9151336840842468, \ 0.0047946609754368, \ 0.9151336840842468, \ 0.0800716549403166, \ 0.0047946609754365, \ 0.0316436115715308, \ 0.9392011922216335, \ 0.0291551962068360, \ 0.9392011922216333, \ 0.0316436115715308, \ 0.0291551962068356, \ 0.0667371225764661, \ 0.8665257548470675, \ 0.0667371225764665, \ 0.0753800475153987, \ 0.8984105884621026, \ 0.0262093640224987, \ 0.8984105884621026, \ 0.0753800475153986, \ 0.0262093640224984, \ 0.0331000343360323, \ 0.9612018477470925, \ 0.0056981179168754, \ 0.9612018477470925, \ 0.0331000343360324, \ 0.0056981179168749, \ 0.0063401164920767, \ 0.9873197670158463, \ 0.0063401164920771, \ 0.1324861896145673, \ 0.8257890876433117, \ 0.0417247227421210, \ 0.8257890876433117, \ 0.1324861896145674, \ 0.0417247227421207, \ 0.1086871329144021, \ 0.7912672079790702, \ 0.1000456591065276, \ 0.7912672079790704, \ 0.1086871329144022, \ 0.1000456591065273, \ 0.4937530328963848, \ 0.4937530328963847, \ 0.0124939342072304, \ 0.2502723132905265, \ 0.6291132845042245, \ 0.1206144022052490, \ 0.6291132845042245, \ 0.2502723132905265, \ 0.1206144022052489, \ 0.3890220620427617, \ 0.5814399954403304, \ 0.0295379425169078, \ 0.5814399954403304, \ 0.3890220620427618, \ 0.0295379425169077, \ 0.3585092964276616, \ 0.5541122384084940, \ 0.0873784651638445, \ 0.5541122384084940, \ 0.3585092964276616, \ 0.0873784651638444, \ 0.3887874971075940, \ 0.3887874971075940, \ 0.2224250057848119, \ 0.1868691794762216, \ 0.7368189190108190, \ 0.0763119015129595, \ 0.7368189190108190, \ 0.1868691794762216, \ 0.0763119015129592, \ 0.2731471009290787, \ 0.4537057981418425, \ 0.2731471009290788, \ 0.4147059095903063, \ 0.5832365594443230, \ 0.0020575309653708, \ 0.5832365594443230, \ 0.4147059095903063, \ 0.0020575309653707, \ 0.3194153053834387, \ 0.5101059661193124, \ 0.1704787284972489, \ 0.5101059661193124, \ 0.3194153053834387, \ 0.1704787284972488, \ 0.1437376261997640, \ 0.8482627657087517, \ 0.0079996080914844, \ 0.8482627657087517, \ 0.1437376261997642, \ 0.0079996080914840, \ 0.4718285633211660, \ 0.4718285633211661, \ 0.0563428733576679, \ 0.1542014303645442, \ 0.6915971392709114, \ 0.1542014303645444, \ 0.2837881388594704, \ 0.6650459874553918, \ 0.0511658736851378, \ 0.6650459874553918, \ 0.2837881388594705, \ 0.0511658736851376, \ 0.2120431633022055, \ 0.5759136733955887, \ 0.2120431633022057, \ 0.4359854193843832, \ 0.4359854193843832, \ 0.1280291612312335, \ 0.2165466664734771, \ 0.7606687342756272, \ 0.0227845992508957, \ 0.7606687342756272, \ 0.2165466664734772, \ 0.0227845992508955, \ 0.3333333333333333, \ 0.3128985030748800, \ 0.6776281990129065, \ 0.0094732979122136, \ 0.6776281990129064, \ 0.3128985030748800, \ 0.0094732979122134, \ 0.2264347974077175, \ 0.7731011948601069, \ 0.0004640077321757, \ 0.7731011948601069, \ 0.2264347974077175, \ 0.0004640077321755 ] ) b = np.array ( [ \ 0.0047946609754367, \ 0.0800716549403165, \ 0.9151336840842469, \ 0.0047946609754367, \ 0.9151336840842469, \ 0.0800716549403169, \ 0.0291551962068358, \ 0.0316436115715307, \ 0.9392011922216336, \ 0.0291551962068358, \ 0.9392011922216336, \ 0.0316436115715311, \ 0.0667371225764664, \ 0.0667371225764660, \ 0.8665257548470677, \ 0.0262093640224987, \ 0.0753800475153986, \ 0.8984105884621029, \ 0.0262093640224987, \ 0.8984105884621030, \ 0.0753800475153990, \ 0.0056981179168752, \ 0.0331000343360323, \ 0.9612018477470927, \ 0.0056981179168752, \ 0.9612018477470927, \ 0.0331000343360326, \ 0.0063401164920770, \ 0.0063401164920766, \ 0.9873197670158466, \ 0.0417247227421209, \ 0.1324861896145673, \ 0.8257890876433118, \ 0.0417247227421209, \ 0.8257890876433118, \ 0.1324861896145676, \ 0.1000456591065276, \ 0.1086871329144021, \ 0.7912672079790705, \ 0.1000456591065276, \ 0.7912672079790705, \ 0.1086871329144024, \ 0.0124939342072305, \ 0.4937530328963848, \ 0.4937530328963849, \ 0.1206144022052490, \ 0.2502723132905265, \ 0.6291132845042247, \ 0.1206144022052490, \ 0.6291132845042245, \ 0.2502723132905267, \ 0.0295379425169078, \ 0.3890220620427618, \ 0.5814399954403305, \ 0.0295379425169078, \ 0.5814399954403304, \ 0.3890220620427621, \ 0.0873784651638445, \ 0.3585092964276616, \ 0.5541122384084942, \ 0.0873784651638445, \ 0.5541122384084941, \ 0.3585092964276618, \ 0.2224250057848120, \ 0.3887874971075941, \ 0.3887874971075941, \ 0.0763119015129594, \ 0.1868691794762216, \ 0.7368189190108192, \ 0.0763119015129594, \ 0.7368189190108192, \ 0.1868691794762219, \ 0.2731471009290788, \ 0.2731471009290788, \ 0.4537057981418426, \ 0.0020575309653709, \ 0.4147059095903063, \ 0.5832365594443231, \ 0.0020575309653709, \ 0.5832365594443230, \ 0.4147059095903066, \ 0.1704787284972490, \ 0.3194153053834388, \ 0.5101059661193126, \ 0.1704787284972490, \ 0.5101059661193125, \ 0.3194153053834389, \ 0.0079996080914843, \ 0.1437376261997640, \ 0.8482627657087518, \ 0.0079996080914843, \ 0.8482627657087518, \ 0.1437376261997644, \ 0.0563428733576680, \ 0.4718285633211661, \ 0.4718285633211662, \ 0.1542014303645444, \ 0.1542014303645442, \ 0.6915971392709116, \ 0.0511658736851378, \ 0.2837881388594705, \ 0.6650459874553920, \ 0.0511658736851378, \ 0.6650459874553919, \ 0.2837881388594707, \ 0.2120431633022057, \ 0.2120431633022056, \ 0.5759136733955889, \ 0.1280291612312336, \ 0.4359854193843832, \ 0.4359854193843834, \ 0.0227845992508957, \ 0.2165466664734771, \ 0.7606687342756275, \ 0.0227845992508957, \ 0.7606687342756273, \ 0.2165466664734774, \ 0.3333333333333334, \ 0.0094732979122136, \ 0.3128985030748800, \ 0.6776281990129066, \ 0.0094732979122136, \ 0.6776281990129066, \ 0.3128985030748803, \ 0.0004640077321757, \ 0.2264347974077175, \ 0.7731011948601070, \ 0.0004640077321757, \ 0.7731011948601070, \ 0.2264347974077178 ] ) c = np.array ( [ \ 0.9151336840842468, \ 0.0047946609754367, \ 0.0800716549403163, \ 0.0800716549403165, \ 0.0047946609754365, \ 0.9151336840842467, \ 0.9392011922216335, \ 0.0291551962068358, \ 0.0316436115715305, \ 0.0316436115715308, \ 0.0291551962068356, \ 0.9392011922216333, \ 0.8665257548470676, \ 0.0667371225764665, \ 0.0667371225764658, \ 0.8984105884621028, \ 0.0262093640224987, \ 0.0753800475153984, \ 0.0753800475153987, \ 0.0262093640224984, \ 0.8984105884621026, \ 0.9612018477470925, \ 0.0056981179168753, \ 0.0331000343360319, \ 0.0331000343360323, \ 0.0056981179168749, \ 0.9612018477470925, \ 0.9873197670158463, \ 0.0063401164920770, \ 0.0063401164920763, \ 0.8257890876433118, \ 0.0417247227421210, \ 0.1324861896145672, \ 0.1324861896145673, \ 0.0417247227421208, \ 0.8257890876433117, \ 0.7912672079790704, \ 0.1000456591065276, \ 0.1086871329144019, \ 0.1086871329144021, \ 0.1000456591065274, \ 0.7912672079790702, \ 0.4937530328963847, \ 0.0124939342072304, \ 0.4937530328963846, \ 0.6291132845042245, \ 0.1206144022052490, \ 0.2502723132905263, \ 0.2502723132905264, \ 0.1206144022052490, \ 0.6291132845042244, \ 0.5814399954403303, \ 0.0295379425169078, \ 0.3890220620427617, \ 0.3890220620427617, \ 0.0295379425169078, \ 0.5814399954403302, \ 0.5541122384084940, \ 0.0873784651638444, \ 0.3585092964276613, \ 0.3585092964276615, \ 0.0873784651638444, \ 0.5541122384084938, \ 0.3887874971075940, \ 0.2224250057848119, \ 0.3887874971075939, \ 0.7368189190108190, \ 0.0763119015129595, \ 0.1868691794762213, \ 0.1868691794762216, \ 0.0763119015129592, \ 0.7368189190108190, \ 0.4537057981418425, \ 0.2731471009290788, \ 0.2731471009290786, \ 0.5832365594443228, \ 0.0020575309653708, \ 0.4147059095903062, \ 0.4147059095903062, \ 0.0020575309653708, \ 0.5832365594443227, \ 0.5101059661193122, \ 0.1704787284972489, \ 0.3194153053834385, \ 0.3194153053834387, \ 0.1704787284972488, \ 0.5101059661193122, \ 0.8482627657087517, \ 0.0079996080914843, \ 0.1437376261997638, \ 0.1437376261997640, \ 0.0079996080914840, \ 0.8482627657087516, \ 0.4718285633211660, \ 0.0563428733576679, \ 0.4718285633211659, \ 0.6915971392709115, \ 0.1542014303645444, \ 0.1542014303645439, \ 0.6650459874553918, \ 0.0511658736851378, \ 0.2837881388594703, \ 0.2837881388594704, \ 0.0511658736851376, \ 0.6650459874553916, \ 0.5759136733955887, \ 0.2120431633022057, \ 0.2120431633022054, \ 0.4359854193843832, \ 0.1280291612312336, \ 0.4359854193843831, \ 0.7606687342756272, \ 0.0227845992508957, \ 0.2165466664734768, \ 0.2165466664734771, \ 0.0227845992508955, \ 0.7606687342756271, \ 0.3333333333333333, \ 0.6776281990129065, \ 0.0094732979122135, \ 0.3128985030748798, \ 0.3128985030748800, \ 0.0094732979122133, \ 0.6776281990129063, \ 0.7731011948601068, \ 0.0004640077321756, \ 0.2264347974077173, \ 0.2264347974077175, \ 0.0004640077321755, \ 0.7731011948601068 ] ) w = np.array ( [ \ 0.0013985264481603, \ 0.0013985264481603, \ 0.0013985264481603, \ 0.0013985264481603, \ 0.0013985264481603, \ 0.0013985264481603, \ 0.0012055647737169, \ 0.0012055647737169, \ 0.0012055647737169, \ 0.0012055647737169, \ 0.0012055647737169, \ 0.0012055647737169, \ 0.0049138253029660, \ 0.0049138253029660, \ 0.0049138253029660, \ 0.0033055447129677, \ 0.0033055447129677, \ 0.0033055447129677, \ 0.0033055447129677, \ 0.0033055447129677, \ 0.0033055447129677, \ 0.0010857073429968, \ 0.0010857073429968, \ 0.0010857073429968, \ 0.0010857073429968, \ 0.0010857073429968, \ 0.0010857073429968, \ 0.0005269531166819, \ 0.0005269531166819, \ 0.0005269531166819, \ 0.0064035978997128, \ 0.0064035978997128, \ 0.0064035978997128, \ 0.0064035978997128, \ 0.0064035978997128, \ 0.0064035978997128, \ 0.0046142110763783, \ 0.0046142110763783, \ 0.0046142110763783, \ 0.0046142110763783, \ 0.0046142110763783, \ 0.0046142110763783, \ 0.0053021591818673, \ 0.0053021591818673, \ 0.0053021591818673, \ 0.0143794732275987, \ 0.0143794732275987, \ 0.0143794732275987, \ 0.0143794732275987, \ 0.0143794732275987, \ 0.0143794732275987, \ 0.0082597672170868, \ 0.0082597672170868, \ 0.0082597672170868, \ 0.0082597672170868, \ 0.0082597672170868, \ 0.0082597672170868, \ 0.0137279582160857, \ 0.0137279582160857, \ 0.0137279582160857, \ 0.0137279582160857, \ 0.0137279582160857, \ 0.0137279582160857, \ 0.0194680678371829, \ 0.0194680678371829, \ 0.0194680678371829, \ 0.0103976455281743, \ 0.0103976455281743, \ 0.0103976455281743, \ 0.0103976455281743, \ 0.0103976455281743, \ 0.0103976455281743, \ 0.0195356469232475, \ 0.0195356469232475, \ 0.0195356469232475, \ 0.0018571474709981, \ 0.0018571474709981, \ 0.0018571474709981, \ 0.0018571474709981, \ 0.0018571474709981, \ 0.0018571474709981, \ 0.0175991671806952, \ 0.0175991671806952, \ 0.0175991671806952, \ 0.0175991671806952, \ 0.0175991671806952, \ 0.0175991671806952, \ 0.0029667616626565, \ 0.0029667616626565, \ 0.0029667616626565, \ 0.0029667616626565, \ 0.0029667616626565, \ 0.0029667616626565, \ 0.0115285036346569, \ 0.0115285036346569, \ 0.0115285036346569, \ 0.0132552594485453, \ 0.0132552594485453, \ 0.0132552594485453, \ 0.0101071244320887, \ 0.0101071244320887, \ 0.0101071244320887, \ 0.0101071244320887, \ 0.0101071244320887, \ 0.0101071244320887, \ 0.0169443450785281, \ 0.0169443450785281, \ 0.0169443450785281, \ 0.0164124006025879, \ 0.0164124006025879, \ 0.0164124006025879, \ 0.0062693378460806, \ 0.0062693378460806, \ 0.0062693378460806, \ 0.0062693378460806, \ 0.0062693378460806, \ 0.0062693378460806, \ 0.0204866625892232, \ 0.0045915583873986, \ 0.0045915583873986, \ 0.0045915583873986, \ 0.0045915583873986, \ 0.0045915583873986, \ 0.0045915583873986, \ 0.0011395489158682, \ 0.0011395489158682, \ 0.0011395489158682, \ 0.0011395489158682, \ 0.0011395489158682, \ 0.0011395489158682 ] ) return a, b, c, w def rule27 ( ): #*****************************************************************************80 # ## rule27() returns the rule of precision 27. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3807140211811871, \ 0.3807140211811871, \ 0.2385719576376256, \ 0.4466678037038646, \ 0.4466678037038646, \ 0.1066643925922708, \ 0.4161413788054121, \ 0.4161413788054121, \ 0.1677172423891756, \ 0.0803046477884383, \ 0.8393907044231230, \ 0.0803046477884388, \ 0.2870421965934966, \ 0.6822271986792305, \ 0.0307306047272730, \ 0.6822271986792305, \ 0.2870421965934966, \ 0.0307306047272727, \ 0.3450878417155684, \ 0.5257595182209819, \ 0.1291526400634497, \ 0.5257595182209819, \ 0.3450878417155684, \ 0.1291526400634496, \ 0.2334004066698710, \ 0.5331991866602577, \ 0.2334004066698712, \ 0.3759301570486618, \ 0.5960363568560882, \ 0.0280334860952500, \ 0.5960363568560882, \ 0.3759301570486618, \ 0.0280334860952499, \ 0.3011654651665091, \ 0.3976690696669817, \ 0.3011654651665091, \ 0.1747799663549000, \ 0.6504400672901998, \ 0.1747799663549002, \ 0.3169455889331320, \ 0.4739234899291993, \ 0.2091309211376687, \ 0.4739234899291992, \ 0.3169455889331320, \ 0.2091309211376686, \ 0.4072283930427198, \ 0.5267326941075414, \ 0.0660389128497386, \ 0.5267326941075414, \ 0.4072283930427199, \ 0.0660389128497386, \ 0.2135535984578239, \ 0.7454158247229943, \ 0.0410305768191818, \ 0.7454158247229943, \ 0.2135535984578240, \ 0.0410305768191816, \ 0.3288528780688926, \ 0.6658474815593083, \ 0.0052996403717991, \ 0.6658474815593083, \ 0.3288528780688927, \ 0.0052996403717989, \ 0.4855650541851628, \ 0.4855650541851628, \ 0.0288698916296744, \ 0.1392953061421487, \ 0.7976306984429004, \ 0.0630739954149511, \ 0.7976306984429004, \ 0.1392953061421489, \ 0.0630739954149507, \ 0.0325715201801815, \ 0.9348569596396367, \ 0.0325715201801819, \ 0.2552462546969780, \ 0.5957908943647818, \ 0.1489628509382402, \ 0.5957908943647818, \ 0.2552462546969780, \ 0.1489628509382400, \ 0.2083760156003741, \ 0.6969269019664952, \ 0.0946970824331307, \ 0.6969269019664952, \ 0.2083760156003741, \ 0.0946970824331305, \ 0.4400105519462155, \ 0.5544087310385245, \ 0.0055807170152600, \ 0.5544087310385244, \ 0.4400105519462155, \ 0.0055807170152600, \ 0.1275709019046775, \ 0.7448581961906449, \ 0.1275709019046778, \ 0.3022209412278211, \ 0.6227021563389826, \ 0.0750769024331963, \ 0.6227021563389826, \ 0.3022209412278211, \ 0.0750769024331961, \ 0.0819468025835337, \ 0.9110706680920073, \ 0.0069825293244591, \ 0.9110706680920073, \ 0.0819468025835338, \ 0.0069825293244588, \ 0.0343649699121420, \ 0.9595414606840931, \ 0.0060935694037650, \ 0.9595414606840931, \ 0.0343649699121421, \ 0.0060935694037646, \ 0.0801120738471011, \ 0.8848535036252014, \ 0.0350344225276975, \ 0.8848535036252014, \ 0.0801120738471012, \ 0.0350344225276972, \ 0.0066392191809586, \ 0.9867215616380824, \ 0.0066392191809590, \ 0.1472134318989225, \ 0.8334345667830385, \ 0.0193520013180390, \ 0.8334345667830385, \ 0.1472134318989225, \ 0.0193520013180388, \ 0.2297196532578432, \ 0.7629478741931164, \ 0.0073324725490405, \ 0.7629478741931163, \ 0.2297196532578433, \ 0.0073324725490403, \ 0.1476555211198698, \ 0.8518541504366672, \ 0.0004903284434630, \ 0.8518541504366672, \ 0.1476555211198698, \ 0.0004903284434627 ] ) b = np.array ( [ \ 0.2385719576376257, \ 0.3807140211811872, \ 0.3807140211811873, \ 0.1066643925922709, \ 0.4466678037038647, \ 0.4466678037038648, \ 0.1677172423891757, \ 0.4161413788054122, \ 0.4161413788054124, \ 0.0803046477884386, \ 0.0803046477884383, \ 0.8393907044231231, \ 0.0307306047272729, \ 0.2870421965934966, \ 0.6822271986792307, \ 0.0307306047272729, \ 0.6822271986792307, \ 0.2870421965934968, \ 0.1291526400634497, \ 0.3450878417155684, \ 0.5257595182209820, \ 0.1291526400634497, \ 0.5257595182209820, \ 0.3450878417155686, \ 0.2334004066698712, \ 0.2334004066698711, \ 0.5331991866602579, \ 0.0280334860952500, \ 0.3759301570486618, \ 0.5960363568560885, \ 0.0280334860952500, \ 0.5960363568560882, \ 0.3759301570486621, \ 0.3011654651665093, \ 0.3011654651665092, \ 0.3976690696669818, \ 0.1747799663549002, \ 0.1747799663549000, \ 0.6504400672902000, \ 0.2091309211376688, \ 0.3169455889331320, \ 0.4739234899291995, \ 0.2091309211376688, \ 0.4739234899291995, \ 0.3169455889331322, \ 0.0660389128497387, \ 0.4072283930427200, \ 0.5267326941075416, \ 0.0660389128497387, \ 0.5267326941075415, \ 0.4072283930427201, \ 0.0410305768191818, \ 0.2135535984578240, \ 0.7454158247229945, \ 0.0410305768191818, \ 0.7454158247229945, \ 0.2135535984578242, \ 0.0052996403717990, \ 0.3288528780688927, \ 0.6658474815593085, \ 0.0052996403717990, \ 0.6658474815593083, \ 0.3288528780688930, \ 0.0288698916296745, \ 0.4855650541851628, \ 0.4855650541851630, \ 0.0630739954149509, \ 0.1392953061421487, \ 0.7976306984429004, \ 0.0630739954149509, \ 0.7976306984429004, \ 0.1392953061421490, \ 0.0325715201801818, \ 0.0325715201801814, \ 0.9348569596396370, \ 0.1489628509382402, \ 0.2552462546969780, \ 0.5957908943647819, \ 0.1489628509382402, \ 0.5957908943647819, \ 0.2552462546969783, \ 0.0946970824331307, \ 0.2083760156003741, \ 0.6969269019664954, \ 0.0946970824331307, \ 0.6969269019664954, \ 0.2083760156003744, \ 0.0055807170152601, \ 0.4400105519462155, \ 0.5544087310385247, \ 0.0055807170152601, \ 0.5544087310385245, \ 0.4400105519462157, \ 0.1275709019046777, \ 0.1275709019046775, \ 0.7448581961906449, \ 0.0750769024331962, \ 0.3022209412278212, \ 0.6227021563389828, \ 0.0750769024331962, \ 0.6227021563389828, \ 0.3022209412278213, \ 0.0069825293244590, \ 0.0819468025835337, \ 0.9110706680920074, \ 0.0069825293244590, \ 0.9110706680920074, \ 0.0819468025835340, \ 0.0060935694037648, \ 0.0343649699121420, \ 0.9595414606840932, \ 0.0060935694037648, \ 0.9595414606840934, \ 0.0343649699121423, \ 0.0350344225276974, \ 0.0801120738471011, \ 0.8848535036252017, \ 0.0350344225276974, \ 0.8848535036252017, \ 0.0801120738471014, \ 0.0066392191809589, \ 0.0066392191809586, \ 0.9867215616380827, \ 0.0193520013180390, \ 0.1472134318989225, \ 0.8334345667830388, \ 0.0193520013180390, \ 0.8334345667830388, \ 0.1472134318989227, \ 0.0073324725490405, \ 0.2297196532578432, \ 0.7629478741931165, \ 0.0073324725490405, \ 0.7629478741931164, \ 0.2297196532578435, \ 0.0004903284434630, \ 0.1476555211198698, \ 0.8518541504366673, \ 0.0004903284434630, \ 0.8518541504366673, \ 0.1476555211198702 ] ) c = np.array ( [ \ 0.3807140211811872, \ 0.2385719576376256, \ 0.3807140211811871, \ 0.4466678037038647, \ 0.1066643925922707, \ 0.4466678037038644, \ 0.4161413788054121, \ 0.1677172423891756, \ 0.4161413788054120, \ 0.8393907044231231, \ 0.0803046477884387, \ 0.0803046477884380, \ 0.6822271986792305, \ 0.0307306047272728, \ 0.2870421965934964, \ 0.2870421965934966, \ 0.0307306047272727, \ 0.6822271986792304, \ 0.5257595182209819, \ 0.1291526400634497, \ 0.3450878417155683, \ 0.3450878417155684, \ 0.1291526400634496, \ 0.5257595182209819, \ 0.5331991866602578, \ 0.2334004066698712, \ 0.2334004066698709, \ 0.5960363568560882, \ 0.0280334860952499, \ 0.3759301570486615, \ 0.3759301570486617, \ 0.0280334860952499, \ 0.5960363568560880, \ 0.3976690696669816, \ 0.3011654651665091, \ 0.3011654651665091, \ 0.6504400672901998, \ 0.1747799663549002, \ 0.1747799663548998, \ 0.4739234899291993, \ 0.2091309211376687, \ 0.3169455889331319, \ 0.3169455889331320, \ 0.2091309211376686, \ 0.4739234899291992, \ 0.5267326941075414, \ 0.0660389128497386, \ 0.4072283930427197, \ 0.4072283930427199, \ 0.0660389128497386, \ 0.5267326941075413, \ 0.7454158247229942, \ 0.0410305768191818, \ 0.2135535984578236, \ 0.2135535984578239, \ 0.0410305768191815, \ 0.7454158247229942, \ 0.6658474815593083, \ 0.0052996403717990, \ 0.3288528780688924, \ 0.3288528780688927, \ 0.0052996403717990, \ 0.6658474815593081, \ 0.4855650541851627, \ 0.0288698916296743, \ 0.4855650541851627, \ 0.7976306984429005, \ 0.0630739954149509, \ 0.1392953061421486, \ 0.1392953061421487, \ 0.0630739954149507, \ 0.7976306984429002, \ 0.9348569596396368, \ 0.0325715201801819, \ 0.0325715201801811, \ 0.5957908943647818, \ 0.1489628509382401, \ 0.2552462546969779, \ 0.2552462546969780, \ 0.1489628509382400, \ 0.5957908943647817, \ 0.6969269019664953, \ 0.0946970824331307, \ 0.2083760156003739, \ 0.2083760156003741, \ 0.0946970824331305, \ 0.6969269019664952, \ 0.5544087310385245, \ 0.0055807170152600, \ 0.4400105519462153, \ 0.4400105519462155, \ 0.0055807170152601, \ 0.5544087310385244, \ 0.7448581961906449, \ 0.1275709019046777, \ 0.1275709019046773, \ 0.6227021563389826, \ 0.0750769024331962, \ 0.3022209412278208, \ 0.3022209412278211, \ 0.0750769024331960, \ 0.6227021563389825, \ 0.9110706680920073, \ 0.0069825293244590, \ 0.0819468025835334, \ 0.0819468025835337, \ 0.0069825293244589, \ 0.9110706680920072, \ 0.9595414606840932, \ 0.0060935694037649, \ 0.0343649699121418, \ 0.0343649699121421, \ 0.0060935694037646, \ 0.9595414606840931, \ 0.8848535036252015, \ 0.0350344225276975, \ 0.0801120738471008, \ 0.0801120738471012, \ 0.0350344225276972, \ 0.8848535036252014, \ 0.9867215616380826, \ 0.0066392191809590, \ 0.0066392191809583, \ 0.8334345667830386, \ 0.0193520013180390, \ 0.1472134318989221, \ 0.1472134318989225, \ 0.0193520013180387, \ 0.8334345667830384, \ 0.7629478741931164, \ 0.0073324725490404, \ 0.2297196532578430, \ 0.2297196532578433, \ 0.0073324725490403, \ 0.7629478741931163, \ 0.8518541504366672, \ 0.0004903284434630, \ 0.1476555211198697, \ 0.1476555211198698, \ 0.0004903284434629, \ 0.8518541504366671 ] ) w = np.array ( [ \ 0.0095600849674599, \ 0.0095600849674599, \ 0.0095600849674599, \ 0.0094101598094542, \ 0.0094101598094542, \ 0.0094101598094542, \ 0.0120502270241504, \ 0.0120502270241504, \ 0.0120502270241504, \ 0.0052126218728019, \ 0.0052126218728019, \ 0.0052126218728019, \ 0.0055317948337667, \ 0.0055317948337667, \ 0.0055317948337667, \ 0.0055317948337667, \ 0.0055317948337667, \ 0.0055317948337667, \ 0.0125574362040365, \ 0.0125574362040365, \ 0.0125574362040365, \ 0.0125574362040365, \ 0.0125574362040365, \ 0.0125574362040365, \ 0.0134713153980494, \ 0.0134713153980494, \ 0.0134713153980494, \ 0.0063951526994544, \ 0.0063951526994544, \ 0.0063951526994544, \ 0.0063951526994544, \ 0.0063951526994544, \ 0.0063951526994544, \ 0.0157479657813627, \ 0.0157479657813627, \ 0.0157479657813627, \ 0.0112824425446984, \ 0.0112824425446984, \ 0.0112824425446984, \ 0.0137153932305508, \ 0.0137153932305508, \ 0.0137153932305508, \ 0.0137153932305508, \ 0.0137153932305508, \ 0.0137153932305508, \ 0.0098622701189896, \ 0.0098622701189896, \ 0.0098622701189896, \ 0.0098622701189896, \ 0.0098622701189896, \ 0.0098622701189896, \ 0.0064553729049297, \ 0.0064553729049297, \ 0.0064553729049297, \ 0.0064553729049297, \ 0.0064553729049297, \ 0.0064553729049297, \ 0.0029278263617991, \ 0.0029278263617991, \ 0.0029278263617991, \ 0.0029278263617991, \ 0.0029278263617991, \ 0.0029278263617991, \ 0.0071172374128746, \ 0.0071172374128746, \ 0.0071172374128746, \ 0.0071306353104870, \ 0.0071306353104870, \ 0.0071306353104870, \ 0.0071306353104870, \ 0.0071306353104870, \ 0.0071306353104870, \ 0.0027773395289542, \ 0.0027773395289542, \ 0.0027773395289542, \ 0.0123476631308614, \ 0.0123476631308614, \ 0.0123476631308614, \ 0.0123476631308614, \ 0.0123476631308614, \ 0.0123476631308614, \ 0.0106937005896163, \ 0.0106937005896163, \ 0.0106937005896163, \ 0.0106937005896163, \ 0.0106937005896163, \ 0.0106937005896163, \ 0.0032424675976393, \ 0.0032424675976393, \ 0.0032424675976393, \ 0.0032424675976393, \ 0.0032424675976393, \ 0.0032424675976393, \ 0.0097432449228177, \ 0.0097432449228177, \ 0.0097432449228177, \ 0.0109306110929133, \ 0.0109306110929133, \ 0.0109306110929133, \ 0.0109306110929133, \ 0.0109306110929133, \ 0.0109306110929133, \ 0.0020151231272897, \ 0.0020151231272897, \ 0.0020151231272897, \ 0.0020151231272897, \ 0.0020151231272897, \ 0.0020151231272897, \ 0.0011967736084732, \ 0.0011967736084732, \ 0.0011967736084732, \ 0.0011967736084732, \ 0.0011967736084732, \ 0.0011967736084732, \ 0.0043271580353607, \ 0.0043271580353607, \ 0.0043271580353607, \ 0.0043271580353607, \ 0.0043271580353607, \ 0.0043271580353607, \ 0.0005754424056705, \ 0.0005754424056705, \ 0.0005754424056705, \ 0.0046223871117811, \ 0.0046223871117811, \ 0.0046223871117811, \ 0.0046223871117811, \ 0.0046223871117811, \ 0.0046223871117811, \ 0.0033942537388070, \ 0.0033942537388070, \ 0.0033942537388070, \ 0.0033942537388070, \ 0.0033942537388070, \ 0.0033942537388070, \ 0.0008466061357639, \ 0.0008466061357639, \ 0.0008466061357639, \ 0.0008466061357639, \ 0.0008466061357639, \ 0.0008466061357639 ] ) return a, b, c, w def rule28 ( ): #*****************************************************************************80 # ## rule28() returns the rule of precision 28. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3039829225164841, \ 0.3920341549670316, \ 0.3039829225164841, \ 0.0455054005583464, \ 0.9329702140721974, \ 0.0215243853694563, \ 0.9329702140721974, \ 0.0455054005583465, \ 0.0215243853694558, \ 0.2133944547670873, \ 0.7375358758753532, \ 0.0490696693575595, \ 0.7375358758753532, \ 0.2133944547670873, \ 0.0490696693575593, \ 0.0048041261966579, \ 0.9903917476066839, \ 0.0048041261966584, \ 0.4582799042404119, \ 0.4582799042404120, \ 0.0834401915191761, \ 0.2421025119193196, \ 0.5802390377843101, \ 0.1776584502963703, \ 0.5802390377843101, \ 0.2421025119193198, \ 0.1776584502963702, \ 0.3862679735700421, \ 0.3862679735700420, \ 0.2274640528599158, \ 0.3271907320191700, \ 0.4829969116880932, \ 0.1898123562927368, \ 0.4829969116880932, \ 0.3271907320191700, \ 0.1898123562927368, \ 0.1419981669331742, \ 0.8535434510435363, \ 0.0044583820232894, \ 0.8535434510435365, \ 0.1419981669331742, \ 0.0044583820232890, \ 0.1753963931914617, \ 0.7369256303241862, \ 0.0876779764843521, \ 0.7369256303241862, \ 0.1753963931914618, \ 0.0876779764843519, \ 0.3921396133344145, \ 0.5446800590311748, \ 0.0631803276344107, \ 0.5446800590311748, \ 0.3921396133344145, \ 0.0631803276344106, \ 0.2582640721504621, \ 0.4834718556990756, \ 0.2582640721504622, \ 0.3341456150359213, \ 0.6617049208301551, \ 0.0041494641339236, \ 0.6617049208301550, \ 0.3341456150359213, \ 0.0041494641339235, \ 0.1741461960511821, \ 0.8030589990229017, \ 0.0227948049259163, \ 0.8030589990229016, \ 0.1741461960511822, \ 0.0227948049259160, \ 0.2758390080718242, \ 0.7014601475563789, \ 0.0227008443717971, \ 0.7014601475563788, \ 0.2758390080718242, \ 0.0227008443717968, \ 0.0262226671646523, \ 0.9676276842926838, \ 0.0061496485426642, \ 0.9676276842926838, \ 0.0262226671646523, \ 0.0061496485426637, \ 0.2430472023659261, \ 0.6449191682918028, \ 0.1120336293422710, \ 0.6449191682918028, \ 0.2430472023659263, \ 0.1120336293422708, \ 0.2299929840579072, \ 0.7652255261691058, \ 0.0047814897729871, \ 0.7652255261691057, \ 0.2299929840579072, \ 0.0047814897729869, \ 0.1058958441786275, \ 0.7882083116427446, \ 0.1058958441786279, \ 0.4295522021188993, \ 0.4295522021188993, \ 0.1408955957622013, \ 0.2956082808724017, \ 0.6419429769479655, \ 0.0624487421796328, \ 0.6419429769479654, \ 0.2956082808724017, \ 0.0624487421796327, \ 0.1213934507540912, \ 0.8283953633324806, \ 0.0502111859134282, \ 0.8283953633324806, \ 0.1213934507540914, \ 0.0502111859134279, \ 0.3738238003102096, \ 0.6004482009469115, \ 0.0257279987428787, \ 0.6004482009469116, \ 0.3738238003102097, \ 0.0257279987428786, \ 0.4427834065202436, \ 0.5515700274862902, \ 0.0056465659934661, \ 0.5515700274862904, \ 0.4427834065202436, \ 0.0056465659934661, \ 0.3377986632005823, \ 0.5441122670843226, \ 0.1180890697150950, \ 0.5441122670843226, \ 0.3377986632005823, \ 0.1180890697150949, \ 0.0922291891952822, \ 0.8895285197924230, \ 0.0182422910122948, \ 0.8895285197924231, \ 0.0922291891952822, \ 0.0182422910122945, \ 0.4848411325625894, \ 0.4848411325625895, \ 0.0303177348748211, \ 0.1586376888630596, \ 0.6827246222738805, \ 0.1586376888630599, \ 0.0608391923927586, \ 0.8783216152144825, \ 0.0608391923927590, \ 0.0702907404781327, \ 0.9285090039203800, \ 0.0012002556014873, \ 0.9285090039203802, \ 0.0702907404781328, \ 0.0012002556014869 ] ) b = np.array ( [ \ 0.3039829225164842, \ 0.3039829225164842, \ 0.3920341549670319, \ 0.0215243853694561, \ 0.0455054005583464, \ 0.9329702140721976, \ 0.0215243853694561, \ 0.9329702140721976, \ 0.0455054005583467, \ 0.0490696693575595, \ 0.2133944547670873, \ 0.7375358758753534, \ 0.0490696693575595, \ 0.7375358758753533, \ 0.2133944547670876, \ 0.0048041261966582, \ 0.0048041261966579, \ 0.9903917476066839, \ 0.0834401915191761, \ 0.4582799042404120, \ 0.4582799042404122, \ 0.1776584502963703, \ 0.2421025119193198, \ 0.5802390377843101, \ 0.1776584502963703, \ 0.5802390377843101, \ 0.2421025119193199, \ 0.2274640528599159, \ 0.3862679735700422, \ 0.3862679735700422, \ 0.1898123562927369, \ 0.3271907320191700, \ 0.4829969116880933, \ 0.1898123562927369, \ 0.4829969116880933, \ 0.3271907320191702, \ 0.0044583820232893, \ 0.1419981669331742, \ 0.8535434510435367, \ 0.0044583820232893, \ 0.8535434510435367, \ 0.1419981669331745, \ 0.0876779764843520, \ 0.1753963931914617, \ 0.7369256303241863, \ 0.0876779764843520, \ 0.7369256303241863, \ 0.1753963931914620, \ 0.0631803276344107, \ 0.3921396133344145, \ 0.5446800590311750, \ 0.0631803276344107, \ 0.5446800590311749, \ 0.3921396133344148, \ 0.2582640721504623, \ 0.2582640721504622, \ 0.4834718556990758, \ 0.0041494641339237, \ 0.3341456150359213, \ 0.6617049208301553, \ 0.0041494641339237, \ 0.6617049208301551, \ 0.3341456150359216, \ 0.0227948049259162, \ 0.1741461960511821, \ 0.8030589990229018, \ 0.0227948049259162, \ 0.8030589990229018, \ 0.1741461960511825, \ 0.0227008443717970, \ 0.2758390080718242, \ 0.7014601475563790, \ 0.0227008443717970, \ 0.7014601475563790, \ 0.2758390080718244, \ 0.0061496485426640, \ 0.0262226671646522, \ 0.9676276842926838, \ 0.0061496485426640, \ 0.9676276842926840, \ 0.0262226671646526, \ 0.1120336293422710, \ 0.2430472023659262, \ 0.6449191682918030, \ 0.1120336293422710, \ 0.6449191682918030, \ 0.2430472023659264, \ 0.0047814897729871, \ 0.2299929840579072, \ 0.7652255261691059, \ 0.0047814897729871, \ 0.7652255261691059, \ 0.2299929840579075, \ 0.1058958441786278, \ 0.1058958441786275, \ 0.7882083116427449, \ 0.1408955957622014, \ 0.4295522021188994, \ 0.4295522021188995, \ 0.0624487421796329, \ 0.2956082808724017, \ 0.6419429769479658, \ 0.0624487421796329, \ 0.6419429769479655, \ 0.2956082808724020, \ 0.0502111859134281, \ 0.1213934507540912, \ 0.8283953633324808, \ 0.0502111859134281, \ 0.8283953633324808, \ 0.1213934507540915, \ 0.0257279987428787, \ 0.3738238003102097, \ 0.6004482009469118, \ 0.0257279987428787, \ 0.6004482009469116, \ 0.3738238003102100, \ 0.0056465659934662, \ 0.4427834065202436, \ 0.5515700274862906, \ 0.0056465659934662, \ 0.5515700274862904, \ 0.4427834065202438, \ 0.1180890697150951, \ 0.3377986632005824, \ 0.5441122670843228, \ 0.1180890697150951, \ 0.5441122670843228, \ 0.3377986632005825, \ 0.0182422910122947, \ 0.0922291891952822, \ 0.8895285197924232, \ 0.0182422910122947, \ 0.8895285197924232, \ 0.0922291891952825, \ 0.0303177348748211, \ 0.4848411325625895, \ 0.4848411325625896, \ 0.1586376888630598, \ 0.1586376888630597, \ 0.6827246222738806, \ 0.0608391923927589, \ 0.0608391923927586, \ 0.8783216152144826, \ 0.0012002556014872, \ 0.0702907404781327, \ 0.9285090039203803, \ 0.0012002556014872, \ 0.9285090039203803, \ 0.0702907404781331 ] ) c = np.array ( [ \ 0.3920341549670317, \ 0.3039829225164841, \ 0.3039829225164841, \ 0.9329702140721975, \ 0.0215243853694563, \ 0.0455054005583461, \ 0.0455054005583465, \ 0.0215243853694559, \ 0.9329702140721975, \ 0.7375358758753532, \ 0.0490696693575595, \ 0.2133944547670871, \ 0.2133944547670873, \ 0.0490696693575593, \ 0.7375358758753531, \ 0.9903917476066840, \ 0.0048041261966582, \ 0.0048041261966577, \ 0.4582799042404119, \ 0.0834401915191760, \ 0.4582799042404118, \ 0.5802390377843101, \ 0.1776584502963702, \ 0.2421025119193196, \ 0.2421025119193196, \ 0.1776584502963702, \ 0.5802390377843100, \ 0.3862679735700420, \ 0.2274640528599158, \ 0.3862679735700420, \ 0.4829969116880931, \ 0.1898123562927367, \ 0.3271907320191699, \ 0.3271907320191699, \ 0.1898123562927367, \ 0.4829969116880931, \ 0.8535434510435365, \ 0.0044583820232895, \ 0.1419981669331739, \ 0.1419981669331742, \ 0.0044583820232891, \ 0.8535434510435363, \ 0.7369256303241862, \ 0.0876779764843520, \ 0.1753963931914616, \ 0.1753963931914617, \ 0.0876779764843519, \ 0.7369256303241862, \ 0.5446800590311749, \ 0.0631803276344107, \ 0.3921396133344143, \ 0.3921396133344145, \ 0.0631803276344106, \ 0.5446800590311747, \ 0.4834718556990756, \ 0.2582640721504622, \ 0.2582640721504620, \ 0.6617049208301550, \ 0.0041494641339236, \ 0.3341456150359210, \ 0.3341456150359213, \ 0.0041494641339236, \ 0.6617049208301549, \ 0.8030589990229017, \ 0.0227948049259162, \ 0.1741461960511819, \ 0.1741461960511822, \ 0.0227948049259160, \ 0.8030589990229016, \ 0.7014601475563788, \ 0.0227008443717970, \ 0.2758390080718239, \ 0.2758390080718242, \ 0.0227008443717968, \ 0.7014601475563786, \ 0.9676276842926838, \ 0.0061496485426640, \ 0.0262226671646520, \ 0.0262226671646523, \ 0.0061496485426636, \ 0.9676276842926838, \ 0.6449191682918028, \ 0.1120336293422710, \ 0.2430472023659260, \ 0.2430472023659262, \ 0.1120336293422708, \ 0.6449191682918027, \ 0.7652255261691058, \ 0.0047814897729870, \ 0.2299929840579069, \ 0.2299929840579072, \ 0.0047814897729869, \ 0.7652255261691057, \ 0.7882083116427447, \ 0.1058958441786279, \ 0.1058958441786272, \ 0.4295522021188993, \ 0.1408955957622013, \ 0.4295522021188992, \ 0.6419429769479654, \ 0.0624487421796328, \ 0.2956082808724014, \ 0.2956082808724017, \ 0.0624487421796328, \ 0.6419429769479653, \ 0.8283953633324806, \ 0.0502111859134282, \ 0.1213934507540910, \ 0.1213934507540912, \ 0.0502111859134279, \ 0.8283953633324806, \ 0.6004482009469115, \ 0.0257279987428788, \ 0.3738238003102096, \ 0.3738238003102096, \ 0.0257279987428787, \ 0.6004482009469114, \ 0.5515700274862902, \ 0.0056465659934662, \ 0.4427834065202433, \ 0.4427834065202435, \ 0.0056465659934660, \ 0.5515700274862902, \ 0.5441122670843227, \ 0.1180890697150950, \ 0.3377986632005822, \ 0.3377986632005823, \ 0.1180890697150949, \ 0.5441122670843226, \ 0.8895285197924231, \ 0.0182422910122948, \ 0.0922291891952820, \ 0.0922291891952822, \ 0.0182422910122946, \ 0.8895285197924230, \ 0.4848411325625894, \ 0.0303177348748210, \ 0.4848411325625892, \ 0.6827246222738805, \ 0.1586376888630598, \ 0.1586376888630595, \ 0.8783216152144825, \ 0.0608391923927590, \ 0.0608391923927584, \ 0.9285090039203800, \ 0.0012002556014872, \ 0.0702907404781324, \ 0.0702907404781327, \ 0.0012002556014870, \ 0.9285090039203799 ] ) w = np.array ( [ \ 0.0143624663006461, \ 0.0143624663006461, \ 0.0143624663006461, \ 0.0021175395576809, \ 0.0021175395576809, \ 0.0021175395576809, \ 0.0021175395576809, \ 0.0021175395576809, \ 0.0021175395576809, \ 0.0058956722345142, \ 0.0058956722345142, \ 0.0058956722345142, \ 0.0058956722345142, \ 0.0058956722345142, \ 0.0058956722345142, \ 0.0003111352086815, \ 0.0003111352086815, \ 0.0003111352086815, \ 0.0088517050108932, \ 0.0088517050108932, \ 0.0088517050108932, \ 0.0125572562166769, \ 0.0125572562166769, \ 0.0125572562166769, \ 0.0125572562166769, \ 0.0125572562166769, \ 0.0125572562166769, \ 0.0142105863904482, \ 0.0142105863904482, \ 0.0142105863904482, \ 0.0131061141240994, \ 0.0131061141240994, \ 0.0131061141240994, \ 0.0131061141240994, \ 0.0131061141240994, \ 0.0131061141240994, \ 0.0017788954192555, \ 0.0017788954192555, \ 0.0017788954192555, \ 0.0017788954192555, \ 0.0017788954192555, \ 0.0017788954192555, \ 0.0080119292866950, \ 0.0080119292866950, \ 0.0080119292866950, \ 0.0080119292866950, \ 0.0080119292866950, \ 0.0080119292866950, \ 0.0084646957342766, \ 0.0084646957342766, \ 0.0084646957342766, \ 0.0084646957342766, \ 0.0084646957342766, \ 0.0084646957342766, \ 0.0130927485890890, \ 0.0130927485890890, \ 0.0130927485890890, \ 0.0023767642676878, \ 0.0023767642676878, \ 0.0023767642676878, \ 0.0023767642676878, \ 0.0023767642676878, \ 0.0023767642676878, \ 0.0042769423350179, \ 0.0042769423350179, \ 0.0042769423350179, \ 0.0042769423350179, \ 0.0042769423350179, \ 0.0042769423350179, \ 0.0051312773820373, \ 0.0051312773820373, \ 0.0051312773820373, \ 0.0051312773820373, \ 0.0051312773820373, \ 0.0051312773820373, \ 0.0009485404258894, \ 0.0009485404258894, \ 0.0009485404258894, \ 0.0009485404258894, \ 0.0009485404258894, \ 0.0009485404258894, \ 0.0102459865617042, \ 0.0102459865617042, \ 0.0102459865617042, \ 0.0102459865617042, \ 0.0102459865617042, \ 0.0102459865617042, \ 0.0023245453644640, \ 0.0023245453644640, \ 0.0023245453644640, \ 0.0023245453644640, \ 0.0023245453644640, \ 0.0023245453644640, \ 0.0078099433710863, \ 0.0078099433710863, \ 0.0078099433710863, \ 0.0135475956033255, \ 0.0135475956033255, \ 0.0135475956033255, \ 0.0089251161402765, \ 0.0089251161402765, \ 0.0089251161402765, \ 0.0089251161402765, \ 0.0089251161402765, \ 0.0089251161402765, \ 0.0059178837723539, \ 0.0059178837723539, \ 0.0059178837723539, \ 0.0059178837723539, \ 0.0059178837723539, \ 0.0059178837723539, \ 0.0062605346429685, \ 0.0062605346429685, \ 0.0062605346429685, \ 0.0062605346429685, \ 0.0062605346429685, \ 0.0062605346429685, \ 0.0031401776434880, \ 0.0031401776434880, \ 0.0031401776434880, \ 0.0031401776434880, \ 0.0031401776434880, \ 0.0031401776434880, \ 0.0127871384229558, \ 0.0127871384229558, \ 0.0127871384229558, \ 0.0127871384229558, \ 0.0127871384229558, \ 0.0127871384229558, \ 0.0032049161907930, \ 0.0032049161907930, \ 0.0032049161907930, \ 0.0032049161907930, \ 0.0032049161907930, \ 0.0032049161907930, \ 0.0076821105785950, \ 0.0076821105785950, \ 0.0076821105785950, \ 0.0119426696402482, \ 0.0119426696402482, \ 0.0119426696402482, \ 0.0051282520046781, \ 0.0051282520046781, \ 0.0051282520046781, \ 0.0007251345949861, \ 0.0007251345949861, \ 0.0007251345949861, \ 0.0007251345949861, \ 0.0007251345949861, \ 0.0007251345949861 ] ) return a, b, c, w def rule29 ( ): #*****************************************************************************80 # ## rule29() returns the rule of precision 29. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.0589421088402292, \ 0.9383291479118497, \ 0.0027287432479212, \ 0.9383291479118497, \ 0.0589421088402293, \ 0.0027287432479208, \ 0.3497880100093318, \ 0.4930342901234747, \ 0.1571776998671934, \ 0.4930342901234748, \ 0.3497880100093319, \ 0.1571776998671934, \ 0.3230018235435502, \ 0.6748972098116223, \ 0.0021009666448276, \ 0.6748972098116223, \ 0.3230018235435501, \ 0.0021009666448274, \ 0.4989148246376862, \ 0.4989148246376862, \ 0.0021703507246276, \ 0.1581458542495161, \ 0.7736883369367373, \ 0.0681658088137465, \ 0.7736883369367374, \ 0.1581458542495162, \ 0.0681658088137463, \ 0.0295494682613534, \ 0.9596195731350373, \ 0.0108309586036096, \ 0.9596195731350373, \ 0.0295494682613534, \ 0.0108309586036091, \ 0.2918191734265371, \ 0.4892484845932904, \ 0.2189323419801725, \ 0.4892484845932904, \ 0.2918191734265371, \ 0.2189323419801724, \ 0.0755221785129958, \ 0.9031909252462709, \ 0.0212868962407334, \ 0.9031909252462710, \ 0.0755221785129958, \ 0.0212868962407330, \ 0.1171166695088989, \ 0.8420361139149987, \ 0.0408472165761026, \ 0.8420361139149987, \ 0.1171166695088989, \ 0.0408472165761022, \ 0.0111662181081692, \ 0.9872302853957871, \ 0.0016034964960439, \ 0.9872302853957869, \ 0.0111662181081692, \ 0.0016034964960435, \ 0.4343804267617306, \ 0.4343804267617307, \ 0.1312391464765387, \ 0.0410973356271179, \ 0.9178053287457638, \ 0.0410973356271184, \ 0.2080456492790871, \ 0.6904083654940788, \ 0.1015459852268340, \ 0.6904083654940788, \ 0.2080456492790871, \ 0.1015459852268338, \ 0.3922101149804348, \ 0.5662628237507425, \ 0.0415270612688227, \ 0.5662628237507424, \ 0.3922101149804348, \ 0.0415270612688226, \ 0.3597112755099758, \ 0.5464396833448917, \ 0.0938490411451324, \ 0.5464396833448917, \ 0.3597112755099759, \ 0.0938490411451323, \ 0.2458746994828754, \ 0.7454392707127403, \ 0.0086860298043842, \ 0.7454392707127405, \ 0.2458746994828755, \ 0.0086860298043840, \ 0.1670027381749231, \ 0.8154081377810313, \ 0.0175891240440457, \ 0.8154081377810313, \ 0.1670027381749231, \ 0.0175891240440454, \ 0.2084053051324008, \ 0.5831893897351982, \ 0.2084053051324009, \ 0.1150085986319464, \ 0.8794678768558409, \ 0.0055235245122127, \ 0.8794678768558410, \ 0.1150085986319465, \ 0.0055235245122124, \ 0.1607458844319635, \ 0.6785082311360726, \ 0.1607458844319638, \ 0.3153953981173191, \ 0.6607456749400253, \ 0.0238589269426557, \ 0.6607456749400252, \ 0.3153953981173192, \ 0.0238589269426554, \ 0.2232226502248206, \ 0.7364820152304076, \ 0.0402953345447719, \ 0.7364820152304076, \ 0.2232226502248207, \ 0.0402953345447716, \ 0.2883958599187324, \ 0.6437257357698205, \ 0.0678784043114471, \ 0.6437257357698205, \ 0.2883958599187324, \ 0.0678784043114470, \ 0.4884016029326027, \ 0.4884016029326027, \ 0.0231967941347945, \ 0.2673663502727756, \ 0.5930980425461417, \ 0.1395356071810827, \ 0.5930980425461417, \ 0.2673663502727755, \ 0.1395356071810825, \ 0.3023864112151284, \ 0.3952271775697430, \ 0.3023864112151284, \ 0.4057653952988916, \ 0.5861680189969418, \ 0.0080665857041666, \ 0.5861680189969418, \ 0.4057653952988916, \ 0.0080665857041665, \ 0.1144268129944254, \ 0.7711463740111488, \ 0.1144268129944257, \ 0.4647624310807389, \ 0.4647624310807389, \ 0.0704751378385221, \ 0.0737218813900997, \ 0.8525562372198003, \ 0.0737218813901001, \ 0.3906191787832637, \ 0.3906191787832638, \ 0.2187616424334725, \ 0.1863207276753595, \ 0.8135558255123531, \ 0.0001234468122875, \ 0.8135558255123529, \ 0.1863207276753596, \ 0.0001234468122872 ] ) b = np.array ( [ \ 0.0027287432479211, \ 0.0589421088402292, \ 0.9383291479118498, \ 0.0027287432479211, \ 0.9383291479118498, \ 0.0589421088402295, \ 0.1571776998671935, \ 0.3497880100093319, \ 0.4930342901234749, \ 0.1571776998671935, \ 0.4930342901234748, \ 0.3497880100093320, \ 0.0021009666448276, \ 0.3230018235435502, \ 0.6748972098116225, \ 0.0021009666448276, \ 0.6748972098116225, \ 0.3230018235435504, \ 0.0021703507246276, \ 0.4989148246376863, \ 0.4989148246376864, \ 0.0681658088137464, \ 0.1581458542495161, \ 0.7736883369367377, \ 0.0681658088137464, \ 0.7736883369367376, \ 0.1581458542495164, \ 0.0108309586036094, \ 0.0295494682613534, \ 0.9596195731350372, \ 0.0108309586036094, \ 0.9596195731350375, \ 0.0295494682613537, \ 0.2189323419801726, \ 0.2918191734265372, \ 0.4892484845932905, \ 0.2189323419801726, \ 0.4892484845932905, \ 0.2918191734265372, \ 0.0212868962407333, \ 0.0755221785129958, \ 0.9031909252462711, \ 0.0212868962407333, \ 0.9031909252462711, \ 0.0755221785129961, \ 0.0408472165761025, \ 0.1171166695088989, \ 0.8420361139149987, \ 0.0408472165761025, \ 0.8420361139149989, \ 0.1171166695088992, \ 0.0016034964960438, \ 0.0111662181081691, \ 0.9872302853957873, \ 0.0016034964960438, \ 0.9872302853957873, \ 0.0111662181081695, \ 0.1312391464765388, \ 0.4343804267617307, \ 0.4343804267617308, \ 0.0410973356271182, \ 0.0410973356271179, \ 0.9178053287457639, \ 0.1015459852268340, \ 0.2080456492790872, \ 0.6904083654940790, \ 0.1015459852268340, \ 0.6904083654940790, \ 0.2080456492790874, \ 0.0415270612688227, \ 0.3922101149804349, \ 0.5662628237507427, \ 0.0415270612688227, \ 0.5662628237507425, \ 0.3922101149804351, \ 0.0938490411451324, \ 0.3597112755099759, \ 0.5464396833448918, \ 0.0938490411451324, \ 0.5464396833448918, \ 0.3597112755099761, \ 0.0086860298043841, \ 0.2458746994828755, \ 0.7454392707127405, \ 0.0086860298043841, \ 0.7454392707127405, \ 0.2458746994828757, \ 0.0175891240440456, \ 0.1670027381749231, \ 0.8154081377810315, \ 0.0175891240440456, \ 0.8154081377810315, \ 0.1670027381749234, \ 0.2084053051324010, \ 0.2084053051324008, \ 0.5831893897351984, \ 0.0055235245122126, \ 0.1150085986319464, \ 0.8794678768558412, \ 0.0055235245122126, \ 0.8794678768558412, \ 0.1150085986319467, \ 0.1607458844319638, \ 0.1607458844319636, \ 0.6785082311360728, \ 0.0238589269426556, \ 0.3153953981173191, \ 0.6607456749400253, \ 0.0238589269426556, \ 0.6607456749400253, \ 0.3153953981173194, \ 0.0402953345447718, \ 0.2232226502248206, \ 0.7364820152304077, \ 0.0402953345447718, \ 0.7364820152304077, \ 0.2232226502248209, \ 0.0678784043114471, \ 0.2883958599187324, \ 0.6437257357698207, \ 0.0678784043114471, \ 0.6437257357698207, \ 0.2883958599187327, \ 0.0231967941347945, \ 0.4884016029326028, \ 0.4884016029326029, \ 0.1395356071810827, \ 0.2673663502727756, \ 0.5930980425461420, \ 0.1395356071810827, \ 0.5930980425461420, \ 0.2673663502727758, \ 0.3023864112151286, \ 0.3023864112151285, \ 0.3952271775697432, \ 0.0080665857041666, \ 0.4057653952988916, \ 0.5861680189969420, \ 0.0080665857041666, \ 0.5861680189969419, \ 0.4057653952988918, \ 0.1144268129944257, \ 0.1144268129944254, \ 0.7711463740111490, \ 0.0704751378385222, \ 0.4647624310807390, \ 0.4647624310807391, \ 0.0737218813901000, \ 0.0737218813900997, \ 0.8525562372198006, \ 0.2187616424334726, \ 0.3906191787832639, \ 0.3906191787832639, \ 0.0001234468122874, \ 0.1863207276753596, \ 0.8135558255123532, \ 0.0001234468122874, \ 0.8135558255123531, \ 0.1863207276753599 ] ) c = np.array ( [ \ 0.9383291479118497, \ 0.0027287432479211, \ 0.0589421088402289, \ 0.0589421088402292, \ 0.0027287432479208, \ 0.9383291479118496, \ 0.4930342901234747, \ 0.1571776998671933, \ 0.3497880100093317, \ 0.3497880100093317, \ 0.1571776998671933, \ 0.4930342901234746, \ 0.6748972098116224, \ 0.0021009666448276, \ 0.3230018235435500, \ 0.3230018235435502, \ 0.0021009666448274, \ 0.6748972098116222, \ 0.4989148246376862, \ 0.0021703507246275, \ 0.4989148246376860, \ 0.7736883369367374, \ 0.0681658088137465, \ 0.1581458542495159, \ 0.1581458542495161, \ 0.0681658088137462, \ 0.7736883369367373, \ 0.9596195731350372, \ 0.0108309586036093, \ 0.0295494682613533, \ 0.0295494682613533, \ 0.0108309586036092, \ 0.9596195731350372, \ 0.4892484845932904, \ 0.2189323419801724, \ 0.2918191734265370, \ 0.2918191734265371, \ 0.2189323419801725, \ 0.4892484845932903, \ 0.9031909252462710, \ 0.0212868962407334, \ 0.0755221785129956, \ 0.0755221785129958, \ 0.0212868962407331, \ 0.9031909252462709, \ 0.8420361139149987, \ 0.0408472165761025, \ 0.1171166695088987, \ 0.1171166695088989, \ 0.0408472165761021, \ 0.8420361139149986, \ 0.9872302853957871, \ 0.0016034964960438, \ 0.0111662181081689, \ 0.0111662181081693, \ 0.0016034964960435, \ 0.9872302853957871, \ 0.4343804267617306, \ 0.1312391464765387, \ 0.4343804267617306, \ 0.9178053287457638, \ 0.0410973356271183, \ 0.0410973356271177, \ 0.6904083654940788, \ 0.1015459852268340, \ 0.2080456492790870, \ 0.2080456492790872, \ 0.1015459852268338, \ 0.6904083654940787, \ 0.5662628237507424, \ 0.0415270612688226, \ 0.3922101149804347, \ 0.3922101149804349, \ 0.0415270612688227, \ 0.5662628237507423, \ 0.5464396833448917, \ 0.0938490411451324, \ 0.3597112755099757, \ 0.3597112755099759, \ 0.0938490411451324, \ 0.5464396833448915, \ 0.7454392707127404, \ 0.0086860298043842, \ 0.2458746994828752, \ 0.2458746994828754, \ 0.0086860298043839, \ 0.7454392707127404, \ 0.8154081377810312, \ 0.0175891240440456, \ 0.1670027381749228, \ 0.1670027381749231, \ 0.0175891240440454, \ 0.8154081377810313, \ 0.5831893897351982, \ 0.2084053051324010, \ 0.2084053051324007, \ 0.8794678768558409, \ 0.0055235245122126, \ 0.1150085986319461, \ 0.1150085986319464, \ 0.0055235245122124, \ 0.8794678768558408, \ 0.6785082311360726, \ 0.1607458844319638, \ 0.1607458844319634, \ 0.6607456749400252, \ 0.0238589269426556, \ 0.3153953981173190, \ 0.3153953981173191, \ 0.0238589269426555, \ 0.6607456749400251, \ 0.7364820152304076, \ 0.0402953345447718, \ 0.2232226502248205, \ 0.2232226502248206, \ 0.0402953345447716, \ 0.7364820152304075, \ 0.6437257357698205, \ 0.0678784043114471, \ 0.2883958599187322, \ 0.2883958599187324, \ 0.0678784043114469, \ 0.6437257357698203, \ 0.4884016029326028, \ 0.0231967941347945, \ 0.4884016029326026, \ 0.5930980425461418, \ 0.1395356071810827, \ 0.2673663502727753, \ 0.2673663502727756, \ 0.1395356071810826, \ 0.5930980425461417, \ 0.3952271775697430, \ 0.3023864112151285, \ 0.3023864112151284, \ 0.5861680189969418, \ 0.0080665857041666, \ 0.4057653952988913, \ 0.4057653952988916, \ 0.0080665857041665, \ 0.5861680189969416, \ 0.7711463740111488, \ 0.1144268129944257, \ 0.1144268129944253, \ 0.4647624310807389, \ 0.0704751378385221, \ 0.4647624310807388, \ 0.8525562372198005, \ 0.0737218813901000, \ 0.0737218813900994, \ 0.3906191787832637, \ 0.2187616424334723, \ 0.3906191787832637, \ 0.8135558255123531, \ 0.0001234468122874, \ 0.1863207276753593, \ 0.1863207276753596, \ 0.0001234468122874, \ 0.8135558255123528 ] ) w = np.array ( [ \ 0.0007692529714762, \ 0.0007692529714762, \ 0.0007692529714762, \ 0.0007692529714762, \ 0.0007692529714762, \ 0.0007692529714762, \ 0.0104522146969224, \ 0.0104522146969224, \ 0.0104522146969224, \ 0.0104522146969224, \ 0.0104522146969224, \ 0.0104522146969224, \ 0.0013528239492524, \ 0.0013528239492524, \ 0.0013528239492524, \ 0.0013528239492524, \ 0.0013528239492524, \ 0.0013528239492524, \ 0.0015164621031569, \ 0.0015164621031569, \ 0.0015164621031569, \ 0.0064391367075338, \ 0.0064391367075338, \ 0.0064391367075338, \ 0.0064391367075338, \ 0.0064391367075338, \ 0.0064391367075338, \ 0.0012721944371716, \ 0.0012721944371716, \ 0.0012721944371716, \ 0.0012721944371716, \ 0.0012721944371716, \ 0.0012721944371716, \ 0.0135452465720076, \ 0.0135452465720076, \ 0.0135452465720076, \ 0.0135452465720076, \ 0.0135452465720076, \ 0.0135452465720076, \ 0.0027615307495904, \ 0.0027615307495904, \ 0.0027615307495904, \ 0.0027615307495904, \ 0.0027615307495904, \ 0.0027615307495904, \ 0.0045126868454873, \ 0.0045126868454873, \ 0.0045126868454873, \ 0.0045126868454873, \ 0.0045126868454873, \ 0.0045126868454873, \ 0.0002694922318587, \ 0.0002694922318587, \ 0.0002694922318587, \ 0.0002694922318587, \ 0.0002694922318587, \ 0.0002694922318587, \ 0.0111711002951679, \ 0.0111711002951679, \ 0.0111711002951679, \ 0.0028604915061569, \ 0.0028604915061569, \ 0.0028604915061569, \ 0.0093863306762837, \ 0.0093863306762837, \ 0.0093863306762837, \ 0.0093863306762837, \ 0.0093863306762837, \ 0.0093863306762837, \ 0.0078229184583065, \ 0.0078229184583065, \ 0.0078229184583065, \ 0.0078229184583065, \ 0.0078229184583065, \ 0.0078229184583065, \ 0.0106303963631966, \ 0.0106303963631966, \ 0.0106303963631966, \ 0.0106303963631966, \ 0.0106303963631966, \ 0.0106303963631966, \ 0.0030512388233452, \ 0.0030512388233452, \ 0.0030512388233452, \ 0.0030512388233452, \ 0.0030512388233452, \ 0.0030512388233452, \ 0.0038253666717300, \ 0.0038253666717300, \ 0.0038253666717300, \ 0.0038253666717300, \ 0.0038253666717300, \ 0.0038253666717300, \ 0.0125392034426232, \ 0.0125392034426232, \ 0.0125392034426232, \ 0.0017416952313017, \ 0.0017416952313017, \ 0.0017416952313017, \ 0.0017416952313017, \ 0.0017416952313017, \ 0.0017416952313017, \ 0.0105714178582276, \ 0.0105714178582276, \ 0.0105714178582276, \ 0.0056691534816655, \ 0.0056691534816655, \ 0.0056691534816655, \ 0.0056691534816655, \ 0.0056691534816655, \ 0.0056691534816655, \ 0.0065819977638522, \ 0.0065819977638522, \ 0.0065819977638522, \ 0.0065819977638522, \ 0.0065819977638522, \ 0.0065819977638522, \ 0.0091789241649276, \ 0.0091789241649276, \ 0.0091789241649276, \ 0.0091789241649276, \ 0.0091789241649276, \ 0.0091789241649276, \ 0.0061344011647189, \ 0.0061344011647189, \ 0.0061344011647189, \ 0.0125183664988344, \ 0.0125183664988344, \ 0.0125183664988344, \ 0.0125183664988344, \ 0.0125183664988344, \ 0.0125183664988344, \ 0.0163102388077432, \ 0.0163102388077432, \ 0.0163102388077432, \ 0.0036413404112807, \ 0.0036413404112807, \ 0.0036413404112807, \ 0.0036413404112807, \ 0.0036413404112807, \ 0.0036413404112807, \ 0.0081728784412271, \ 0.0081728784412271, \ 0.0081728784412271, \ 0.0103131166352585, \ 0.0103131166352585, \ 0.0103131166352585, \ 0.0056088471328313, \ 0.0056088471328313, \ 0.0056088471328313, \ 0.0159132152840889, \ 0.0159132152840889, \ 0.0159132152840889, \ 0.0006886726250418, \ 0.0006886726250418, \ 0.0006886726250418, \ 0.0006886726250418, \ 0.0006886726250418, \ 0.0006886726250418 ] ) return a, b, c, w def rule30 ( ): #*****************************************************************************80 # ## rule30() returns the rule of precision 30. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.2590538845210674, \ 0.6931109923381602, \ 0.0478351231407726, \ 0.6931109923381601, \ 0.2590538845210674, \ 0.0478351231407724, \ 0.0033187249366444, \ 0.9933625501267108, \ 0.0033187249366448, \ 0.3915721882912563, \ 0.5287682847771430, \ 0.0796595269316006, \ 0.5287682847771430, \ 0.3915721882912564, \ 0.0796595269316005, \ 0.3561402832962335, \ 0.5861663154298922, \ 0.0576934012738742, \ 0.5861663154298922, \ 0.3561402832962335, \ 0.0576934012738741, \ 0.0723724072246778, \ 0.8552551855506439, \ 0.0723724072246782, \ 0.2830124973495888, \ 0.6397260650735270, \ 0.0772614375768841, \ 0.6397260650735271, \ 0.2830124973495887, \ 0.0772614375768839, \ 0.0471579102421718, \ 0.9056841795156562, \ 0.0471579102421721, \ 0.2416137624515244, \ 0.7356278532534756, \ 0.0227583842950001, \ 0.7356278532534756, \ 0.2416137624515244, \ 0.0227583842949999, \ 0.2527812471879329, \ 0.6234067740413924, \ 0.1238119787706746, \ 0.6234067740413924, \ 0.2527812471879329, \ 0.1238119787706745, \ 0.1849061063839171, \ 0.6992119263799822, \ 0.1158819672361006, \ 0.6992119263799822, \ 0.1849061063839172, \ 0.1158819672361004, \ 0.4680301736511254, \ 0.4680301736511254, \ 0.0639396526977491, \ 0.0126866046744676, \ 0.9746267906510645, \ 0.0126866046744680, \ 0.1937043771536401, \ 0.7397781780644782, \ 0.0665174447818817, \ 0.7397781780644782, \ 0.1937043771536401, \ 0.0665174447818814, \ 0.0764012484393875, \ 0.9191599701835511, \ 0.0044387813770616, \ 0.9191599701835510, \ 0.0764012484393877, \ 0.0044387813770611, \ 0.1215915082227279, \ 0.7568169835545440, \ 0.1215915082227282, \ 0.2090480874526896, \ 0.7862883331546218, \ 0.0046635793926887, \ 0.7862883331546218, \ 0.2090480874526897, \ 0.0046635793926884, \ 0.2985429940592427, \ 0.6967533241762803, \ 0.0047036817644771, \ 0.6967533241762803, \ 0.2985429940592427, \ 0.0047036817644769, \ 0.3343790400340311, \ 0.6404388932621004, \ 0.0251820667038687, \ 0.6404388932621002, \ 0.3343790400340311, \ 0.0251820667038686, \ 0.1232308023806951, \ 0.8109926237945619, \ 0.0657765738247430, \ 0.8109926237945619, \ 0.1232308023806952, \ 0.0657765738247426, \ 0.3385141624298457, \ 0.5353617425851648, \ 0.1261240949849894, \ 0.5353617425851648, \ 0.3385141624298457, \ 0.1261240949849893, \ 0.3544036021806874, \ 0.4507254468957941, \ 0.1948709509235184, \ 0.4507254468957941, \ 0.3544036021806874, \ 0.1948709509235184, \ 0.2630682977578083, \ 0.5459302776699086, \ 0.1910014245722831, \ 0.5459302776699086, \ 0.2630682977578084, \ 0.1910014245722829, \ 0.1824095615174529, \ 0.6351808769650940, \ 0.1824095615174532, \ 0.4345661739646696, \ 0.5379004199107804, \ 0.0275334061245499, \ 0.5379004199107805, \ 0.4345661739646697, \ 0.0275334061245498, \ 0.1640709870698783, \ 0.8078650909487486, \ 0.0280639219813731, \ 0.8078650909487487, \ 0.1640709870698785, \ 0.0280639219813727, \ 0.3622872793529498, \ 0.3622872793529498, \ 0.2754254412941003, \ 0.0426819997060804, \ 0.9414155840249848, \ 0.0159024162689350, \ 0.9414155840249848, \ 0.0426819997060806, \ 0.0159024162689344, \ 0.0939597946527299, \ 0.8787459746951742, \ 0.0272942306520959, \ 0.8787459746951743, \ 0.0939597946527300, \ 0.0272942306520955, \ 0.1354088535199345, \ 0.8588999350346495, \ 0.0056912114454161, \ 0.8588999350346495, \ 0.1354088535199345, \ 0.0056912114454159, \ 0.4367432485484602, \ 0.4367432485484602, \ 0.1265135029030796, \ 0.2724280407839282, \ 0.4551439184321434, \ 0.2724280407839283, \ 0.3962215147396591, \ 0.5986161382437196, \ 0.0051623470166213, \ 0.5986161382437196, \ 0.3962215147396591, \ 0.0051623470166212, \ 0.4973193390003086, \ 0.4973193390003087, \ 0.0053613219993828, \ 0.0294840425976739, \ 0.9699822487416315, \ 0.0005337086606946, \ 0.9699822487416316, \ 0.0294840425976741, \ 0.0005337086606942 ] ) b = np.array ( [ \ 0.0478351231407726, \ 0.2590538845210673, \ 0.6931109923381603, \ 0.0478351231407726, \ 0.6931109923381602, \ 0.2590538845210676, \ 0.0033187249366447, \ 0.0033187249366444, \ 0.9933625501267112, \ 0.0796595269316007, \ 0.3915721882912564, \ 0.5287682847771432, \ 0.0796595269316007, \ 0.5287682847771431, \ 0.3915721882912566, \ 0.0576934012738742, \ 0.3561402832962335, \ 0.5861663154298924, \ 0.0576934012738742, \ 0.5861663154298923, \ 0.3561402832962338, \ 0.0723724072246781, \ 0.0723724072246778, \ 0.8552551855506442, \ 0.0772614375768841, \ 0.2830124973495888, \ 0.6397260650735274, \ 0.0772614375768841, \ 0.6397260650735274, \ 0.2830124973495890, \ 0.0471579102421721, \ 0.0471579102421717, \ 0.9056841795156564, \ 0.0227583842950001, \ 0.2416137624515244, \ 0.7356278532534757, \ 0.0227583842950001, \ 0.7356278532534757, \ 0.2416137624515247, \ 0.1238119787706747, \ 0.2527812471879330, \ 0.6234067740413927, \ 0.1238119787706747, \ 0.6234067740413927, \ 0.2527812471879332, \ 0.1158819672361006, \ 0.1849061063839172, \ 0.6992119263799824, \ 0.1158819672361006, \ 0.6992119263799824, \ 0.1849061063839174, \ 0.0639396526977492, \ 0.4680301736511254, \ 0.4680301736511256, \ 0.0126866046744679, \ 0.0126866046744676, \ 0.9746267906510646, \ 0.0665174447818816, \ 0.1937043771536401, \ 0.7397781780644784, \ 0.0665174447818816, \ 0.7397781780644784, \ 0.1937043771536404, \ 0.0044387813770614, \ 0.0764012484393875, \ 0.9191599701835511, \ 0.0044387813770614, \ 0.9191599701835511, \ 0.0764012484393879, \ 0.1215915082227282, \ 0.1215915082227279, \ 0.7568169835545441, \ 0.0046635793926886, \ 0.2090480874526896, \ 0.7862883331546219, \ 0.0046635793926886, \ 0.7862883331546219, \ 0.2090480874526899, \ 0.0047036817644770, \ 0.2985429940592426, \ 0.6967533241762806, \ 0.0047036817644770, \ 0.6967533241762803, \ 0.2985429940592429, \ 0.0251820667038687, \ 0.3343790400340311, \ 0.6404388932621005, \ 0.0251820667038687, \ 0.6404388932621004, \ 0.3343790400340313, \ 0.0657765738247429, \ 0.1232308023806951, \ 0.8109926237945622, \ 0.0657765738247429, \ 0.8109926237945622, \ 0.1232308023806954, \ 0.1261240949849895, \ 0.3385141624298458, \ 0.5353617425851650, \ 0.1261240949849895, \ 0.5353617425851650, \ 0.3385141624298459, \ 0.1948709509235185, \ 0.3544036021806876, \ 0.4507254468957942, \ 0.1948709509235185, \ 0.4507254468957941, \ 0.3544036021806876, \ 0.1910014245722831, \ 0.2630682977578084, \ 0.5459302776699086, \ 0.1910014245722831, \ 0.5459302776699086, \ 0.2630682977578085, \ 0.1824095615174531, \ 0.1824095615174529, \ 0.6351808769650941, \ 0.0275334061245499, \ 0.4345661739646697, \ 0.5379004199107807, \ 0.0275334061245499, \ 0.5379004199107805, \ 0.4345661739646698, \ 0.0280639219813730, \ 0.1640709870698784, \ 0.8078650909487487, \ 0.0280639219813730, \ 0.8078650909487487, \ 0.1640709870698787, \ 0.2754254412941004, \ 0.3622872793529499, \ 0.3622872793529500, \ 0.0159024162689347, \ 0.0426819997060803, \ 0.9414155840249849, \ 0.0159024162689347, \ 0.9414155840249849, \ 0.0426819997060808, \ 0.0272942306520958, \ 0.0939597946527299, \ 0.8787459746951745, \ 0.0272942306520958, \ 0.8787459746951745, \ 0.0939597946527302, \ 0.0056912114454161, \ 0.1354088535199344, \ 0.8588999350346497, \ 0.0056912114454161, \ 0.8588999350346497, \ 0.1354088535199348, \ 0.1265135029030796, \ 0.4367432485484603, \ 0.4367432485484604, \ 0.2724280407839283, \ 0.2724280407839283, \ 0.4551439184321436, \ 0.0051623470166213, \ 0.3962215147396591, \ 0.5986161382437198, \ 0.0051623470166213, \ 0.5986161382437197, \ 0.3962215147396594, \ 0.0053613219993829, \ 0.4973193390003086, \ 0.4973193390003088, \ 0.0005337086606945, \ 0.0294840425976739, \ 0.9699822487416317, \ 0.0005337086606945, \ 0.9699822487416317, \ 0.0294840425976742 ] ) c = np.array ( [ \ 0.6931109923381601, \ 0.0478351231407725, \ 0.2590538845210671, \ 0.2590538845210673, \ 0.0478351231407724, \ 0.6931109923381600, \ 0.9933625501267110, \ 0.0033187249366448, \ 0.0033187249366441, \ 0.5287682847771430, \ 0.0796595269316006, \ 0.3915721882912562, \ 0.3915721882912563, \ 0.0796595269316005, \ 0.5287682847771429, \ 0.5861663154298923, \ 0.0576934012738743, \ 0.3561402832962334, \ 0.3561402832962336, \ 0.0576934012738742, \ 0.5861663154298921, \ 0.8552551855506441, \ 0.0723724072246782, \ 0.0723724072246775, \ 0.6397260650735271, \ 0.0772614375768842, \ 0.2830124973495886, \ 0.2830124973495887, \ 0.0772614375768840, \ 0.6397260650735271, \ 0.9056841795156562, \ 0.0471579102421721, \ 0.0471579102421714, \ 0.7356278532534755, \ 0.0227583842950000, \ 0.2416137624515242, \ 0.2416137624515244, \ 0.0227583842949999, \ 0.7356278532534755, \ 0.6234067740413924, \ 0.1238119787706746, \ 0.2527812471879327, \ 0.2527812471879329, \ 0.1238119787706744, \ 0.6234067740413923, \ 0.6992119263799823, \ 0.1158819672361006, \ 0.1849061063839169, \ 0.1849061063839172, \ 0.1158819672361003, \ 0.6992119263799823, \ 0.4680301736511254, \ 0.0639396526977491, \ 0.4680301736511252, \ 0.9746267906510645, \ 0.0126866046744679, \ 0.0126866046744674, \ 0.7397781780644782, \ 0.0665174447818817, \ 0.1937043771536399, \ 0.1937043771536402, \ 0.0665174447818814, \ 0.7397781780644782, \ 0.9191599701835511, \ 0.0044387813770613, \ 0.0764012484393873, \ 0.0764012484393876, \ 0.0044387813770612, \ 0.9191599701835510, \ 0.7568169835545440, \ 0.1215915082227281, \ 0.1215915082227278, \ 0.7862883331546218, \ 0.0046635793926886, \ 0.2090480874526894, \ 0.2090480874526896, \ 0.0046635793926885, \ 0.7862883331546215, \ 0.6967533241762803, \ 0.0047036817644771, \ 0.2985429940592425, \ 0.2985429940592426, \ 0.0047036817644769, \ 0.6967533241762802, \ 0.6404388932621002, \ 0.0251820667038686, \ 0.3343790400340308, \ 0.3343790400340311, \ 0.0251820667038686, \ 0.6404388932621001, \ 0.8109926237945619, \ 0.0657765738247430, \ 0.1232308023806948, \ 0.1232308023806952, \ 0.0657765738247427, \ 0.8109926237945619, \ 0.5353617425851648, \ 0.1261240949849894, \ 0.3385141624298456, \ 0.3385141624298458, \ 0.1261240949849892, \ 0.5353617425851648, \ 0.4507254468957941, \ 0.1948709509235184, \ 0.3544036021806874, \ 0.3544036021806874, \ 0.1948709509235184, \ 0.4507254468957940, \ 0.5459302776699086, \ 0.1910014245722830, \ 0.2630682977578083, \ 0.2630682977578082, \ 0.1910014245722830, \ 0.5459302776699084, \ 0.6351808769650941, \ 0.1824095615174531, \ 0.1824095615174527, \ 0.5379004199107805, \ 0.0275334061245499, \ 0.4345661739646695, \ 0.4345661739646696, \ 0.0275334061245497, \ 0.5379004199107804, \ 0.8078650909487487, \ 0.0280639219813731, \ 0.1640709870698781, \ 0.1640709870698783, \ 0.0280639219813729, \ 0.8078650909487486, \ 0.3622872793529498, \ 0.2754254412941003, \ 0.3622872793529497, \ 0.9414155840249848, \ 0.0159024162689349, \ 0.0426819997060801, \ 0.0426819997060805, \ 0.0159024162689345, \ 0.9414155840249848, \ 0.8787459746951743, \ 0.0272942306520959, \ 0.0939597946527296, \ 0.0939597946527299, \ 0.0272942306520956, \ 0.8787459746951742, \ 0.8588999350346495, \ 0.0056912114454161, \ 0.1354088535199341, \ 0.1354088535199345, \ 0.0056912114454158, \ 0.8588999350346493, \ 0.4367432485484603, \ 0.1265135029030796, \ 0.4367432485484601, \ 0.4551439184321435, \ 0.2724280407839283, \ 0.2724280407839281, \ 0.5986161382437196, \ 0.0051623470166213, \ 0.3962215147396588, \ 0.3962215147396591, \ 0.0051623470166212, \ 0.5986161382437194, \ 0.4973193390003086, \ 0.0053613219993827, \ 0.4973193390003083, \ 0.9699822487416316, \ 0.0005337086606946, \ 0.0294840425976736, \ 0.0294840425976739, \ 0.0005337086606941, \ 0.9699822487416315 ] ) w = np.array ( [ \ 0.0042147584639124, \ 0.0042147584639124, \ 0.0042147584639124, \ 0.0042147584639124, \ 0.0042147584639124, \ 0.0042147584639124, \ 0.0001717299013710, \ 0.0001717299013710, \ 0.0001717299013710, \ 0.0059249227450920, \ 0.0059249227450920, \ 0.0059249227450920, \ 0.0059249227450920, \ 0.0059249227450920, \ 0.0059249227450920, \ 0.0059442201844245, \ 0.0059442201844245, \ 0.0059442201844245, \ 0.0059442201844245, \ 0.0059442201844245, \ 0.0059442201844245, \ 0.0038019326684155, \ 0.0038019326684155, \ 0.0038019326684155, \ 0.0068771843875359, \ 0.0068771843875359, \ 0.0068771843875359, \ 0.0068771843875359, \ 0.0068771843875359, \ 0.0068771843875359, \ 0.0028444336676875, \ 0.0028444336676875, \ 0.0028444336676875, \ 0.0040924989683472, \ 0.0040924989683472, \ 0.0040924989683472, \ 0.0040924989683472, \ 0.0040924989683472, \ 0.0040924989683472, \ 0.0088726545060173, \ 0.0088726545060173, \ 0.0088726545060173, \ 0.0088726545060173, \ 0.0088726545060173, \ 0.0088726545060173, \ 0.0075343229295465, \ 0.0075343229295465, \ 0.0075343229295465, \ 0.0075343229295465, \ 0.0075343229295465, \ 0.0075343229295465, \ 0.0077841287323308, \ 0.0077841287323308, \ 0.0077841287323308, \ 0.0008465501453289, \ 0.0008465501453289, \ 0.0008465501453289, \ 0.0068040067561019, \ 0.0068040067561019, \ 0.0068040067561019, \ 0.0068040067561019, \ 0.0068040067561019, \ 0.0068040067561019, \ 0.0012066965685421, \ 0.0012066965685421, \ 0.0012066965685421, \ 0.0012066965685421, \ 0.0012066965685421, \ 0.0012066965685421, \ 0.0073869118349143, \ 0.0073869118349143, \ 0.0073869118349143, \ 0.0019589485778932, \ 0.0019589485778932, \ 0.0019589485778932, \ 0.0019589485778932, \ 0.0019589485778932, \ 0.0019589485778932, \ 0.0022744459009987, \ 0.0022744459009987, \ 0.0022744459009987, \ 0.0022744459009987, \ 0.0022744459009987, \ 0.0022744459009987, \ 0.0053646848461863, \ 0.0053646848461863, \ 0.0053646848461863, \ 0.0053646848461863, \ 0.0053646848461863, \ 0.0053646848461863, \ 0.0058700698030655, \ 0.0058700698030655, \ 0.0058700698030655, \ 0.0058700698030655, \ 0.0058700698030655, \ 0.0058700698030655, \ 0.0113030235429375, \ 0.0113030235429375, \ 0.0113030235429375, \ 0.0113030235429375, \ 0.0113030235429375, \ 0.0113030235429375, \ 0.0143164852696676, \ 0.0143164852696676, \ 0.0143164852696676, \ 0.0143164852696676, \ 0.0143164852696676, \ 0.0143164852696676, \ 0.0129260234501183, \ 0.0129260234501183, \ 0.0129260234501183, \ 0.0129260234501183, \ 0.0129260234501183, \ 0.0129260234501183, \ 0.0107528509654328, \ 0.0107528509654328, \ 0.0107528509654328, \ 0.0062815965808917, \ 0.0062815965808917, \ 0.0062815965808917, \ 0.0062815965808917, \ 0.0062815965808917, \ 0.0062815965808917, \ 0.0047019369941060, \ 0.0047019369941060, \ 0.0047019369941060, \ 0.0047019369941060, \ 0.0047019369941060, \ 0.0047019369941060, \ 0.0155960913258258, \ 0.0155960913258258, \ 0.0155960913258258, \ 0.0018305068761488, \ 0.0018305068761488, \ 0.0018305068761488, \ 0.0018305068761488, \ 0.0018305068761488, \ 0.0018305068761488, \ 0.0038218805470950, \ 0.0038218805470950, \ 0.0038218805470950, \ 0.0038218805470950, \ 0.0038218805470950, \ 0.0038218805470950, \ 0.0019198805574689, \ 0.0019198805574689, \ 0.0019198805574689, \ 0.0019198805574689, \ 0.0019198805574689, \ 0.0019198805574689, \ 0.0124049590281460, \ 0.0124049590281460, \ 0.0124049590281460, \ 0.0149145507626858, \ 0.0149145507626858, \ 0.0149145507626858, \ 0.0026425679231633, \ 0.0026425679231633, \ 0.0026425679231633, \ 0.0026425679231633, \ 0.0026425679231633, \ 0.0026425679231633, \ 0.0027913181197408, \ 0.0027913181197408, \ 0.0027913181197408, \ 0.0003356217114664, \ 0.0003356217114664, \ 0.0003356217114664, \ 0.0003356217114664, \ 0.0003356217114664, \ 0.0003356217114664 ] ) return a, b, c, w def rule31 ( ): #*****************************************************************************80 # ## rule31() returns the rule of precision 31. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3333333333333333, \ 0.4861524679130598, \ 0.4861524679130598, \ 0.0276950641738803, \ 0.1390906284720946, \ 0.7542396906638279, \ 0.1066696808640776, \ 0.7542396906638279, \ 0.1390906284720947, \ 0.1066696808640773, \ 0.4195880808642605, \ 0.4195880808642605, \ 0.1608238382714789, \ 0.1972331307896530, \ 0.7995057135466186, \ 0.0032611556637284, \ 0.7995057135466186, \ 0.1972331307896531, \ 0.0032611556637281, \ 0.2385241509843100, \ 0.7483360311752862, \ 0.0131398178404037, \ 0.7483360311752864, \ 0.2385241509843100, \ 0.0131398178404035, \ 0.0792067965066985, \ 0.8415864069866026, \ 0.0792067965066989, \ 0.0297507293859900, \ 0.9679050494853231, \ 0.0023442211286871, \ 0.9679050494853232, \ 0.0297507293859901, \ 0.0023442211286867, \ 0.0177313492497139, \ 0.9645373015005718, \ 0.0177313492497143, \ 0.3957839332968854, \ 0.6022546663332196, \ 0.0019614003698950, \ 0.6022546663332196, \ 0.3957839332968854, \ 0.0019614003698949, \ 0.3516800587760809, \ 0.4956833754486993, \ 0.1526365657752197, \ 0.4956833754486993, \ 0.3516800587760809, \ 0.1526365657752196, \ 0.2024821942617583, \ 0.6840925273907388, \ 0.1134252783475029, \ 0.6840925273907387, \ 0.2024821942617585, \ 0.1134252783475028, \ 0.4225539552222151, \ 0.5229246603331018, \ 0.0545213844446831, \ 0.5229246603331018, \ 0.4225539552222151, \ 0.0545213844446831, \ 0.1246805088474440, \ 0.8147145619917838, \ 0.0606049291607723, \ 0.8147145619917838, \ 0.1246805088474441, \ 0.0606049291607719, \ 0.2555462364028573, \ 0.7068648114396249, \ 0.0375889521575178, \ 0.7068648114396250, \ 0.2555462364028574, \ 0.0375889521575175, \ 0.0745031299353863, \ 0.9211105398945520, \ 0.0043863301700618, \ 0.9211105398945520, \ 0.0745031299353864, \ 0.0043863301700614, \ 0.4168072755236505, \ 0.5659193101514124, \ 0.0172734143249371, \ 0.5659193101514123, \ 0.4168072755236506, \ 0.0172734143249370, \ 0.1928717230061985, \ 0.7445502549794906, \ 0.0625780220143110, \ 0.7445502549794907, \ 0.1928717230061984, \ 0.0625780220143108, \ 0.0473478189395525, \ 0.9342442340291646, \ 0.0184079470312831, \ 0.9342442340291646, \ 0.0473478189395526, \ 0.0184079470312826, \ 0.2184364967909280, \ 0.5631270064181437, \ 0.2184364967909281, \ 0.1724507871838860, \ 0.6550984256322278, \ 0.1724507871838863, \ 0.0510951808223813, \ 0.8978096383552372, \ 0.0510951808223817, \ 0.3419050053475277, \ 0.6151917857097009, \ 0.0429032089427714, \ 0.6151917857097009, \ 0.3419050053475278, \ 0.0429032089427713, \ 0.3258139530575097, \ 0.6609969631634746, \ 0.0131890837790157, \ 0.6609969631634747, \ 0.3258139530575097, \ 0.0131890837790155, \ 0.2894259487571373, \ 0.7093771696121531, \ 0.0011968816307096, \ 0.7093771696121531, \ 0.2894259487571372, \ 0.0011968816307094, \ 0.2987897956760133, \ 0.4820774428938099, \ 0.2191327614301768, \ 0.4820774428938098, \ 0.2987897956760134, \ 0.2191327614301767, \ 0.2744757477427950, \ 0.6443943606878740, \ 0.0811298915693310, \ 0.6443943606878740, \ 0.2744757477427950, \ 0.0811298915693308, \ 0.3532298738914156, \ 0.5514920116265676, \ 0.0952781144820168, \ 0.5514920116265676, \ 0.3532298738914156, \ 0.0952781144820166, \ 0.4977486206264703, \ 0.4977486206264703, \ 0.0045027587470594, \ 0.2663678824750718, \ 0.5867434095228163, \ 0.1468887080021118, \ 0.5867434095228162, \ 0.2663678824750718, \ 0.1468887080021118, \ 0.3851684692456800, \ 0.3851684692456801, \ 0.2296630615086398, \ 0.2974914903679928, \ 0.4050170192640142, \ 0.2974914903679928, \ 0.0960481521010511, \ 0.8764212178203614, \ 0.0275306300785876, \ 0.8764212178203614, \ 0.0960481521010512, \ 0.0275306300785873, \ 0.0050828094627277, \ 0.9898343810745441, \ 0.0050828094627282, \ 0.1674078247783561, \ 0.8067170670017056, \ 0.0258751082199382, \ 0.8067170670017058, \ 0.1674078247783561, \ 0.0258751082199379, \ 0.4503409417390182, \ 0.4503409417390182, \ 0.0993181165219635, \ 0.1306776337702883, \ 0.8635250475449717, \ 0.0057973186847399, \ 0.8635250475449718, \ 0.1306776337702885, \ 0.0057973186847396 ] ) b = np.array ( [ \ 0.3333333333333334, \ 0.0276950641738804, \ 0.4861524679130599, \ 0.4861524679130600, \ 0.1066696808640776, \ 0.1390906284720946, \ 0.7542396906638279, \ 0.1066696808640776, \ 0.7542396906638279, \ 0.1390906284720949, \ 0.1608238382714791, \ 0.4195880808642605, \ 0.4195880808642607, \ 0.0032611556637283, \ 0.1972331307896530, \ 0.7995057135466188, \ 0.0032611556637283, \ 0.7995057135466188, \ 0.1972331307896533, \ 0.0131398178404037, \ 0.2385241509843100, \ 0.7483360311752866, \ 0.0131398178404037, \ 0.7483360311752866, \ 0.2385241509843103, \ 0.0792067965066988, \ 0.0792067965066985, \ 0.8415864069866028, \ 0.0023442211286869, \ 0.0297507293859899, \ 0.9679050494853232, \ 0.0023442211286869, \ 0.9679050494853232, \ 0.0297507293859903, \ 0.0177313492497142, \ 0.0177313492497139, \ 0.9645373015005720, \ 0.0019614003698950, \ 0.3957839332968854, \ 0.6022546663332198, \ 0.0019614003698950, \ 0.6022546663332197, \ 0.3957839332968856, \ 0.1526365657752198, \ 0.3516800587760810, \ 0.4956833754486996, \ 0.1526365657752198, \ 0.4956833754486994, \ 0.3516800587760812, \ 0.1134252783475029, \ 0.2024821942617584, \ 0.6840925273907389, \ 0.1134252783475029, \ 0.6840925273907389, \ 0.2024821942617586, \ 0.0545213844446831, \ 0.4225539552222151, \ 0.5229246603331020, \ 0.0545213844446831, \ 0.5229246603331019, \ 0.4225539552222153, \ 0.0606049291607722, \ 0.1246805088474439, \ 0.8147145619917839, \ 0.0606049291607722, \ 0.8147145619917839, \ 0.1246805088474443, \ 0.0375889521575178, \ 0.2555462364028573, \ 0.7068648114396252, \ 0.0375889521575178, \ 0.7068648114396251, \ 0.2555462364028576, \ 0.0043863301700617, \ 0.0745031299353863, \ 0.9211105398945522, \ 0.0043863301700617, \ 0.9211105398945522, \ 0.0745031299353866, \ 0.0172734143249371, \ 0.4168072755236506, \ 0.5659193101514125, \ 0.0172734143249371, \ 0.5659193101514124, \ 0.4168072755236508, \ 0.0625780220143109, \ 0.1928717230061985, \ 0.7445502549794908, \ 0.0625780220143109, \ 0.7445502549794908, \ 0.1928717230061987, \ 0.0184079470312829, \ 0.0473478189395524, \ 0.9342442340291647, \ 0.0184079470312829, \ 0.9342442340291647, \ 0.0473478189395528, \ 0.2184364967909282, \ 0.2184364967909281, \ 0.5631270064181439, \ 0.1724507871838862, \ 0.1724507871838861, \ 0.6550984256322279, \ 0.0510951808223816, \ 0.0510951808223813, \ 0.8978096383552373, \ 0.0429032089427714, \ 0.3419050053475277, \ 0.6151917857097011, \ 0.0429032089427714, \ 0.6151917857097009, \ 0.3419050053475279, \ 0.0131890837790157, \ 0.3258139530575097, \ 0.6609969631634748, \ 0.0131890837790157, \ 0.6609969631634748, \ 0.3258139530575100, \ 0.0011968816307096, \ 0.2894259487571373, \ 0.7093771696121534, \ 0.0011968816307096, \ 0.7093771696121534, \ 0.2894259487571375, \ 0.2191327614301768, \ 0.2987897956760134, \ 0.4820774428938099, \ 0.2191327614301768, \ 0.4820774428938099, \ 0.2987897956760135, \ 0.0811298915693310, \ 0.2744757477427950, \ 0.6443943606878743, \ 0.0811298915693310, \ 0.6443943606878741, \ 0.2744757477427952, \ 0.0952781144820168, \ 0.3532298738914157, \ 0.5514920116265677, \ 0.0952781144820168, \ 0.5514920116265677, \ 0.3532298738914159, \ 0.0045027587470595, \ 0.4977486206264704, \ 0.4977486206264705, \ 0.1468887080021119, \ 0.2663678824750718, \ 0.5867434095228166, \ 0.1468887080021119, \ 0.5867434095228163, \ 0.2663678824750720, \ 0.2296630615086399, \ 0.3851684692456802, \ 0.3851684692456802, \ 0.2974914903679930, \ 0.2974914903679929, \ 0.4050170192640143, \ 0.0275306300785875, \ 0.0960481521010511, \ 0.8764212178203615, \ 0.0275306300785875, \ 0.8764212178203615, \ 0.0960481521010514, \ 0.0050828094627280, \ 0.0050828094627277, \ 0.9898343810745442, \ 0.0258751082199382, \ 0.1674078247783561, \ 0.8067170670017060, \ 0.0258751082199382, \ 0.8067170670017060, \ 0.1674078247783564, \ 0.0993181165219637, \ 0.4503409417390183, \ 0.4503409417390184, \ 0.0057973186847398, \ 0.1306776337702883, \ 0.8635250475449719, \ 0.0057973186847398, \ 0.8635250475449719, \ 0.1306776337702887 ] ) c = np.array ( [ \ 0.3333333333333333, \ 0.4861524679130598, \ 0.0276950641738803, \ 0.4861524679130597, \ 0.7542396906638279, \ 0.1066696808640775, \ 0.1390906284720944, \ 0.1390906284720945, \ 0.1066696808640774, \ 0.7542396906638278, \ 0.4195880808642605, \ 0.1608238382714790, \ 0.4195880808642604, \ 0.7995057135466186, \ 0.0032611556637284, \ 0.1972331307896529, \ 0.1972331307896531, \ 0.0032611556637281, \ 0.7995057135466186, \ 0.7483360311752864, \ 0.0131398178404037, \ 0.2385241509843098, \ 0.2385241509843100, \ 0.0131398178404035, \ 0.7483360311752864, \ 0.8415864069866027, \ 0.0792067965066989, \ 0.0792067965066983, \ 0.9679050494853231, \ 0.0023442211286870, \ 0.0297507293859898, \ 0.0297507293859899, \ 0.0023442211286867, \ 0.9679050494853230, \ 0.9645373015005719, \ 0.0177313492497143, \ 0.0177313492497136, \ 0.6022546663332197, \ 0.0019614003698950, \ 0.3957839332968852, \ 0.3957839332968854, \ 0.0019614003698950, \ 0.6022546663332196, \ 0.4956833754486993, \ 0.1526365657752197, \ 0.3516800587760808, \ 0.3516800587760809, \ 0.1526365657752197, \ 0.4956833754486992, \ 0.6840925273907388, \ 0.1134252783475028, \ 0.2024821942617582, \ 0.2024821942617584, \ 0.1134252783475026, \ 0.6840925273907387, \ 0.5229246603331018, \ 0.0545213844446831, \ 0.4225539552222149, \ 0.4225539552222151, \ 0.0545213844446830, \ 0.5229246603331017, \ 0.8147145619917838, \ 0.0606049291607722, \ 0.1246805088474437, \ 0.1246805088474440, \ 0.0606049291607720, \ 0.8147145619917837, \ 0.7068648114396249, \ 0.0375889521575178, \ 0.2555462364028570, \ 0.2555462364028572, \ 0.0375889521575176, \ 0.7068648114396248, \ 0.9211105398945520, \ 0.0043863301700617, \ 0.0745031299353861, \ 0.0745031299353863, \ 0.0043863301700614, \ 0.9211105398945519, \ 0.5659193101514124, \ 0.0172734143249370, \ 0.4168072755236504, \ 0.4168072755236506, \ 0.0172734143249370, \ 0.5659193101514122, \ 0.7445502549794906, \ 0.0625780220143110, \ 0.1928717230061983, \ 0.1928717230061984, \ 0.0625780220143107, \ 0.7445502549794906, \ 0.9342442340291647, \ 0.0184079470312830, \ 0.0473478189395523, \ 0.0473478189395525, \ 0.0184079470312827, \ 0.9342442340291645, \ 0.5631270064181437, \ 0.2184364967909282, \ 0.2184364967909279, \ 0.6550984256322278, \ 0.1724507871838862, \ 0.1724507871838858, \ 0.8978096383552372, \ 0.0510951808223815, \ 0.0510951808223811, \ 0.6151917857097009, \ 0.0429032089427714, \ 0.3419050053475274, \ 0.3419050053475277, \ 0.0429032089427713, \ 0.6151917857097007, \ 0.6609969631634746, \ 0.0131890837790157, \ 0.3258139530575095, \ 0.3258139530575096, \ 0.0131890837790155, \ 0.6609969631634744, \ 0.7093771696121530, \ 0.0011968816307096, \ 0.2894259487571371, \ 0.2894259487571373, \ 0.0011968816307094, \ 0.7093771696121531, \ 0.4820774428938099, \ 0.2191327614301767, \ 0.2987897956760133, \ 0.2987897956760133, \ 0.2191327614301767, \ 0.4820774428938098, \ 0.6443943606878740, \ 0.0811298915693309, \ 0.2744757477427947, \ 0.2744757477427950, \ 0.0811298915693308, \ 0.6443943606878739, \ 0.5514920116265676, \ 0.0952781144820167, \ 0.3532298738914156, \ 0.3532298738914156, \ 0.0952781144820166, \ 0.5514920116265676, \ 0.4977486206264702, \ 0.0045027587470594, \ 0.4977486206264701, \ 0.5867434095228163, \ 0.1468887080021118, \ 0.2663678824750716, \ 0.2663678824750719, \ 0.1468887080021118, \ 0.5867434095228162, \ 0.3851684692456800, \ 0.2296630615086398, \ 0.3851684692456800, \ 0.4050170192640142, \ 0.2974914903679929, \ 0.2974914903679928, \ 0.8764212178203614, \ 0.0275306300785875, \ 0.0960481521010509, \ 0.0960481521010511, \ 0.0275306300785872, \ 0.8764212178203613, \ 0.9898343810745441, \ 0.0050828094627281, \ 0.0050828094627275, \ 0.8067170670017058, \ 0.0258751082199383, \ 0.1674078247783558, \ 0.1674078247783561, \ 0.0258751082199379, \ 0.8067170670017056, \ 0.4503409417390182, \ 0.0993181165219635, \ 0.4503409417390181, \ 0.8635250475449718, \ 0.0057973186847400, \ 0.1306776337702881, \ 0.1306776337702883, \ 0.0057973186847396, \ 0.8635250475449716 ] ) w = np.array ( [ \ 0.0083431208138864, \ 0.0040439883965194, \ 0.0040439883965194, \ 0.0040439883965194, \ 0.0058062932483637, \ 0.0058062932483637, \ 0.0058062932483637, \ 0.0058062932483637, \ 0.0058062932483637, \ 0.0058062932483637, \ 0.0088430826430883, \ 0.0088430826430883, \ 0.0088430826430883, \ 0.0012838516987697, \ 0.0012838516987697, \ 0.0012838516987697, \ 0.0012838516987697, \ 0.0012838516987697, \ 0.0012838516987697, \ 0.0028265142759277, \ 0.0028265142759277, \ 0.0028265142759277, \ 0.0028265142759277, \ 0.0028265142759277, \ 0.0028265142759277, \ 0.0042237298511032, \ 0.0042237298511032, \ 0.0042237298511032, \ 0.0005055090468723, \ 0.0005055090468723, \ 0.0005055090468723, \ 0.0005055090468723, \ 0.0005055090468723, \ 0.0005055090468723, \ 0.0009868661450271, \ 0.0009868661450271, \ 0.0009868661450271, \ 0.0013026954489735, \ 0.0013026954489735, \ 0.0013026954489735, \ 0.0013026954489735, \ 0.0013026954489735, \ 0.0013026954489735, \ 0.0101925794443413, \ 0.0101925794443413, \ 0.0101925794443413, \ 0.0101925794443413, \ 0.0101925794443413, \ 0.0101925794443413, \ 0.0078668704957381, \ 0.0078668704957381, \ 0.0078668704957381, \ 0.0078668704957381, \ 0.0078668704957381, \ 0.0078668704957381, \ 0.0071208092414188, \ 0.0071208092414188, \ 0.0071208092414188, \ 0.0071208092414188, \ 0.0071208092414188, \ 0.0071208092414188, \ 0.0049641144765077, \ 0.0049641144765077, \ 0.0049641144765077, \ 0.0049641144765077, \ 0.0049641144765077, \ 0.0049641144765077, \ 0.0054364374730136, \ 0.0054364374730136, \ 0.0054364374730136, \ 0.0054364374730136, \ 0.0054364374730136, \ 0.0054364374730136, \ 0.0011525829400843, \ 0.0011525829400843, \ 0.0011525829400843, \ 0.0011525829400843, \ 0.0011525829400843, \ 0.0011525829400843, \ 0.0041783326918215, \ 0.0041783326918215, \ 0.0041783326918215, \ 0.0041783326918215, \ 0.0041783326918215, \ 0.0041783326918215, \ 0.0063624230528669, \ 0.0063624230528669, \ 0.0063624230528669, \ 0.0063624230528669, \ 0.0063624230528669, \ 0.0063624230528669, \ 0.0018127692882839, \ 0.0018127692882839, \ 0.0018127692882839, \ 0.0018127692882839, \ 0.0018127692882839, \ 0.0018127692882839, \ 0.0112370035080132, \ 0.0112370035080132, \ 0.0112370035080132, \ 0.0095591959667284, \ 0.0095591959667284, \ 0.0095591959667284, \ 0.0032590866501858, \ 0.0032590866501858, \ 0.0032590866501858, \ 0.0066899592450456, \ 0.0066899592450456, \ 0.0066899592450456, \ 0.0066899592450456, \ 0.0066899592450456, \ 0.0066899592450456, \ 0.0036397134849474, \ 0.0036397134849474, \ 0.0036397134849474, \ 0.0036397134849474, \ 0.0036397134849474, \ 0.0036397134849474, \ 0.0009293703376931, \ 0.0009293703376931, \ 0.0009293703376931, \ 0.0009293703376931, \ 0.0009293703376931, \ 0.0009293703376931, \ 0.0128955867879842, \ 0.0128955867879842, \ 0.0128955867879842, \ 0.0128955867879842, \ 0.0128955867879842, \ 0.0128955867879842, \ 0.0084758977171366, \ 0.0084758977171366, \ 0.0084758977171366, \ 0.0084758977171366, \ 0.0084758977171366, \ 0.0084758977171366, \ 0.0096222755316967, \ 0.0096222755316967, \ 0.0096222755316967, \ 0.0096222755316967, \ 0.0096222755316967, \ 0.0096222755316967, \ 0.0023276606420564, \ 0.0023276606420564, \ 0.0023276606420564, \ 0.0115996690313856, \ 0.0115996690313856, \ 0.0115996690313856, \ 0.0115996690313856, \ 0.0115996690313856, \ 0.0115996690313856, \ 0.0137393951965683, \ 0.0137393951965683, \ 0.0137393951965683, \ 0.0123590405093469, \ 0.0123590405093469, \ 0.0123590405093469, \ 0.0036665867049268, \ 0.0036665867049268, \ 0.0036665867049268, \ 0.0036665867049268, \ 0.0036665867049268, \ 0.0036665867049268, \ 0.0003444013792726, \ 0.0003444013792726, \ 0.0003444013792726, \ 0.0044453379912524, \ 0.0044453379912524, \ 0.0044453379912524, \ 0.0044453379912524, \ 0.0044453379912524, \ 0.0044453379912524, \ 0.0104339772957806, \ 0.0104339772957806, \ 0.0104339772957806, \ 0.0018212527841225, \ 0.0018212527841225, \ 0.0018212527841225, \ 0.0018212527841225, \ 0.0018212527841225, \ 0.0018212527841225 ] ) return a, b, c, w def rule32 ( ): #*****************************************************************************80 # ## rule32() returns the rule of precision 32. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.0014574454623699, \ 0.9970851090752599, \ 0.0014574454623703, \ 0.2068316863159020, \ 0.6343003724550512, \ 0.1588679412290467, \ 0.6343003724550512, \ 0.2068316863159020, \ 0.1588679412290465, \ 0.4467614265331670, \ 0.5384721310359784, \ 0.0147664424308546, \ 0.5384721310359784, \ 0.4467614265331671, \ 0.0147664424308546, \ 0.4986508935788473, \ 0.4986508935788473, \ 0.0026982128423053, \ 0.2324662076463787, \ 0.7161026651133882, \ 0.0514311272402331, \ 0.7161026651133883, \ 0.2324662076463787, \ 0.0514311272402328, \ 0.1168349267069579, \ 0.8636053329284497, \ 0.0195597403645925, \ 0.8636053329284497, \ 0.1168349267069580, \ 0.0195597403645921, \ 0.3282405458449340, \ 0.6591408874049088, \ 0.0126185667501573, \ 0.6591408874049087, \ 0.3282405458449340, \ 0.0126185667501570, \ 0.2593509320031201, \ 0.7195869113212406, \ 0.0210621566756393, \ 0.7195869113212405, \ 0.2593509320031203, \ 0.0210621566756391, \ 0.1654639982373495, \ 0.7169924925083024, \ 0.1175435092543480, \ 0.7169924925083024, \ 0.1654639982373496, \ 0.1175435092543477, \ 0.3824649073809372, \ 0.5882362420785776, \ 0.0292988505404852, \ 0.5882362420785775, \ 0.3824649073809373, \ 0.0292988505404851, \ 0.3978170726467208, \ 0.5987401057010048, \ 0.0034428216522743, \ 0.5987401057010048, \ 0.3978170726467208, \ 0.0034428216522742, \ 0.4811681159958368, \ 0.4811681159958369, \ 0.0376637680083264, \ 0.3254174696466901, \ 0.5842122492084456, \ 0.0903702811448643, \ 0.5842122492084456, \ 0.3254174696466901, \ 0.0903702811448641, \ 0.4522857565116005, \ 0.4522857565116005, \ 0.0954284869767989, \ 0.1133391914876031, \ 0.8359631725856564, \ 0.0506976359267406, \ 0.8359631725856566, \ 0.1133391914876031, \ 0.0506976359267403, \ 0.3110416328276417, \ 0.6410138882567965, \ 0.0479444789155618, \ 0.6410138882567965, \ 0.3110416328276417, \ 0.0479444789155617, \ 0.2988371353889130, \ 0.6998862072308072, \ 0.0012766573802799, \ 0.6998862072308072, \ 0.2988371353889130, \ 0.0012766573802797, \ 0.3763287580479190, \ 0.3763287580479190, \ 0.2473424839041620, \ 0.1521122809437838, \ 0.8436251556411046, \ 0.0042625634151116, \ 0.8436251556411045, \ 0.1521122809437838, \ 0.0042625634151113, \ 0.0886617050339115, \ 0.9074857829773694, \ 0.0038525119887192, \ 0.9074857829773694, \ 0.0886617050339115, \ 0.0038525119887188, \ 0.2830182798495732, \ 0.4339634403008535, \ 0.2830182798495733, \ 0.3191525805930605, \ 0.4789472707744628, \ 0.2019001486324766, \ 0.4789472707744628, \ 0.3191525805930605, \ 0.2019001486324766, \ 0.4136797843254134, \ 0.4136797843254134, \ 0.1726404313491732, \ 0.1667556935821333, \ 0.7655339131965976, \ 0.0677103932212692, \ 0.7655339131965975, \ 0.1667556935821334, \ 0.0677103932212689, \ 0.0302691910404442, \ 0.9394616179191112, \ 0.0302691910404446, \ 0.0128101964801118, \ 0.9743796070397761, \ 0.0128101964801123, \ 0.2421379240194328, \ 0.6622896588699126, \ 0.0955724171106545, \ 0.6622896588699126, \ 0.2421379240194329, \ 0.0955724171106544, \ 0.2798617479978297, \ 0.5697673874287119, \ 0.1503708645734583, \ 0.5697673874287120, \ 0.2798617479978297, \ 0.1503708645734581, \ 0.0673984002072567, \ 0.9082517491081563, \ 0.0243498506845873, \ 0.9082517491081562, \ 0.0673984002072567, \ 0.0243498506845868, \ 0.3716879666934204, \ 0.4989241659396562, \ 0.1293878673669234, \ 0.4989241659396562, \ 0.3716879666934203, \ 0.1293878673669233, \ 0.4056281490658828, \ 0.5311444304776159, \ 0.0632274204565012, \ 0.5311444304776159, \ 0.4056281490658829, \ 0.0632274204565011, \ 0.3333333333333333, \ 0.0620106498262642, \ 0.8759787003474712, \ 0.0620106498262646, \ 0.2219801657374810, \ 0.7727532012417533, \ 0.0052666330207657, \ 0.7727532012417532, \ 0.2219801657374811, \ 0.0052666330207656, \ 0.1783256820378629, \ 0.7955154359824860, \ 0.0261588819796511, \ 0.7955154359824860, \ 0.1783256820378630, \ 0.0261588819796509, \ 0.0426221905914095, \ 0.9518230415381582, \ 0.0055547678704324, \ 0.9518230415381583, \ 0.0426221905914095, \ 0.0055547678704320, \ 0.2292779969280699, \ 0.5414440061438599, \ 0.2292779969280701, \ 0.1019588269002696, \ 0.7960823461994605, \ 0.1019588269002699, \ 0.0143443003792804, \ 0.9850326016003745, \ 0.0006230980203453, \ 0.9850326016003746, \ 0.0143443003792806, \ 0.0006230980203448 ] ) b = np.array ( [ \ 0.0014574454623702, \ 0.0014574454623698, \ 0.9970851090752600, \ 0.1588679412290467, \ 0.2068316863159021, \ 0.6343003724550514, \ 0.1588679412290467, \ 0.6343003724550514, \ 0.2068316863159023, \ 0.0147664424308547, \ 0.4467614265331671, \ 0.5384721310359786, \ 0.0147664424308547, \ 0.5384721310359784, \ 0.4467614265331673, \ 0.0026982128423054, \ 0.4986508935788474, \ 0.4986508935788476, \ 0.0514311272402331, \ 0.2324662076463787, \ 0.7161026651133885, \ 0.0514311272402331, \ 0.7161026651133884, \ 0.2324662076463790, \ 0.0195597403645924, \ 0.1168349267069579, \ 0.8636053329284498, \ 0.0195597403645924, \ 0.8636053329284498, \ 0.1168349267069583, \ 0.0126185667501572, \ 0.3282405458449341, \ 0.6591408874049089, \ 0.0126185667501572, \ 0.6591408874049089, \ 0.3282405458449343, \ 0.0210621566756392, \ 0.2593509320031202, \ 0.7195869113212408, \ 0.0210621566756392, \ 0.7195869113212406, \ 0.2593509320031205, \ 0.1175435092543480, \ 0.1654639982373496, \ 0.7169924925083025, \ 0.1175435092543480, \ 0.7169924925083027, \ 0.1654639982373498, \ 0.0292988505404852, \ 0.3824649073809372, \ 0.5882362420785777, \ 0.0292988505404852, \ 0.5882362420785776, \ 0.3824649073809375, \ 0.0034428216522744, \ 0.3978170726467209, \ 0.5987401057010050, \ 0.0034428216522744, \ 0.5987401057010049, \ 0.3978170726467211, \ 0.0376637680083265, \ 0.4811681159958368, \ 0.4811681159958370, \ 0.0903702811448643, \ 0.3254174696466902, \ 0.5842122492084457, \ 0.0903702811448643, \ 0.5842122492084457, \ 0.3254174696466903, \ 0.0954284869767990, \ 0.4522857565116006, \ 0.4522857565116007, \ 0.0506976359267405, \ 0.1133391914876030, \ 0.8359631725856566, \ 0.0506976359267405, \ 0.8359631725856566, \ 0.1133391914876034, \ 0.0479444789155618, \ 0.3110416328276418, \ 0.6410138882567966, \ 0.0479444789155618, \ 0.6410138882567966, \ 0.3110416328276420, \ 0.0012766573802798, \ 0.2988371353889130, \ 0.6998862072308073, \ 0.0012766573802798, \ 0.6998862072308073, \ 0.2988371353889133, \ 0.2473424839041621, \ 0.3763287580479191, \ 0.3763287580479191, \ 0.0042625634151116, \ 0.1521122809437838, \ 0.8436251556411049, \ 0.0042625634151116, \ 0.8436251556411049, \ 0.1521122809437842, \ 0.0038525119887191, \ 0.0886617050339115, \ 0.9074857829773696, \ 0.0038525119887191, \ 0.9074857829773696, \ 0.0886617050339118, \ 0.2830182798495733, \ 0.2830182798495732, \ 0.4339634403008537, \ 0.2019001486324767, \ 0.3191525805930606, \ 0.4789472707744629, \ 0.2019001486324767, \ 0.4789472707744629, \ 0.3191525805930607, \ 0.1726404313491733, \ 0.4136797843254134, \ 0.4136797843254136, \ 0.0677103932212692, \ 0.1667556935821333, \ 0.7655339131965977, \ 0.0677103932212692, \ 0.7655339131965977, \ 0.1667556935821336, \ 0.0302691910404445, \ 0.0302691910404442, \ 0.9394616179191115, \ 0.0128101964801121, \ 0.0128101964801118, \ 0.9743796070397761, \ 0.0955724171106545, \ 0.2421379240194328, \ 0.6622896588699130, \ 0.0955724171106545, \ 0.6622896588699128, \ 0.2421379240194330, \ 0.1503708645734583, \ 0.2798617479978298, \ 0.5697673874287121, \ 0.1503708645734583, \ 0.5697673874287121, \ 0.2798617479978299, \ 0.0243498506845871, \ 0.0673984002072566, \ 0.9082517491081563, \ 0.0243498506845871, \ 0.9082517491081563, \ 0.0673984002072569, \ 0.1293878673669234, \ 0.3716879666934204, \ 0.4989241659396564, \ 0.1293878673669234, \ 0.4989241659396564, \ 0.3716879666934205, \ 0.0632274204565012, \ 0.4056281490658829, \ 0.5311444304776161, \ 0.0632274204565012, \ 0.5311444304776159, \ 0.4056281490658831, \ 0.3333333333333334, \ 0.0620106498262645, \ 0.0620106498262642, \ 0.8759787003474714, \ 0.0052666330207658, \ 0.2219801657374810, \ 0.7727532012417535, \ 0.0052666330207658, \ 0.7727532012417533, \ 0.2219801657374814, \ 0.0261588819796510, \ 0.1783256820378630, \ 0.7955154359824862, \ 0.0261588819796510, \ 0.7955154359824862, \ 0.1783256820378632, \ 0.0055547678704322, \ 0.0426221905914095, \ 0.9518230415381584, \ 0.0055547678704322, \ 0.9518230415381584, \ 0.0426221905914099, \ 0.2292779969280701, \ 0.2292779969280700, \ 0.5414440061438600, \ 0.1019588269002698, \ 0.1019588269002696, \ 0.7960823461994607, \ 0.0006230980203451, \ 0.0143443003792804, \ 0.9850326016003745, \ 0.0006230980203451, \ 0.9850326016003745, \ 0.0143443003792807 ] ) c = np.array ( [ \ 0.9970851090752600, \ 0.0014574454623702, \ 0.0014574454623696, \ 0.6343003724550513, \ 0.1588679412290467, \ 0.2068316863159019, \ 0.2068316863159020, \ 0.1588679412290465, \ 0.6343003724550511, \ 0.5384721310359784, \ 0.0147664424308546, \ 0.4467614265331668, \ 0.4467614265331670, \ 0.0147664424308546, \ 0.5384721310359781, \ 0.4986508935788472, \ 0.0026982128423053, \ 0.4986508935788471, \ 0.7161026651133883, \ 0.0514311272402331, \ 0.2324662076463785, \ 0.2324662076463787, \ 0.0514311272402329, \ 0.7161026651133883, \ 0.8636053329284497, \ 0.0195597403645924, \ 0.1168349267069578, \ 0.1168349267069580, \ 0.0195597403645923, \ 0.8636053329284495, \ 0.6591408874049088, \ 0.0126185667501571, \ 0.3282405458449338, \ 0.3282405458449341, \ 0.0126185667501570, \ 0.6591408874049086, \ 0.7195869113212405, \ 0.0210621566756392, \ 0.2593509320031200, \ 0.2593509320031203, \ 0.0210621566756392, \ 0.7195869113212403, \ 0.7169924925083024, \ 0.1175435092543480, \ 0.1654639982373495, \ 0.1654639982373496, \ 0.1175435092543478, \ 0.7169924925083024, \ 0.5882362420785776, \ 0.0292988505404851, \ 0.3824649073809371, \ 0.3824649073809373, \ 0.0292988505404851, \ 0.5882362420785774, \ 0.5987401057010048, \ 0.0034428216522743, \ 0.3978170726467206, \ 0.3978170726467209, \ 0.0034428216522743, \ 0.5987401057010047, \ 0.4811681159958368, \ 0.0376637680083263, \ 0.4811681159958366, \ 0.5842122492084457, \ 0.0903702811448642, \ 0.3254174696466899, \ 0.3254174696466902, \ 0.0903702811448642, \ 0.5842122492084456, \ 0.4522857565116005, \ 0.0954284869767989, \ 0.4522857565116003, \ 0.8359631725856564, \ 0.0506976359267405, \ 0.1133391914876029, \ 0.1133391914876030, \ 0.0506976359267403, \ 0.8359631725856563, \ 0.6410138882567965, \ 0.0479444789155617, \ 0.3110416328276415, \ 0.3110416328276417, \ 0.0479444789155616, \ 0.6410138882567964, \ 0.6998862072308072, \ 0.0012766573802798, \ 0.2988371353889129, \ 0.2988371353889130, \ 0.0012766573802797, \ 0.6998862072308070, \ 0.3763287580479189, \ 0.2473424839041619, \ 0.3763287580479189, \ 0.8436251556411046, \ 0.0042625634151116, \ 0.1521122809437835, \ 0.1521122809437839, \ 0.0042625634151113, \ 0.8436251556411045, \ 0.9074857829773694, \ 0.0038525119887192, \ 0.0886617050339112, \ 0.0886617050339116, \ 0.0038525119887188, \ 0.9074857829773694, \ 0.4339634403008535, \ 0.2830182798495732, \ 0.2830182798495731, \ 0.4789472707744628, \ 0.2019001486324766, \ 0.3191525805930605, \ 0.3191525805930606, \ 0.2019001486324766, \ 0.4789472707744628, \ 0.4136797843254133, \ 0.1726404313491732, \ 0.4136797843254132, \ 0.7655339131965976, \ 0.0677103932212691, \ 0.1667556935821330, \ 0.1667556935821334, \ 0.0677103932212689, \ 0.7655339131965975, \ 0.9394616179191114, \ 0.0302691910404446, \ 0.0302691910404439, \ 0.9743796070397761, \ 0.0128101964801121, \ 0.0128101964801116, \ 0.6622896588699126, \ 0.0955724171106545, \ 0.2421379240194326, \ 0.2421379240194328, \ 0.0955724171106543, \ 0.6622896588699126, \ 0.5697673874287120, \ 0.1503708645734583, \ 0.2798617479978296, \ 0.2798617479978297, \ 0.1503708645734582, \ 0.5697673874287120, \ 0.9082517491081562, \ 0.0243498506845871, \ 0.0673984002072564, \ 0.0673984002072567, \ 0.0243498506845869, \ 0.9082517491081562, \ 0.4989241659396563, \ 0.1293878673669234, \ 0.3716879666934201, \ 0.3716879666934204, \ 0.1293878673669233, \ 0.4989241659396562, \ 0.5311444304776159, \ 0.0632274204565011, \ 0.4056281490658827, \ 0.4056281490658828, \ 0.0632274204565012, \ 0.5311444304776158, \ 0.3333333333333333, \ 0.8759787003474713, \ 0.0620106498262646, \ 0.0620106498262639, \ 0.7727532012417532, \ 0.0052666330207657, \ 0.2219801657374807, \ 0.2219801657374811, \ 0.0052666330207656, \ 0.7727532012417531, \ 0.7955154359824861, \ 0.0261588819796510, \ 0.1783256820378627, \ 0.1783256820378630, \ 0.0261588819796509, \ 0.7955154359824859, \ 0.9518230415381583, \ 0.0055547678704323, \ 0.0426221905914091, \ 0.0426221905914094, \ 0.0055547678704321, \ 0.9518230415381582, \ 0.5414440061438600, \ 0.2292779969280701, \ 0.2292779969280699, \ 0.7960823461994606, \ 0.1019588269002699, \ 0.1019588269002695, \ 0.9850326016003745, \ 0.0006230980203451, \ 0.0143443003792801, \ 0.0143443003792803, \ 0.0006230980203449, \ 0.9850326016003745 ] ) w = np.array ( [ \ 0.0000533239023334, \ 0.0000533239023334, \ 0.0000533239023334, \ 0.0083492191295379, \ 0.0083492191295379, \ 0.0083492191295379, \ 0.0083492191295379, \ 0.0083492191295379, \ 0.0083492191295379, \ 0.0030406522577730, \ 0.0030406522577730, \ 0.0030406522577730, \ 0.0030406522577730, \ 0.0030406522577730, \ 0.0030406522577730, \ 0.0014146272476628, \ 0.0014146272476628, \ 0.0014146272476628, \ 0.0052860436025325, \ 0.0052860436025325, \ 0.0052860436025325, \ 0.0052860436025325, \ 0.0052860436025325, \ 0.0052860436025325, \ 0.0024932699246691, \ 0.0024932699246691, \ 0.0024932699246691, \ 0.0024932699246691, \ 0.0024932699246691, \ 0.0024932699246691, \ 0.0030205810567136, \ 0.0030205810567136, \ 0.0030205810567136, \ 0.0030205810567136, \ 0.0030205810567136, \ 0.0030205810567136, \ 0.0036441755768762, \ 0.0036441755768762, \ 0.0036441755768762, \ 0.0036441755768762, \ 0.0036441755768762, \ 0.0036441755768762, \ 0.0074810896991602, \ 0.0074810896991602, \ 0.0074810896991602, \ 0.0074810896991602, \ 0.0074810896991602, \ 0.0074810896991602, \ 0.0045681541355720, \ 0.0045681541355720, \ 0.0045681541355720, \ 0.0045681541355720, \ 0.0045681541355720, \ 0.0045681541355720, \ 0.0016852036405343, \ 0.0016852036405343, \ 0.0016852036405343, \ 0.0016852036405343, \ 0.0016852036405343, \ 0.0016852036405343, \ 0.0055800151424133, \ 0.0055800151424133, \ 0.0055800151424133, \ 0.0082092066464793, \ 0.0082092066464793, \ 0.0082092066464793, \ 0.0082092066464793, \ 0.0082092066464793, \ 0.0082092066464793, \ 0.0083785907041262, \ 0.0083785907041262, \ 0.0083785907041262, \ 0.0044656768476199, \ 0.0044656768476199, \ 0.0044656768476199, \ 0.0044656768476199, \ 0.0044656768476199, \ 0.0044656768476199, \ 0.0062028347215228, \ 0.0062028347215228, \ 0.0062028347215228, \ 0.0062028347215228, \ 0.0062028347215228, \ 0.0062028347215228, \ 0.0008888925431519, \ 0.0008888925431519, \ 0.0008888925431519, \ 0.0008888925431519, \ 0.0008888925431519, \ 0.0008888925431519, \ 0.0126612945604860, \ 0.0126612945604860, \ 0.0126612945604860, \ 0.0014852293291852, \ 0.0014852293291852, \ 0.0014852293291852, \ 0.0014852293291852, \ 0.0014852293291852, \ 0.0014852293291852, \ 0.0011127063455906, \ 0.0011127063455906, \ 0.0011127063455906, \ 0.0011127063455906, \ 0.0011127063455906, \ 0.0011127063455906, \ 0.0128827331771754, \ 0.0128827331771754, \ 0.0128827331771754, \ 0.0119733591024828, \ 0.0119733591024828, \ 0.0119733591024828, \ 0.0119733591024828, \ 0.0119733591024828, \ 0.0119733591024828, \ 0.0108804660269342, \ 0.0108804660269342, \ 0.0108804660269342, \ 0.0058823160628199, \ 0.0058823160628199, \ 0.0058823160628199, \ 0.0058823160628199, \ 0.0058823160628199, \ 0.0058823160628199, \ 0.0018592782531939, \ 0.0018592782531939, \ 0.0018592782531939, \ 0.0008017410516731, \ 0.0008017410516731, \ 0.0008017410516731, \ 0.0084487434719511, \ 0.0084487434719511, \ 0.0084487434719511, \ 0.0084487434719511, \ 0.0084487434719511, \ 0.0084487434719511, \ 0.0102114559163661, \ 0.0102114559163661, \ 0.0102114559163661, \ 0.0102114559163661, \ 0.0102114559163661, \ 0.0102114559163661, \ 0.0024899591532165, \ 0.0024899591532165, \ 0.0024899591532165, \ 0.0024899591532165, \ 0.0024899591532165, \ 0.0024899591532165, \ 0.0098885056550223, \ 0.0098885056550223, \ 0.0098885056550223, \ 0.0098885056550223, \ 0.0098885056550223, \ 0.0098885056550223, \ 0.0074091131429365, \ 0.0074091131429365, \ 0.0074091131429365, \ 0.0074091131429365, \ 0.0074091131429365, \ 0.0074091131429365, \ 0.0130300709957626, \ 0.0039763485949254, \ 0.0039763485949254, \ 0.0039763485949254, \ 0.0019455932409831, \ 0.0019455932409831, \ 0.0019455932409831, \ 0.0019455932409831, \ 0.0019455932409831, \ 0.0019455932409831, \ 0.0042608365965002, \ 0.0042608365965002, \ 0.0042608365965002, \ 0.0042608365965002, \ 0.0042608365965002, \ 0.0042608365965002, \ 0.0010553743696176, \ 0.0010553743696176, \ 0.0010553743696176, \ 0.0010553743696176, \ 0.0010553743696176, \ 0.0010553743696176, \ 0.0125355977256489, \ 0.0125355977256489, \ 0.0125355977256489, \ 0.0066293991150592, \ 0.0066293991150592, \ 0.0066293991150592, \ 0.0001700882477425, \ 0.0001700882477425, \ 0.0001700882477425, \ 0.0001700882477425, \ 0.0001700882477425, \ 0.0001700882477425 ] ) return a, b, c, w def rule33 ( ): #*****************************************************************************80 # ## rule33() returns the rule of precision 33. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.0866842399345696, \ 0.8266315201308605, \ 0.0866842399345699, \ 0.4094279608026433, \ 0.4094279608026433, \ 0.1811440783947132, \ 0.2581529287895067, \ 0.6549184352472063, \ 0.0869286359632870, \ 0.6549184352472063, \ 0.2581529287895068, \ 0.0869286359632869, \ 0.2849624019720829, \ 0.6009455627050857, \ 0.1140920353228314, \ 0.6009455627050857, \ 0.2849624019720829, \ 0.1140920353228312, \ 0.3783335382962427, \ 0.3783335382962427, \ 0.2433329234075145, \ 0.4989797178600512, \ 0.4989797178600512, \ 0.0020405642798976, \ 0.1340676338419341, \ 0.7742670347180146, \ 0.0916653314400512, \ 0.7742670347180146, \ 0.1340676338419342, \ 0.0916653314400510, \ 0.3269137502096716, \ 0.4571468585469127, \ 0.2159393912434156, \ 0.4571468585469128, \ 0.3269137502096715, \ 0.2159393912434155, \ 0.2596606680087211, \ 0.4806786639825575, \ 0.2596606680087213, \ 0.1008457159827756, \ 0.8767639677306408, \ 0.0223903162865836, \ 0.8767639677306409, \ 0.1008457159827757, \ 0.0223903162865833, \ 0.3552328254047640, \ 0.5455252367072077, \ 0.0992419378880283, \ 0.5455252367072078, \ 0.3552328254047640, \ 0.0992419378880282, \ 0.1584027341957248, \ 0.8211535906601003, \ 0.0204436751441749, \ 0.8211535906601004, \ 0.1584027341957248, \ 0.0204436751441747, \ 0.4785119732563822, \ 0.4785119732563822, \ 0.0429760534872356, \ 0.4012397484580547, \ 0.5401481330852944, \ 0.0586121184566509, \ 0.5401481330852945, \ 0.4012397484580547, \ 0.0586121184566507, \ 0.2273220131649666, \ 0.7532530766694563, \ 0.0194249101655773, \ 0.7532530766694562, \ 0.2273220131649666, \ 0.0194249101655771, \ 0.1040040001314270, \ 0.8451258076748079, \ 0.0508701921937651, \ 0.8451258076748080, \ 0.1040040001314272, \ 0.0508701921937648, \ 0.2516190193630367, \ 0.7445747285081441, \ 0.0038062521288191, \ 0.7445747285081442, \ 0.2516190193630368, \ 0.0038062521288190, \ 0.1946715273720462, \ 0.7113747622583637, \ 0.0939537103695900, \ 0.7113747622583638, \ 0.1946715273720463, \ 0.0939537103695898, \ 0.1756396314580331, \ 0.8206933909179547, \ 0.0036669776240122, \ 0.8206933909179547, \ 0.1756396314580332, \ 0.0036669776240119, \ 0.1654225039506263, \ 0.7841517925433079, \ 0.0504257035060658, \ 0.7841517925433079, \ 0.1654225039506264, \ 0.0504257035060656, \ 0.0604829240909603, \ 0.9354049276280985, \ 0.0041121482809413, \ 0.9354049276280986, \ 0.0604829240909603, \ 0.0041121482809409, \ 0.3321035653575233, \ 0.6635597637774838, \ 0.0043366708649930, \ 0.6635597637774838, \ 0.3321035653575233, \ 0.0043366708649928, \ 0.3794132168456387, \ 0.4768226069138183, \ 0.1437641762405430, \ 0.4768226069138183, \ 0.3794132168456387, \ 0.1437641762405429, \ 0.0235174430579130, \ 0.9529651138841736, \ 0.0235174430579135, \ 0.0565688972489456, \ 0.9215652847226834, \ 0.0218658180283709, \ 0.9215652847226835, \ 0.0565688972489457, \ 0.0218658180283706, \ 0.3060238617603606, \ 0.3879522764792787, \ 0.3060238617603606, \ 0.1464890507166427, \ 0.7070218985667143, \ 0.1464890507166430, \ 0.0543792032794963, \ 0.8912415934410072, \ 0.0543792032794967, \ 0.2909849162693301, \ 0.5407077523881676, \ 0.1683073313425023, \ 0.5407077523881676, \ 0.2909849162693300, \ 0.1683073313425022, \ 0.2368453944831515, \ 0.7146406256116400, \ 0.0485139799052084, \ 0.7146406256116401, \ 0.2368453944831516, \ 0.0485139799052082, \ 0.4145491529764430, \ 0.5807136071426248, \ 0.0047372398809322, \ 0.5807136071426248, \ 0.4145491529764430, \ 0.0047372398809321, \ 0.3075361882409410, \ 0.6703285978516907, \ 0.0221352139073682, \ 0.6703285978516907, \ 0.3075361882409411, \ 0.0221352139073681, \ 0.1109266644334704, \ 0.8846799404570630, \ 0.0043933951094668, \ 0.8846799404570630, \ 0.1109266644334704, \ 0.0043933951094664, \ 0.2181920158632539, \ 0.5636159682734920, \ 0.2181920158632540, \ 0.3188631220563678, \ 0.6259766725873849, \ 0.0551602053562473, \ 0.6259766725873848, \ 0.3188631220563678, \ 0.0551602053562472, \ 0.4919913444565532, \ 0.4919913444565532, \ 0.0160173110868935, \ 0.3953677591013828, \ 0.5802323524289785, \ 0.0243998884696386, \ 0.5802323524289785, \ 0.3953677591013828, \ 0.0243998884696386, \ 0.4533999616178053, \ 0.4533999616178053, \ 0.0932000767643894, \ 0.2137578302973531, \ 0.6356072278734608, \ 0.1506349418291862, \ 0.6356072278734608, \ 0.2137578302973531, \ 0.1506349418291860, \ 0.0047266605105680, \ 0.9905466789788636, \ 0.0047266605105684, \ 0.0247793702175406, \ 0.9707182444941620, \ 0.0045023852882976, \ 0.9707182444941620, \ 0.0247793702175407, \ 0.0045023852882971 ] ) b = np.array ( [ \ 0.0866842399345699, \ 0.0866842399345696, \ 0.8266315201308606, \ 0.1811440783947133, \ 0.4094279608026434, \ 0.4094279608026435, \ 0.0869286359632870, \ 0.2581529287895068, \ 0.6549184352472064, \ 0.0869286359632870, \ 0.6549184352472064, \ 0.2581529287895070, \ 0.1140920353228314, \ 0.2849624019720829, \ 0.6009455627050859, \ 0.1140920353228314, \ 0.6009455627050859, \ 0.2849624019720831, \ 0.2433329234075146, \ 0.3783335382962428, \ 0.3783335382962429, \ 0.0020405642798976, \ 0.4989797178600513, \ 0.4989797178600514, \ 0.0916653314400512, \ 0.1340676338419342, \ 0.7742670347180148, \ 0.0916653314400512, \ 0.7742670347180148, \ 0.1340676338419345, \ 0.2159393912434157, \ 0.3269137502096717, \ 0.4571468585469129, \ 0.2159393912434157, \ 0.4571468585469129, \ 0.3269137502096717, \ 0.2596606680087213, \ 0.2596606680087212, \ 0.4806786639825577, \ 0.0223903162865835, \ 0.1008457159827756, \ 0.8767639677306410, \ 0.0223903162865835, \ 0.8767639677306409, \ 0.1008457159827759, \ 0.0992419378880283, \ 0.3552328254047640, \ 0.5455252367072079, \ 0.0992419378880283, \ 0.5455252367072079, \ 0.3552328254047642, \ 0.0204436751441748, \ 0.1584027341957248, \ 0.8211535906601005, \ 0.0204436751441748, \ 0.8211535906601006, \ 0.1584027341957251, \ 0.0429760534872357, \ 0.4785119732563822, \ 0.4785119732563824, \ 0.0586121184566509, \ 0.4012397484580547, \ 0.5401481330852946, \ 0.0586121184566509, \ 0.5401481330852945, \ 0.4012397484580549, \ 0.0194249101655772, \ 0.2273220131649666, \ 0.7532530766694563, \ 0.0194249101655772, \ 0.7532530766694563, \ 0.2273220131649669, \ 0.0508701921937650, \ 0.1040040001314270, \ 0.8451258076748080, \ 0.0508701921937650, \ 0.8451258076748080, \ 0.1040040001314274, \ 0.0038062521288191, \ 0.2516190193630367, \ 0.7445747285081444, \ 0.0038062521288191, \ 0.7445747285081442, \ 0.2516190193630370, \ 0.0939537103695900, \ 0.1946715273720463, \ 0.7113747622583638, \ 0.0939537103695900, \ 0.7113747622583639, \ 0.1946715273720465, \ 0.0036669776240121, \ 0.1756396314580332, \ 0.8206933909179549, \ 0.0036669776240121, \ 0.8206933909179549, \ 0.1756396314580335, \ 0.0504257035060658, \ 0.1654225039506263, \ 0.7841517925433081, \ 0.0504257035060658, \ 0.7841517925433080, \ 0.1654225039506266, \ 0.0041121482809412, \ 0.0604829240909602, \ 0.9354049276280987, \ 0.0041121482809412, \ 0.9354049276280987, \ 0.0604829240909606, \ 0.0043366708649929, \ 0.3321035653575233, \ 0.6635597637774840, \ 0.0043366708649929, \ 0.6635597637774838, \ 0.3321035653575235, \ 0.1437641762405430, \ 0.3794132168456388, \ 0.4768226069138184, \ 0.1437641762405430, \ 0.4768226069138183, \ 0.3794132168456389, \ 0.0235174430579133, \ 0.0235174430579130, \ 0.9529651138841736, \ 0.0218658180283708, \ 0.0565688972489457, \ 0.9215652847226837, \ 0.0218658180283708, \ 0.9215652847226837, \ 0.0565688972489460, \ 0.3060238617603607, \ 0.3060238617603607, \ 0.3879522764792788, \ 0.1464890507166429, \ 0.1464890507166427, \ 0.7070218985667144, \ 0.0543792032794966, \ 0.0543792032794963, \ 0.8912415934410073, \ 0.1683073313425024, \ 0.2909849162693301, \ 0.5407077523881677, \ 0.1683073313425024, \ 0.5407077523881677, \ 0.2909849162693303, \ 0.0485139799052084, \ 0.2368453944831516, \ 0.7146406256116403, \ 0.0485139799052084, \ 0.7146406256116402, \ 0.2368453944831518, \ 0.0047372398809322, \ 0.4145491529764431, \ 0.5807136071426250, \ 0.0047372398809322, \ 0.5807136071426249, \ 0.4145491529764432, \ 0.0221352139073682, \ 0.3075361882409411, \ 0.6703285978516910, \ 0.0221352139073682, \ 0.6703285978516909, \ 0.3075361882409413, \ 0.0043933951094667, \ 0.1109266644334704, \ 0.8846799404570631, \ 0.0043933951094667, \ 0.8846799404570631, \ 0.1109266644334707, \ 0.2181920158632541, \ 0.2181920158632540, \ 0.5636159682734921, \ 0.0551602053562474, \ 0.3188631220563678, \ 0.6259766725873851, \ 0.0551602053562474, \ 0.6259766725873850, \ 0.3188631220563680, \ 0.0160173110868935, \ 0.4919913444565533, \ 0.4919913444565535, \ 0.0243998884696387, \ 0.3953677591013828, \ 0.5802323524289787, \ 0.0243998884696387, \ 0.5802323524289786, \ 0.3953677591013830, \ 0.0932000767643895, \ 0.4533999616178053, \ 0.4533999616178054, \ 0.1506349418291862, \ 0.2137578302973531, \ 0.6356072278734609, \ 0.1506349418291862, \ 0.6356072278734609, \ 0.2137578302973533, \ 0.0047266605105683, \ 0.0047266605105680, \ 0.9905466789788638, \ 0.0045023852882974, \ 0.0247793702175406, \ 0.9707182444941621, \ 0.0045023852882974, \ 0.9707182444941621, \ 0.0247793702175410 ] ) c = np.array ( [ \ 0.8266315201308605, \ 0.0866842399345699, \ 0.0866842399345694, \ 0.4094279608026433, \ 0.1811440783947132, \ 0.4094279608026433, \ 0.6549184352472062, \ 0.0869286359632869, \ 0.2581529287895066, \ 0.2581529287895067, \ 0.0869286359632868, \ 0.6549184352472062, \ 0.6009455627050857, \ 0.1140920353228314, \ 0.2849624019720827, \ 0.2849624019720829, \ 0.1140920353228312, \ 0.6009455627050857, \ 0.3783335382962427, \ 0.2433329234075144, \ 0.3783335382962427, \ 0.4989797178600511, \ 0.0020405642798975, \ 0.4989797178600510, \ 0.7742670347180147, \ 0.0916653314400512, \ 0.1340676338419339, \ 0.1340676338419342, \ 0.0916653314400510, \ 0.7742670347180146, \ 0.4571468585469128, \ 0.2159393912434156, \ 0.3269137502096715, \ 0.3269137502096716, \ 0.2159393912434156, \ 0.4571468585469127, \ 0.4806786639825576, \ 0.2596606680087212, \ 0.2596606680087211, \ 0.8767639677306409, \ 0.0223903162865836, \ 0.1008457159827754, \ 0.1008457159827755, \ 0.0223903162865834, \ 0.8767639677306408, \ 0.5455252367072078, \ 0.0992419378880283, \ 0.3552328254047639, \ 0.3552328254047640, \ 0.0992419378880282, \ 0.5455252367072077, \ 0.8211535906601003, \ 0.0204436751441749, \ 0.1584027341957245, \ 0.1584027341957248, \ 0.0204436751441746, \ 0.8211535906601003, \ 0.4785119732563821, \ 0.0429760534872355, \ 0.4785119732563820, \ 0.5401481330852944, \ 0.0586121184566509, \ 0.4012397484580545, \ 0.4012397484580545, \ 0.0586121184566507, \ 0.5401481330852944, \ 0.7532530766694562, \ 0.0194249101655771, \ 0.2273220131649664, \ 0.2273220131649666, \ 0.0194249101655771, \ 0.7532530766694561, \ 0.8451258076748079, \ 0.0508701921937651, \ 0.1040040001314269, \ 0.1040040001314270, \ 0.0508701921937648, \ 0.8451258076748078, \ 0.7445747285081442, \ 0.0038062521288192, \ 0.2516190193630364, \ 0.2516190193630367, \ 0.0038062521288190, \ 0.7445747285081441, \ 0.7113747622583637, \ 0.0939537103695900, \ 0.1946715273720462, \ 0.1946715273720462, \ 0.0939537103695898, \ 0.7113747622583637, \ 0.8206933909179548, \ 0.0036669776240122, \ 0.1756396314580330, \ 0.1756396314580332, \ 0.0036669776240118, \ 0.8206933909179546, \ 0.7841517925433079, \ 0.0504257035060658, \ 0.1654225039506261, \ 0.1654225039506262, \ 0.0504257035060657, \ 0.7841517925433077, \ 0.9354049276280986, \ 0.0041121482809413, \ 0.0604829240909600, \ 0.0604829240909602, \ 0.0041121482809410, \ 0.9354049276280985, \ 0.6635597637774838, \ 0.0043366708649929, \ 0.3321035653575229, \ 0.3321035653575233, \ 0.0043366708649929, \ 0.6635597637774837, \ 0.4768226069138182, \ 0.1437641762405429, \ 0.3794132168456386, \ 0.3794132168456387, \ 0.1437641762405430, \ 0.4768226069138181, \ 0.9529651138841736, \ 0.0235174430579134, \ 0.0235174430579129, \ 0.9215652847226835, \ 0.0218658180283709, \ 0.0565688972489454, \ 0.0565688972489456, \ 0.0218658180283705, \ 0.9215652847226834, \ 0.3879522764792787, \ 0.3060238617603607, \ 0.3060238617603606, \ 0.7070218985667143, \ 0.1464890507166430, \ 0.1464890507166426, \ 0.8912415934410072, \ 0.0543792032794966, \ 0.0543792032794960, \ 0.5407077523881676, \ 0.1683073313425023, \ 0.2909849162693300, \ 0.2909849162693300, \ 0.1683073313425022, \ 0.5407077523881675, \ 0.7146406256116400, \ 0.0485139799052084, \ 0.2368453944831513, \ 0.2368453944831515, \ 0.0485139799052082, \ 0.7146406256116400, \ 0.5807136071426249, \ 0.0047372398809322, \ 0.4145491529764428, \ 0.4145491529764431, \ 0.0047372398809321, \ 0.5807136071426248, \ 0.6703285978516907, \ 0.0221352139073682, \ 0.3075361882409408, \ 0.3075361882409410, \ 0.0221352139073681, \ 0.6703285978516906, \ 0.8846799404570629, \ 0.0043933951094666, \ 0.1109266644334701, \ 0.1109266644334703, \ 0.0043933951094665, \ 0.8846799404570630, \ 0.5636159682734920, \ 0.2181920158632540, \ 0.2181920158632539, \ 0.6259766725873849, \ 0.0551602053562473, \ 0.3188631220563676, \ 0.3188631220563679, \ 0.0551602053562472, \ 0.6259766725873848, \ 0.4919913444565532, \ 0.0160173110868935, \ 0.4919913444565530, \ 0.5802323524289785, \ 0.0243998884696386, \ 0.3953677591013827, \ 0.3953677591013828, \ 0.0243998884696385, \ 0.5802323524289784, \ 0.4533999616178052, \ 0.0932000767643894, \ 0.4533999616178051, \ 0.6356072278734608, \ 0.1506349418291861, \ 0.2137578302973530, \ 0.2137578302973530, \ 0.1506349418291860, \ 0.6356072278734608, \ 0.9905466789788637, \ 0.0047266605105684, \ 0.0047266605105677, \ 0.9707182444941620, \ 0.0045023852882974, \ 0.0247793702175404, \ 0.0247793702175406, \ 0.0045023852882972, \ 0.9707182444941619 ] ) w = np.array ( [ \ 0.0032023640124142, \ 0.0032023640124142, \ 0.0032023640124142, \ 0.0068346799344681, \ 0.0068346799344681, \ 0.0068346799344681, \ 0.0050108234565749, \ 0.0050108234565749, \ 0.0050108234565749, \ 0.0050108234565749, \ 0.0050108234565749, \ 0.0050108234565749, \ 0.0062666715145980, \ 0.0062666715145980, \ 0.0062666715145980, \ 0.0062666715145980, \ 0.0062666715145980, \ 0.0062666715145980, \ 0.0089341618081367, \ 0.0089341618081367, \ 0.0089341618081367, \ 0.0010410912372864, \ 0.0010410912372864, \ 0.0010410912372864, \ 0.0051060923018633, \ 0.0051060923018633, \ 0.0051060923018633, \ 0.0051060923018633, \ 0.0051060923018633, \ 0.0051060923018633, \ 0.0096392468588408, \ 0.0096392468588408, \ 0.0096392468588408, \ 0.0096392468588408, \ 0.0096392468588408, \ 0.0096392468588408, \ 0.0097388572366854, \ 0.0097388572366854, \ 0.0097388572366854, \ 0.0024212380388685, \ 0.0024212380388685, \ 0.0024212380388685, \ 0.0024212380388685, \ 0.0024212380388685, \ 0.0024212380388685, \ 0.0076973467270549, \ 0.0076973467270549, \ 0.0076973467270549, \ 0.0076973467270549, \ 0.0076973467270549, \ 0.0076973467270549, \ 0.0029882446919490, \ 0.0029882446919490, \ 0.0029882446919490, \ 0.0029882446919490, \ 0.0029882446919490, \ 0.0029882446919490, \ 0.0054643256840460, \ 0.0054643256840460, \ 0.0054643256840460, \ 0.0061988540259434, \ 0.0061988540259434, \ 0.0061988540259434, \ 0.0061988540259434, \ 0.0061988540259434, \ 0.0061988540259434, \ 0.0033169972939131, \ 0.0033169972939131, \ 0.0033169972939131, \ 0.0033169972939131, \ 0.0033169972939131, \ 0.0033169972939131, \ 0.0037089296125893, \ 0.0037089296125893, \ 0.0037089296125893, \ 0.0037089296125893, \ 0.0037089296125893, \ 0.0037089296125893, \ 0.0015426465184706, \ 0.0015426465184706, \ 0.0015426465184706, \ 0.0015426465184706, \ 0.0015426465184706, \ 0.0015426465184706, \ 0.0066121724110684, \ 0.0066121724110684, \ 0.0066121724110684, \ 0.0066121724110684, \ 0.0066121724110684, \ 0.0066121724110684, \ 0.0013551781957506, \ 0.0013551781957506, \ 0.0013551781957506, \ 0.0013551781957506, \ 0.0013551781957506, \ 0.0013551781957506, \ 0.0049036283435529, \ 0.0049036283435529, \ 0.0049036283435529, \ 0.0049036283435529, \ 0.0049036283435529, \ 0.0049036283435529, \ 0.0009157661571810, \ 0.0009157661571810, \ 0.0009157661571810, \ 0.0009157661571810, \ 0.0009157661571810, \ 0.0009157661571810, \ 0.0018218162644265, \ 0.0018218162644265, \ 0.0018218162644265, \ 0.0018218162644265, \ 0.0018218162644265, \ 0.0018218162644265, \ 0.0092423799017096, \ 0.0092423799017096, \ 0.0092423799017096, \ 0.0092423799017096, \ 0.0092423799017096, \ 0.0092423799017096, \ 0.0013813690630279, \ 0.0013813690630279, \ 0.0013813690630279, \ 0.0019606312336932, \ 0.0019606312336932, \ 0.0019606312336932, \ 0.0019606312336932, \ 0.0019606312336932, \ 0.0019606312336932, \ 0.0120887399809166, \ 0.0120887399809166, \ 0.0120887399809166, \ 0.0073774464967342, \ 0.0073774464967342, \ 0.0073774464967342, \ 0.0032093504439416, \ 0.0032093504439416, \ 0.0032093504439416, \ 0.0102099177863965, \ 0.0102099177863965, \ 0.0102099177863965, \ 0.0102099177863965, \ 0.0102099177863965, \ 0.0102099177863965, \ 0.0054637704373722, \ 0.0054637704373722, \ 0.0054637704373722, \ 0.0054637704373722, \ 0.0054637704373722, \ 0.0054637704373722, \ 0.0020111020097847, \ 0.0020111020097847, \ 0.0020111020097847, \ 0.0020111020097847, \ 0.0020111020097847, \ 0.0020111020097847, \ 0.0042683347026345, \ 0.0042683347026345, \ 0.0042683347026345, \ 0.0042683347026345, \ 0.0042683347026345, \ 0.0042683347026345, \ 0.0012878764088954, \ 0.0012878764088954, \ 0.0012878764088954, \ 0.0012878764088954, \ 0.0012878764088954, \ 0.0012878764088954, \ 0.0099263761795442, \ 0.0099263761795442, \ 0.0099263761795442, \ 0.0065998833272568, \ 0.0065998833272568, \ 0.0065998833272568, \ 0.0065998833272568, \ 0.0065998833272568, \ 0.0065998833272568, \ 0.0038623620299660, \ 0.0038623620299660, \ 0.0038623620299660, \ 0.0049474328088082, \ 0.0049474328088082, \ 0.0049474328088082, \ 0.0049474328088082, \ 0.0049474328088082, \ 0.0049474328088082, \ 0.0093337977696466, \ 0.0093337977696466, \ 0.0093337977696466, \ 0.0091814815579271, \ 0.0091814815579271, \ 0.0091814815579271, \ 0.0091814815579271, \ 0.0091814815579271, \ 0.0091814815579271, \ 0.0002934827335780, \ 0.0002934827335780, \ 0.0002934827335780, \ 0.0006440017743474, \ 0.0006440017743474, \ 0.0006440017743474, \ 0.0006440017743474, \ 0.0006440017743474, \ 0.0006440017743474 ] ) return a, b, c, w def rule34 ( ): #*****************************************************************************80 # ## rule34() returns the rule of precision 34. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3851262518382810, \ 0.5937769878916170, \ 0.0210967602701019, \ 0.5937769878916170, \ 0.3851262518382810, \ 0.0210967602701018, \ 0.0528200673454988, \ 0.9437918205041110, \ 0.0033881121503903, \ 0.9437918205041111, \ 0.0528200673454988, \ 0.0033881121503898, \ 0.0459825951541271, \ 0.9080348096917454, \ 0.0459825951541276, \ 0.0508987652831316, \ 0.9308929059173959, \ 0.0182083287994725, \ 0.9308929059173960, \ 0.0508987652831318, \ 0.0182083287994721, \ 0.0208387475149684, \ 0.9583225049700629, \ 0.0208387475149688, \ 0.1291243720726085, \ 0.8103648572840793, \ 0.0605107706433124, \ 0.8103648572840793, \ 0.1291243720726087, \ 0.0605107706433121, \ 0.0878179027775245, \ 0.8762622058588977, \ 0.0359198913635778, \ 0.8762622058588977, \ 0.0878179027775245, \ 0.0359198913635776, \ 0.0757621741867908, \ 0.8484756516264180, \ 0.0757621741867912, \ 0.3766019805175457, \ 0.3766019805175457, \ 0.2467960389649085, \ 0.2735537380248192, \ 0.5623852333049681, \ 0.1640610286702127, \ 0.5623852333049681, \ 0.2735537380248192, \ 0.1640610286702125, \ 0.0944770656323742, \ 0.8948396708440374, \ 0.0106832635235886, \ 0.8948396708440374, \ 0.0944770656323743, \ 0.0106832635235882, \ 0.2873558398221649, \ 0.4252883203556701, \ 0.2873558398221651, \ 0.4111522333036005, \ 0.5577150863900258, \ 0.0311326803063737, \ 0.5577150863900259, \ 0.4111522333036006, \ 0.0311326803063736, \ 0.3594475694982553, \ 0.5073598072800389, \ 0.1331926232217058, \ 0.5073598072800389, \ 0.3594475694982553, \ 0.1331926232217057, \ 0.3884100853304371, \ 0.5372925954322688, \ 0.0742973192372942, \ 0.5372925954322687, \ 0.3884100853304370, \ 0.0742973192372941, \ 0.3253550433420577, \ 0.4694784588431804, \ 0.2051664978147619, \ 0.4694784588431803, \ 0.3253550433420578, \ 0.2051664978147618, \ 0.1747804794810684, \ 0.7349999143937561, \ 0.0902196061251755, \ 0.7349999143937561, \ 0.1747804794810685, \ 0.0902196061251753, \ 0.1941646181495633, \ 0.7619195089459252, \ 0.0439158729045115, \ 0.7619195089459252, \ 0.1941646181495633, \ 0.0439158729045113, \ 0.4744124989028456, \ 0.4744124989028456, \ 0.0511750021943088, \ 0.2483278734045790, \ 0.6827082966308193, \ 0.0689638299646018, \ 0.6827082966308193, \ 0.2483278734045790, \ 0.0689638299646015, \ 0.2229920412612009, \ 0.6518261605959125, \ 0.1251817981428867, \ 0.6518261605959125, \ 0.2229920412612009, \ 0.1251817981428865, \ 0.1496044235489511, \ 0.8457252778897656, \ 0.0046702985612834, \ 0.8457252778897657, \ 0.1496044235489512, \ 0.0046702985612830, \ 0.1111727012858456, \ 0.7776545974283084, \ 0.1111727012858459, \ 0.4918649619576897, \ 0.4918649619576897, \ 0.0162700760846206, \ 0.3283914136921266, \ 0.6226826638040091, \ 0.0489259225038643, \ 0.6226826638040089, \ 0.3283914136921267, \ 0.0489259225038643, \ 0.1508877227628729, \ 0.6982245544742539, \ 0.1508877227628732, \ 0.1423855003245428, \ 0.8329562498972498, \ 0.0246582497782074, \ 0.8329562498972499, \ 0.1423855003245429, \ 0.0246582497782072, \ 0.4238402997203689, \ 0.5701997570298869, \ 0.0059599432497442, \ 0.5701997570298869, \ 0.4238402997203689, \ 0.0059599432497442, \ 0.0041579573923189, \ 0.9916840852153618, \ 0.0041579573923194, \ 0.2404349104138168, \ 0.5191301791723664, \ 0.2404349104138169, \ 0.2676904193443056, \ 0.7037908578134091, \ 0.0285187228422855, \ 0.7037908578134090, \ 0.2676904193443056, \ 0.0285187228422852, \ 0.4155115967448372, \ 0.4155115967448372, \ 0.1689768065103256, \ 0.4995421826615118, \ 0.4995421826615117, \ 0.0009156346769764, \ 0.3454113789529011, \ 0.6390259777460834, \ 0.0155626433010154, \ 0.6390259777460834, \ 0.3454113789529011, \ 0.0155626433010154, \ 0.3534495196576637, \ 0.6456247621084024, \ 0.0009257182339338, \ 0.6456247621084025, \ 0.3534495196576638, \ 0.0009257182339337, \ 0.4485642658787082, \ 0.4485642658787082, \ 0.1028714682425834, \ 0.3033356394717892, \ 0.5973781489096254, \ 0.0992862116185854, \ 0.5973781489096254, \ 0.3033356394717892, \ 0.0992862116185853, \ 0.0217555603201839, \ 0.9742699338072974, \ 0.0039745058725186, \ 0.9742699338072975, \ 0.0217555603201841, \ 0.0039745058725182, \ 0.3333333333333333, \ 0.2075468682735205, \ 0.7786734923211107, \ 0.0137796394053689, \ 0.7786734923211107, \ 0.2075468682735205, \ 0.0137796394053686, \ 0.1943865435789661, \ 0.6112269128420674, \ 0.1943865435789664, \ 0.2135602395179478, \ 0.7856676213617251, \ 0.0007721391203271, \ 0.7856676213617252, \ 0.2135602395179479, \ 0.0007721391203269, \ 0.2793864317822237, \ 0.7151517773234828, \ 0.0054617908942934, \ 0.7151517773234828, \ 0.2793864317822238, \ 0.0054617908942933, \ 0.0968669225755472, \ 0.9031283677334342, \ 0.0000047096910187, \ 0.9031283677334343, \ 0.0968669225755472, \ 0.0000047096910183 ] ) b = np.array ( [ \ 0.0210967602701019, \ 0.3851262518382811, \ 0.5937769878916171, \ 0.0210967602701019, \ 0.5937769878916171, \ 0.3851262518382813, \ 0.0033881121503900, \ 0.0528200673454988, \ 0.9437918205041111, \ 0.0033881121503900, \ 0.9437918205041114, \ 0.0528200673454991, \ 0.0459825951541274, \ 0.0459825951541271, \ 0.9080348096917455, \ 0.0182083287994724, \ 0.0508987652831316, \ 0.9308929059173960, \ 0.0182083287994724, \ 0.9308929059173960, \ 0.0508987652831320, \ 0.0208387475149687, \ 0.0208387475149684, \ 0.9583225049700631, \ 0.0605107706433123, \ 0.1291243720726085, \ 0.8103648572840793, \ 0.0605107706433123, \ 0.8103648572840793, \ 0.1291243720726088, \ 0.0359198913635778, \ 0.0878179027775245, \ 0.8762622058588979, \ 0.0359198913635778, \ 0.8762622058588979, \ 0.0878179027775248, \ 0.0757621741867911, \ 0.0757621741867908, \ 0.8484756516264182, \ 0.2467960389649086, \ 0.3766019805175458, \ 0.3766019805175458, \ 0.1640610286702127, \ 0.2735537380248192, \ 0.5623852333049683, \ 0.1640610286702127, \ 0.5623852333049683, \ 0.2735537380248194, \ 0.0106832635235884, \ 0.0944770656323742, \ 0.8948396708440375, \ 0.0106832635235884, \ 0.8948396708440375, \ 0.0944770656323745, \ 0.2873558398221651, \ 0.2873558398221650, \ 0.4252883203556702, \ 0.0311326803063737, \ 0.4111522333036006, \ 0.5577150863900260, \ 0.0311326803063737, \ 0.5577150863900259, \ 0.4111522333036007, \ 0.1331926232217058, \ 0.3594475694982554, \ 0.5073598072800390, \ 0.1331926232217058, \ 0.5073598072800389, \ 0.3594475694982555, \ 0.0742973192372942, \ 0.3884100853304371, \ 0.5372925954322689, \ 0.0742973192372942, \ 0.5372925954322688, \ 0.3884100853304373, \ 0.2051664978147620, \ 0.3253550433420578, \ 0.4694784588431805, \ 0.2051664978147620, \ 0.4694784588431805, \ 0.3253550433420579, \ 0.0902196061251755, \ 0.1747804794810684, \ 0.7349999143937562, \ 0.0902196061251755, \ 0.7349999143937561, \ 0.1747804794810687, \ 0.0439158729045114, \ 0.1941646181495633, \ 0.7619195089459254, \ 0.0439158729045114, \ 0.7619195089459254, \ 0.1941646181495635, \ 0.0511750021943088, \ 0.4744124989028456, \ 0.4744124989028458, \ 0.0689638299646017, \ 0.2483278734045790, \ 0.6827082966308194, \ 0.0689638299646017, \ 0.6827082966308194, \ 0.2483278734045792, \ 0.1251817981428867, \ 0.2229920412612009, \ 0.6518261605959126, \ 0.1251817981428867, \ 0.6518261605959126, \ 0.2229920412612011, \ 0.0046702985612833, \ 0.1496044235489511, \ 0.8457252778897658, \ 0.0046702985612833, \ 0.8457252778897657, \ 0.1496044235489514, \ 0.1111727012858459, \ 0.1111727012858457, \ 0.7776545974283087, \ 0.0162700760846207, \ 0.4918649619576898, \ 0.4918649619576899, \ 0.0489259225038644, \ 0.3283914136921267, \ 0.6226826638040092, \ 0.0489259225038644, \ 0.6226826638040091, \ 0.3283914136921268, \ 0.1508877227628732, \ 0.1508877227628729, \ 0.6982245544742540, \ 0.0246582497782073, \ 0.1423855003245428, \ 0.8329562498972500, \ 0.0246582497782073, \ 0.8329562498972499, \ 0.1423855003245431, \ 0.0059599432497443, \ 0.4238402997203689, \ 0.5701997570298871, \ 0.0059599432497443, \ 0.5701997570298870, \ 0.4238402997203691, \ 0.0041579573923192, \ 0.0041579573923189, \ 0.9916840852153619, \ 0.2404349104138169, \ 0.2404349104138168, \ 0.5191301791723665, \ 0.0285187228422854, \ 0.2676904193443056, \ 0.7037908578134091, \ 0.0285187228422854, \ 0.7037908578134091, \ 0.2676904193443059, \ 0.1689768065103257, \ 0.4155115967448372, \ 0.4155115967448373, \ 0.0009156346769765, \ 0.4995421826615118, \ 0.4995421826615120, \ 0.0155626433010155, \ 0.3454113789529012, \ 0.6390259777460836, \ 0.0155626433010155, \ 0.6390259777460835, \ 0.3454113789529014, \ 0.0009257182339338, \ 0.3534495196576638, \ 0.6456247621084026, \ 0.0009257182339338, \ 0.6456247621084026, \ 0.3534495196576640, \ 0.1028714682425835, \ 0.4485642658787083, \ 0.4485642658787085, \ 0.0992862116185854, \ 0.3033356394717893, \ 0.5973781489096255, \ 0.0992862116185854, \ 0.5973781489096255, \ 0.3033356394717894, \ 0.0039745058725185, \ 0.0217555603201839, \ 0.9742699338072977, \ 0.0039745058725185, \ 0.9742699338072977, \ 0.0217555603201842, \ 0.3333333333333334, \ 0.0137796394053688, \ 0.2075468682735205, \ 0.7786734923211108, \ 0.0137796394053688, \ 0.7786734923211108, \ 0.2075468682735207, \ 0.1943865435789664, \ 0.1943865435789662, \ 0.6112269128420676, \ 0.0007721391203270, \ 0.2135602395179478, \ 0.7856676213617252, \ 0.0007721391203270, \ 0.7856676213617252, \ 0.2135602395179481, \ 0.0054617908942934, \ 0.2793864317822238, \ 0.7151517773234830, \ 0.0054617908942934, \ 0.7151517773234830, \ 0.2793864317822241, \ 0.0000047096910185, \ 0.0968669225755471, \ 0.9031283677334344, \ 0.0000047096910185, \ 0.9031283677334344, \ 0.0968669225755475 ] ) c = np.array ( [ \ 0.5937769878916170, \ 0.0210967602701019, \ 0.3851262518382809, \ 0.3851262518382810, \ 0.0210967602701019, \ 0.5937769878916168, \ 0.9437918205041113, \ 0.0033881121503902, \ 0.0528200673454986, \ 0.0528200673454988, \ 0.0033881121503898, \ 0.9437918205041110, \ 0.9080348096917454, \ 0.0459825951541274, \ 0.0459825951541269, \ 0.9308929059173959, \ 0.0182083287994725, \ 0.0508987652831314, \ 0.0508987652831316, \ 0.0182083287994722, \ 0.9308929059173959, \ 0.9583225049700629, \ 0.0208387475149687, \ 0.0208387475149682, \ 0.8103648572840793, \ 0.0605107706433123, \ 0.1291243720726084, \ 0.1291243720726085, \ 0.0605107706433120, \ 0.8103648572840791, \ 0.8762622058588978, \ 0.0359198913635778, \ 0.0878179027775242, \ 0.0878179027775245, \ 0.0359198913635775, \ 0.8762622058588976, \ 0.8484756516264181, \ 0.0757621741867912, \ 0.0757621741867905, \ 0.3766019805175457, \ 0.2467960389649085, \ 0.3766019805175456, \ 0.5623852333049681, \ 0.1640610286702126, \ 0.2735537380248191, \ 0.2735537380248192, \ 0.1640610286702125, \ 0.5623852333049681, \ 0.8948396708440375, \ 0.0106832635235885, \ 0.0944770656323740, \ 0.0944770656323742, \ 0.0106832635235882, \ 0.8948396708440374, \ 0.4252883203556700, \ 0.2873558398221649, \ 0.2873558398221648, \ 0.5577150863900258, \ 0.0311326803063737, \ 0.4111522333036004, \ 0.4111522333036004, \ 0.0311326803063735, \ 0.5577150863900256, \ 0.5073598072800389, \ 0.1331926232217057, \ 0.3594475694982552, \ 0.3594475694982552, \ 0.1331926232217058, \ 0.5073598072800387, \ 0.5372925954322687, \ 0.0742973192372940, \ 0.3884100853304369, \ 0.3884100853304371, \ 0.0742973192372941, \ 0.5372925954322686, \ 0.4694784588431803, \ 0.2051664978147618, \ 0.3253550433420577, \ 0.3253550433420577, \ 0.2051664978147618, \ 0.4694784588431803, \ 0.7349999143937561, \ 0.0902196061251755, \ 0.1747804794810682, \ 0.1747804794810684, \ 0.0902196061251753, \ 0.7349999143937560, \ 0.7619195089459252, \ 0.0439158729045115, \ 0.1941646181495631, \ 0.1941646181495634, \ 0.0439158729045113, \ 0.7619195089459252, \ 0.4744124989028456, \ 0.0511750021943088, \ 0.4744124989028454, \ 0.6827082966308193, \ 0.0689638299646017, \ 0.2483278734045787, \ 0.2483278734045790, \ 0.0689638299646015, \ 0.6827082966308193, \ 0.6518261605959125, \ 0.1251817981428866, \ 0.2229920412612008, \ 0.2229920412612009, \ 0.1251817981428865, \ 0.6518261605959124, \ 0.8457252778897656, \ 0.0046702985612833, \ 0.1496044235489508, \ 0.1496044235489510, \ 0.0046702985612831, \ 0.8457252778897656, \ 0.7776545974283084, \ 0.1111727012858459, \ 0.1111727012858454, \ 0.4918649619576896, \ 0.0162700760846206, \ 0.4918649619576895, \ 0.6226826638040089, \ 0.0489259225038643, \ 0.3283914136921265, \ 0.3283914136921267, \ 0.0489259225038643, \ 0.6226826638040088, \ 0.6982245544742540, \ 0.1508877227628732, \ 0.1508877227628728, \ 0.8329562498972499, \ 0.0246582497782074, \ 0.1423855003245426, \ 0.1423855003245427, \ 0.0246582497782072, \ 0.8329562498972497, \ 0.5701997570298869, \ 0.0059599432497442, \ 0.4238402997203686, \ 0.4238402997203689, \ 0.0059599432497440, \ 0.5701997570298867, \ 0.9916840852153619, \ 0.0041579573923193, \ 0.0041579573923187, \ 0.5191301791723663, \ 0.2404349104138168, \ 0.2404349104138167, \ 0.7037908578134090, \ 0.0285187228422853, \ 0.2676904193443054, \ 0.2676904193443056, \ 0.0285187228422853, \ 0.7037908578134089, \ 0.4155115967448372, \ 0.1689768065103256, \ 0.4155115967448370, \ 0.4995421826615117, \ 0.0009156346769764, \ 0.4995421826615116, \ 0.6390259777460833, \ 0.0155626433010154, \ 0.3454113789529010, \ 0.3454113789529011, \ 0.0155626433010153, \ 0.6390259777460832, \ 0.6456247621084025, \ 0.0009257182339338, \ 0.3534495196576636, \ 0.3534495196576637, \ 0.0009257182339336, \ 0.6456247621084023, \ 0.4485642658787082, \ 0.1028714682425834, \ 0.4485642658787081, \ 0.5973781489096254, \ 0.0992862116185854, \ 0.3033356394717891, \ 0.3033356394717892, \ 0.0992862116185853, \ 0.5973781489096253, \ 0.9742699338072977, \ 0.0039745058725186, \ 0.0217555603201837, \ 0.0217555603201840, \ 0.0039745058725184, \ 0.9742699338072975, \ 0.3333333333333333, \ 0.7786734923211107, \ 0.0137796394053688, \ 0.2075468682735203, \ 0.2075468682735205, \ 0.0137796394053687, \ 0.7786734923211107, \ 0.6112269128420675, \ 0.1943865435789664, \ 0.1943865435789659, \ 0.7856676213617251, \ 0.0007721391203271, \ 0.2135602395179477, \ 0.2135602395179478, \ 0.0007721391203269, \ 0.7856676213617251, \ 0.7151517773234829, \ 0.0054617908942934, \ 0.2793864317822236, \ 0.2793864317822238, \ 0.0054617908942932, \ 0.7151517773234826, \ 0.9031283677334343, \ 0.0000047096910187, \ 0.0968669225755469, \ 0.0968669225755472, \ 0.0000047096910184, \ 0.9031283677334342 ] ) w = np.array ( [ \ 0.0001016859723671, \ 0.0001016859723671, \ 0.0001016859723671, \ 0.0001016859723671, \ 0.0001016859723671, \ 0.0001016859723671, \ 0.0006540479665875, \ 0.0006540479665875, \ 0.0006540479665875, \ 0.0006540479665875, \ 0.0006540479665875, \ 0.0006540479665875, \ 0.0022989665688091, \ 0.0022989665688091, \ 0.0022989665688091, \ 0.0015198116582616, \ 0.0015198116582616, \ 0.0015198116582616, \ 0.0015198116582616, \ 0.0015198116582616, \ 0.0015198116582616, \ 0.0010996805664632, \ 0.0010996805664632, \ 0.0010996805664632, \ 0.0046696376839459, \ 0.0046696376839459, \ 0.0046696376839459, \ 0.0046696376839459, \ 0.0046696376839459, \ 0.0046696376839459, \ 0.0029521156305622, \ 0.0029521156305622, \ 0.0029521156305622, \ 0.0029521156305622, \ 0.0029521156305622, \ 0.0029521156305622, \ 0.0039973734536493, \ 0.0039973734536493, \ 0.0039973734536493, \ 0.0117400065912576, \ 0.0117400065912576, \ 0.0117400065912576, \ 0.0098609303129047, \ 0.0098609303129047, \ 0.0098609303129047, \ 0.0098609303129047, \ 0.0098609303129047, \ 0.0098609303129047, \ 0.0017262732588417, \ 0.0017262732588417, \ 0.0017262732588417, \ 0.0017262732588417, \ 0.0017262732588417, \ 0.0017262732588417, \ 0.0117612076394136, \ 0.0117612076394136, \ 0.0117612076394136, \ 0.0050361825013339, \ 0.0050361825013339, \ 0.0050361825013339, \ 0.0050361825013339, \ 0.0050361825013339, \ 0.0050361825013339, \ 0.0096578802294468, \ 0.0096578802294468, \ 0.0096578802294468, \ 0.0096578802294468, \ 0.0096578802294468, \ 0.0096578802294468, \ 0.0076119150208859, \ 0.0076119150208859, \ 0.0076119150208859, \ 0.0076119150208859, \ 0.0076119150208859, \ 0.0076119150208859, \ 0.0110658638875991, \ 0.0110658638875991, \ 0.0110658638875991, \ 0.0110658638875991, \ 0.0110658638875991, \ 0.0110658638875991, \ 0.0065038397126497, \ 0.0065038397126497, \ 0.0065038397126497, \ 0.0065038397126497, \ 0.0065038397126497, \ 0.0065038397126497, \ 0.0048326872534851, \ 0.0048326872534851, \ 0.0048326872534851, \ 0.0048326872534851, \ 0.0048326872534851, \ 0.0048326872534851, \ 0.0064842252138385, \ 0.0064842252138385, \ 0.0064842252138385, \ 0.0065935144677494, \ 0.0065935144677494, \ 0.0065935144677494, \ 0.0065935144677494, \ 0.0065935144677494, \ 0.0065935144677494, \ 0.0082852665131007, \ 0.0082852665131007, \ 0.0082852665131007, \ 0.0082852665131007, \ 0.0082852665131007, \ 0.0082852665131007, \ 0.0013994293854031, \ 0.0013994293854031, \ 0.0013994293854031, \ 0.0013994293854031, \ 0.0013994293854031, \ 0.0013994293854031, \ 0.0058334336795542, \ 0.0058334336795542, \ 0.0058334336795542, \ 0.0037293709434182, \ 0.0037293709434182, \ 0.0037293709434182, \ 0.0060952640324883, \ 0.0060952640324883, \ 0.0060952640324883, \ 0.0060952640324883, \ 0.0060952640324883, \ 0.0060952640324883, \ 0.0076873106859637, \ 0.0076873106859637, \ 0.0076873106859637, \ 0.0031432061481593, \ 0.0031432061481593, \ 0.0031432061481593, \ 0.0031432061481593, \ 0.0031432061481593, \ 0.0031432061481593, \ 0.0022313317933533, \ 0.0022313317933533, \ 0.0022313317933533, \ 0.0022313317933533, \ 0.0022313317933533, \ 0.0022313317933533, \ 0.0002269613567709, \ 0.0002269613567709, \ 0.0002269613567709, \ 0.0108136993162696, \ 0.0108136993162696, \ 0.0108136993162696, \ 0.0044357309734420, \ 0.0044357309734420, \ 0.0044357309734420, \ 0.0044357309734420, \ 0.0044357309734420, \ 0.0044357309734420, \ 0.0106474448424889, \ 0.0106474448424889, \ 0.0106474448424889, \ 0.0007609261662181, \ 0.0007609261662181, \ 0.0007609261662181, \ 0.0034883273457438, \ 0.0034883273457438, \ 0.0034883273457438, \ 0.0034883273457438, \ 0.0034883273457438, \ 0.0034883273457438, \ 0.0007318458736701, \ 0.0007318458736701, \ 0.0007318458736701, \ 0.0007318458736701, \ 0.0007318458736701, \ 0.0007318458736701, \ 0.0088609393001530, \ 0.0088609393001530, \ 0.0088609393001530, \ 0.0082507974307530, \ 0.0082507974307530, \ 0.0082507974307530, \ 0.0082507974307530, \ 0.0082507974307530, \ 0.0082507974307530, \ 0.0004979675731971, \ 0.0004979675731971, \ 0.0004979675731971, \ 0.0004979675731971, \ 0.0004979675731971, \ 0.0004979675731971, \ 0.0121009649301711, \ 0.0028058181373137, \ 0.0028058181373137, \ 0.0028058181373137, \ 0.0028058181373137, \ 0.0028058181373137, \ 0.0028058181373137, \ 0.0094001410371984, \ 0.0094001410371984, \ 0.0094001410371984, \ 0.0005776505742348, \ 0.0005776505742348, \ 0.0005776505742348, \ 0.0005776505742348, \ 0.0005776505742348, \ 0.0005776505742348, \ 0.0019626288054833, \ 0.0019626288054833, \ 0.0019626288054833, \ 0.0019626288054833, \ 0.0019626288054833, \ 0.0019626288054833, \ 0.0002873453546081, \ 0.0002873453546081, \ 0.0002873453546081, \ 0.0002873453546081, \ 0.0002873453546081, \ 0.0002873453546081 ] ) return a, b, c, w def rule35 ( ): #*****************************************************************************80 # ## rule35() returns the rule of precision 35. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3014351686173180, \ 0.3971296627653639, \ 0.3014351686173180, \ 0.4916414039828907, \ 0.4916414039828907, \ 0.0167171920342186, \ 0.3577931357985971, \ 0.3577931357985971, \ 0.2844137284028057, \ 0.0550454796915316, \ 0.9428863000930624, \ 0.0020682202154061, \ 0.9428863000930625, \ 0.0550454796915318, \ 0.0020682202154057, \ 0.4453764649152975, \ 0.5457185408985746, \ 0.0089049941861278, \ 0.5457185408985746, \ 0.4453764649152976, \ 0.0089049941861277, \ 0.1523840025243152, \ 0.8455000199126449, \ 0.0021159775630399, \ 0.8455000199126449, \ 0.1523840025243154, \ 0.0021159775630396, \ 0.2624139601093454, \ 0.4751720797813089, \ 0.2624139601093456, \ 0.3975166100282313, \ 0.5992221165426375, \ 0.0032612734291312, \ 0.5992221165426374, \ 0.3975166100282314, \ 0.0032612734291311, \ 0.4028164505857819, \ 0.4028164505857819, \ 0.1943670988284362, \ 0.1560787694034761, \ 0.7987533357833951, \ 0.0451678948131288, \ 0.7987533357833952, \ 0.1560787694034762, \ 0.0451678948131284, \ 0.4730889655006641, \ 0.4730889655006641, \ 0.0538220689986716, \ 0.1972956762765587, \ 0.7940983020176844, \ 0.0086060217057569, \ 0.7940983020176845, \ 0.1972956762765588, \ 0.0086060217057566, \ 0.0500938368999262, \ 0.9359318098485054, \ 0.0139743532515686, \ 0.9359318098485054, \ 0.0500938368999261, \ 0.0139743532515681, \ 0.2988590630143191, \ 0.5136696044857865, \ 0.1874713324998944, \ 0.5136696044857865, \ 0.2988590630143191, \ 0.1874713324998943, \ 0.0628680490440657, \ 0.8742639019118683, \ 0.0628680490440661, \ 0.4415974337549303, \ 0.4415974337549303, \ 0.1168051324901392, \ 0.0196271599834707, \ 0.9607456800330582, \ 0.0196271599834711, \ 0.3347633432653314, \ 0.4325143126587202, \ 0.2327223440759484, \ 0.4325143126587202, \ 0.3347633432653314, \ 0.2327223440759484, \ 0.2093728249763754, \ 0.7616252904089401, \ 0.0290018846146846, \ 0.7616252904089401, \ 0.2093728249763754, \ 0.0290018846146844, \ 0.1065647448613834, \ 0.8398677722708630, \ 0.0535674828677536, \ 0.8398677722708631, \ 0.1065647448613836, \ 0.0535674828677533, \ 0.3213626276695433, \ 0.6751411779813131, \ 0.0034961943491436, \ 0.6751411779813131, \ 0.3213626276695434, \ 0.0034961943491434, \ 0.2415870263479875, \ 0.7572369308551706, \ 0.0011760427968418, \ 0.7572369308551707, \ 0.2415870263479876, \ 0.0011760427968416, \ 0.3331530997207648, \ 0.5528929715350868, \ 0.1139539287441483, \ 0.5528929715350868, \ 0.3331530997207648, \ 0.1139539287441482, \ 0.1551165548133034, \ 0.7599448456751416, \ 0.0849385995115551, \ 0.7599448456751415, \ 0.1551165548133034, \ 0.0849385995115548, \ 0.3710141516774619, \ 0.4764206619753218, \ 0.1525651863472163, \ 0.4764206619753217, \ 0.3710141516774620, \ 0.1525651863472163, \ 0.0402868688301934, \ 0.9194262623396129, \ 0.0402868688301939, \ 0.2708836618077721, \ 0.7154976600831513, \ 0.0136186781090767, \ 0.7154976600831513, \ 0.2708836618077720, \ 0.0136186781090765, \ 0.3525067484154665, \ 0.5912668641409812, \ 0.0562263874435524, \ 0.5912668641409811, \ 0.3525067484154665, \ 0.0562263874435522, \ 0.4057201327781905, \ 0.5125263777821213, \ 0.0817534894396881, \ 0.5125263777821213, \ 0.4057201327781905, \ 0.0817534894396881, \ 0.2189496810149983, \ 0.7174078887952542, \ 0.0636424301897475, \ 0.7174078887952543, \ 0.2189496810149983, \ 0.0636424301897472, \ 0.2067092480855645, \ 0.6778965310783613, \ 0.1153942208360741, \ 0.6778965310783613, \ 0.2067092480855646, \ 0.1153942208360739, \ 0.0985261546687924, \ 0.8029476906624150, \ 0.0985261546687927, \ 0.2566010878790922, \ 0.5952117958375970, \ 0.1481871162833107, \ 0.5952117958375971, \ 0.2566010878790923, \ 0.1481871162833105, \ 0.1382062952112500, \ 0.8431958337273686, \ 0.0185978710613815, \ 0.8431958337273686, \ 0.1382062952112501, \ 0.0185978710613812, \ 0.1395344629893073, \ 0.7209310740213852, \ 0.1395344629893076, \ 0.2215360105096920, \ 0.5569279789806159, \ 0.2215360105096921, \ 0.4258102085854810, \ 0.5412187714875727, \ 0.0329710199269463, \ 0.5412187714875726, \ 0.4258102085854810, \ 0.0329710199269463, \ 0.1807503221352996, \ 0.6384993557294008, \ 0.1807503221352998, \ 0.2797259269522402, \ 0.6348945214748060, \ 0.0853795515729538, \ 0.6348945214748060, \ 0.2797259269522402, \ 0.0853795515729537, \ 0.0224666835802112, \ 0.9739002605768547, \ 0.0036330558429342, \ 0.9739002605768547, \ 0.0224666835802113, \ 0.0036330558429336, \ 0.0838622585244554, \ 0.8901176638131806, \ 0.0260200776623640, \ 0.8901176638131806, \ 0.0838622585244554, \ 0.0260200776623637, \ 0.2848003464144683, \ 0.6757427274290935, \ 0.0394569261564381, \ 0.6757427274290936, \ 0.2848003464144683, \ 0.0394569261564380, \ 0.3565941035365738, \ 0.6236351787590180, \ 0.0197707177044082, \ 0.6236351787590180, \ 0.3565941035365738, \ 0.0197707177044081, \ 0.0974242311151380, \ 0.8975470714692345, \ 0.0050286974156275, \ 0.8975470714692346, \ 0.0974242311151381, \ 0.0050286974156271, \ 0.0042772072684830, \ 0.9914455854630337, \ 0.0042772072684834, \ 0.4999132224862251, \ 0.4999132224862251, \ 0.0001735550275497 ] ) b = np.array ( [ \ 0.3014351686173181, \ 0.3014351686173181, \ 0.3971296627653640, \ 0.0167171920342186, \ 0.4916414039828907, \ 0.4916414039828909, \ 0.2844137284028058, \ 0.3577931357985972, \ 0.3577931357985973, \ 0.0020682202154059, \ 0.0550454796915316, \ 0.9428863000930624, \ 0.0020682202154059, \ 0.9428863000930624, \ 0.0550454796915320, \ 0.0089049941861278, \ 0.4453764649152975, \ 0.5457185408985749, \ 0.0089049941861278, \ 0.5457185408985747, \ 0.4453764649152978, \ 0.0021159775630399, \ 0.1523840025243152, \ 0.8455000199126450, \ 0.0021159775630399, \ 0.8455000199126450, \ 0.1523840025243156, \ 0.2624139601093456, \ 0.2624139601093455, \ 0.4751720797813091, \ 0.0032612734291312, \ 0.3975166100282314, \ 0.5992221165426377, \ 0.0032612734291312, \ 0.5992221165426375, \ 0.3975166100282316, \ 0.1943670988284363, \ 0.4028164505857819, \ 0.4028164505857820, \ 0.0451678948131287, \ 0.1560787694034761, \ 0.7987533357833954, \ 0.0451678948131287, \ 0.7987533357833954, \ 0.1560787694034764, \ 0.0538220689986717, \ 0.4730889655006642, \ 0.4730889655006644, \ 0.0086060217057568, \ 0.1972956762765587, \ 0.7940983020176846, \ 0.0086060217057568, \ 0.7940983020176846, \ 0.1972956762765590, \ 0.0139743532515684, \ 0.0500938368999262, \ 0.9359318098485054, \ 0.0139743532515684, \ 0.9359318098485058, \ 0.0500938368999265, \ 0.1874713324998945, \ 0.2988590630143192, \ 0.5136696044857866, \ 0.1874713324998945, \ 0.5136696044857866, \ 0.2988590630143193, \ 0.0628680490440660, \ 0.0628680490440657, \ 0.8742639019118684, \ 0.1168051324901393, \ 0.4415974337549304, \ 0.4415974337549305, \ 0.0196271599834710, \ 0.0196271599834707, \ 0.9607456800330584, \ 0.2327223440759485, \ 0.3347633432653315, \ 0.4325143126587203, \ 0.2327223440759485, \ 0.4325143126587202, \ 0.3347633432653315, \ 0.0290018846146845, \ 0.2093728249763754, \ 0.7616252904089403, \ 0.0290018846146845, \ 0.7616252904089402, \ 0.2093728249763756, \ 0.0535674828677535, \ 0.1065647448613835, \ 0.8398677722708632, \ 0.0535674828677535, \ 0.8398677722708632, \ 0.1065647448613838, \ 0.0034961943491435, \ 0.3213626276695434, \ 0.6751411779813132, \ 0.0034961943491435, \ 0.6751411779813132, \ 0.3213626276695436, \ 0.0011760427968418, \ 0.2415870263479876, \ 0.7572369308551709, \ 0.0011760427968418, \ 0.7572369308551709, \ 0.2415870263479878, \ 0.1139539287441484, \ 0.3331530997207649, \ 0.5528929715350870, \ 0.1139539287441484, \ 0.5528929715350869, \ 0.3331530997207651, \ 0.0849385995115550, \ 0.1551165548133034, \ 0.7599448456751416, \ 0.0849385995115550, \ 0.7599448456751416, \ 0.1551165548133037, \ 0.1525651863472164, \ 0.3710141516774620, \ 0.4764206619753220, \ 0.1525651863472164, \ 0.4764206619753218, \ 0.3710141516774621, \ 0.0402868688301937, \ 0.0402868688301934, \ 0.9194262623396129, \ 0.0136186781090766, \ 0.2708836618077721, \ 0.7154976600831515, \ 0.0136186781090766, \ 0.7154976600831515, \ 0.2708836618077723, \ 0.0562263874435524, \ 0.3525067484154665, \ 0.5912668641409813, \ 0.0562263874435524, \ 0.5912668641409812, \ 0.3525067484154668, \ 0.0817534894396882, \ 0.4057201327781905, \ 0.5125263777821215, \ 0.0817534894396882, \ 0.5125263777821214, \ 0.4057201327781906, \ 0.0636424301897474, \ 0.2189496810149984, \ 0.7174078887952544, \ 0.0636424301897474, \ 0.7174078887952544, \ 0.2189496810149986, \ 0.1153942208360741, \ 0.2067092480855645, \ 0.6778965310783615, \ 0.1153942208360741, \ 0.6778965310783615, \ 0.2067092480855648, \ 0.0985261546687926, \ 0.0985261546687924, \ 0.8029476906624151, \ 0.1481871162833107, \ 0.2566010878790924, \ 0.5952117958375971, \ 0.1481871162833107, \ 0.5952117958375971, \ 0.2566010878790925, \ 0.0185978710613814, \ 0.1382062952112499, \ 0.8431958337273687, \ 0.0185978710613814, \ 0.8431958337273687, \ 0.1382062952112503, \ 0.1395344629893075, \ 0.1395344629893073, \ 0.7209310740213853, \ 0.2215360105096922, \ 0.2215360105096921, \ 0.5569279789806160, \ 0.0329710199269464, \ 0.4258102085854810, \ 0.5412187714875728, \ 0.0329710199269464, \ 0.5412187714875727, \ 0.4258102085854812, \ 0.1807503221352998, \ 0.1807503221352996, \ 0.6384993557294009, \ 0.0853795515729539, \ 0.2797259269522402, \ 0.6348945214748062, \ 0.0853795515729539, \ 0.6348945214748061, \ 0.2797259269522404, \ 0.0036330558429340, \ 0.0224666835802112, \ 0.9739002605768550, \ 0.0036330558429340, \ 0.9739002605768550, \ 0.0224666835802115, \ 0.0260200776623640, \ 0.0838622585244554, \ 0.8901176638131808, \ 0.0260200776623640, \ 0.8901176638131808, \ 0.0838622585244558, \ 0.0394569261564381, \ 0.2848003464144683, \ 0.6757427274290937, \ 0.0394569261564381, \ 0.6757427274290937, \ 0.2848003464144686, \ 0.0197707177044082, \ 0.3565941035365738, \ 0.6236351787590181, \ 0.0197707177044082, \ 0.6236351787590181, \ 0.3565941035365741, \ 0.0050286974156274, \ 0.0974242311151380, \ 0.8975470714692347, \ 0.0050286974156274, \ 0.8975470714692347, \ 0.0974242311151384, \ 0.0042772072684833, \ 0.0042772072684829, \ 0.9914455854630339, \ 0.0001735550275498, \ 0.4999132224862252, \ 0.4999132224862253 ] ) c = np.array ( [ \ 0.3971296627653639, \ 0.3014351686173179, \ 0.3014351686173180, \ 0.4916414039828907, \ 0.0167171920342186, \ 0.4916414039828905, \ 0.3577931357985971, \ 0.2844137284028057, \ 0.3577931357985971, \ 0.9428863000930624, \ 0.0020682202154060, \ 0.0550454796915315, \ 0.0550454796915315, \ 0.0020682202154058, \ 0.9428863000930622, \ 0.5457185408985747, \ 0.0089049941861278, \ 0.4453764649152973, \ 0.4453764649152975, \ 0.0089049941861277, \ 0.5457185408985745, \ 0.8455000199126449, \ 0.0021159775630399, \ 0.1523840025243151, \ 0.1523840025243152, \ 0.0021159775630396, \ 0.8455000199126448, \ 0.4751720797813090, \ 0.2624139601093455, \ 0.2624139601093453, \ 0.5992221165426375, \ 0.0032612734291312, \ 0.3975166100282311, \ 0.3975166100282314, \ 0.0032612734291312, \ 0.5992221165426372, \ 0.4028164505857818, \ 0.1943670988284362, \ 0.4028164505857818, \ 0.7987533357833952, \ 0.0451678948131287, \ 0.1560787694034759, \ 0.1560787694034761, \ 0.0451678948131284, \ 0.7987533357833951, \ 0.4730889655006641, \ 0.0538220689986716, \ 0.4730889655006639, \ 0.7940983020176844, \ 0.0086060217057569, \ 0.1972956762765585, \ 0.1972956762765587, \ 0.0086060217057566, \ 0.7940983020176844, \ 0.9359318098485054, \ 0.0139743532515684, \ 0.0500938368999260, \ 0.0500938368999262, \ 0.0139743532515680, \ 0.9359318098485053, \ 0.5136696044857865, \ 0.1874713324998943, \ 0.2988590630143190, \ 0.2988590630143190, \ 0.1874713324998943, \ 0.5136696044857864, \ 0.8742639019118683, \ 0.0628680490440660, \ 0.0628680490440655, \ 0.4415974337549304, \ 0.1168051324901392, \ 0.4415974337549302, \ 0.9607456800330582, \ 0.0196271599834711, \ 0.0196271599834704, \ 0.4325143126587201, \ 0.2327223440759483, \ 0.3347633432653313, \ 0.3347633432653313, \ 0.2327223440759484, \ 0.4325143126587201, \ 0.7616252904089401, \ 0.0290018846146845, \ 0.2093728249763751, \ 0.2093728249763754, \ 0.0290018846146843, \ 0.7616252904089400, \ 0.8398677722708631, \ 0.0535674828677536, \ 0.1065647448613832, \ 0.1065647448613834, \ 0.0535674828677533, \ 0.8398677722708630, \ 0.6751411779813131, \ 0.0034961943491435, \ 0.3213626276695432, \ 0.3213626276695434, \ 0.0034961943491434, \ 0.6751411779813130, \ 0.7572369308551706, \ 0.0011760427968418, \ 0.2415870263479873, \ 0.2415870263479875, \ 0.0011760427968416, \ 0.7572369308551705, \ 0.5528929715350869, \ 0.1139539287441483, \ 0.3331530997207647, \ 0.3331530997207648, \ 0.1139539287441483, \ 0.5528929715350867, \ 0.7599448456751415, \ 0.0849385995115549, \ 0.1551165548133032, \ 0.1551165548133034, \ 0.0849385995115549, \ 0.7599448456751414, \ 0.4764206619753217, \ 0.1525651863472163, \ 0.3710141516774618, \ 0.3710141516774619, \ 0.1525651863472162, \ 0.4764206619753216, \ 0.9194262623396129, \ 0.0402868688301937, \ 0.0402868688301933, \ 0.7154976600831513, \ 0.0136186781090766, \ 0.2708836618077718, \ 0.2708836618077721, \ 0.0136186781090765, \ 0.7154976600831512, \ 0.5912668641409812, \ 0.0562263874435523, \ 0.3525067484154663, \ 0.3525067484154665, \ 0.0562263874435524, \ 0.5912668641409811, \ 0.5125263777821213, \ 0.0817534894396882, \ 0.4057201327781904, \ 0.4057201327781905, \ 0.0817534894396881, \ 0.5125263777821213, \ 0.7174078887952543, \ 0.0636424301897474, \ 0.2189496810149981, \ 0.2189496810149983, \ 0.0636424301897472, \ 0.7174078887952542, \ 0.6778965310783613, \ 0.1153942208360741, \ 0.2067092480855645, \ 0.2067092480855646, \ 0.1153942208360740, \ 0.6778965310783613, \ 0.8029476906624151, \ 0.0985261546687926, \ 0.0985261546687922, \ 0.5952117958375970, \ 0.1481871162833107, \ 0.2566010878790922, \ 0.2566010878790922, \ 0.1481871162833106, \ 0.5952117958375969, \ 0.8431958337273686, \ 0.0185978710613814, \ 0.1382062952112498, \ 0.1382062952112500, \ 0.0185978710613811, \ 0.8431958337273685, \ 0.7209310740213852, \ 0.1395344629893075, \ 0.1395344629893071, \ 0.5569279789806159, \ 0.2215360105096921, \ 0.2215360105096918, \ 0.5412187714875726, \ 0.0329710199269463, \ 0.4258102085854808, \ 0.4258102085854810, \ 0.0329710199269463, \ 0.5412187714875725, \ 0.6384993557294008, \ 0.1807503221352997, \ 0.1807503221352994, \ 0.6348945214748060, \ 0.0853795515729538, \ 0.2797259269522400, \ 0.2797259269522402, \ 0.0853795515729537, \ 0.6348945214748060, \ 0.9739002605768549, \ 0.0036330558429341, \ 0.0224666835802109, \ 0.0224666835802113, \ 0.0036330558429337, \ 0.9739002605768549, \ 0.8901176638131807, \ 0.0260200776623640, \ 0.0838622585244552, \ 0.0838622585244555, \ 0.0260200776623637, \ 0.8901176638131805, \ 0.6757427274290936, \ 0.0394569261564382, \ 0.2848003464144682, \ 0.2848003464144683, \ 0.0394569261564380, \ 0.6757427274290935, \ 0.6236351787590180, \ 0.0197707177044082, \ 0.3565941035365737, \ 0.3565941035365738, \ 0.0197707177044081, \ 0.6236351787590179, \ 0.8975470714692345, \ 0.0050286974156274, \ 0.0974242311151378, \ 0.0974242311151380, \ 0.0050286974156272, \ 0.8975470714692345, \ 0.9914455854630339, \ 0.0042772072684833, \ 0.0042772072684828, \ 0.4999132224862252, \ 0.0001735550275497, \ 0.4999132224862250 ] ) w = np.array ( [ \ 0.0057479340296702, \ 0.0057479340296702, \ 0.0057479340296702, \ 0.0022963680920994, \ 0.0022963680920994, \ 0.0022963680920994, \ 0.0079953508418643, \ 0.0079953508418643, \ 0.0079953508418643, \ 0.0004541993823754, \ 0.0004541993823754, \ 0.0004541993823754, \ 0.0004541993823754, \ 0.0004541993823754, \ 0.0004541993823754, \ 0.0019717493309842, \ 0.0019717493309842, \ 0.0019717493309842, \ 0.0019717493309842, \ 0.0019717493309842, \ 0.0019717493309842, \ 0.0007826663054394, \ 0.0007826663054394, \ 0.0007826663054394, \ 0.0007826663054394, \ 0.0007826663054394, \ 0.0007826663054394, \ 0.0087901858933278, \ 0.0087901858933278, \ 0.0087901858933278, \ 0.0012646931023972, \ 0.0012646931023972, \ 0.0012646931023972, \ 0.0012646931023972, \ 0.0012646931023972, \ 0.0012646931023972, \ 0.0083203666123256, \ 0.0083203666123256, \ 0.0083203666123256, \ 0.0035572562609095, \ 0.0035572562609095, \ 0.0035572562609095, \ 0.0035572562609095, \ 0.0035572562609095, \ 0.0035572562609095, \ 0.0052751882851615, \ 0.0052751882851615, \ 0.0052751882851615, \ 0.0018428326631755, \ 0.0018428326631755, \ 0.0018428326631755, \ 0.0018428326631755, \ 0.0018428326631755, \ 0.0018428326631755, \ 0.0013289799356542, \ 0.0013289799356542, \ 0.0013289799356542, \ 0.0013289799356542, \ 0.0013289799356542, \ 0.0013289799356542, \ 0.0090234128551062, \ 0.0090234128551062, \ 0.0090234128551062, \ 0.0090234128551062, \ 0.0090234128551062, \ 0.0090234128551062, \ 0.0029682066390516, \ 0.0029682066390516, \ 0.0029682066390516, \ 0.0076051825305364, \ 0.0076051825305364, \ 0.0076051825305364, \ 0.0010131210327381, \ 0.0010131210327381, \ 0.0010131210327381, \ 0.0086055044940838, \ 0.0086055044940838, \ 0.0086055044940838, \ 0.0086055044940838, \ 0.0086055044940838, \ 0.0086055044940838, \ 0.0036104679969938, \ 0.0036104679969938, \ 0.0036104679969938, \ 0.0036104679969938, \ 0.0036104679969938, \ 0.0036104679969938, \ 0.0035235607672108, \ 0.0035235607672108, \ 0.0035235607672108, \ 0.0035235607672108, \ 0.0035235607672108, \ 0.0035235607672108, \ 0.0013780765220064, \ 0.0013780765220064, \ 0.0013780765220064, \ 0.0013780765220064, \ 0.0013780765220064, \ 0.0013780765220064, \ 0.0006950295859519, \ 0.0006950295859519, \ 0.0006950295859519, \ 0.0006950295859519, \ 0.0006950295859519, \ 0.0006950295859519, \ 0.0081297205980780, \ 0.0081297205980780, \ 0.0081297205980780, \ 0.0081297205980780, \ 0.0081297205980780, \ 0.0081297205980780, \ 0.0054896563598667, \ 0.0054896563598667, \ 0.0054896563598667, \ 0.0054896563598667, \ 0.0054896563598667, \ 0.0054896563598667, \ 0.0082359873228582, \ 0.0082359873228582, \ 0.0082359873228582, \ 0.0082359873228582, \ 0.0082359873228582, \ 0.0082359873228582, \ 0.0020648356265983, \ 0.0020648356265983, \ 0.0020648356265983, \ 0.0027797735193626, \ 0.0027797735193626, \ 0.0027797735193626, \ 0.0027797735193626, \ 0.0027797735193626, \ 0.0027797735193626, \ 0.0063317818814834, \ 0.0063317818814834, \ 0.0063317818814834, \ 0.0063317818814834, \ 0.0063317818814834, \ 0.0063317818814834, \ 0.0069457107199416, \ 0.0069457107199416, \ 0.0069457107199416, \ 0.0069457107199416, \ 0.0069457107199416, \ 0.0069457107199416, \ 0.0055659411156861, \ 0.0055659411156861, \ 0.0055659411156861, \ 0.0055659411156861, \ 0.0055659411156861, \ 0.0055659411156861, \ 0.0073376101567627, \ 0.0073376101567627, \ 0.0073376101567627, \ 0.0073376101567627, \ 0.0073376101567627, \ 0.0073376101567627, \ 0.0050036396155573, \ 0.0050036396155573, \ 0.0050036396155573, \ 0.0087114266235609, \ 0.0087114266235609, \ 0.0087114266235609, \ 0.0087114266235609, \ 0.0087114266235609, \ 0.0087114266235609, \ 0.0027367494327220, \ 0.0027367494327220, \ 0.0027367494327220, \ 0.0027367494327220, \ 0.0027367494327220, \ 0.0027367494327220, \ 0.0067190798124174, \ 0.0067190798124174, \ 0.0067190798124174, \ 0.0091619089409373, \ 0.0091619089409373, \ 0.0091619089409373, \ 0.0047016575809322, \ 0.0047016575809322, \ 0.0047016575809322, \ 0.0047016575809322, \ 0.0047016575809322, \ 0.0047016575809322, \ 0.0083719066370130, \ 0.0083719066370130, \ 0.0083719066370130, \ 0.0071750089599327, \ 0.0071750089599327, \ 0.0071750089599327, \ 0.0071750089599327, \ 0.0071750089599327, \ 0.0071750089599327, \ 0.0004732469738005, \ 0.0004732469738005, \ 0.0004732469738005, \ 0.0004732469738005, \ 0.0004732469738005, \ 0.0004732469738005, \ 0.0025346621113678, \ 0.0025346621113678, \ 0.0025346621113678, \ 0.0025346621113678, \ 0.0025346621113678, \ 0.0025346621113678, \ 0.0050701573000114, \ 0.0050701573000114, \ 0.0050701573000114, \ 0.0050701573000114, \ 0.0050701573000114, \ 0.0050701573000114, \ 0.0040540720868840, \ 0.0040540720868840, \ 0.0040540720868840, \ 0.0040540720868840, \ 0.0040540720868840, \ 0.0040540720868840, \ 0.0012544783872410, \ 0.0012544783872410, \ 0.0012544783872410, \ 0.0012544783872410, \ 0.0012544783872410, \ 0.0012544783872410, \ 0.0002403337374048, \ 0.0002403337374048, \ 0.0002403337374048, \ 0.0006275843410706, \ 0.0006275843410706, \ 0.0006275843410706 ] ) return a, b, c, w def rule36 ( ): #*****************************************************************************80 # ## rule36() returns the rule of precision 36. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.2550023360754195, \ 0.7127053999508112, \ 0.0322922639737694, \ 0.7127053999508112, \ 0.2550023360754196, \ 0.0322922639737692, \ 0.2711215136033400, \ 0.6347382765922519, \ 0.0941402098044082, \ 0.6347382765922519, \ 0.2711215136033400, \ 0.0941402098044080, \ 0.0926886044848755, \ 0.8423177234108842, \ 0.0649936721042403, \ 0.8423177234108843, \ 0.0926886044848757, \ 0.0649936721042400, \ 0.3294543765845505, \ 0.5968319589620307, \ 0.0737136644534188, \ 0.5968319589620307, \ 0.3294543765845505, \ 0.0737136644534187, \ 0.2883788411304420, \ 0.6615561707226660, \ 0.0500649881468920, \ 0.6615561707226659, \ 0.2883788411304421, \ 0.0500649881468918, \ 0.3921724164051739, \ 0.5419312451199315, \ 0.0658963384748946, \ 0.5419312451199314, \ 0.3921724164051738, \ 0.0658963384748946, \ 0.0076222500155876, \ 0.9911436314566491, \ 0.0012341185277635, \ 0.9911436314566491, \ 0.0076222500155876, \ 0.0012341185277630, \ 0.4123573403136303, \ 0.4123573403136303, \ 0.1752853193727393, \ 0.1782079366279757, \ 0.7160962360444145, \ 0.1056958273276099, \ 0.7160962360444145, \ 0.1782079366279757, \ 0.1056958273276097, \ 0.3102489314599136, \ 0.5658793981445355, \ 0.1238716703955509, \ 0.5658793981445355, \ 0.3102489314599136, \ 0.1238716703955508, \ 0.4390483832458435, \ 0.4390483832458435, \ 0.1219032335083129, \ 0.0829157021331252, \ 0.9142769002483087, \ 0.0028073976185662, \ 0.9142769002483088, \ 0.0829157021331253, \ 0.0028073976185659, \ 0.3796386793469431, \ 0.5096715423270356, \ 0.1106897783260212, \ 0.5096715423270356, \ 0.3796386793469431, \ 0.1106897783260211, \ 0.2350523254582137, \ 0.5298953490835725, \ 0.2350523254582138, \ 0.1980682921145434, \ 0.7991752852717510, \ 0.0027564226137057, \ 0.7991752852717511, \ 0.1980682921145434, \ 0.0027564226137055, \ 0.1479479453220730, \ 0.7800003555819109, \ 0.0720516990960159, \ 0.7800003555819111, \ 0.1479479453220731, \ 0.0720516990960157, \ 0.2292027665534673, \ 0.7563686218758484, \ 0.0144286115706843, \ 0.7563686218758484, \ 0.2292027665534674, \ 0.0144286115706841, \ 0.3574738503443845, \ 0.6397835829582036, \ 0.0027425666974119, \ 0.6397835829582036, \ 0.3574738503443844, \ 0.0027425666974117, \ 0.1252496722294377, \ 0.8357259979283462, \ 0.0390243298422160, \ 0.8357259979283463, \ 0.1252496722294378, \ 0.0390243298422157, \ 0.0209805646004062, \ 0.9715447719336604, \ 0.0074746634659335, \ 0.9715447719336604, \ 0.0209805646004063, \ 0.0074746634659331, \ 0.2691316117440097, \ 0.5552966096544709, \ 0.1755717786015192, \ 0.5552966096544710, \ 0.2691316117440098, \ 0.1755717786015191, \ 0.1508217347798915, \ 0.6983565304402166, \ 0.1508217347798919, \ 0.3462198724218936, \ 0.4825533687273535, \ 0.1712267588507529, \ 0.4825533687273536, \ 0.3462198724218935, \ 0.1712267588507528, \ 0.4423877426580685, \ 0.5233061138878379, \ 0.0343061434540937, \ 0.5233061138878379, \ 0.4423877426580686, \ 0.0343061434540936, \ 0.2746338837226588, \ 0.7223364807654942, \ 0.0030296355118472, \ 0.7223364807654941, \ 0.2746338837226588, \ 0.0030296355118469, \ 0.2237012846551441, \ 0.7038117568892118, \ 0.0724869584556441, \ 0.7038117568892117, \ 0.2237012846551442, \ 0.0724869584556440, \ 0.2264729475116298, \ 0.6397100291477062, \ 0.1338170233406640, \ 0.6397100291477064, \ 0.2264729475116297, \ 0.1338170233406638, \ 0.1633619668293704, \ 0.8189638129323793, \ 0.0176742202382503, \ 0.8189638129323793, \ 0.1633619668293705, \ 0.0176742202382500, \ 0.1907912728543789, \ 0.7670005101060391, \ 0.0422082170395822, \ 0.7670005101060390, \ 0.1907912728543789, \ 0.0422082170395819, \ 0.3581658706314307, \ 0.6074178089715797, \ 0.0344163203969896, \ 0.6074178089715797, \ 0.3581658706314307, \ 0.0344163203969895, \ 0.0993849892050522, \ 0.8831620205339272, \ 0.0174529902610207, \ 0.8831620205339273, \ 0.0993849892050523, \ 0.0174529902610203, \ 0.4502328978916524, \ 0.5485392672636246, \ 0.0012278348447230, \ 0.5485392672636246, \ 0.4502328978916525, \ 0.0012278348447230, \ 0.4642737776346700, \ 0.4642737776346701, \ 0.0714524447306599, \ 0.3048602929866793, \ 0.4588765169470121, \ 0.2362631900663086, \ 0.4588765169470121, \ 0.3048602929866793, \ 0.2362631900663085, \ 0.3135836062706951, \ 0.6708934652005731, \ 0.0155229285287318, \ 0.6708934652005731, \ 0.3135836062706952, \ 0.0155229285287316, \ 0.1348062882666829, \ 0.8613456659624720, \ 0.0038480457708451, \ 0.8613456659624721, \ 0.1348062882666830, \ 0.0038480457708449, \ 0.1911613618773089, \ 0.6176772762453819, \ 0.1911613618773091, \ 0.0658281924328199, \ 0.8960993382441670, \ 0.0380724693230132, \ 0.8960993382441671, \ 0.0658281924328200, \ 0.0380724693230129, \ 0.0293500490934269, \ 0.9412999018131458, \ 0.0293500490934273, \ 0.3081452189910933, \ 0.3837095620178134, \ 0.3081452189910933, \ 0.0531928439194577, \ 0.9346369019266020, \ 0.0121702541539404, \ 0.9346369019266021, \ 0.0531928439194579, \ 0.0121702541539399, \ 0.1111782647883809, \ 0.7776434704232379, \ 0.1111782647883812, \ 0.0406479626359586, \ 0.9584934783193574, \ 0.0008585590446841, \ 0.9584934783193575, \ 0.0406479626359587, \ 0.0008585590446836, \ 0.4064475672122849, \ 0.5812165949773879, \ 0.0123358378103273, \ 0.5812165949773879, \ 0.4064475672122848, \ 0.0123358378103271, \ 0.3810023496034419, \ 0.3810023496034418, \ 0.2379953007931161, \ 0.4944809967477004, \ 0.4944809967477005, \ 0.0110380065045990 ] ) b = np.array ( [ \ 0.0322922639737694, \ 0.2550023360754195, \ 0.7127053999508113, \ 0.0322922639737694, \ 0.7127053999508113, \ 0.2550023360754198, \ 0.0941402098044082, \ 0.2711215136033400, \ 0.6347382765922520, \ 0.0941402098044082, \ 0.6347382765922520, \ 0.2711215136033402, \ 0.0649936721042402, \ 0.0926886044848756, \ 0.8423177234108843, \ 0.0649936721042402, \ 0.8423177234108843, \ 0.0926886044848759, \ 0.0737136644534188, \ 0.3294543765845505, \ 0.5968319589620309, \ 0.0737136644534188, \ 0.5968319589620308, \ 0.3294543765845507, \ 0.0500649881468919, \ 0.2883788411304421, \ 0.6615561707226660, \ 0.0500649881468919, \ 0.6615561707226660, \ 0.2883788411304423, \ 0.0658963384748947, \ 0.3921724164051739, \ 0.5419312451199317, \ 0.0658963384748947, \ 0.5419312451199316, \ 0.3921724164051740, \ 0.0012341185277633, \ 0.0076222500155876, \ 0.9911436314566491, \ 0.0012341185277633, \ 0.9911436314566494, \ 0.0076222500155880, \ 0.1752853193727394, \ 0.4123573403136304, \ 0.4123573403136305, \ 0.1056958273276099, \ 0.1782079366279757, \ 0.7160962360444146, \ 0.1056958273276099, \ 0.7160962360444146, \ 0.1782079366279760, \ 0.1238716703955509, \ 0.3102489314599137, \ 0.5658793981445357, \ 0.1238716703955509, \ 0.5658793981445357, \ 0.3102489314599138, \ 0.1219032335083130, \ 0.4390483832458436, \ 0.4390483832458437, \ 0.0028073976185661, \ 0.0829157021331252, \ 0.9142769002483089, \ 0.0028073976185661, \ 0.9142769002483089, \ 0.0829157021331255, \ 0.1106897783260212, \ 0.3796386793469432, \ 0.5096715423270358, \ 0.1106897783260212, \ 0.5096715423270358, \ 0.3796386793469433, \ 0.2350523254582139, \ 0.2350523254582138, \ 0.5298953490835726, \ 0.0027564226137057, \ 0.1980682921145434, \ 0.7991752852717512, \ 0.0027564226137057, \ 0.7991752852717511, \ 0.1980682921145436, \ 0.0720516990960159, \ 0.1479479453220730, \ 0.7800003555819113, \ 0.0720516990960159, \ 0.7800003555819113, \ 0.1479479453220733, \ 0.0144286115706843, \ 0.2292027665534674, \ 0.7563686218758485, \ 0.0144286115706843, \ 0.7563686218758484, \ 0.2292027665534676, \ 0.0027425666974119, \ 0.3574738503443846, \ 0.6397835829582038, \ 0.0027425666974119, \ 0.6397835829582038, \ 0.3574738503443848, \ 0.0390243298422159, \ 0.1252496722294378, \ 0.8357259979283465, \ 0.0390243298422159, \ 0.8357259979283465, \ 0.1252496722294380, \ 0.0074746634659333, \ 0.0209805646004062, \ 0.9715447719336605, \ 0.0074746634659333, \ 0.9715447719336605, \ 0.0209805646004066, \ 0.1755717786015193, \ 0.2691316117440098, \ 0.5552966096544713, \ 0.1755717786015193, \ 0.5552966096544711, \ 0.2691316117440100, \ 0.1508217347798918, \ 0.1508217347798916, \ 0.6983565304402167, \ 0.1712267588507529, \ 0.3462198724218936, \ 0.4825533687273537, \ 0.1712267588507529, \ 0.4825533687273537, \ 0.3462198724218937, \ 0.0343061434540937, \ 0.4423877426580686, \ 0.5233061138878380, \ 0.0343061434540937, \ 0.5233061138878379, \ 0.4423877426580687, \ 0.0030296355118471, \ 0.2746338837226588, \ 0.7223364807654942, \ 0.0030296355118471, \ 0.7223364807654942, \ 0.2746338837226592, \ 0.0724869584556441, \ 0.2237012846551441, \ 0.7038117568892120, \ 0.0724869584556441, \ 0.7038117568892119, \ 0.2237012846551444, \ 0.1338170233406639, \ 0.2264729475116298, \ 0.6397100291477065, \ 0.1338170233406639, \ 0.6397100291477065, \ 0.2264729475116300, \ 0.0176742202382503, \ 0.1633619668293704, \ 0.8189638129323794, \ 0.0176742202382503, \ 0.8189638129323794, \ 0.1633619668293707, \ 0.0422082170395821, \ 0.1907912728543789, \ 0.7670005101060392, \ 0.0422082170395821, \ 0.7670005101060391, \ 0.1907912728543791, \ 0.0344163203969896, \ 0.3581658706314307, \ 0.6074178089715798, \ 0.0344163203969896, \ 0.6074178089715798, \ 0.3581658706314309, \ 0.0174529902610205, \ 0.0993849892050522, \ 0.8831620205339273, \ 0.0174529902610205, \ 0.8831620205339273, \ 0.0993849892050526, \ 0.0012278348447231, \ 0.4502328978916525, \ 0.5485392672636248, \ 0.0012278348447231, \ 0.5485392672636246, \ 0.4502328978916527, \ 0.0714524447306600, \ 0.4642737776346700, \ 0.4642737776346703, \ 0.2362631900663087, \ 0.3048602929866794, \ 0.4588765169470122, \ 0.2362631900663087, \ 0.4588765169470121, \ 0.3048602929866794, \ 0.0155229285287317, \ 0.3135836062706952, \ 0.6708934652005732, \ 0.0155229285287317, \ 0.6708934652005732, \ 0.3135836062706954, \ 0.0038480457708451, \ 0.1348062882666829, \ 0.8613456659624722, \ 0.0038480457708451, \ 0.8613456659624722, \ 0.1348062882666833, \ 0.1911613618773092, \ 0.1911613618773090, \ 0.6176772762453820, \ 0.0380724693230131, \ 0.0658281924328199, \ 0.8960993382441672, \ 0.0380724693230131, \ 0.8960993382441672, \ 0.0658281924328202, \ 0.0293500490934272, \ 0.0293500490934269, \ 0.9412999018131460, \ 0.3081452189910934, \ 0.3081452189910934, \ 0.3837095620178135, \ 0.0121702541539402, \ 0.0531928439194577, \ 0.9346369019266021, \ 0.0121702541539402, \ 0.9346369019266021, \ 0.0531928439194581, \ 0.1111782647883812, \ 0.1111782647883809, \ 0.7776434704232381, \ 0.0008585590446839, \ 0.0406479626359585, \ 0.9584934783193576, \ 0.0008585590446839, \ 0.9584934783193576, \ 0.0406479626359589, \ 0.0123358378103272, \ 0.4064475672122849, \ 0.5812165949773881, \ 0.0123358378103272, \ 0.5812165949773881, \ 0.4064475672122851, \ 0.2379953007931163, \ 0.3810023496034420, \ 0.3810023496034420, \ 0.0110380065045991, \ 0.4944809967477005, \ 0.4944809967477007 ] ) c = np.array ( [ \ 0.7127053999508112, \ 0.0322922639737693, \ 0.2550023360754192, \ 0.2550023360754194, \ 0.0322922639737692, \ 0.7127053999508109, \ 0.6347382765922518, \ 0.0941402098044081, \ 0.2711215136033398, \ 0.2711215136033399, \ 0.0941402098044080, \ 0.6347382765922518, \ 0.8423177234108842, \ 0.0649936721042403, \ 0.0926886044848754, \ 0.0926886044848755, \ 0.0649936721042400, \ 0.8423177234108841, \ 0.5968319589620307, \ 0.0737136644534188, \ 0.3294543765845502, \ 0.3294543765845506, \ 0.0737136644534188, \ 0.5968319589620306, \ 0.6615561707226660, \ 0.0500649881468919, \ 0.2883788411304420, \ 0.2883788411304422, \ 0.0500649881468919, \ 0.6615561707226659, \ 0.5419312451199314, \ 0.0658963384748946, \ 0.3921724164051736, \ 0.3921724164051739, \ 0.0658963384748946, \ 0.5419312451199314, \ 0.9911436314566492, \ 0.0012341185277633, \ 0.0076222500155874, \ 0.0076222500155877, \ 0.0012341185277630, \ 0.9911436314566491, \ 0.4123573403136304, \ 0.1752853193727394, \ 0.4123573403136302, \ 0.7160962360444145, \ 0.1056958273276098, \ 0.1782079366279755, \ 0.1782079366279756, \ 0.1056958273276097, \ 0.7160962360444144, \ 0.5658793981445355, \ 0.1238716703955509, \ 0.3102489314599134, \ 0.3102489314599136, \ 0.1238716703955508, \ 0.5658793981445354, \ 0.4390483832458435, \ 0.1219032335083129, \ 0.4390483832458434, \ 0.9142769002483087, \ 0.0028073976185661, \ 0.0829157021331249, \ 0.0829157021331251, \ 0.0028073976185659, \ 0.9142769002483084, \ 0.5096715423270357, \ 0.1106897783260212, \ 0.3796386793469430, \ 0.3796386793469432, \ 0.1106897783260211, \ 0.5096715423270355, \ 0.5298953490835724, \ 0.2350523254582137, \ 0.2350523254582136, \ 0.7991752852717510, \ 0.0027564226137057, \ 0.1980682921145430, \ 0.1980682921145433, \ 0.0027564226137056, \ 0.7991752852717509, \ 0.7800003555819111, \ 0.0720516990960160, \ 0.1479479453220728, \ 0.1479479453220731, \ 0.0720516990960156, \ 0.7800003555819111, \ 0.7563686218758484, \ 0.0144286115706842, \ 0.2292027665534672, \ 0.2292027665534673, \ 0.0144286115706841, \ 0.7563686218758482, \ 0.6397835829582036, \ 0.0027425666974119, \ 0.3574738503443843, \ 0.3574738503443846, \ 0.0027425666974118, \ 0.6397835829582035, \ 0.8357259979283463, \ 0.0390243298422160, \ 0.1252496722294375, \ 0.1252496722294377, \ 0.0390243298422157, \ 0.8357259979283462, \ 0.9715447719336605, \ 0.0074746634659334, \ 0.0209805646004060, \ 0.0209805646004063, \ 0.0074746634659332, \ 0.9715447719336603, \ 0.5552966096544710, \ 0.1755717786015193, \ 0.2691316117440096, \ 0.2691316117440097, \ 0.1755717786015191, \ 0.5552966096544709, \ 0.6983565304402167, \ 0.1508217347798918, \ 0.1508217347798914, \ 0.4825533687273535, \ 0.1712267588507528, \ 0.3462198724218934, \ 0.3462198724218936, \ 0.1712267588507529, \ 0.4825533687273535, \ 0.5233061138878379, \ 0.0343061434540936, \ 0.4423877426580684, \ 0.4423877426580685, \ 0.0343061434540936, \ 0.5233061138878377, \ 0.7223364807654941, \ 0.0030296355118470, \ 0.2746338837226586, \ 0.2746338837226588, \ 0.0030296355118470, \ 0.7223364807654939, \ 0.7038117568892118, \ 0.0724869584556440, \ 0.2237012846551438, \ 0.2237012846551442, \ 0.0724869584556439, \ 0.7038117568892116, \ 0.6397100291477062, \ 0.1338170233406640, \ 0.2264729475116296, \ 0.2264729475116297, \ 0.1338170233406638, \ 0.6397100291477062, \ 0.8189638129323793, \ 0.0176742202382503, \ 0.1633619668293703, \ 0.1633619668293704, \ 0.0176742202382502, \ 0.8189638129323793, \ 0.7670005101060391, \ 0.0422082170395821, \ 0.1907912728543787, \ 0.1907912728543789, \ 0.0422082170395820, \ 0.7670005101060390, \ 0.6074178089715797, \ 0.0344163203969896, \ 0.3581658706314306, \ 0.3581658706314307, \ 0.0344163203969895, \ 0.6074178089715796, \ 0.8831620205339272, \ 0.0174529902610206, \ 0.0993849892050520, \ 0.0993849892050521, \ 0.0174529902610204, \ 0.8831620205339271, \ 0.5485392672636246, \ 0.0012278348447229, \ 0.4502328978916522, \ 0.4502328978916524, \ 0.0012278348447229, \ 0.5485392672636243, \ 0.4642737776346700, \ 0.0714524447306598, \ 0.4642737776346698, \ 0.4588765169470120, \ 0.2362631900663085, \ 0.3048602929866792, \ 0.3048602929866792, \ 0.2362631900663086, \ 0.4588765169470121, \ 0.6708934652005731, \ 0.0155229285287317, \ 0.3135836062706950, \ 0.3135836062706951, \ 0.0155229285287316, \ 0.6708934652005729, \ 0.8613456659624720, \ 0.0038480457708451, \ 0.1348062882666826, \ 0.1348062882666829, \ 0.0038480457708449, \ 0.8613456659624719, \ 0.6176772762453819, \ 0.1911613618773091, \ 0.1911613618773088, \ 0.8960993382441670, \ 0.0380724693230132, \ 0.0658281924328196, \ 0.0658281924328198, \ 0.0380724693230129, \ 0.8960993382441669, \ 0.9412999018131459, \ 0.0293500490934273, \ 0.0293500490934266, \ 0.3837095620178134, \ 0.3081452189910933, \ 0.3081452189910932, \ 0.9346369019266020, \ 0.0121702541539403, \ 0.0531928439194576, \ 0.0531928439194577, \ 0.0121702541539400, \ 0.9346369019266020, \ 0.7776434704232380, \ 0.1111782647883812, \ 0.1111782647883807, \ 0.9584934783193575, \ 0.0008585590446841, \ 0.0406479626359583, \ 0.0406479626359586, \ 0.0008585590446838, \ 0.9584934783193574, \ 0.5812165949773879, \ 0.0123358378103273, \ 0.4064475672122846, \ 0.4064475672122849, \ 0.0123358378103272, \ 0.5812165949773878, \ 0.3810023496034419, \ 0.2379953007931162, \ 0.3810023496034418, \ 0.4944809967477005, \ 0.0110380065045990, \ 0.4944809967477002 ] ) w = np.array ( [ \ 0.0030616831670682, \ 0.0030616831670682, \ 0.0030616831670682, \ 0.0030616831670682, \ 0.0030616831670682, \ 0.0030616831670682, \ 0.0049232719752900, \ 0.0049232719752900, \ 0.0049232719752900, \ 0.0049232719752900, \ 0.0049232719752900, \ 0.0049232719752900, \ 0.0033237208433952, \ 0.0033237208433952, \ 0.0033237208433952, \ 0.0033237208433952, \ 0.0033237208433952, \ 0.0033237208433952, \ 0.0047427364930338, \ 0.0047427364930338, \ 0.0047427364930338, \ 0.0047427364930338, \ 0.0047427364930338, \ 0.0047427364930338, \ 0.0041138012926497, \ 0.0041138012926497, \ 0.0041138012926497, \ 0.0041138012926497, \ 0.0041138012926497, \ 0.0041138012926497, \ 0.0052353425228938, \ 0.0052353425228938, \ 0.0052353425228938, \ 0.0052353425228938, \ 0.0052353425228938, \ 0.0052353425228938, \ 0.0001303399284527, \ 0.0001303399284527, \ 0.0001303399284527, \ 0.0001303399284527, \ 0.0001303399284527, \ 0.0001303399284527, \ 0.0076704945179086, \ 0.0076704945179086, \ 0.0076704945179086, \ 0.0052277042839384, \ 0.0052277042839384, \ 0.0052277042839384, \ 0.0052277042839384, \ 0.0052277042839384, \ 0.0052277042839384, \ 0.0066311375415485, \ 0.0066311375415485, \ 0.0066311375415485, \ 0.0066311375415485, \ 0.0066311375415485, \ 0.0066311375415485, \ 0.0068762957093961, \ 0.0068762957093961, \ 0.0068762957093961, \ 0.0006952346397171, \ 0.0006952346397171, \ 0.0006952346397171, \ 0.0006952346397171, \ 0.0006952346397171, \ 0.0006952346397171, \ 0.0069183724873925, \ 0.0069183724873925, \ 0.0069183724873925, \ 0.0069183724873925, \ 0.0069183724873925, \ 0.0069183724873925, \ 0.0080679977166382, \ 0.0080679977166382, \ 0.0080679977166382, \ 0.0010177068493549, \ 0.0010177068493549, \ 0.0010177068493549, \ 0.0010177068493549, \ 0.0010177068493549, \ 0.0010177068493549, \ 0.0045309912970645, \ 0.0045309912970645, \ 0.0045309912970645, \ 0.0045309912970645, \ 0.0045309912970645, \ 0.0045309912970645, \ 0.0023792804956386, \ 0.0023792804956386, \ 0.0023792804956386, \ 0.0023792804956386, \ 0.0023792804956386, \ 0.0023792804956386, \ 0.0012168791097054, \ 0.0012168791097054, \ 0.0012168791097054, \ 0.0012168791097054, \ 0.0012168791097054, \ 0.0012168791097054, \ 0.0031130272403783, \ 0.0031130272403783, \ 0.0031130272403783, \ 0.0031130272403783, \ 0.0031130272403783, \ 0.0031130272403783, \ 0.0006481853328131, \ 0.0006481853328131, \ 0.0006481853328131, \ 0.0006481853328131, \ 0.0006481853328131, \ 0.0006481853328131, \ 0.0083451647460546, \ 0.0083451647460546, \ 0.0083451647460546, \ 0.0083451647460546, \ 0.0083451647460546, \ 0.0083451647460546, \ 0.0061710606814515, \ 0.0061710606814515, \ 0.0061710606814515, \ 0.0089038028492518, \ 0.0089038028492518, \ 0.0089038028492518, \ 0.0089038028492518, \ 0.0089038028492518, \ 0.0089038028492518, \ 0.0047638139693883, \ 0.0047638139693883, \ 0.0047638139693883, \ 0.0047638139693883, \ 0.0047638139693883, \ 0.0047638139693883, \ 0.0012331434914374, \ 0.0012331434914374, \ 0.0012331434914374, \ 0.0012331434914374, \ 0.0012331434914374, \ 0.0012331434914374, \ 0.0052810362353661, \ 0.0052810362353661, \ 0.0052810362353661, \ 0.0052810362353661, \ 0.0052810362353661, \ 0.0052810362353661, \ 0.0072039581630510, \ 0.0072039581630510, \ 0.0072039581630510, \ 0.0072039581630510, \ 0.0072039581630510, \ 0.0072039581630510, \ 0.0025500464663513, \ 0.0025500464663513, \ 0.0025500464663513, \ 0.0025500464663513, \ 0.0025500464663513, \ 0.0025500464663513, \ 0.0040931211574027, \ 0.0040931211574027, \ 0.0040931211574027, \ 0.0040931211574027, \ 0.0040931211574027, \ 0.0040931211574027, \ 0.0044693917436126, \ 0.0044693917436126, \ 0.0044693917436126, \ 0.0044693917436126, \ 0.0044693917436126, \ 0.0044693917436126, \ 0.0021012224230352, \ 0.0021012224230352, \ 0.0021012224230352, \ 0.0021012224230352, \ 0.0021012224230352, \ 0.0021012224230352, \ 0.0008220891073142, \ 0.0008220891073142, \ 0.0008220891073142, \ 0.0008220891073142, \ 0.0008220891073142, \ 0.0008220891073142, \ 0.0066612336212475, \ 0.0066612336212475, \ 0.0066612336212475, \ 0.0102133456155291, \ 0.0102133456155291, \ 0.0102133456155291, \ 0.0102133456155291, \ 0.0102133456155291, \ 0.0102133456155291, \ 0.0030402213548301, \ 0.0030402213548301, \ 0.0030402213548301, \ 0.0030402213548301, \ 0.0030402213548301, \ 0.0030402213548301, \ 0.0011096101536171, \ 0.0011096101536171, \ 0.0011096101536171, \ 0.0011096101536171, \ 0.0011096101536171, \ 0.0011096101536171, \ 0.0080932250756891, \ 0.0080932250756891, \ 0.0080932250756891, \ 0.0026669011660035, \ 0.0026669011660035, \ 0.0026669011660035, \ 0.0026669011660035, \ 0.0026669011660035, \ 0.0026669011660035, \ 0.0015674237111509, \ 0.0015674237111509, \ 0.0015674237111509, \ 0.0110082761617136, \ 0.0110082761617136, \ 0.0110082761617136, \ 0.0013356087640650, \ 0.0013356087640650, \ 0.0013356087640650, \ 0.0013356087640650, \ 0.0013356087640650, \ 0.0013356087640650, \ 0.0054235489241326, \ 0.0054235489241326, \ 0.0054235489241326, \ 0.0002661778238934, \ 0.0002661778238934, \ 0.0002661778238934, \ 0.0002661778238934, \ 0.0002661778238934, \ 0.0002661778238934, \ 0.0028876869913215, \ 0.0028876869913215, \ 0.0028876869913215, \ 0.0028876869913215, \ 0.0028876869913215, \ 0.0028876869913215, \ 0.0105063460068171, \ 0.0105063460068171, \ 0.0105063460068171, \ 0.0028959157634686, \ 0.0028959157634686, \ 0.0028959157634686 ] ) return a, b, c, w def rule37 ( ): #*****************************************************************************80 # ## rule37() returns the rule of precision 37. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1023039321577603, \ 0.7953921356844791, \ 0.1023039321577607, \ 0.3160240964966399, \ 0.6501468128206388, \ 0.0338290906827213, \ 0.6501468128206388, \ 0.3160240964966400, \ 0.0338290906827212, \ 0.0350202358754684, \ 0.9299595282490629, \ 0.0350202358754688, \ 0.1053594119602819, \ 0.8614945984835296, \ 0.0331459895561886, \ 0.8614945984835296, \ 0.1053594119602819, \ 0.0331459895561881, \ 0.0749810217841138, \ 0.9229855021397688, \ 0.0020334760761175, \ 0.9229855021397688, \ 0.0749810217841139, \ 0.0020334760761171, \ 0.1194865933803552, \ 0.8250030034571860, \ 0.0555104031624590, \ 0.8250030034571859, \ 0.1194865933803553, \ 0.0555104031624586, \ 0.3192351650459891, \ 0.4427039878369861, \ 0.2380608471170247, \ 0.4427039878369861, \ 0.3192351650459891, \ 0.2380608471170247, \ 0.3917882577236701, \ 0.5329411933388201, \ 0.0752705489375098, \ 0.5329411933388201, \ 0.3917882577236701, \ 0.0752705489375098, \ 0.2592434904565495, \ 0.4815130190869007, \ 0.2592434904565497, \ 0.3175434072141983, \ 0.6288357611566886, \ 0.0536208316291132, \ 0.6288357611566886, \ 0.3175434072141983, \ 0.0536208316291130, \ 0.3267645245927318, \ 0.5819407083122254, \ 0.0912947670950428, \ 0.5819407083122254, \ 0.3267645245927318, \ 0.0912947670950427, \ 0.3187496668271801, \ 0.5461345841025351, \ 0.1351157490702847, \ 0.5461345841025351, \ 0.3187496668271802, \ 0.1351157490702846, \ 0.0674578790813868, \ 0.8917719971619344, \ 0.0407701237566788, \ 0.8917719971619346, \ 0.0674578790813870, \ 0.0407701237566784, \ 0.0183794409210812, \ 0.9786302812023548, \ 0.0029902778765640, \ 0.9786302812023550, \ 0.0183794409210812, \ 0.0029902778765637, \ 0.0476569358622159, \ 0.9350921036839764, \ 0.0172509604538077, \ 0.9350921036839764, \ 0.0476569358622161, \ 0.0172509604538073, \ 0.3357227870380101, \ 0.4831608037664580, \ 0.1811164091955319, \ 0.4831608037664580, \ 0.3357227870380101, \ 0.1811164091955318, \ 0.1394412358722927, \ 0.7211175282554143, \ 0.1394412358722930, \ 0.4611684588908100, \ 0.4611684588908100, \ 0.0776630822183799, \ 0.1356716079161176, \ 0.7741981202355922, \ 0.0901302718482901, \ 0.7741981202355922, \ 0.1356716079161178, \ 0.0901302718482899, \ 0.0417693614359698, \ 0.9542135414767989, \ 0.0040170970872315, \ 0.9542135414767989, \ 0.0417693614359699, \ 0.0040170970872310, \ 0.3791537179550378, \ 0.3791537179550378, \ 0.2416925640899243, \ 0.1912637374380762, \ 0.7277709423326696, \ 0.0809653202292542, \ 0.7277709423326697, \ 0.1912637374380762, \ 0.0809653202292539, \ 0.4489203299566428, \ 0.5341982115332263, \ 0.0168814585101307, \ 0.5341982115332264, \ 0.4489203299566429, \ 0.0168814585101307, \ 0.3970833791349885, \ 0.5614399423313745, \ 0.0414766785336368, \ 0.5614399423313746, \ 0.3970833791349885, \ 0.0414766785336368, \ 0.0862263440628872, \ 0.9000390697749006, \ 0.0137345861622123, \ 0.9000390697749007, \ 0.0862263440628872, \ 0.0137345861622120, \ 0.0173411753639024, \ 0.9653176492721949, \ 0.0173411753639029, \ 0.2814879599422820, \ 0.7005934357274263, \ 0.0179186043302919, \ 0.7005934357274262, \ 0.2814879599422819, \ 0.0179186043302916, \ 0.1923768347442593, \ 0.6791517751989478, \ 0.1284713900567929, \ 0.6791517751989478, \ 0.1923768347442593, \ 0.1284713900567927, \ 0.2517942475174331, \ 0.6108845927509712, \ 0.1373211597315956, \ 0.6108845927509713, \ 0.2517942475174332, \ 0.1373211597315955, \ 0.0779889301806426, \ 0.8440221396387144, \ 0.0779889301806430, \ 0.3650347949363280, \ 0.6175233785692882, \ 0.0174418264943838, \ 0.6175233785692882, \ 0.3650347949363280, \ 0.0174418264943837, \ 0.4792449355569203, \ 0.4792449355569204, \ 0.0415101288861593, \ 0.4120614054796895, \ 0.4120614054796895, \ 0.1758771890406210, \ 0.2571566355502535, \ 0.6566451941716462, \ 0.0861981702781003, \ 0.6566451941716462, \ 0.2571566355502535, \ 0.0861981702781001, \ 0.4984105744139570, \ 0.4984105744139570, \ 0.0031788511720860, \ 0.3091259486853505, \ 0.3817481026292989, \ 0.3091259486853505, \ 0.1241816119341110, \ 0.8724071202650543, \ 0.0034112678008348, \ 0.8724071202650543, \ 0.1241816119341111, \ 0.0034112678008344, \ 0.1716507278093692, \ 0.7837937554788413, \ 0.0445555167117896, \ 0.7837937554788413, \ 0.1716507278093692, \ 0.0445555167117893, \ 0.3977231091982856, \ 0.4801793419171518, \ 0.1220975488845627, \ 0.4801793419171518, \ 0.3977231091982856, \ 0.1220975488845626, \ 0.0036715668219831, \ 0.9926568663560335, \ 0.0036715668219836, \ 0.2578966456698565, \ 0.5463929830937153, \ 0.1957103712364281, \ 0.5463929830937154, \ 0.2578966456698565, \ 0.1957103712364280, \ 0.1441500744811936, \ 0.8375385335389723, \ 0.0183113919798341, \ 0.8375385335389725, \ 0.1441500744811937, \ 0.0183113919798338, \ 0.4122595610017910, \ 0.5844781809630051, \ 0.0032622580352039, \ 0.5844781809630052, \ 0.4122595610017911, \ 0.0032622580352037, \ 0.2524284647914363, \ 0.7440960937012480, \ 0.0034754415073158, \ 0.7440960937012480, \ 0.2524284647914364, \ 0.0034754415073155, \ 0.3293669274857745, \ 0.6670942824316437, \ 0.0035387900825819, \ 0.6670942824316437, \ 0.3293669274857746, \ 0.0035387900825817, \ 0.2095814817005154, \ 0.7715735792437323, \ 0.0188449390557522, \ 0.7715735792437323, \ 0.2095814817005155, \ 0.0188449390557521, \ 0.1836401694462322, \ 0.8127217284450714, \ 0.0036381021086965, \ 0.8127217284450714, \ 0.1836401694462323, \ 0.0036381021086962, \ 0.2416962324693375, \ 0.7125504805693451, \ 0.0457532869613175, \ 0.7125504805693450, \ 0.2416962324693376, \ 0.0457532869613173, \ 0.1893642612001962, \ 0.6212714775996074, \ 0.1893642612001963 ] ) b = np.array ( [ \ 0.1023039321577605, \ 0.1023039321577603, \ 0.7953921356844793, \ 0.0338290906827213, \ 0.3160240964966399, \ 0.6501468128206390, \ 0.0338290906827213, \ 0.6501468128206389, \ 0.3160240964966402, \ 0.0350202358754687, \ 0.0350202358754684, \ 0.9299595282490630, \ 0.0331459895561884, \ 0.1053594119602819, \ 0.8614945984835296, \ 0.0331459895561884, \ 0.8614945984835299, \ 0.1053594119602822, \ 0.0020334760761173, \ 0.0749810217841138, \ 0.9229855021397689, \ 0.0020334760761173, \ 0.9229855021397689, \ 0.0749810217841142, \ 0.0555104031624589, \ 0.1194865933803552, \ 0.8250030034571860, \ 0.0555104031624589, \ 0.8250030034571860, \ 0.1194865933803555, \ 0.2380608471170249, \ 0.3192351650459893, \ 0.4427039878369862, \ 0.2380608471170249, \ 0.4427039878369862, \ 0.3192351650459893, \ 0.0752705489375098, \ 0.3917882577236702, \ 0.5329411933388202, \ 0.0752705489375098, \ 0.5329411933388202, \ 0.3917882577236704, \ 0.2592434904565497, \ 0.2592434904565497, \ 0.4815130190869009, \ 0.0536208316291131, \ 0.3175434072141983, \ 0.6288357611566887, \ 0.0536208316291131, \ 0.6288357611566887, \ 0.3175434072141985, \ 0.0912947670950428, \ 0.3267645245927318, \ 0.5819407083122257, \ 0.0912947670950428, \ 0.5819407083122256, \ 0.3267645245927320, \ 0.1351157490702847, \ 0.3187496668271802, \ 0.5461345841025353, \ 0.1351157490702847, \ 0.5461345841025353, \ 0.3187496668271803, \ 0.0407701237566787, \ 0.0674578790813868, \ 0.8917719971619346, \ 0.0407701237566787, \ 0.8917719971619346, \ 0.0674578790813871, \ 0.0029902778765639, \ 0.0183794409210811, \ 0.9786302812023551, \ 0.0029902778765639, \ 0.9786302812023551, \ 0.0183794409210815, \ 0.0172509604538075, \ 0.0476569358622160, \ 0.9350921036839765, \ 0.0172509604538075, \ 0.9350921036839765, \ 0.0476569358622163, \ 0.1811164091955320, \ 0.3357227870380101, \ 0.4831608037664581, \ 0.1811164091955320, \ 0.4831608037664581, \ 0.3357227870380102, \ 0.1394412358722930, \ 0.1394412358722927, \ 0.7211175282554145, \ 0.0776630822183800, \ 0.4611684588908101, \ 0.4611684588908102, \ 0.0901302718482901, \ 0.1356716079161177, \ 0.7741981202355923, \ 0.0901302718482901, \ 0.7741981202355923, \ 0.1356716079161179, \ 0.0040170970872313, \ 0.0417693614359697, \ 0.9542135414767990, \ 0.0040170970872313, \ 0.9542135414767990, \ 0.0417693614359701, \ 0.2416925640899244, \ 0.3791537179550379, \ 0.3791537179550379, \ 0.0809653202292541, \ 0.1912637374380763, \ 0.7277709423326698, \ 0.0809653202292541, \ 0.7277709423326699, \ 0.1912637374380765, \ 0.0168814585101308, \ 0.4489203299566429, \ 0.5341982115332266, \ 0.0168814585101308, \ 0.5341982115332264, \ 0.4489203299566431, \ 0.0414766785336369, \ 0.3970833791349886, \ 0.5614399423313748, \ 0.0414766785336369, \ 0.5614399423313746, \ 0.3970833791349888, \ 0.0137345861622122, \ 0.0862263440628872, \ 0.9000390697749008, \ 0.0137345861622122, \ 0.9000390697749008, \ 0.0862263440628875, \ 0.0173411753639027, \ 0.0173411753639024, \ 0.9653176492721949, \ 0.0179186043302918, \ 0.2814879599422820, \ 0.7005934357274264, \ 0.0179186043302918, \ 0.7005934357274264, \ 0.2814879599422823, \ 0.1284713900567929, \ 0.1923768347442593, \ 0.6791517751989480, \ 0.1284713900567929, \ 0.6791517751989480, \ 0.1923768347442595, \ 0.1373211597315956, \ 0.2517942475174332, \ 0.6108845927509714, \ 0.1373211597315956, \ 0.6108845927509713, \ 0.2517942475174334, \ 0.0779889301806429, \ 0.0779889301806426, \ 0.8440221396387146, \ 0.0174418264943838, \ 0.3650347949363281, \ 0.6175233785692883, \ 0.0174418264943838, \ 0.6175233785692883, \ 0.3650347949363282, \ 0.0415101288861593, \ 0.4792449355569204, \ 0.4792449355569205, \ 0.1758771890406211, \ 0.4120614054796896, \ 0.4120614054796897, \ 0.0861981702781003, \ 0.2571566355502535, \ 0.6566451941716464, \ 0.0861981702781003, \ 0.6566451941716464, \ 0.2571566355502538, \ 0.0031788511720861, \ 0.4984105744139570, \ 0.4984105744139572, \ 0.3091259486853506, \ 0.3091259486853506, \ 0.3817481026292990, \ 0.0034112678008347, \ 0.1241816119341110, \ 0.8724071202650543, \ 0.0034112678008347, \ 0.8724071202650543, \ 0.1241816119341114, \ 0.0445555167117895, \ 0.1716507278093692, \ 0.7837937554788414, \ 0.0445555167117895, \ 0.7837937554788414, \ 0.1716507278093694, \ 0.1220975488845627, \ 0.3977231091982856, \ 0.4801793419171519, \ 0.1220975488845627, \ 0.4801793419171518, \ 0.3977231091982857, \ 0.0036715668219834, \ 0.0036715668219831, \ 0.9926568663560336, \ 0.1957103712364281, \ 0.2578966456698565, \ 0.5463929830937155, \ 0.1957103712364281, \ 0.5463929830937155, \ 0.2578966456698567, \ 0.0183113919798340, \ 0.1441500744811936, \ 0.8375385335389725, \ 0.0183113919798340, \ 0.8375385335389725, \ 0.1441500744811939, \ 0.0032622580352038, \ 0.4122595610017911, \ 0.5844781809630053, \ 0.0032622580352038, \ 0.5844781809630052, \ 0.4122595610017913, \ 0.0034754415073157, \ 0.2524284647914364, \ 0.7440960937012481, \ 0.0034754415073157, \ 0.7440960937012481, \ 0.2524284647914367, \ 0.0035387900825818, \ 0.3293669274857746, \ 0.6670942824316438, \ 0.0035387900825818, \ 0.6670942824316437, \ 0.3293669274857748, \ 0.0188449390557523, \ 0.2095814817005154, \ 0.7715735792437326, \ 0.0188449390557523, \ 0.7715735792437324, \ 0.2095814817005157, \ 0.0036381021086963, \ 0.1836401694462322, \ 0.8127217284450715, \ 0.0036381021086963, \ 0.8127217284450715, \ 0.1836401694462325, \ 0.0457532869613174, \ 0.2416962324693375, \ 0.7125504805693452, \ 0.0457532869613174, \ 0.7125504805693452, \ 0.2416962324693378, \ 0.1893642612001964, \ 0.1893642612001962, \ 0.6212714775996077 ] ) c = np.array ( [ \ 0.7953921356844791, \ 0.1023039321577606, \ 0.1023039321577600, \ 0.6501468128206388, \ 0.0338290906827213, \ 0.3160240964966398, \ 0.3160240964966399, \ 0.0338290906827211, \ 0.6501468128206387, \ 0.9299595282490629, \ 0.0350202358754687, \ 0.0350202358754682, \ 0.8614945984835297, \ 0.0331459895561885, \ 0.1053594119602818, \ 0.1053594119602820, \ 0.0331459895561882, \ 0.8614945984835297, \ 0.9229855021397688, \ 0.0020334760761174, \ 0.0749810217841136, \ 0.0749810217841139, \ 0.0020334760761173, \ 0.9229855021397688, \ 0.8250030034571860, \ 0.0555104031624588, \ 0.1194865933803551, \ 0.1194865933803552, \ 0.0555104031624587, \ 0.8250030034571859, \ 0.4427039878369860, \ 0.2380608471170247, \ 0.3192351650459891, \ 0.3192351650459891, \ 0.2380608471170248, \ 0.4427039878369860, \ 0.5329411933388201, \ 0.0752705489375098, \ 0.3917882577236700, \ 0.3917882577236701, \ 0.0752705489375097, \ 0.5329411933388200, \ 0.4815130190869008, \ 0.2592434904565497, \ 0.2592434904565494, \ 0.6288357611566886, \ 0.0536208316291131, \ 0.3175434072141982, \ 0.3175434072141983, \ 0.0536208316291130, \ 0.6288357611566884, \ 0.5819407083122254, \ 0.0912947670950428, \ 0.3267645245927315, \ 0.3267645245927318, \ 0.0912947670950427, \ 0.5819407083122253, \ 0.5461345841025352, \ 0.1351157490702847, \ 0.3187496668271800, \ 0.3187496668271802, \ 0.1351157490702845, \ 0.5461345841025351, \ 0.8917719971619346, \ 0.0407701237566787, \ 0.0674578790813867, \ 0.0674578790813868, \ 0.0407701237566785, \ 0.8917719971619344, \ 0.9786302812023550, \ 0.0029902778765640, \ 0.0183794409210809, \ 0.0183794409210811, \ 0.0029902778765637, \ 0.9786302812023547, \ 0.9350921036839765, \ 0.0172509604538076, \ 0.0476569358622158, \ 0.0476569358622160, \ 0.0172509604538074, \ 0.9350921036839764, \ 0.4831608037664580, \ 0.1811164091955319, \ 0.3357227870380099, \ 0.3357227870380101, \ 0.1811164091955318, \ 0.4831608037664579, \ 0.7211175282554143, \ 0.1394412358722930, \ 0.1394412358722925, \ 0.4611684588908100, \ 0.0776630822183799, \ 0.4611684588908099, \ 0.7741981202355923, \ 0.0901302718482901, \ 0.1356716079161175, \ 0.1356716079161177, \ 0.0901302718482899, \ 0.7741981202355923, \ 0.9542135414767989, \ 0.0040170970872313, \ 0.0417693614359694, \ 0.0417693614359698, \ 0.0040170970872310, \ 0.9542135414767989, \ 0.3791537179550378, \ 0.2416925640899242, \ 0.3791537179550377, \ 0.7277709423326697, \ 0.0809653202292542, \ 0.1912637374380760, \ 0.1912637374380762, \ 0.0809653202292538, \ 0.7277709423326697, \ 0.5341982115332263, \ 0.0168814585101308, \ 0.4489203299566428, \ 0.4489203299566428, \ 0.0168814585101307, \ 0.5341982115332262, \ 0.5614399423313746, \ 0.0414766785336369, \ 0.3970833791349883, \ 0.3970833791349885, \ 0.0414766785336368, \ 0.5614399423313745, \ 0.9000390697749007, \ 0.0137345861622123, \ 0.0862263440628869, \ 0.0862263440628872, \ 0.0137345861622120, \ 0.9000390697749004, \ 0.9653176492721949, \ 0.0173411753639027, \ 0.0173411753639022, \ 0.7005934357274263, \ 0.0179186043302917, \ 0.2814879599422817, \ 0.2814879599422820, \ 0.0179186043302917, \ 0.7005934357274261, \ 0.6791517751989478, \ 0.1284713900567929, \ 0.1923768347442592, \ 0.1923768347442593, \ 0.1284713900567928, \ 0.6791517751989478, \ 0.6108845927509713, \ 0.1373211597315956, \ 0.2517942475174331, \ 0.2517942475174331, \ 0.1373211597315954, \ 0.6108845927509711, \ 0.8440221396387144, \ 0.0779889301806430, \ 0.0779889301806423, \ 0.6175233785692882, \ 0.0174418264943837, \ 0.3650347949363278, \ 0.3650347949363280, \ 0.0174418264943837, \ 0.6175233785692880, \ 0.4792449355569203, \ 0.0415101288861592, \ 0.4792449355569202, \ 0.4120614054796894, \ 0.1758771890406209, \ 0.4120614054796893, \ 0.6566451941716462, \ 0.0861981702781002, \ 0.2571566355502534, \ 0.2571566355502534, \ 0.0861981702781002, \ 0.6566451941716460, \ 0.4984105744139569, \ 0.0031788511720860, \ 0.4984105744139568, \ 0.3817481026292989, \ 0.3091259486853504, \ 0.3091259486853505, \ 0.8724071202650543, \ 0.0034112678008347, \ 0.1241816119341108, \ 0.1241816119341110, \ 0.0034112678008346, \ 0.8724071202650542, \ 0.7837937554788413, \ 0.0445555167117895, \ 0.1716507278093690, \ 0.1716507278093692, \ 0.0445555167117894, \ 0.7837937554788413, \ 0.4801793419171517, \ 0.1220975488845625, \ 0.3977231091982854, \ 0.3977231091982855, \ 0.1220975488845626, \ 0.4801793419171517, \ 0.9926568663560335, \ 0.0036715668219834, \ 0.0036715668219829, \ 0.5463929830937153, \ 0.1957103712364281, \ 0.2578966456698564, \ 0.2578966456698564, \ 0.1957103712364280, \ 0.5463929830937153, \ 0.8375385335389723, \ 0.0183113919798340, \ 0.1441500744811934, \ 0.1441500744811935, \ 0.0183113919798339, \ 0.8375385335389723, \ 0.5844781809630052, \ 0.0032622580352038, \ 0.4122595610017908, \ 0.4122595610017910, \ 0.0032622580352036, \ 0.5844781809630050, \ 0.7440960937012480, \ 0.0034754415073157, \ 0.2524284647914362, \ 0.2524284647914363, \ 0.0034754415073156, \ 0.7440960937012479, \ 0.6670942824316437, \ 0.0035387900825817, \ 0.3293669274857743, \ 0.3293669274857745, \ 0.0035387900825817, \ 0.6670942824316435, \ 0.7715735792437323, \ 0.0188449390557523, \ 0.2095814817005152, \ 0.2095814817005154, \ 0.0188449390557521, \ 0.7715735792437322, \ 0.8127217284450715, \ 0.0036381021086964, \ 0.1836401694462321, \ 0.1836401694462323, \ 0.0036381021086961, \ 0.8127217284450713, \ 0.7125504805693451, \ 0.0457532869613174, \ 0.2416962324693372, \ 0.2416962324693376, \ 0.0457532869613172, \ 0.7125504805693449, \ 0.6212714775996074, \ 0.1893642612001964, \ 0.1893642612001961 ] ) w = np.array ( [ \ 0.0015139897718580, \ 0.0015139897718580, \ 0.0015139897718580, \ 0.0020991920973495, \ 0.0020991920973495, \ 0.0020991920973495, \ 0.0020991920973495, \ 0.0020991920973495, \ 0.0020991920973495, \ 0.0011046836690446, \ 0.0011046836690446, \ 0.0011046836690446, \ 0.0019226251721821, \ 0.0019226251721821, \ 0.0019226251721821, \ 0.0019226251721821, \ 0.0019226251721821, \ 0.0019226251721821, \ 0.0004804430100019, \ 0.0004804430100019, \ 0.0004804430100019, \ 0.0004804430100019, \ 0.0004804430100019, \ 0.0004804430100019, \ 0.0030325474600895, \ 0.0030325474600895, \ 0.0030325474600895, \ 0.0030325474600895, \ 0.0030325474600895, \ 0.0030325474600895, \ 0.0073189063292417, \ 0.0073189063292417, \ 0.0073189063292417, \ 0.0073189063292417, \ 0.0073189063292417, \ 0.0073189063292417, \ 0.0053883188429810, \ 0.0053883188429810, \ 0.0053883188429810, \ 0.0053883188429810, \ 0.0053883188429810, \ 0.0053883188429810, \ 0.0075850923563705, \ 0.0075850923563705, \ 0.0075850923563705, \ 0.0045692159189815, \ 0.0045692159189815, \ 0.0045692159189815, \ 0.0045692159189815, \ 0.0045692159189815, \ 0.0045692159189815, \ 0.0057203599064585, \ 0.0057203599064585, \ 0.0057203599064585, \ 0.0057203599064585, \ 0.0057203599064585, \ 0.0057203599064585, \ 0.0067120048490857, \ 0.0067120048490857, \ 0.0067120048490857, \ 0.0067120048490857, \ 0.0067120048490857, \ 0.0067120048490857, \ 0.0023170775093131, \ 0.0023170775093131, \ 0.0023170775093131, \ 0.0023170775093131, \ 0.0023170775093131, \ 0.0023170775093131, \ 0.0003086692619705, \ 0.0003086692619705, \ 0.0003086692619705, \ 0.0003086692619705, \ 0.0003086692619705, \ 0.0003086692619705, \ 0.0012047027694411, \ 0.0012047027694411, \ 0.0012047027694411, \ 0.0012047027694411, \ 0.0012047027694411, \ 0.0012047027694411, \ 0.0081637462521436, \ 0.0081637462521436, \ 0.0081637462521436, \ 0.0081637462521436, \ 0.0081637462521436, \ 0.0081637462521436, \ 0.0052500601543288, \ 0.0052500601543288, \ 0.0052500601543288, \ 0.0058808346792778, \ 0.0058808346792778, \ 0.0058808346792778, \ 0.0043645240281899, \ 0.0043645240281899, \ 0.0043645240281899, \ 0.0043645240281899, \ 0.0043645240281899, \ 0.0043645240281899, \ 0.0005497965506473, \ 0.0005497965506473, \ 0.0005497965506473, \ 0.0005497965506473, \ 0.0005497965506473, \ 0.0005497965506473, \ 0.0086445565740853, \ 0.0086445565740853, \ 0.0086445565740853, \ 0.0052464381586922, \ 0.0052464381586922, \ 0.0052464381586922, \ 0.0052464381586922, \ 0.0052464381586922, \ 0.0052464381586922, \ 0.0032584894563913, \ 0.0032584894563913, \ 0.0032584894563913, \ 0.0032584894563913, \ 0.0032584894563913, \ 0.0032584894563913, \ 0.0047812349883804, \ 0.0047812349883804, \ 0.0047812349883804, \ 0.0047812349883804, \ 0.0047812349883804, \ 0.0047812349883804, \ 0.0016087719028869, \ 0.0016087719028869, \ 0.0016087719028869, \ 0.0016087719028869, \ 0.0016087719028869, \ 0.0016087719028869, \ 0.0008775872521508, \ 0.0008775872521508, \ 0.0008775872521508, \ 0.0029825665052993, \ 0.0029825665052993, \ 0.0029825665052993, \ 0.0029825665052993, \ 0.0029825665052993, \ 0.0029825665052993, \ 0.0060939488435529, \ 0.0060939488435529, \ 0.0060939488435529, \ 0.0060939488435529, \ 0.0060939488435529, \ 0.0060939488435529, \ 0.0070873407460566, \ 0.0070873407460566, \ 0.0070873407460566, \ 0.0070873407460566, \ 0.0070873407460566, \ 0.0070873407460566, \ 0.0035862336027497, \ 0.0035862336027497, \ 0.0035862336027497, \ 0.0031497526280812, \ 0.0031497526280812, \ 0.0031497526280812, \ 0.0031497526280812, \ 0.0031497526280812, \ 0.0031497526280812, \ 0.0049992428284758, \ 0.0049992428284758, \ 0.0049992428284758, \ 0.0090788425055397, \ 0.0090788425055397, \ 0.0090788425055397, \ 0.0062518699531210, \ 0.0062518699531210, \ 0.0062518699531210, \ 0.0062518699531210, \ 0.0062518699531210, \ 0.0062518699531210, \ 0.0014156781091945, \ 0.0014156781091945, \ 0.0014156781091945, \ 0.0102066366491736, \ 0.0102066366491736, \ 0.0102066366491736, \ 0.0009493053225472, \ 0.0009493053225472, \ 0.0009493053225472, \ 0.0009493053225472, \ 0.0009493053225472, \ 0.0009493053225472, \ 0.0040312520842928, \ 0.0040312520842928, \ 0.0040312520842928, \ 0.0040312520842928, \ 0.0040312520842928, \ 0.0040312520842928, \ 0.0081722175482304, \ 0.0081722175482304, \ 0.0081722175482304, \ 0.0081722175482304, \ 0.0081722175482304, \ 0.0081722175482304, \ 0.0001732953357809, \ 0.0001732953357809, \ 0.0001732953357809, \ 0.0089586590287218, \ 0.0089586590287218, \ 0.0089586590287218, \ 0.0089586590287218, \ 0.0089586590287218, \ 0.0089586590287218, \ 0.0024620987414923, \ 0.0024620987414923, \ 0.0024620987414923, \ 0.0024620987414923, \ 0.0024620987414923, \ 0.0024620987414923, \ 0.0014212929213219, \ 0.0014212929213219, \ 0.0014212929213219, \ 0.0014212929213219, \ 0.0014212929213219, \ 0.0014212929213219, \ 0.0013051564959187, \ 0.0013051564959187, \ 0.0013051564959187, \ 0.0013051564959187, \ 0.0013051564959187, \ 0.0013051564959187, \ 0.0014459095277887, \ 0.0014459095277887, \ 0.0014459095277887, \ 0.0014459095277887, \ 0.0014459095277887, \ 0.0014459095277887, \ 0.0029345950580795, \ 0.0029345950580795, \ 0.0029345950580795, \ 0.0029345950580795, \ 0.0029345950580795, \ 0.0029345950580795, \ 0.0011964590052698, \ 0.0011964590052698, \ 0.0011964590052698, \ 0.0011964590052698, \ 0.0011964590052698, \ 0.0011964590052698, \ 0.0048735044199229, \ 0.0048735044199229, \ 0.0048735044199229, \ 0.0048735044199229, \ 0.0048735044199229, \ 0.0048735044199229, \ 0.0082906132570537, \ 0.0082906132570537, \ 0.0082906132570537 ] ) return a, b, c, w def rule38 ( ): #*****************************************************************************80 # ## rule38() returns the rule of precision 38. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4590721360317646, \ 0.4590721360317646, \ 0.0818557279364708, \ 0.2837655147017407, \ 0.6639373713962480, \ 0.0522971139020114, \ 0.6639373713962479, \ 0.2837655147017407, \ 0.0522971139020114, \ 0.3932680062553601, \ 0.3932680062553601, \ 0.2134639874892798, \ 0.1285165649696939, \ 0.7724036723284647, \ 0.0990797627018414, \ 0.7724036723284647, \ 0.1285165649696941, \ 0.0990797627018411, \ 0.4681825892069357, \ 0.4681825892069357, \ 0.0636348215861285, \ 0.0413075041428614, \ 0.9566280907078333, \ 0.0020644051493054, \ 0.9566280907078334, \ 0.0413075041428616, \ 0.0020644051493049, \ 0.0892719800534145, \ 0.8739978442972371, \ 0.0367301756493484, \ 0.8739978442972371, \ 0.0892719800534145, \ 0.0367301756493481, \ 0.3372052923179872, \ 0.4368488831942271, \ 0.2259458244877856, \ 0.4368488831942271, \ 0.3372052923179872, \ 0.2259458244877856, \ 0.2738513741241787, \ 0.6934474438857674, \ 0.0327011819900538, \ 0.6934474438857675, \ 0.2738513741241788, \ 0.0327011819900536, \ 0.0399162626294194, \ 0.9470142283262505, \ 0.0130695090443302, \ 0.9470142283262506, \ 0.0399162626294196, \ 0.0130695090443297, \ 0.0175045040462673, \ 0.9649909919074650, \ 0.0175045040462677, \ 0.3081068327593843, \ 0.6181755526695998, \ 0.0737176145710159, \ 0.6181755526695998, \ 0.3081068327593843, \ 0.0737176145710158, \ 0.1454801146528607, \ 0.7090397706942783, \ 0.1454801146528609, \ 0.2196247131384356, \ 0.7776714046470208, \ 0.0027038822145437, \ 0.7776714046470208, \ 0.2196247131384357, \ 0.0027038822145434, \ 0.2734646071142814, \ 0.5073771294396898, \ 0.2191582634460287, \ 0.5073771294396898, \ 0.2734646071142814, \ 0.2191582634460286, \ 0.0686830028555527, \ 0.9105941852629332, \ 0.0207228118815142, \ 0.9105941852629332, \ 0.0686830028555528, \ 0.0207228118815138, \ 0.1830135998401795, \ 0.7163646792677445, \ 0.1006217208920760, \ 0.7163646792677445, \ 0.1830135998401795, \ 0.1006217208920759, \ 0.0030471742663605, \ 0.9939056514672787, \ 0.0030471742663609, \ 0.2287994832299253, \ 0.7017106989365653, \ 0.0694898178335093, \ 0.7017106989365655, \ 0.2287994832299252, \ 0.0694898178335091, \ 0.0587361601120220, \ 0.8825276797759557, \ 0.0587361601120223, \ 0.1018827114869391, \ 0.8297399330905469, \ 0.0683773554225139, \ 0.8297399330905471, \ 0.1018827114869392, \ 0.0683773554225136, \ 0.2435636733958171, \ 0.7421158852408665, \ 0.0143204413633164, \ 0.7421158852408665, \ 0.2435636733958172, \ 0.0143204413633164, \ 0.2058877165179012, \ 0.7551444267398045, \ 0.0389678567422944, \ 0.7551444267398045, \ 0.2058877165179013, \ 0.0389678567422941, \ 0.2018695088876031, \ 0.6487340291944527, \ 0.1493964619179441, \ 0.6487340291944528, \ 0.2018695088876032, \ 0.1493964619179440, \ 0.1591160210105452, \ 0.7786557671705014, \ 0.0622282118189533, \ 0.7786557671705016, \ 0.1591160210105452, \ 0.0622282118189531, \ 0.1779476358555918, \ 0.8044331226739222, \ 0.0176192414704860, \ 0.8044331226739222, \ 0.1779476358555919, \ 0.0176192414704858, \ 0.1620367479496921, \ 0.8340155243850955, \ 0.0039477276652125, \ 0.8340155243850954, \ 0.1620367479496921, \ 0.0039477276652123, \ 0.2918549838585246, \ 0.7052138362553024, \ 0.0029311798861729, \ 0.7052138362553025, \ 0.2918549838585245, \ 0.0029311798861727, \ 0.3718786917495892, \ 0.6253433272679723, \ 0.0027779809824385, \ 0.6253433272679723, \ 0.3718786917495892, \ 0.0027779809824384, \ 0.1349693726524653, \ 0.8307084415116845, \ 0.0343221858358503, \ 0.8307084415116845, \ 0.1349693726524654, \ 0.0343221858358500, \ 0.0373835575017465, \ 0.9252328849965067, \ 0.0373835575017469, \ 0.2855047782912640, \ 0.4289904434174718, \ 0.2855047782912640, \ 0.2524534299064219, \ 0.6388225307516531, \ 0.1087240393419249, \ 0.6388225307516532, \ 0.2524534299064219, \ 0.1087240393419247, \ 0.4203335017700142, \ 0.4203335017700143, \ 0.1593329964599715, \ 0.3242351641083045, \ 0.6608157279836501, \ 0.0149491079080454, \ 0.6608157279836501, \ 0.3242351641083045, \ 0.0149491079080453, \ 0.2076894216538629, \ 0.5846211566922740, \ 0.2076894216538630, \ 0.4921962729553108, \ 0.4921962729553108, \ 0.0156074540893784, \ 0.4374161906466257, \ 0.5252597321941108, \ 0.0373240771592634, \ 0.5252597321941108, \ 0.4374161906466257, \ 0.0373240771592634, \ 0.4559988036612093, \ 0.5410379244071537, \ 0.0029632719316369, \ 0.5410379244071537, \ 0.4559988036612093, \ 0.0029632719316369, \ 0.0754872857005683, \ 0.9203097361386582, \ 0.0042029781607736, \ 0.9203097361386582, \ 0.0754872857005683, \ 0.0042029781607733, \ 0.3260541266529466, \ 0.5596716859665990, \ 0.1142741873804544, \ 0.5596716859665990, \ 0.3260541266529467, \ 0.1142741873804543, \ 0.4011995885054882, \ 0.4859123261815903, \ 0.1128880853129214, \ 0.4859123261815903, \ 0.4011995885054881, \ 0.1128880853129214, \ 0.2687606603412640, \ 0.5710426617589802, \ 0.1601966778997558, \ 0.5710426617589801, \ 0.2687606603412641, \ 0.1601966778997558, \ 0.4060147025738772, \ 0.5788301687858335, \ 0.0151551286402894, \ 0.5788301687858335, \ 0.4060147025738773, \ 0.0151551286402893, \ 0.3565655939830261, \ 0.3565655939830261, \ 0.2868688120339477, \ 0.3835103468343402, \ 0.5464474716652220, \ 0.0700421815004378, \ 0.5464474716652219, \ 0.3835103468343402, \ 0.0700421815004378, \ 0.0164470646369432, \ 0.9801099468614760, \ 0.0034429885015809, \ 0.9801099468614760, \ 0.0164470646369433, \ 0.0034429885015805, \ 0.3542977861626948, \ 0.6080345993586279, \ 0.0376676144786774, \ 0.6080345993586279, \ 0.3542977861626948, \ 0.0376676144786772, \ 0.3419951757983160, \ 0.4920063975249682, \ 0.1659984266767156, \ 0.4920063975249683, \ 0.3419951757983161, \ 0.1659984266767155, \ 0.1152888910792784, \ 0.8726785778095564, \ 0.0120325311111653, \ 0.8726785778095565, \ 0.1152888910792785, \ 0.0120325311111650, \ 0.1165281018124025, \ 0.8831736765060774, \ 0.0002982216815202, \ 0.8831736765060774, \ 0.1165281018124027, \ 0.0002982216815200 ] ) b = np.array ( [ \ 0.0818557279364709, \ 0.4590721360317646, \ 0.4590721360317648, \ 0.0522971139020114, \ 0.2837655147017407, \ 0.6639373713962481, \ 0.0522971139020114, \ 0.6639373713962480, \ 0.2837655147017409, \ 0.2134639874892799, \ 0.3932680062553601, \ 0.3932680062553602, \ 0.0990797627018413, \ 0.1285165649696940, \ 0.7724036723284649, \ 0.0990797627018413, \ 0.7724036723284649, \ 0.1285165649696943, \ 0.0636348215861286, \ 0.4681825892069358, \ 0.4681825892069360, \ 0.0020644051493052, \ 0.0413075041428614, \ 0.9566280907078335, \ 0.0020644051493052, \ 0.9566280907078335, \ 0.0413075041428617, \ 0.0367301756493483, \ 0.0892719800534144, \ 0.8739978442972374, \ 0.0367301756493483, \ 0.8739978442972374, \ 0.0892719800534148, \ 0.2259458244877857, \ 0.3372052923179873, \ 0.4368488831942272, \ 0.2259458244877857, \ 0.4368488831942272, \ 0.3372052923179874, \ 0.0327011819900538, \ 0.2738513741241788, \ 0.6934474438857677, \ 0.0327011819900538, \ 0.6934474438857677, \ 0.2738513741241790, \ 0.0130695090443300, \ 0.0399162626294194, \ 0.9470142283262506, \ 0.0130695090443300, \ 0.9470142283262506, \ 0.0399162626294198, \ 0.0175045040462676, \ 0.0175045040462673, \ 0.9649909919074653, \ 0.0737176145710159, \ 0.3081068327593843, \ 0.6181755526695999, \ 0.0737176145710159, \ 0.6181755526695998, \ 0.3081068327593845, \ 0.1454801146528609, \ 0.1454801146528608, \ 0.7090397706942786, \ 0.0027038822145435, \ 0.2196247131384356, \ 0.7776714046470209, \ 0.0027038822145435, \ 0.7776714046470209, \ 0.2196247131384359, \ 0.2191582634460288, \ 0.2734646071142815, \ 0.5073771294396899, \ 0.2191582634460288, \ 0.5073771294396899, \ 0.2734646071142816, \ 0.0207228118815140, \ 0.0686830028555526, \ 0.9105941852629333, \ 0.0207228118815140, \ 0.9105941852629333, \ 0.0686830028555530, \ 0.1006217208920761, \ 0.1830135998401795, \ 0.7163646792677447, \ 0.1006217208920761, \ 0.7163646792677446, \ 0.1830135998401798, \ 0.0030471742663608, \ 0.0030471742663604, \ 0.9939056514672788, \ 0.0694898178335093, \ 0.2287994832299253, \ 0.7017106989365657, \ 0.0694898178335093, \ 0.7017106989365657, \ 0.2287994832299255, \ 0.0587361601120223, \ 0.0587361601120220, \ 0.8825276797759559, \ 0.0683773554225139, \ 0.1018827114869391, \ 0.8297399330905472, \ 0.0683773554225139, \ 0.8297399330905472, \ 0.1018827114869394, \ 0.0143204413633165, \ 0.2435636733958171, \ 0.7421158852408667, \ 0.0143204413633165, \ 0.7421158852408665, \ 0.2435636733958174, \ 0.0389678567422943, \ 0.2058877165179012, \ 0.7551444267398046, \ 0.0389678567422943, \ 0.7551444267398046, \ 0.2058877165179015, \ 0.1493964619179442, \ 0.2018695088876032, \ 0.6487340291944529, \ 0.1493964619179442, \ 0.6487340291944529, \ 0.2018695088876034, \ 0.0622282118189533, \ 0.1591160210105452, \ 0.7786557671705017, \ 0.0622282118189533, \ 0.7786557671705017, \ 0.1591160210105455, \ 0.0176192414704860, \ 0.1779476358555918, \ 0.8044331226739224, \ 0.0176192414704860, \ 0.8044331226739224, \ 0.1779476358555921, \ 0.0039477276652125, \ 0.1620367479496921, \ 0.8340155243850956, \ 0.0039477276652125, \ 0.8340155243850956, \ 0.1620367479496924, \ 0.0029311798861729, \ 0.2918549838585247, \ 0.7052138362553028, \ 0.0029311798861729, \ 0.7052138362553028, \ 0.2918549838585249, \ 0.0027779809824386, \ 0.3718786917495892, \ 0.6253433272679726, \ 0.0027779809824386, \ 0.6253433272679724, \ 0.3718786917495893, \ 0.0343221858358502, \ 0.1349693726524653, \ 0.8307084415116845, \ 0.0343221858358502, \ 0.8307084415116845, \ 0.1349693726524656, \ 0.0373835575017468, \ 0.0373835575017464, \ 0.9252328849965068, \ 0.2855047782912642, \ 0.2855047782912641, \ 0.4289904434174719, \ 0.1087240393419249, \ 0.2524534299064219, \ 0.6388225307516533, \ 0.1087240393419249, \ 0.6388225307516533, \ 0.2524534299064221, \ 0.1593329964599716, \ 0.4203335017700143, \ 0.4203335017700144, \ 0.0149491079080454, \ 0.3242351641083045, \ 0.6608157279836503, \ 0.0149491079080454, \ 0.6608157279836503, \ 0.3242351641083048, \ 0.2076894216538631, \ 0.2076894216538630, \ 0.5846211566922742, \ 0.0156074540893784, \ 0.4921962729553109, \ 0.4921962729553110, \ 0.0373240771592635, \ 0.4374161906466258, \ 0.5252597321941110, \ 0.0373240771592635, \ 0.5252597321941109, \ 0.4374161906466259, \ 0.0029632719316370, \ 0.4559988036612094, \ 0.5410379244071539, \ 0.0029632719316370, \ 0.5410379244071538, \ 0.4559988036612095, \ 0.0042029781607735, \ 0.0754872857005682, \ 0.9203097361386584, \ 0.0042029781607735, \ 0.9203097361386584, \ 0.0754872857005686, \ 0.1142741873804544, \ 0.3260541266529467, \ 0.5596716859665991, \ 0.1142741873804544, \ 0.5596716859665990, \ 0.3260541266529468, \ 0.1128880853129215, \ 0.4011995885054883, \ 0.4859123261815905, \ 0.1128880853129215, \ 0.4859123261815904, \ 0.4011995885054884, \ 0.1601966778997559, \ 0.2687606603412641, \ 0.5710426617589803, \ 0.1601966778997559, \ 0.5710426617589802, \ 0.2687606603412642, \ 0.0151551286402894, \ 0.4060147025738772, \ 0.5788301687858336, \ 0.0151551286402894, \ 0.5788301687858335, \ 0.4060147025738775, \ 0.2868688120339477, \ 0.3565655939830263, \ 0.3565655939830263, \ 0.0700421815004379, \ 0.3835103468343402, \ 0.5464474716652222, \ 0.0700421815004379, \ 0.5464474716652220, \ 0.3835103468343404, \ 0.0034429885015808, \ 0.0164470646369432, \ 0.9801099468614761, \ 0.0034429885015808, \ 0.9801099468614761, \ 0.0164470646369435, \ 0.0376676144786773, \ 0.3542977861626948, \ 0.6080345993586280, \ 0.0376676144786773, \ 0.6080345993586280, \ 0.3542977861626950, \ 0.1659984266767157, \ 0.3419951757983162, \ 0.4920063975249684, \ 0.1659984266767157, \ 0.4920063975249684, \ 0.3419951757983163, \ 0.0120325311111652, \ 0.1152888910792784, \ 0.8726785778095566, \ 0.0120325311111652, \ 0.8726785778095566, \ 0.1152888910792787, \ 0.0002982216815201, \ 0.1165281018124025, \ 0.8831736765060775, \ 0.0002982216815201, \ 0.8831736765060774, \ 0.1165281018124029 ] ) c = np.array ( [ \ 0.4590721360317646, \ 0.0818557279364708, \ 0.4590721360317643, \ 0.6639373713962479, \ 0.0522971139020113, \ 0.2837655147017405, \ 0.2837655147017407, \ 0.0522971139020113, \ 0.6639373713962476, \ 0.3932680062553600, \ 0.2134639874892798, \ 0.3932680062553600, \ 0.7724036723284647, \ 0.0990797627018413, \ 0.1285165649696938, \ 0.1285165649696940, \ 0.0990797627018410, \ 0.7724036723284646, \ 0.4681825892069357, \ 0.0636348215861285, \ 0.4681825892069355, \ 0.9566280907078334, \ 0.0020644051493053, \ 0.0413075041428611, \ 0.0413075041428614, \ 0.0020644051493049, \ 0.9566280907078334, \ 0.8739978442972371, \ 0.0367301756493484, \ 0.0892719800534142, \ 0.0892719800534145, \ 0.0367301756493481, \ 0.8739978442972371, \ 0.4368488831942270, \ 0.2259458244877856, \ 0.3372052923179872, \ 0.3372052923179872, \ 0.2259458244877856, \ 0.4368488831942270, \ 0.6934474438857675, \ 0.0327011819900538, \ 0.2738513741241785, \ 0.2738513741241787, \ 0.0327011819900535, \ 0.6934474438857674, \ 0.9470142283262506, \ 0.0130695090443301, \ 0.0399162626294192, \ 0.0399162626294194, \ 0.0130695090443298, \ 0.9470142283262505, \ 0.9649909919074652, \ 0.0175045040462678, \ 0.0175045040462670, \ 0.6181755526695998, \ 0.0737176145710159, \ 0.3081068327593842, \ 0.3081068327593843, \ 0.0737176145710159, \ 0.6181755526695998, \ 0.7090397706942784, \ 0.1454801146528610, \ 0.1454801146528605, \ 0.7776714046470208, \ 0.0027038822145436, \ 0.2196247131384355, \ 0.2196247131384357, \ 0.0027038822145434, \ 0.7776714046470208, \ 0.5073771294396898, \ 0.2191582634460287, \ 0.2734646071142813, \ 0.2734646071142814, \ 0.2191582634460286, \ 0.5073771294396898, \ 0.9105941852629332, \ 0.0207228118815141, \ 0.0686830028555525, \ 0.0686830028555527, \ 0.0207228118815138, \ 0.9105941852629332, \ 0.7163646792677445, \ 0.1006217208920760, \ 0.1830135998401792, \ 0.1830135998401794, \ 0.1006217208920760, \ 0.7163646792677443, \ 0.9939056514672787, \ 0.0030471742663608, \ 0.0030471742663603, \ 0.7017106989365655, \ 0.0694898178335094, \ 0.2287994832299250, \ 0.2287994832299253, \ 0.0694898178335092, \ 0.7017106989365653, \ 0.8825276797759557, \ 0.0587361601120223, \ 0.0587361601120219, \ 0.8297399330905469, \ 0.0683773554225139, \ 0.1018827114869388, \ 0.1018827114869391, \ 0.0683773554225137, \ 0.8297399330905468, \ 0.7421158852408665, \ 0.0143204413633164, \ 0.2435636733958169, \ 0.2435636733958171, \ 0.0143204413633163, \ 0.7421158852408662, \ 0.7551444267398045, \ 0.0389678567422943, \ 0.2058877165179009, \ 0.2058877165179012, \ 0.0389678567422941, \ 0.7551444267398044, \ 0.6487340291944528, \ 0.1493964619179442, \ 0.2018695088876029, \ 0.2018695088876030, \ 0.1493964619179439, \ 0.6487340291944527, \ 0.7786557671705016, \ 0.0622282118189533, \ 0.1591160210105450, \ 0.1591160210105451, \ 0.0622282118189531, \ 0.7786557671705014, \ 0.8044331226739222, \ 0.0176192414704860, \ 0.1779476358555916, \ 0.1779476358555918, \ 0.0176192414704858, \ 0.8044331226739220, \ 0.8340155243850955, \ 0.0039477276652124, \ 0.1620367479496919, \ 0.1620367479496921, \ 0.0039477276652123, \ 0.8340155243850953, \ 0.7052138362553025, \ 0.0029311798861729, \ 0.2918549838585244, \ 0.2918549838585245, \ 0.0029311798861728, \ 0.7052138362553024, \ 0.6253433272679724, \ 0.0027779809824385, \ 0.3718786917495890, \ 0.3718786917495892, \ 0.0027779809824385, \ 0.6253433272679723, \ 0.8307084415116845, \ 0.0343221858358502, \ 0.1349693726524651, \ 0.1349693726524652, \ 0.0343221858358500, \ 0.8307084415116844, \ 0.9252328849965067, \ 0.0373835575017469, \ 0.0373835575017463, \ 0.4289904434174717, \ 0.2855047782912640, \ 0.2855047782912640, \ 0.6388225307516532, \ 0.1087240393419250, \ 0.2524534299064218, \ 0.2524534299064219, \ 0.1087240393419248, \ 0.6388225307516531, \ 0.4203335017700142, \ 0.1593329964599714, \ 0.4203335017700142, \ 0.6608157279836501, \ 0.0149491079080454, \ 0.3242351641083042, \ 0.3242351641083045, \ 0.0149491079080452, \ 0.6608157279836500, \ 0.5846211566922739, \ 0.2076894216538630, \ 0.2076894216538628, \ 0.4921962729553108, \ 0.0156074540893784, \ 0.4921962729553107, \ 0.5252597321941109, \ 0.0373240771592634, \ 0.4374161906466255, \ 0.4374161906466257, \ 0.0373240771592634, \ 0.5252597321941106, \ 0.5410379244071538, \ 0.0029632719316369, \ 0.4559988036612092, \ 0.4559988036612093, \ 0.0029632719316369, \ 0.5410379244071535, \ 0.9203097361386582, \ 0.0042029781607736, \ 0.0754872857005680, \ 0.0754872857005683, \ 0.0042029781607732, \ 0.9203097361386581, \ 0.5596716859665989, \ 0.1142741873804543, \ 0.3260541266529464, \ 0.3260541266529466, \ 0.1142741873804544, \ 0.5596716859665989, \ 0.4859123261815903, \ 0.1128880853129214, \ 0.4011995885054880, \ 0.4011995885054882, \ 0.1128880853129214, \ 0.4859123261815902, \ 0.5710426617589801, \ 0.1601966778997557, \ 0.2687606603412638, \ 0.2687606603412640, \ 0.1601966778997558, \ 0.5710426617589801, \ 0.5788301687858334, \ 0.0151551286402893, \ 0.4060147025738771, \ 0.4060147025738771, \ 0.0151551286402892, \ 0.5788301687858333, \ 0.3565655939830262, \ 0.2868688120339476, \ 0.3565655939830261, \ 0.5464474716652219, \ 0.0700421815004378, \ 0.3835103468343400, \ 0.3835103468343402, \ 0.0700421815004378, \ 0.5464474716652218, \ 0.9801099468614761, \ 0.0034429885015808, \ 0.0164470646369429, \ 0.0164470646369432, \ 0.0034429885015806, \ 0.9801099468614759, \ 0.6080345993586279, \ 0.0376676144786773, \ 0.3542977861626946, \ 0.3542977861626948, \ 0.0376676144786772, \ 0.6080345993586278, \ 0.4920063975249683, \ 0.1659984266767156, \ 0.3419951757983160, \ 0.3419951757983161, \ 0.1659984266767155, \ 0.4920063975249681, \ 0.8726785778095564, \ 0.0120325311111653, \ 0.1152888910792781, \ 0.1152888910792783, \ 0.0120325311111650, \ 0.8726785778095563, \ 0.8831736765060773, \ 0.0002982216815201, \ 0.1165281018124024, \ 0.1165281018124025, \ 0.0002982216815199, \ 0.8831736765060771 ] ) w = np.array ( [ \ 0.0031639644402839, \ 0.0031639644402839, \ 0.0031639644402839, \ 0.0024850052311427, \ 0.0024850052311427, \ 0.0024850052311427, \ 0.0024850052311427, \ 0.0024850052311427, \ 0.0024850052311427, \ 0.0058616582191086, \ 0.0058616582191086, \ 0.0058616582191086, \ 0.0036964891607068, \ 0.0036964891607068, \ 0.0036964891607068, \ 0.0036964891607068, \ 0.0036964891607068, \ 0.0036964891607068, \ 0.0039302169037011, \ 0.0039302169037011, \ 0.0039302169037011, \ 0.0003477043989937, \ 0.0003477043989937, \ 0.0003477043989937, \ 0.0003477043989937, \ 0.0003477043989937, \ 0.0003477043989937, \ 0.0020738268739408, \ 0.0020738268739408, \ 0.0020738268739408, \ 0.0020738268739408, \ 0.0020738268739408, \ 0.0020738268739408, \ 0.0073710410900113, \ 0.0073710410900113, \ 0.0073710410900113, \ 0.0073710410900113, \ 0.0073710410900113, \ 0.0073710410900113, \ 0.0031253981144399, \ 0.0031253981144399, \ 0.0031253981144399, \ 0.0031253981144399, \ 0.0031253981144399, \ 0.0031253981144399, \ 0.0009061762144521, \ 0.0009061762144521, \ 0.0009061762144521, \ 0.0009061762144521, \ 0.0009061762144521, \ 0.0009061762144521, \ 0.0006994697673296, \ 0.0006994697673296, \ 0.0006994697673296, \ 0.0049956277697467, \ 0.0049956277697467, \ 0.0049956277697467, \ 0.0049956277697467, \ 0.0049956277697467, \ 0.0049956277697467, \ 0.0052024225110439, \ 0.0052024225110439, \ 0.0052024225110439, \ 0.0009256681988499, \ 0.0009256681988499, \ 0.0009256681988499, \ 0.0009256681988499, \ 0.0009256681988499, \ 0.0009256681988499, \ 0.0082821664626930, \ 0.0082821664626930, \ 0.0082821664626930, \ 0.0082821664626930, \ 0.0082821664626930, \ 0.0082821664626930, \ 0.0015368424658073, \ 0.0015368424658073, \ 0.0015368424658073, \ 0.0015368424658073, \ 0.0015368424658073, \ 0.0015368424658073, \ 0.0052227407388144, \ 0.0052227407388144, \ 0.0052227407388144, \ 0.0052227407388144, \ 0.0052227407388144, \ 0.0052227407388144, \ 0.0001240466626531, \ 0.0001240466626531, \ 0.0001240466626531, \ 0.0047183927884199, \ 0.0047183927884199, \ 0.0047183927884199, \ 0.0047183927884199, \ 0.0047183927884199, \ 0.0047183927884199, \ 0.0025063822165145, \ 0.0025063822165145, \ 0.0025063822165145, \ 0.0036021170049529, \ 0.0036021170049529, \ 0.0036021170049529, \ 0.0036021170049529, \ 0.0036021170049529, \ 0.0036021170049529, \ 0.0023702904673934, \ 0.0023702904673934, \ 0.0023702904673934, \ 0.0023702904673934, \ 0.0023702904673934, \ 0.0023702904673934, \ 0.0036104898333758, \ 0.0036104898333758, \ 0.0036104898333758, \ 0.0036104898333758, \ 0.0036104898333758, \ 0.0036104898333758, \ 0.0065404545307455, \ 0.0065404545307455, \ 0.0065404545307455, \ 0.0065404545307455, \ 0.0065404545307455, \ 0.0065404545307455, \ 0.0040792214803126, \ 0.0040792214803126, \ 0.0040792214803126, \ 0.0040792214803126, \ 0.0040792214803126, \ 0.0040792214803126, \ 0.0023256389181058, \ 0.0023256389181058, \ 0.0023256389181058, \ 0.0023256389181058, \ 0.0023256389181058, \ 0.0023256389181058, \ 0.0010057440220833, \ 0.0010057440220833, \ 0.0010057440220833, \ 0.0010057440220833, \ 0.0010057440220833, \ 0.0010057440220833, \ 0.0011431617714117, \ 0.0011431617714117, \ 0.0011431617714117, \ 0.0011431617714117, \ 0.0011431617714117, \ 0.0011431617714117, \ 0.0011884613225083, \ 0.0011884613225083, \ 0.0011884613225083, \ 0.0011884613225083, \ 0.0011884613225083, \ 0.0011884613225083, \ 0.0029052189452109, \ 0.0029052189452109, \ 0.0029052189452109, \ 0.0029052189452109, \ 0.0029052189452109, \ 0.0029052189452109, \ 0.0017075502039157, \ 0.0017075502039157, \ 0.0017075502039157, \ 0.0089856095188050, \ 0.0089856095188050, \ 0.0089856095188050, \ 0.0063267151975866, \ 0.0063267151975866, \ 0.0063267151975866, \ 0.0063267151975866, \ 0.0063267151975866, \ 0.0063267151975866, \ 0.0079377042751205, \ 0.0079377042751205, \ 0.0079377042751205, \ 0.0027256862207201, \ 0.0027256862207201, \ 0.0027256862207201, \ 0.0027256862207201, \ 0.0027256862207201, \ 0.0027256862207201, \ 0.0077485531926675, \ 0.0077485531926675, \ 0.0077485531926675, \ 0.0030358975545344, \ 0.0030358975545344, \ 0.0030358975545344, \ 0.0045215915998052, \ 0.0045215915998052, \ 0.0045215915998052, \ 0.0045215915998052, \ 0.0045215915998052, \ 0.0045215915998052, \ 0.0012891742774294, \ 0.0012891742774294, \ 0.0012891742774294, \ 0.0012891742774294, \ 0.0012891742774294, \ 0.0012891742774294, \ 0.0008166839181728, \ 0.0008166839181728, \ 0.0008166839181728, \ 0.0008166839181728, \ 0.0008166839181728, \ 0.0008166839181728, \ 0.0069477793235522, \ 0.0069477793235522, \ 0.0069477793235522, \ 0.0069477793235522, \ 0.0069477793235522, \ 0.0069477793235522, \ 0.0070986179394903, \ 0.0070986179394903, \ 0.0070986179394903, \ 0.0070986179394903, \ 0.0070986179394903, \ 0.0070986179394903, \ 0.0076919203485779, \ 0.0076919203485779, \ 0.0076919203485779, \ 0.0076919203485779, \ 0.0076919203485779, \ 0.0076919203485779, \ 0.0029252190187241, \ 0.0029252190187241, \ 0.0029252190187241, \ 0.0029252190187241, \ 0.0029252190187241, \ 0.0029252190187241, \ 0.0099759936103826, \ 0.0099759936103826, \ 0.0099759936103826, \ 0.0060566969964858, \ 0.0060566969964858, \ 0.0060566969964858, \ 0.0060566969964858, \ 0.0060566969964858, \ 0.0060566969964858, \ 0.0003337056331188, \ 0.0003337056331188, \ 0.0003337056331188, \ 0.0003337056331188, \ 0.0003337056331188, \ 0.0003337056331188, \ 0.0045294689209488, \ 0.0045294689209488, \ 0.0045294689209488, \ 0.0045294689209488, \ 0.0045294689209488, \ 0.0045294689209488, \ 0.0084025374143198, \ 0.0084025374143198, \ 0.0084025374143198, \ 0.0084025374143198, \ 0.0084025374143198, \ 0.0084025374143198, \ 0.0018109718524034, \ 0.0018109718524034, \ 0.0018109718524034, \ 0.0018109718524034, \ 0.0018109718524034, \ 0.0018109718524034, \ 0.0002922856631828, \ 0.0002922856631828, \ 0.0002922856631828, \ 0.0002922856631828, \ 0.0002922856631828, \ 0.0002922856631828 ] ) return a, b, c, w def rule39 ( ): #*****************************************************************************80 # ## rule39() returns the rule of precision 39. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.2382752085845570, \ 0.7573503089771818, \ 0.0043744824382613, \ 0.7573503089771818, \ 0.2382752085845571, \ 0.0043744824382611, \ 0.5022902013149184, \ 0.2662727227960811, \ 0.2314370758890004, \ 0.2662727227960811, \ 0.5022902013149184, \ 0.2314370758890005, \ 0.3506827341571583, \ 0.4132178184063219, \ 0.2360994474365198, \ 0.4132178184063219, \ 0.3506827341571582, \ 0.2360994474365199, \ 0.2778089177192840, \ 0.7195287425328243, \ 0.0026623397478918, \ 0.7195287425328242, \ 0.2778089177192840, \ 0.0026623397478915, \ 0.4724094821505567, \ 0.4724094821505566, \ 0.0551810356988866, \ 0.3212034826826168, \ 0.4713569053824377, \ 0.2074396119349455, \ 0.4713569053824377, \ 0.3212034826826168, \ 0.2074396119349454, \ 0.4575079686738243, \ 0.4575079686738243, \ 0.0849840626523514, \ 0.4574242168529821, \ 0.5306666306702293, \ 0.0119091524767885, \ 0.5306666306702292, \ 0.4574242168529821, \ 0.0119091524767886, \ 0.1910383428521846, \ 0.8068046948089155, \ 0.0021569623388999, \ 0.8068046948089155, \ 0.1910383428521847, \ 0.0021569623388998, \ 0.3538472919168833, \ 0.3538472919168833, \ 0.2923054161662332, \ 0.4991061498602990, \ 0.4991061498602990, \ 0.0017877002794020, \ 0.2063519407328363, \ 0.6863905655155179, \ 0.1072574937516458, \ 0.6863905655155178, \ 0.2063519407328364, \ 0.1072574937516456, \ 0.2612383827874719, \ 0.6263232239210454, \ 0.1124383932914825, \ 0.6263232239210456, \ 0.2612383827874720, \ 0.1124383932914823, \ 0.1133316581963653, \ 0.7733366836072691, \ 0.1133316581963656, \ 0.1593888996231203, \ 0.7265207753801600, \ 0.1140903249967197, \ 0.7265207753801599, \ 0.1593888996231204, \ 0.1140903249967195, \ 0.3988695132240669, \ 0.5391856448598707, \ 0.0619448419160624, \ 0.5391856448598707, \ 0.3988695132240669, \ 0.0619448419160624, \ 0.3122725792733609, \ 0.5657645375013545, \ 0.1219628832252846, \ 0.5657645375013546, \ 0.3122725792733608, \ 0.1219628832252845, \ 0.3644362623584764, \ 0.5969189412939834, \ 0.0386447963475403, \ 0.5969189412939834, \ 0.3644362623584764, \ 0.0386447963475401, \ 0.2305648342404432, \ 0.7522011939909903, \ 0.0172339717685666, \ 0.7522011939909903, \ 0.2305648342404432, \ 0.0172339717685664, \ 0.0157787047228343, \ 0.9684425905543310, \ 0.0157787047228348, \ 0.0392682833818940, \ 0.9461693463150468, \ 0.0145623703030595, \ 0.9461693463150468, \ 0.0392682833818942, \ 0.0145623703030590, \ 0.3582577335477227, \ 0.4875811564549278, \ 0.1541611099973494, \ 0.4875811564549278, \ 0.3582577335477227, \ 0.1541611099973493, \ 0.3805078825483125, \ 0.5183519867727387, \ 0.1011401306789488, \ 0.5183519867727387, \ 0.3805078825483125, \ 0.1011401306789487, \ 0.1318865755866089, \ 0.7948276077652688, \ 0.0732858166481222, \ 0.7948276077652688, \ 0.1318865755866089, \ 0.0732858166481220, \ 0.1726302550688860, \ 0.8138522815338993, \ 0.0135174633972147, \ 0.8138522815338993, \ 0.1726302550688861, \ 0.0135174633972144, \ 0.0707756358900086, \ 0.8860757177287693, \ 0.0431486463812223, \ 0.8860757177287693, \ 0.0707756358900087, \ 0.0431486463812219, \ 0.0473824731204699, \ 0.9497691880411768, \ 0.0028483388383533, \ 0.9497691880411769, \ 0.0473824731204700, \ 0.0028483388383529, \ 0.1640091847666056, \ 0.6719816304667885, \ 0.1640091847666059, \ 0.4084715607291340, \ 0.4084715607291340, \ 0.1830568785417320, \ 0.2971932482957449, \ 0.6624092975072737, \ 0.0403974541969814, \ 0.6624092975072737, \ 0.2971932482957449, \ 0.0403974541969812, \ 0.4437652399535983, \ 0.5252322117028740, \ 0.0310025483435276, \ 0.5252322117028740, \ 0.4437652399535983, \ 0.0310025483435276, \ 0.2298548902498229, \ 0.7308596458500963, \ 0.0392854639000808, \ 0.7308596458500963, \ 0.2298548902498229, \ 0.0392854639000805, \ 0.4365416551079566, \ 0.4365416551079566, \ 0.1269166897840867, \ 0.2515254271389071, \ 0.6769104408114252, \ 0.0715641320496676, \ 0.6769104408114253, \ 0.2515254271389073, \ 0.0715641320496676, \ 0.2206287919327525, \ 0.6249766162864728, \ 0.1543945917807746, \ 0.6249766162864728, \ 0.2206287919327525, \ 0.1543945917807745, \ 0.0370326513393936, \ 0.9259346973212126, \ 0.0370326513393939, \ 0.4164031820468178, \ 0.5808233445804072, \ 0.0027734733727750, \ 0.5808233445804072, \ 0.4164031820468178, \ 0.0027734733727749, \ 0.2780372435840275, \ 0.5501168873807294, \ 0.1718458690352431, \ 0.5501168873807294, \ 0.2780372435840275, \ 0.1718458690352429, \ 0.3420758322145085, \ 0.6546717575274422, \ 0.0032524102580493, \ 0.6546717575274422, \ 0.3420758322145085, \ 0.0032524102580491, \ 0.2117317495651855, \ 0.5765365008696287, \ 0.2117317495651856, \ 0.3766515227420243, \ 0.6072672777807482, \ 0.0160811994772276, \ 0.6072672777807481, \ 0.3766515227420243, \ 0.0160811994772275, \ 0.1122979167412356, \ 0.8440428845538768, \ 0.0436591987048877, \ 0.8440428845538769, \ 0.1122979167412357, \ 0.0436591987048873, \ 0.1861411558417737, \ 0.7455631517971735, \ 0.0682956923610529, \ 0.7455631517971736, \ 0.1861411558417738, \ 0.0682956923610526, \ 0.3217033982751871, \ 0.6035740986139331, \ 0.0747225031108797, \ 0.6035740986139331, \ 0.3217033982751872, \ 0.0747225031108797, \ 0.1660126851788667, \ 0.7978319404567993, \ 0.0361553743643340, \ 0.7978319404567994, \ 0.1660126851788668, \ 0.0361553743643337, \ 0.0193576952354285, \ 0.9778092140653304, \ 0.0028330906992414, \ 0.9778092140653304, \ 0.0193576952354286, \ 0.0028330906992409, \ 0.0719904092251254, \ 0.9100597072441559, \ 0.0179498835307189, \ 0.9100597072441557, \ 0.0719904092251255, \ 0.0179498835307185, \ 0.2869572884590686, \ 0.4260854230818626, \ 0.2869572884590688, \ 0.1333327168798979, \ 0.8634747432495302, \ 0.0031925398705718, \ 0.8634747432495303, \ 0.1333327168798978, \ 0.0031925398705716, \ 0.2994455291729939, \ 0.6842620134079914, \ 0.0162924574190148, \ 0.6842620134079914, \ 0.2994455291729938, \ 0.0162924574190146, \ 0.1171078851891533, \ 0.8649767156294978, \ 0.0179153991813488, \ 0.8649767156294980, \ 0.1171078851891534, \ 0.0179153991813485, \ 0.0806765828829425, \ 0.8386468342341147, \ 0.0806765828829429, \ 0.0853676016562655, \ 0.9110651490396003, \ 0.0035672493041343, \ 0.9110651490396005, \ 0.0853676016562656, \ 0.0035672493041339, \ 0.0036432199207299, \ 0.9927135601585398, \ 0.0036432199207303 ] ) b = np.array ( [ \ 0.0043744824382613, \ 0.2382752085845570, \ 0.7573503089771819, \ 0.0043744824382613, \ 0.7573503089771818, \ 0.2382752085845573, \ 0.2314370758890006, \ 0.5022902013149185, \ 0.2662727227960813, \ 0.2314370758890006, \ 0.2662727227960812, \ 0.5022902013149185, \ 0.2360994474365199, \ 0.3506827341571583, \ 0.4132178184063220, \ 0.2360994474365199, \ 0.4132178184063219, \ 0.3506827341571584, \ 0.0026623397478917, \ 0.2778089177192841, \ 0.7195287425328244, \ 0.0026623397478917, \ 0.7195287425328244, \ 0.2778089177192843, \ 0.0551810356988867, \ 0.4724094821505568, \ 0.4724094821505569, \ 0.2074396119349455, \ 0.3212034826826168, \ 0.4713569053824378, \ 0.2074396119349455, \ 0.4713569053824377, \ 0.3212034826826170, \ 0.0849840626523515, \ 0.4575079686738243, \ 0.4575079686738245, \ 0.0119091524767886, \ 0.4574242168529821, \ 0.5306666306702296, \ 0.0119091524767886, \ 0.5306666306702293, \ 0.4574242168529823, \ 0.0021569623388999, \ 0.1910383428521846, \ 0.8068046948089157, \ 0.0021569623388999, \ 0.8068046948089155, \ 0.1910383428521849, \ 0.2923054161662334, \ 0.3538472919168835, \ 0.3538472919168835, \ 0.0017877002794021, \ 0.4991061498602991, \ 0.4991061498602992, \ 0.1072574937516458, \ 0.2063519407328363, \ 0.6863905655155180, \ 0.1072574937516458, \ 0.6863905655155180, \ 0.2063519407328365, \ 0.1124383932914825, \ 0.2612383827874720, \ 0.6263232239210457, \ 0.1124383932914825, \ 0.6263232239210456, \ 0.2612383827874722, \ 0.1133316581963656, \ 0.1133316581963653, \ 0.7733366836072691, \ 0.1140903249967197, \ 0.1593888996231203, \ 0.7265207753801601, \ 0.1140903249967197, \ 0.7265207753801601, \ 0.1593888996231206, \ 0.0619448419160625, \ 0.3988695132240669, \ 0.5391856448598709, \ 0.0619448419160625, \ 0.5391856448598707, \ 0.3988695132240671, \ 0.1219628832252846, \ 0.3122725792733609, \ 0.5657645375013547, \ 0.1219628832252846, \ 0.5657645375013547, \ 0.3122725792733611, \ 0.0386447963475402, \ 0.3644362623584764, \ 0.5969189412939835, \ 0.0386447963475402, \ 0.5969189412939835, \ 0.3644362623584766, \ 0.0172339717685666, \ 0.2305648342404432, \ 0.7522011939909904, \ 0.0172339717685666, \ 0.7522011939909904, \ 0.2305648342404434, \ 0.0157787047228346, \ 0.0157787047228343, \ 0.9684425905543311, \ 0.0145623703030592, \ 0.0392682833818940, \ 0.9461693463150468, \ 0.0145623703030592, \ 0.9461693463150468, \ 0.0392682833818944, \ 0.1541611099973495, \ 0.3582577335477228, \ 0.4875811564549280, \ 0.1541611099973495, \ 0.4875811564549279, \ 0.3582577335477229, \ 0.1011401306789488, \ 0.3805078825483126, \ 0.5183519867727389, \ 0.1011401306789488, \ 0.5183519867727387, \ 0.3805078825483127, \ 0.0732858166481222, \ 0.1318865755866089, \ 0.7948276077652691, \ 0.0732858166481222, \ 0.7948276077652691, \ 0.1318865755866092, \ 0.0135174633972146, \ 0.1726302550688860, \ 0.8138522815338995, \ 0.0135174633972146, \ 0.8138522815338995, \ 0.1726302550688863, \ 0.0431486463812222, \ 0.0707756358900086, \ 0.8860757177287693, \ 0.0431486463812222, \ 0.8860757177287693, \ 0.0707756358900089, \ 0.0028483388383532, \ 0.0473824731204699, \ 0.9497691880411770, \ 0.0028483388383532, \ 0.9497691880411770, \ 0.0473824731204703, \ 0.1640091847666058, \ 0.1640091847666057, \ 0.6719816304667886, \ 0.1830568785417320, \ 0.4084715607291341, \ 0.4084715607291342, \ 0.0403974541969814, \ 0.2971932482957449, \ 0.6624092975072738, \ 0.0403974541969814, \ 0.6624092975072738, \ 0.2971932482957452, \ 0.0310025483435277, \ 0.4437652399535983, \ 0.5252322117028743, \ 0.0310025483435277, \ 0.5252322117028742, \ 0.4437652399535986, \ 0.0392854639000807, \ 0.2298548902498229, \ 0.7308596458500966, \ 0.0392854639000807, \ 0.7308596458500966, \ 0.2298548902498232, \ 0.1269166897840868, \ 0.4365416551079567, \ 0.4365416551079568, \ 0.0715641320496677, \ 0.2515254271389071, \ 0.6769104408114255, \ 0.0715641320496677, \ 0.6769104408114252, \ 0.2515254271389074, \ 0.1543945917807747, \ 0.2206287919327525, \ 0.6249766162864731, \ 0.1543945917807747, \ 0.6249766162864731, \ 0.2206287919327527, \ 0.0370326513393939, \ 0.0370326513393935, \ 0.9259346973212128, \ 0.0027734733727750, \ 0.4164031820468178, \ 0.5808233445804074, \ 0.0027734733727750, \ 0.5808233445804073, \ 0.4164031820468180, \ 0.1718458690352430, \ 0.2780372435840276, \ 0.5501168873807295, \ 0.1718458690352430, \ 0.5501168873807295, \ 0.2780372435840278, \ 0.0032524102580493, \ 0.3420758322145085, \ 0.6546717575274423, \ 0.0032524102580493, \ 0.6546717575274423, \ 0.3420758322145088, \ 0.2117317495651857, \ 0.2117317495651856, \ 0.5765365008696289, \ 0.0160811994772277, \ 0.3766515227420243, \ 0.6072672777807483, \ 0.0160811994772277, \ 0.6072672777807482, \ 0.3766515227420245, \ 0.0436591987048876, \ 0.1122979167412356, \ 0.8440428845538770, \ 0.0436591987048876, \ 0.8440428845538770, \ 0.1122979167412359, \ 0.0682956923610528, \ 0.1861411558417737, \ 0.7455631517971736, \ 0.0682956923610528, \ 0.7455631517971735, \ 0.1861411558417740, \ 0.0747225031108798, \ 0.3217033982751872, \ 0.6035740986139333, \ 0.0747225031108798, \ 0.6035740986139331, \ 0.3217033982751874, \ 0.0361553743643339, \ 0.1660126851788667, \ 0.7978319404567995, \ 0.0361553743643339, \ 0.7978319404567995, \ 0.1660126851788670, \ 0.0028330906992412, \ 0.0193576952354285, \ 0.9778092140653304, \ 0.0028330906992412, \ 0.9778092140653306, \ 0.0193576952354288, \ 0.0179498835307188, \ 0.0719904092251254, \ 0.9100597072441560, \ 0.0179498835307188, \ 0.9100597072441560, \ 0.0719904092251257, \ 0.2869572884590688, \ 0.2869572884590687, \ 0.4260854230818627, \ 0.0031925398705718, \ 0.1333327168798978, \ 0.8634747432495306, \ 0.0031925398705718, \ 0.8634747432495306, \ 0.1333327168798982, \ 0.0162924574190147, \ 0.2994455291729939, \ 0.6842620134079915, \ 0.0162924574190147, \ 0.6842620134079915, \ 0.2994455291729942, \ 0.0179153991813487, \ 0.1171078851891533, \ 0.8649767156294981, \ 0.0179153991813487, \ 0.8649767156294981, \ 0.1171078851891536, \ 0.0806765828829428, \ 0.0806765828829425, \ 0.8386468342341149, \ 0.0035672493041342, \ 0.0853676016562654, \ 0.9110651490396005, \ 0.0035672493041342, \ 0.9110651490396005, \ 0.0853676016562658, \ 0.0036432199207302, \ 0.0036432199207299, \ 0.9927135601585401 ] ) c = np.array ( [ \ 0.7573503089771818, \ 0.0043744824382612, \ 0.2382752085845569, \ 0.2382752085845569, \ 0.0043744824382611, \ 0.7573503089771817, \ 0.2662727227960810, \ 0.2314370758890004, \ 0.5022902013149183, \ 0.5022902013149184, \ 0.2314370758890004, \ 0.2662727227960809, \ 0.4132178184063218, \ 0.2360994474365198, \ 0.3506827341571581, \ 0.3506827341571582, \ 0.2360994474365198, \ 0.4132178184063217, \ 0.7195287425328243, \ 0.0026623397478917, \ 0.2778089177192838, \ 0.2778089177192841, \ 0.0026623397478917, \ 0.7195287425328241, \ 0.4724094821505567, \ 0.0551810356988865, \ 0.4724094821505564, \ 0.4713569053824377, \ 0.2074396119349455, \ 0.3212034826826167, \ 0.3212034826826168, \ 0.2074396119349455, \ 0.4713569053824377, \ 0.4575079686738243, \ 0.0849840626523514, \ 0.4575079686738240, \ 0.5306666306702292, \ 0.0119091524767885, \ 0.4574242168529820, \ 0.4574242168529821, \ 0.0119091524767886, \ 0.5306666306702290, \ 0.8068046948089155, \ 0.0021569623388999, \ 0.1910383428521844, \ 0.1910383428521846, \ 0.0021569623388998, \ 0.8068046948089154, \ 0.3538472919168832, \ 0.2923054161662332, \ 0.3538472919168832, \ 0.4991061498602989, \ 0.0017877002794019, \ 0.4991061498602988, \ 0.6863905655155179, \ 0.1072574937516458, \ 0.2063519407328361, \ 0.2063519407328364, \ 0.1072574937516456, \ 0.6863905655155178, \ 0.6263232239210456, \ 0.1124383932914826, \ 0.2612383827874718, \ 0.2612383827874719, \ 0.1124383932914824, \ 0.6263232239210454, \ 0.7733366836072691, \ 0.1133316581963655, \ 0.1133316581963651, \ 0.7265207753801600, \ 0.1140903249967197, \ 0.1593888996231201, \ 0.1593888996231204, \ 0.1140903249967194, \ 0.7265207753801600, \ 0.5391856448598706, \ 0.0619448419160623, \ 0.3988695132240667, \ 0.3988695132240668, \ 0.0619448419160623, \ 0.5391856448598705, \ 0.5657645375013545, \ 0.1219628832252846, \ 0.3122725792733607, \ 0.3122725792733608, \ 0.1219628832252845, \ 0.5657645375013545, \ 0.5969189412939834, \ 0.0386447963475402, \ 0.3644362623584763, \ 0.3644362623584764, \ 0.0386447963475401, \ 0.5969189412939833, \ 0.7522011939909903, \ 0.0172339717685665, \ 0.2305648342404431, \ 0.2305648342404432, \ 0.0172339717685664, \ 0.7522011939909903, \ 0.9684425905543311, \ 0.0157787047228347, \ 0.0157787047228340, \ 0.9461693463150469, \ 0.0145623703030592, \ 0.0392682833818937, \ 0.0392682833818940, \ 0.0145623703030590, \ 0.9461693463150466, \ 0.4875811564549278, \ 0.1541611099973494, \ 0.3582577335477226, \ 0.3582577335477227, \ 0.1541611099973494, \ 0.4875811564549277, \ 0.5183519867727386, \ 0.1011401306789487, \ 0.3805078825483124, \ 0.3805078825483125, \ 0.1011401306789487, \ 0.5183519867727385, \ 0.7948276077652688, \ 0.0732858166481222, \ 0.1318865755866087, \ 0.1318865755866090, \ 0.0732858166481219, \ 0.7948276077652687, \ 0.8138522815338993, \ 0.0135174633972147, \ 0.1726302550688857, \ 0.1726302550688860, \ 0.0135174633972144, \ 0.8138522815338993, \ 0.8860757177287693, \ 0.0431486463812222, \ 0.0707756358900085, \ 0.0707756358900086, \ 0.0431486463812221, \ 0.8860757177287691, \ 0.9497691880411768, \ 0.0028483388383533, \ 0.0473824731204696, \ 0.0473824731204699, \ 0.0028483388383530, \ 0.9497691880411768, \ 0.6719816304667885, \ 0.1640091847666058, \ 0.1640091847666055, \ 0.4084715607291339, \ 0.1830568785417319, \ 0.4084715607291339, \ 0.6624092975072737, \ 0.0403974541969814, \ 0.2971932482957448, \ 0.2971932482957449, \ 0.0403974541969813, \ 0.6624092975072735, \ 0.5252322117028740, \ 0.0310025483435276, \ 0.4437652399535981, \ 0.4437652399535983, \ 0.0310025483435276, \ 0.5252322117028738, \ 0.7308596458500963, \ 0.0392854639000808, \ 0.2298548902498226, \ 0.2298548902498230, \ 0.0392854639000805, \ 0.7308596458500963, \ 0.4365416551079566, \ 0.1269166897840867, \ 0.4365416551079564, \ 0.6769104408114252, \ 0.0715641320496677, \ 0.2515254271389069, \ 0.2515254271389070, \ 0.0715641320496675, \ 0.6769104408114250, \ 0.6249766162864728, \ 0.1543945917807746, \ 0.2206287919327523, \ 0.2206287919327525, \ 0.1543945917807744, \ 0.6249766162864727, \ 0.9259346973212126, \ 0.0370326513393939, \ 0.0370326513393933, \ 0.5808233445804073, \ 0.0027734733727750, \ 0.4164031820468176, \ 0.4164031820468178, \ 0.0027734733727750, \ 0.5808233445804071, \ 0.5501168873807295, \ 0.1718458690352430, \ 0.2780372435840274, \ 0.2780372435840276, \ 0.1718458690352430, \ 0.5501168873807294, \ 0.6546717575274421, \ 0.0032524102580492, \ 0.3420758322145083, \ 0.3420758322145085, \ 0.0032524102580491, \ 0.6546717575274421, \ 0.5765365008696287, \ 0.2117317495651857, \ 0.2117317495651855, \ 0.6072672777807481, \ 0.0160811994772275, \ 0.3766515227420241, \ 0.3766515227420243, \ 0.0160811994772275, \ 0.6072672777807480, \ 0.8440428845538769, \ 0.0436591987048877, \ 0.1122979167412353, \ 0.1122979167412356, \ 0.0436591987048873, \ 0.8440428845538768, \ 0.7455631517971735, \ 0.0682956923610528, \ 0.1861411558417735, \ 0.1861411558417736, \ 0.0682956923610527, \ 0.7455631517971734, \ 0.6035740986139331, \ 0.0747225031108797, \ 0.3217033982751869, \ 0.3217033982751871, \ 0.0747225031108797, \ 0.6035740986139329, \ 0.7978319404567993, \ 0.0361553743643340, \ 0.1660126851788665, \ 0.1660126851788667, \ 0.0361553743643337, \ 0.7978319404567993, \ 0.9778092140653303, \ 0.0028330906992411, \ 0.0193576952354283, \ 0.0193576952354284, \ 0.0028330906992408, \ 0.9778092140653303, \ 0.9100597072441557, \ 0.0179498835307187, \ 0.0719904092251252, \ 0.0719904092251255, \ 0.0179498835307185, \ 0.9100597072441557, \ 0.4260854230818627, \ 0.2869572884590687, \ 0.2869572884590685, \ 0.8634747432495303, \ 0.0031925398705719, \ 0.1333327168798976, \ 0.1333327168798979, \ 0.0031925398705716, \ 0.8634747432495302, \ 0.6842620134079914, \ 0.0162924574190147, \ 0.2994455291729936, \ 0.2994455291729938, \ 0.0162924574190146, \ 0.6842620134079912, \ 0.8649767156294980, \ 0.0179153991813489, \ 0.1171078851891532, \ 0.1171078851891533, \ 0.0179153991813485, \ 0.8649767156294980, \ 0.8386468342341147, \ 0.0806765828829429, \ 0.0806765828829422, \ 0.9110651490396003, \ 0.0035672493041342, \ 0.0853676016562652, \ 0.0853676016562654, \ 0.0035672493041340, \ 0.9110651490396003, \ 0.9927135601585400, \ 0.0036432199207303, \ 0.0036432199207296 ] ) w = np.array ( [ \ 0.0007824030328396, \ 0.0007824030328396, \ 0.0007824030328396, \ 0.0007824030328396, \ 0.0007824030328396, \ 0.0007824030328396, \ 0.0054259258789525, \ 0.0054259258789525, \ 0.0054259258789525, \ 0.0054259258789525, \ 0.0054259258789525, \ 0.0054259258789525, \ 0.0064335649832209, \ 0.0064335649832209, \ 0.0064335649832209, \ 0.0064335649832209, \ 0.0064335649832209, \ 0.0064335649832209, \ 0.0007645106376317, \ 0.0007645106376317, \ 0.0007645106376317, \ 0.0007645106376317, \ 0.0007645106376317, \ 0.0007645106376317, \ 0.0038004729776007, \ 0.0038004729776007, \ 0.0038004729776007, \ 0.0062594886810264, \ 0.0062594886810264, \ 0.0062594886810264, \ 0.0062594886810264, \ 0.0062594886810264, \ 0.0062594886810264, \ 0.0048090357401686, \ 0.0048090357401686, \ 0.0048090357401686, \ 0.0021620874068945, \ 0.0021620874068945, \ 0.0021620874068945, \ 0.0021620874068945, \ 0.0021620874068945, \ 0.0021620874068945, \ 0.0006908539783223, \ 0.0006908539783223, \ 0.0006908539783223, \ 0.0006908539783223, \ 0.0006908539783223, \ 0.0006908539783223, \ 0.0080789945453473, \ 0.0080789945453473, \ 0.0080789945453473, \ 0.0008384766818292, \ 0.0008384766818292, \ 0.0008384766818292, \ 0.0043810960857082, \ 0.0043810960857082, \ 0.0043810960857082, \ 0.0043810960857082, \ 0.0043810960857082, \ 0.0043810960857082, \ 0.0048977390707915, \ 0.0048977390707915, \ 0.0048977390707915, \ 0.0048977390707915, \ 0.0048977390707915, \ 0.0048977390707915, \ 0.0037089356213762, \ 0.0037089356213762, \ 0.0037089356213762, \ 0.0044309896508941, \ 0.0044309896508941, \ 0.0044309896508941, \ 0.0044309896508941, \ 0.0044309896508941, \ 0.0044309896508941, \ 0.0046998784286279, \ 0.0046998784286279, \ 0.0046998784286279, \ 0.0046998784286279, \ 0.0046998784286279, \ 0.0046998784286279, \ 0.0056949471589669, \ 0.0056949471589669, \ 0.0056949471589669, \ 0.0056949471589669, \ 0.0056949471589669, \ 0.0056949471589669, \ 0.0037232299887488, \ 0.0037232299887488, \ 0.0037232299887488, \ 0.0037232299887488, \ 0.0037232299887488, \ 0.0037232299887488, \ 0.0022711066220262, \ 0.0022711066220262, \ 0.0022711066220262, \ 0.0022711066220262, \ 0.0022711066220262, \ 0.0022711066220262, \ 0.0006686069116893, \ 0.0006686069116893, \ 0.0006686069116893, \ 0.0009501856551478, \ 0.0009501856551478, \ 0.0009501856551478, \ 0.0009501856551478, \ 0.0009501856551478, \ 0.0009501856551478, \ 0.0074331006305706, \ 0.0074331006305706, \ 0.0074331006305706, \ 0.0074331006305706, \ 0.0074331006305706, \ 0.0074331006305706, \ 0.0061864305337419, \ 0.0061864305337419, \ 0.0061864305337419, \ 0.0061864305337419, \ 0.0061864305337419, \ 0.0061864305337419, \ 0.0038374222817439, \ 0.0038374222817439, \ 0.0038374222817439, \ 0.0038374222817439, \ 0.0038374222817439, \ 0.0038374222817439, \ 0.0018958729657531, \ 0.0018958729657531, \ 0.0018958729657531, \ 0.0018958729657531, \ 0.0018958729657531, \ 0.0018958729657531, \ 0.0023158771686324, \ 0.0023158771686324, \ 0.0023158771686324, \ 0.0023158771686324, \ 0.0023158771686324, \ 0.0023158771686324, \ 0.0004882707622038, \ 0.0004882707622038, \ 0.0004882707622038, \ 0.0004882707622038, \ 0.0004882707622038, \ 0.0004882707622038, \ 0.0058035379196036, \ 0.0058035379196036, \ 0.0058035379196036, \ 0.0076992066322763, \ 0.0076992066322763, \ 0.0076992066322763, \ 0.0039332470075349, \ 0.0039332470075349, \ 0.0039332470075349, \ 0.0039332470075349, \ 0.0039332470075349, \ 0.0039332470075349, \ 0.0037369831874343, \ 0.0037369831874343, \ 0.0037369831874343, \ 0.0037369831874343, \ 0.0037369831874343, \ 0.0037369831874343, \ 0.0035306268703356, \ 0.0035306268703356, \ 0.0035306268703356, \ 0.0035306268703356, \ 0.0035306268703356, \ 0.0035306268703356, \ 0.0067765032180855, \ 0.0067765032180855, \ 0.0067765032180855, \ 0.0048733014906139, \ 0.0048733014906139, \ 0.0048733014906139, \ 0.0048733014906139, \ 0.0048733014906139, \ 0.0048733014906139, \ 0.0060696924219261, \ 0.0060696924219261, \ 0.0060696924219261, \ 0.0060696924219261, \ 0.0060696924219261, \ 0.0060696924219261, \ 0.0015920496320693, \ 0.0015920496320693, \ 0.0015920496320693, \ 0.0011017635807508, \ 0.0011017635807508, \ 0.0011017635807508, \ 0.0011017635807508, \ 0.0011017635807508, \ 0.0011017635807508, \ 0.0073091828155223, \ 0.0073091828155223, \ 0.0073091828155223, \ 0.0073091828155223, \ 0.0073091828155223, \ 0.0073091828155223, \ 0.0011736195277390, \ 0.0011736195277390, \ 0.0011736195277390, \ 0.0011736195277390, \ 0.0011736195277390, \ 0.0011736195277390, \ 0.0071255638341493, \ 0.0071255638341493, \ 0.0071255638341493, \ 0.0028277464204102, \ 0.0028277464204102, \ 0.0028277464204102, \ 0.0028277464204102, \ 0.0028277464204102, \ 0.0028277464204102, \ 0.0028118195580629, \ 0.0028118195580629, \ 0.0028118195580629, \ 0.0028118195580629, \ 0.0028118195580629, \ 0.0028118195580629, \ 0.0043776217728844, \ 0.0043776217728844, \ 0.0043776217728844, \ 0.0043776217728844, \ 0.0043776217728844, \ 0.0043776217728844, \ 0.0057797851749689, \ 0.0057797851749689, \ 0.0057797851749689, \ 0.0057797851749689, \ 0.0057797851749689, \ 0.0057797851749689, \ 0.0033216883150331, \ 0.0033216883150331, \ 0.0033216883150331, \ 0.0033216883150331, \ 0.0033216883150331, \ 0.0033216883150331, \ 0.0003234214385767, \ 0.0003234214385767, \ 0.0003234214385767, \ 0.0003234214385767, \ 0.0003234214385767, \ 0.0003234214385767, \ 0.0015599585117589, \ 0.0015599585117589, \ 0.0015599585117589, \ 0.0015599585117589, \ 0.0015599585117589, \ 0.0015599585117589, \ 0.0087287285098108, \ 0.0087287285098108, \ 0.0087287285098108, \ 0.0008684596573017, \ 0.0008684596573017, \ 0.0008684596573017, \ 0.0008684596573017, \ 0.0008684596573017, \ 0.0008684596573017, \ 0.0027516782565965, \ 0.0027516782565965, \ 0.0027516782565965, \ 0.0027516782565965, \ 0.0027516782565965, \ 0.0027516782565965, \ 0.0020505862443132, \ 0.0020505862443132, \ 0.0020505862443132, \ 0.0020505862443132, \ 0.0020505862443132, \ 0.0020505862443132, \ 0.0037076853680653, \ 0.0037076853680653, \ 0.0037076853680653, \ 0.0007841501256460, \ 0.0007841501256460, \ 0.0007841501256460, \ 0.0007841501256460, \ 0.0007841501256460, \ 0.0007841501256460, \ 0.0001749077815533, \ 0.0001749077815533, \ 0.0001749077815533 ] ) return a, b, c, w def rule40 ( ): #*****************************************************************************80 # ## rule40() returns the rule of precision 40. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1671778383557105, \ 0.8312942125952762, \ 0.0015279490490133, \ 0.8312942125952764, \ 0.1671778383557105, \ 0.0015279490490130, \ 0.3714780994452375, \ 0.6135500780826215, \ 0.0149718224721411, \ 0.6135500780826214, \ 0.3714780994452375, \ 0.0149718224721410, \ 0.1590238847123736, \ 0.8341718564884986, \ 0.0068042587991279, \ 0.8341718564884986, \ 0.1590238847123738, \ 0.0068042587991276, \ 0.0462179329282665, \ 0.9184680923701788, \ 0.0353139747015547, \ 0.9184680923701789, \ 0.0462179329282665, \ 0.0353139747015544, \ 0.1148651673800807, \ 0.8835508461723146, \ 0.0015839864476049, \ 0.8835508461723147, \ 0.1148651673800808, \ 0.0015839864476045, \ 0.3342460081847144, \ 0.6442373197308038, \ 0.0215166720844818, \ 0.6442373197308038, \ 0.3342460081847144, \ 0.0215166720844817, \ 0.0723711649483900, \ 0.9256035733590469, \ 0.0020252616925632, \ 0.9256035733590469, \ 0.0723711649483901, \ 0.0020252616925628, \ 0.2236842466647887, \ 0.7609545495861244, \ 0.0153612037490869, \ 0.7609545495861244, \ 0.2236842466647888, \ 0.0153612037490867, \ 0.1111290169905849, \ 0.8787050390615000, \ 0.0101659439479151, \ 0.8787050390615001, \ 0.1111290169905850, \ 0.0101659439479147, \ 0.2764445418077909, \ 0.6935416044083799, \ 0.0300138537838293, \ 0.6935416044083799, \ 0.2764445418077908, \ 0.0300138537838291, \ 0.1692633554656758, \ 0.8117666018943027, \ 0.0189700426400217, \ 0.8117666018943026, \ 0.1692633554656758, \ 0.0189700426400213, \ 0.1196509552487583, \ 0.8536082605291146, \ 0.0267407842221271, \ 0.8536082605291146, \ 0.1196509552487584, \ 0.0267407842221267, \ 0.2830190971292686, \ 0.7161270841771937, \ 0.0008538186935376, \ 0.7161270841771938, \ 0.2830190971292687, \ 0.0008538186935374, \ 0.0704045501511468, \ 0.9173369798048715, \ 0.0122584700439818, \ 0.9173369798048715, \ 0.0704045501511468, \ 0.0122584700439815, \ 0.2164720987514121, \ 0.7463578541350908, \ 0.0371700471134971, \ 0.7463578541350909, \ 0.2164720987514122, \ 0.0371700471134968, \ 0.0769268815632591, \ 0.8908789177732704, \ 0.0321942006634706, \ 0.8908789177732706, \ 0.0769268815632591, \ 0.0321942006634703, \ 0.4292227320385513, \ 0.5618451152501334, \ 0.0089321527113154, \ 0.5618451152501333, \ 0.4292227320385513, \ 0.0089321527113153, \ 0.0157037453637930, \ 0.9685925092724137, \ 0.0157037453637935, \ 0.2938899628974431, \ 0.4122200742051138, \ 0.2938899628974431, \ 0.3701028684237416, \ 0.3701028684237416, \ 0.2597942631525166, \ 0.3251479248852048, \ 0.4508068598872954, \ 0.2240452152274997, \ 0.4508068598872955, \ 0.3251479248852048, \ 0.2240452152274996, \ 0.2782727102869363, \ 0.5341010727223879, \ 0.1876262169906756, \ 0.5341010727223879, \ 0.2782727102869363, \ 0.1876262169906754, \ 0.2852102535187100, \ 0.7050312251574219, \ 0.0097585213238682, \ 0.7050312251574219, \ 0.2852102535187100, \ 0.0097585213238680, \ 0.2727256318298310, \ 0.6685680775484955, \ 0.0587062906216736, \ 0.6685680775484953, \ 0.2727256318298311, \ 0.0587062906216735, \ 0.4154695947712394, \ 0.5537884055426003, \ 0.0307419996861603, \ 0.5537884055426003, \ 0.4154695947712395, \ 0.0307419996861602, \ 0.2205774465337091, \ 0.7761657998291807, \ 0.0032567536371101, \ 0.7761657998291808, \ 0.2205774465337091, \ 0.0032567536371099, \ 0.3428856203943587, \ 0.6119267566451521, \ 0.0451876229604891, \ 0.6119267566451522, \ 0.3428856203943588, \ 0.0451876229604890, \ 0.2315038606116803, \ 0.6176776291642629, \ 0.1508185102240567, \ 0.6176776291642631, \ 0.2315038606116803, \ 0.1508185102240566, \ 0.0381017129649182, \ 0.9452246129976019, \ 0.0166736740374801, \ 0.9452246129976020, \ 0.0381017129649182, \ 0.0166736740374796, \ 0.3528911085101677, \ 0.4850036493442883, \ 0.1621052421455439, \ 0.4850036493442883, \ 0.3528911085101677, \ 0.1621052421455439, \ 0.4000760699195811, \ 0.5353980699804886, \ 0.0645258600999303, \ 0.5353980699804887, \ 0.4000760699195811, \ 0.0645258600999302, \ 0.1877843415465376, \ 0.6978359629848933, \ 0.1143796954685691, \ 0.6978359629848933, \ 0.1877843415465377, \ 0.1143796954685689, \ 0.2073769376903412, \ 0.7230510664568768, \ 0.0695719958527821, \ 0.7230510664568768, \ 0.2073769376903412, \ 0.0695719958527819, \ 0.1078038302263755, \ 0.8361618100730819, \ 0.0560343597005427, \ 0.8361618100730819, \ 0.1078038302263756, \ 0.0560343597005424, \ 0.1479014660731261, \ 0.7705088681427068, \ 0.0815896657841672, \ 0.7705088681427068, \ 0.1479014660731260, \ 0.0815896657841669, \ 0.1600426684113588, \ 0.7953280578174164, \ 0.0446292737712248, \ 0.7953280578174164, \ 0.1600426684113588, \ 0.0446292737712245, \ 0.3778766696887720, \ 0.5133314537120106, \ 0.1087918765992173, \ 0.5133314537120106, \ 0.3778766696887720, \ 0.1087918765992173, \ 0.2526963148522067, \ 0.4946073702955864, \ 0.2526963148522068, \ 0.0392233696648084, \ 0.9575704817506674, \ 0.0032061485845244, \ 0.9575704817506674, \ 0.0392233696648085, \ 0.0032061485845240, \ 0.3243044450771381, \ 0.5927190068639427, \ 0.0829765480589191, \ 0.5927190068639427, \ 0.3243044450771381, \ 0.0829765480589190, \ 0.2105771295148042, \ 0.5788457409703914, \ 0.2105771295148043, \ 0.0030575106285418, \ 0.9938849787429160, \ 0.0030575106285423, \ 0.4032922222742628, \ 0.4032922222742628, \ 0.1934155554514743, \ 0.4767516468002929, \ 0.4767516468002928, \ 0.0464967063994142, \ 0.3509848476225047, \ 0.6454944173675070, \ 0.0035207350099882, \ 0.6454944173675071, \ 0.3509848476225048, \ 0.0035207350099881, \ 0.0648562451597025, \ 0.8702875096805947, \ 0.0648562451597030, \ 0.1688963797829617, \ 0.6622072404340762, \ 0.1688963797829621, \ 0.3333333333333333, \ 0.4208708276256937, \ 0.5785308776456697, \ 0.0005982947286367, \ 0.5785308776456696, \ 0.4208708276256937, \ 0.0005982947286367, \ 0.0962980341591576, \ 0.8074039316816845, \ 0.0962980341591579, \ 0.2526560385602647, \ 0.6476602419795359, \ 0.0996837194601995, \ 0.6476602419795359, \ 0.2526560385602647, \ 0.0996837194601994, \ 0.4907015691302040, \ 0.4907015691302040, \ 0.0185968617395920, \ 0.4984645792365976, \ 0.4984645792365976, \ 0.0030708415268047, \ 0.3016703335605275, \ 0.5675057520644238, \ 0.1308239143750486, \ 0.5675057520644238, \ 0.3016703335605276, \ 0.1308239143750485, \ 0.4322719776068064, \ 0.4322719776068064, \ 0.1354560447863873, \ 0.1302416069902091, \ 0.7395167860195814, \ 0.1302416069902094, \ 0.4568717371543228, \ 0.4568717371543228, \ 0.0862565256913544, \ 0.0160613879667907, \ 0.9809430242931965, \ 0.0029955877400129, \ 0.9809430242931966, \ 0.0160613879667909, \ 0.0029955877400125 ] ) b = np.array ( [ \ 0.0015279490490132, \ 0.1671778383557105, \ 0.8312942125952765, \ 0.0015279490490132, \ 0.8312942125952765, \ 0.1671778383557108, \ 0.0149718224721411, \ 0.3714780994452375, \ 0.6135500780826216, \ 0.0149718224721411, \ 0.6135500780826215, \ 0.3714780994452377, \ 0.0068042587991278, \ 0.1590238847123736, \ 0.8341718564884987, \ 0.0068042587991278, \ 0.8341718564884987, \ 0.1590238847123739, \ 0.0353139747015546, \ 0.0462179329282665, \ 0.9184680923701790, \ 0.0353139747015546, \ 0.9184680923701790, \ 0.0462179329282669, \ 0.0015839864476047, \ 0.1148651673800806, \ 0.8835508461723147, \ 0.0015839864476047, \ 0.8835508461723147, \ 0.1148651673800810, \ 0.0215166720844818, \ 0.3342460081847145, \ 0.6442373197308039, \ 0.0215166720844818, \ 0.6442373197308039, \ 0.3342460081847147, \ 0.0020252616925631, \ 0.0723711649483900, \ 0.9256035733590470, \ 0.0020252616925631, \ 0.9256035733590470, \ 0.0723711649483903, \ 0.0153612037490869, \ 0.2236842466647887, \ 0.7609545495861246, \ 0.0153612037490869, \ 0.7609545495861246, \ 0.2236842466647890, \ 0.0101659439479150, \ 0.1111290169905849, \ 0.8787050390615002, \ 0.0101659439479150, \ 0.8787050390615003, \ 0.1111290169905853, \ 0.0300138537838293, \ 0.2764445418077909, \ 0.6935416044083801, \ 0.0300138537838293, \ 0.6935416044083801, \ 0.2764445418077912, \ 0.0189700426400216, \ 0.1692633554656758, \ 0.8117666018943028, \ 0.0189700426400216, \ 0.8117666018943028, \ 0.1692633554656761, \ 0.0267407842221270, \ 0.1196509552487583, \ 0.8536082605291148, \ 0.0267407842221270, \ 0.8536082605291149, \ 0.1196509552487586, \ 0.0008538186935375, \ 0.2830190971292687, \ 0.7161270841771940, \ 0.0008538186935375, \ 0.7161270841771940, \ 0.2830190971292690, \ 0.0122584700439817, \ 0.0704045501511468, \ 0.9173369798048717, \ 0.0122584700439817, \ 0.9173369798048717, \ 0.0704045501511471, \ 0.0371700471134970, \ 0.2164720987514121, \ 0.7463578541350910, \ 0.0371700471134970, \ 0.7463578541350910, \ 0.2164720987514124, \ 0.0321942006634705, \ 0.0769268815632591, \ 0.8908789177732706, \ 0.0321942006634705, \ 0.8908789177732707, \ 0.0769268815632594, \ 0.0089321527113154, \ 0.4292227320385513, \ 0.5618451152501336, \ 0.0089321527113154, \ 0.5618451152501334, \ 0.4292227320385515, \ 0.0157037453637933, \ 0.0157037453637930, \ 0.9685925092724137, \ 0.2938899628974431, \ 0.2938899628974431, \ 0.4122200742051139, \ 0.2597942631525167, \ 0.3701028684237417, \ 0.3701028684237418, \ 0.2240452152274997, \ 0.3251479248852049, \ 0.4508068598872956, \ 0.2240452152274997, \ 0.4508068598872956, \ 0.3251479248852050, \ 0.1876262169906757, \ 0.2782727102869364, \ 0.5341010727223882, \ 0.1876262169906757, \ 0.5341010727223882, \ 0.2782727102869366, \ 0.0097585213238681, \ 0.2852102535187100, \ 0.7050312251574220, \ 0.0097585213238681, \ 0.7050312251574220, \ 0.2852102535187103, \ 0.0587062906216736, \ 0.2727256318298311, \ 0.6685680775484956, \ 0.0587062906216736, \ 0.6685680775484956, \ 0.2727256318298313, \ 0.0307419996861603, \ 0.4154695947712395, \ 0.5537884055426004, \ 0.0307419996861603, \ 0.5537884055426003, \ 0.4154695947712397, \ 0.0032567536371102, \ 0.2205774465337091, \ 0.7761657998291810, \ 0.0032567536371102, \ 0.7761657998291810, \ 0.2205774465337094, \ 0.0451876229604891, \ 0.3428856203943588, \ 0.6119267566451523, \ 0.0451876229604891, \ 0.6119267566451522, \ 0.3428856203943590, \ 0.1508185102240568, \ 0.2315038606116803, \ 0.6176776291642632, \ 0.1508185102240568, \ 0.6176776291642631, \ 0.2315038606116805, \ 0.0166736740374799, \ 0.0381017129649183, \ 0.9452246129976019, \ 0.0166736740374799, \ 0.9452246129976022, \ 0.0381017129649186, \ 0.1621052421455440, \ 0.3528911085101678, \ 0.4850036493442885, \ 0.1621052421455440, \ 0.4850036493442884, \ 0.3528911085101679, \ 0.0645258600999304, \ 0.4000760699195811, \ 0.5353980699804888, \ 0.0645258600999304, \ 0.5353980699804887, \ 0.4000760699195813, \ 0.1143796954685691, \ 0.1877843415465376, \ 0.6978359629848935, \ 0.1143796954685691, \ 0.6978359629848934, \ 0.1877843415465379, \ 0.0695719958527821, \ 0.2073769376903412, \ 0.7230510664568770, \ 0.0695719958527821, \ 0.7230510664568770, \ 0.2073769376903414, \ 0.0560343597005426, \ 0.1078038302263755, \ 0.8361618100730821, \ 0.0560343597005426, \ 0.8361618100730820, \ 0.1078038302263758, \ 0.0815896657841671, \ 0.1479014660731261, \ 0.7705088681427070, \ 0.0815896657841671, \ 0.7705088681427070, \ 0.1479014660731263, \ 0.0446292737712247, \ 0.1600426684113588, \ 0.7953280578174167, \ 0.0446292737712247, \ 0.7953280578174167, \ 0.1600426684113591, \ 0.1087918765992174, \ 0.3778766696887721, \ 0.5133314537120108, \ 0.1087918765992174, \ 0.5133314537120107, \ 0.3778766696887723, \ 0.2526963148522068, \ 0.2526963148522067, \ 0.4946073702955866, \ 0.0032061485845242, \ 0.0392233696648084, \ 0.9575704817506674, \ 0.0032061485845242, \ 0.9575704817506674, \ 0.0392233696648088, \ 0.0829765480589191, \ 0.3243044450771382, \ 0.5927190068639430, \ 0.0829765480589191, \ 0.5927190068639429, \ 0.3243044450771383, \ 0.2105771295148044, \ 0.2105771295148043, \ 0.5788457409703917, \ 0.0030575106285422, \ 0.0030575106285418, \ 0.9938849787429160, \ 0.1934155554514744, \ 0.4032922222742629, \ 0.4032922222742630, \ 0.0464967063994142, \ 0.4767516468002930, \ 0.4767516468002931, \ 0.0035207350099882, \ 0.3509848476225048, \ 0.6454944173675073, \ 0.0035207350099882, \ 0.6454944173675070, \ 0.3509848476225050, \ 0.0648562451597028, \ 0.0648562451597025, \ 0.8702875096805948, \ 0.1688963797829620, \ 0.1688963797829618, \ 0.6622072404340763, \ 0.3333333333333334, \ 0.0005982947286368, \ 0.4208708276256937, \ 0.5785308776456698, \ 0.0005982947286368, \ 0.5785308776456696, \ 0.4208708276256939, \ 0.0962980341591579, \ 0.0962980341591576, \ 0.8074039316816847, \ 0.0996837194601995, \ 0.2526560385602647, \ 0.6476602419795360, \ 0.0996837194601995, \ 0.6476602419795360, \ 0.2526560385602649, \ 0.0185968617395921, \ 0.4907015691302040, \ 0.4907015691302042, \ 0.0030708415268048, \ 0.4984645792365977, \ 0.4984645792365979, \ 0.1308239143750487, \ 0.3016703335605276, \ 0.5675057520644240, \ 0.1308239143750487, \ 0.5675057520644239, \ 0.3016703335605278, \ 0.1354560447863873, \ 0.4322719776068065, \ 0.4322719776068065, \ 0.1302416069902094, \ 0.1302416069902092, \ 0.7395167860195816, \ 0.0862565256913544, \ 0.4568717371543228, \ 0.4568717371543230, \ 0.0029955877400127, \ 0.0160613879667907, \ 0.9809430242931966, \ 0.0029955877400127, \ 0.9809430242931966, \ 0.0160613879667911 ] ) c = np.array ( [ \ 0.8312942125952764, \ 0.0015279490490133, \ 0.1671778383557102, \ 0.1671778383557104, \ 0.0015279490490130, \ 0.8312942125952762, \ 0.6135500780826214, \ 0.0149718224721410, \ 0.3714780994452372, \ 0.3714780994452375, \ 0.0149718224721410, \ 0.6135500780826213, \ 0.8341718564884986, \ 0.0068042587991278, \ 0.1590238847123734, \ 0.1590238847123737, \ 0.0068042587991276, \ 0.8341718564884986, \ 0.9184680923701788, \ 0.0353139747015547, \ 0.0462179329282663, \ 0.0462179329282665, \ 0.0353139747015544, \ 0.9184680923701787, \ 0.8835508461723147, \ 0.0015839864476048, \ 0.1148651673800805, \ 0.1148651673800806, \ 0.0015839864476045, \ 0.8835508461723145, \ 0.6442373197308037, \ 0.0215166720844817, \ 0.3342460081847143, \ 0.3342460081847144, \ 0.0215166720844816, \ 0.6442373197308036, \ 0.9256035733590469, \ 0.0020252616925631, \ 0.0723711649483898, \ 0.0723711649483900, \ 0.0020252616925630, \ 0.9256035733590467, \ 0.7609545495861244, \ 0.0153612037490869, \ 0.2236842466647885, \ 0.2236842466647887, \ 0.0153612037490866, \ 0.7609545495861243, \ 0.8787050390615000, \ 0.0101659439479151, \ 0.1111290169905846, \ 0.1111290169905849, \ 0.0101659439479147, \ 0.8787050390615000, \ 0.6935416044083799, \ 0.0300138537838292, \ 0.2764445418077907, \ 0.2764445418077909, \ 0.0300138537838291, \ 0.6935416044083798, \ 0.8117666018943027, \ 0.0189700426400215, \ 0.1692633554656755, \ 0.1692633554656758, \ 0.0189700426400213, \ 0.8117666018943026, \ 0.8536082605291146, \ 0.0267407842221270, \ 0.1196509552487581, \ 0.1196509552487584, \ 0.0267407842221268, \ 0.8536082605291145, \ 0.7161270841771938, \ 0.0008538186935376, \ 0.2830190971292684, \ 0.2830190971292686, \ 0.0008538186935373, \ 0.7161270841771936, \ 0.9173369798048715, \ 0.0122584700439817, \ 0.0704045501511464, \ 0.0704045501511468, \ 0.0122584700439815, \ 0.9173369798048714, \ 0.7463578541350908, \ 0.0371700471134971, \ 0.2164720987514119, \ 0.2164720987514120, \ 0.0371700471134968, \ 0.7463578541350908, \ 0.8908789177732704, \ 0.0321942006634705, \ 0.0769268815632589, \ 0.0769268815632590, \ 0.0321942006634702, \ 0.8908789177732704, \ 0.5618451152501333, \ 0.0089321527113153, \ 0.4292227320385511, \ 0.4292227320385513, \ 0.0089321527113153, \ 0.5618451152501331, \ 0.9685925092724137, \ 0.0157037453637933, \ 0.0157037453637928, \ 0.4122200742051138, \ 0.2938899628974431, \ 0.2938899628974430, \ 0.3701028684237416, \ 0.2597942631525166, \ 0.3701028684237416, \ 0.4508068598872954, \ 0.2240452152274997, \ 0.3251479248852048, \ 0.3251479248852048, \ 0.2240452152274996, \ 0.4508068598872954, \ 0.5341010727223880, \ 0.1876262169906757, \ 0.2782727102869362, \ 0.2782727102869364, \ 0.1876262169906756, \ 0.5341010727223879, \ 0.7050312251574219, \ 0.0097585213238681, \ 0.2852102535187098, \ 0.2852102535187100, \ 0.0097585213238680, \ 0.7050312251574217, \ 0.6685680775484953, \ 0.0587062906216735, \ 0.2727256318298309, \ 0.2727256318298311, \ 0.0587062906216734, \ 0.6685680775484952, \ 0.5537884055426002, \ 0.0307419996861601, \ 0.4154695947712393, \ 0.4154695947712394, \ 0.0307419996861602, \ 0.5537884055426001, \ 0.7761657998291807, \ 0.0032567536371102, \ 0.2205774465337088, \ 0.2205774465337091, \ 0.0032567536371099, \ 0.7761657998291808, \ 0.6119267566451522, \ 0.0451876229604891, \ 0.3428856203943587, \ 0.3428856203943587, \ 0.0451876229604889, \ 0.6119267566451519, \ 0.6176776291642629, \ 0.1508185102240568, \ 0.2315038606116802, \ 0.2315038606116802, \ 0.1508185102240566, \ 0.6176776291642629, \ 0.9452246129976020, \ 0.0166736740374799, \ 0.0381017129649180, \ 0.0381017129649182, \ 0.0166736740374797, \ 0.9452246129976017, \ 0.4850036493442883, \ 0.1621052421455439, \ 0.3528911085101676, \ 0.3528911085101677, \ 0.1621052421455439, \ 0.4850036493442882, \ 0.5353980699804886, \ 0.0645258600999303, \ 0.4000760699195809, \ 0.4000760699195810, \ 0.0645258600999302, \ 0.5353980699804886, \ 0.6978359629848934, \ 0.1143796954685691, \ 0.1877843415465373, \ 0.1877843415465376, \ 0.1143796954685690, \ 0.6978359629848931, \ 0.7230510664568768, \ 0.0695719958527820, \ 0.2073769376903409, \ 0.2073769376903412, \ 0.0695719958527818, \ 0.7230510664568766, \ 0.8361618100730819, \ 0.0560343597005426, \ 0.1078038302263753, \ 0.1078038302263755, \ 0.0560343597005425, \ 0.8361618100730819, \ 0.7705088681427068, \ 0.0815896657841671, \ 0.1479014660731258, \ 0.1479014660731261, \ 0.0815896657841669, \ 0.7705088681427068, \ 0.7953280578174166, \ 0.0446292737712247, \ 0.1600426684113585, \ 0.1600426684113588, \ 0.0446292737712245, \ 0.7953280578174164, \ 0.5133314537120105, \ 0.1087918765992172, \ 0.3778766696887719, \ 0.3778766696887720, \ 0.1087918765992172, \ 0.5133314537120104, \ 0.4946073702955865, \ 0.2526963148522068, \ 0.2526963148522066, \ 0.9575704817506674, \ 0.0032061485845242, \ 0.0392233696648082, \ 0.0392233696648084, \ 0.0032061485845241, \ 0.9575704817506673, \ 0.5927190068639426, \ 0.0829765480589191, \ 0.3243044450771380, \ 0.3243044450771381, \ 0.0829765480589190, \ 0.5927190068639427, \ 0.5788457409703913, \ 0.2105771295148043, \ 0.2105771295148041, \ 0.9938849787429159, \ 0.0030575106285421, \ 0.0030575106285416, \ 0.4032922222742629, \ 0.1934155554514743, \ 0.4032922222742628, \ 0.4767516468002930, \ 0.0464967063994142, \ 0.4767516468002927, \ 0.6454944173675070, \ 0.0035207350099882, \ 0.3509848476225045, \ 0.3509848476225046, \ 0.0035207350099882, \ 0.6454944173675068, \ 0.8702875096805947, \ 0.0648562451597028, \ 0.0648562451597022, \ 0.6622072404340763, \ 0.1688963797829620, \ 0.1688963797829616, \ 0.3333333333333333, \ 0.5785308776456696, \ 0.0005982947286366, \ 0.4208708276256935, \ 0.4208708276256937, \ 0.0005982947286368, \ 0.5785308776456694, \ 0.8074039316816846, \ 0.0962980341591579, \ 0.0962980341591574, \ 0.6476602419795358, \ 0.0996837194601994, \ 0.2526560385602645, \ 0.2526560385602646, \ 0.0996837194601993, \ 0.6476602419795356, \ 0.4907015691302040, \ 0.0185968617395921, \ 0.4907015691302037, \ 0.4984645792365976, \ 0.0030708415268047, \ 0.4984645792365974, \ 0.5675057520644238, \ 0.1308239143750486, \ 0.3016703335605274, \ 0.3016703335605275, \ 0.1308239143750486, \ 0.5675057520644238, \ 0.4322719776068064, \ 0.1354560447863872, \ 0.4322719776068062, \ 0.7395167860195815, \ 0.1302416069902095, \ 0.1302416069902089, \ 0.4568717371543228, \ 0.0862565256913544, \ 0.4568717371543227, \ 0.9809430242931965, \ 0.0029955877400128, \ 0.0160613879667905, \ 0.0160613879667907, \ 0.0029955877400126, \ 0.9809430242931964 ] ) w = np.array ( [ \ 0.0003775523678536, \ 0.0003775523678536, \ 0.0003775523678536, \ 0.0003775523678536, \ 0.0003775523678536, \ 0.0003775523678536, \ 0.0015516849698550, \ 0.0015516849698550, \ 0.0015516849698550, \ 0.0015516849698550, \ 0.0015516849698550, \ 0.0015516849698550, \ 0.0008644145607466, \ 0.0008644145607466, \ 0.0008644145607466, \ 0.0008644145607466, \ 0.0008644145607466, \ 0.0008644145607466, \ 0.0009971849318732, \ 0.0009971849318732, \ 0.0009971849318732, \ 0.0009971849318732, \ 0.0009971849318732, \ 0.0009971849318732, \ 0.0004090770312980, \ 0.0004090770312980, \ 0.0004090770312980, \ 0.0004090770312980, \ 0.0004090770312980, \ 0.0004090770312980, \ 0.0020436671600844, \ 0.0020436671600844, \ 0.0020436671600844, \ 0.0020436671600844, \ 0.0020436671600844, \ 0.0020436671600844, \ 0.0004126443326276, \ 0.0004126443326276, \ 0.0004126443326276, \ 0.0004126443326276, \ 0.0004126443326276, \ 0.0004126443326276, \ 0.0019146967543968, \ 0.0019146967543968, \ 0.0019146967543968, \ 0.0019146967543968, \ 0.0019146967543968, \ 0.0019146967543968, \ 0.0011640031359899, \ 0.0011640031359899, \ 0.0011640031359899, \ 0.0011640031359899, \ 0.0011640031359899, \ 0.0011640031359899, \ 0.0029186737106524, \ 0.0029186737106524, \ 0.0029186737106524, \ 0.0029186737106524, \ 0.0029186737106524, \ 0.0029186737106524, \ 0.0019423381723224, \ 0.0019423381723224, \ 0.0019423381723224, \ 0.0019423381723224, \ 0.0019423381723224, \ 0.0019423381723224, \ 0.0020437160642330, \ 0.0020437160642330, \ 0.0020437160642330, \ 0.0020437160642330, \ 0.0020437160642330, \ 0.0020437160642330, \ 0.0004561788584349, \ 0.0004561788584349, \ 0.0004561788584349, \ 0.0004561788584349, \ 0.0004561788584349, \ 0.0004561788584349, \ 0.0011181526506985, \ 0.0011181526506985, \ 0.0011181526506985, \ 0.0011181526506985, \ 0.0011181526506985, \ 0.0011181526506985, \ 0.0030364724116124, \ 0.0030364724116124, \ 0.0030364724116124, \ 0.0030364724116124, \ 0.0030364724116124, \ 0.0030364724116124, \ 0.0019401856791114, \ 0.0019401856791114, \ 0.0019401856791114, \ 0.0019401856791114, \ 0.0019401856791114, \ 0.0019401856791114, \ 0.0019149234843930, \ 0.0019149234843930, \ 0.0019149234843930, \ 0.0019149234843930, \ 0.0019149234843930, \ 0.0019149234843930, \ 0.0006256066196749, \ 0.0006256066196749, \ 0.0006256066196749, \ 0.0085945289589868, \ 0.0085945289589868, \ 0.0085945289589868, \ 0.0085993323415620, \ 0.0085993323415620, \ 0.0085993323415620, \ 0.0082321340562276, \ 0.0082321340562276, \ 0.0082321340562276, \ 0.0082321340562276, \ 0.0082321340562276, \ 0.0082321340562276, \ 0.0075395204858702, \ 0.0075395204858702, \ 0.0075395204858702, \ 0.0075395204858702, \ 0.0075395204858702, \ 0.0075395204858702, \ 0.0018551746248727, \ 0.0018551746248727, \ 0.0018551746248727, \ 0.0018551746248727, \ 0.0018551746248727, \ 0.0018551746248727, \ 0.0044048213741681, \ 0.0044048213741681, \ 0.0044048213741681, \ 0.0044048213741681, \ 0.0044048213741681, \ 0.0044048213741681, \ 0.0038072050061859, \ 0.0038072050061859, \ 0.0038072050061859, \ 0.0038072050061859, \ 0.0038072050061859, \ 0.0038072050061859, \ 0.0009694445790545, \ 0.0009694445790545, \ 0.0009694445790545, \ 0.0009694445790545, \ 0.0009694445790545, \ 0.0009694445790545, \ 0.0042240803334808, \ 0.0042240803334808, \ 0.0042240803334808, \ 0.0042240803334808, \ 0.0042240803334808, \ 0.0042240803334808, \ 0.0066193255529404, \ 0.0066193255529404, \ 0.0066193255529404, \ 0.0066193255529404, \ 0.0066193255529404, \ 0.0066193255529404, \ 0.0010014072888268, \ 0.0010014072888268, \ 0.0010014072888268, \ 0.0010014072888268, \ 0.0010014072888268, \ 0.0010014072888268, \ 0.0075563110745215, \ 0.0075563110745215, \ 0.0075563110745215, \ 0.0075563110745215, \ 0.0075563110745215, \ 0.0075563110745215, \ 0.0052987050439936, \ 0.0052987050439936, \ 0.0052987050439936, \ 0.0052987050439936, \ 0.0052987050439936, \ 0.0052987050439936, \ 0.0055546897961284, \ 0.0055546897961284, \ 0.0055546897961284, \ 0.0055546897961284, \ 0.0055546897961284, \ 0.0055546897961284, \ 0.0045059845609494, \ 0.0045059845609494, \ 0.0045059845609494, \ 0.0045059845609494, \ 0.0045059845609494, \ 0.0045059845609494, \ 0.0031131351389203, \ 0.0031131351389203, \ 0.0031131351389203, \ 0.0031131351389203, \ 0.0031131351389203, \ 0.0031131351389203, \ 0.0043898382162027, \ 0.0043898382162027, \ 0.0043898382162027, \ 0.0043898382162027, \ 0.0043898382162027, \ 0.0043898382162027, \ 0.0032385523720829, \ 0.0032385523720829, \ 0.0032385523720829, \ 0.0032385523720829, \ 0.0032385523720829, \ 0.0032385523720829, \ 0.0065742981116095, \ 0.0065742981116095, \ 0.0065742981116095, \ 0.0065742981116095, \ 0.0065742981116095, \ 0.0065742981116095, \ 0.0080391355993214, \ 0.0080391355993214, \ 0.0080391355993214, \ 0.0004619375803747, \ 0.0004619375803747, \ 0.0004619375803747, \ 0.0004619375803747, \ 0.0004619375803747, \ 0.0004619375803747, \ 0.0056203298622696, \ 0.0056203298622696, \ 0.0056203298622696, \ 0.0056203298622696, \ 0.0056203298622696, \ 0.0056203298622696, \ 0.0072118235949089, \ 0.0072118235949089, \ 0.0072118235949089, \ 0.0001229638851333, \ 0.0001229638851333, \ 0.0001229638851333, \ 0.0080668049674519, \ 0.0080668049674519, \ 0.0080668049674519, \ 0.0046789762284529, \ 0.0046789762284529, \ 0.0046789762284529, \ 0.0012327695569297, \ 0.0012327695569297, \ 0.0012327695569297, \ 0.0012327695569297, \ 0.0012327695569297, \ 0.0012327695569297, \ 0.0027172985719248, \ 0.0027172985719248, \ 0.0027172985719248, \ 0.0062399420305303, \ 0.0062399420305303, \ 0.0062399420305303, \ 0.0087854844528631, \ 0.0004490102381961, \ 0.0004490102381961, \ 0.0004490102381961, \ 0.0004490102381961, \ 0.0004490102381961, \ 0.0004490102381961, \ 0.0038909093796050, \ 0.0038909093796050, \ 0.0038909093796050, \ 0.0056881832653567, \ 0.0056881832653567, \ 0.0056881832653567, \ 0.0056881832653567, \ 0.0056881832653567, \ 0.0056881832653567, \ 0.0030289691062773, \ 0.0030289691062773, \ 0.0030289691062773, \ 0.0012050280622555, \ 0.0012050280622555, \ 0.0012050280622555, \ 0.0067479088961223, \ 0.0067479088961223, \ 0.0067479088961223, \ 0.0067479088961223, \ 0.0067479088961223, \ 0.0067479088961223, \ 0.0072248857349589, \ 0.0072248857349589, \ 0.0072248857349589, \ 0.0051363917261404, \ 0.0051363917261404, \ 0.0051363917261404, \ 0.0060844538754953, \ 0.0060844538754953, \ 0.0060844538754953, \ 0.0002785606250486, \ 0.0002785606250486, \ 0.0002785606250486, \ 0.0002785606250486, \ 0.0002785606250486, \ 0.0002785606250486 ] ) return a, b, c, w def rule41 ( ): #*****************************************************************************80 # ## rule41() returns the rule of precision 41. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.0018100550930815, \ 0.9963798898138365, \ 0.0018100550930819, \ 0.3146077513838778, \ 0.3707844972322443, \ 0.3146077513838778, \ 0.3718324578394357, \ 0.3718324578394359, \ 0.2563350843211283, \ 0.9338478958692606, \ 0.0393793019220240, \ 0.0267728022087153, \ 0.0393793019220239, \ 0.9338478958692605, \ 0.0267728022087157, \ 0.0708749727266859, \ 0.9076576411610010, \ 0.0214673861123131, \ 0.9076576411610010, \ 0.0708749727266859, \ 0.0214673861123128, \ 0.0227676589099524, \ 0.9652472298472927, \ 0.0119851112427549, \ 0.9652472298472928, \ 0.0227676589099525, \ 0.0119851112427545, \ 0.2127026585190979, \ 0.6908861388566330, \ 0.0964112026242691, \ 0.6908861388566331, \ 0.2127026585190979, \ 0.0964112026242688, \ 0.1970799949415202, \ 0.6749417822120469, \ 0.1279782228464328, \ 0.6749417822120470, \ 0.1970799949415203, \ 0.1279782228464326, \ 0.4818489601758344, \ 0.4818489601758343, \ 0.0363020796483312, \ 0.0639130414360007, \ 0.8936878519528431, \ 0.0423991066111563, \ 0.8936878519528432, \ 0.0639130414360007, \ 0.0423991066111560, \ 0.0916254632757577, \ 0.8966875393230677, \ 0.0116869974011748, \ 0.8966875393230677, \ 0.0916254632757578, \ 0.0116869974011745, \ 0.0889175403557380, \ 0.8478409267056788, \ 0.0632415329385833, \ 0.8478409267056788, \ 0.0889175403557381, \ 0.0632415329385829, \ 0.4592305589036990, \ 0.5259284962555215, \ 0.0148409448407795, \ 0.5259284962555214, \ 0.4592305589036990, \ 0.0148409448407795, \ 0.0338843822348439, \ 0.9642755781495430, \ 0.0018400396156133, \ 0.9642755781495431, \ 0.0338843822348439, \ 0.0018400396156128, \ 0.3200752104066154, \ 0.4218676758535129, \ 0.2580571137398716, \ 0.4218676758535129, \ 0.3200752104066154, \ 0.2580571137398715, \ 0.1422819983084207, \ 0.7154360033831583, \ 0.1422819983084210, \ 0.4220684925318889, \ 0.5417122820340925, \ 0.0362192254340186, \ 0.5417122820340925, \ 0.4220684925318889, \ 0.0362192254340186, \ 0.0478764410729284, \ 0.9415795928827051, \ 0.0105439660443666, \ 0.9415795928827051, \ 0.0478764410729285, \ 0.0105439660443662, \ 0.1746336148663416, \ 0.6507327702673166, \ 0.1746336148663419, \ 0.4251980784151399, \ 0.4251980784151399, \ 0.1496038431697200, \ 0.3617990227060762, \ 0.4871740897943582, \ 0.1510268874995655, \ 0.4871740897943583, \ 0.3617990227060763, \ 0.1510268874995655, \ 0.2099773723379177, \ 0.5800452553241643, \ 0.2099773723379179, \ 0.0684569430922210, \ 0.9290609960060465, \ 0.0024820609017325, \ 0.9290609960060466, \ 0.0684569430922210, \ 0.0024820609017321, \ 0.2362884725964560, \ 0.6087537603815811, \ 0.1549577670219628, \ 0.6087537603815811, \ 0.2362884725964560, \ 0.1549577670219627, \ 0.2978954189850496, \ 0.5501430273498515, \ 0.1519615536650988, \ 0.5501430273498515, \ 0.2978954189850496, \ 0.1519615536650987, \ 0.1125572515239218, \ 0.8850652027457061, \ 0.0023775457303723, \ 0.8850652027457061, \ 0.1125572515239218, \ 0.0023775457303719, \ 0.0120658629713076, \ 0.9848848989428542, \ 0.0030492380858384, \ 0.9848848989428541, \ 0.0120658629713077, \ 0.0030492380858379, \ 0.3906530970863169, \ 0.5942714371631589, \ 0.0150754657505243, \ 0.5942714371631588, \ 0.3906530970863170, \ 0.0150754657505242, \ 0.4274107273739702, \ 0.5697047185184613, \ 0.0028845541075684, \ 0.5697047185184614, \ 0.4274107273739702, \ 0.0028845541075684, \ 0.2627399736253427, \ 0.4745200527493144, \ 0.2627399736253428, \ 0.4118455220977197, \ 0.4833893401764346, \ 0.1047651377258456, \ 0.4833893401764346, \ 0.4118455220977197, \ 0.1047651377258456, \ 0.4986036392311143, \ 0.4986036392311143, \ 0.0027927215377713, \ 0.3222211945168437, \ 0.6629470379075842, \ 0.0148317675755723, \ 0.6629470379075841, \ 0.3222211945168438, \ 0.0148317675755720, \ 0.3545249016308813, \ 0.6087299048044915, \ 0.0367451935646271, \ 0.6087299048044915, \ 0.3545249016308814, \ 0.0367451935646270, \ 0.3320276172987797, \ 0.4651394056449660, \ 0.2028329770562542, \ 0.4651394056449660, \ 0.3320276172987797, \ 0.2028329770562542, \ 0.2530297390847723, \ 0.6813809432255311, \ 0.0655893176896967, \ 0.6813809432255310, \ 0.2530297390847723, \ 0.0655893176896965, \ 0.3570399048945097, \ 0.6401266872236777, \ 0.0028334078818126, \ 0.6401266872236777, \ 0.3570399048945097, \ 0.0028334078818124, \ 0.2870606892116554, \ 0.6768867950216703, \ 0.0360525157666745, \ 0.6768867950216702, \ 0.2870606892116554, \ 0.0360525157666742, \ 0.1361313516311361, \ 0.8497124512417364, \ 0.0141561971271276, \ 0.8497124512417363, \ 0.1361313516311361, \ 0.0141561971271272, \ 0.1322241256617750, \ 0.8040030646660921, \ 0.0637728096721329, \ 0.8040030646660922, \ 0.1322241256617751, \ 0.0637728096721326, \ 0.1079242198395523, \ 0.8585223406145746, \ 0.0335534395458731, \ 0.8585223406145744, \ 0.1079242198395524, \ 0.0335534395458729, \ 0.1528869021413866, \ 0.7475340532550706, \ 0.0995790446035428, \ 0.7475340532550706, \ 0.1528869021413866, \ 0.0995790446035426, \ 0.1881017719296066, \ 0.7472490760453540, \ 0.0646491520250393, \ 0.7472490760453540, \ 0.1881017719296067, \ 0.0646491520250392, \ 0.2549824291508879, \ 0.7301188439783041, \ 0.0148987268708080, \ 0.7301188439783041, \ 0.2549824291508879, \ 0.0148987268708078, \ 0.2230780804812777, \ 0.7740674722407084, \ 0.0028544472780139, \ 0.7740674722407084, \ 0.2230780804812778, \ 0.0028544472780137, \ 0.3995665255269703, \ 0.3995665255269703, \ 0.2008669489460594, \ 0.1640507360210325, \ 0.8331184921577857, \ 0.0028307718211819, \ 0.8331184921577858, \ 0.1640507360210327, \ 0.0028307718211816, \ 0.2881511174189886, \ 0.7090129357844225, \ 0.0028359467965890, \ 0.7090129357844225, \ 0.2881511174189885, \ 0.0028359467965888, \ 0.3409577888740615, \ 0.5534095248477606, \ 0.1056326862781778, \ 0.5534095248477606, \ 0.3409577888740616, \ 0.1056326862781778, \ 0.2682934480692839, \ 0.5262976561479694, \ 0.2054088957827467, \ 0.5262976561479694, \ 0.2682934480692839, \ 0.2054088957827466, \ 0.3194090035283247, \ 0.6131123654037490, \ 0.0674786310679263, \ 0.6131123654037490, \ 0.3194090035283247, \ 0.0674786310679262, \ 0.1922954651859523, \ 0.7927714274510961, \ 0.0149331073629516, \ 0.7927714274510962, \ 0.1922954651859524, \ 0.0149331073629514, \ 0.1604140534029236, \ 0.8042006531916337, \ 0.0353852934054428, \ 0.8042006531916338, \ 0.1604140534029238, \ 0.0353852934054425, \ 0.2212534989804217, \ 0.7424945051857205, \ 0.0362519958338579, \ 0.7424945051857206, \ 0.2212534989804218, \ 0.0362519958338575, \ 0.2711942240688135, \ 0.6222060789581492, \ 0.1065996969730373, \ 0.6222060789581491, \ 0.2711942240688137, \ 0.1065996969730372, \ 0.3923234112997704, \ 0.5411068810465550, \ 0.0665697076536745, \ 0.5411068810465550, \ 0.3923234112997703, \ 0.0665697076536745, \ 0.4667610577855150, \ 0.4667610577855150, \ 0.0664778844289700, \ 0.1030954855760305, \ 0.7938090288479388, \ 0.1030954855760309 ] ) b = np.array ( [ \ 0.0018100550930818, \ 0.0018100550930815, \ 0.9963798898138368, \ 0.3146077513838779, \ 0.3146077513838779, \ 0.3707844972322444, \ 0.2563350843211284, \ 0.3718324578394359, \ 0.3718324578394359, \ 0.0267728022087155, \ 0.9338478958692606, \ 0.0393793019220242, \ 0.0267728022087155, \ 0.0393793019220238, \ 0.9338478958692606, \ 0.0214673861123130, \ 0.0708749727266859, \ 0.9076576411610012, \ 0.0214673861123130, \ 0.9076576411610013, \ 0.0708749727266862, \ 0.0119851112427548, \ 0.0227676589099523, \ 0.9652472298472929, \ 0.0119851112427548, \ 0.9652472298472929, \ 0.0227676589099527, \ 0.0964112026242690, \ 0.2127026585190980, \ 0.6908861388566332, \ 0.0964112026242690, \ 0.6908861388566333, \ 0.2127026585190982, \ 0.1279782228464328, \ 0.1970799949415202, \ 0.6749417822120471, \ 0.1279782228464328, \ 0.6749417822120471, \ 0.1970799949415204, \ 0.0363020796483313, \ 0.4818489601758345, \ 0.4818489601758346, \ 0.0423991066111562, \ 0.0639130414360007, \ 0.8936878519528434, \ 0.0423991066111562, \ 0.8936878519528434, \ 0.0639130414360010, \ 0.0116869974011747, \ 0.0916254632757577, \ 0.8966875393230677, \ 0.0116869974011747, \ 0.8966875393230677, \ 0.0916254632757580, \ 0.0632415329385832, \ 0.0889175403557380, \ 0.8478409267056790, \ 0.0632415329385832, \ 0.8478409267056790, \ 0.0889175403557383, \ 0.0148409448407795, \ 0.4592305589036991, \ 0.5259284962555217, \ 0.0148409448407795, \ 0.5259284962555215, \ 0.4592305589036992, \ 0.0018400396156131, \ 0.0338843822348439, \ 0.9642755781495430, \ 0.0018400396156131, \ 0.9642755781495433, \ 0.0338843822348442, \ 0.2580571137398717, \ 0.3200752104066155, \ 0.4218676758535131, \ 0.2580571137398717, \ 0.4218676758535130, \ 0.3200752104066156, \ 0.1422819983084210, \ 0.1422819983084208, \ 0.7154360033831585, \ 0.0362192254340186, \ 0.4220684925318890, \ 0.5417122820340926, \ 0.0362192254340186, \ 0.5417122820340925, \ 0.4220684925318892, \ 0.0105439660443664, \ 0.0478764410729283, \ 0.9415795928827053, \ 0.0105439660443664, \ 0.9415795928827053, \ 0.0478764410729287, \ 0.1746336148663418, \ 0.1746336148663417, \ 0.6507327702673166, \ 0.1496038431697201, \ 0.4251980784151401, \ 0.4251980784151402, \ 0.1510268874995656, \ 0.3617990227060763, \ 0.4871740897943584, \ 0.1510268874995656, \ 0.4871740897943583, \ 0.3617990227060764, \ 0.2099773723379179, \ 0.2099773723379178, \ 0.5800452553241644, \ 0.0024820609017324, \ 0.0684569430922209, \ 0.9290609960060469, \ 0.0024820609017324, \ 0.9290609960060469, \ 0.0684569430922213, \ 0.1549577670219629, \ 0.2362884725964561, \ 0.6087537603815814, \ 0.1549577670219629, \ 0.6087537603815814, \ 0.2362884725964562, \ 0.1519615536650989, \ 0.2978954189850497, \ 0.5501430273498518, \ 0.1519615536650989, \ 0.5501430273498517, \ 0.2978954189850498, \ 0.0023775457303722, \ 0.1125572515239218, \ 0.8850652027457062, \ 0.0023775457303722, \ 0.8850652027457062, \ 0.1125572515239221, \ 0.0030492380858382, \ 0.0120658629713075, \ 0.9848848989428544, \ 0.0030492380858382, \ 0.9848848989428544, \ 0.0120658629713080, \ 0.0150754657505243, \ 0.3906530970863170, \ 0.5942714371631590, \ 0.0150754657505243, \ 0.5942714371631588, \ 0.3906530970863172, \ 0.0028845541075685, \ 0.4274107273739702, \ 0.5697047185184615, \ 0.0028845541075685, \ 0.5697047185184614, \ 0.4274107273739705, \ 0.2627399736253429, \ 0.2627399736253428, \ 0.4745200527493146, \ 0.1047651377258457, \ 0.4118455220977198, \ 0.4833893401764348, \ 0.1047651377258457, \ 0.4833893401764347, \ 0.4118455220977200, \ 0.0027927215377714, \ 0.4986036392311144, \ 0.4986036392311146, \ 0.0148317675755722, \ 0.3222211945168437, \ 0.6629470379075844, \ 0.0148317675755722, \ 0.6629470379075841, \ 0.3222211945168439, \ 0.0367451935646272, \ 0.3545249016308813, \ 0.6087299048044917, \ 0.0367451935646272, \ 0.6087299048044916, \ 0.3545249016308816, \ 0.2028329770562543, \ 0.3320276172987798, \ 0.4651394056449663, \ 0.2028329770562543, \ 0.4651394056449661, \ 0.3320276172987799, \ 0.0655893176896967, \ 0.2530297390847723, \ 0.6813809432255312, \ 0.0655893176896967, \ 0.6813809432255311, \ 0.2530297390847726, \ 0.0028334078818125, \ 0.3570399048945098, \ 0.6401266872236778, \ 0.0028334078818125, \ 0.6401266872236778, \ 0.3570399048945100, \ 0.0360525157666744, \ 0.2870606892116554, \ 0.6768867950216704, \ 0.0360525157666744, \ 0.6768867950216704, \ 0.2870606892116557, \ 0.0141561971271275, \ 0.1361313516311361, \ 0.8497124512417367, \ 0.0141561971271275, \ 0.8497124512417367, \ 0.1361313516311364, \ 0.0637728096721328, \ 0.1322241256617750, \ 0.8040030646660923, \ 0.0637728096721328, \ 0.8040030646660923, \ 0.1322241256617753, \ 0.0335534395458731, \ 0.1079242198395524, \ 0.8585223406145748, \ 0.0335534395458731, \ 0.8585223406145748, \ 0.1079242198395527, \ 0.0995790446035428, \ 0.1528869021413866, \ 0.7475340532550708, \ 0.0995790446035428, \ 0.7475340532550708, \ 0.1528869021413868, \ 0.0646491520250394, \ 0.1881017719296067, \ 0.7472490760453542, \ 0.0646491520250394, \ 0.7472490760453542, \ 0.1881017719296069, \ 0.0148987268708080, \ 0.2549824291508879, \ 0.7301188439783043, \ 0.0148987268708080, \ 0.7301188439783043, \ 0.2549824291508882, \ 0.0028544472780139, \ 0.2230780804812777, \ 0.7740674722407086, \ 0.0028544472780139, \ 0.7740674722407086, \ 0.2230780804812780, \ 0.2008669489460595, \ 0.3995665255269704, \ 0.3995665255269705, \ 0.0028307718211818, \ 0.1640507360210326, \ 0.8331184921577858, \ 0.0028307718211818, \ 0.8331184921577858, \ 0.1640507360210328, \ 0.0028359467965890, \ 0.2881511174189886, \ 0.7090129357844227, \ 0.0028359467965890, \ 0.7090129357844227, \ 0.2881511174189888, \ 0.1056326862781779, \ 0.3409577888740616, \ 0.5534095248477607, \ 0.1056326862781779, \ 0.5534095248477606, \ 0.3409577888740618, \ 0.2054088957827467, \ 0.2682934480692840, \ 0.5262976561479695, \ 0.2054088957827467, \ 0.5262976561479695, \ 0.2682934480692841, \ 0.0674786310679263, \ 0.3194090035283247, \ 0.6131123654037492, \ 0.0674786310679263, \ 0.6131123654037491, \ 0.3194090035283249, \ 0.0149331073629516, \ 0.1922954651859523, \ 0.7927714274510964, \ 0.0149331073629516, \ 0.7927714274510963, \ 0.1922954651859526, \ 0.0353852934054427, \ 0.1604140534029236, \ 0.8042006531916338, \ 0.0353852934054427, \ 0.8042006531916338, \ 0.1604140534029239, \ 0.0362519958338577, \ 0.2212534989804218, \ 0.7424945051857206, \ 0.0362519958338577, \ 0.7424945051857206, \ 0.2212534989804221, \ 0.1065996969730374, \ 0.2711942240688135, \ 0.6222060789581494, \ 0.1065996969730374, \ 0.6222060789581492, \ 0.2711942240688138, \ 0.0665697076536746, \ 0.3923234112997704, \ 0.5411068810465552, \ 0.0665697076536746, \ 0.5411068810465551, \ 0.3923234112997706, \ 0.0664778844289701, \ 0.4667610577855150, \ 0.4667610577855152, \ 0.1030954855760308, \ 0.1030954855760305, \ 0.7938090288479389 ] ) c = np.array ( [ \ 0.9963798898138366, \ 0.0018100550930820, \ 0.0018100550930812, \ 0.3707844972322443, \ 0.3146077513838778, \ 0.3146077513838778, \ 0.3718324578394358, \ 0.2563350843211282, \ 0.3718324578394358, \ 0.0393793019220238, \ 0.0267728022087154, \ 0.9338478958692605, \ 0.9338478958692605, \ 0.0267728022087156, \ 0.0393793019220237, \ 0.9076576411610010, \ 0.0214673861123131, \ 0.0708749727266856, \ 0.0708749727266860, \ 0.0214673861123128, \ 0.9076576411610010, \ 0.9652472298472928, \ 0.0119851112427549, \ 0.0227676589099521, \ 0.0227676589099524, \ 0.0119851112427546, \ 0.9652472298472928, \ 0.6908861388566330, \ 0.0964112026242691, \ 0.2127026585190978, \ 0.2127026585190979, \ 0.0964112026242688, \ 0.6908861388566330, \ 0.6749417822120470, \ 0.1279782228464328, \ 0.1970799949415201, \ 0.1970799949415202, \ 0.1279782228464326, \ 0.6749417822120470, \ 0.4818489601758343, \ 0.0363020796483312, \ 0.4818489601758342, \ 0.8936878519528431, \ 0.0423991066111563, \ 0.0639130414360004, \ 0.0639130414360007, \ 0.0423991066111559, \ 0.8936878519528431, \ 0.8966875393230676, \ 0.0116869974011747, \ 0.0916254632757575, \ 0.0916254632757577, \ 0.0116869974011745, \ 0.8966875393230674, \ 0.8478409267056789, \ 0.0632415329385832, \ 0.0889175403557377, \ 0.0889175403557380, \ 0.0632415329385829, \ 0.8478409267056788, \ 0.5259284962555214, \ 0.0148409448407794, \ 0.4592305589036988, \ 0.4592305589036991, \ 0.0148409448407795, \ 0.5259284962555213, \ 0.9642755781495431, \ 0.0018400396156131, \ 0.0338843822348437, \ 0.0338843822348438, \ 0.0018400396156127, \ 0.9642755781495430, \ 0.4218676758535130, \ 0.2580571137398716, \ 0.3200752104066153, \ 0.3200752104066154, \ 0.2580571137398716, \ 0.4218676758535129, \ 0.7154360033831584, \ 0.1422819983084209, \ 0.1422819983084206, \ 0.5417122820340924, \ 0.0362192254340185, \ 0.4220684925318888, \ 0.4220684925318889, \ 0.0362192254340186, \ 0.5417122820340923, \ 0.9415795928827051, \ 0.0105439660443666, \ 0.0478764410729281, \ 0.0478764410729285, \ 0.0105439660443661, \ 0.9415795928827052, \ 0.6507327702673167, \ 0.1746336148663418, \ 0.1746336148663415, \ 0.4251980784151400, \ 0.1496038431697200, \ 0.4251980784151398, \ 0.4871740897943582, \ 0.1510268874995655, \ 0.3617990227060761, \ 0.3617990227060762, \ 0.1510268874995654, \ 0.4871740897943581, \ 0.5800452553241644, \ 0.2099773723379179, \ 0.2099773723379177, \ 0.9290609960060467, \ 0.0024820609017325, \ 0.0684569430922207, \ 0.0684569430922210, \ 0.0024820609017321, \ 0.9290609960060465, \ 0.6087537603815811, \ 0.1549577670219628, \ 0.2362884725964558, \ 0.2362884725964560, \ 0.1549577670219626, \ 0.6087537603815811, \ 0.5501430273498515, \ 0.1519615536650988, \ 0.2978954189850495, \ 0.2978954189850496, \ 0.1519615536650988, \ 0.5501430273498515, \ 0.8850652027457060, \ 0.0023775457303721, \ 0.1125572515239215, \ 0.1125572515239217, \ 0.0023775457303720, \ 0.8850652027457059, \ 0.9848848989428542, \ 0.0030492380858382, \ 0.0120658629713072, \ 0.0120658629713077, \ 0.0030492380858379, \ 0.9848848989428541, \ 0.5942714371631588, \ 0.0150754657505242, \ 0.3906530970863167, \ 0.3906530970863169, \ 0.0150754657505242, \ 0.5942714371631587, \ 0.5697047185184613, \ 0.0028845541075685, \ 0.4274107273739701, \ 0.4274107273739701, \ 0.0028845541075684, \ 0.5697047185184612, \ 0.4745200527493144, \ 0.2627399736253428, \ 0.2627399736253426, \ 0.4833893401764346, \ 0.1047651377258456, \ 0.4118455220977196, \ 0.4118455220977197, \ 0.1047651377258456, \ 0.4833893401764344, \ 0.4986036392311142, \ 0.0027927215377713, \ 0.4986036392311141, \ 0.6629470379075842, \ 0.0148317675755721, \ 0.3222211945168434, \ 0.3222211945168437, \ 0.0148317675755720, \ 0.6629470379075840, \ 0.6087299048044915, \ 0.0367451935646272, \ 0.3545249016308811, \ 0.3545249016308814, \ 0.0367451935646270, \ 0.6087299048044914, \ 0.4651394056449660, \ 0.2028329770562542, \ 0.3320276172987795, \ 0.3320276172987797, \ 0.2028329770562542, \ 0.4651394056449660, \ 0.6813809432255311, \ 0.0655893176896966, \ 0.2530297390847721, \ 0.2530297390847723, \ 0.0655893176896966, \ 0.6813809432255310, \ 0.6401266872236778, \ 0.0028334078818125, \ 0.3570399048945095, \ 0.3570399048945098, \ 0.0028334078818125, \ 0.6401266872236776, \ 0.6768867950216702, \ 0.0360525157666743, \ 0.2870606892116552, \ 0.2870606892116555, \ 0.0360525157666742, \ 0.6768867950216702, \ 0.8497124512417364, \ 0.0141561971271275, \ 0.1361313516311358, \ 0.1361313516311362, \ 0.0141561971271272, \ 0.8497124512417363, \ 0.8040030646660922, \ 0.0637728096721329, \ 0.1322241256617749, \ 0.1322241256617750, \ 0.0637728096721326, \ 0.8040030646660921, \ 0.8585223406145746, \ 0.0335534395458731, \ 0.1079242198395520, \ 0.1079242198395524, \ 0.0335534395458729, \ 0.8585223406145744, \ 0.7475340532550706, \ 0.0995790446035428, \ 0.1528869021413863, \ 0.1528869021413866, \ 0.0995790446035426, \ 0.7475340532550705, \ 0.7472490760453540, \ 0.0646491520250394, \ 0.1881017719296064, \ 0.1881017719296067, \ 0.0646491520250391, \ 0.7472490760453538, \ 0.7301188439783041, \ 0.0148987268708080, \ 0.2549824291508876, \ 0.2549824291508879, \ 0.0148987268708077, \ 0.7301188439783040, \ 0.7740674722407084, \ 0.0028544472780139, \ 0.2230780804812775, \ 0.2230780804812778, \ 0.0028544472780136, \ 0.7740674722407084, \ 0.3995665255269703, \ 0.2008669489460594, \ 0.3995665255269701, \ 0.8331184921577857, \ 0.0028307718211818, \ 0.1640507360210324, \ 0.1640507360210325, \ 0.0028307718211816, \ 0.8331184921577856, \ 0.7090129357844225, \ 0.0028359467965889, \ 0.2881511174189882, \ 0.2881511174189886, \ 0.0028359467965887, \ 0.7090129357844224, \ 0.5534095248477605, \ 0.1056326862781777, \ 0.3409577888740615, \ 0.3409577888740615, \ 0.1056326862781778, \ 0.5534095248477604, \ 0.5262976561479693, \ 0.2054088957827466, \ 0.2682934480692838, \ 0.2682934480692838, \ 0.2054088957827466, \ 0.5262976561479693, \ 0.6131123654037490, \ 0.0674786310679262, \ 0.3194090035283245, \ 0.3194090035283246, \ 0.0674786310679262, \ 0.6131123654037488, \ 0.7927714274510961, \ 0.0149331073629516, \ 0.1922954651859521, \ 0.1922954651859523, \ 0.0149331073629514, \ 0.7927714274510961, \ 0.8042006531916337, \ 0.0353852934054427, \ 0.1604140534029234, \ 0.1604140534029235, \ 0.0353852934054425, \ 0.8042006531916336, \ 0.7424945051857205, \ 0.0362519958338578, \ 0.2212534989804216, \ 0.2212534989804217, \ 0.0362519958338576, \ 0.7424945051857204, \ 0.6222060789581491, \ 0.1065996969730373, \ 0.2711942240688133, \ 0.2711942240688135, \ 0.1065996969730372, \ 0.6222060789581491, \ 0.5411068810465549, \ 0.0665697076536745, \ 0.3923234112997702, \ 0.3923234112997703, \ 0.0665697076536745, \ 0.5411068810465549, \ 0.4667610577855149, \ 0.0664778844289700, \ 0.4667610577855147, \ 0.7938090288479388, \ 0.1030954855760307, \ 0.1030954855760302 ] ) w = np.array ( [ \ 0.0000522093231255, \ 0.0000522093231255, \ 0.0000522093231255, \ 0.0064432696708827, \ 0.0064432696708827, \ 0.0064432696708827, \ 0.0056462037725046, \ 0.0056462037725046, \ 0.0056462037725046, \ 0.0009466339964529, \ 0.0009466339964529, \ 0.0009466339964529, \ 0.0009466339964529, \ 0.0009466339964529, \ 0.0009466339964529, \ 0.0010778383293871, \ 0.0010778383293871, \ 0.0010778383293871, \ 0.0010778383293871, \ 0.0010778383293871, \ 0.0010778383293871, \ 0.0005535514063046, \ 0.0005535514063046, \ 0.0005535514063046, \ 0.0005535514063046, \ 0.0005535514063046, \ 0.0005535514063046, \ 0.0037447209152800, \ 0.0037447209152800, \ 0.0037447209152800, \ 0.0037447209152800, \ 0.0037447209152800, \ 0.0037447209152800, \ 0.0040737392096224, \ 0.0040737392096224, \ 0.0040737392096224, \ 0.0040737392096224, \ 0.0040737392096224, \ 0.0040737392096224, \ 0.0029751068247424, \ 0.0029751068247424, \ 0.0029751068247424, \ 0.0017887545706646, \ 0.0017887545706646, \ 0.0017887545706646, \ 0.0017887545706646, \ 0.0017887545706646, \ 0.0017887545706646, \ 0.0010314247381435, \ 0.0010314247381435, \ 0.0010314247381435, \ 0.0010314247381435, \ 0.0010314247381435, \ 0.0010314247381435, \ 0.0025322072683271, \ 0.0025322072683271, \ 0.0025322072683271, \ 0.0025322072683271, \ 0.0025322072683271, \ 0.0025322072683271, \ 0.0022524785579246, \ 0.0022524785579246, \ 0.0022524785579246, \ 0.0022524785579246, \ 0.0022524785579246, \ 0.0022524785579246, \ 0.0002818375084659, \ 0.0002818375084659, \ 0.0002818375084659, \ 0.0002818375084659, \ 0.0002818375084659, \ 0.0002818375084659, \ 0.0061093730696482, \ 0.0061093730696482, \ 0.0061093730696482, \ 0.0061093730696482, \ 0.0061093730696482, \ 0.0061093730696482, \ 0.0042449557771112, \ 0.0042449557771112, \ 0.0042449557771112, \ 0.0033089712153024, \ 0.0033089712153024, \ 0.0033089712153024, \ 0.0033089712153024, \ 0.0033089712153024, \ 0.0033089712153024, \ 0.0007503403741006, \ 0.0007503403741006, \ 0.0007503403741006, \ 0.0007503403741006, \ 0.0007503403741006, \ 0.0007503403741006, \ 0.0050362517089764, \ 0.0050362517089764, \ 0.0050362517089764, \ 0.0060101004771622, \ 0.0060101004771622, \ 0.0060101004771622, \ 0.0062236592332096, \ 0.0062236592332096, \ 0.0062236592332096, \ 0.0062236592332096, \ 0.0062236592332096, \ 0.0062236592332096, \ 0.0060772289969774, \ 0.0060772289969774, \ 0.0060772289969774, \ 0.0004904208710143, \ 0.0004904208710143, \ 0.0004904208710143, \ 0.0004904208710143, \ 0.0004904208710143, \ 0.0004904208710143, \ 0.0058906442657042, \ 0.0058906442657042, \ 0.0058906442657042, \ 0.0058906442657042, \ 0.0058906442657042, \ 0.0058906442657042, \ 0.0062381201191140, \ 0.0062381201191140, \ 0.0062381201191140, \ 0.0062381201191140, \ 0.0062381201191140, \ 0.0062381201191140, \ 0.0005889181881281, \ 0.0005889181881281, \ 0.0005889181881281, \ 0.0005889181881281, \ 0.0005889181881281, \ 0.0005889181881281, \ 0.0002390515618048, \ 0.0002390515618048, \ 0.0002390515618048, \ 0.0002390515618048, \ 0.0002390515618048, \ 0.0002390515618048, \ 0.0023381337598691, \ 0.0023381337598691, \ 0.0023381337598691, \ 0.0023381337598691, \ 0.0023381337598691, \ 0.0023381337598691, \ 0.0010454329707756, \ 0.0010454329707756, \ 0.0010454329707756, \ 0.0010454329707756, \ 0.0010454329707756, \ 0.0010454329707756, \ 0.0067671402084225, \ 0.0067671402084225, \ 0.0067671402084225, \ 0.0059901891203096, \ 0.0059901891203096, \ 0.0059901891203096, \ 0.0059901891203096, \ 0.0059901891203096, \ 0.0059901891203096, \ 0.0010236399703004, \ 0.0010236399703004, \ 0.0010236399703004, \ 0.0022882495872613, \ 0.0022882495872613, \ 0.0022882495872613, \ 0.0022882495872613, \ 0.0022882495872613, \ 0.0022882495872613, \ 0.0036104870565558, \ 0.0036104870565558, \ 0.0036104870565558, \ 0.0036104870565558, \ 0.0036104870565558, \ 0.0036104870565558, \ 0.0070586578085502, \ 0.0070586578085502, \ 0.0070586578085502, \ 0.0070586578085502, \ 0.0070586578085502, \ 0.0070586578085502, \ 0.0043785525737028, \ 0.0043785525737028, \ 0.0043785525737028, \ 0.0043785525737028, \ 0.0043785525737028, \ 0.0043785525737028, \ 0.0010171383589503, \ 0.0010171383589503, \ 0.0010171383589503, \ 0.0010171383589503, \ 0.0010171383589503, \ 0.0010171383589503, \ 0.0034554845247205, \ 0.0034554845247205, \ 0.0034554845247205, \ 0.0034554845247205, \ 0.0034554845247205, \ 0.0034554845247205, \ 0.0016626192415772, \ 0.0016626192415772, \ 0.0016626192415772, \ 0.0016626192415772, \ 0.0016626192415772, \ 0.0016626192415772, \ 0.0033511706532687, \ 0.0033511706532687, \ 0.0033511706532687, \ 0.0033511706532687, \ 0.0033511706532687, \ 0.0033511706532687, \ 0.0023865646505329, \ 0.0023865646505329, \ 0.0023865646505329, \ 0.0023865646505329, \ 0.0023865646505329, \ 0.0023865646505329, \ 0.0041753789931688, \ 0.0041753789931688, \ 0.0041753789931688, \ 0.0041753789931688, \ 0.0041753789931688, \ 0.0041753789931688, \ 0.0038711214885426, \ 0.0038711214885426, \ 0.0038711214885426, \ 0.0038711214885426, \ 0.0038711214885426, \ 0.0038711214885426, \ 0.0021923391960439, \ 0.0021923391960439, \ 0.0021923391960439, \ 0.0021923391960439, \ 0.0021923391960439, \ 0.0021923391960439, \ 0.0009127323365215, \ 0.0009127323365215, \ 0.0009127323365215, \ 0.0009127323365215, \ 0.0009127323365215, \ 0.0009127323365215, \ 0.0072301097329517, \ 0.0072301097329517, \ 0.0072301097329517, \ 0.0008028346526154, \ 0.0008028346526154, \ 0.0008028346526154, \ 0.0008028346526154, \ 0.0008028346526154, \ 0.0008028346526154, \ 0.0009793596015786, \ 0.0009793596015786, \ 0.0009793596015786, \ 0.0009793596015786, \ 0.0009793596015786, \ 0.0009793596015786, \ 0.0059550867608881, \ 0.0059550867608881, \ 0.0059550867608881, \ 0.0059550867608881, \ 0.0059550867608881, \ 0.0059550867608881, \ 0.0067525153387175, \ 0.0067525153387175, \ 0.0067525153387175, \ 0.0067525153387175, \ 0.0067525153387175, \ 0.0067525153387175, \ 0.0049326746082459, \ 0.0049326746082459, \ 0.0049326746082459, \ 0.0049326746082459, \ 0.0049326746082459, \ 0.0049326746082459, \ 0.0019995171236440, \ 0.0019995171236440, \ 0.0019995171236440, \ 0.0019995171236440, \ 0.0019995171236440, \ 0.0019995171236440, \ 0.0028581698928275, \ 0.0028581698928275, \ 0.0028581698928275, \ 0.0028581698928275, \ 0.0028581698928275, \ 0.0028581698928275, \ 0.0032573829494494, \ 0.0032573829494494, \ 0.0032573829494494, \ 0.0032573829494494, \ 0.0032573829494494, \ 0.0032573829494494, \ 0.0058722816583725, \ 0.0058722816583725, \ 0.0058722816583725, \ 0.0058722816583725, \ 0.0058722816583725, \ 0.0058722816583725, \ 0.0050950784475005, \ 0.0050950784475005, \ 0.0050950784475005, \ 0.0050950784475005, \ 0.0050950784475005, \ 0.0050950784475005, \ 0.0051338703252384, \ 0.0051338703252384, \ 0.0051338703252384, \ 0.0039695690393596, \ 0.0039695690393596, \ 0.0039695690393596 ] ) return a, b, c, w def rule42 ( ): #*****************************************************************************80 # ## rule42() returns the rule of precision 42. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4023719251097932, \ 0.4023719251097932, \ 0.1952561497804134, \ 0.0013653925759540, \ 0.9972692148480916, \ 0.0013653925759544, \ 0.3305538536843531, \ 0.6678757207141839, \ 0.0015704256014629, \ 0.6678757207141840, \ 0.3305538536843532, \ 0.0015704256014628, \ 0.4975317296252054, \ 0.4975317296252054, \ 0.0049365407495892, \ 0.9699539651466832, \ 0.0204313657326067, \ 0.0096146691207099, \ 0.0204313657326067, \ 0.9699539651466832, \ 0.0096146691207102, \ 0.0571983061939757, \ 0.9208981351903950, \ 0.0219035586156294, \ 0.9208981351903950, \ 0.0571983061939758, \ 0.0219035586156291, \ 0.4799002957544191, \ 0.4799002957544192, \ 0.0401994084911617, \ 0.0664663290557836, \ 0.8670673418884325, \ 0.0664663290557839, \ 0.4532709716379456, \ 0.5452354770717635, \ 0.0014935512902909, \ 0.5452354770717635, \ 0.4532709716379456, \ 0.0014935512902909, \ 0.1407324739067203, \ 0.8038260264189151, \ 0.0554414996743646, \ 0.8038260264189151, \ 0.1407324739067203, \ 0.0554414996743643, \ 0.1837886303019410, \ 0.6975178002766640, \ 0.1186935694213951, \ 0.6975178002766639, \ 0.1837886303019411, \ 0.1186935694213948, \ 0.0432363893877460, \ 0.9135272212245076, \ 0.0432363893877464, \ 0.0321121524868778, \ 0.9664947902959359, \ 0.0013930572171864, \ 0.9664947902959361, \ 0.0321121524868780, \ 0.0013930572171859, \ 0.4903050142016467, \ 0.4903050142016467, \ 0.0193899715967066, \ 0.0429640722006761, \ 0.9467364526174824, \ 0.0102994751818416, \ 0.9467364526174824, \ 0.0429640722006762, \ 0.0102994751818411, \ 0.0105248427300749, \ 0.9868904472776370, \ 0.0025847099922883, \ 0.9868904472776370, \ 0.0105248427300750, \ 0.0025847099922879, \ 0.0753790285629703, \ 0.8851466587208721, \ 0.0394743127161577, \ 0.8851466587208721, \ 0.0753790285629704, \ 0.0394743127161574, \ 0.4363333620899560, \ 0.5513727993854914, \ 0.0122938385245525, \ 0.5513727993854914, \ 0.4363333620899560, \ 0.0122938385245524, \ 0.2704907465149770, \ 0.7269194442371774, \ 0.0025898092478457, \ 0.7269194442371772, \ 0.2704907465149770, \ 0.0025898092478455, \ 0.3508136433810974, \ 0.6116299677466058, \ 0.0375563888722968, \ 0.6116299677466057, \ 0.3508136433810974, \ 0.0375563888722968, \ 0.3727655119742921, \ 0.6101399413050006, \ 0.0170945467207073, \ 0.6101399413050006, \ 0.3727655119742921, \ 0.0170945467207072, \ 0.2171073522633415, \ 0.6971343314423426, \ 0.0857583162943159, \ 0.6971343314423426, \ 0.2171073522633415, \ 0.0857583162943157, \ 0.1927563650090058, \ 0.7492579900268798, \ 0.0579856449641145, \ 0.7492579900268798, \ 0.1927563650090059, \ 0.0579856449641142, \ 0.4206850306864163, \ 0.5454667964305935, \ 0.0338481728829903, \ 0.5454667964305935, \ 0.4206850306864162, \ 0.0338481728829902, \ 0.0269988226283730, \ 0.9460023547432537, \ 0.0269988226283734, \ 0.2124851854370911, \ 0.7849881231777003, \ 0.0025266913852087, \ 0.7849881231777003, \ 0.2124851854370911, \ 0.0025266913852085, \ 0.3192572087291873, \ 0.6700862491552849, \ 0.0106565421155276, \ 0.6700862491552850, \ 0.3192572087291874, \ 0.0106565421155275, \ 0.1385048069103228, \ 0.7229903861793542, \ 0.1385048069103231, \ 0.4670132073557640, \ 0.4670132073557640, \ 0.0659735852884720, \ 0.2516382355125726, \ 0.7349320912451689, \ 0.0134296732422586, \ 0.7349320912451689, \ 0.2516382355125727, \ 0.0134296732422583, \ 0.1522119814568094, \ 0.7594462402499256, \ 0.0883417782932651, \ 0.7594462402499256, \ 0.1522119814568094, \ 0.0883417782932648, \ 0.1111420947940333, \ 0.8559357869948059, \ 0.0329221182111609, \ 0.8559357869948060, \ 0.1111420947940334, \ 0.0329221182111606, \ 0.3581500588512503, \ 0.4470491803714221, \ 0.1948007607773276, \ 0.4470491803714221, \ 0.3581500588512503, \ 0.1948007607773276, \ 0.1637998569561501, \ 0.8047391270819582, \ 0.0314610159618919, \ 0.8047391270819582, \ 0.1637998569561501, \ 0.0314610159618916, \ 0.1021127733366743, \ 0.8305189164987998, \ 0.0673683101645260, \ 0.8305189164987997, \ 0.1021127733366744, \ 0.0673683101645256, \ 0.2335557030193516, \ 0.5798790527806756, \ 0.1865652441999727, \ 0.5798790527806756, \ 0.2335557030193516, \ 0.1865652441999726, \ 0.3214164628317113, \ 0.6147000537558933, \ 0.0638834834123954, \ 0.6147000537558933, \ 0.3214164628317114, \ 0.0638834834123952, \ 0.2233361848957126, \ 0.7440925933093376, \ 0.0325712217949499, \ 0.7440925933093376, \ 0.2233361848957126, \ 0.0325712217949497, \ 0.1905881189463203, \ 0.7961383982975219, \ 0.0132734827561579, \ 0.7961383982975220, \ 0.1905881189463203, \ 0.0132734827561576, \ 0.2273558402454795, \ 0.6364103842453923, \ 0.1362337755091281, \ 0.6364103842453924, \ 0.2273558402454797, \ 0.1362337755091279, \ 0.1065804258588588, \ 0.7868391482822822, \ 0.1065804258588591, \ 0.1567679227871600, \ 0.8406166996789507, \ 0.0026153775338892, \ 0.8406166996789507, \ 0.1567679227871602, \ 0.0026153775338890, \ 0.1340333349867785, \ 0.8524854538080647, \ 0.0134812112051569, \ 0.8524854538080647, \ 0.1340333349867785, \ 0.0134812112051566, \ 0.2957211757454536, \ 0.5123947199023402, \ 0.1918841043522062, \ 0.5123947199023402, \ 0.2957211757454536, \ 0.1918841043522061, \ 0.1067192718130004, \ 0.8907334465548298, \ 0.0025472816321699, \ 0.8907334465548298, \ 0.1067192718130003, \ 0.0025472816321696, \ 0.4125664194839165, \ 0.4863962861603238, \ 0.1010372943557596, \ 0.4863962861603238, \ 0.4125664194839165, \ 0.1010372943557596, \ 0.3078519829928861, \ 0.4423972758418252, \ 0.2497507411652887, \ 0.4423972758418251, \ 0.3078519829928861, \ 0.2497507411652886, \ 0.0870205486996966, \ 0.8992668260117453, \ 0.0137126252885581, \ 0.8992668260117453, \ 0.0870205486996967, \ 0.0137126252885578, \ 0.3894283316812197, \ 0.6072270728853777, \ 0.0033445954334026, \ 0.6072270728853777, \ 0.3894283316812197, \ 0.0033445954334026, \ 0.3117353910725873, \ 0.3765292178548252, \ 0.3117353910725873, \ 0.2612939703141770, \ 0.6830313992552178, \ 0.0556746304306052, \ 0.6830313992552177, \ 0.2612939703141770, \ 0.0556746304306051, \ 0.0649755331098119, \ 0.9322207082966478, \ 0.0028037585935404, \ 0.9322207082966478, \ 0.0649755331098119, \ 0.0028037585935401, \ 0.2719500060981310, \ 0.6316994938246291, \ 0.0963505000772399, \ 0.6316994938246292, \ 0.2719500060981311, \ 0.0963505000772396, \ 0.2930903642725462, \ 0.6777105291270178, \ 0.0291991066004360, \ 0.6777105291270178, \ 0.2930903642725463, \ 0.0291991066004358, \ 0.3946648265878192, \ 0.5417606227500117, \ 0.0635745506621692, \ 0.5417606227500116, \ 0.3946648265878193, \ 0.0635745506621691, \ 0.3568522181929828, \ 0.4992192017414733, \ 0.1439285800655438, \ 0.4992192017414734, \ 0.3568522181929829, \ 0.1439285800655437, \ 0.2448605758688817, \ 0.5102788482622364, \ 0.2448605758688818, \ 0.3413613516388763, \ 0.5594299486078240, \ 0.0992086997532998, \ 0.5594299486078240, \ 0.3413613516388763, \ 0.0992086997532997, \ 0.2895129410795146, \ 0.5700981374990226, \ 0.1403889214214628, \ 0.5700981374990226, \ 0.2895129410795146, \ 0.1403889214214627, \ 0.1748351458111906, \ 0.6503297083776184, \ 0.1748351458111909, \ 0.4275693341501904, \ 0.4275693341501904, \ 0.1448613316996191, \ 0.3742701566784477, \ 0.3742701566784477, \ 0.2514596866431046 ] ) b = np.array ( [ \ 0.1952561497804135, \ 0.4023719251097934, \ 0.4023719251097935, \ 0.0013653925759543, \ 0.0013653925759540, \ 0.9972692148480918, \ 0.0015704256014629, \ 0.3305538536843532, \ 0.6678757207141842, \ 0.0015704256014629, \ 0.6678757207141840, \ 0.3305538536843535, \ 0.0049365407495893, \ 0.4975317296252054, \ 0.4975317296252056, \ 0.0096146691207101, \ 0.9699539651466834, \ 0.0204313657326070, \ 0.0096146691207101, \ 0.0204313657326066, \ 0.9699539651466834, \ 0.0219035586156294, \ 0.0571983061939757, \ 0.9208981351903952, \ 0.0219035586156294, \ 0.9208981351903952, \ 0.0571983061939760, \ 0.0401994084911617, \ 0.4799002957544192, \ 0.4799002957544193, \ 0.0664663290557839, \ 0.0664663290557836, \ 0.8670673418884327, \ 0.0014935512902910, \ 0.4532709716379457, \ 0.5452354770717637, \ 0.0014935512902910, \ 0.5452354770717636, \ 0.4532709716379458, \ 0.0554414996743645, \ 0.1407324739067203, \ 0.8038260264189153, \ 0.0554414996743645, \ 0.8038260264189153, \ 0.1407324739067206, \ 0.1186935694213950, \ 0.1837886303019410, \ 0.6975178002766641, \ 0.1186935694213950, \ 0.6975178002766641, \ 0.1837886303019413, \ 0.0432363893877463, \ 0.0432363893877460, \ 0.9135272212245078, \ 0.0013930572171862, \ 0.0321121524868778, \ 0.9664947902959360, \ 0.0013930572171862, \ 0.9664947902959360, \ 0.0321121524868782, \ 0.0193899715967067, \ 0.4903050142016467, \ 0.4903050142016469, \ 0.0102994751818414, \ 0.0429640722006761, \ 0.9467364526174826, \ 0.0102994751818414, \ 0.9467364526174826, \ 0.0429640722006765, \ 0.0025847099922882, \ 0.0105248427300749, \ 0.9868904472776371, \ 0.0025847099922882, \ 0.9868904472776371, \ 0.0105248427300752, \ 0.0394743127161577, \ 0.0753790285629703, \ 0.8851466587208722, \ 0.0394743127161577, \ 0.8851466587208722, \ 0.0753790285629706, \ 0.0122938385245525, \ 0.4363333620899560, \ 0.5513727993854917, \ 0.0122938385245525, \ 0.5513727993854916, \ 0.4363333620899563, \ 0.0025898092478457, \ 0.2704907465149770, \ 0.7269194442371776, \ 0.0025898092478457, \ 0.7269194442371776, \ 0.2704907465149773, \ 0.0375563888722969, \ 0.3508136433810974, \ 0.6116299677466061, \ 0.0375563888722969, \ 0.6116299677466058, \ 0.3508136433810976, \ 0.0170945467207073, \ 0.3727655119742921, \ 0.6101399413050007, \ 0.0170945467207073, \ 0.6101399413050007, \ 0.3727655119742924, \ 0.0857583162943159, \ 0.2171073522633416, \ 0.6971343314423428, \ 0.0857583162943159, \ 0.6971343314423428, \ 0.2171073522633418, \ 0.0579856449641144, \ 0.1927563650090059, \ 0.7492579900268799, \ 0.0579856449641144, \ 0.7492579900268799, \ 0.1927563650090061, \ 0.0338481728829903, \ 0.4206850306864163, \ 0.5454667964305936, \ 0.0338481728829903, \ 0.5454667964305936, \ 0.4206850306864165, \ 0.0269988226283733, \ 0.0269988226283730, \ 0.9460023547432538, \ 0.0025266913852086, \ 0.2124851854370911, \ 0.7849881231777005, \ 0.0025266913852086, \ 0.7849881231777005, \ 0.2124851854370913, \ 0.0106565421155276, \ 0.3192572087291874, \ 0.6700862491552853, \ 0.0106565421155276, \ 0.6700862491552851, \ 0.3192572087291877, \ 0.1385048069103230, \ 0.1385048069103228, \ 0.7229903861793542, \ 0.0659735852884721, \ 0.4670132073557641, \ 0.4670132073557642, \ 0.0134296732422585, \ 0.2516382355125726, \ 0.7349320912451690, \ 0.0134296732422585, \ 0.7349320912451689, \ 0.2516382355125729, \ 0.0883417782932651, \ 0.1522119814568094, \ 0.7594462402499257, \ 0.0883417782932651, \ 0.7594462402499258, \ 0.1522119814568096, \ 0.0329221182111608, \ 0.1111420947940333, \ 0.8559357869948060, \ 0.0329221182111608, \ 0.8559357869948060, \ 0.1111420947940336, \ 0.1948007607773277, \ 0.3581500588512503, \ 0.4470491803714222, \ 0.1948007607773277, \ 0.4470491803714221, \ 0.3581500588512505, \ 0.0314610159618918, \ 0.1637998569561501, \ 0.8047391270819583, \ 0.0314610159618918, \ 0.8047391270819583, \ 0.1637998569561504, \ 0.0673683101645259, \ 0.1021127733366743, \ 0.8305189164987999, \ 0.0673683101645259, \ 0.8305189164987999, \ 0.1021127733366746, \ 0.1865652441999728, \ 0.2335557030193517, \ 0.5798790527806759, \ 0.1865652441999728, \ 0.5798790527806759, \ 0.2335557030193518, \ 0.0638834834123953, \ 0.3214164628317114, \ 0.6147000537558934, \ 0.0638834834123953, \ 0.6147000537558934, \ 0.3214164628317117, \ 0.0325712217949499, \ 0.2233361848957126, \ 0.7440925933093379, \ 0.0325712217949499, \ 0.7440925933093377, \ 0.2233361848957128, \ 0.0132734827561578, \ 0.1905881189463202, \ 0.7961383982975221, \ 0.0132734827561578, \ 0.7961383982975221, \ 0.1905881189463206, \ 0.1362337755091281, \ 0.2273558402454796, \ 0.6364103842453925, \ 0.1362337755091281, \ 0.6364103842453924, \ 0.2273558402454798, \ 0.1065804258588591, \ 0.1065804258588588, \ 0.7868391482822823, \ 0.0026153775338892, \ 0.1567679227871601, \ 0.8406166996789509, \ 0.0026153775338892, \ 0.8406166996789507, \ 0.1567679227871604, \ 0.0134812112051568, \ 0.1340333349867785, \ 0.8524854538080648, \ 0.0134812112051568, \ 0.8524854538080648, \ 0.1340333349867788, \ 0.1918841043522063, \ 0.2957211757454537, \ 0.5123947199023403, \ 0.1918841043522063, \ 0.5123947199023402, \ 0.2957211757454539, \ 0.0025472816321698, \ 0.1067192718130003, \ 0.8907334465548301, \ 0.0025472816321698, \ 0.8907334465548301, \ 0.1067192718130007, \ 0.1010372943557597, \ 0.4125664194839166, \ 0.4863962861603239, \ 0.1010372943557597, \ 0.4863962861603238, \ 0.4125664194839167, \ 0.2497507411652888, \ 0.3078519829928861, \ 0.4423972758418253, \ 0.2497507411652888, \ 0.4423972758418253, \ 0.3078519829928862, \ 0.0137126252885580, \ 0.0870205486996967, \ 0.8992668260117456, \ 0.0137126252885580, \ 0.8992668260117456, \ 0.0870205486996970, \ 0.0033445954334026, \ 0.3894283316812198, \ 0.6072270728853779, \ 0.0033445954334026, \ 0.6072270728853778, \ 0.3894283316812200, \ 0.3117353910725875, \ 0.3117353910725874, \ 0.3765292178548253, \ 0.0556746304306052, \ 0.2612939703141770, \ 0.6830313992552181, \ 0.0556746304306052, \ 0.6830313992552179, \ 0.2612939703141772, \ 0.0028037585935403, \ 0.0649755331098119, \ 0.9322207082966479, \ 0.0028037585935403, \ 0.9322207082966479, \ 0.0649755331098122, \ 0.0963505000772398, \ 0.2719500060981311, \ 0.6316994938246292, \ 0.0963505000772398, \ 0.6316994938246292, \ 0.2719500060981313, \ 0.0291991066004360, \ 0.2930903642725463, \ 0.6777105291270180, \ 0.0291991066004360, \ 0.6777105291270179, \ 0.2930903642725465, \ 0.0635745506621692, \ 0.3946648265878193, \ 0.5417606227500118, \ 0.0635745506621692, \ 0.5417606227500117, \ 0.3946648265878194, \ 0.1439285800655438, \ 0.3568522181929829, \ 0.4992192017414736, \ 0.1439285800655438, \ 0.4992192017414734, \ 0.3568522181929830, \ 0.2448605758688819, \ 0.2448605758688818, \ 0.5102788482622366, \ 0.0992086997532998, \ 0.3413613516388764, \ 0.5594299486078241, \ 0.0992086997532998, \ 0.5594299486078240, \ 0.3413613516388765, \ 0.1403889214214629, \ 0.2895129410795146, \ 0.5700981374990227, \ 0.1403889214214629, \ 0.5700981374990226, \ 0.2895129410795148, \ 0.1748351458111909, \ 0.1748351458111907, \ 0.6503297083776187, \ 0.1448613316996193, \ 0.4275693341501904, \ 0.4275693341501906, \ 0.2514596866431047, \ 0.3742701566784478, \ 0.3742701566784478 ] ) c = np.array ( [ \ 0.4023719251097932, \ 0.1952561497804133, \ 0.4023719251097931, \ 0.9972692148480916, \ 0.0013653925759544, \ 0.0013653925759537, \ 0.6678757207141840, \ 0.0015704256014629, \ 0.3305538536843530, \ 0.3305538536843531, \ 0.0015704256014627, \ 0.6678757207141837, \ 0.4975317296252054, \ 0.0049365407495893, \ 0.4975317296252051, \ 0.0204313657326067, \ 0.0096146691207099, \ 0.9699539651466832, \ 0.9699539651466833, \ 0.0096146691207102, \ 0.0204313657326064, \ 0.9208981351903950, \ 0.0219035586156293, \ 0.0571983061939754, \ 0.0571983061939757, \ 0.0219035586156290, \ 0.9208981351903949, \ 0.4799002957544191, \ 0.0401994084911617, \ 0.4799002957544190, \ 0.8670673418884325, \ 0.0664663290557839, \ 0.0664663290557834, \ 0.5452354770717635, \ 0.0014935512902909, \ 0.4532709716379454, \ 0.4532709716379456, \ 0.0014935512902908, \ 0.5452354770717632, \ 0.8038260264189151, \ 0.0554414996743646, \ 0.1407324739067201, \ 0.1407324739067204, \ 0.0554414996743643, \ 0.8038260264189151, \ 0.6975178002766640, \ 0.1186935694213950, \ 0.1837886303019408, \ 0.1837886303019411, \ 0.1186935694213948, \ 0.6975178002766640, \ 0.9135272212245077, \ 0.0432363893877464, \ 0.0432363893877458, \ 0.9664947902959360, \ 0.0013930572171863, \ 0.0321121524868776, \ 0.0321121524868777, \ 0.0013930572171860, \ 0.9664947902959359, \ 0.4903050142016466, \ 0.0193899715967066, \ 0.4903050142016465, \ 0.9467364526174825, \ 0.0102994751818415, \ 0.0429640722006758, \ 0.0429640722006762, \ 0.0102994751818412, \ 0.9467364526174823, \ 0.9868904472776369, \ 0.0025847099922882, \ 0.0105248427300747, \ 0.0105248427300748, \ 0.0025847099922879, \ 0.9868904472776370, \ 0.8851466587208721, \ 0.0394743127161577, \ 0.0753790285629702, \ 0.0753790285629703, \ 0.0394743127161575, \ 0.8851466587208719, \ 0.5513727993854914, \ 0.0122938385245525, \ 0.4363333620899558, \ 0.4363333620899560, \ 0.0122938385245525, \ 0.5513727993854913, \ 0.7269194442371774, \ 0.0025898092478457, \ 0.2704907465149767, \ 0.2704907465149771, \ 0.0025898092478455, \ 0.7269194442371772, \ 0.6116299677466058, \ 0.0375563888722968, \ 0.3508136433810972, \ 0.3508136433810974, \ 0.0375563888722968, \ 0.6116299677466057, \ 0.6101399413050006, \ 0.0170945467207073, \ 0.3727655119742920, \ 0.3727655119742921, \ 0.0170945467207072, \ 0.6101399413050004, \ 0.6971343314423426, \ 0.0857583162943158, \ 0.2171073522633413, \ 0.2171073522633415, \ 0.0857583162943156, \ 0.6971343314423424, \ 0.7492579900268798, \ 0.0579856449641144, \ 0.1927563650090056, \ 0.1927563650090058, \ 0.0579856449641142, \ 0.7492579900268797, \ 0.5454667964305934, \ 0.0338481728829902, \ 0.4206850306864162, \ 0.4206850306864162, \ 0.0338481728829901, \ 0.5454667964305933, \ 0.9460023547432537, \ 0.0269988226283734, \ 0.0269988226283727, \ 0.7849881231777003, \ 0.0025266913852086, \ 0.2124851854370908, \ 0.2124851854370911, \ 0.0025266913852084, \ 0.7849881231777003, \ 0.6700862491552849, \ 0.0106565421155277, \ 0.3192572087291872, \ 0.3192572087291873, \ 0.0106565421155275, \ 0.6700862491552848, \ 0.7229903861793543, \ 0.1385048069103230, \ 0.1385048069103226, \ 0.4670132073557639, \ 0.0659735852884719, \ 0.4670132073557638, \ 0.7349320912451689, \ 0.0134296732422585, \ 0.2516382355125725, \ 0.2516382355125726, \ 0.0134296732422584, \ 0.7349320912451688, \ 0.7594462402499256, \ 0.0883417782932650, \ 0.1522119814568091, \ 0.1522119814568094, \ 0.0883417782932648, \ 0.7594462402499256, \ 0.8559357869948060, \ 0.0329221182111608, \ 0.1111420947940330, \ 0.1111420947940332, \ 0.0329221182111606, \ 0.8559357869948059, \ 0.4470491803714220, \ 0.1948007607773276, \ 0.3581500588512502, \ 0.3581500588512502, \ 0.1948007607773276, \ 0.4470491803714220, \ 0.8047391270819582, \ 0.0314610159618918, \ 0.1637998569561498, \ 0.1637998569561500, \ 0.0314610159618917, \ 0.8047391270819580, \ 0.8305189164987998, \ 0.0673683101645259, \ 0.1021127733366741, \ 0.1021127733366744, \ 0.0673683101645256, \ 0.8305189164987997, \ 0.5798790527806756, \ 0.1865652441999727, \ 0.2335557030193514, \ 0.2335557030193516, \ 0.1865652441999726, \ 0.5798790527806756, \ 0.6147000537558933, \ 0.0638834834123953, \ 0.3214164628317112, \ 0.3214164628317113, \ 0.0638834834123952, \ 0.6147000537558932, \ 0.7440925933093376, \ 0.0325712217949498, \ 0.2233361848957123, \ 0.2233361848957125, \ 0.0325712217949498, \ 0.7440925933093375, \ 0.7961383982975219, \ 0.0132734827561579, \ 0.1905881189463200, \ 0.1905881189463202, \ 0.0132734827561576, \ 0.7961383982975219, \ 0.6364103842453924, \ 0.1362337755091281, \ 0.2273558402454794, \ 0.2273558402454795, \ 0.1362337755091280, \ 0.6364103842453923, \ 0.7868391482822822, \ 0.1065804258588590, \ 0.1065804258588586, \ 0.8406166996789508, \ 0.0026153775338892, \ 0.1567679227871598, \ 0.1567679227871601, \ 0.0026153775338892, \ 0.8406166996789505, \ 0.8524854538080647, \ 0.0134812112051568, \ 0.1340333349867783, \ 0.1340333349867785, \ 0.0134812112051567, \ 0.8524854538080646, \ 0.5123947199023401, \ 0.1918841043522061, \ 0.2957211757454535, \ 0.2957211757454535, \ 0.1918841043522062, \ 0.5123947199023400, \ 0.8907334465548298, \ 0.0025472816321699, \ 0.1067192718130000, \ 0.1067192718130004, \ 0.0025472816321696, \ 0.8907334465548297, \ 0.4863962861603238, \ 0.1010372943557597, \ 0.4125664194839165, \ 0.4125664194839166, \ 0.1010372943557597, \ 0.4863962861603237, \ 0.4423972758418251, \ 0.2497507411652887, \ 0.3078519829928861, \ 0.3078519829928861, \ 0.2497507411652886, \ 0.4423972758418251, \ 0.8992668260117453, \ 0.0137126252885580, \ 0.0870205486996963, \ 0.0870205486996966, \ 0.0137126252885578, \ 0.8992668260117452, \ 0.6072270728853777, \ 0.0033445954334025, \ 0.3894283316812195, \ 0.3894283316812197, \ 0.0033445954334025, \ 0.6072270728853775, \ 0.3765292178548252, \ 0.3117353910725874, \ 0.3117353910725874, \ 0.6830313992552178, \ 0.0556746304306052, \ 0.2612939703141767, \ 0.2612939703141771, \ 0.0556746304306051, \ 0.6830313992552177, \ 0.9322207082966478, \ 0.0028037585935403, \ 0.0649755331098116, \ 0.0649755331098119, \ 0.0028037585935402, \ 0.9322207082966477, \ 0.6316994938246291, \ 0.0963505000772398, \ 0.2719500060981309, \ 0.2719500060981310, \ 0.0963505000772397, \ 0.6316994938246290, \ 0.6777105291270178, \ 0.0291991066004360, \ 0.2930903642725460, \ 0.2930903642725462, \ 0.0291991066004359, \ 0.6777105291270177, \ 0.5417606227500116, \ 0.0635745506621690, \ 0.3946648265878190, \ 0.3946648265878193, \ 0.0635745506621691, \ 0.5417606227500115, \ 0.4992192017414734, \ 0.1439285800655438, \ 0.3568522181929827, \ 0.3568522181929827, \ 0.1439285800655437, \ 0.4992192017414732, \ 0.5102788482622364, \ 0.2448605758688819, \ 0.2448605758688817, \ 0.5594299486078239, \ 0.0992086997532996, \ 0.3413613516388762, \ 0.3413613516388762, \ 0.0992086997532997, \ 0.5594299486078238, \ 0.5700981374990226, \ 0.1403889214214628, \ 0.2895129410795144, \ 0.2895129410795145, \ 0.1403889214214628, \ 0.5700981374990224, \ 0.6503297083776185, \ 0.1748351458111909, \ 0.1748351458111904, \ 0.4275693341501904, \ 0.1448613316996192, \ 0.4275693341501903, \ 0.3742701566784477, \ 0.2514596866431046, \ 0.3742701566784476 ] ) w = np.array ( [ \ 0.0035464400159772, \ 0.0035464400159772, \ 0.0035464400159772, \ 0.0000347195354366, \ 0.0000347195354366, \ 0.0000347195354366, \ 0.0005327316943405, \ 0.0005327316943405, \ 0.0005327316943405, \ 0.0005327316943405, \ 0.0005327316943405, \ 0.0005327316943405, \ 0.0010141696428327, \ 0.0010141696428327, \ 0.0010141696428327, \ 0.0004390770271698, \ 0.0004390770271698, \ 0.0004390770271698, \ 0.0004390770271698, \ 0.0004390770271698, \ 0.0004390770271698, \ 0.0010370250465354, \ 0.0010370250465354, \ 0.0010370250465354, \ 0.0010370250465354, \ 0.0010370250465354, \ 0.0010370250465354, \ 0.0028441859570122, \ 0.0028441859570122, \ 0.0028441859570122, \ 0.0018709815380229, \ 0.0018709815380229, \ 0.0018709815380229, \ 0.0005595519502280, \ 0.0005595519502280, \ 0.0005595519502280, \ 0.0005595519502280, \ 0.0005595519502280, \ 0.0005595519502280, \ 0.0025379205064648, \ 0.0025379205064648, \ 0.0025379205064648, \ 0.0025379205064648, \ 0.0025379205064648, \ 0.0025379205064648, \ 0.0040581577981140, \ 0.0040581577981140, \ 0.0040581577981140, \ 0.0040581577981140, \ 0.0040581577981140, \ 0.0040581577981140, \ 0.0013326250004080, \ 0.0013326250004080, \ 0.0013326250004080, \ 0.0002266425752075, \ 0.0002266425752075, \ 0.0002266425752075, \ 0.0002266425752075, \ 0.0002266425752075, \ 0.0002266425752075, \ 0.0021926816815859, \ 0.0021926816815859, \ 0.0021926816815859, \ 0.0006818533431415, \ 0.0006818533431415, \ 0.0006818533431415, \ 0.0006818533431415, \ 0.0006818533431415, \ 0.0006818533431415, \ 0.0001870930686156, \ 0.0001870930686156, \ 0.0001870930686156, \ 0.0001870930686156, \ 0.0001870930686156, \ 0.0001870930686156, \ 0.0016866296698237, \ 0.0016866296698237, \ 0.0016866296698237, \ 0.0016866296698237, \ 0.0016866296698237, \ 0.0016866296698237, \ 0.0019025497964579, \ 0.0019025497964579, \ 0.0019025497964579, \ 0.0019025497964579, \ 0.0019025497964579, \ 0.0019025497964579, \ 0.0007733670252998, \ 0.0007733670252998, \ 0.0007733670252998, \ 0.0007733670252998, \ 0.0007733670252998, \ 0.0007733670252998, \ 0.0031723878909002, \ 0.0031723878909002, \ 0.0031723878909002, \ 0.0031723878909002, \ 0.0031723878909002, \ 0.0031723878909002, \ 0.0021685247098617, \ 0.0021685247098617, \ 0.0021685247098617, \ 0.0021685247098617, \ 0.0021685247098617, \ 0.0021685247098617, \ 0.0040741174736407, \ 0.0040741174736407, \ 0.0040741174736407, \ 0.0040741174736407, \ 0.0040741174736407, \ 0.0040741174736407, \ 0.0033720890143962, \ 0.0033720890143962, \ 0.0033720890143962, \ 0.0033720890143962, \ 0.0033720890143962, \ 0.0033720890143962, \ 0.0033374654153493, \ 0.0033374654153493, \ 0.0033374654153493, \ 0.0033374654153493, \ 0.0033374654153493, \ 0.0033374654153493, \ 0.0009524059556547, \ 0.0009524059556547, \ 0.0009524059556547, \ 0.0007443004607122, \ 0.0007443004607122, \ 0.0007443004607122, \ 0.0007443004607122, \ 0.0007443004607122, \ 0.0007443004607122, \ 0.0017490056575093, \ 0.0017490056575093, \ 0.0017490056575093, \ 0.0017490056575093, \ 0.0017490056575093, \ 0.0017490056575093, \ 0.0043598500418925, \ 0.0043598500418925, \ 0.0043598500418925, \ 0.0045325322550328, \ 0.0045325322550328, \ 0.0045325322550328, \ 0.0019031683954380, \ 0.0019031683954380, \ 0.0019031683954380, \ 0.0019031683954380, \ 0.0019031683954380, \ 0.0019031683954380, \ 0.0039581444907566, \ 0.0039581444907566, \ 0.0039581444907566, \ 0.0039581444907566, \ 0.0039581444907566, \ 0.0039581444907566, \ 0.0021633300119175, \ 0.0021633300119175, \ 0.0021633300119175, \ 0.0021633300119175, \ 0.0021633300119175, \ 0.0021633300119175, \ 0.0062667413965418, \ 0.0062667413965418, \ 0.0062667413965418, \ 0.0062667413965418, \ 0.0062667413965418, \ 0.0062667413965418, \ 0.0024314709447528, \ 0.0024314709447528, \ 0.0024314709447528, \ 0.0024314709447528, \ 0.0024314709447528, \ 0.0024314709447528, \ 0.0028265780976025, \ 0.0028265780976025, \ 0.0028265780976025, \ 0.0028265780976025, \ 0.0028265780976025, \ 0.0028265780976025, \ 0.0064753562254833, \ 0.0064753562254833, \ 0.0064753562254833, \ 0.0064753562254833, \ 0.0064753562254833, \ 0.0064753562254833, \ 0.0042484824512542, \ 0.0042484824512542, \ 0.0042484824512542, \ 0.0042484824512542, \ 0.0042484824512542, \ 0.0042484824512542, \ 0.0029100859090623, \ 0.0029100859090623, \ 0.0029100859090623, \ 0.0029100859090623, \ 0.0029100859090623, \ 0.0029100859090623, \ 0.0017543943309314, \ 0.0017543943309314, \ 0.0017543943309314, \ 0.0017543943309314, \ 0.0017543943309314, \ 0.0017543943309314, \ 0.0053278143635326, \ 0.0053278143635326, \ 0.0053278143635326, \ 0.0053278143635326, \ 0.0053278143635326, \ 0.0053278143635326, \ 0.0036960706615539, \ 0.0036960706615539, \ 0.0036960706615539, \ 0.0007117355150534, \ 0.0007117355150534, \ 0.0007117355150534, \ 0.0007117355150534, \ 0.0007117355150534, \ 0.0007117355150534, \ 0.0015685196181434, \ 0.0015685196181434, \ 0.0015685196181434, \ 0.0015685196181434, \ 0.0015685196181434, \ 0.0015685196181434, \ 0.0069096837033853, \ 0.0069096837033853, \ 0.0069096837033853, \ 0.0069096837033853, \ 0.0069096837033853, \ 0.0069096837033853, \ 0.0006077668893384, \ 0.0006077668893384, \ 0.0006077668893384, \ 0.0006077668893384, \ 0.0006077668893384, \ 0.0006077668893384, \ 0.0058599060505518, \ 0.0058599060505518, \ 0.0058599060505518, \ 0.0058599060505518, \ 0.0058599060505518, \ 0.0058599060505518, \ 0.0077651860406297, \ 0.0077651860406297, \ 0.0077651860406297, \ 0.0077651860406297, \ 0.0077651860406297, \ 0.0077651860406297, \ 0.0013100408329861, \ 0.0013100408329861, \ 0.0013100408329861, \ 0.0013100408329861, \ 0.0013100408329861, \ 0.0013100408329861, \ 0.0010570972491723, \ 0.0010570972491723, \ 0.0010570972491723, \ 0.0010570972491723, \ 0.0010570972491723, \ 0.0010570972491723, \ 0.0080973376090284, \ 0.0080973376090284, \ 0.0080973376090284, \ 0.0040411976507506, \ 0.0040411976507506, \ 0.0040411976507506, \ 0.0040411976507506, \ 0.0040411976507506, \ 0.0040411976507506, \ 0.0005242478913459, \ 0.0005242478913459, \ 0.0005242478913459, \ 0.0005242478913459, \ 0.0005242478913459, \ 0.0005242478913459, \ 0.0052048680063201, \ 0.0052048680063201, \ 0.0052048680063201, \ 0.0052048680063201, \ 0.0052048680063201, \ 0.0052048680063201, \ 0.0030333113262699, \ 0.0030333113262699, \ 0.0030333113262699, \ 0.0030333113262699, \ 0.0030333113262699, \ 0.0030333113262699, \ 0.0048685523603979, \ 0.0048685523603979, \ 0.0048685523603979, \ 0.0048685523603979, \ 0.0048685523603979, \ 0.0048685523603979, \ 0.0066028726180890, \ 0.0066028726180890, \ 0.0066028726180890, \ 0.0066028726180890, \ 0.0066028726180890, \ 0.0066028726180890, \ 0.0072906010527868, \ 0.0072906010527868, \ 0.0072906010527868, \ 0.0056531366883124, \ 0.0056531366883124, \ 0.0056531366883124, \ 0.0056531366883124, \ 0.0056531366883124, \ 0.0056531366883124, \ 0.0061919290123439, \ 0.0061919290123439, \ 0.0061919290123439, \ 0.0061919290123439, \ 0.0061919290123439, \ 0.0061919290123439, \ 0.0060555267820254, \ 0.0060555267820254, \ 0.0060555267820254, \ 0.0067589446392298, \ 0.0067589446392298, \ 0.0067589446392298, \ 0.0079220445765913, \ 0.0079220445765913, \ 0.0079220445765913 ] ) return a, b, c, w def rule43 ( ): #*****************************************************************************80 # ## rule43() returns the rule of precision 43. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4117801708599338, \ 0.4117801708599338, \ 0.1764396582801323, \ 0.4755758670991315, \ 0.4755758670991315, \ 0.0488482658017370, \ 0.2297394365272492, \ 0.6248067680849181, \ 0.1454537953878327, \ 0.6248067680849182, \ 0.2297394365272493, \ 0.1454537953878325, \ 0.4991798367344780, \ 0.4991798367344780, \ 0.0016403265310439, \ 0.2962479881688698, \ 0.4075040236622601, \ 0.2962479881688698, \ 0.3605580760887838, \ 0.6070264490694377, \ 0.0324154748417785, \ 0.6070264490694376, \ 0.3605580760887839, \ 0.0324154748417784, \ 0.0959172276669437, \ 0.8916698641086179, \ 0.0124129082244385, \ 0.8916698641086179, \ 0.0959172276669437, \ 0.0124129082244381, \ 0.1898015101110885, \ 0.6723403719974184, \ 0.1378581178914931, \ 0.6723403719974185, \ 0.1898015101110885, \ 0.1378581178914929, \ 0.4010584512926051, \ 0.4636054175537986, \ 0.1353361311535962, \ 0.4636054175537986, \ 0.4010584512926052, \ 0.1353361311535961, \ 0.2775825322761021, \ 0.5788906758314212, \ 0.1435267918924767, \ 0.5788906758314212, \ 0.2775825322761021, \ 0.1435267918924765, \ 0.3531888048870007, \ 0.3531888048870007, \ 0.2936223902259985, \ 0.3061183766903350, \ 0.6584300317131508, \ 0.0354515915965141, \ 0.6584300317131508, \ 0.3061183766903349, \ 0.0354515915965140, \ 0.4951059808027699, \ 0.4951059808027699, \ 0.0097880383944601, \ 0.4182891701734248, \ 0.5462922966952530, \ 0.0354185331313221, \ 0.5462922966952531, \ 0.4182891701734248, \ 0.0354185331313221, \ 0.0329098159605346, \ 0.9341803680789306, \ 0.0329098159605350, \ 0.0965099243357524, \ 0.8476962075384494, \ 0.0557938681257983, \ 0.8476962075384494, \ 0.0965099243357524, \ 0.0557938681257979, \ 0.1328397411105292, \ 0.8031840240996622, \ 0.0639762347898087, \ 0.8031840240996622, \ 0.1328397411105293, \ 0.0639762347898084, \ 0.0969643297980663, \ 0.8727730904601626, \ 0.0302625797417711, \ 0.8727730904601626, \ 0.0969643297980663, \ 0.0302625797417709, \ 0.4865637511306883, \ 0.4865637511306884, \ 0.0268724977386232, \ 0.4287537536910129, \ 0.5566086299500186, \ 0.0146376163589685, \ 0.5566086299500185, \ 0.4287537536910130, \ 0.0146376163589684, \ 0.0627150483897617, \ 0.8745699032204765, \ 0.0627150483897621, \ 0.1368534453260830, \ 0.8495413037445184, \ 0.0136052509293986, \ 0.8495413037445184, \ 0.1368534453260831, \ 0.0136052509293983, \ 0.3635619090992528, \ 0.6339620502785548, \ 0.0024760406221923, \ 0.6339620502785549, \ 0.3635619090992528, \ 0.0024760406221921, \ 0.1447435597702214, \ 0.7105128804595570, \ 0.1447435597702216, \ 0.3361435723276197, \ 0.5209304542944508, \ 0.1429259733779294, \ 0.5209304542944510, \ 0.3361435723276198, \ 0.1429259733779293, \ 0.0133646206082616, \ 0.9732707587834765, \ 0.0133646206082620, \ 0.0940988534499003, \ 0.9034803688043024, \ 0.0024207777457974, \ 0.9034803688043024, \ 0.0940988534499004, \ 0.0024207777457970, \ 0.2427105866699005, \ 0.5621390733405861, \ 0.1951503399895134, \ 0.5621390733405861, \ 0.2427105866699005, \ 0.1951503399895132, \ 0.4252384428310576, \ 0.5107064553472853, \ 0.0640551018216570, \ 0.5107064553472853, \ 0.4252384428310577, \ 0.0640551018216569, \ 0.3642781269741873, \ 0.6225342617933295, \ 0.0131876112324832, \ 0.6225342617933295, \ 0.3642781269741873, \ 0.0131876112324831, \ 0.1776637264896365, \ 0.7604631914033508, \ 0.0618730821070127, \ 0.7604631914033508, \ 0.1776637264896365, \ 0.0618730821070125, \ 0.0588456479492051, \ 0.9385418797080261, \ 0.0026124723427690, \ 0.9385418797080262, \ 0.0588456479492050, \ 0.0026124723427685, \ 0.2500996019098293, \ 0.7157099945300758, \ 0.0341904035600950, \ 0.7157099945300757, \ 0.2500996019098293, \ 0.0341904035600948, \ 0.0319725865365346, \ 0.9653765821329179, \ 0.0026508313305476, \ 0.9653765821329179, \ 0.0319725865365347, \ 0.0026508313305472, \ 0.2417239613576790, \ 0.7556844695525968, \ 0.0025915690897241, \ 0.7556844695525969, \ 0.2417239613576790, \ 0.0025915690897238, \ 0.1844047074392018, \ 0.8013219460698174, \ 0.0142733464909807, \ 0.8013219460698174, \ 0.1844047074392019, \ 0.0142733464909806, \ 0.0612563890152720, \ 0.9248872032992935, \ 0.0138564076854347, \ 0.9248872032992935, \ 0.0612563890152721, \ 0.0138564076854343, \ 0.0132571416922719, \ 0.9842490320417303, \ 0.0024938262659979, \ 0.9842490320417302, \ 0.0132571416922719, \ 0.0024938262659976, \ 0.0025649413700201, \ 0.9948701172599593, \ 0.0025649413700206, \ 0.1877722427785784, \ 0.6244555144428430, \ 0.1877722427785786, \ 0.1379731400814552, \ 0.7615859288601728, \ 0.1004409310583720, \ 0.7615859288601727, \ 0.1379731400814552, \ 0.1004409310583717, \ 0.0332056799273113, \ 0.9530968777199650, \ 0.0136974423527239, \ 0.9530968777199650, \ 0.0332056799273114, \ 0.0136974423527234, \ 0.3825643087869355, \ 0.3825643087869355, \ 0.2348713824261289, \ 0.1944661967811065, \ 0.7713906073293495, \ 0.0341431958895441, \ 0.7713906073293495, \ 0.1944661967811065, \ 0.0341431958895439, \ 0.2394826350852045, \ 0.7467127396201542, \ 0.0138046252946413, \ 0.7467127396201542, \ 0.2394826350852046, \ 0.0138046252946411, \ 0.3645542277763408, \ 0.4489485579241042, \ 0.1864972142995550, \ 0.4489485579241042, \ 0.3645542277763408, \ 0.1864972142995550, \ 0.1373564023661998, \ 0.8601018382691165, \ 0.0025417593646838, \ 0.8601018382691165, \ 0.1373564023661998, \ 0.0025417593646835, \ 0.2322320373188904, \ 0.7047330289764286, \ 0.0630349337046811, \ 0.7047330289764286, \ 0.2322320373188905, \ 0.0630349337046808, \ 0.2926613950722469, \ 0.6434616923483870, \ 0.0638769125793660, \ 0.6434616923483871, \ 0.2926613950722470, \ 0.0638769125793659, \ 0.3176481163981567, \ 0.4403990384263681, \ 0.2419528451754751, \ 0.4403990384263682, \ 0.3176481163981567, \ 0.2419528451754750, \ 0.3003015966157783, \ 0.6850991321252453, \ 0.0145992712589764, \ 0.6850991321252453, \ 0.3003015966157784, \ 0.0145992712589763, \ 0.3005613537168110, \ 0.6966205316862629, \ 0.0028181145969260, \ 0.6966205316862629, \ 0.3005613537168111, \ 0.0028181145969259, \ 0.0605239793987312, \ 0.9053415210418889, \ 0.0341344995593799, \ 0.9053415210418890, \ 0.0605239793987313, \ 0.0341344995593795, \ 0.3007859192338894, \ 0.5058586034896924, \ 0.1933554772764183, \ 0.5058586034896924, \ 0.3007859192338894, \ 0.1933554772764182, \ 0.1895507039776852, \ 0.7130863262721638, \ 0.0973629697501509, \ 0.7130863262721640, \ 0.1895507039776853, \ 0.0973629697501507, \ 0.4301399033621489, \ 0.5670717942327397, \ 0.0027883024051114, \ 0.5670717942327397, \ 0.4301399033621489, \ 0.0027883024051113, \ 0.1870185722176647, \ 0.8102254653358516, \ 0.0027559624464837, \ 0.8102254653358516, \ 0.1870185722176648, \ 0.0027559624464835, \ 0.3791895225090074, \ 0.5229833703321247, \ 0.0978271071588677, \ 0.5229833703321248, \ 0.3791895225090075, \ 0.0978271071588676, \ 0.3129669769821593, \ 0.5874593373809698, \ 0.0995736856368709, \ 0.5874593373809698, \ 0.3129669769821594, \ 0.0995736856368708, \ 0.1418044870172890, \ 0.8240811613164462, \ 0.0341143516662649, \ 0.8240811613164462, \ 0.1418044870172891, \ 0.0341143516662646, \ 0.4528922608459510, \ 0.4528922608459510, \ 0.0942154783080979, \ 0.2481814600155885, \ 0.6513210967114831, \ 0.1004974432729285, \ 0.6513210967114831, \ 0.2481814600155886, \ 0.1004974432729282, \ 0.3587978354079987, \ 0.5795283608954496, \ 0.0616738036965517, \ 0.5795283608954497, \ 0.3587978354079988, \ 0.0616738036965515, \ 0.0928670462140479, \ 0.8142659075719040, \ 0.0928670462140481, \ 0.2524849326490907, \ 0.4950301347018184, \ 0.2524849326490909 ] ) b = np.array ( [ \ 0.1764396582801324, \ 0.4117801708599339, \ 0.4117801708599340, \ 0.0488482658017371, \ 0.4755758670991315, \ 0.4755758670991317, \ 0.1454537953878326, \ 0.2297394365272493, \ 0.6248067680849183, \ 0.1454537953878326, \ 0.6248067680849183, \ 0.2297394365272494, \ 0.0016403265310440, \ 0.4991798367344781, \ 0.4991798367344782, \ 0.2962479881688700, \ 0.2962479881688700, \ 0.4075040236622604, \ 0.0324154748417785, \ 0.3605580760887839, \ 0.6070264490694378, \ 0.0324154748417785, \ 0.6070264490694377, \ 0.3605580760887841, \ 0.0124129082244384, \ 0.0959172276669437, \ 0.8916698641086181, \ 0.0124129082244384, \ 0.8916698641086181, \ 0.0959172276669440, \ 0.1378581178914931, \ 0.1898015101110885, \ 0.6723403719974186, \ 0.1378581178914931, \ 0.6723403719974186, \ 0.1898015101110887, \ 0.1353361311535962, \ 0.4010584512926053, \ 0.4636054175537988, \ 0.1353361311535962, \ 0.4636054175537987, \ 0.4010584512926054, \ 0.1435267918924767, \ 0.2775825322761022, \ 0.5788906758314213, \ 0.1435267918924767, \ 0.5788906758314213, \ 0.2775825322761024, \ 0.2936223902259986, \ 0.3531888048870008, \ 0.3531888048870009, \ 0.0354515915965142, \ 0.3061183766903350, \ 0.6584300317131511, \ 0.0354515915965142, \ 0.6584300317131511, \ 0.3061183766903353, \ 0.0097880383944602, \ 0.4951059808027700, \ 0.4951059808027701, \ 0.0354185331313222, \ 0.4182891701734248, \ 0.5462922966952534, \ 0.0354185331313222, \ 0.5462922966952531, \ 0.4182891701734250, \ 0.0329098159605348, \ 0.0329098159605345, \ 0.9341803680789307, \ 0.0557938681257981, \ 0.0965099243357524, \ 0.8476962075384495, \ 0.0557938681257981, \ 0.8476962075384497, \ 0.0965099243357527, \ 0.0639762347898086, \ 0.1328397411105292, \ 0.8031840240996623, \ 0.0639762347898086, \ 0.8031840240996623, \ 0.1328397411105295, \ 0.0302625797417711, \ 0.0969643297980663, \ 0.8727730904601628, \ 0.0302625797417711, \ 0.8727730904601628, \ 0.0969643297980667, \ 0.0268724977386233, \ 0.4865637511306884, \ 0.4865637511306886, \ 0.0146376163589685, \ 0.4287537536910130, \ 0.5566086299500187, \ 0.0146376163589685, \ 0.5566086299500186, \ 0.4287537536910132, \ 0.0627150483897619, \ 0.0627150483897616, \ 0.8745699032204766, \ 0.0136052509293985, \ 0.1368534453260830, \ 0.8495413037445185, \ 0.0136052509293985, \ 0.8495413037445186, \ 0.1368534453260834, \ 0.0024760406221923, \ 0.3635619090992529, \ 0.6339620502785551, \ 0.0024760406221923, \ 0.6339620502785550, \ 0.3635619090992531, \ 0.1447435597702217, \ 0.1447435597702214, \ 0.7105128804595572, \ 0.1429259733779294, \ 0.3361435723276198, \ 0.5209304542944510, \ 0.1429259733779294, \ 0.5209304542944510, \ 0.3361435723276199, \ 0.0133646206082619, \ 0.0133646206082616, \ 0.9732707587834766, \ 0.0024207777457973, \ 0.0940988534499003, \ 0.9034803688043025, \ 0.0024207777457973, \ 0.9034803688043025, \ 0.0940988534499007, \ 0.1951503399895134, \ 0.2427105866699006, \ 0.5621390733405862, \ 0.1951503399895134, \ 0.5621390733405862, \ 0.2427105866699007, \ 0.0640551018216570, \ 0.4252384428310577, \ 0.5107064553472855, \ 0.0640551018216570, \ 0.5107064553472854, \ 0.4252384428310579, \ 0.0131876112324832, \ 0.3642781269741873, \ 0.6225342617933296, \ 0.0131876112324832, \ 0.6225342617933296, \ 0.3642781269741875, \ 0.0618730821070127, \ 0.1776637264896365, \ 0.7604631914033511, \ 0.0618730821070127, \ 0.7604631914033509, \ 0.1776637264896368, \ 0.0026124723427688, \ 0.0588456479492050, \ 0.9385418797080262, \ 0.0026124723427688, \ 0.9385418797080264, \ 0.0588456479492054, \ 0.0341904035600950, \ 0.2500996019098293, \ 0.7157099945300760, \ 0.0341904035600950, \ 0.7157099945300759, \ 0.2500996019098295, \ 0.0026508313305474, \ 0.0319725865365346, \ 0.9653765821329181, \ 0.0026508313305474, \ 0.9653765821329181, \ 0.0319725865365349, \ 0.0025915690897240, \ 0.2417239613576791, \ 0.7556844695525970, \ 0.0025915690897240, \ 0.7556844695525970, \ 0.2417239613576793, \ 0.0142733464909807, \ 0.1844047074392018, \ 0.8013219460698178, \ 0.0142733464909807, \ 0.8013219460698175, \ 0.1844047074392021, \ 0.0138564076854345, \ 0.0612563890152719, \ 0.9248872032992936, \ 0.0138564076854345, \ 0.9248872032992936, \ 0.0612563890152723, \ 0.0024938262659979, \ 0.0132571416922719, \ 0.9842490320417305, \ 0.0024938262659979, \ 0.9842490320417305, \ 0.0132571416922722, \ 0.0025649413700205, \ 0.0025649413700201, \ 0.9948701172599594, \ 0.1877722427785786, \ 0.1877722427785785, \ 0.6244555144428431, \ 0.1004409310583719, \ 0.1379731400814553, \ 0.7615859288601730, \ 0.1004409310583719, \ 0.7615859288601730, \ 0.1379731400814555, \ 0.0136974423527237, \ 0.0332056799273113, \ 0.9530968777199650, \ 0.0136974423527237, \ 0.9530968777199653, \ 0.0332056799273116, \ 0.2348713824261290, \ 0.3825643087869356, \ 0.3825643087869356, \ 0.0341431958895440, \ 0.1944661967811065, \ 0.7713906073293497, \ 0.0341431958895440, \ 0.7713906073293496, \ 0.1944661967811067, \ 0.0138046252946413, \ 0.2394826350852046, \ 0.7467127396201543, \ 0.0138046252946413, \ 0.7467127396201543, \ 0.2394826350852048, \ 0.1864972142995551, \ 0.3645542277763408, \ 0.4489485579241043, \ 0.1864972142995551, \ 0.4489485579241042, \ 0.3645542277763409, \ 0.0025417593646838, \ 0.1373564023661998, \ 0.8601018382691167, \ 0.0025417593646838, \ 0.8601018382691167, \ 0.1373564023662001, \ 0.0630349337046810, \ 0.2322320373188904, \ 0.7047330289764286, \ 0.0630349337046810, \ 0.7047330289764286, \ 0.2322320373188907, \ 0.0638769125793660, \ 0.2926613950722469, \ 0.6434616923483873, \ 0.0638769125793660, \ 0.6434616923483871, \ 0.2926613950722471, \ 0.2419528451754752, \ 0.3176481163981568, \ 0.4403990384263682, \ 0.2419528451754752, \ 0.4403990384263682, \ 0.3176481163981569, \ 0.0145992712589763, \ 0.3003015966157783, \ 0.6850991321252455, \ 0.0145992712589763, \ 0.6850991321252453, \ 0.3003015966157786, \ 0.0028181145969261, \ 0.3005613537168110, \ 0.6966205316862633, \ 0.0028181145969261, \ 0.6966205316862629, \ 0.3005613537168113, \ 0.0341344995593797, \ 0.0605239793987312, \ 0.9053415210418891, \ 0.0341344995593797, \ 0.9053415210418891, \ 0.0605239793987315, \ 0.1933554772764183, \ 0.3007859192338894, \ 0.5058586034896925, \ 0.1933554772764183, \ 0.5058586034896925, \ 0.3007859192338895, \ 0.0973629697501509, \ 0.1895507039776853, \ 0.7130863262721642, \ 0.0973629697501509, \ 0.7130863262721641, \ 0.1895507039776855, \ 0.0027883024051114, \ 0.4301399033621490, \ 0.5670717942327399, \ 0.0027883024051114, \ 0.5670717942327398, \ 0.4301399033621491, \ 0.0027559624464837, \ 0.1870185722176647, \ 0.8102254653358518, \ 0.0027559624464837, \ 0.8102254653358517, \ 0.1870185722176650, \ 0.0978271071588678, \ 0.3791895225090076, \ 0.5229833703321249, \ 0.0978271071588678, \ 0.5229833703321249, \ 0.3791895225090077, \ 0.0995736856368710, \ 0.3129669769821593, \ 0.5874593373809700, \ 0.0995736856368710, \ 0.5874593373809698, \ 0.3129669769821595, \ 0.0341143516662649, \ 0.1418044870172890, \ 0.8240811613164464, \ 0.0341143516662649, \ 0.8240811613164463, \ 0.1418044870172893, \ 0.0942154783080980, \ 0.4528922608459511, \ 0.4528922608459512, \ 0.1004974432729284, \ 0.2481814600155886, \ 0.6513210967114832, \ 0.1004974432729284, \ 0.6513210967114832, \ 0.2481814600155887, \ 0.0616738036965517, \ 0.3587978354079987, \ 0.5795283608954498, \ 0.0616738036965517, \ 0.5795283608954497, \ 0.3587978354079990, \ 0.0928670462140481, \ 0.0928670462140479, \ 0.8142659075719042, \ 0.2524849326490909, \ 0.2524849326490908, \ 0.4950301347018185 ] ) c = np.array ( [ \ 0.4117801708599338, \ 0.1764396582801323, \ 0.4117801708599337, \ 0.4755758670991314, \ 0.0488482658017370, \ 0.4755758670991312, \ 0.6248067680849181, \ 0.1454537953878327, \ 0.2297394365272490, \ 0.2297394365272492, \ 0.1454537953878324, \ 0.6248067680849181, \ 0.4991798367344780, \ 0.0016403265310440, \ 0.4991798367344778, \ 0.4075040236622602, \ 0.2962479881688699, \ 0.2962479881688699, \ 0.6070264490694376, \ 0.0324154748417784, \ 0.3605580760887837, \ 0.3605580760887839, \ 0.0324154748417784, \ 0.6070264490694375, \ 0.8916698641086179, \ 0.0124129082244384, \ 0.0959172276669434, \ 0.0959172276669437, \ 0.0124129082244381, \ 0.8916698641086179, \ 0.6723403719974185, \ 0.1378581178914932, \ 0.1898015101110884, \ 0.1898015101110885, \ 0.1378581178914929, \ 0.6723403719974185, \ 0.4636054175537986, \ 0.1353361311535962, \ 0.4010584512926051, \ 0.4010584512926051, \ 0.1353361311535961, \ 0.4636054175537985, \ 0.5788906758314213, \ 0.1435267918924766, \ 0.2775825322761020, \ 0.2775825322761022, \ 0.1435267918924766, \ 0.5788906758314212, \ 0.3531888048870007, \ 0.2936223902259986, \ 0.3531888048870007, \ 0.6584300317131508, \ 0.0354515915965142, \ 0.3061183766903348, \ 0.3061183766903350, \ 0.0354515915965140, \ 0.6584300317131507, \ 0.4951059808027699, \ 0.0097880383944601, \ 0.4951059808027697, \ 0.5462922966952530, \ 0.0354185331313221, \ 0.4182891701734245, \ 0.4182891701734247, \ 0.0354185331313220, \ 0.5462922966952530, \ 0.9341803680789306, \ 0.0329098159605349, \ 0.0329098159605343, \ 0.8476962075384495, \ 0.0557938681257982, \ 0.0965099243357521, \ 0.0965099243357524, \ 0.0557938681257980, \ 0.8476962075384494, \ 0.8031840240996622, \ 0.0639762347898086, \ 0.1328397411105290, \ 0.1328397411105292, \ 0.0639762347898084, \ 0.8031840240996621, \ 0.8727730904601625, \ 0.0302625797417711, \ 0.0969643297980661, \ 0.0969643297980663, \ 0.0302625797417709, \ 0.8727730904601624, \ 0.4865637511306883, \ 0.0268724977386232, \ 0.4865637511306882, \ 0.5566086299500186, \ 0.0146376163589684, \ 0.4287537536910128, \ 0.4287537536910130, \ 0.0146376163589684, \ 0.5566086299500184, \ 0.8745699032204765, \ 0.0627150483897619, \ 0.0627150483897614, \ 0.8495413037445185, \ 0.0136052509293985, \ 0.1368534453260828, \ 0.1368534453260831, \ 0.0136052509293983, \ 0.8495413037445183, \ 0.6339620502785549, \ 0.0024760406221923, \ 0.3635619090992527, \ 0.3635619090992528, \ 0.0024760406221922, \ 0.6339620502785547, \ 0.7105128804595570, \ 0.1447435597702217, \ 0.1447435597702212, \ 0.5209304542944508, \ 0.1429259733779293, \ 0.3361435723276197, \ 0.3361435723276196, \ 0.1429259733779292, \ 0.5209304542944507, \ 0.9732707587834766, \ 0.0133646206082620, \ 0.0133646206082614, \ 0.9034803688043024, \ 0.0024207777457973, \ 0.0940988534499001, \ 0.0940988534499004, \ 0.0024207777457971, \ 0.9034803688043024, \ 0.5621390733405861, \ 0.1951503399895133, \ 0.2427105866699004, \ 0.2427105866699005, \ 0.1951503399895133, \ 0.5621390733405861, \ 0.5107064553472853, \ 0.0640551018216570, \ 0.4252384428310575, \ 0.4252384428310577, \ 0.0640551018216570, \ 0.5107064553472852, \ 0.6225342617933295, \ 0.0131876112324832, \ 0.3642781269741872, \ 0.3642781269741873, \ 0.0131876112324831, \ 0.6225342617933294, \ 0.7604631914033508, \ 0.0618730821070127, \ 0.1776637264896362, \ 0.1776637264896365, \ 0.0618730821070125, \ 0.7604631914033507, \ 0.9385418797080261, \ 0.0026124723427689, \ 0.0588456479492049, \ 0.0588456479492050, \ 0.0026124723427686, \ 0.9385418797080262, \ 0.7157099945300758, \ 0.0341904035600950, \ 0.2500996019098289, \ 0.2500996019098294, \ 0.0341904035600947, \ 0.7157099945300756, \ 0.9653765821329180, \ 0.0026508313305475, \ 0.0319725865365343, \ 0.0319725865365347, \ 0.0026508313305472, \ 0.9653765821329180, \ 0.7556844695525969, \ 0.0025915690897241, \ 0.2417239613576789, \ 0.2417239613576791, \ 0.0025915690897239, \ 0.7556844695525968, \ 0.8013219460698174, \ 0.0142733464909807, \ 0.1844047074392015, \ 0.1844047074392018, \ 0.0142733464909806, \ 0.8013219460698173, \ 0.9248872032992935, \ 0.0138564076854345, \ 0.0612563890152718, \ 0.0612563890152719, \ 0.0138564076854343, \ 0.9248872032992934, \ 0.9842490320417303, \ 0.0024938262659978, \ 0.0132571416922715, \ 0.0132571416922719, \ 0.0024938262659976, \ 0.9842490320417302, \ 0.9948701172599593, \ 0.0025649413700205, \ 0.0025649413700199, \ 0.6244555144428430, \ 0.1877722427785785, \ 0.1877722427785783, \ 0.7615859288601728, \ 0.1004409310583719, \ 0.1379731400814550, \ 0.1379731400814553, \ 0.1004409310583718, \ 0.7615859288601728, \ 0.9530968777199651, \ 0.0136974423527237, \ 0.0332056799273112, \ 0.0332056799273113, \ 0.0136974423527233, \ 0.9530968777199650, \ 0.3825643087869355, \ 0.2348713824261289, \ 0.3825643087869354, \ 0.7713906073293495, \ 0.0341431958895440, \ 0.1944661967811062, \ 0.1944661967811065, \ 0.0341431958895438, \ 0.7713906073293494, \ 0.7467127396201543, \ 0.0138046252946413, \ 0.2394826350852044, \ 0.2394826350852046, \ 0.0138046252946411, \ 0.7467127396201541, \ 0.4489485579241042, \ 0.1864972142995550, \ 0.3645542277763407, \ 0.3645542277763407, \ 0.1864972142995550, \ 0.4489485579241040, \ 0.8601018382691163, \ 0.0025417593646838, \ 0.1373564023661995, \ 0.1373564023661998, \ 0.0025417593646836, \ 0.8601018382691163, \ 0.7047330289764286, \ 0.0630349337046809, \ 0.2322320373188903, \ 0.2322320373188904, \ 0.0630349337046808, \ 0.7047330289764285, \ 0.6434616923483871, \ 0.0638769125793661, \ 0.2926613950722466, \ 0.2926613950722469, \ 0.0638769125793659, \ 0.6434616923483869, \ 0.4403990384263681, \ 0.2419528451754751, \ 0.3176481163981567, \ 0.3176481163981567, \ 0.2419528451754751, \ 0.4403990384263681, \ 0.6850991321252454, \ 0.0145992712589764, \ 0.3003015966157780, \ 0.3003015966157783, \ 0.0145992712589763, \ 0.6850991321252452, \ 0.6966205316862629, \ 0.0028181145969260, \ 0.3005613537168107, \ 0.3005613537168110, \ 0.0028181145969260, \ 0.6966205316862628, \ 0.9053415210418890, \ 0.0341344995593799, \ 0.0605239793987310, \ 0.0605239793987312, \ 0.0341344995593795, \ 0.9053415210418889, \ 0.5058586034896924, \ 0.1933554772764182, \ 0.3007859192338892, \ 0.3007859192338893, \ 0.1933554772764182, \ 0.5058586034896922, \ 0.7130863262721640, \ 0.0973629697501509, \ 0.1895507039776850, \ 0.1895507039776852, \ 0.0973629697501507, \ 0.7130863262721638, \ 0.5670717942327397, \ 0.0027883024051114, \ 0.4301399033621487, \ 0.4301399033621489, \ 0.0027883024051113, \ 0.5670717942327396, \ 0.8102254653358516, \ 0.0027559624464837, \ 0.1870185722176645, \ 0.1870185722176647, \ 0.0027559624464836, \ 0.8102254653358514, \ 0.5229833703321248, \ 0.0978271071588677, \ 0.3791895225090074, \ 0.3791895225090074, \ 0.0978271071588676, \ 0.5229833703321246, \ 0.5874593373809698, \ 0.0995736856368709, \ 0.3129669769821590, \ 0.3129669769821593, \ 0.0995736856368709, \ 0.5874593373809696, \ 0.8240811613164462, \ 0.0341143516662649, \ 0.1418044870172886, \ 0.1418044870172890, \ 0.0341143516662646, \ 0.8240811613164462, \ 0.4528922608459510, \ 0.0942154783080978, \ 0.4528922608459508, \ 0.6513210967114831, \ 0.1004974432729284, \ 0.2481814600155884, \ 0.2481814600155885, \ 0.1004974432729283, \ 0.6513210967114831, \ 0.5795283608954496, \ 0.0616738036965517, \ 0.3587978354079986, \ 0.3587978354079986, \ 0.0616738036965515, \ 0.5795283608954496, \ 0.8142659075719041, \ 0.0928670462140481, \ 0.0928670462140476, \ 0.4950301347018183, \ 0.2524849326490907, \ 0.2524849326490906 ] ) w = np.array ( [ \ 0.0030799655691816, \ 0.0030799655691816, \ 0.0030799655691816, \ 0.0024873482202465, \ 0.0024873482202465, \ 0.0024873482202465, \ 0.0039126383408176, \ 0.0039126383408176, \ 0.0039126383408176, \ 0.0039126383408176, \ 0.0039126383408176, \ 0.0039126383408176, \ 0.0006086157221808, \ 0.0006086157221808, \ 0.0006086157221808, \ 0.0058780823337592, \ 0.0058780823337592, \ 0.0058780823337592, \ 0.0026575597720771, \ 0.0026575597720771, \ 0.0026575597720771, \ 0.0026575597720771, \ 0.0026575597720771, \ 0.0026575597720771, \ 0.0010403858576164, \ 0.0010403858576164, \ 0.0010403858576164, \ 0.0010403858576164, \ 0.0010403858576164, \ 0.0010403858576164, \ 0.0038688222455242, \ 0.0038688222455242, \ 0.0038688222455242, \ 0.0038688222455242, \ 0.0038688222455242, \ 0.0038688222455242, \ 0.0054360079215851, \ 0.0054360079215851, \ 0.0054360079215851, \ 0.0054360079215851, \ 0.0054360079215851, \ 0.0054360079215851, \ 0.0051330210770134, \ 0.0051330210770134, \ 0.0051330210770134, \ 0.0051330210770134, \ 0.0051330210770134, \ 0.0051330210770134, \ 0.0068684889665150, \ 0.0068684889665150, \ 0.0068684889665150, \ 0.0027248852604065, \ 0.0027248852604065, \ 0.0027248852604065, \ 0.0027248852604065, \ 0.0027248852604065, \ 0.0027248852604065, \ 0.0016143072439158, \ 0.0016143072439158, \ 0.0016143072439158, \ 0.0030819278277026, \ 0.0030819278277026, \ 0.0030819278277026, \ 0.0030819278277026, \ 0.0030819278277026, \ 0.0030819278277026, \ 0.0010836224292710, \ 0.0010836224292710, \ 0.0010836224292710, \ 0.0021960146608965, \ 0.0021960146608965, \ 0.0021960146608965, \ 0.0021960146608965, \ 0.0021960146608965, \ 0.0021960146608965, \ 0.0027071716291895, \ 0.0027071716291895, \ 0.0027071716291895, \ 0.0027071716291895, \ 0.0027071716291895, \ 0.0027071716291895, \ 0.0017732505663030, \ 0.0017732505663030, \ 0.0017732505663030, \ 0.0017732505663030, \ 0.0017732505663030, \ 0.0017732505663030, \ 0.0027166050682952, \ 0.0027166050682952, \ 0.0027166050682952, \ 0.0021194095320856, \ 0.0021194095320856, \ 0.0021194095320856, \ 0.0021194095320856, \ 0.0021194095320856, \ 0.0021194095320856, \ 0.0020243293045497, \ 0.0020243293045497, \ 0.0020243293045497, \ 0.0013822658273997, \ 0.0013822658273997, \ 0.0013822658273997, \ 0.0013822658273997, \ 0.0013822658273997, \ 0.0013822658273997, \ 0.0008287796022760, \ 0.0008287796022760, \ 0.0008287796022760, \ 0.0008287796022760, \ 0.0008287796022760, \ 0.0008287796022760, \ 0.0042454319210643, \ 0.0042454319210643, \ 0.0042454319210643, \ 0.0057609299703683, \ 0.0057609299703683, \ 0.0057609299703683, \ 0.0057609299703683, \ 0.0057609299703683, \ 0.0057609299703683, \ 0.0004721021055792, \ 0.0004721021055792, \ 0.0004721021055792, \ 0.0004866406535789, \ 0.0004866406535789, \ 0.0004866406535789, \ 0.0004866406535789, \ 0.0004866406535789, \ 0.0004866406535789, \ 0.0060611706044967, \ 0.0060611706044967, \ 0.0060611706044967, \ 0.0060611706044967, \ 0.0060611706044967, \ 0.0060611706044967, \ 0.0039591603530013, \ 0.0039591603530013, \ 0.0039591603530013, \ 0.0039591603530013, \ 0.0039591603530013, \ 0.0039591603530013, \ 0.0019515305614847, \ 0.0019515305614847, \ 0.0019515305614847, \ 0.0019515305614847, \ 0.0019515305614847, \ 0.0019515305614847, \ 0.0031758640195785, \ 0.0031758640195785, \ 0.0031758640195785, \ 0.0031758640195785, \ 0.0031758640195785, \ 0.0031758640195785, \ 0.0004177689784025, \ 0.0004177689784025, \ 0.0004177689784025, \ 0.0004177689784025, \ 0.0004177689784025, \ 0.0004177689784025, \ 0.0028037985130037, \ 0.0028037985130037, \ 0.0028037985130037, \ 0.0028037985130037, \ 0.0028037985130037, \ 0.0028037985130037, \ 0.0003074323001241, \ 0.0003074323001241, \ 0.0003074323001241, \ 0.0003074323001241, \ 0.0003074323001241, \ 0.0003074323001241, \ 0.0007580478745157, \ 0.0007580478745157, \ 0.0007580478745157, \ 0.0007580478745157, \ 0.0007580478745157, \ 0.0007580478745157, \ 0.0016285601871914, \ 0.0016285601871914, \ 0.0016285601871914, \ 0.0016285601871914, \ 0.0016285601871914, \ 0.0016285601871914, \ 0.0010015815151317, \ 0.0010015815151317, \ 0.0010015815151317, \ 0.0010015815151317, \ 0.0010015815151317, \ 0.0010015815151317, \ 0.0001897035092211, \ 0.0001897035092211, \ 0.0001897035092211, \ 0.0001897035092211, \ 0.0001897035092211, \ 0.0001897035092211, \ 0.0000857325766799, \ 0.0000857325766799, \ 0.0000857325766799, \ 0.0053352753423962, \ 0.0053352753423962, \ 0.0053352753423962, \ 0.0039225937188264, \ 0.0039225937188264, \ 0.0039225937188264, \ 0.0039225937188264, \ 0.0039225937188264, \ 0.0039225937188264, \ 0.0007352644490711, \ 0.0007352644490711, \ 0.0007352644490711, \ 0.0007352644490711, \ 0.0007352644490711, \ 0.0007352644490711, \ 0.0069496808690566, \ 0.0069496808690566, \ 0.0069496808690566, \ 0.0026277500982666, \ 0.0026277500982666, \ 0.0026277500982666, \ 0.0026277500982666, \ 0.0026277500982666, \ 0.0026277500982666, \ 0.0018416339190279, \ 0.0018416339190279, \ 0.0018416339190279, \ 0.0018416339190279, \ 0.0018416339190279, \ 0.0018416339190279, \ 0.0059250327726738, \ 0.0059250327726738, \ 0.0059250327726738, \ 0.0059250327726738, \ 0.0059250327726738, \ 0.0059250327726738, \ 0.0006123388408143, \ 0.0006123388408143, \ 0.0006123388408143, \ 0.0006123388408143, \ 0.0006123388408143, \ 0.0006123388408143, \ 0.0038249634484789, \ 0.0038249634484789, \ 0.0038249634484789, \ 0.0038249634484789, \ 0.0038249634484789, \ 0.0038249634484789, \ 0.0041283032222063, \ 0.0041283032222063, \ 0.0041283032222063, \ 0.0041283032222063, \ 0.0041283032222063, \ 0.0041283032222063, \ 0.0066920320417412, \ 0.0066920320417412, \ 0.0066920320417412, \ 0.0066920320417412, \ 0.0066920320417412, \ 0.0066920320417412, \ 0.0020472829473930, \ 0.0020472829473930, \ 0.0020472829473930, \ 0.0020472829473930, \ 0.0020472829473930, \ 0.0020472829473930, \ 0.0008780156791651, \ 0.0008780156791651, \ 0.0008780156791651, \ 0.0008780156791651, \ 0.0008780156791651, \ 0.0008780156791651, \ 0.0015777851185459, \ 0.0015777851185459, \ 0.0015777851185459, \ 0.0015777851185459, \ 0.0015777851185459, \ 0.0015777851185459, \ 0.0063074359109884, \ 0.0063074359109884, \ 0.0063074359109884, \ 0.0063074359109884, \ 0.0063074359109884, \ 0.0063074359109884, \ 0.0042726398210532, \ 0.0042726398210532, \ 0.0042726398210532, \ 0.0042726398210532, \ 0.0042726398210532, \ 0.0042726398210532, \ 0.0009698373462393, \ 0.0009698373462393, \ 0.0009698373462393, \ 0.0009698373462393, \ 0.0009698373462393, \ 0.0009698373462393, \ 0.0007380182704579, \ 0.0007380182704579, \ 0.0007380182704579, \ 0.0007380182704579, \ 0.0007380182704579, \ 0.0007380182704579, \ 0.0052618813601275, \ 0.0052618813601275, \ 0.0052618813601275, \ 0.0052618813601275, \ 0.0052618813601275, \ 0.0052618813601275, \ 0.0053002719749983, \ 0.0053002719749983, \ 0.0053002719749983, \ 0.0053002719749983, \ 0.0053002719749983, \ 0.0053002719749983, \ 0.0024558010102792, \ 0.0024558010102792, \ 0.0024558010102792, \ 0.0024558010102792, \ 0.0024558010102792, \ 0.0024558010102792, \ 0.0053328054204010, \ 0.0053328054204010, \ 0.0053328054204010, \ 0.0050556103951577, \ 0.0050556103951577, \ 0.0050556103951577, \ 0.0050556103951577, \ 0.0050556103951577, \ 0.0050556103951577, \ 0.0044341909691302, \ 0.0044341909691302, \ 0.0044341909691302, \ 0.0044341909691302, \ 0.0044341909691302, \ 0.0044341909691302, \ 0.0032907061458540, \ 0.0032907061458540, \ 0.0032907061458540, \ 0.0073142091431203, \ 0.0073142091431203, \ 0.0073142091431203 ] ) return a, b, c, w def rule44 ( ): #*****************************************************************************80 # ## rule44() returns the rule of precision 44. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.0017123075799637, \ 0.9965753848400722, \ 0.0017123075799641, \ 0.0197551676157197, \ 0.9694881128275959, \ 0.0107567195566844, \ 0.9694881128275961, \ 0.0197551676157198, \ 0.0107567195566840, \ 0.0995165813818446, \ 0.8997028327182934, \ 0.0007805858998620, \ 0.8997028327182934, \ 0.0995165813818448, \ 0.0007805858998617, \ 0.1534945447552139, \ 0.8445671223319955, \ 0.0019383329127907, \ 0.8445671223319955, \ 0.1534945447552140, \ 0.0019383329127904, \ 0.4606074520039989, \ 0.5376064055154758, \ 0.0017861424805254, \ 0.5376064055154757, \ 0.4606074520039989, \ 0.0017861424805253, \ 0.0296420604264444, \ 0.9686037144025027, \ 0.0017542251710529, \ 0.9686037144025029, \ 0.0296420604264444, \ 0.0017542251710524, \ 0.3338406248248118, \ 0.6656420809155281, \ 0.0005172942596601, \ 0.6656420809155281, \ 0.3338406248248119, \ 0.0005172942596599, \ 0.0291673514653005, \ 0.9416652970693987, \ 0.0291673514653009, \ 0.0495499879123024, \ 0.9009000241753948, \ 0.0495499879123029, \ 0.1194266872274120, \ 0.8730274418468819, \ 0.0075458709257062, \ 0.8730274418468820, \ 0.1194266872274120, \ 0.0075458709257059, \ 0.1733118066994289, \ 0.8151956468477657, \ 0.0114925464528055, \ 0.8151956468477658, \ 0.1733118066994291, \ 0.0114925464528051, \ 0.0593978633857566, \ 0.9163391688931388, \ 0.0242629677211046, \ 0.9163391688931388, \ 0.0593978633857567, \ 0.0242629677211044, \ 0.2594461646278431, \ 0.7307561420696972, \ 0.0097976933024596, \ 0.7307561420696972, \ 0.2594461646278433, \ 0.0097976933024595, \ 0.2696648795311178, \ 0.7284359696406738, \ 0.0018991508282084, \ 0.7284359696406739, \ 0.2696648795311180, \ 0.0018991508282082, \ 0.3234284104109564, \ 0.6688969097328992, \ 0.0076746798561443, \ 0.6688969097328992, \ 0.3234284104109564, \ 0.0076746798561442, \ 0.2093976094351925, \ 0.7878951862570389, \ 0.0027072043077686, \ 0.7878951862570389, \ 0.2093976094351925, \ 0.0027072043077684, \ 0.0107937373867395, \ 0.9864998660560905, \ 0.0027063965571701, \ 0.9864998660560905, \ 0.0107937373867397, \ 0.0027063965571697, \ 0.0416577600266789, \ 0.9478795059436815, \ 0.0104627340296397, \ 0.9478795059436816, \ 0.0416577600266790, \ 0.0104627340296393, \ 0.1393007744184822, \ 0.8391863652965978, \ 0.0215128602849200, \ 0.8391863652965978, \ 0.1393007744184823, \ 0.0215128602849197, \ 0.4877239805831534, \ 0.4877239805831534, \ 0.0245520388336932, \ 0.0971407574555291, \ 0.8800347069095190, \ 0.0228245356349520, \ 0.8800347069095190, \ 0.0971407574555291, \ 0.0228245356349517, \ 0.1511248097389706, \ 0.7487866599562394, \ 0.1000885303047901, \ 0.7487866599562394, \ 0.1511248097389706, \ 0.1000885303047898, \ 0.4960618044654749, \ 0.4960618044654750, \ 0.0078763910690500, \ 0.3939323955351545, \ 0.6029080349282100, \ 0.0031595695366355, \ 0.6029080349282100, \ 0.3939323955351544, \ 0.0031595695366353, \ 0.1276374594173248, \ 0.8287949653018399, \ 0.0435675752808352, \ 0.8287949653018402, \ 0.1276374594173247, \ 0.0435675752808349, \ 0.2153427859170523, \ 0.7218418378371082, \ 0.0628153762458395, \ 0.7218418378371081, \ 0.2153427859170524, \ 0.0628153762458394, \ 0.1805238872560285, \ 0.7847849261270403, \ 0.0346911866169312, \ 0.7847849261270403, \ 0.1805238872560286, \ 0.0346911866169310, \ 0.3706974787497283, \ 0.6133503854822405, \ 0.0159521357680312, \ 0.6133503854822404, \ 0.3706974787497284, \ 0.0159521357680310, \ 0.2389043466345939, \ 0.7245299623844421, \ 0.0365656909809640, \ 0.7245299623844421, \ 0.2389043466345939, \ 0.0365656909809638, \ 0.0765961156051737, \ 0.8468077687896521, \ 0.0765961156051742, \ 0.4035445047649169, \ 0.4735882468281119, \ 0.1228672484069711, \ 0.4735882468281119, \ 0.4035445047649169, \ 0.1228672484069711, \ 0.2510886184010617, \ 0.6268501895654275, \ 0.1220611920335108, \ 0.6268501895654275, \ 0.2510886184010617, \ 0.1220611920335106, \ 0.3100924603530019, \ 0.6020796526141913, \ 0.0878278870328068, \ 0.6020796526141913, \ 0.3100924603530019, \ 0.0878278870328066, \ 0.4171889370681111, \ 0.5171299598756924, \ 0.0656811030561965, \ 0.5171299598756924, \ 0.4171889370681111, \ 0.0656811030561964, \ 0.4759518460527712, \ 0.4759518460527714, \ 0.0480963078944574, \ 0.0842771975158688, \ 0.8700026552993007, \ 0.0457201471848306, \ 0.8700026552993007, \ 0.0842771975158688, \ 0.0457201471848303, \ 0.2875172818904952, \ 0.6596793072144378, \ 0.0528034108950670, \ 0.6596793072144378, \ 0.2875172818904952, \ 0.0528034108950669, \ 0.1090955419572377, \ 0.7818089160855244, \ 0.1090955419572380, \ 0.3421421849069924, \ 0.6245951075427290, \ 0.0332627075502785, \ 0.6245951075427290, \ 0.3421421849069924, \ 0.0332627075502785, \ 0.2312470036938409, \ 0.5375059926123180, \ 0.2312470036938411, \ 0.1959081982236505, \ 0.6081836035526987, \ 0.1959081982236506, \ 0.2907813356274843, \ 0.6861277132074860, \ 0.0230909511650299, \ 0.6861277132074859, \ 0.2907813356274844, \ 0.0230909511650297, \ 0.0777385297161003, \ 0.9138493473952539, \ 0.0084121228886461, \ 0.9138493473952539, \ 0.0777385297161003, \ 0.0084121228886456, \ 0.0583538087981567, \ 0.9397903465114041, \ 0.0018558446904393, \ 0.9397903465114043, \ 0.0583538087981568, \ 0.0018558446904388, \ 0.3537362173911874, \ 0.4944025611096592, \ 0.1518612214991533, \ 0.4944025611096592, \ 0.3537362173911875, \ 0.1518612214991532, \ 0.1941036834219221, \ 0.6592024700825740, \ 0.1466938464955038, \ 0.6592024700825740, \ 0.1941036834219222, \ 0.1466938464955036, \ 0.1152446802620743, \ 0.8116970473144409, \ 0.0730582724234849, \ 0.8116970473144409, \ 0.1152446802620743, \ 0.0730582724234846, \ 0.2526489188568274, \ 0.6640305665631259, \ 0.0833205145800467, \ 0.6640305665631260, \ 0.2526489188568274, \ 0.0833205145800466, \ 0.3706381279110351, \ 0.5316917725696112, \ 0.0976700995193537, \ 0.5316917725696112, \ 0.3706381279110351, \ 0.0976700995193536, \ 0.1975107662353285, \ 0.7003617605288512, \ 0.1021274732358203, \ 0.7003617605288514, \ 0.1975107662353285, \ 0.1021274732358200, \ 0.2191021787766396, \ 0.7639576985765668, \ 0.0169401226467936, \ 0.7639576985765668, \ 0.2191021787766396, \ 0.0169401226467933, \ 0.1647494714555341, \ 0.7706431138900716, \ 0.0646074146543943, \ 0.7706431138900717, \ 0.1647494714555343, \ 0.0646074146543940, \ 0.3487568874306149, \ 0.4569496207074597, \ 0.1942934918619253, \ 0.4569496207074596, \ 0.3487568874306151, \ 0.1942934918619253, \ 0.3558533300586623, \ 0.5853570821660166, \ 0.0587895877753212, \ 0.5853570821660165, \ 0.3558533300586624, \ 0.0587895877753211, \ 0.3487165289854694, \ 0.4076984951293575, \ 0.2435849758851730, \ 0.4076984951293575, \ 0.3487165289854693, \ 0.2435849758851730, \ 0.4223218082071514, \ 0.4223218082071514, \ 0.1553563835856973, \ 0.4548817499595059, \ 0.4548817499595060, \ 0.0902365000809880, \ 0.2907043355496960, \ 0.5231696984941406, \ 0.1861259659561632, \ 0.5231696984941406, \ 0.2907043355496960, \ 0.1861259659561631, \ 0.1439001195404208, \ 0.7121997609191582, \ 0.1439001195404210, \ 0.2898629348171137, \ 0.4717800456303300, \ 0.2383570195525562, \ 0.4717800456303302, \ 0.2898629348171137, \ 0.2383570195525561, \ 0.4023404478547354, \ 0.4023404478547353, \ 0.1953191042905292, \ 0.3093835754454580, \ 0.5593868077625690, \ 0.1312296167919730, \ 0.5593868077625690, \ 0.3093835754454579, \ 0.1312296167919728, \ 0.2469795390992444, \ 0.5845614823482763, \ 0.1684589785524792, \ 0.5845614823482763, \ 0.2469795390992445, \ 0.1684589785524790, \ 0.4353451951214652, \ 0.5515293353673113, \ 0.0131254695112235, \ 0.5515293353673113, \ 0.4353451951214652, \ 0.0131254695112233, \ 0.2942957656908339, \ 0.4114084686183320, \ 0.2942957656908339, \ 0.3516157887957689, \ 0.3516157887957689, \ 0.2967684224084619, \ 0.4137012893148831, \ 0.5518852701665368, \ 0.0344134405185802, \ 0.5518852701665367, \ 0.4137012893148831, \ 0.0344134405185801 ] ) b = np.array ( [ \ 0.0017123075799640, \ 0.0017123075799637, \ 0.9965753848400725, \ 0.0107567195566843, \ 0.0197551676157197, \ 0.9694881128275962, \ 0.0107567195566843, \ 0.9694881128275962, \ 0.0197551676157201, \ 0.0007805858998619, \ 0.0995165813818446, \ 0.8997028327182935, \ 0.0007805858998619, \ 0.8997028327182935, \ 0.0995165813818450, \ 0.0019383329127906, \ 0.1534945447552139, \ 0.8445671223319957, \ 0.0019383329127906, \ 0.8445671223319957, \ 0.1534945447552142, \ 0.0017861424805254, \ 0.4606074520039989, \ 0.5376064055154759, \ 0.0017861424805254, \ 0.5376064055154758, \ 0.4606074520039992, \ 0.0017542251710528, \ 0.0296420604264444, \ 0.9686037144025029, \ 0.0017542251710528, \ 0.9686037144025031, \ 0.0296420604264447, \ 0.0005172942596601, \ 0.3338406248248119, \ 0.6656420809155283, \ 0.0005172942596601, \ 0.6656420809155282, \ 0.3338406248248121, \ 0.0291673514653008, \ 0.0291673514653005, \ 0.9416652970693989, \ 0.0495499879123027, \ 0.0495499879123024, \ 0.9009000241753949, \ 0.0075458709257061, \ 0.1194266872274120, \ 0.8730274418468821, \ 0.0075458709257061, \ 0.8730274418468821, \ 0.1194266872274123, \ 0.0114925464528053, \ 0.1733118066994289, \ 0.8151956468477658, \ 0.0114925464528053, \ 0.8151956468477658, \ 0.1733118066994292, \ 0.0242629677211045, \ 0.0593978633857566, \ 0.9163391688931390, \ 0.0242629677211045, \ 0.9163391688931390, \ 0.0593978633857569, \ 0.0097976933024596, \ 0.2594461646278432, \ 0.7307561420696975, \ 0.0097976933024596, \ 0.7307561420696972, \ 0.2594461646278435, \ 0.0018991508282083, \ 0.2696648795311178, \ 0.7284359696406740, \ 0.0018991508282083, \ 0.7284359696406739, \ 0.2696648795311181, \ 0.0076746798561443, \ 0.3234284104109565, \ 0.6688969097328994, \ 0.0076746798561443, \ 0.6688969097328994, \ 0.3234284104109568, \ 0.0027072043077686, \ 0.2093976094351925, \ 0.7878951862570391, \ 0.0027072043077686, \ 0.7878951862570391, \ 0.2093976094351928, \ 0.0027063965571699, \ 0.0107937373867395, \ 0.9864998660560906, \ 0.0027063965571699, \ 0.9864998660560906, \ 0.0107937373867399, \ 0.0104627340296395, \ 0.0416577600266789, \ 0.9478795059436816, \ 0.0104627340296395, \ 0.9478795059436816, \ 0.0416577600266793, \ 0.0215128602849199, \ 0.1393007744184823, \ 0.8391863652965980, \ 0.0215128602849199, \ 0.8391863652965980, \ 0.1393007744184826, \ 0.0245520388336933, \ 0.4877239805831535, \ 0.4877239805831536, \ 0.0228245356349520, \ 0.0971407574555291, \ 0.8800347069095191, \ 0.0228245356349520, \ 0.8800347069095191, \ 0.0971407574555294, \ 0.1000885303047900, \ 0.1511248097389706, \ 0.7487866599562395, \ 0.1000885303047900, \ 0.7487866599562395, \ 0.1511248097389709, \ 0.0078763910690501, \ 0.4960618044654750, \ 0.4960618044654752, \ 0.0031595695366355, \ 0.3939323955351545, \ 0.6029080349282102, \ 0.0031595695366355, \ 0.6029080349282102, \ 0.3939323955351547, \ 0.0435675752808352, \ 0.1276374594173248, \ 0.8287949653018403, \ 0.0435675752808352, \ 0.8287949653018403, \ 0.1276374594173251, \ 0.0628153762458396, \ 0.2153427859170523, \ 0.7218418378371083, \ 0.0628153762458396, \ 0.7218418378371083, \ 0.2153427859170526, \ 0.0346911866169312, \ 0.1805238872560285, \ 0.7847849261270404, \ 0.0346911866169312, \ 0.7847849261270404, \ 0.1805238872560288, \ 0.0159521357680312, \ 0.3706974787497284, \ 0.6133503854822406, \ 0.0159521357680312, \ 0.6133503854822405, \ 0.3706974787497286, \ 0.0365656909809640, \ 0.2389043466345939, \ 0.7245299623844423, \ 0.0365656909809640, \ 0.7245299623844423, \ 0.2389043466345942, \ 0.0765961156051741, \ 0.0765961156051737, \ 0.8468077687896522, \ 0.1228672484069712, \ 0.4035445047649170, \ 0.4735882468281121, \ 0.1228672484069712, \ 0.4735882468281120, \ 0.4035445047649171, \ 0.1220611920335108, \ 0.2510886184010618, \ 0.6268501895654277, \ 0.1220611920335108, \ 0.6268501895654277, \ 0.2510886184010619, \ 0.0878278870328068, \ 0.3100924603530020, \ 0.6020796526141915, \ 0.0878278870328068, \ 0.6020796526141915, \ 0.3100924603530022, \ 0.0656811030561965, \ 0.4171889370681111, \ 0.5171299598756927, \ 0.0656811030561965, \ 0.5171299598756924, \ 0.4171889370681113, \ 0.0480963078944575, \ 0.4759518460527713, \ 0.4759518460527715, \ 0.0457201471848306, \ 0.0842771975158688, \ 0.8700026552993009, \ 0.0457201471848306, \ 0.8700026552993009, \ 0.0842771975158691, \ 0.0528034108950670, \ 0.2875172818904953, \ 0.6596793072144379, \ 0.0528034108950670, \ 0.6596793072144379, \ 0.2875172818904955, \ 0.1090955419572379, \ 0.1090955419572376, \ 0.7818089160855246, \ 0.0332627075502786, \ 0.3421421849069925, \ 0.6245951075427292, \ 0.0332627075502786, \ 0.6245951075427292, \ 0.3421421849069927, \ 0.2312470036938411, \ 0.2312470036938410, \ 0.5375059926123180, \ 0.1959081982236507, \ 0.1959081982236506, \ 0.6081836035526990, \ 0.0230909511650298, \ 0.2907813356274843, \ 0.6861277132074860, \ 0.0230909511650298, \ 0.6861277132074860, \ 0.2907813356274845, \ 0.0084121228886458, \ 0.0777385297161002, \ 0.9138493473952539, \ 0.0084121228886458, \ 0.9138493473952539, \ 0.0777385297161006, \ 0.0018558446904391, \ 0.0583538087981567, \ 0.9397903465114043, \ 0.0018558446904391, \ 0.9397903465114043, \ 0.0583538087981571, \ 0.1518612214991534, \ 0.3537362173911875, \ 0.4944025611096594, \ 0.1518612214991534, \ 0.4944025611096593, \ 0.3537362173911877, \ 0.1466938464955038, \ 0.1941036834219222, \ 0.6592024700825742, \ 0.1466938464955038, \ 0.6592024700825742, \ 0.1941036834219224, \ 0.0730582724234848, \ 0.1152446802620743, \ 0.8116970473144410, \ 0.0730582724234848, \ 0.8116970473144410, \ 0.1152446802620745, \ 0.0833205145800467, \ 0.2526489188568274, \ 0.6640305665631261, \ 0.0833205145800467, \ 0.6640305665631261, \ 0.2526489188568276, \ 0.0976700995193538, \ 0.3706381279110351, \ 0.5316917725696113, \ 0.0976700995193538, \ 0.5316917725696113, \ 0.3706381279110353, \ 0.1021274732358202, \ 0.1975107662353285, \ 0.7003617605288514, \ 0.1021274732358202, \ 0.7003617605288514, \ 0.1975107662353287, \ 0.0169401226467935, \ 0.2191021787766396, \ 0.7639576985765670, \ 0.0169401226467935, \ 0.7639576985765670, \ 0.2191021787766399, \ 0.0646074146543942, \ 0.1647494714555342, \ 0.7706431138900717, \ 0.0646074146543942, \ 0.7706431138900717, \ 0.1647494714555344, \ 0.1942934918619254, \ 0.3487568874306151, \ 0.4569496207074598, \ 0.1942934918619254, \ 0.4569496207074597, \ 0.3487568874306152, \ 0.0587895877753212, \ 0.3558533300586624, \ 0.5853570821660167, \ 0.0587895877753212, \ 0.5853570821660166, \ 0.3558533300586625, \ 0.2435849758851731, \ 0.3487165289854695, \ 0.4076984951293576, \ 0.2435849758851731, \ 0.4076984951293576, \ 0.3487165289854696, \ 0.1553563835856973, \ 0.4223218082071514, \ 0.4223218082071515, \ 0.0902365000809881, \ 0.4548817499595060, \ 0.4548817499595061, \ 0.1861259659561633, \ 0.2907043355496962, \ 0.5231696984941409, \ 0.1861259659561633, \ 0.5231696984941409, \ 0.2907043355496963, \ 0.1439001195404211, \ 0.1439001195404208, \ 0.7121997609191584, \ 0.2383570195525562, \ 0.2898629348171138, \ 0.4717800456303302, \ 0.2383570195525562, \ 0.4717800456303302, \ 0.2898629348171138, \ 0.1953191042905293, \ 0.4023404478547354, \ 0.4023404478547355, \ 0.1312296167919730, \ 0.3093835754454580, \ 0.5593868077625692, \ 0.1312296167919730, \ 0.5593868077625692, \ 0.3093835754454582, \ 0.1684589785524792, \ 0.2469795390992445, \ 0.5845614823482764, \ 0.1684589785524792, \ 0.5845614823482764, \ 0.2469795390992447, \ 0.0131254695112235, \ 0.4353451951214652, \ 0.5515293353673115, \ 0.0131254695112235, \ 0.5515293353673113, \ 0.4353451951214655, \ 0.2942957656908340, \ 0.2942957656908340, \ 0.4114084686183322, \ 0.2967684224084621, \ 0.3516157887957691, \ 0.3516157887957691, \ 0.0344134405185802, \ 0.4137012893148831, \ 0.5518852701665369, \ 0.0344134405185802, \ 0.5518852701665368, \ 0.4137012893148834 ] ) c = np.array ( [ \ 0.9965753848400724, \ 0.0017123075799641, \ 0.0017123075799634, \ 0.9694881128275959, \ 0.0107567195566844, \ 0.0197551676157194, \ 0.0197551676157196, \ 0.0107567195566841, \ 0.9694881128275959, \ 0.8997028327182934, \ 0.0007805858998619, \ 0.0995165813818445, \ 0.0995165813818446, \ 0.0007805858998616, \ 0.8997028327182933, \ 0.8445671223319956, \ 0.0019383329127906, \ 0.1534945447552136, \ 0.1534945447552139, \ 0.0019383329127903, \ 0.8445671223319955, \ 0.5376064055154757, \ 0.0017861424805253, \ 0.4606074520039987, \ 0.4606074520039989, \ 0.0017861424805253, \ 0.5376064055154756, \ 0.9686037144025029, \ 0.0017542251710529, \ 0.0296420604264441, \ 0.0296420604264443, \ 0.0017542251710524, \ 0.9686037144025029, \ 0.6656420809155281, \ 0.0005172942596600, \ 0.3338406248248116, \ 0.3338406248248118, \ 0.0005172942596600, \ 0.6656420809155280, \ 0.9416652970693987, \ 0.0291673514653008, \ 0.0291673514653003, \ 0.9009000241753948, \ 0.0495499879123028, \ 0.0495499879123021, \ 0.8730274418468819, \ 0.0075458709257062, \ 0.1194266872274118, \ 0.1194266872274119, \ 0.0075458709257060, \ 0.8730274418468817, \ 0.8151956468477658, \ 0.0114925464528054, \ 0.1733118066994287, \ 0.1733118066994289, \ 0.0114925464528052, \ 0.8151956468477657, \ 0.9163391688931388, \ 0.0242629677211045, \ 0.0593978633857564, \ 0.0593978633857566, \ 0.0242629677211043, \ 0.9163391688931387, \ 0.7307561420696972, \ 0.0097976933024596, \ 0.2594461646278429, \ 0.2594461646278431, \ 0.0097976933024596, \ 0.7307561420696971, \ 0.7284359696406738, \ 0.0018991508282084, \ 0.2696648795311175, \ 0.2696648795311177, \ 0.0018991508282081, \ 0.7284359696406737, \ 0.6688969097328993, \ 0.0076746798561443, \ 0.3234284104109563, \ 0.3234284104109565, \ 0.0076746798561442, \ 0.6688969097328989, \ 0.7878951862570389, \ 0.0027072043077686, \ 0.2093976094351923, \ 0.2093976094351925, \ 0.0027072043077684, \ 0.7878951862570389, \ 0.9864998660560906, \ 0.0027063965571700, \ 0.0107937373867393, \ 0.0107937373867396, \ 0.0027063965571696, \ 0.9864998660560905, \ 0.9478795059436815, \ 0.0104627340296396, \ 0.0416577600266786, \ 0.0416577600266789, \ 0.0104627340296394, \ 0.9478795059436814, \ 0.8391863652965978, \ 0.0215128602849199, \ 0.1393007744184821, \ 0.1393007744184823, \ 0.0215128602849198, \ 0.8391863652965976, \ 0.4877239805831534, \ 0.0245520388336932, \ 0.4877239805831531, \ 0.8800347069095189, \ 0.0228245356349519, \ 0.0971407574555289, \ 0.0971407574555290, \ 0.0228245356349518, \ 0.8800347069095188, \ 0.7487866599562394, \ 0.1000885303047900, \ 0.1511248097389705, \ 0.1511248097389706, \ 0.1000885303047899, \ 0.7487866599562393, \ 0.4960618044654749, \ 0.0078763910690500, \ 0.4960618044654748, \ 0.6029080349282100, \ 0.0031595695366355, \ 0.3939323955351542, \ 0.3939323955351545, \ 0.0031595695366354, \ 0.6029080349282099, \ 0.8287949653018400, \ 0.0435675752808353, \ 0.1276374594173245, \ 0.1276374594173247, \ 0.0435675752808350, \ 0.8287949653018400, \ 0.7218418378371082, \ 0.0628153762458395, \ 0.2153427859170521, \ 0.2153427859170524, \ 0.0628153762458393, \ 0.7218418378371080, \ 0.7847849261270403, \ 0.0346911866169312, \ 0.1805238872560283, \ 0.1805238872560285, \ 0.0346911866169309, \ 0.7847849261270403, \ 0.6133503854822404, \ 0.0159521357680311, \ 0.3706974787497281, \ 0.3706974787497284, \ 0.0159521357680311, \ 0.6133503854822404, \ 0.7245299623844421, \ 0.0365656909809640, \ 0.2389043466345937, \ 0.2389043466345939, \ 0.0365656909809637, \ 0.7245299623844421, \ 0.8468077687896521, \ 0.0765961156051742, \ 0.0765961156051735, \ 0.4735882468281119, \ 0.1228672484069712, \ 0.4035445047649167, \ 0.4035445047649169, \ 0.1228672484069712, \ 0.4735882468281118, \ 0.6268501895654275, \ 0.1220611920335107, \ 0.2510886184010614, \ 0.2510886184010617, \ 0.1220611920335106, \ 0.6268501895654275, \ 0.6020796526141913, \ 0.0878278870328068, \ 0.3100924603530018, \ 0.3100924603530019, \ 0.0878278870328065, \ 0.6020796526141912, \ 0.5171299598756924, \ 0.0656811030561965, \ 0.4171889370681109, \ 0.4171889370681111, \ 0.0656811030561965, \ 0.5171299598756923, \ 0.4759518460527713, \ 0.0480963078944573, \ 0.4759518460527711, \ 0.8700026552993007, \ 0.0457201471848306, \ 0.0842771975158686, \ 0.0842771975158688, \ 0.0457201471848304, \ 0.8700026552993005, \ 0.6596793072144378, \ 0.0528034108950669, \ 0.2875172818904951, \ 0.2875172818904952, \ 0.0528034108950669, \ 0.6596793072144376, \ 0.7818089160855244, \ 0.1090955419572380, \ 0.1090955419572374, \ 0.6245951075427290, \ 0.0332627075502785, \ 0.3421421849069923, \ 0.3421421849069924, \ 0.0332627075502784, \ 0.6245951075427288, \ 0.5375059926123179, \ 0.2312470036938410, \ 0.2312470036938409, \ 0.6081836035526988, \ 0.1959081982236507, \ 0.1959081982236505, \ 0.6861277132074860, \ 0.0230909511650297, \ 0.2907813356274841, \ 0.2907813356274843, \ 0.0230909511650296, \ 0.6861277132074858, \ 0.9138493473952539, \ 0.0084121228886459, \ 0.0777385297161001, \ 0.0777385297161002, \ 0.0084121228886457, \ 0.9138493473952537, \ 0.9397903465114041, \ 0.0018558446904391, \ 0.0583538087981564, \ 0.0583538087981567, \ 0.0018558446904390, \ 0.9397903465114040, \ 0.4944025611096592, \ 0.1518612214991533, \ 0.3537362173911873, \ 0.3537362173911874, \ 0.1518612214991532, \ 0.4944025611096591, \ 0.6592024700825742, \ 0.1466938464955038, \ 0.1941036834219220, \ 0.1941036834219222, \ 0.1466938464955035, \ 0.6592024700825739, \ 0.8116970473144409, \ 0.0730582724234848, \ 0.1152446802620740, \ 0.1152446802620743, \ 0.0730582724234846, \ 0.8116970473144408, \ 0.6640305665631259, \ 0.0833205145800467, \ 0.2526489188568272, \ 0.2526489188568273, \ 0.0833205145800465, \ 0.6640305665631258, \ 0.5316917725696111, \ 0.0976700995193537, \ 0.3706381279110349, \ 0.3706381279110350, \ 0.0976700995193536, \ 0.5316917725696111, \ 0.7003617605288512, \ 0.1021274732358203, \ 0.1975107662353283, \ 0.1975107662353284, \ 0.1021274732358201, \ 0.7003617605288512, \ 0.7639576985765669, \ 0.0169401226467936, \ 0.2191021787766394, \ 0.2191021787766397, \ 0.0169401226467933, \ 0.7639576985765668, \ 0.7706431138900716, \ 0.0646074146543943, \ 0.1647494714555340, \ 0.1647494714555341, \ 0.0646074146543941, \ 0.7706431138900716, \ 0.4569496207074596, \ 0.1942934918619252, \ 0.3487568874306149, \ 0.3487568874306150, \ 0.1942934918619252, \ 0.4569496207074596, \ 0.5853570821660165, \ 0.0587895877753211, \ 0.3558533300586620, \ 0.3558533300586623, \ 0.0587895877753211, \ 0.5853570821660163, \ 0.4076984951293574, \ 0.2435849758851730, \ 0.3487165289854693, \ 0.3487165289854693, \ 0.2435849758851731, \ 0.4076984951293575, \ 0.4223218082071513, \ 0.1553563835856972, \ 0.4223218082071513, \ 0.4548817499595059, \ 0.0902365000809880, \ 0.4548817499595058, \ 0.5231696984941406, \ 0.1861259659561632, \ 0.2907043355496960, \ 0.2907043355496961, \ 0.1861259659561630, \ 0.5231696984941407, \ 0.7121997609191582, \ 0.1439001195404210, \ 0.1439001195404206, \ 0.4717800456303301, \ 0.2383570195525562, \ 0.2898629348171136, \ 0.2898629348171136, \ 0.2383570195525561, \ 0.4717800456303301, \ 0.4023404478547353, \ 0.1953191042905292, \ 0.4023404478547353, \ 0.5593868077625691, \ 0.1312296167919730, \ 0.3093835754454578, \ 0.3093835754454580, \ 0.1312296167919729, \ 0.5593868077625690, \ 0.5845614823482763, \ 0.1684589785524792, \ 0.2469795390992443, \ 0.2469795390992445, \ 0.1684589785524792, \ 0.5845614823482763, \ 0.5515293353673113, \ 0.0131254695112235, \ 0.4353451951214650, \ 0.4353451951214652, \ 0.0131254695112234, \ 0.5515293353673112, \ 0.4114084686183320, \ 0.2942957656908339, \ 0.2942957656908339, \ 0.3516157887957689, \ 0.2967684224084620, \ 0.3516157887957690, \ 0.5518852701665368, \ 0.0344134405185801, \ 0.4137012893148829, \ 0.4137012893148831, \ 0.0344134405185802, \ 0.5518852701665365 ] ) w = np.array ( [ \ 0.0000443040909141, \ 0.0000443040909141, \ 0.0000443040909141, \ 0.0004119756464370, \ 0.0004119756464370, \ 0.0004119756464370, \ 0.0004119756464370, \ 0.0004119756464370, \ 0.0004119756464370, \ 0.0002732408460037, \ 0.0002732408460037, \ 0.0002732408460037, \ 0.0002732408460037, \ 0.0002732408460037, \ 0.0002732408460037, \ 0.0005393284439299, \ 0.0005393284439299, \ 0.0005393284439299, \ 0.0005393284439299, \ 0.0005393284439299, \ 0.0005393284439299, \ 0.0006709789705820, \ 0.0006709789705820, \ 0.0006709789705820, \ 0.0006709789705820, \ 0.0006709789705820, \ 0.0006709789705820, \ 0.0002259315361139, \ 0.0002259315361139, \ 0.0002259315361139, \ 0.0002259315361139, \ 0.0002259315361139, \ 0.0002259315361139, \ 0.0003220663094183, \ 0.0003220663094183, \ 0.0003220663094183, \ 0.0003220663094183, \ 0.0003220663094183, \ 0.0003220663094183, \ 0.0011229773828237, \ 0.0011229773828237, \ 0.0011229773828237, \ 0.0017451515655329, \ 0.0017451515655329, \ 0.0017451515655329, \ 0.0009677673027951, \ 0.0009677673027951, \ 0.0009677673027951, \ 0.0009677673027951, \ 0.0009677673027951, \ 0.0009677673027951, \ 0.0013466648921818, \ 0.0013466648921818, \ 0.0013466648921818, \ 0.0013466648921818, \ 0.0013466648921818, \ 0.0013466648921818, \ 0.0013375082839812, \ 0.0013375082839812, \ 0.0013375082839812, \ 0.0013375082839812, \ 0.0013375082839812, \ 0.0013375082839812, \ 0.0012094280366882, \ 0.0012094280366882, \ 0.0012094280366882, \ 0.0012094280366882, \ 0.0012094280366882, \ 0.0012094280366882, \ 0.0005973761417619, \ 0.0005973761417619, \ 0.0005973761417619, \ 0.0005973761417619, \ 0.0005973761417619, \ 0.0005973761417619, \ 0.0014682010637336, \ 0.0014682010637336, \ 0.0014682010637336, \ 0.0014682010637336, \ 0.0014682010637336, \ 0.0014682010637336, \ 0.0008010544852012, \ 0.0008010544852012, \ 0.0008010544852012, \ 0.0008010544852012, \ 0.0008010544852012, \ 0.0008010544852012, \ 0.0001855670423377, \ 0.0001855670423377, \ 0.0001855670423377, \ 0.0001855670423377, \ 0.0001855670423377, \ 0.0001855670423377, \ 0.0007214220264261, \ 0.0007214220264261, \ 0.0007214220264261, \ 0.0007214220264261, \ 0.0007214220264261, \ 0.0007214220264261, \ 0.0015321667240474, \ 0.0015321667240474, \ 0.0015321667240474, \ 0.0015321667240474, \ 0.0015321667240474, \ 0.0015321667240474, \ 0.0027296527164899, \ 0.0027296527164899, \ 0.0027296527164899, \ 0.0015090266204283, \ 0.0015090266204283, \ 0.0015090266204283, \ 0.0015090266204283, \ 0.0015090266204283, \ 0.0015090266204283, \ 0.0034017224729490, \ 0.0034017224729490, \ 0.0034017224729490, \ 0.0034017224729490, \ 0.0034017224729490, \ 0.0034017224729490, \ 0.0012045060134119, \ 0.0012045060134119, \ 0.0012045060134119, \ 0.0010359881638064, \ 0.0010359881638064, \ 0.0010359881638064, \ 0.0010359881638064, \ 0.0010359881638064, \ 0.0010359881638064, \ 0.0023774876927799, \ 0.0023774876927799, \ 0.0023774876927799, \ 0.0023774876927799, \ 0.0023774876927799, \ 0.0023774876927799, \ 0.0033953912341847, \ 0.0033953912341847, \ 0.0033953912341847, \ 0.0033953912341847, \ 0.0033953912341847, \ 0.0033953912341847, \ 0.0027040883824818, \ 0.0027040883824818, \ 0.0027040883824818, \ 0.0027040883824818, \ 0.0027040883824818, \ 0.0027040883824818, \ 0.0020170033902913, \ 0.0020170033902913, \ 0.0020170033902913, \ 0.0020170033902913, \ 0.0020170033902913, \ 0.0020170033902913, \ 0.0027918811324258, \ 0.0027918811324258, \ 0.0027918811324258, \ 0.0027918811324258, \ 0.0027918811324258, \ 0.0027918811324258, \ 0.0023657933107792, \ 0.0023657933107792, \ 0.0023657933107792, \ 0.0043004588657305, \ 0.0043004588657305, \ 0.0043004588657305, \ 0.0043004588657305, \ 0.0043004588657305, \ 0.0043004588657305, \ 0.0049838565291938, \ 0.0049838565291938, \ 0.0049838565291938, \ 0.0049838565291938, \ 0.0049838565291938, \ 0.0049838565291938, \ 0.0046532962756670, \ 0.0046532962756670, \ 0.0046532962756670, \ 0.0046532962756670, \ 0.0046532962756670, \ 0.0046532962756670, \ 0.0041278760422565, \ 0.0041278760422565, \ 0.0041278760422565, \ 0.0041278760422565, \ 0.0041278760422565, \ 0.0041278760422565, \ 0.0035111942683412, \ 0.0035111942683412, \ 0.0035111942683412, \ 0.0020578217623525, \ 0.0020578217623525, \ 0.0020578217623525, \ 0.0020578217623525, \ 0.0020578217623525, \ 0.0020578217623525, \ 0.0038938204584288, \ 0.0038938204584288, \ 0.0038938204584288, \ 0.0038938204584288, \ 0.0038938204584288, \ 0.0038938204584288, \ 0.0029434680471958, \ 0.0029434680471958, \ 0.0029434680471958, \ 0.0027707613965555, \ 0.0027707613965555, \ 0.0027707613965555, \ 0.0027707613965555, \ 0.0027707613965555, \ 0.0027707613965555, \ 0.0067232428984731, \ 0.0067232428984731, \ 0.0067232428984731, \ 0.0049798588125189, \ 0.0049798588125189, \ 0.0049798588125189, \ 0.0024801439985068, \ 0.0024801439985068, \ 0.0024801439985068, \ 0.0024801439985068, \ 0.0024801439985068, \ 0.0024801439985068, \ 0.0008629021808335, \ 0.0008629021808335, \ 0.0008629021808335, \ 0.0008629021808335, \ 0.0008629021808335, \ 0.0008629021808335, \ 0.0003209331775743, \ 0.0003209331775743, \ 0.0003209331775743, \ 0.0003209331775743, \ 0.0003209331775743, \ 0.0003209331775743, \ 0.0049810086106174, \ 0.0049810086106174, \ 0.0049810086106174, \ 0.0049810086106174, \ 0.0049810086106174, \ 0.0049810086106174, \ 0.0050195779180815, \ 0.0050195779180815, \ 0.0050195779180815, \ 0.0050195779180815, \ 0.0050195779180815, \ 0.0050195779180815, \ 0.0027692328182935, \ 0.0027692328182935, \ 0.0027692328182935, \ 0.0027692328182935, \ 0.0027692328182935, \ 0.0027692328182935, \ 0.0037015806596788, \ 0.0037015806596788, \ 0.0037015806596788, \ 0.0037015806596788, \ 0.0037015806596788, \ 0.0037015806596788, \ 0.0050750374591620, \ 0.0050750374591620, \ 0.0050750374591620, \ 0.0050750374591620, \ 0.0050750374591620, \ 0.0050750374591620, \ 0.0042676766915482, \ 0.0042676766915482, \ 0.0042676766915482, \ 0.0042676766915482, \ 0.0042676766915482, \ 0.0042676766915482, \ 0.0017292273039881, \ 0.0017292273039881, \ 0.0017292273039881, \ 0.0017292273039881, \ 0.0017292273039881, \ 0.0017292273039881, \ 0.0032247399122439, \ 0.0032247399122439, \ 0.0032247399122439, \ 0.0032247399122439, \ 0.0032247399122439, \ 0.0032247399122439, \ 0.0052879477129619, \ 0.0052879477129619, \ 0.0052879477129619, \ 0.0052879477129619, \ 0.0052879477129619, \ 0.0052879477129619, \ 0.0040195842863651, \ 0.0040195842863651, \ 0.0040195842863651, \ 0.0040195842863651, \ 0.0040195842863651, \ 0.0040195842863651, \ 0.0060608332073000, \ 0.0060608332073000, \ 0.0060608332073000, \ 0.0060608332073000, \ 0.0060608332073000, \ 0.0060608332073000, \ 0.0049208372452468, \ 0.0049208372452468, \ 0.0049208372452468, \ 0.0050214750285976, \ 0.0050214750285976, \ 0.0050214750285976, \ 0.0057991370585633, \ 0.0057991370585633, \ 0.0057991370585633, \ 0.0057991370585633, \ 0.0057991370585633, \ 0.0057991370585633, \ 0.0044465932407613, \ 0.0044465932407613, \ 0.0044465932407613, \ 0.0063931475211100, \ 0.0063931475211100, \ 0.0063931475211100, \ 0.0063931475211100, \ 0.0063931475211100, \ 0.0063931475211100, \ 0.0046466127645844, \ 0.0046466127645844, \ 0.0046466127645844, \ 0.0056546750089884, \ 0.0056546750089884, \ 0.0056546750089884, \ 0.0056546750089884, \ 0.0056546750089884, \ 0.0056546750089884, \ 0.0053110494169000, \ 0.0053110494169000, \ 0.0053110494169000, \ 0.0053110494169000, \ 0.0053110494169000, \ 0.0053110494169000, \ 0.0019732304214759, \ 0.0019732304214759, \ 0.0019732304214759, \ 0.0019732304214759, \ 0.0019732304214759, \ 0.0019732304214759, \ 0.0064254720501743, \ 0.0064254720501743, \ 0.0064254720501743, \ 0.0062655878836268, \ 0.0062655878836268, \ 0.0062655878836268, \ 0.0035554794715669, \ 0.0035554794715669, \ 0.0035554794715669, \ 0.0035554794715669, \ 0.0035554794715669, \ 0.0035554794715669 ] ) return a, b, c, w def rule45 ( ): #*****************************************************************************80 # ## rule45() returns the rule of precision 45. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.0126048038307362, \ 0.9801027666184203, \ 0.0072924295508435, \ 0.9801027666184204, \ 0.0126048038307363, \ 0.0072924295508431, \ 0.0046054766314413, \ 0.9940445261864481, \ 0.0013499971821107, \ 0.9940445261864482, \ 0.0046054766314413, \ 0.0013499971821102, \ 0.0679464966039112, \ 0.9251943274580282, \ 0.0068591759380607, \ 0.9251943274580283, \ 0.0679464966039112, \ 0.0068591759380603, \ 0.0693380043634408, \ 0.9294322276406242, \ 0.0012297679959350, \ 0.9294322276406243, \ 0.0693380043634408, \ 0.0012297679959347, \ 0.4682708598709480, \ 0.5229490399283573, \ 0.0087801002006947, \ 0.5229490399283572, \ 0.4682708598709480, \ 0.0087801002006947, \ 0.2504951703352215, \ 0.7478218033035982, \ 0.0016830263611803, \ 0.7478218033035983, \ 0.2504951703352215, \ 0.0016830263611800, \ 0.0179231013398374, \ 0.9803189260766274, \ 0.0017579725835354, \ 0.9803189260766274, \ 0.0179231013398374, \ 0.0017579725835349, \ 0.3594568419950528, \ 0.6390675443517843, \ 0.0014756136531630, \ 0.6390675443517843, \ 0.3594568419950528, \ 0.0014756136531628, \ 0.2211539847849475, \ 0.6251828877524599, \ 0.1536631274625926, \ 0.6251828877524600, \ 0.2211539847849475, \ 0.1536631274625923, \ 0.2389731948786961, \ 0.5334015889840547, \ 0.2276252161372492, \ 0.5334015889840547, \ 0.2389731948786961, \ 0.2276252161372491, \ 0.1298066533002767, \ 0.7403866933994464, \ 0.1298066533002770, \ 0.2265228859811758, \ 0.6592740762673123, \ 0.1142030377515119, \ 0.6592740762673124, \ 0.2265228859811758, \ 0.1142030377515117, \ 0.2395905240377902, \ 0.6800344164936584, \ 0.0803750594685514, \ 0.6800344164936585, \ 0.2395905240377902, \ 0.0803750594685512, \ 0.1782914029925923, \ 0.7910902333249177, \ 0.0306183636824901, \ 0.7910902333249177, \ 0.1782914029925923, \ 0.0306183636824899, \ 0.2063496656308830, \ 0.5873006687382336, \ 0.2063496656308832, \ 0.1750845888069398, \ 0.6498308223861201, \ 0.1750845888069402, \ 0.2825866891204175, \ 0.6904712080981594, \ 0.0269421027814231, \ 0.6904712080981593, \ 0.2825866891204175, \ 0.0269421027814229, \ 0.1372571102587296, \ 0.8299456761943377, \ 0.0327972135469328, \ 0.8299456761943378, \ 0.1372571102587296, \ 0.0327972135469324, \ 0.4995045768679594, \ 0.4995045768679594, \ 0.0009908462640811, \ 0.1002544152365696, \ 0.8670184720297813, \ 0.0327271127336490, \ 0.8670184720297813, \ 0.1002544152365697, \ 0.0327271127336487, \ 0.0517074765599653, \ 0.9331324221261621, \ 0.0151601013138727, \ 0.9331324221261622, \ 0.0517074765599654, \ 0.0151601013138723, \ 0.2606148551376569, \ 0.5685004919093655, \ 0.1708846529529776, \ 0.5685004919093656, \ 0.2606148551376569, \ 0.1708846529529774, \ 0.2272143249599573, \ 0.7441223888358753, \ 0.0286632862041673, \ 0.7441223888358756, \ 0.2272143249599574, \ 0.0286632862041670, \ 0.3110404872350509, \ 0.6762638411989882, \ 0.0126956715659609, \ 0.6762638411989881, \ 0.3110404872350510, \ 0.0126956715659608, \ 0.0552204190605028, \ 0.8895591618789941, \ 0.0552204190605031, \ 0.1856238762990532, \ 0.7264745884520657, \ 0.0879015352488812, \ 0.7264745884520657, \ 0.1856238762990533, \ 0.0879015352488808, \ 0.0658626437608178, \ 0.9034170100624399, \ 0.0307203461767425, \ 0.9034170100624398, \ 0.0658626437608178, \ 0.0307203461767422, \ 0.3015904700953623, \ 0.6955949792647613, \ 0.0028145506398765, \ 0.6955949792647613, \ 0.3015904700953622, \ 0.0028145506398762, \ 0.2925426576542363, \ 0.6276179259734721, \ 0.0798394163722916, \ 0.6276179259734721, \ 0.2925426576542364, \ 0.0798394163722914, \ 0.0273024847528849, \ 0.9593763173443479, \ 0.0133211979027673, \ 0.9593763173443479, \ 0.0273024847528850, \ 0.0133211979027669, \ 0.2991527658365939, \ 0.4016944683268121, \ 0.2991527658365939, \ 0.3715719205775442, \ 0.6188258934043402, \ 0.0096021860181155, \ 0.6188258934043402, \ 0.3715719205775442, \ 0.0096021860181154, \ 0.2010073039936871, \ 0.7964902586210802, \ 0.0025024373852327, \ 0.7964902586210802, \ 0.2010073039936872, \ 0.0025024373852325, \ 0.2931831293722664, \ 0.5050860425617371, \ 0.2017308280659965, \ 0.5050860425617371, \ 0.2931831293722664, \ 0.2017308280659964, \ 0.2333318911036226, \ 0.7139904265957288, \ 0.0526776823006487, \ 0.7139904265957289, \ 0.2333318911036226, \ 0.0526776823006484, \ 0.1792991418970043, \ 0.7649317119922271, \ 0.0557691461107687, \ 0.7649317119922271, \ 0.1792991418970044, \ 0.0557691461107684, \ 0.3669822772564582, \ 0.3669822772564582, \ 0.2660354454870835, \ 0.2934353311290930, \ 0.6583279675616898, \ 0.0482367013092171, \ 0.6583279675616899, \ 0.2934353311290930, \ 0.0482367013092171, \ 0.3298405962756192, \ 0.4364618201712586, \ 0.2336975835531220, \ 0.4364618201712586, \ 0.3298405962756192, \ 0.2336975835531221, \ 0.1381756936115276, \ 0.7691621557796962, \ 0.0926621506087763, \ 0.7691621557796963, \ 0.1381756936115277, \ 0.0926621506087759, \ 0.3585128657761011, \ 0.4680323661208265, \ 0.1734547681030723, \ 0.4680323661208265, \ 0.3585128657761011, \ 0.1734547681030723, \ 0.4203377834665488, \ 0.5618113228868684, \ 0.0178508936465827, \ 0.5618113228868684, \ 0.4203377834665488, \ 0.0178508936465827, \ 0.2790511330034806, \ 0.6010021745006722, \ 0.1199466924958471, \ 0.6010021745006722, \ 0.2790511330034807, \ 0.1199466924958470, \ 0.0934626722493711, \ 0.8925527104988681, \ 0.0139846172517610, \ 0.8925527104988681, \ 0.0934626722493711, \ 0.0139846172517607, \ 0.3874089876890199, \ 0.4932332479959026, \ 0.1193577643150775, \ 0.4932332479959027, \ 0.3874089876890199, \ 0.1193577643150774, \ 0.4071846956615202, \ 0.5192306493531181, \ 0.0735846549853617, \ 0.5192306493531181, \ 0.4071846956615202, \ 0.0735846549853617, \ 0.1876405833897097, \ 0.7996426687617495, \ 0.0127167478485408, \ 0.7996426687617495, \ 0.1876405833897097, \ 0.0127167478485406, \ 0.2649216423903805, \ 0.4701567152192389, \ 0.2649216423903806, \ 0.1522255260382763, \ 0.8453340935540358, \ 0.0024403804076879, \ 0.8453340935540359, \ 0.1522255260382763, \ 0.0024403804076877, \ 0.1741420017865634, \ 0.6959673722361421, \ 0.1298906259772944, \ 0.6959673722361421, \ 0.1741420017865634, \ 0.1298906259772943, \ 0.3984690684139450, \ 0.3984690684139450, \ 0.2030618631721098, \ 0.3214081551755261, \ 0.5347112144371693, \ 0.1438806303873045, \ 0.5347112144371693, \ 0.3214081551755262, \ 0.1438806303873043, \ 0.0888043361734265, \ 0.8523358545382167, \ 0.0588598092883569, \ 0.8523358545382167, \ 0.0888043361734265, \ 0.0588598092883565, \ 0.1304289155517122, \ 0.8092737430634784, \ 0.0602973413848094, \ 0.8092737430634784, \ 0.1304289155517123, \ 0.0602973413848091, \ 0.4526201907514942, \ 0.4526201907514942, \ 0.0947596184970115, \ 0.1368379127222100, \ 0.8499366346784312, \ 0.0132254525993589, \ 0.8499366346784312, \ 0.1368379127222101, \ 0.0132254525993586, \ 0.3528533591796706, \ 0.5898753813183408, \ 0.0572712595019886, \ 0.5898753813183407, \ 0.3528533591796706, \ 0.0572712595019886, \ 0.2463869002171422, \ 0.7426794521965718, \ 0.0109336475862860, \ 0.7426794521965718, \ 0.2463869002171423, \ 0.0109336475862858, \ 0.4268610495333074, \ 0.4268610495333074, \ 0.1462779009333850, \ 0.3333333333333333, \ 0.3435200440594713, \ 0.5605547908509811, \ 0.0959251650895475, \ 0.5605547908509811, \ 0.3435200440594713, \ 0.0959251650895474, \ 0.4162089636364642, \ 0.5441206066477789, \ 0.0396704297157567, \ 0.5441206066477789, \ 0.4162089636364643, \ 0.0396704297157567, \ 0.0945724371334944, \ 0.8108551257330109, \ 0.0945724371334948, \ 0.4729894708688973, \ 0.4729894708688974, \ 0.0540210582622052, \ 0.0390118106999858, \ 0.9581931415494848, \ 0.0027950477505296, \ 0.9581931415494848, \ 0.0390118106999859, \ 0.0027950477505291, \ 0.1071807141346061, \ 0.8901526742127170, \ 0.0026666116526771, \ 0.8901526742127172, \ 0.1071807141346060, \ 0.0026666116526766, \ 0.4264238197063261, \ 0.5710366502174161, \ 0.0025395300762577, \ 0.5710366502174161, \ 0.4264238197063261, \ 0.0025395300762577, \ 0.0340851411567991, \ 0.9318297176864013, \ 0.0340851411567996, \ 0.3519601313638296, \ 0.6193084930778816, \ 0.0287313755582888, \ 0.6193084930778816, \ 0.3519601313638297, \ 0.0287313755582886, \ 0.4869989968257815, \ 0.4869989968257815, \ 0.0260020063484370 ] ) b = np.array ( [ \ 0.0072924295508434, \ 0.0126048038307362, \ 0.9801027666184206, \ 0.0072924295508434, \ 0.9801027666184206, \ 0.0126048038307365, \ 0.0013499971821105, \ 0.0046054766314413, \ 0.9940445261864482, \ 0.0013499971821105, \ 0.9940445261864485, \ 0.0046054766314416, \ 0.0068591759380605, \ 0.0679464966039111, \ 0.9251943274580284, \ 0.0068591759380605, \ 0.9251943274580284, \ 0.0679464966039115, \ 0.0012297679959349, \ 0.0693380043634408, \ 0.9294322276406244, \ 0.0012297679959349, \ 0.9294322276406244, \ 0.0693380043634411, \ 0.0087801002006948, \ 0.4682708598709480, \ 0.5229490399283575, \ 0.0087801002006948, \ 0.5229490399283574, \ 0.4682708598709482, \ 0.0016830263611803, \ 0.2504951703352215, \ 0.7478218033035984, \ 0.0016830263611803, \ 0.7478218033035984, \ 0.2504951703352218, \ 0.0017579725835351, \ 0.0179231013398374, \ 0.9803189260766274, \ 0.0017579725835351, \ 0.9803189260766277, \ 0.0179231013398377, \ 0.0014756136531629, \ 0.3594568419950528, \ 0.6390675443517844, \ 0.0014756136531629, \ 0.6390675443517843, \ 0.3594568419950530, \ 0.1536631274625925, \ 0.2211539847849475, \ 0.6251828877524600, \ 0.1536631274625925, \ 0.6251828877524601, \ 0.2211539847849477, \ 0.2276252161372493, \ 0.2389731948786962, \ 0.5334015889840548, \ 0.2276252161372493, \ 0.5334015889840548, \ 0.2389731948786963, \ 0.1298066533002769, \ 0.1298066533002767, \ 0.7403866933994465, \ 0.1142030377515119, \ 0.2265228859811758, \ 0.6592740762673125, \ 0.1142030377515119, \ 0.6592740762673125, \ 0.2265228859811760, \ 0.0803750594685514, \ 0.2395905240377902, \ 0.6800344164936586, \ 0.0803750594685514, \ 0.6800344164936585, \ 0.2395905240377905, \ 0.0306183636824900, \ 0.1782914029925923, \ 0.7910902333249178, \ 0.0306183636824900, \ 0.7910902333249178, \ 0.1782914029925926, \ 0.2063496656308833, \ 0.2063496656308831, \ 0.5873006687382338, \ 0.1750845888069401, \ 0.1750845888069399, \ 0.6498308223861201, \ 0.0269421027814231, \ 0.2825866891204175, \ 0.6904712080981597, \ 0.0269421027814231, \ 0.6904712080981594, \ 0.2825866891204177, \ 0.0327972135469327, \ 0.1372571102587296, \ 0.8299456761943379, \ 0.0327972135469327, \ 0.8299456761943380, \ 0.1372571102587299, \ 0.0009908462640811, \ 0.4995045768679595, \ 0.4995045768679597, \ 0.0327271127336490, \ 0.1002544152365696, \ 0.8670184720297816, \ 0.0327271127336490, \ 0.8670184720297816, \ 0.1002544152365700, \ 0.0151601013138726, \ 0.0517074765599653, \ 0.9331324221261622, \ 0.0151601013138726, \ 0.9331324221261622, \ 0.0517074765599656, \ 0.1708846529529776, \ 0.2606148551376569, \ 0.5685004919093657, \ 0.1708846529529776, \ 0.5685004919093657, \ 0.2606148551376571, \ 0.0286632862041672, \ 0.2272143249599573, \ 0.7441223888358756, \ 0.0286632862041672, \ 0.7441223888358756, \ 0.2272143249599576, \ 0.0126956715659609, \ 0.3110404872350509, \ 0.6762638411989884, \ 0.0126956715659609, \ 0.6762638411989882, \ 0.3110404872350512, \ 0.0552204190605031, \ 0.0552204190605028, \ 0.8895591618789943, \ 0.0879015352488811, \ 0.1856238762990532, \ 0.7264745884520658, \ 0.0879015352488811, \ 0.7264745884520658, \ 0.1856238762990535, \ 0.0307203461767424, \ 0.0658626437608177, \ 0.9034170100624400, \ 0.0307203461767424, \ 0.9034170100624400, \ 0.0658626437608181, \ 0.0028145506398764, \ 0.3015904700953623, \ 0.6955949792647615, \ 0.0028145506398764, \ 0.6955949792647615, \ 0.3015904700953626, \ 0.0798394163722916, \ 0.2925426576542363, \ 0.6276179259734722, \ 0.0798394163722916, \ 0.6276179259734722, \ 0.2925426576542366, \ 0.0133211979027671, \ 0.0273024847528849, \ 0.9593763173443480, \ 0.0133211979027671, \ 0.9593763173443480, \ 0.0273024847528853, \ 0.2991527658365941, \ 0.2991527658365941, \ 0.4016944683268122, \ 0.0096021860181156, \ 0.3715719205775442, \ 0.6188258934043405, \ 0.0096021860181156, \ 0.6188258934043404, \ 0.3715719205775445, \ 0.0025024373852327, \ 0.2010073039936871, \ 0.7964902586210805, \ 0.0025024373852327, \ 0.7964902586210802, \ 0.2010073039936874, \ 0.2017308280659965, \ 0.2931831293722665, \ 0.5050860425617372, \ 0.2017308280659965, \ 0.5050860425617372, \ 0.2931831293722666, \ 0.0526776823006486, \ 0.2333318911036226, \ 0.7139904265957290, \ 0.0526776823006486, \ 0.7139904265957289, \ 0.2333318911036229, \ 0.0557691461107686, \ 0.1792991418970043, \ 0.7649317119922272, \ 0.0557691461107686, \ 0.7649317119922272, \ 0.1792991418970046, \ 0.2660354454870836, \ 0.3669822772564583, \ 0.3669822772564584, \ 0.0482367013092172, \ 0.2934353311290930, \ 0.6583279675616901, \ 0.0482367013092172, \ 0.6583279675616900, \ 0.2934353311290932, \ 0.2336975835531222, \ 0.3298405962756193, \ 0.4364618201712588, \ 0.2336975835531222, \ 0.4364618201712587, \ 0.3298405962756194, \ 0.0926621506087761, \ 0.1381756936115276, \ 0.7691621557796964, \ 0.0926621506087761, \ 0.7691621557796964, \ 0.1381756936115279, \ 0.1734547681030724, \ 0.3585128657761012, \ 0.4680323661208267, \ 0.1734547681030724, \ 0.4680323661208267, \ 0.3585128657761013, \ 0.0178508936465828, \ 0.4203377834665488, \ 0.5618113228868687, \ 0.0178508936465828, \ 0.5618113228868685, \ 0.4203377834665490, \ 0.1199466924958472, \ 0.2790511330034807, \ 0.6010021745006724, \ 0.1199466924958472, \ 0.6010021745006723, \ 0.2790511330034809, \ 0.0139846172517609, \ 0.0934626722493711, \ 0.8925527104988682, \ 0.0139846172517609, \ 0.8925527104988682, \ 0.0934626722493714, \ 0.1193577643150775, \ 0.3874089876890200, \ 0.4932332479959028, \ 0.1193577643150775, \ 0.4932332479959027, \ 0.3874089876890201, \ 0.0735846549853618, \ 0.4071846956615202, \ 0.5192306493531184, \ 0.0735846549853618, \ 0.5192306493531181, \ 0.4071846956615204, \ 0.0127167478485408, \ 0.1876405833897097, \ 0.7996426687617497, \ 0.0127167478485408, \ 0.7996426687617497, \ 0.1876405833897100, \ 0.2649216423903806, \ 0.2649216423903806, \ 0.4701567152192390, \ 0.0024403804076879, \ 0.1522255260382763, \ 0.8453340935540361, \ 0.0024403804076879, \ 0.8453340935540361, \ 0.1522255260382766, \ 0.1298906259772945, \ 0.1741420017865634, \ 0.6959673722361424, \ 0.1298906259772945, \ 0.6959673722361424, \ 0.1741420017865636, \ 0.2030618631721099, \ 0.3984690684139451, \ 0.3984690684139452, \ 0.1438806303873045, \ 0.3214081551755262, \ 0.5347112144371695, \ 0.1438806303873045, \ 0.5347112144371694, \ 0.3214081551755264, \ 0.0588598092883568, \ 0.0888043361734265, \ 0.8523358545382169, \ 0.0588598092883568, \ 0.8523358545382169, \ 0.0888043361734268, \ 0.0602973413848094, \ 0.1304289155517122, \ 0.8092737430634785, \ 0.0602973413848094, \ 0.8092737430634785, \ 0.1304289155517125, \ 0.0947596184970116, \ 0.4526201907514942, \ 0.4526201907514944, \ 0.0132254525993588, \ 0.1368379127222100, \ 0.8499366346784313, \ 0.0132254525993588, \ 0.8499366346784313, \ 0.1368379127222104, \ 0.0572712595019887, \ 0.3528533591796706, \ 0.5898753813183411, \ 0.0572712595019887, \ 0.5898753813183409, \ 0.3528533591796708, \ 0.0109336475862860, \ 0.2463869002171422, \ 0.7426794521965722, \ 0.0109336475862860, \ 0.7426794521965718, \ 0.2463869002171425, \ 0.1462779009333851, \ 0.4268610495333075, \ 0.4268610495333077, \ 0.3333333333333334, \ 0.0959251650895476, \ 0.3435200440594713, \ 0.5605547908509814, \ 0.0959251650895476, \ 0.5605547908509813, \ 0.3435200440594715, \ 0.0396704297157568, \ 0.4162089636364643, \ 0.5441206066477793, \ 0.0396704297157568, \ 0.5441206066477792, \ 0.4162089636364644, \ 0.0945724371334947, \ 0.0945724371334944, \ 0.8108551257330111, \ 0.0540210582622053, \ 0.4729894708688974, \ 0.4729894708688976, \ 0.0027950477505294, \ 0.0390118106999857, \ 0.9581931415494850, \ 0.0027950477505294, \ 0.9581931415494850, \ 0.0390118106999862, \ 0.0026666116526769, \ 0.1071807141346060, \ 0.8901526742127170, \ 0.0026666116526769, \ 0.8901526742127174, \ 0.1071807141346064, \ 0.0025395300762578, \ 0.4264238197063261, \ 0.5710366502174163, \ 0.0025395300762578, \ 0.5710366502174162, \ 0.4264238197063264, \ 0.0340851411567994, \ 0.0340851411567991, \ 0.9318297176864015, \ 0.0287313755582888, \ 0.3519601313638296, \ 0.6193084930778818, \ 0.0287313755582888, \ 0.6193084930778817, \ 0.3519601313638299, \ 0.0260020063484371, \ 0.4869989968257816, \ 0.4869989968257817 ] ) c = np.array ( [ \ 0.9801027666184204, \ 0.0072924295508435, \ 0.0126048038307359, \ 0.0126048038307362, \ 0.0072924295508432, \ 0.9801027666184203, \ 0.9940445261864482, \ 0.0013499971821106, \ 0.0046054766314411, \ 0.0046054766314413, \ 0.0013499971821102, \ 0.9940445261864481, \ 0.9251943274580283, \ 0.0068591759380607, \ 0.0679464966039108, \ 0.0679464966039111, \ 0.0068591759380604, \ 0.9251943274580282, \ 0.9294322276406243, \ 0.0012297679959350, \ 0.0693380043634406, \ 0.0693380043634408, \ 0.0012297679959348, \ 0.9294322276406242, \ 0.5229490399283573, \ 0.0087801002006947, \ 0.4682708598709479, \ 0.4682708598709481, \ 0.0087801002006946, \ 0.5229490399283572, \ 0.7478218033035983, \ 0.0016830263611803, \ 0.2504951703352213, \ 0.2504951703352215, \ 0.0016830263611801, \ 0.7478218033035982, \ 0.9803189260766274, \ 0.0017579725835352, \ 0.0179231013398372, \ 0.0179231013398374, \ 0.0017579725835349, \ 0.9803189260766273, \ 0.6390675443517843, \ 0.0014756136531629, \ 0.3594568419950526, \ 0.3594568419950528, \ 0.0014756136531630, \ 0.6390675443517841, \ 0.6251828877524599, \ 0.1536631274625926, \ 0.2211539847849474, \ 0.2211539847849475, \ 0.1536631274625924, \ 0.6251828877524599, \ 0.5334015889840545, \ 0.2276252161372492, \ 0.2389731948786961, \ 0.2389731948786961, \ 0.2276252161372491, \ 0.5334015889840545, \ 0.7403866933994465, \ 0.1298066533002769, \ 0.1298066533002765, \ 0.6592740762673124, \ 0.1142030377515119, \ 0.2265228859811755, \ 0.2265228859811758, \ 0.1142030377515116, \ 0.6592740762673124, \ 0.6800344164936584, \ 0.0803750594685514, \ 0.2395905240377899, \ 0.2395905240377901, \ 0.0803750594685513, \ 0.6800344164936583, \ 0.7910902333249177, \ 0.0306183636824900, \ 0.1782914029925921, \ 0.1782914029925923, \ 0.0306183636824898, \ 0.7910902333249177, \ 0.5873006687382337, \ 0.2063496656308832, \ 0.2063496656308830, \ 0.6498308223861200, \ 0.1750845888069400, \ 0.1750845888069398, \ 0.6904712080981594, \ 0.0269421027814231, \ 0.2825866891204173, \ 0.2825866891204176, \ 0.0269421027814231, \ 0.6904712080981593, \ 0.8299456761943378, \ 0.0327972135469327, \ 0.1372571102587293, \ 0.1372571102587296, \ 0.0327972135469324, \ 0.8299456761943377, \ 0.4995045768679595, \ 0.0009908462640812, \ 0.4995045768679592, \ 0.8670184720297814, \ 0.0327271127336490, \ 0.1002544152365694, \ 0.1002544152365697, \ 0.0327271127336487, \ 0.8670184720297813, \ 0.9331324221261621, \ 0.0151601013138726, \ 0.0517074765599651, \ 0.0517074765599652, \ 0.0151601013138724, \ 0.9331324221261621, \ 0.5685004919093655, \ 0.1708846529529776, \ 0.2606148551376568, \ 0.2606148551376569, \ 0.1708846529529774, \ 0.5685004919093655, \ 0.7441223888358754, \ 0.0286632862041673, \ 0.2272143249599571, \ 0.2272143249599572, \ 0.0286632862041670, \ 0.7441223888358753, \ 0.6762638411989881, \ 0.0126956715659609, \ 0.3110404872350506, \ 0.3110404872350510, \ 0.0126956715659609, \ 0.6762638411989881, \ 0.8895591618789941, \ 0.0552204190605031, \ 0.0552204190605027, \ 0.7264745884520657, \ 0.0879015352488811, \ 0.1856238762990530, \ 0.1856238762990532, \ 0.0879015352488809, \ 0.7264745884520658, \ 0.9034170100624398, \ 0.0307203461767424, \ 0.0658626437608175, \ 0.0658626437608178, \ 0.0307203461767421, \ 0.9034170100624398, \ 0.6955949792647614, \ 0.0028145506398763, \ 0.3015904700953620, \ 0.3015904700953623, \ 0.0028145506398762, \ 0.6955949792647612, \ 0.6276179259734721, \ 0.0798394163722916, \ 0.2925426576542361, \ 0.2925426576542363, \ 0.0798394163722914, \ 0.6276179259734720, \ 0.9593763173443480, \ 0.0133211979027672, \ 0.0273024847528847, \ 0.0273024847528849, \ 0.0133211979027669, \ 0.9593763173443478, \ 0.4016944683268120, \ 0.2991527658365938, \ 0.2991527658365939, \ 0.6188258934043401, \ 0.0096021860181155, \ 0.3715719205775441, \ 0.3715719205775442, \ 0.0096021860181154, \ 0.6188258934043400, \ 0.7964902586210802, \ 0.0025024373852326, \ 0.2010073039936868, \ 0.2010073039936870, \ 0.0025024373852326, \ 0.7964902586210801, \ 0.5050860425617371, \ 0.2017308280659965, \ 0.2931831293722663, \ 0.2931831293722664, \ 0.2017308280659964, \ 0.5050860425617369, \ 0.7139904265957288, \ 0.0526776823006486, \ 0.2333318911036223, \ 0.2333318911036225, \ 0.0526776823006485, \ 0.7139904265957286, \ 0.7649317119922271, \ 0.0557691461107686, \ 0.1792991418970041, \ 0.1792991418970043, \ 0.0557691461107684, \ 0.7649317119922271, \ 0.3669822772564583, \ 0.2660354454870835, \ 0.3669822772564582, \ 0.6583279675616899, \ 0.0482367013092172, \ 0.2934353311290928, \ 0.2934353311290929, \ 0.0482367013092170, \ 0.6583279675616898, \ 0.4364618201712586, \ 0.2336975835531220, \ 0.3298405962756191, \ 0.3298405962756191, \ 0.2336975835531220, \ 0.4364618201712585, \ 0.7691621557796963, \ 0.0926621506087762, \ 0.1381756936115274, \ 0.1381756936115276, \ 0.0926621506087759, \ 0.7691621557796962, \ 0.4680323661208265, \ 0.1734547681030723, \ 0.3585128657761010, \ 0.3585128657761011, \ 0.1734547681030721, \ 0.4680323661208264, \ 0.5618113228868685, \ 0.0178508936465828, \ 0.4203377834665486, \ 0.4203377834665488, \ 0.0178508936465828, \ 0.5618113228868683, \ 0.6010021745006722, \ 0.1199466924958471, \ 0.2790511330034805, \ 0.2790511330034807, \ 0.1199466924958471, \ 0.6010021745006722, \ 0.8925527104988680, \ 0.0139846172517608, \ 0.0934626722493708, \ 0.0934626722493710, \ 0.0139846172517607, \ 0.8925527104988679, \ 0.4932332479959026, \ 0.1193577643150775, \ 0.3874089876890197, \ 0.3874089876890198, \ 0.1193577643150774, \ 0.4932332479959025, \ 0.5192306493531180, \ 0.0735846549853617, \ 0.4071846956615199, \ 0.4071846956615201, \ 0.0735846549853617, \ 0.5192306493531180, \ 0.7996426687617495, \ 0.0127167478485408, \ 0.1876405833897095, \ 0.1876405833897097, \ 0.0127167478485406, \ 0.7996426687617494, \ 0.4701567152192389, \ 0.2649216423903806, \ 0.2649216423903804, \ 0.8453340935540358, \ 0.0024403804076879, \ 0.1522255260382760, \ 0.1522255260382763, \ 0.0024403804076876, \ 0.8453340935540357, \ 0.6959673722361421, \ 0.1298906259772944, \ 0.1741420017865631, \ 0.1741420017865634, \ 0.1298906259772943, \ 0.6959673722361421, \ 0.3984690684139450, \ 0.2030618631721098, \ 0.3984690684139450, \ 0.5347112144371693, \ 0.1438806303873045, \ 0.3214081551755260, \ 0.3214081551755262, \ 0.1438806303873045, \ 0.5347112144371693, \ 0.8523358545382167, \ 0.0588598092883569, \ 0.0888043361734262, \ 0.0888043361734265, \ 0.0588598092883565, \ 0.8523358545382168, \ 0.8092737430634784, \ 0.0602973413848094, \ 0.1304289155517121, \ 0.1304289155517122, \ 0.0602973413848092, \ 0.8092737430634783, \ 0.4526201907514942, \ 0.0947596184970116, \ 0.4526201907514941, \ 0.8499366346784312, \ 0.0132254525993588, \ 0.1368379127222098, \ 0.1368379127222100, \ 0.0132254525993586, \ 0.8499366346784311, \ 0.5898753813183408, \ 0.0572712595019885, \ 0.3528533591796703, \ 0.3528533591796706, \ 0.0572712595019885, \ 0.5898753813183406, \ 0.7426794521965718, \ 0.0109336475862860, \ 0.2463869002171418, \ 0.2463869002171422, \ 0.0109336475862859, \ 0.7426794521965717, \ 0.4268610495333075, \ 0.1462779009333851, \ 0.4268610495333073, \ 0.3333333333333333, \ 0.5605547908509813, \ 0.0959251650895475, \ 0.3435200440594711, \ 0.3435200440594713, \ 0.0959251650895475, \ 0.5605547908509811, \ 0.5441206066477791, \ 0.0396704297157568, \ 0.4162089636364640, \ 0.4162089636364643, \ 0.0396704297157565, \ 0.5441206066477789, \ 0.8108551257330110, \ 0.0945724371334948, \ 0.0945724371334941, \ 0.4729894708688974, \ 0.0540210582622052, \ 0.4729894708688971, \ 0.9581931415494849, \ 0.0027950477505295, \ 0.0390118106999854, \ 0.0390118106999858, \ 0.0027950477505291, \ 0.9581931415494848, \ 0.8901526742127170, \ 0.0026666116526769, \ 0.1071807141346058, \ 0.1071807141346060, \ 0.0026666116526767, \ 0.8901526742127169, \ 0.5710366502174161, \ 0.0025395300762577, \ 0.4264238197063259, \ 0.4264238197063261, \ 0.0025395300762576, \ 0.5710366502174160, \ 0.9318297176864014, \ 0.0340851411567995, \ 0.0340851411567989, \ 0.6193084930778816, \ 0.0287313755582888, \ 0.3519601313638294, \ 0.3519601313638296, \ 0.0287313755582886, \ 0.6193084930778815, \ 0.4869989968257814, \ 0.0260020063484369, \ 0.4869989968257813 ] ) w = np.array ( [ \ 0.0001943064247755, \ 0.0001943064247755, \ 0.0001943064247755, \ 0.0001943064247755, \ 0.0001943064247755, \ 0.0001943064247755, \ 0.0000593664802978, \ 0.0000593664802978, \ 0.0000593664802978, \ 0.0000593664802978, \ 0.0000593664802978, \ 0.0000593664802978, \ 0.0004806887075027, \ 0.0004806887075027, \ 0.0004806887075027, \ 0.0004806887075027, \ 0.0004806887075027, \ 0.0004806887075027, \ 0.0002301249335002, \ 0.0002301249335002, \ 0.0002301249335002, \ 0.0002301249335002, \ 0.0002301249335002, \ 0.0002301249335002, \ 0.0012944627170681, \ 0.0012944627170681, \ 0.0012944627170681, \ 0.0012944627170681, \ 0.0012944627170681, \ 0.0012944627170681, \ 0.0004605208982907, \ 0.0004605208982907, \ 0.0004605208982907, \ 0.0004605208982907, \ 0.0004605208982907, \ 0.0004605208982907, \ 0.0001550690080029, \ 0.0001550690080029, \ 0.0001550690080029, \ 0.0001550690080029, \ 0.0001550690080029, \ 0.0001550690080029, \ 0.0005264320168997, \ 0.0005264320168997, \ 0.0005264320168997, \ 0.0005264320168997, \ 0.0005264320168997, \ 0.0005264320168997, \ 0.0040776028008772, \ 0.0040776028008772, \ 0.0040776028008772, \ 0.0040776028008772, \ 0.0040776028008772, \ 0.0040776028008772, \ 0.0027273371555633, \ 0.0027273371555633, \ 0.0027273371555633, \ 0.0027273371555633, \ 0.0027273371555633, \ 0.0027273371555633, \ 0.0032024171503526, \ 0.0032024171503526, \ 0.0032024171503526, \ 0.0038178383600418, \ 0.0038178383600418, \ 0.0038178383600418, \ 0.0038178383600418, \ 0.0038178383600418, \ 0.0038178383600418, \ 0.0032435899284887, \ 0.0032435899284887, \ 0.0032435899284887, \ 0.0032435899284887, \ 0.0032435899284887, \ 0.0032435899284887, \ 0.0018849657183849, \ 0.0018849657183849, \ 0.0018849657183849, \ 0.0018849657183849, \ 0.0018849657183849, \ 0.0018849657183849, \ 0.0046373488411220, \ 0.0046373488411220, \ 0.0046373488411220, \ 0.0040870604654873, \ 0.0040870604654873, \ 0.0040870604654873, \ 0.0021807223876070, \ 0.0021807223876070, \ 0.0021807223876070, \ 0.0021807223876070, \ 0.0021807223876070, \ 0.0021807223876070, \ 0.0018345812391610, \ 0.0018345812391610, \ 0.0018345812391610, \ 0.0018345812391610, \ 0.0018345812391610, \ 0.0018345812391610, \ 0.0004831135230320, \ 0.0004831135230320, \ 0.0004831135230320, \ 0.0016273397954327, \ 0.0016273397954327, \ 0.0016273397954327, \ 0.0016273397954327, \ 0.0016273397954327, \ 0.0016273397954327, \ 0.0008285328211727, \ 0.0008285328211727, \ 0.0008285328211727, \ 0.0008285328211727, \ 0.0008285328211727, \ 0.0008285328211727, \ 0.0051074900867677, \ 0.0051074900867677, \ 0.0051074900867677, \ 0.0051074900867677, \ 0.0051074900867677, \ 0.0051074900867677, \ 0.0022391133588916, \ 0.0022391133588916, \ 0.0022391133588916, \ 0.0022391133588916, \ 0.0022391133588916, \ 0.0022391133588916, \ 0.0016401723644210, \ 0.0016401723644210, \ 0.0016401723644210, \ 0.0016401723644210, \ 0.0016401723644210, \ 0.0016401723644210, \ 0.0016926101405552, \ 0.0016926101405552, \ 0.0016926101405552, \ 0.0036716713931777, \ 0.0036716713931777, \ 0.0036716713931777, \ 0.0036716713931777, \ 0.0036716713931777, \ 0.0036716713931777, \ 0.0014130049415994, \ 0.0014130049415994, \ 0.0014130049415994, \ 0.0014130049415994, \ 0.0014130049415994, \ 0.0014130049415994, \ 0.0007644420008621, \ 0.0007644420008621, \ 0.0007644420008621, \ 0.0007644420008621, \ 0.0007644420008621, \ 0.0007644420008621, \ 0.0039540316260532, \ 0.0039540316260532, \ 0.0039540316260532, \ 0.0039540316260532, \ 0.0039540316260532, \ 0.0039540316260532, \ 0.0006448335449571, \ 0.0006448335449571, \ 0.0006448335449571, \ 0.0006448335449571, \ 0.0006448335449571, \ 0.0006448335449571, \ 0.0068337553756981, \ 0.0068337553756981, \ 0.0068337553756981, \ 0.0015547569025381, \ 0.0015547569025381, \ 0.0015547569025381, \ 0.0015547569025381, \ 0.0015547569025381, \ 0.0015547569025381, \ 0.0006264797924812, \ 0.0006264797924812, \ 0.0006264797924812, \ 0.0006264797924812, \ 0.0006264797924812, \ 0.0006264797924812, \ 0.0059918057501739, \ 0.0059918057501739, \ 0.0059918057501739, \ 0.0059918057501739, \ 0.0059918057501739, \ 0.0059918057501739, \ 0.0030584178145640, \ 0.0030584178145640, \ 0.0030584178145640, \ 0.0030584178145640, \ 0.0030584178145640, \ 0.0030584178145640, \ 0.0029964079041531, \ 0.0029964079041531, \ 0.0029964079041531, \ 0.0029964079041531, \ 0.0029964079041531, \ 0.0029964079041531, \ 0.0068925047985870, \ 0.0068925047985870, \ 0.0068925047985870, \ 0.0032333735833172, \ 0.0032333735833172, \ 0.0032333735833172, \ 0.0032333735833172, \ 0.0032333735833172, \ 0.0032333735833172, \ 0.0066463643649800, \ 0.0066463643649800, \ 0.0066463643649800, \ 0.0066463643649800, \ 0.0066463643649800, \ 0.0066463643649800, \ 0.0031949049329089, \ 0.0031949049329089, \ 0.0031949049329089, \ 0.0031949049329089, \ 0.0031949049329089, \ 0.0031949049329089, \ 0.0061619916829777, \ 0.0061619916829777, \ 0.0061619916829777, \ 0.0061619916829777, \ 0.0061619916829777, \ 0.0061619916829777, \ 0.0021838177312897, \ 0.0021838177312897, \ 0.0021838177312897, \ 0.0021838177312897, \ 0.0021838177312897, \ 0.0021838177312897, \ 0.0048382287535973, \ 0.0048382287535973, \ 0.0048382287535973, \ 0.0048382287535973, \ 0.0048382287535973, \ 0.0048382287535973, \ 0.0011709435195081, \ 0.0011709435195081, \ 0.0011709435195081, \ 0.0011709435195081, \ 0.0011709435195081, \ 0.0011709435195081, \ 0.0054074968564398, \ 0.0054074968564398, \ 0.0054074968564398, \ 0.0054074968564398, \ 0.0054074968564398, \ 0.0054074968564398, \ 0.0045333891237490, \ 0.0045333891237490, \ 0.0045333891237490, \ 0.0045333891237490, \ 0.0045333891237490, \ 0.0045333891237490, \ 0.0015268444445366, \ 0.0015268444445366, \ 0.0015268444445366, \ 0.0015268444445366, \ 0.0015268444445366, \ 0.0015268444445366, \ 0.0063146569930329, \ 0.0063146569930329, \ 0.0063146569930329, \ 0.0005985557587521, \ 0.0005985557587521, \ 0.0005985557587521, \ 0.0005985557587521, \ 0.0005985557587521, \ 0.0005985557587521, \ 0.0042213374314073, \ 0.0042213374314073, \ 0.0042213374314073, \ 0.0042213374314073, \ 0.0042213374314073, \ 0.0042213374314073, \ 0.0065583075001979, \ 0.0065583075001979, \ 0.0065583075001979, \ 0.0055145622313395, \ 0.0055145622313395, \ 0.0055145622313395, \ 0.0055145622313395, \ 0.0055145622313395, \ 0.0055145622313395, \ 0.0023371778099107, \ 0.0023371778099107, \ 0.0023371778099107, \ 0.0023371778099107, \ 0.0023371778099107, \ 0.0023371778099107, \ 0.0027879889526797, \ 0.0027879889526797, \ 0.0027879889526797, \ 0.0027879889526797, \ 0.0027879889526797, \ 0.0027879889526797, \ 0.0050168594859682, \ 0.0050168594859682, \ 0.0050168594859682, \ 0.0014305749953706, \ 0.0014305749953706, \ 0.0014305749953706, \ 0.0014305749953706, \ 0.0014305749953706, \ 0.0014305749953706, \ 0.0039720422418774, \ 0.0039720422418774, \ 0.0039720422418774, \ 0.0039720422418774, \ 0.0039720422418774, \ 0.0039720422418774, \ 0.0016230214293911, \ 0.0016230214293911, \ 0.0016230214293911, \ 0.0016230214293911, \ 0.0016230214293911, \ 0.0016230214293911, \ 0.0058825091261753, \ 0.0058825091261753, \ 0.0058825091261753, \ 0.0069414696543850, \ 0.0048308548778951, \ 0.0048308548778951, \ 0.0048308548778951, \ 0.0048308548778951, \ 0.0048308548778951, \ 0.0048308548778951, \ 0.0035396788161465, \ 0.0035396788161465, \ 0.0035396788161465, \ 0.0035396788161465, \ 0.0035396788161465, \ 0.0035396788161465, \ 0.0031371434621643, \ 0.0031371434621643, \ 0.0031371434621643, \ 0.0040930651478197, \ 0.0040930651478197, \ 0.0040930651478197, \ 0.0003670659894181, \ 0.0003670659894181, \ 0.0003670659894181, \ 0.0003670659894181, \ 0.0003670659894181, \ 0.0003670659894181, \ 0.0005709699094042, \ 0.0005709699094042, \ 0.0005709699094042, \ 0.0005709699094042, \ 0.0005709699094042, \ 0.0005709699094042, \ 0.0008761135391688, \ 0.0008761135391688, \ 0.0008761135391688, \ 0.0008761135391688, \ 0.0008761135391688, \ 0.0008761135391688, \ 0.0012513146853205, \ 0.0012513146853205, \ 0.0012513146853205, \ 0.0030871109749242, \ 0.0030871109749242, \ 0.0030871109749242, \ 0.0030871109749242, \ 0.0030871109749242, \ 0.0030871109749242, \ 0.0030558057702988, \ 0.0030558057702988, \ 0.0030558057702988 ] ) return a, b, c, w def rule46 ( ): #*****************************************************************************80 # ## rule46() returns the rule of precision 46. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.4791627094810211, \ 0.4791627094810211, \ 0.0416745810379577, \ 0.3979697646407098, \ 0.4479070861932129, \ 0.1541231491660771, \ 0.4479070861932128, \ 0.3979697646407099, \ 0.1541231491660771, \ 0.4143076079881758, \ 0.4725556860878008, \ 0.1131367059240233, \ 0.4725556860878007, \ 0.4143076079881759, \ 0.1131367059240234, \ 0.3297282498766237, \ 0.5972534223436730, \ 0.0730183277797033, \ 0.5972534223436731, \ 0.3297282498766237, \ 0.0730183277797032, \ 0.2257592423300578, \ 0.6644373808625786, \ 0.1098033768073635, \ 0.6644373808625786, \ 0.2257592423300578, \ 0.1098033768073634, \ 0.0486830795833199, \ 0.9026338408333598, \ 0.0486830795833202, \ 0.4868494344525785, \ 0.4868494344525786, \ 0.0263011310948430, \ 0.3286993475605237, \ 0.5684647770684034, \ 0.1028358753710730, \ 0.5684647770684034, \ 0.3286993475605237, \ 0.1028358753710729, \ 0.0570245183292809, \ 0.9325204663263090, \ 0.0104550153444102, \ 0.9325204663263090, \ 0.0570245183292810, \ 0.0104550153444098, \ 0.2181534906276071, \ 0.6343242478263365, \ 0.1475222615460565, \ 0.6343242478263365, \ 0.2181534906276072, \ 0.1475222615460563, \ 0.2023063458834636, \ 0.7455675573091064, \ 0.0521260968074301, \ 0.7455675573091063, \ 0.2023063458834636, \ 0.0521260968074299, \ 0.2132832098088080, \ 0.7066325944250231, \ 0.0800841957661689, \ 0.7066325944250231, \ 0.2132832098088080, \ 0.0800841957661687, \ 0.0082133588712220, \ 0.9896258607741097, \ 0.0021607803546684, \ 0.9896258607741097, \ 0.0082133588712220, \ 0.0021607803546680, \ 0.4615153616123003, \ 0.5271208360379724, \ 0.0113638023497272, \ 0.5271208360379723, \ 0.4615153616123003, \ 0.0113638023497272, \ 0.3546224673127057, \ 0.5155990090696432, \ 0.1297785236176510, \ 0.5155990090696433, \ 0.3546224673127058, \ 0.1297785236176509, \ 0.3109206435860316, \ 0.6401420778067229, \ 0.0489372786072454, \ 0.6401420778067229, \ 0.3109206435860316, \ 0.0489372786072453, \ 0.3049557841332307, \ 0.5366266568593034, \ 0.1584175590074660, \ 0.5366266568593034, \ 0.3049557841332306, \ 0.1584175590074658, \ 0.2507944375639041, \ 0.5737054769976868, \ 0.1755000854384091, \ 0.5737054769976868, \ 0.2507944375639042, \ 0.1755000854384089, \ 0.1962948092294495, \ 0.6074103815411007, \ 0.1962948092294496, \ 0.1657987165670959, \ 0.6684025668658078, \ 0.1657987165670963, \ 0.4338692218644805, \ 0.5130043968250232, \ 0.0531263813104962, \ 0.5130043968250232, \ 0.4338692218644806, \ 0.0531263813104962, \ 0.0770376986253196, \ 0.8720533240163508, \ 0.0509089773583296, \ 0.8720533240163508, \ 0.0770376986253197, \ 0.0509089773583293, \ 0.2768361860195224, \ 0.7120424143833398, \ 0.0111213995971378, \ 0.7120424143833398, \ 0.2768361860195226, \ 0.0111213995971376, \ 0.1736371621034214, \ 0.8145830842158606, \ 0.0117797536807180, \ 0.8145830842158606, \ 0.1736371621034215, \ 0.0117797536807177, \ 0.3354336886613770, \ 0.6527581850349298, \ 0.0118081263036934, \ 0.6527581850349297, \ 0.3354336886613770, \ 0.0118081263036932, \ 0.3750642184523966, \ 0.5736918975567098, \ 0.0512438839908936, \ 0.5736918975567098, \ 0.3750642184523967, \ 0.0512438839908935, \ 0.3467112861299004, \ 0.4707474573939668, \ 0.1825412564761328, \ 0.4707474573939667, \ 0.3467112861299005, \ 0.1825412564761327, \ 0.2559685112606641, \ 0.6901296172890430, \ 0.0539018714502929, \ 0.6901296172890431, \ 0.2559685112606642, \ 0.0539018714502927, \ 0.2920069207885316, \ 0.6806497657499146, \ 0.0273433134615538, \ 0.6806497657499146, \ 0.2920069207885317, \ 0.0273433134615535, \ 0.2364172395795756, \ 0.7338403785411441, \ 0.0297423818792803, \ 0.7338403785411441, \ 0.2364172395795756, \ 0.0297423818792801, \ 0.4661508981294354, \ 0.5316578071895072, \ 0.0021912946810573, \ 0.5316578071895072, \ 0.4661508981294354, \ 0.0021912946810573, \ 0.2234826291455856, \ 0.7639437050178102, \ 0.0125736658366042, \ 0.7639437050178102, \ 0.2234826291455856, \ 0.0125736658366041, \ 0.3973680138780006, \ 0.5911123169924868, \ 0.0115196691295125, \ 0.5911123169924869, \ 0.3973680138780006, \ 0.0115196691295124, \ 0.2856792432449899, \ 0.5036527190882436, \ 0.2106680376667663, \ 0.5036527190882436, \ 0.2856792432449899, \ 0.2106680376667662, \ 0.2290071177870446, \ 0.5419857644259105, \ 0.2290071177870448, \ 0.2998981018797286, \ 0.4002037962405427, \ 0.2998981018797286, \ 0.4009919122964068, \ 0.5968372374211253, \ 0.0021708502824680, \ 0.5968372374211253, \ 0.4009919122964067, \ 0.0021708502824680, \ 0.1562735104040767, \ 0.7879600672161253, \ 0.0557664223797980, \ 0.7879600672161253, \ 0.1562735104040768, \ 0.0557664223797977, \ 0.0477858936846818, \ 0.9501161980450165, \ 0.0020979082703018, \ 0.9501161980450166, \ 0.0477858936846819, \ 0.0020979082703013, \ 0.1822491599313741, \ 0.7886726424890335, \ 0.0290781975795925, \ 0.7886726424890333, \ 0.1822491599313742, \ 0.0290781975795923, \ 0.3660812614114254, \ 0.3660812614114254, \ 0.2678374771771491, \ 0.0893475681919859, \ 0.8990694649639888, \ 0.0115829668440254, \ 0.8990694649639889, \ 0.0893475681919860, \ 0.0115829668440250, \ 0.1652198812399128, \ 0.7473177571098144, \ 0.0874623616502729, \ 0.7473177571098144, \ 0.1652198812399128, \ 0.0874623616502726, \ 0.0805280047391684, \ 0.9173934916626123, \ 0.0020785035982195, \ 0.9173934916626122, \ 0.0805280047391685, \ 0.0020785035982190, \ 0.3305415015675990, \ 0.4329807146876172, \ 0.2364777837447837, \ 0.4329807146876172, \ 0.3305415015675991, \ 0.2364777837447836, \ 0.1750740132522936, \ 0.7021169686939935, \ 0.1228090180537130, \ 0.7021169686939934, \ 0.1750740132522937, \ 0.1228090180537126, \ 0.1133949730294224, \ 0.8315999985260938, \ 0.0550050284444840, \ 0.8315999985260938, \ 0.1133949730294224, \ 0.0550050284444836, \ 0.0945442284064488, \ 0.8766622383664391, \ 0.0287935332271122, \ 0.8766622383664391, \ 0.0945442284064488, \ 0.0287935332271118, \ 0.0589589423608463, \ 0.9147477258472858, \ 0.0262933317918678, \ 0.9147477258472859, \ 0.0589589423608463, \ 0.0262933317918676, \ 0.3554461171023697, \ 0.6162465555124068, \ 0.0283073273852236, \ 0.6162465555124067, \ 0.3554461171023696, \ 0.0283073273852235, \ 0.4206278444454289, \ 0.5512452167474322, \ 0.0281269388071388, \ 0.5512452167474322, \ 0.4206278444454289, \ 0.0281269388071388, \ 0.0307693439520818, \ 0.9384613120958362, \ 0.0307693439520821, \ 0.2763424771664457, \ 0.7215566217404850, \ 0.0021009010930694, \ 0.7215566217404851, \ 0.2763424771664458, \ 0.0021009010930691, \ 0.1358344051381373, \ 0.8336434944596028, \ 0.0305221004022600, \ 0.8336434944596030, \ 0.1358344051381374, \ 0.0305221004022596, \ 0.1214324449203873, \ 0.7904245130980823, \ 0.0881430419815304, \ 0.7904245130980824, \ 0.1214324449203874, \ 0.0881430419815301, \ 0.0824986937635583, \ 0.8350026124728831, \ 0.0824986937635587, \ 0.1292544813329482, \ 0.8581647113948480, \ 0.0125808072722039, \ 0.8581647113948480, \ 0.1292544813329483, \ 0.0125808072722036, \ 0.2729393183303263, \ 0.6431846260118416, \ 0.0838760556578322, \ 0.6431846260118415, \ 0.2729393183303264, \ 0.0838760556578320, \ 0.4608230043475881, \ 0.4608230043475881, \ 0.0783539913048237, \ 0.2762244316742870, \ 0.5989839678810083, \ 0.1247916004447048, \ 0.5989839678810083, \ 0.2762244316742870, \ 0.1247916004447046, \ 0.1665310619918011, \ 0.8312386887187595, \ 0.0022302492894395, \ 0.8312386887187594, \ 0.1665310619918010, \ 0.0022302492894393, \ 0.3373238618789556, \ 0.6603914710100434, \ 0.0022846671110011, \ 0.6603914710100434, \ 0.3373238618789556, \ 0.0022846671110009, \ 0.2666157086976967, \ 0.4667685826046064, \ 0.2666157086976969, \ 0.1284394349475123, \ 0.7431211301049753, \ 0.1284394349475125, \ 0.3899848376803788, \ 0.5268218597395553, \ 0.0831933025800658, \ 0.5268218597395553, \ 0.3899848376803788, \ 0.0831933025800657, \ 0.3333333333333333, \ 0.2190574020296069, \ 0.7785355668785605, \ 0.0024070310918327, \ 0.7785355668785605, \ 0.2190574020296069, \ 0.0024070310918324, \ 0.1203413424430903, \ 0.8772415939384313, \ 0.0024170636184784, \ 0.8772415939384313, \ 0.1203413424430904, \ 0.0024170636184781, \ 0.3975115754020483, \ 0.3975115754020484, \ 0.2049768491959033, \ 0.0321434597854268, \ 0.9549696683961201, \ 0.0128868718184532, \ 0.9549696683961202, \ 0.0321434597854269, \ 0.0128868718184528, \ 0.0128796984358850, \ 0.9742406031282296, \ 0.0128796984358854, \ 0.0239783625881974, \ 0.9734342386997918, \ 0.0025873987120110, \ 0.9734342386997918, \ 0.0239783625881975, \ 0.0025873987120104, \ 0.0004929222424058, \ 0.9990141555151880, \ 0.0004929222424063 ] ) b = np.array ( [ \ 0.0416745810379578, \ 0.4791627094810212, \ 0.4791627094810214, \ 0.1541231491660773, \ 0.3979697646407100, \ 0.4479070861932131, \ 0.1541231491660773, \ 0.4479070861932130, \ 0.3979697646407100, \ 0.1131367059240234, \ 0.4143076079881759, \ 0.4725556860878009, \ 0.1131367059240234, \ 0.4725556860878009, \ 0.4143076079881760, \ 0.0730183277797033, \ 0.3297282498766238, \ 0.5972534223436732, \ 0.0730183277797033, \ 0.5972534223436731, \ 0.3297282498766239, \ 0.1098033768073636, \ 0.2257592423300578, \ 0.6644373808625790, \ 0.1098033768073636, \ 0.6644373808625788, \ 0.2257592423300580, \ 0.0486830795833202, \ 0.0486830795833199, \ 0.9026338408333601, \ 0.0263011310948430, \ 0.4868494344525785, \ 0.4868494344525787, \ 0.1028358753710730, \ 0.3286993475605237, \ 0.5684647770684035, \ 0.1028358753710730, \ 0.5684647770684035, \ 0.3286993475605239, \ 0.0104550153444101, \ 0.0570245183292809, \ 0.9325204663263091, \ 0.0104550153444101, \ 0.9325204663263091, \ 0.0570245183292812, \ 0.1475222615460564, \ 0.2181534906276071, \ 0.6343242478263366, \ 0.1475222615460564, \ 0.6343242478263366, \ 0.2181534906276073, \ 0.0521260968074301, \ 0.2023063458834636, \ 0.7455675573091065, \ 0.0521260968074301, \ 0.7455675573091065, \ 0.2023063458834639, \ 0.0800841957661689, \ 0.2132832098088080, \ 0.7066325944250232, \ 0.0800841957661689, \ 0.7066325944250232, \ 0.2132832098088083, \ 0.0021607803546683, \ 0.0082133588712219, \ 0.9896258607741099, \ 0.0021607803546683, \ 0.9896258607741099, \ 0.0082133588712223, \ 0.0113638023497273, \ 0.4615153616123004, \ 0.5271208360379727, \ 0.0113638023497273, \ 0.5271208360379724, \ 0.4615153616123006, \ 0.1297785236176510, \ 0.3546224673127058, \ 0.5155990090696434, \ 0.1297785236176510, \ 0.5155990090696433, \ 0.3546224673127060, \ 0.0489372786072454, \ 0.3109206435860317, \ 0.6401420778067232, \ 0.0489372786072454, \ 0.6401420778067232, \ 0.3109206435860319, \ 0.1584175590074660, \ 0.3049557841332307, \ 0.5366266568593036, \ 0.1584175590074660, \ 0.5366266568593036, \ 0.3049557841332309, \ 0.1755000854384091, \ 0.2507944375639042, \ 0.5737054769976869, \ 0.1755000854384091, \ 0.5737054769976868, \ 0.2507944375639043, \ 0.1962948092294497, \ 0.1962948092294495, \ 0.6074103815411009, \ 0.1657987165670962, \ 0.1657987165670960, \ 0.6684025668658079, \ 0.0531263813104963, \ 0.4338692218644806, \ 0.5130043968250234, \ 0.0531263813104963, \ 0.5130043968250232, \ 0.4338692218644807, \ 0.0509089773583296, \ 0.0770376986253196, \ 0.8720533240163509, \ 0.0509089773583296, \ 0.8720533240163509, \ 0.0770376986253199, \ 0.0111213995971377, \ 0.2768361860195225, \ 0.7120424143833399, \ 0.0111213995971377, \ 0.7120424143833398, \ 0.2768361860195228, \ 0.0117797536807180, \ 0.1736371621034214, \ 0.8145830842158608, \ 0.0117797536807180, \ 0.8145830842158608, \ 0.1736371621034218, \ 0.0118081263036934, \ 0.3354336886613770, \ 0.6527581850349299, \ 0.0118081263036934, \ 0.6527581850349298, \ 0.3354336886613772, \ 0.0512438839908936, \ 0.3750642184523967, \ 0.5736918975567099, \ 0.0512438839908936, \ 0.5736918975567098, \ 0.3750642184523969, \ 0.1825412564761328, \ 0.3467112861299005, \ 0.4707474573939669, \ 0.1825412564761328, \ 0.4707474573939668, \ 0.3467112861299007, \ 0.0539018714502929, \ 0.2559685112606642, \ 0.6901296172890432, \ 0.0539018714502929, \ 0.6901296172890431, \ 0.2559685112606644, \ 0.0273433134615537, \ 0.2920069207885316, \ 0.6806497657499148, \ 0.0273433134615537, \ 0.6806497657499148, \ 0.2920069207885319, \ 0.0297423818792803, \ 0.2364172395795756, \ 0.7338403785411444, \ 0.0297423818792803, \ 0.7338403785411444, \ 0.2364172395795759, \ 0.0021912946810574, \ 0.4661508981294356, \ 0.5316578071895074, \ 0.0021912946810574, \ 0.5316578071895073, \ 0.4661508981294357, \ 0.0125736658366043, \ 0.2234826291455856, \ 0.7639437050178104, \ 0.0125736658366043, \ 0.7639437050178103, \ 0.2234826291455859, \ 0.0115196691295125, \ 0.3973680138780006, \ 0.5911123169924871, \ 0.0115196691295125, \ 0.5911123169924870, \ 0.3973680138780009, \ 0.2106680376667663, \ 0.2856792432449901, \ 0.5036527190882438, \ 0.2106680376667663, \ 0.5036527190882438, \ 0.2856792432449901, \ 0.2290071177870448, \ 0.2290071177870447, \ 0.5419857644259106, \ 0.2998981018797288, \ 0.2998981018797287, \ 0.4002037962405428, \ 0.0021708502824680, \ 0.4009919122964068, \ 0.5968372374211254, \ 0.0021708502824680, \ 0.5968372374211253, \ 0.4009919122964070, \ 0.0557664223797979, \ 0.1562735104040768, \ 0.7879600672161254, \ 0.0557664223797979, \ 0.7879600672161254, \ 0.1562735104040771, \ 0.0020979082703016, \ 0.0477858936846818, \ 0.9501161980450167, \ 0.0020979082703016, \ 0.9501161980450167, \ 0.0477858936846822, \ 0.0290781975795925, \ 0.1822491599313741, \ 0.7886726424890337, \ 0.0290781975795925, \ 0.7886726424890335, \ 0.1822491599313744, \ 0.2678374771771493, \ 0.3660812614114254, \ 0.3660812614114256, \ 0.0115829668440253, \ 0.0893475681919859, \ 0.8990694649639890, \ 0.0115829668440253, \ 0.8990694649639890, \ 0.0893475681919862, \ 0.0874623616502728, \ 0.1652198812399128, \ 0.7473177571098146, \ 0.0874623616502728, \ 0.7473177571098146, \ 0.1652198812399130, \ 0.0020785035982193, \ 0.0805280047391684, \ 0.9173934916626123, \ 0.0020785035982193, \ 0.9173934916626123, \ 0.0805280047391688, \ 0.2364777837447838, \ 0.3305415015675991, \ 0.4329807146876173, \ 0.2364777837447838, \ 0.4329807146876173, \ 0.3305415015675992, \ 0.1228090180537129, \ 0.1750740132522937, \ 0.7021169686939935, \ 0.1228090180537129, \ 0.7021169686939936, \ 0.1750740132522939, \ 0.0550050284444838, \ 0.1133949730294223, \ 0.8315999985260939, \ 0.0550050284444838, \ 0.8315999985260939, \ 0.1133949730294226, \ 0.0287935332271121, \ 0.0945442284064488, \ 0.8766622383664393, \ 0.0287935332271121, \ 0.8766622383664393, \ 0.0945442284064491, \ 0.0262933317918678, \ 0.0589589423608463, \ 0.9147477258472861, \ 0.0262933317918678, \ 0.9147477258472861, \ 0.0589589423608466, \ 0.0283073273852236, \ 0.3554461171023697, \ 0.6162465555124070, \ 0.0283073273852236, \ 0.6162465555124069, \ 0.3554461171023699, \ 0.0281269388071389, \ 0.4206278444454289, \ 0.5512452167474324, \ 0.0281269388071389, \ 0.5512452167474323, \ 0.4206278444454292, \ 0.0307693439520821, \ 0.0307693439520817, \ 0.9384613120958364, \ 0.0021009010930693, \ 0.2763424771664457, \ 0.7215566217404851, \ 0.0021009010930693, \ 0.7215566217404851, \ 0.2763424771664461, \ 0.0305221004022599, \ 0.1358344051381373, \ 0.8336434944596030, \ 0.0305221004022599, \ 0.8336434944596030, \ 0.1358344051381376, \ 0.0881430419815303, \ 0.1214324449203873, \ 0.7904245130980825, \ 0.0881430419815303, \ 0.7904245130980825, \ 0.1214324449203876, \ 0.0824986937635586, \ 0.0824986937635583, \ 0.8350026124728833, \ 0.0125808072722039, \ 0.1292544813329482, \ 0.8581647113948481, \ 0.0125808072722039, \ 0.8581647113948480, \ 0.1292544813329486, \ 0.0838760556578322, \ 0.2729393183303264, \ 0.6431846260118417, \ 0.0838760556578322, \ 0.6431846260118417, \ 0.2729393183303265, \ 0.0783539913048238, \ 0.4608230043475882, \ 0.4608230043475884, \ 0.1247916004447048, \ 0.2762244316742871, \ 0.5989839678810084, \ 0.1247916004447048, \ 0.5989839678810084, \ 0.2762244316742872, \ 0.0022302492894395, \ 0.1665310619918011, \ 0.8312386887187597, \ 0.0022302492894395, \ 0.8312386887187597, \ 0.1665310619918013, \ 0.0022846671110010, \ 0.3373238618789556, \ 0.6603914710100435, \ 0.0022846671110010, \ 0.6603914710100435, \ 0.3373238618789559, \ 0.2666157086976969, \ 0.2666157086976969, \ 0.4667685826046065, \ 0.1284394349475125, \ 0.1284394349475123, \ 0.7431211301049754, \ 0.0831933025800659, \ 0.3899848376803789, \ 0.5268218597395556, \ 0.0831933025800659, \ 0.5268218597395554, \ 0.3899848376803791, \ 0.3333333333333334, \ 0.0024070310918326, \ 0.2190574020296069, \ 0.7785355668785606, \ 0.0024070310918326, \ 0.7785355668785606, \ 0.2190574020296072, \ 0.0024170636184783, \ 0.1203413424430903, \ 0.8772415939384315, \ 0.0024170636184783, \ 0.8772415939384315, \ 0.1203413424430907, \ 0.2049768491959034, \ 0.3975115754020485, \ 0.3975115754020485, \ 0.0128868718184530, \ 0.0321434597854268, \ 0.9549696683961202, \ 0.0128868718184530, \ 0.9549696683961204, \ 0.0321434597854271, \ 0.0128796984358853, \ 0.0128796984358850, \ 0.9742406031282298, \ 0.0025873987120107, \ 0.0239783625881974, \ 0.9734342386997918, \ 0.0025873987120107, \ 0.9734342386997921, \ 0.0239783625881978, \ 0.0004929222424061, \ 0.0004929222424058, \ 0.9990141555151881 ] ) c = np.array ( [ \ 0.4791627094810211, \ 0.0416745810379577, \ 0.4791627094810209, \ 0.4479070861932128, \ 0.1541231491660772, \ 0.3979697646407097, \ 0.3979697646407099, \ 0.1541231491660771, \ 0.4479070861932128, \ 0.4725556860878008, \ 0.1131367059240233, \ 0.4143076079881757, \ 0.4143076079881758, \ 0.1131367059240233, \ 0.4725556860878006, \ 0.5972534223436731, \ 0.0730183277797032, \ 0.3297282498766235, \ 0.3297282498766236, \ 0.0730183277797033, \ 0.5972534223436730, \ 0.6644373808625788, \ 0.1098033768073635, \ 0.2257592423300575, \ 0.2257592423300578, \ 0.1098033768073634, \ 0.6644373808625785, \ 0.9026338408333600, \ 0.0486830795833202, \ 0.0486830795833197, \ 0.4868494344525785, \ 0.0263011310948429, \ 0.4868494344525783, \ 0.5684647770684034, \ 0.1028358753710729, \ 0.3286993475605235, \ 0.3286993475605237, \ 0.1028358753710729, \ 0.5684647770684033, \ 0.9325204663263090, \ 0.0104550153444101, \ 0.0570245183292806, \ 0.0570245183292809, \ 0.0104550153444098, \ 0.9325204663263090, \ 0.6343242478263366, \ 0.1475222615460564, \ 0.2181534906276069, \ 0.2181534906276071, \ 0.1475222615460562, \ 0.6343242478263365, \ 0.7455675573091064, \ 0.0521260968074300, \ 0.2023063458834634, \ 0.2023063458834636, \ 0.0521260968074299, \ 0.7455675573091063, \ 0.7066325944250231, \ 0.0800841957661688, \ 0.2132832098088079, \ 0.2132832098088080, \ 0.0800841957661688, \ 0.7066325944250230, \ 0.9896258607741097, \ 0.0021607803546683, \ 0.0082133588712218, \ 0.0082133588712219, \ 0.0021607803546680, \ 0.9896258607741096, \ 0.5271208360379724, \ 0.0113638023497272, \ 0.4615153616123001, \ 0.4615153616123004, \ 0.0113638023497272, \ 0.5271208360379722, \ 0.5155990090696433, \ 0.1297785236176510, \ 0.3546224673127056, \ 0.3546224673127056, \ 0.1297785236176509, \ 0.5155990090696431, \ 0.6401420778067229, \ 0.0489372786072454, \ 0.3109206435860313, \ 0.3109206435860317, \ 0.0489372786072452, \ 0.6401420778067228, \ 0.5366266568593034, \ 0.1584175590074658, \ 0.3049557841332305, \ 0.3049557841332306, \ 0.1584175590074658, \ 0.5366266568593033, \ 0.5737054769976867, \ 0.1755000854384089, \ 0.2507944375639041, \ 0.2507944375639041, \ 0.1755000854384090, \ 0.5737054769976868, \ 0.6074103815411007, \ 0.1962948092294498, \ 0.1962948092294494, \ 0.6684025668658078, \ 0.1657987165670962, \ 0.1657987165670959, \ 0.5130043968250232, \ 0.0531263813104962, \ 0.4338692218644803, \ 0.4338692218644805, \ 0.0531263813104962, \ 0.5130043968250230, \ 0.8720533240163508, \ 0.0509089773583296, \ 0.0770376986253195, \ 0.0770376986253196, \ 0.0509089773583294, \ 0.8720533240163507, \ 0.7120424143833398, \ 0.0111213995971377, \ 0.2768361860195223, \ 0.2768361860195224, \ 0.0111213995971376, \ 0.7120424143833397, \ 0.8145830842158607, \ 0.0117797536807180, \ 0.1736371621034212, \ 0.1736371621034214, \ 0.0117797536807177, \ 0.8145830842158606, \ 0.6527581850349298, \ 0.0118081263036933, \ 0.3354336886613768, \ 0.3354336886613770, \ 0.0118081263036932, \ 0.6527581850349296, \ 0.5736918975567097, \ 0.0512438839908935, \ 0.3750642184523966, \ 0.3750642184523966, \ 0.0512438839908935, \ 0.5736918975567096, \ 0.4707474573939667, \ 0.1825412564761327, \ 0.3467112861299004, \ 0.3467112861299004, \ 0.1825412564761327, \ 0.4707474573939667, \ 0.6901296172890430, \ 0.0539018714502928, \ 0.2559685112606639, \ 0.2559685112606641, \ 0.0539018714502927, \ 0.6901296172890430, \ 0.6806497657499146, \ 0.0273433134615537, \ 0.2920069207885315, \ 0.2920069207885316, \ 0.0273433134615536, \ 0.6806497657499146, \ 0.7338403785411441, \ 0.0297423818792803, \ 0.2364172395795753, \ 0.2364172395795756, \ 0.0297423818792800, \ 0.7338403785411441, \ 0.5316578071895072, \ 0.0021912946810573, \ 0.4661508981294352, \ 0.4661508981294354, \ 0.0021912946810573, \ 0.5316578071895071, \ 0.7639437050178102, \ 0.0125736658366042, \ 0.2234826291455854, \ 0.2234826291455856, \ 0.0125736658366041, \ 0.7639437050178101, \ 0.5911123169924869, \ 0.0115196691295126, \ 0.3973680138780004, \ 0.3973680138780006, \ 0.0115196691295124, \ 0.5911123169924868, \ 0.5036527190882437, \ 0.2106680376667663, \ 0.2856792432449899, \ 0.2856792432449901, \ 0.2106680376667662, \ 0.5036527190882436, \ 0.5419857644259105, \ 0.2290071177870448, \ 0.2290071177870446, \ 0.4002037962405426, \ 0.2998981018797286, \ 0.2998981018797285, \ 0.5968372374211253, \ 0.0021708502824679, \ 0.4009919122964066, \ 0.4009919122964067, \ 0.0021708502824680, \ 0.5968372374211250, \ 0.7879600672161253, \ 0.0557664223797979, \ 0.1562735104040766, \ 0.1562735104040767, \ 0.0557664223797977, \ 0.7879600672161251, \ 0.9501161980450165, \ 0.0020979082703017, \ 0.0477858936846814, \ 0.0477858936846818, \ 0.0020979082703013, \ 0.9501161980450166, \ 0.7886726424890335, \ 0.0290781975795925, \ 0.1822491599313738, \ 0.1822491599313741, \ 0.0290781975795923, \ 0.7886726424890333, \ 0.3660812614114253, \ 0.2678374771771492, \ 0.3660812614114253, \ 0.8990694649639888, \ 0.0115829668440253, \ 0.0893475681919856, \ 0.0893475681919859, \ 0.0115829668440250, \ 0.8990694649639888, \ 0.7473177571098144, \ 0.0874623616502728, \ 0.1652198812399125, \ 0.1652198812399128, \ 0.0874623616502725, \ 0.7473177571098144, \ 0.9173934916626123, \ 0.0020785035982193, \ 0.0805280047391682, \ 0.0805280047391685, \ 0.0020785035982192, \ 0.9173934916626122, \ 0.4329807146876172, \ 0.2364777837447836, \ 0.3305415015675990, \ 0.3305415015675990, \ 0.2364777837447836, \ 0.4329807146876172, \ 0.7021169686939934, \ 0.1228090180537128, \ 0.1750740132522935, \ 0.1750740132522937, \ 0.1228090180537127, \ 0.7021169686939934, \ 0.8315999985260938, \ 0.0550050284444839, \ 0.1133949730294221, \ 0.1133949730294224, \ 0.0550050284444837, \ 0.8315999985260938, \ 0.8766622383664391, \ 0.0287935332271121, \ 0.0945442284064485, \ 0.0945442284064488, \ 0.0287935332271119, \ 0.8766622383664391, \ 0.9147477258472859, \ 0.0262933317918679, \ 0.0589589423608460, \ 0.0589589423608463, \ 0.0262933317918675, \ 0.9147477258472857, \ 0.6162465555124067, \ 0.0283073273852235, \ 0.3554461171023694, \ 0.3554461171023697, \ 0.0283073273852236, \ 0.6162465555124066, \ 0.5512452167474322, \ 0.0281269388071388, \ 0.4206278444454288, \ 0.4206278444454289, \ 0.0281269388071387, \ 0.5512452167474320, \ 0.9384613120958362, \ 0.0307693439520821, \ 0.0307693439520814, \ 0.7215566217404850, \ 0.0021009010930693, \ 0.2763424771664456, \ 0.2763424771664457, \ 0.0021009010930692, \ 0.7215566217404850, \ 0.8336434944596028, \ 0.0305221004022599, \ 0.1358344051381370, \ 0.1358344051381372, \ 0.0305221004022597, \ 0.8336434944596028, \ 0.7904245130980824, \ 0.0881430419815304, \ 0.1214324449203871, \ 0.1214324449203873, \ 0.0881430419815301, \ 0.7904245130980823, \ 0.8350026124728831, \ 0.0824986937635586, \ 0.0824986937635580, \ 0.8581647113948480, \ 0.0125808072722038, \ 0.1292544813329480, \ 0.1292544813329482, \ 0.0125808072722037, \ 0.8581647113948477, \ 0.6431846260118415, \ 0.0838760556578321, \ 0.2729393183303261, \ 0.2729393183303264, \ 0.0838760556578320, \ 0.6431846260118415, \ 0.4608230043475882, \ 0.0783539913048238, \ 0.4608230043475879, \ 0.5989839678810082, \ 0.1247916004447047, \ 0.2762244316742869, \ 0.2762244316742870, \ 0.1247916004447046, \ 0.5989839678810082, \ 0.8312386887187595, \ 0.0022302492894394, \ 0.1665310619918008, \ 0.1665310619918011, \ 0.0022302492894393, \ 0.8312386887187594, \ 0.6603914710100434, \ 0.0022846671110010, \ 0.3373238618789555, \ 0.3373238618789556, \ 0.0022846671110009, \ 0.6603914710100431, \ 0.4667685826046063, \ 0.2666157086976967, \ 0.2666157086976967, \ 0.7431211301049753, \ 0.1284394349475124, \ 0.1284394349475121, \ 0.5268218597395554, \ 0.0831933025800658, \ 0.3899848376803786, \ 0.3899848376803788, \ 0.0831933025800659, \ 0.5268218597395552, \ 0.3333333333333333, \ 0.7785355668785605, \ 0.0024070310918325, \ 0.2190574020296067, \ 0.2190574020296069, \ 0.0024070310918324, \ 0.7785355668785604, \ 0.8772415939384313, \ 0.0024170636184784, \ 0.1203413424430901, \ 0.1203413424430904, \ 0.0024170636184782, \ 0.8772415939384312, \ 0.3975115754020483, \ 0.2049768491959031, \ 0.3975115754020483, \ 0.9549696683961202, \ 0.0128868718184531, \ 0.0321434597854267, \ 0.0321434597854268, \ 0.0128868718184527, \ 0.9549696683961202, \ 0.9742406031282297, \ 0.0128796984358854, \ 0.0128796984358848, \ 0.9734342386997918, \ 0.0025873987120108, \ 0.0239783625881972, \ 0.0239783625881974, \ 0.0025873987120104, \ 0.9734342386997918, \ 0.9990141555151881, \ 0.0004929222424062, \ 0.0004929222424056 ] ) w = np.array ( [ \ 0.0015063623878996, \ 0.0015063623878996, \ 0.0015063623878996, \ 0.0044537081869330, \ 0.0044537081869330, \ 0.0044537081869330, \ 0.0044537081869330, \ 0.0044537081869330, \ 0.0044537081869330, \ 0.0043200095246416, \ 0.0043200095246416, \ 0.0043200095246416, \ 0.0043200095246416, \ 0.0043200095246416, \ 0.0043200095246416, \ 0.0030868796559389, \ 0.0030868796559389, \ 0.0030868796559389, \ 0.0030868796559389, \ 0.0030868796559389, \ 0.0030868796559389, \ 0.0034302258154803, \ 0.0034302258154803, \ 0.0034302258154803, \ 0.0034302258154803, \ 0.0034302258154803, \ 0.0034302258154803, \ 0.0012474691816453, \ 0.0012474691816453, \ 0.0012474691816453, \ 0.0021895163833001, \ 0.0021895163833001, \ 0.0021895163833001, \ 0.0037827619823913, \ 0.0037827619823913, \ 0.0037827619823913, \ 0.0037827619823913, \ 0.0037827619823913, \ 0.0037827619823913, \ 0.0006704306400626, \ 0.0006704306400626, \ 0.0006704306400626, \ 0.0006704306400626, \ 0.0006704306400626, \ 0.0006704306400626, \ 0.0041741147673405, \ 0.0041741147673405, \ 0.0041741147673405, \ 0.0041741147673405, \ 0.0041741147673405, \ 0.0041741147673405, \ 0.0025583666569760, \ 0.0025583666569760, \ 0.0025583666569760, \ 0.0025583666569760, \ 0.0025583666569760, \ 0.0025583666569760, \ 0.0031839869521233, \ 0.0031839869521233, \ 0.0031839869521233, \ 0.0031839869521233, \ 0.0031839869521233, \ 0.0031839869521233, \ 0.0001317170927954, \ 0.0001317170927954, \ 0.0001317170927954, \ 0.0001317170927954, \ 0.0001317170927954, \ 0.0001317170927954, \ 0.0016456723831060, \ 0.0016456723831060, \ 0.0016456723831060, \ 0.0016456723831060, \ 0.0016456723831060, \ 0.0016456723831060, \ 0.0045954830932586, \ 0.0045954830932586, \ 0.0045954830932586, \ 0.0045954830932586, \ 0.0045954830932586, \ 0.0045954830932586, \ 0.0028688601568156, \ 0.0028688601568156, \ 0.0028688601568156, \ 0.0028688601568156, \ 0.0028688601568156, \ 0.0028688601568156, \ 0.0047267340609202, \ 0.0047267340609202, \ 0.0047267340609202, \ 0.0047267340609202, \ 0.0047267340609202, \ 0.0047267340609202, \ 0.0048087317688295, \ 0.0048087317688295, \ 0.0048087317688295, \ 0.0048087317688295, \ 0.0048087317688295, \ 0.0048087317688295, \ 0.0045326165183418, \ 0.0045326165183418, \ 0.0045326165183418, \ 0.0041121335512161, \ 0.0041121335512161, \ 0.0041121335512161, \ 0.0031927670836935, \ 0.0031927670836935, \ 0.0031927670836935, \ 0.0031927670836935, \ 0.0031927670836935, \ 0.0031927670836935, \ 0.0017487650502894, \ 0.0017487650502894, \ 0.0017487650502894, \ 0.0017487650502894, \ 0.0017487650502894, \ 0.0017487650502894, \ 0.0014306703323830, \ 0.0014306703323830, \ 0.0014306703323830, \ 0.0014306703323830, \ 0.0014306703323830, \ 0.0014306703323830, \ 0.0012681752789353, \ 0.0012681752789353, \ 0.0012681752789353, \ 0.0012681752789353, \ 0.0012681752789353, \ 0.0012681752789353, \ 0.0015790337439117, \ 0.0015790337439117, \ 0.0015790337439117, \ 0.0015790337439117, \ 0.0015790337439117, \ 0.0015790337439117, \ 0.0032154452084321, \ 0.0032154452084321, \ 0.0032154452084321, \ 0.0032154452084321, \ 0.0032154452084321, \ 0.0032154452084321, \ 0.0053977058220170, \ 0.0053977058220170, \ 0.0053977058220170, \ 0.0053977058220170, \ 0.0053977058220170, \ 0.0053977058220170, \ 0.0030627052030109, \ 0.0030627052030109, \ 0.0030627052030109, \ 0.0030627052030109, \ 0.0030627052030109, \ 0.0030627052030109, \ 0.0023192184096375, \ 0.0023192184096375, \ 0.0023192184096375, \ 0.0023192184096375, \ 0.0023192184096375, \ 0.0023192184096375, \ 0.0022961002901773, \ 0.0022961002901773, \ 0.0022961002901773, \ 0.0022961002901773, \ 0.0022961002901773, \ 0.0022961002901773, \ 0.0007338103320712, \ 0.0007338103320712, \ 0.0007338103320712, \ 0.0007338103320712, \ 0.0007338103320712, \ 0.0007338103320712, \ 0.0014437602767408, \ 0.0014437602767408, \ 0.0014437602767408, \ 0.0014437602767408, \ 0.0014437602767408, \ 0.0014437602767408, \ 0.0016586663239643, \ 0.0016586663239643, \ 0.0016586663239643, \ 0.0016586663239643, \ 0.0016586663239643, \ 0.0016586663239643, \ 0.0055707293081133, \ 0.0055707293081133, \ 0.0055707293081133, \ 0.0055707293081133, \ 0.0055707293081133, \ 0.0055707293081133, \ 0.0053362839978633, \ 0.0053362839978633, \ 0.0053362839978633, \ 0.0064756219278226, \ 0.0064756219278226, \ 0.0064756219278226, \ 0.0007214374344646, \ 0.0007214374344646, \ 0.0007214374344646, \ 0.0007214374344646, \ 0.0007214374344646, \ 0.0007214374344646, \ 0.0026221278244148, \ 0.0026221278244148, \ 0.0026221278244148, \ 0.0026221278244148, \ 0.0026221278244148, \ 0.0026221278244148, \ 0.0003035796033724, \ 0.0003035796033724, \ 0.0003035796033724, \ 0.0003035796033724, \ 0.0003035796033724, \ 0.0003035796033724, \ 0.0021000870011484, \ 0.0021000870011484, \ 0.0021000870011484, \ 0.0021000870011484, \ 0.0021000870011484, \ 0.0021000870011484, \ 0.0065283169454314, \ 0.0065283169454314, \ 0.0065283169454314, \ 0.0009662986187413, \ 0.0009662986187413, \ 0.0009662986187413, \ 0.0009662986187413, \ 0.0009662986187413, \ 0.0009662986187413, \ 0.0032046723702290, \ 0.0032046723702290, \ 0.0032046723702290, \ 0.0032046723702290, \ 0.0032046723702290, \ 0.0032046723702290, \ 0.0003922950453873, \ 0.0003922950453873, \ 0.0003922950453873, \ 0.0003922950453873, \ 0.0003922950453873, \ 0.0003922950453873, \ 0.0062575812080365, \ 0.0062575812080365, \ 0.0062575812080365, \ 0.0062575812080365, \ 0.0062575812080365, \ 0.0062575812080365, \ 0.0037812405140909, \ 0.0037812405140909, \ 0.0037812405140909, \ 0.0037812405140909, \ 0.0037812405140909, \ 0.0037812405140909, \ 0.0023063619647722, \ 0.0023063619647722, \ 0.0023063619647722, \ 0.0023063619647722, \ 0.0023063619647722, \ 0.0023063619647722, \ 0.0015964303372989, \ 0.0015964303372989, \ 0.0015964303372989, \ 0.0015964303372989, \ 0.0015964303372989, \ 0.0015964303372989, \ 0.0012488360135939, \ 0.0012488360135939, \ 0.0012488360135939, \ 0.0012488360135939, \ 0.0012488360135939, \ 0.0012488360135939, \ 0.0025556284082945, \ 0.0025556284082945, \ 0.0025556284082945, \ 0.0025556284082945, \ 0.0025556284082945, \ 0.0025556284082945, \ 0.0026782849316906, \ 0.0026782849316906, \ 0.0026782849316906, \ 0.0026782849316906, \ 0.0026782849316906, \ 0.0026782849316906, \ 0.0009717097001371, \ 0.0009717097001371, \ 0.0009717097001371, \ 0.0006413900158338, \ 0.0006413900158338, \ 0.0006413900158338, \ 0.0006413900158338, \ 0.0006413900158338, \ 0.0006413900158338, \ 0.0019107173540585, \ 0.0019107173540585, \ 0.0019107173540585, \ 0.0019107173540585, \ 0.0019107173540585, \ 0.0019107173540585, \ 0.0030285648566490, \ 0.0030285648566490, \ 0.0030285648566490, \ 0.0030285648566490, \ 0.0030285648566490, \ 0.0030285648566490, \ 0.0024386979014754, \ 0.0024386979014754, \ 0.0024386979014754, \ 0.0011940194745138, \ 0.0011940194745138, \ 0.0011940194745138, \ 0.0011940194745138, \ 0.0011940194745138, \ 0.0011940194745138, \ 0.0039897861442201, \ 0.0039897861442201, \ 0.0039897861442201, \ 0.0039897861442201, \ 0.0039897861442201, \ 0.0039897861442201, \ 0.0041882040717764, \ 0.0041882040717764, \ 0.0041882040717764, \ 0.0047741598764475, \ 0.0047741598764475, \ 0.0047741598764475, \ 0.0047741598764475, \ 0.0047741598764475, \ 0.0047741598764475, \ 0.0005681012975307, \ 0.0005681012975307, \ 0.0005681012975307, \ 0.0005681012975307, \ 0.0005681012975307, \ 0.0005681012975307, \ 0.0007292897898915, \ 0.0007292897898915, \ 0.0007292897898915, \ 0.0007292897898915, \ 0.0007292897898915, \ 0.0007292897898915, \ 0.0059862742964751, \ 0.0059862742964751, \ 0.0059862742964751, \ 0.0037734801565331, \ 0.0037734801565331, \ 0.0037734801565331, \ 0.0043995561699861, \ 0.0043995561699861, \ 0.0043995561699861, \ 0.0043995561699861, \ 0.0043995561699861, \ 0.0043995561699861, \ 0.0066350471232072, \ 0.0006789589985773, \ 0.0006789589985773, \ 0.0006789589985773, \ 0.0006789589985773, \ 0.0006789589985773, \ 0.0006789589985773, \ 0.0005314441134062, \ 0.0005314441134062, \ 0.0005314441134062, \ 0.0005314441134062, \ 0.0005314441134062, \ 0.0005314441134062, \ 0.0064816472544865, \ 0.0064816472544865, \ 0.0064816472544865, \ 0.0006475246634133, \ 0.0006475246634133, \ 0.0006475246634133, \ 0.0006475246634133, \ 0.0006475246634133, \ 0.0006475246634133, \ 0.0004493467102800, \ 0.0004493467102800, \ 0.0004493467102800, \ 0.0002613279460023, \ 0.0002613279460023, \ 0.0002613279460023, \ 0.0002613279460023, \ 0.0002613279460023, \ 0.0002613279460023, \ 0.0000140952201360, \ 0.0000140952201360, \ 0.0000140952201360 ] ) return a, b, c, w def rule47 ( ): #*****************************************************************************80 # ## rule47() returns the rule of precision 47. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3491775041543910, \ 0.3491775041543910, \ 0.3016449916912180, \ 0.0132182347742615, \ 0.9798556571067439, \ 0.0069261081189949, \ 0.9798556571067438, \ 0.0132182347742616, \ 0.0069261081189944, \ 0.1820741432615592, \ 0.7362900096274552, \ 0.0816358471109855, \ 0.7362900096274553, \ 0.1820741432615592, \ 0.0816358471109853, \ 0.1505809273177014, \ 0.7632227066935655, \ 0.0861963659887331, \ 0.7632227066935656, \ 0.1505809273177015, \ 0.0861963659887328, \ 0.3028965441179143, \ 0.3942069117641712, \ 0.3028965441179143, \ 0.0764329826567075, \ 0.8732738368131011, \ 0.0502931805301914, \ 0.8732738368131011, \ 0.0764329826567076, \ 0.0502931805301912, \ 0.0138326160976293, \ 0.9851184849524532, \ 0.0010488989499177, \ 0.9851184849524532, \ 0.0138326160976294, \ 0.0010488989499173, \ 0.0267452272430761, \ 0.9632342751915716, \ 0.0100204975653523, \ 0.9632342751915717, \ 0.0267452272430762, \ 0.0100204975653520, \ 0.0505319024623014, \ 0.8989361950753969, \ 0.0505319024623018, \ 0.3711902367525145, \ 0.4251355102023056, \ 0.2036742530451798, \ 0.4251355102023055, \ 0.3711902367525146, \ 0.2036742530451798, \ 0.3688949727921184, \ 0.4717783433339480, \ 0.1593266838739336, \ 0.4717783433339479, \ 0.3688949727921184, \ 0.1593266838739335, \ 0.4215093928787094, \ 0.4215093928787095, \ 0.1569812142425811, \ 0.1070745798931199, \ 0.8395567175421841, \ 0.0533687025646961, \ 0.8395567175421841, \ 0.1070745798931200, \ 0.0533687025646957, \ 0.1152179121673602, \ 0.7994860233403234, \ 0.0852960644923165, \ 0.7994860233403234, \ 0.1152179121673603, \ 0.0852960644923162, \ 0.4746270243429588, \ 0.4746270243429588, \ 0.0507459513140823, \ 0.4179628539698995, \ 0.5305548481010338, \ 0.0514822979290668, \ 0.5305548481010337, \ 0.4179628539698995, \ 0.0514822979290667, \ 0.0795728420692438, \ 0.8408543158615120, \ 0.0795728420692443, \ 0.0462992599159319, \ 0.9261471086445946, \ 0.0275536314394737, \ 0.9261471086445946, \ 0.0462992599159320, \ 0.0275536314394733, \ 0.3250299373159994, \ 0.5562680355150597, \ 0.1187020271689408, \ 0.5562680355150598, \ 0.3250299373159994, \ 0.1187020271689407, \ 0.2230214568534538, \ 0.6919169659768531, \ 0.0850615771696930, \ 0.6919169659768531, \ 0.2230214568534538, \ 0.0850615771696929, \ 0.3822400802517831, \ 0.4996324113070245, \ 0.1181275084411924, \ 0.4996324113070245, \ 0.3822400802517831, \ 0.1181275084411923, \ 0.3186810168040575, \ 0.4286106325432008, \ 0.2527083506527416, \ 0.4286106325432009, \ 0.3186810168040575, \ 0.2527083506527416, \ 0.3161024291972920, \ 0.4781516295945364, \ 0.2057459412081715, \ 0.4781516295945364, \ 0.3161024291972920, \ 0.2057459412081715, \ 0.0236802291430403, \ 0.9526395417139191, \ 0.0236802291430406, \ 0.2017143602625017, \ 0.7696399026320835, \ 0.0286457371054150, \ 0.7696399026320834, \ 0.2017143602625018, \ 0.0286457371054148, \ 0.3040953744572968, \ 0.6672038004510813, \ 0.0287008250916218, \ 0.6672038004510813, \ 0.3040953744572970, \ 0.0287008250916217, \ 0.2509406000944529, \ 0.7199771640567535, \ 0.0290822358487937, \ 0.7199771640567536, \ 0.2509406000944530, \ 0.0290822358487933, \ 0.2701136854877469, \ 0.6081440785715926, \ 0.1217422359406605, \ 0.6081440785715926, \ 0.2701136854877470, \ 0.1217422359406603, \ 0.4230078867718429, \ 0.5490451947911587, \ 0.0279469184369985, \ 0.5490451947911587, \ 0.4230078867718429, \ 0.0279469184369984, \ 0.2188381084082620, \ 0.6590218248333656, \ 0.1221400667583725, \ 0.6590218248333655, \ 0.2188381084082620, \ 0.1221400667583722, \ 0.2630564357703722, \ 0.4738871284592553, \ 0.2630564357703724, \ 0.3155582824301563, \ 0.5240287324788191, \ 0.1604129850910246, \ 0.5240287324788190, \ 0.3155582824301562, \ 0.1604129850910245, \ 0.3599942050767867, \ 0.5879673898202077, \ 0.0520384051030056, \ 0.5879673898202077, \ 0.3599942050767868, \ 0.0520384051030055, \ 0.0761492805627097, \ 0.8958426221108554, \ 0.0280080973264349, \ 0.8958426221108555, \ 0.0761492805627098, \ 0.0280080973264346, \ 0.3616871250428565, \ 0.6099486756638904, \ 0.0283641992932530, \ 0.6099486756638904, \ 0.3616871250428564, \ 0.0283641992932528, \ 0.4420693972638305, \ 0.4420693972638306, \ 0.1158612054723388, \ 0.4861601074836898, \ 0.4861601074836898, \ 0.0276797850326204, \ 0.3969570429794791, \ 0.5212280019989164, \ 0.0818149550216045, \ 0.5212280019989164, \ 0.3969570429794791, \ 0.0818149550216044, \ 0.2635821046503857, \ 0.5242839990330530, \ 0.2121338963165611, \ 0.5242839990330530, \ 0.2635821046503858, \ 0.2121338963165610, \ 0.1925350542122712, \ 0.7550197415648126, \ 0.0524452042229163, \ 0.7550197415648127, \ 0.1925350542122711, \ 0.0524452042229161, \ 0.1550537980019329, \ 0.8157685255653345, \ 0.0291776764327327, \ 0.8157685255653344, \ 0.1550537980019330, \ 0.0291776764327324, \ 0.0808139183670610, \ 0.9075107861434476, \ 0.0116752954894916, \ 0.9075107861434475, \ 0.0808139183670610, \ 0.0116752954894912, \ 0.1621461225224503, \ 0.6757077549550992, \ 0.1621461225224506, \ 0.0494903005695828, \ 0.9391567442455215, \ 0.0113529551848958, \ 0.9391567442455215, \ 0.0494903005695828, \ 0.0113529551848954, \ 0.3736911818051820, \ 0.3736911818051820, \ 0.2526176363896359, \ 0.3013661191750608, \ 0.6458926721701388, \ 0.0527412086548005, \ 0.6458926721701387, \ 0.3013661191750608, \ 0.0527412086548003, \ 0.2125512689048137, \ 0.5748974621903724, \ 0.2125512689048139, \ 0.1455590941243064, \ 0.8005045213785598, \ 0.0539363844971339, \ 0.8005045213785598, \ 0.1455590941243065, \ 0.0539363844971336, \ 0.0339239311459584, \ 0.9640491722702409, \ 0.0020268965838009, \ 0.9640491722702410, \ 0.0339239311459585, \ 0.0020268965838004, \ 0.4598321741495011, \ 0.4598321741495011, \ 0.0803356517009977, \ 0.4609203982983521, \ 0.5277054877228970, \ 0.0113741139787508, \ 0.5277054877228969, \ 0.4609203982983522, \ 0.0113741139787508, \ 0.2096506369927426, \ 0.6256296272091983, \ 0.1647197357980590, \ 0.6256296272091983, \ 0.2096506369927426, \ 0.1647197357980589, \ 0.3356188307276363, \ 0.5818958864945520, \ 0.0824852827778115, \ 0.5818958864945520, \ 0.3356188307276363, \ 0.0824852827778114, \ 0.1191983560948026, \ 0.8689356180957589, \ 0.0118660258094385, \ 0.8689356180957590, \ 0.1191983560948028, \ 0.0118660258094381, \ 0.1127517427175889, \ 0.8582596771591932, \ 0.0289885801232180, \ 0.8582596771591932, \ 0.1127517427175889, \ 0.0289885801232177, \ 0.2446044849937105, \ 0.7017862630356211, \ 0.0536092519706684, \ 0.7017862630356212, \ 0.2446044849937105, \ 0.0536092519706682, \ 0.2613278952130154, \ 0.5737048122005965, \ 0.1649672925863881, \ 0.5737048122005964, \ 0.2613278952130155, \ 0.1649672925863880, \ 0.2767102223588470, \ 0.6391563190057649, \ 0.0841334586353880, \ 0.6391563190057650, \ 0.2767102223588471, \ 0.0841334586353878, \ 0.3310576983055140, \ 0.6572241609092210, \ 0.0117181407852651, \ 0.6572241609092210, \ 0.3310576983055140, \ 0.0117181407852649, \ 0.1711659603535230, \ 0.7090088803710917, \ 0.1198251592753853, \ 0.7090088803710918, \ 0.1711659603535231, \ 0.1198251592753851, \ 0.2148380935404156, \ 0.7733534324086832, \ 0.0118084740509012, \ 0.7733534324086832, \ 0.2148380935404157, \ 0.0118084740509010, \ 0.1640325957882373, \ 0.8240691684958087, \ 0.0118982357159542, \ 0.8240691684958087, \ 0.1640325957882374, \ 0.0118982357159538, \ 0.2705995205192744, \ 0.7175528792727295, \ 0.0118476002079961, \ 0.7175528792727296, \ 0.2705995205192745, \ 0.0118476002079958, \ 0.3948815299054212, \ 0.5935890233675787, \ 0.0115294467270000, \ 0.5935890233675788, \ 0.3948815299054213, \ 0.0115294467269999, \ 0.4989185291486734, \ 0.4989185291486734, \ 0.0021629417026531, \ 0.0976801440609630, \ 0.9000701501104615, \ 0.0022497058285756, \ 0.9000701501104615, \ 0.0976801440609631, \ 0.0022497058285752, \ 0.4316631884764961, \ 0.5661587284043652, \ 0.0021780831191386, \ 0.5661587284043652, \ 0.4316631884764962, \ 0.0021780831191386, \ 0.1403238605725803, \ 0.8574167083299471, \ 0.0022594310974726, \ 0.8574167083299471, \ 0.1403238605725803, \ 0.0022594310974724, \ 0.1249745067489113, \ 0.7500509865021772, \ 0.1249745067489116, \ 0.2437969001075017, \ 0.7539541488475877, \ 0.0022489510449106, \ 0.7539541488475877, \ 0.2437969001075018, \ 0.0022489510449104, \ 0.0619939934379152, \ 0.9357952236180167, \ 0.0022107829440681, \ 0.9357952236180167, \ 0.0619939934379153, \ 0.0022107829440677, \ 0.3029504928419904, \ 0.6947995757284657, \ 0.0022499314295440, \ 0.6947995757284656, \ 0.3029504928419905, \ 0.0022499314295438, \ 0.1892661005029103, \ 0.8084698602350489, \ 0.0022640392620409, \ 0.8084698602350490, \ 0.1892661005029104, \ 0.0022640392620406, \ 0.3659190279368091, \ 0.6318674601421832, \ 0.0022135119210076, \ 0.6318674601421833, \ 0.3659190279368091, \ 0.0022135119210075, \ 0.0026050966947360, \ 0.9947898066105276, \ 0.0026050966947365 ] ) b = np.array ( [ \ 0.3016449916912181, \ 0.3491775041543910, \ 0.3491775041543911, \ 0.0069261081189947, \ 0.0132182347742614, \ 0.9798556571067439, \ 0.0069261081189947, \ 0.9798556571067439, \ 0.0132182347742619, \ 0.0816358471109855, \ 0.1820741432615593, \ 0.7362900096274555, \ 0.0816358471109855, \ 0.7362900096274555, \ 0.1820741432615595, \ 0.0861963659887331, \ 0.1505809273177014, \ 0.7632227066935657, \ 0.0861963659887331, \ 0.7632227066935657, \ 0.1505809273177016, \ 0.3028965441179145, \ 0.3028965441179144, \ 0.3942069117641713, \ 0.0502931805301914, \ 0.0764329826567075, \ 0.8732738368131013, \ 0.0502931805301914, \ 0.8732738368131013, \ 0.0764329826567078, \ 0.0010488989499175, \ 0.0138326160976293, \ 0.9851184849524532, \ 0.0010488989499175, \ 0.9851184849524532, \ 0.0138326160976297, \ 0.0100204975653523, \ 0.0267452272430761, \ 0.9632342751915718, \ 0.0100204975653523, \ 0.9632342751915718, \ 0.0267452272430765, \ 0.0505319024623017, \ 0.0505319024623013, \ 0.8989361950753971, \ 0.2036742530451799, \ 0.3711902367525146, \ 0.4251355102023057, \ 0.2036742530451799, \ 0.4251355102023057, \ 0.3711902367525147, \ 0.1593266838739337, \ 0.3688949727921184, \ 0.4717783433339481, \ 0.1593266838739337, \ 0.4717783433339481, \ 0.3688949727921186, \ 0.1569812142425812, \ 0.4215093928787095, \ 0.4215093928787095, \ 0.0533687025646960, \ 0.1070745798931199, \ 0.8395567175421843, \ 0.0533687025646960, \ 0.8395567175421843, \ 0.1070745798931203, \ 0.0852960644923164, \ 0.1152179121673602, \ 0.7994860233403235, \ 0.0852960644923164, \ 0.7994860233403235, \ 0.1152179121673605, \ 0.0507459513140824, \ 0.4746270243429588, \ 0.4746270243429590, \ 0.0514822979290668, \ 0.4179628539698995, \ 0.5305548481010339, \ 0.0514822979290668, \ 0.5305548481010338, \ 0.4179628539698997, \ 0.0795728420692441, \ 0.0795728420692439, \ 0.8408543158615122, \ 0.0275536314394735, \ 0.0462992599159318, \ 0.9261471086445947, \ 0.0275536314394735, \ 0.9261471086445947, \ 0.0462992599159322, \ 0.1187020271689408, \ 0.3250299373159995, \ 0.5562680355150599, \ 0.1187020271689408, \ 0.5562680355150599, \ 0.3250299373159996, \ 0.0850615771696930, \ 0.2230214568534538, \ 0.6919169659768534, \ 0.0850615771696930, \ 0.6919169659768533, \ 0.2230214568534540, \ 0.1181275084411924, \ 0.3822400802517831, \ 0.4996324113070247, \ 0.1181275084411924, \ 0.4996324113070246, \ 0.3822400802517833, \ 0.2527083506527417, \ 0.3186810168040576, \ 0.4286106325432010, \ 0.2527083506527417, \ 0.4286106325432010, \ 0.3186810168040576, \ 0.2057459412081716, \ 0.3161024291972920, \ 0.4781516295945366, \ 0.2057459412081716, \ 0.4781516295945365, \ 0.3161024291972921, \ 0.0236802291430406, \ 0.0236802291430402, \ 0.9526395417139194, \ 0.0286457371054149, \ 0.2017143602625017, \ 0.7696399026320836, \ 0.0286457371054149, \ 0.7696399026320834, \ 0.2017143602625020, \ 0.0287008250916218, \ 0.3040953744572970, \ 0.6672038004510815, \ 0.0287008250916218, \ 0.6672038004510813, \ 0.3040953744572972, \ 0.0290822358487935, \ 0.2509406000944530, \ 0.7199771640567536, \ 0.0290822358487935, \ 0.7199771640567536, \ 0.2509406000944532, \ 0.1217422359406605, \ 0.2701136854877469, \ 0.6081440785715928, \ 0.1217422359406605, \ 0.6081440785715927, \ 0.2701136854877472, \ 0.0279469184369985, \ 0.4230078867718430, \ 0.5490451947911588, \ 0.0279469184369985, \ 0.5490451947911587, \ 0.4230078867718431, \ 0.1221400667583725, \ 0.2188381084082620, \ 0.6590218248333657, \ 0.1221400667583725, \ 0.6590218248333657, \ 0.2188381084082622, \ 0.2630564357703725, \ 0.2630564357703724, \ 0.4738871284592555, \ 0.1604129850910247, \ 0.3155582824301563, \ 0.5240287324788192, \ 0.1604129850910247, \ 0.5240287324788192, \ 0.3155582824301565, \ 0.0520384051030056, \ 0.3599942050767868, \ 0.5879673898202079, \ 0.0520384051030056, \ 0.5879673898202077, \ 0.3599942050767870, \ 0.0280080973264348, \ 0.0761492805627097, \ 0.8958426221108556, \ 0.0280080973264348, \ 0.8958426221108556, \ 0.0761492805627100, \ 0.0283641992932530, \ 0.3616871250428565, \ 0.6099486756638907, \ 0.0283641992932530, \ 0.6099486756638907, \ 0.3616871250428568, \ 0.1158612054723389, \ 0.4420693972638307, \ 0.4420693972638308, \ 0.0276797850326205, \ 0.4861601074836898, \ 0.4861601074836900, \ 0.0818149550216045, \ 0.3969570429794792, \ 0.5212280019989165, \ 0.0818149550216045, \ 0.5212280019989165, \ 0.3969570429794793, \ 0.2121338963165612, \ 0.2635821046503858, \ 0.5242839990330532, \ 0.2121338963165612, \ 0.5242839990330532, \ 0.2635821046503860, \ 0.0524452042229163, \ 0.1925350542122712, \ 0.7550197415648128, \ 0.0524452042229163, \ 0.7550197415648128, \ 0.1925350542122714, \ 0.0291776764327326, \ 0.1550537980019329, \ 0.8157685255653346, \ 0.0291776764327326, \ 0.8157685255653346, \ 0.1550537980019333, \ 0.0116752954894915, \ 0.0808139183670610, \ 0.9075107861434477, \ 0.0116752954894915, \ 0.9075107861434477, \ 0.0808139183670613, \ 0.1621461225224505, \ 0.1621461225224504, \ 0.6757077549550993, \ 0.0113529551848956, \ 0.0494903005695827, \ 0.9391567442455218, \ 0.0113529551848956, \ 0.9391567442455218, \ 0.0494903005695831, \ 0.2526176363896360, \ 0.3736911818051821, \ 0.3736911818051821, \ 0.0527412086548005, \ 0.3013661191750608, \ 0.6458926721701389, \ 0.0527412086548005, \ 0.6458926721701388, \ 0.3013661191750611, \ 0.2125512689048139, \ 0.2125512689048138, \ 0.5748974621903725, \ 0.0539363844971338, \ 0.1455590941243064, \ 0.8005045213785600, \ 0.0539363844971338, \ 0.8005045213785600, \ 0.1455590941243067, \ 0.0020268965838007, \ 0.0339239311459583, \ 0.9640491722702410, \ 0.0020268965838007, \ 0.9640491722702410, \ 0.0339239311459588, \ 0.0803356517009978, \ 0.4598321741495012, \ 0.4598321741495013, \ 0.0113741139787509, \ 0.4609203982983522, \ 0.5277054877228973, \ 0.0113741139787509, \ 0.5277054877228970, \ 0.4609203982983524, \ 0.1647197357980591, \ 0.2096506369927426, \ 0.6256296272091985, \ 0.1647197357980591, \ 0.6256296272091985, \ 0.2096506369927428, \ 0.0824852827778116, \ 0.3356188307276364, \ 0.5818958864945523, \ 0.0824852827778116, \ 0.5818958864945523, \ 0.3356188307276366, \ 0.0118660258094384, \ 0.1191983560948026, \ 0.8689356180957590, \ 0.0118660258094384, \ 0.8689356180957590, \ 0.1191983560948030, \ 0.0289885801232180, \ 0.1127517427175889, \ 0.8582596771591934, \ 0.0289885801232180, \ 0.8582596771591934, \ 0.1127517427175892, \ 0.0536092519706684, \ 0.2446044849937105, \ 0.7017862630356213, \ 0.0536092519706684, \ 0.7017862630356212, \ 0.2446044849937108, \ 0.1649672925863881, \ 0.2613278952130155, \ 0.5737048122005965, \ 0.1649672925863881, \ 0.5737048122005965, \ 0.2613278952130156, \ 0.0841334586353880, \ 0.2767102223588471, \ 0.6391563190057651, \ 0.0841334586353880, \ 0.6391563190057651, \ 0.2767102223588473, \ 0.0117181407852650, \ 0.3310576983055140, \ 0.6572241609092212, \ 0.0117181407852650, \ 0.6572241609092211, \ 0.3310576983055142, \ 0.1198251592753853, \ 0.1711659603535231, \ 0.7090088803710918, \ 0.1198251592753853, \ 0.7090088803710918, \ 0.1711659603535233, \ 0.0118084740509012, \ 0.2148380935404156, \ 0.7733534324086834, \ 0.0118084740509012, \ 0.7733534324086833, \ 0.2148380935404159, \ 0.0118982357159540, \ 0.1640325957882373, \ 0.8240691684958088, \ 0.0118982357159540, \ 0.8240691684958088, \ 0.1640325957882376, \ 0.0118476002079960, \ 0.2705995205192745, \ 0.7175528792727297, \ 0.0118476002079960, \ 0.7175528792727297, \ 0.2705995205192748, \ 0.0115294467270000, \ 0.3948815299054213, \ 0.5935890233675789, \ 0.0115294467270000, \ 0.5935890233675788, \ 0.3948815299054215, \ 0.0021629417026532, \ 0.4989185291486735, \ 0.4989185291486736, \ 0.0022497058285755, \ 0.0976801440609630, \ 0.9000701501104617, \ 0.0022497058285755, \ 0.9000701501104617, \ 0.0976801440609633, \ 0.0021780831191386, \ 0.4316631884764962, \ 0.5661587284043654, \ 0.0021780831191386, \ 0.5661587284043653, \ 0.4316631884764964, \ 0.0022594310974726, \ 0.1403238605725803, \ 0.8574167083299473, \ 0.0022594310974726, \ 0.8574167083299473, \ 0.1403238605725806, \ 0.1249745067489116, \ 0.1249745067489113, \ 0.7500509865021772, \ 0.0022489510449106, \ 0.2437969001075017, \ 0.7539541488475879, \ 0.0022489510449106, \ 0.7539541488475878, \ 0.2437969001075020, \ 0.0022107829440680, \ 0.0619939934379152, \ 0.9357952236180170, \ 0.0022107829440680, \ 0.9357952236180170, \ 0.0619939934379155, \ 0.0022499314295439, \ 0.3029504928419904, \ 0.6947995757284657, \ 0.0022499314295439, \ 0.6947995757284657, \ 0.3029504928419907, \ 0.0022640392620408, \ 0.1892661005029103, \ 0.8084698602350490, \ 0.0022640392620408, \ 0.8084698602350490, \ 0.1892661005029106, \ 0.0022135119210076, \ 0.3659190279368091, \ 0.6318674601421835, \ 0.0022135119210076, \ 0.6318674601421833, \ 0.3659190279368094, \ 0.0026050966947363, \ 0.0026050966947360, \ 0.9947898066105276 ] ) c = np.array ( [ \ 0.3491775041543909, \ 0.3016449916912180, \ 0.3491775041543909, \ 0.9798556571067439, \ 0.0069261081189946, \ 0.0132182347742612, \ 0.0132182347742615, \ 0.0069261081189945, \ 0.9798556571067437, \ 0.7362900096274552, \ 0.0816358471109856, \ 0.1820741432615590, \ 0.1820741432615592, \ 0.0816358471109854, \ 0.7362900096274553, \ 0.7632227066935656, \ 0.0861963659887331, \ 0.1505809273177011, \ 0.1505809273177013, \ 0.0861963659887328, \ 0.7632227066935655, \ 0.3942069117641712, \ 0.3028965441179144, \ 0.3028965441179144, \ 0.8732738368131011, \ 0.0502931805301914, \ 0.0764329826567073, \ 0.0764329826567075, \ 0.0502931805301911, \ 0.8732738368131009, \ 0.9851184849524532, \ 0.0010488989499175, \ 0.0138326160976291, \ 0.0138326160976293, \ 0.0010488989499173, \ 0.9851184849524531, \ 0.9632342751915716, \ 0.0100204975653523, \ 0.0267452272430758, \ 0.0267452272430761, \ 0.0100204975653521, \ 0.9632342751915716, \ 0.8989361950753969, \ 0.0505319024623018, \ 0.0505319024623011, \ 0.4251355102023056, \ 0.2036742530451798, \ 0.3711902367525145, \ 0.3711902367525145, \ 0.2036742530451797, \ 0.4251355102023054, \ 0.4717783433339480, \ 0.1593266838739336, \ 0.3688949727921183, \ 0.3688949727921184, \ 0.1593266838739335, \ 0.4717783433339479, \ 0.4215093928787094, \ 0.1569812142425810, \ 0.4215093928787093, \ 0.8395567175421841, \ 0.0533687025646960, \ 0.1070745798931196, \ 0.1070745798931199, \ 0.0533687025646957, \ 0.8395567175421840, \ 0.7994860233403234, \ 0.0852960644923164, \ 0.1152179121673601, \ 0.1152179121673602, \ 0.0852960644923163, \ 0.7994860233403233, \ 0.4746270243429588, \ 0.0507459513140824, \ 0.4746270243429587, \ 0.5305548481010337, \ 0.0514822979290667, \ 0.4179628539698993, \ 0.4179628539698995, \ 0.0514822979290667, \ 0.5305548481010335, \ 0.8408543158615120, \ 0.0795728420692441, \ 0.0795728420692435, \ 0.9261471086445946, \ 0.0275536314394736, \ 0.0462992599159315, \ 0.0462992599159319, \ 0.0275536314394733, \ 0.9261471086445946, \ 0.5562680355150597, \ 0.1187020271689408, \ 0.3250299373159993, \ 0.3250299373159994, \ 0.1187020271689406, \ 0.5562680355150597, \ 0.6919169659768531, \ 0.0850615771696930, \ 0.2230214568534536, \ 0.2230214568534538, \ 0.0850615771696929, \ 0.6919169659768531, \ 0.4996324113070245, \ 0.1181275084411924, \ 0.3822400802517830, \ 0.3822400802517831, \ 0.1181275084411922, \ 0.4996324113070245, \ 0.4286106325432009, \ 0.2527083506527416, \ 0.3186810168040574, \ 0.3186810168040575, \ 0.2527083506527415, \ 0.4286106325432008, \ 0.4781516295945364, \ 0.2057459412081716, \ 0.3161024291972919, \ 0.3161024291972919, \ 0.2057459412081715, \ 0.4781516295945364, \ 0.9526395417139192, \ 0.0236802291430407, \ 0.0236802291430399, \ 0.7696399026320834, \ 0.0286457371054148, \ 0.2017143602625014, \ 0.2017143602625017, \ 0.0286457371054148, \ 0.7696399026320832, \ 0.6672038004510813, \ 0.0287008250916218, \ 0.3040953744572966, \ 0.3040953744572968, \ 0.0287008250916218, \ 0.6672038004510812, \ 0.7199771640567535, \ 0.0290822358487935, \ 0.2509406000944527, \ 0.2509406000944528, \ 0.0290822358487934, \ 0.7199771640567535, \ 0.6081440785715926, \ 0.1217422359406605, \ 0.2701136854877467, \ 0.2701136854877469, \ 0.1217422359406602, \ 0.6081440785715925, \ 0.5490451947911585, \ 0.0279469184369984, \ 0.4230078867718428, \ 0.4230078867718428, \ 0.0279469184369984, \ 0.5490451947911585, \ 0.6590218248333655, \ 0.1221400667583724, \ 0.2188381084082618, \ 0.2188381084082621, \ 0.1221400667583723, \ 0.6590218248333655, \ 0.4738871284592553, \ 0.2630564357703724, \ 0.2630564357703721, \ 0.5240287324788191, \ 0.1604129850910246, \ 0.3155582824301562, \ 0.3155582824301563, \ 0.1604129850910246, \ 0.5240287324788190, \ 0.5879673898202077, \ 0.0520384051030055, \ 0.3599942050767865, \ 0.3599942050767868, \ 0.0520384051030055, \ 0.5879673898202076, \ 0.8958426221108555, \ 0.0280080973264349, \ 0.0761492805627094, \ 0.0761492805627097, \ 0.0280080973264346, \ 0.8958426221108554, \ 0.6099486756638904, \ 0.0283641992932530, \ 0.3616871250428563, \ 0.3616871250428565, \ 0.0283641992932530, \ 0.6099486756638903, \ 0.4420693972638305, \ 0.1158612054723388, \ 0.4420693972638304, \ 0.4861601074836898, \ 0.0276797850326204, \ 0.4861601074836896, \ 0.5212280019989164, \ 0.0818149550216044, \ 0.3969570429794790, \ 0.3969570429794791, \ 0.0818149550216044, \ 0.5212280019989163, \ 0.5242839990330531, \ 0.2121338963165612, \ 0.2635821046503857, \ 0.2635821046503858, \ 0.2121338963165610, \ 0.5242839990330529, \ 0.7550197415648126, \ 0.0524452042229163, \ 0.1925350542122709, \ 0.1925350542122711, \ 0.0524452042229161, \ 0.7550197415648124, \ 0.8157685255653345, \ 0.0291776764327325, \ 0.1550537980019326, \ 0.1550537980019330, \ 0.0291776764327324, \ 0.8157685255653343, \ 0.9075107861434475, \ 0.0116752954894914, \ 0.0808139183670606, \ 0.0808139183670610, \ 0.0116752954894913, \ 0.9075107861434475, \ 0.6757077549550992, \ 0.1621461225224504, \ 0.1621461225224502, \ 0.9391567442455215, \ 0.0113529551848957, \ 0.0494903005695825, \ 0.0494903005695828, \ 0.0113529551848954, \ 0.9391567442455216, \ 0.3736911818051820, \ 0.2526176363896359, \ 0.3736911818051819, \ 0.6458926721701387, \ 0.0527412086548004, \ 0.3013661191750606, \ 0.3013661191750608, \ 0.0527412086548004, \ 0.6458926721701386, \ 0.5748974621903724, \ 0.2125512689048138, \ 0.2125512689048136, \ 0.8005045213785599, \ 0.0539363844971338, \ 0.1455590941243061, \ 0.1455590941243064, \ 0.0539363844971336, \ 0.8005045213785598, \ 0.9640491722702410, \ 0.0020268965838008, \ 0.0339239311459582, \ 0.0339239311459583, \ 0.0020268965838005, \ 0.9640491722702408, \ 0.4598321741495012, \ 0.0803356517009977, \ 0.4598321741495010, \ 0.5277054877228970, \ 0.0113741139787508, \ 0.4609203982983520, \ 0.4609203982983522, \ 0.0113741139787508, \ 0.5277054877228968, \ 0.6256296272091982, \ 0.1647197357980590, \ 0.2096506369927426, \ 0.2096506369927426, \ 0.1647197357980589, \ 0.6256296272091983, \ 0.5818958864945520, \ 0.0824852827778115, \ 0.3356188307276362, \ 0.3356188307276363, \ 0.0824852827778114, \ 0.5818958864945520, \ 0.8689356180957589, \ 0.0118660258094384, \ 0.1191983560948024, \ 0.1191983560948026, \ 0.0118660258094382, \ 0.8689356180957588, \ 0.8582596771591932, \ 0.0289885801232179, \ 0.1127517427175887, \ 0.1127517427175889, \ 0.0289885801232178, \ 0.8582596771591930, \ 0.7017862630356212, \ 0.0536092519706684, \ 0.2446044849937103, \ 0.2446044849937104, \ 0.0536092519706682, \ 0.7017862630356210, \ 0.5737048122005965, \ 0.1649672925863880, \ 0.2613278952130154, \ 0.2613278952130155, \ 0.1649672925863880, \ 0.5737048122005964, \ 0.6391563190057650, \ 0.0841334586353881, \ 0.2767102223588469, \ 0.2767102223588470, \ 0.0841334586353878, \ 0.6391563190057650, \ 0.6572241609092210, \ 0.0117181407852650, \ 0.3310576983055137, \ 0.3310576983055140, \ 0.0117181407852649, \ 0.6572241609092209, \ 0.7090088803710918, \ 0.1198251592753853, \ 0.1711659603535228, \ 0.1711659603535229, \ 0.1198251592753851, \ 0.7090088803710917, \ 0.7733534324086833, \ 0.0118084740509012, \ 0.2148380935404154, \ 0.2148380935404157, \ 0.0118084740509010, \ 0.7733534324086830, \ 0.8240691684958087, \ 0.0118982357159540, \ 0.1640325957882370, \ 0.1640325957882373, \ 0.0118982357159538, \ 0.8240691684958086, \ 0.7175528792727296, \ 0.0118476002079960, \ 0.2705995205192742, \ 0.2705995205192744, \ 0.0118476002079958, \ 0.7175528792727295, \ 0.5935890233675787, \ 0.0115294467270000, \ 0.3948815299054211, \ 0.3948815299054212, \ 0.0115294467269998, \ 0.5935890233675787, \ 0.4989185291486735, \ 0.0021629417026531, \ 0.4989185291486732, \ 0.9000701501104614, \ 0.0022497058285755, \ 0.0976801440609628, \ 0.0976801440609630, \ 0.0022497058285752, \ 0.9000701501104615, \ 0.5661587284043652, \ 0.0021780831191386, \ 0.4316631884764959, \ 0.4316631884764962, \ 0.0021780831191386, \ 0.5661587284043650, \ 0.8574167083299471, \ 0.0022594310974726, \ 0.1403238605725801, \ 0.1403238605725803, \ 0.0022594310974724, \ 0.8574167083299470, \ 0.7500509865021772, \ 0.1249745067489115, \ 0.1249745067489112, \ 0.7539541488475877, \ 0.0022489510449106, \ 0.2437969001075014, \ 0.2437969001075017, \ 0.0022489510449104, \ 0.7539541488475876, \ 0.9357952236180168, \ 0.0022107829440681, \ 0.0619939934379149, \ 0.0619939934379153, \ 0.0022107829440677, \ 0.9357952236180168, \ 0.6947995757284657, \ 0.0022499314295438, \ 0.3029504928419903, \ 0.3029504928419904, \ 0.0022499314295438, \ 0.6947995757284655, \ 0.8084698602350490, \ 0.0022640392620409, \ 0.1892661005029100, \ 0.1892661005029102, \ 0.0022640392620407, \ 0.8084698602350489, \ 0.6318674601421833, \ 0.0022135119210077, \ 0.3659190279368089, \ 0.3659190279368091, \ 0.0022135119210075, \ 0.6318674601421832, \ 0.9947898066105277, \ 0.0026050966947364, \ 0.0026050966947359 ] ) w = np.array ( [ \ 0.0043146569583335, \ 0.0043146569583335, \ 0.0043146569583335, \ 0.0002127820065249, \ 0.0002127820065249, \ 0.0002127820065249, \ 0.0002127820065249, \ 0.0002127820065249, \ 0.0002127820065249, \ 0.0022514827449286, \ 0.0022514827449286, \ 0.0022514827449286, \ 0.0022514827449286, \ 0.0022514827449286, \ 0.0022514827449286, \ 0.0022650701154880, \ 0.0022650701154880, \ 0.0022650701154880, \ 0.0022650701154880, \ 0.0022650701154880, \ 0.0022650701154880, \ 0.0046991712312519, \ 0.0046991712312519, \ 0.0046991712312519, \ 0.0014027295746802, \ 0.0014027295746802, \ 0.0014027295746802, \ 0.0014027295746802, \ 0.0014027295746802, \ 0.0014027295746802, \ 0.0000978099168127, \ 0.0000978099168127, \ 0.0000978099168127, \ 0.0000978099168127, \ 0.0000978099168127, \ 0.0000978099168127, \ 0.0004038629868035, \ 0.0004038629868035, \ 0.0004038629868035, \ 0.0004038629868035, \ 0.0004038629868035, \ 0.0004038629868035, \ 0.0012364924097053, \ 0.0012364924097053, \ 0.0012364924097053, \ 0.0051536553206131, \ 0.0051536553206131, \ 0.0051536553206131, \ 0.0051536553206131, \ 0.0051536553206131, \ 0.0051536553206131, \ 0.0045094710563839, \ 0.0045094710563839, \ 0.0045094710563839, \ 0.0045094710563839, \ 0.0045094710563839, \ 0.0045094710563839, \ 0.0045159973781931, \ 0.0045159973781931, \ 0.0045159973781931, \ 0.0019145889672060, \ 0.0019145889672060, \ 0.0019145889672060, \ 0.0019145889672060, \ 0.0019145889672060, \ 0.0019145889672060, \ 0.0026062651829993, \ 0.0026062651829993, \ 0.0026062651829993, \ 0.0026062651829993, \ 0.0026062651829993, \ 0.0026062651829993, \ 0.0029444810662743, \ 0.0029444810662743, \ 0.0029444810662743, \ 0.0030761572742866, \ 0.0030761572742866, \ 0.0030761572742866, \ 0.0030761572742866, \ 0.0030761572742866, \ 0.0030761572742866, \ 0.0020830024863947, \ 0.0020830024863947, \ 0.0020830024863947, \ 0.0010328123125119, \ 0.0010328123125119, \ 0.0010328123125119, \ 0.0010328123125119, \ 0.0010328123125119, \ 0.0010328123125119, \ 0.0043543612304128, \ 0.0043543612304128, \ 0.0043543612304128, \ 0.0043543612304128, \ 0.0043543612304128, \ 0.0043543612304128, \ 0.0033920879178230, \ 0.0033920879178230, \ 0.0033920879178230, \ 0.0033920879178230, \ 0.0033920879178230, \ 0.0033920879178230, \ 0.0045331567046035, \ 0.0045331567046035, \ 0.0045331567046035, \ 0.0045331567046035, \ 0.0045331567046035, \ 0.0045331567046035, \ 0.0053697193075647, \ 0.0053697193075647, \ 0.0053697193075647, \ 0.0053697193075647, \ 0.0053697193075647, \ 0.0053697193075647, \ 0.0050112518902677, \ 0.0050112518902677, \ 0.0050112518902677, \ 0.0050112518902677, \ 0.0050112518902677, \ 0.0050112518902677, \ 0.0006630078632668, \ 0.0006630078632668, \ 0.0006630078632668, \ 0.0019533942747889, \ 0.0019533942747889, \ 0.0019533942747889, \ 0.0019533942747889, \ 0.0019533942747889, \ 0.0019533942747889, \ 0.0022701532915994, \ 0.0022701532915994, \ 0.0022701532915994, \ 0.0022701532915994, \ 0.0022701532915994, \ 0.0022701532915994, \ 0.0021386729830485, \ 0.0021386729830485, \ 0.0021386729830485, \ 0.0021386729830485, \ 0.0021386729830485, \ 0.0021386729830485, \ 0.0042781341832724, \ 0.0042781341832724, \ 0.0042781341832724, \ 0.0042781341832724, \ 0.0042781341832724, \ 0.0042781341832724, \ 0.0025070193444428, \ 0.0025070193444428, \ 0.0025070193444428, \ 0.0025070193444428, \ 0.0025070193444428, \ 0.0025070193444428, \ 0.0039737311003985, \ 0.0039737311003985, \ 0.0039737311003985, \ 0.0039737311003985, \ 0.0039737311003985, \ 0.0039737311003985, \ 0.0055982544326031, \ 0.0055982544326031, \ 0.0055982544326031, \ 0.0047404136863378, \ 0.0047404136863378, \ 0.0047404136863378, \ 0.0047404136863378, \ 0.0047404136863378, \ 0.0047404136863378, \ 0.0031609021577845, \ 0.0031609021577845, \ 0.0031609021577845, \ 0.0031609021577845, \ 0.0031609021577845, \ 0.0031609021577845, \ 0.0013064930317837, \ 0.0013064930317837, \ 0.0013064930317837, \ 0.0013064930317837, \ 0.0013064930317837, \ 0.0013064930317837, \ 0.0024224165705941, \ 0.0024224165705941, \ 0.0024224165705941, \ 0.0024224165705941, \ 0.0024224165705941, \ 0.0024224165705941, \ 0.0045518145135699, \ 0.0045518145135699, \ 0.0045518145135699, \ 0.0025072813505809, \ 0.0025072813505809, \ 0.0025072813505809, \ 0.0041337585903884, \ 0.0041337585903884, \ 0.0041337585903884, \ 0.0041337585903884, \ 0.0041337585903884, \ 0.0041337585903884, \ 0.0051051331812112, \ 0.0051051331812112, \ 0.0051051331812112, \ 0.0051051331812112, \ 0.0051051331812112, \ 0.0051051331812112, \ 0.0026976233339834, \ 0.0026976233339834, \ 0.0026976233339834, \ 0.0026976233339834, \ 0.0026976233339834, \ 0.0026976233339834, \ 0.0018809643979073, \ 0.0018809643979073, \ 0.0018809643979073, \ 0.0018809643979073, \ 0.0018809643979073, \ 0.0018809643979073, \ 0.0009142190102743, \ 0.0009142190102743, \ 0.0009142190102743, \ 0.0009142190102743, \ 0.0009142190102743, \ 0.0009142190102743, \ 0.0040644299258672, \ 0.0040644299258672, \ 0.0040644299258672, \ 0.0007010656028691, \ 0.0007010656028691, \ 0.0007010656028691, \ 0.0007010656028691, \ 0.0007010656028691, \ 0.0007010656028691, \ 0.0055051135413514, \ 0.0055051135413514, \ 0.0055051135413514, \ 0.0031901056487151, \ 0.0031901056487151, \ 0.0031901056487151, \ 0.0031901056487151, \ 0.0031901056487151, \ 0.0031901056487151, \ 0.0049446615998697, \ 0.0049446615998697, \ 0.0049446615998697, \ 0.0024338258411055, \ 0.0024338258411055, \ 0.0024338258411055, \ 0.0024338258411055, \ 0.0024338258411055, \ 0.0024338258411055, \ 0.0002508474514575, \ 0.0002508474514575, \ 0.0002508474514575, \ 0.0002508474514575, \ 0.0002508474514575, \ 0.0002508474514575, \ 0.0040657898075942, \ 0.0040657898075942, \ 0.0040657898075942, \ 0.0017108131277605, \ 0.0017108131277605, \ 0.0017108131277605, \ 0.0017108131277605, \ 0.0017108131277605, \ 0.0017108131277605, \ 0.0045280121334294, \ 0.0045280121334294, \ 0.0045280121334294, \ 0.0045280121334294, \ 0.0045280121334294, \ 0.0045280121334294, \ 0.0040081392301490, \ 0.0040081392301490, \ 0.0040081392301490, \ 0.0040081392301490, \ 0.0040081392301490, \ 0.0040081392301490, \ 0.0011195403999073, \ 0.0011195403999073, \ 0.0011195403999073, \ 0.0011195403999073, \ 0.0011195403999073, \ 0.0011195403999073, \ 0.0016556490812277, \ 0.0016556490812277, \ 0.0016556490812277, \ 0.0016556490812277, \ 0.0016556490812277, \ 0.0016556490812277, \ 0.0030745572112736, \ 0.0030745572112736, \ 0.0030745572112736, \ 0.0030745572112736, \ 0.0030745572112736, \ 0.0030745572112736, \ 0.0048300704241971, \ 0.0048300704241971, \ 0.0048300704241971, \ 0.0048300704241971, \ 0.0048300704241971, \ 0.0048300704241971, \ 0.0038986974038214, \ 0.0038986974038214, \ 0.0038986974038214, \ 0.0038986974038214, \ 0.0038986974038214, \ 0.0038986974038214, \ 0.0016458519911547, \ 0.0016458519911547, \ 0.0016458519911547, \ 0.0016458519911547, \ 0.0016458519911547, \ 0.0016458519911547, \ 0.0037119048709275, \ 0.0037119048709275, \ 0.0037119048709275, \ 0.0037119048709275, \ 0.0037119048709275, \ 0.0037119048709275, \ 0.0014185756078616, \ 0.0014185756078616, \ 0.0014185756078616, \ 0.0014185756078616, \ 0.0014185756078616, \ 0.0014185756078616, \ 0.0012890581955709, \ 0.0012890581955709, \ 0.0012890581955709, \ 0.0012890581955709, \ 0.0012890581955709, \ 0.0012890581955709, \ 0.0015614900549058, \ 0.0015614900549058, \ 0.0015614900549058, \ 0.0015614900549058, \ 0.0015614900549058, \ 0.0015614900549058, \ 0.0016952718909460, \ 0.0016952718909460, \ 0.0016952718909460, \ 0.0016952718909460, \ 0.0016952718909460, \ 0.0016952718909460, \ 0.0007488308612040, \ 0.0007488308612040, \ 0.0007488308612040, \ 0.0004528022725679, \ 0.0004528022725679, \ 0.0004528022725679, \ 0.0004528022725679, \ 0.0004528022725679, \ 0.0004528022725679, \ 0.0007453398310664, \ 0.0007453398310664, \ 0.0007453398310664, \ 0.0007453398310664, \ 0.0007453398310664, \ 0.0007453398310664, \ 0.0005323481472587, \ 0.0005323481472587, \ 0.0005323481472587, \ 0.0005323481472587, \ 0.0005323481472587, \ 0.0005323481472587, \ 0.0036321398556638, \ 0.0036321398556638, \ 0.0036321398556638, \ 0.0006576196836264, \ 0.0006576196836264, \ 0.0006576196836264, \ 0.0006576196836264, \ 0.0006576196836264, \ 0.0006576196836264, \ 0.0003620690511307, \ 0.0003620690511307, \ 0.0003620690511307, \ 0.0003620690511307, \ 0.0003620690511307, \ 0.0003620690511307, \ 0.0007060119456705, \ 0.0007060119456705, \ 0.0007060119456705, \ 0.0007060119456705, \ 0.0007060119456705, \ 0.0007060119456705, \ 0.0006018771022200, \ 0.0006018771022200, \ 0.0006018771022200, \ 0.0006018771022200, \ 0.0006018771022200, \ 0.0006018771022200, \ 0.0007326393465497, \ 0.0007326393465497, \ 0.0007326393465497, \ 0.0007326393465497, \ 0.0007326393465497, \ 0.0007326393465497, \ 0.0000892536614181, \ 0.0000892536614181, \ 0.0000892536614181 ] ) return a, b, c, w def rule48 ( ): #*****************************************************************************80 # ## rule48() returns the rule of precision 48. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.3477244587108094, \ 0.3477244587108095, \ 0.3045510825783810, \ 0.3695672915901662, \ 0.4147320642402169, \ 0.2157006441696168, \ 0.4147320642402170, \ 0.3695672915901662, \ 0.2157006441696168, \ 0.3084818979933622, \ 0.5832166020846338, \ 0.1083014999220039, \ 0.5832166020846338, \ 0.3084818979933622, \ 0.1083014999220039, \ 0.3196427292245513, \ 0.6456613180043123, \ 0.0346959527711365, \ 0.6456613180043123, \ 0.3196427292245514, \ 0.0346959527711363, \ 0.3734312712553221, \ 0.3734312712553221, \ 0.2531374574893558, \ 0.9962559654771519, \ 0.0023979705918987, \ 0.0013460639309493, \ 0.0023979705918986, \ 0.9962559654771519, \ 0.0013460639309497, \ 0.3280848178088313, \ 0.6527443981108471, \ 0.0191707840803216, \ 0.6527443981108471, \ 0.3280848178088314, \ 0.0191707840803215, \ 0.3198129082727195, \ 0.4038255264164708, \ 0.2763615653108096, \ 0.4038255264164707, \ 0.3198129082727195, \ 0.2763615653108096, \ 0.1589266013618200, \ 0.8394322302943624, \ 0.0016411683438175, \ 0.8394322302943625, \ 0.1589266013618200, \ 0.0016411683438173, \ 0.1962759771972356, \ 0.7504008293814409, \ 0.0533231934213236, \ 0.7504008293814409, \ 0.1962759771972357, \ 0.0533231934213233, \ 0.4893390535628532, \ 0.4893390535628532, \ 0.0213218928742936, \ 0.2933421845901817, \ 0.6237289790086799, \ 0.0829288364011385, \ 0.6237289790086799, \ 0.2933421845901818, \ 0.0829288364011382, \ 0.0484109248251399, \ 0.9031781503497199, \ 0.0484109248251403, \ 0.0801595487479756, \ 0.8396809025040485, \ 0.0801595487479760, \ 0.1247273258813976, \ 0.8519536569694208, \ 0.0233190171491816, \ 0.8519536569694209, \ 0.1247273258813976, \ 0.0233190171491812, \ 0.3115932459432796, \ 0.5496936600973348, \ 0.1387130939593856, \ 0.5496936600973348, \ 0.3115932459432795, \ 0.1387130939593854, \ 0.4790902659592135, \ 0.4790902659592136, \ 0.0418194680815729, \ 0.4666424153484346, \ 0.4666424153484346, \ 0.0667151693031307, \ 0.1105414410318808, \ 0.8789179195599967, \ 0.0105406394081227, \ 0.8789179195599968, \ 0.1105414410318809, \ 0.0105406394081222, \ 0.2974171962759172, \ 0.6922355531565748, \ 0.0103472505675080, \ 0.6922355531565748, \ 0.2974171962759173, \ 0.0103472505675078, \ 0.2940680586522785, \ 0.6521500596889448, \ 0.0537818816587767, \ 0.6521500596889448, \ 0.2940680586522786, \ 0.0537818816587766, \ 0.1114012176063108, \ 0.8188384243732427, \ 0.0697603580204465, \ 0.8188384243732427, \ 0.1114012176063108, \ 0.0697603580204462, \ 0.4437434538636293, \ 0.5407542433571197, \ 0.0155023027792509, \ 0.5407542433571196, \ 0.4437434538636293, \ 0.0155023027792509, \ 0.3676357119294025, \ 0.5927417808117805, \ 0.0396225072588170, \ 0.5927417808117805, \ 0.3676357119294025, \ 0.0396225072588168, \ 0.0483834188936243, \ 0.9398058801827116, \ 0.0118107009236643, \ 0.9398058801827116, \ 0.0483834188936244, \ 0.0118107009236638, \ 0.4261985460348483, \ 0.5385135616187795, \ 0.0352878923463722, \ 0.5385135616187795, \ 0.4261985460348482, \ 0.0352878923463721, \ 0.3464037075083426, \ 0.5888811994896823, \ 0.0647150930019751, \ 0.5888811994896823, \ 0.3464037075083425, \ 0.0647150930019750, \ 0.0761686440792015, \ 0.9134087843531564, \ 0.0104225715676421, \ 0.9134087843531565, \ 0.0761686440792015, \ 0.0104225715676419, \ 0.3198558059892070, \ 0.4530392764801240, \ 0.2271049175306689, \ 0.4530392764801241, \ 0.3198558059892070, \ 0.2271049175306689, \ 0.1149767499763278, \ 0.8418683619431016, \ 0.0431548880805707, \ 0.8418683619431017, \ 0.1149767499763279, \ 0.0431548880805703, \ 0.1553411874863350, \ 0.7956838642952746, \ 0.0489749482183905, \ 0.7956838642952746, \ 0.1553411874863350, \ 0.0489749482183902, \ 0.1536641394780652, \ 0.8368813116799081, \ 0.0094545488420268, \ 0.8368813116799082, \ 0.1536641394780653, \ 0.0094545488420265, \ 0.0798538207718234, \ 0.9182518733490639, \ 0.0018943058791128, \ 0.9182518733490640, \ 0.0798538207718235, \ 0.0018943058791124, \ 0.0117045744671133, \ 0.9765908510657730, \ 0.0117045744671137, \ 0.1978601121285484, \ 0.7901115654677587, \ 0.0120283224036928, \ 0.7901115654677586, \ 0.1978601121285484, \ 0.0120283224036928, \ 0.3169153803807818, \ 0.6811801518412819, \ 0.0019044677779363, \ 0.6811801518412819, \ 0.3169153803807819, \ 0.0019044677779362, \ 0.1645639771634135, \ 0.8092307990442300, \ 0.0262052237923566, \ 0.8092307990442301, \ 0.1645639771634135, \ 0.0262052237923562, \ 0.3611298359799379, \ 0.5443992424960357, \ 0.0944709215240264, \ 0.5443992424960357, \ 0.3611298359799380, \ 0.0944709215240263, \ 0.4198259774542294, \ 0.4838506735119869, \ 0.0963233490337836, \ 0.4838506735119869, \ 0.4198259774542294, \ 0.0963233490337836, \ 0.2431752245746631, \ 0.7033344581619095, \ 0.0534903172634275, \ 0.7033344581619095, \ 0.2431752245746631, \ 0.0534903172634272, \ 0.1459832231136435, \ 0.7744922982855192, \ 0.0795244786008372, \ 0.7744922982855195, \ 0.1459832231136434, \ 0.0795244786008370, \ 0.0272392832679803, \ 0.9617299619505478, \ 0.0110307547814721, \ 0.9617299619505478, \ 0.0272392832679803, \ 0.0110307547814717, \ 0.2453137089647784, \ 0.7425000580712428, \ 0.0121862329639789, \ 0.7425000580712428, \ 0.2453137089647784, \ 0.0121862329639786, \ 0.2678465137111688, \ 0.4643069725776622, \ 0.2678465137111689, \ 0.1165542190734529, \ 0.8813325626640695, \ 0.0021132182624777, \ 0.8813325626640695, \ 0.1165542190734529, \ 0.0021132182624774, \ 0.0535856828700446, \ 0.9191953264718842, \ 0.0272189906580713, \ 0.9191953264718841, \ 0.0535856828700446, \ 0.0272189906580709, \ 0.0851355181500169, \ 0.8886082228375111, \ 0.0262562590124721, \ 0.8886082228375112, \ 0.0851355181500170, \ 0.0262562590124718, \ 0.4084926257856331, \ 0.5290322767639966, \ 0.0624750974503704, \ 0.5290322767639964, \ 0.4084926257856331, \ 0.0624750974503703, \ 0.3822510450948138, \ 0.4439727450289927, \ 0.1737762098761934, \ 0.4439727450289928, \ 0.3822510450948139, \ 0.1737762098761934, \ 0.0259740322065890, \ 0.9719768417503413, \ 0.0020491260430698, \ 0.9719768417503415, \ 0.0259740322065892, \ 0.0020491260430693, \ 0.3856891887600643, \ 0.5954207695783936, \ 0.0188900416615421, \ 0.5954207695783936, \ 0.3856891887600644, \ 0.0188900416615419, \ 0.1907464794314031, \ 0.7266345676228985, \ 0.0826189529456984, \ 0.7266345676228985, \ 0.1907464794314032, \ 0.0826189529456982, \ 0.0493146516048518, \ 0.9484053916083951, \ 0.0022799567867532, \ 0.9484053916083951, \ 0.0493146516048519, \ 0.0022799567867528, \ 0.4264825454980466, \ 0.5687452023816508, \ 0.0047722521203026, \ 0.5687452023816508, \ 0.4264825454980467, \ 0.0047722521203026, \ 0.1513647526705651, \ 0.7324328909178469, \ 0.1162023564115880, \ 0.7324328909178468, \ 0.1513647526705652, \ 0.1162023564115878, \ 0.2410855603909864, \ 0.6733891753666466, \ 0.0855252642423671, \ 0.6733891753666466, \ 0.2410855603909864, \ 0.0855252642423669, \ 0.2120362112054797, \ 0.7581870004717137, \ 0.0297767883228067, \ 0.7581870004717137, \ 0.2120362112054797, \ 0.0297767883228064, \ 0.0773420280842538, \ 0.8724044348798747, \ 0.0502535370358714, \ 0.8724044348798747, \ 0.0773420280842540, \ 0.0502535370358712, \ 0.2659270236545313, \ 0.5177727692431142, \ 0.2163002071023543, \ 0.5177727692431143, \ 0.2659270236545314, \ 0.2163002071023542, \ 0.2131382724801908, \ 0.5737234550396183, \ 0.2131382724801909, \ 0.0102781124040352, \ 0.9874036799114877, \ 0.0023182076844773, \ 0.9874036799114878, \ 0.0102781124040354, \ 0.0023182076844769, \ 0.4336266613666109, \ 0.4336266613666109, \ 0.1327466772667780, \ 0.3637486804898151, \ 0.6298211317204232, \ 0.0064301877897617, \ 0.6298211317204232, \ 0.3637486804898151, \ 0.0064301877897616, \ 0.3698202051067137, \ 0.4970686798278148, \ 0.1331111150654714, \ 0.4970686798278148, \ 0.3698202051067137, \ 0.1331111150654714, \ 0.1599009144405388, \ 0.6801981711189222, \ 0.1599009144405390, \ 0.0280636634926782, \ 0.9438726730146434, \ 0.0280636634926786, \ 0.2622368556255414, \ 0.5695106590028955, \ 0.1682524853715630, \ 0.5695106590028955, \ 0.2622368556255415, \ 0.1682524853715628, \ 0.2058652741989988, \ 0.7917570821001609, \ 0.0023776437008403, \ 0.7917570821001609, \ 0.2058652741989988, \ 0.0023776437008400, \ 0.3210612992391711, \ 0.4996635238460939, \ 0.1792751769147349, \ 0.4996635238460939, \ 0.3210612992391711, \ 0.1792751769147348, \ 0.2670089253528111, \ 0.7045277230351698, \ 0.0284633516120191, \ 0.7045277230351698, \ 0.2670089253528112, \ 0.0284633516120189, \ 0.2586045410103510, \ 0.7391689918977531, \ 0.0022264670918959, \ 0.7391689918977531, \ 0.2586045410103511, \ 0.0022264670918957, \ 0.1996247626773604, \ 0.6800108677503900, \ 0.1203643695722495, \ 0.6800108677503900, \ 0.1996247626773605, \ 0.1203643695722494, \ 0.2088908643844065, \ 0.6267746739288779, \ 0.1643344616867157, \ 0.6267746739288779, \ 0.2088908643844065, \ 0.1643344616867155, \ 0.1080471292423059, \ 0.7839057415153878, \ 0.1080471292423062, \ 0.2533336006018089, \ 0.6227789405605143, \ 0.1238874588376767, \ 0.6227789405605143, \ 0.2533336006018089, \ 0.1238874588376766, \ 0.4971756372384661, \ 0.4971756372384660, \ 0.0056487255230678, \ 0.4637961227465663, \ 0.5360438668640494, \ 0.0001600103893842, \ 0.5360438668640494, \ 0.4637961227465663, \ 0.0001600103893842, \ 0.3837177990505464, \ 0.6161736917477099, \ 0.0001085092017437, \ 0.6161736917477099, \ 0.3837177990505465, \ 0.0001085092017435 ] ) b = np.array ( [ \ 0.3045510825783811, \ 0.3477244587108095, \ 0.3477244587108096, \ 0.2157006441696169, \ 0.3695672915901663, \ 0.4147320642402171, \ 0.2157006441696169, \ 0.4147320642402170, \ 0.3695672915901664, \ 0.1083014999220040, \ 0.3084818979933623, \ 0.5832166020846340, \ 0.1083014999220040, \ 0.5832166020846339, \ 0.3084818979933624, \ 0.0346959527711364, \ 0.3196427292245514, \ 0.6456613180043125, \ 0.0346959527711364, \ 0.6456613180043123, \ 0.3196427292245516, \ 0.2531374574893559, \ 0.3734312712553222, \ 0.3734312712553222, \ 0.0013460639309495, \ 0.9962559654771520, \ 0.0023979705918990, \ 0.0013460639309495, \ 0.0023979705918986, \ 0.9962559654771520, \ 0.0191707840803216, \ 0.3280848178088313, \ 0.6527443981108473, \ 0.0191707840803216, \ 0.6527443981108472, \ 0.3280848178088315, \ 0.2763615653108097, \ 0.3198129082727196, \ 0.4038255264164710, \ 0.2763615653108097, \ 0.4038255264164710, \ 0.3198129082727196, \ 0.0016411683438175, \ 0.1589266013618200, \ 0.8394322302943628, \ 0.0016411683438175, \ 0.8394322302943628, \ 0.1589266013618204, \ 0.0533231934213235, \ 0.1962759771972356, \ 0.7504008293814409, \ 0.0533231934213235, \ 0.7504008293814409, \ 0.1962759771972359, \ 0.0213218928742936, \ 0.4893390535628533, \ 0.4893390535628534, \ 0.0829288364011384, \ 0.2933421845901818, \ 0.6237289790086800, \ 0.0829288364011384, \ 0.6237289790086800, \ 0.2933421845901819, \ 0.0484109248251402, \ 0.0484109248251399, \ 0.9031781503497200, \ 0.0801595487479759, \ 0.0801595487479756, \ 0.8396809025040486, \ 0.0233190171491815, \ 0.1247273258813976, \ 0.8519536569694212, \ 0.0233190171491815, \ 0.8519536569694212, \ 0.1247273258813979, \ 0.1387130939593856, \ 0.3115932459432796, \ 0.5496936600973350, \ 0.1387130939593856, \ 0.5496936600973350, \ 0.3115932459432798, \ 0.0418194680815730, \ 0.4790902659592136, \ 0.4790902659592137, \ 0.0667151693031307, \ 0.4666424153484347, \ 0.4666424153484348, \ 0.0105406394081225, \ 0.1105414410318807, \ 0.8789179195599968, \ 0.0105406394081225, \ 0.8789179195599968, \ 0.1105414410318811, \ 0.0103472505675079, \ 0.2974171962759173, \ 0.6922355531565749, \ 0.0103472505675079, \ 0.6922355531565749, \ 0.2974171962759176, \ 0.0537818816587767, \ 0.2940680586522786, \ 0.6521500596889449, \ 0.0537818816587767, \ 0.6521500596889449, \ 0.2940680586522788, \ 0.0697603580204464, \ 0.1114012176063108, \ 0.8188384243732429, \ 0.0697603580204464, \ 0.8188384243732429, \ 0.1114012176063111, \ 0.0155023027792511, \ 0.4437434538636293, \ 0.5407542433571200, \ 0.0155023027792511, \ 0.5407542433571197, \ 0.4437434538636296, \ 0.0396225072588169, \ 0.3676357119294025, \ 0.5927417808117806, \ 0.0396225072588169, \ 0.5927417808117806, \ 0.3676357119294028, \ 0.0118107009236641, \ 0.0483834188936242, \ 0.9398058801827117, \ 0.0118107009236641, \ 0.9398058801827117, \ 0.0483834188936246, \ 0.0352878923463722, \ 0.4261985460348483, \ 0.5385135616187797, \ 0.0352878923463722, \ 0.5385135616187796, \ 0.4261985460348485, \ 0.0647150930019751, \ 0.3464037075083426, \ 0.5888811994896825, \ 0.0647150930019751, \ 0.5888811994896824, \ 0.3464037075083428, \ 0.0104225715676421, \ 0.0761686440792014, \ 0.9134087843531568, \ 0.0104225715676421, \ 0.9134087843531568, \ 0.0761686440792017, \ 0.2271049175306690, \ 0.3198558059892071, \ 0.4530392764801242, \ 0.2271049175306690, \ 0.4530392764801242, \ 0.3198558059892072, \ 0.0431548880805706, \ 0.1149767499763278, \ 0.8418683619431018, \ 0.0431548880805706, \ 0.8418683619431018, \ 0.1149767499763281, \ 0.0489749482183904, \ 0.1553411874863350, \ 0.7956838642952748, \ 0.0489749482183904, \ 0.7956838642952748, \ 0.1553411874863353, \ 0.0094545488420267, \ 0.1536641394780652, \ 0.8368813116799082, \ 0.0094545488420267, \ 0.8368813116799082, \ 0.1536641394780656, \ 0.0018943058791126, \ 0.0798538207718234, \ 0.9182518733490641, \ 0.0018943058791126, \ 0.9182518733490641, \ 0.0798538207718237, \ 0.0117045744671136, \ 0.0117045744671133, \ 0.9765908510657733, \ 0.0120283224036929, \ 0.1978601121285484, \ 0.7901115654677591, \ 0.0120283224036929, \ 0.7901115654677587, \ 0.1978601121285486, \ 0.0019044677779363, \ 0.3169153803807819, \ 0.6811801518412820, \ 0.0019044677779363, \ 0.6811801518412820, \ 0.3169153803807821, \ 0.0262052237923565, \ 0.1645639771634134, \ 0.8092307990442302, \ 0.0262052237923565, \ 0.8092307990442302, \ 0.1645639771634138, \ 0.0944709215240264, \ 0.3611298359799380, \ 0.5443992424960359, \ 0.0944709215240264, \ 0.5443992424960358, \ 0.3611298359799381, \ 0.0963233490337837, \ 0.4198259774542294, \ 0.4838506735119871, \ 0.0963233490337837, \ 0.4838506735119870, \ 0.4198259774542296, \ 0.0534903172634274, \ 0.2431752245746631, \ 0.7033344581619096, \ 0.0534903172634274, \ 0.7033344581619096, \ 0.2431752245746634, \ 0.0795244786008372, \ 0.1459832231136435, \ 0.7744922982855196, \ 0.0795244786008372, \ 0.7744922982855196, \ 0.1459832231136438, \ 0.0110307547814719, \ 0.0272392832679802, \ 0.9617299619505479, \ 0.0110307547814719, \ 0.9617299619505479, \ 0.0272392832679806, \ 0.0121862329639789, \ 0.2453137089647784, \ 0.7425000580712430, \ 0.0121862329639789, \ 0.7425000580712430, \ 0.2453137089647787, \ 0.2678465137111690, \ 0.2678465137111689, \ 0.4643069725776624, \ 0.0021132182624776, \ 0.1165542190734529, \ 0.8813325626640697, \ 0.0021132182624776, \ 0.8813325626640697, \ 0.1165542190734533, \ 0.0272189906580712, \ 0.0535856828700446, \ 0.9191953264718844, \ 0.0272189906580712, \ 0.9191953264718844, \ 0.0535856828700449, \ 0.0262562590124721, \ 0.0851355181500168, \ 0.8886082228375113, \ 0.0262562590124721, \ 0.8886082228375112, \ 0.0851355181500172, \ 0.0624750974503704, \ 0.4084926257856331, \ 0.5290322767639968, \ 0.0624750974503704, \ 0.5290322767639967, \ 0.4084926257856333, \ 0.1737762098761935, \ 0.3822510450948139, \ 0.4439727450289929, \ 0.1737762098761935, \ 0.4439727450289928, \ 0.3822510450948140, \ 0.0020491260430696, \ 0.0259740322065890, \ 0.9719768417503415, \ 0.0020491260430696, \ 0.9719768417503415, \ 0.0259740322065894, \ 0.0188900416615420, \ 0.3856891887600644, \ 0.5954207695783937, \ 0.0188900416615420, \ 0.5954207695783937, \ 0.3856891887600646, \ 0.0826189529456984, \ 0.1907464794314031, \ 0.7266345676228987, \ 0.0826189529456984, \ 0.7266345676228986, \ 0.1907464794314034, \ 0.0022799567867531, \ 0.0493146516048518, \ 0.9484053916083952, \ 0.0022799567867531, \ 0.9484053916083952, \ 0.0493146516048521, \ 0.0047722521203026, \ 0.4264825454980467, \ 0.5687452023816510, \ 0.0047722521203026, \ 0.5687452023816508, \ 0.4264825454980468, \ 0.1162023564115881, \ 0.1513647526705651, \ 0.7324328909178470, \ 0.1162023564115881, \ 0.7324328909178470, \ 0.1513647526705654, \ 0.0855252642423671, \ 0.2410855603909865, \ 0.6733891753666467, \ 0.0855252642423671, \ 0.6733891753666467, \ 0.2410855603909867, \ 0.0297767883228067, \ 0.2120362112054797, \ 0.7581870004717138, \ 0.0297767883228067, \ 0.7581870004717138, \ 0.2120362112054800, \ 0.0502535370358714, \ 0.0773420280842539, \ 0.8724044348798750, \ 0.0502535370358714, \ 0.8724044348798748, \ 0.0773420280842542, \ 0.2163002071023544, \ 0.2659270236545314, \ 0.5177727692431144, \ 0.2163002071023544, \ 0.5177727692431144, \ 0.2659270236545315, \ 0.2131382724801910, \ 0.2131382724801908, \ 0.5737234550396184, \ 0.0023182076844771, \ 0.0102781124040352, \ 0.9874036799114877, \ 0.0023182076844771, \ 0.9874036799114877, \ 0.0102781124040356, \ 0.1327466772667781, \ 0.4336266613666110, \ 0.4336266613666112, \ 0.0064301877897617, \ 0.3637486804898151, \ 0.6298211317204234, \ 0.0064301877897617, \ 0.6298211317204232, \ 0.3637486804898154, \ 0.1331111150654715, \ 0.3698202051067138, \ 0.4970686798278151, \ 0.1331111150654715, \ 0.4970686798278149, \ 0.3698202051067139, \ 0.1599009144405390, \ 0.1599009144405389, \ 0.6801981711189224, \ 0.0280636634926785, \ 0.0280636634926781, \ 0.9438726730146435, \ 0.1682524853715630, \ 0.2622368556255416, \ 0.5695106590028957, \ 0.1682524853715630, \ 0.5695106590028957, \ 0.2622368556255417, \ 0.0023776437008402, \ 0.2058652741989988, \ 0.7917570821001612, \ 0.0023776437008402, \ 0.7917570821001612, \ 0.2058652741989991, \ 0.1792751769147349, \ 0.3210612992391713, \ 0.4996635238460941, \ 0.1792751769147349, \ 0.4996635238460940, \ 0.3210612992391713, \ 0.0284633516120191, \ 0.2670089253528111, \ 0.7045277230351701, \ 0.0284633516120191, \ 0.7045277230351698, \ 0.2670089253528115, \ 0.0022264670918959, \ 0.2586045410103511, \ 0.7391689918977533, \ 0.0022264670918959, \ 0.7391689918977531, \ 0.2586045410103514, \ 0.1203643695722496, \ 0.1996247626773605, \ 0.6800108677503902, \ 0.1203643695722496, \ 0.6800108677503902, \ 0.1996247626773607, \ 0.1643344616867156, \ 0.2088908643844065, \ 0.6267746739288781, \ 0.1643344616867156, \ 0.6267746739288781, \ 0.2088908643844067, \ 0.1080471292423062, \ 0.1080471292423059, \ 0.7839057415153881, \ 0.1238874588376767, \ 0.2533336006018089, \ 0.6227789405605146, \ 0.1238874588376767, \ 0.6227789405605145, \ 0.2533336006018092, \ 0.0056487255230679, \ 0.4971756372384661, \ 0.4971756372384663, \ 0.0001600103893843, \ 0.4637961227465663, \ 0.5360438668640496, \ 0.0001600103893843, \ 0.5360438668640495, \ 0.4637961227465666, \ 0.0001085092017437, \ 0.3837177990505464, \ 0.6161736917477101, \ 0.0001085092017437, \ 0.6161736917477100, \ 0.3837177990505467 ] ) c = np.array ( [ \ 0.3477244587108094, \ 0.3045510825783810, \ 0.3477244587108094, \ 0.4147320642402169, \ 0.2157006441696168, \ 0.3695672915901662, \ 0.3695672915901661, \ 0.2157006441696168, \ 0.4147320642402169, \ 0.5832166020846338, \ 0.1083014999220039, \ 0.3084818979933620, \ 0.3084818979933622, \ 0.1083014999220039, \ 0.5832166020846337, \ 0.6456613180043121, \ 0.0346959527711364, \ 0.3196427292245511, \ 0.3196427292245513, \ 0.0346959527711364, \ 0.6456613180043120, \ 0.3734312712553221, \ 0.2531374574893557, \ 0.3734312712553220, \ 0.0023979705918986, \ 0.0013460639309494, \ 0.9962559654771518, \ 0.9962559654771519, \ 0.0013460639309495, \ 0.0023979705918983, \ 0.6527443981108471, \ 0.0191707840803216, \ 0.3280848178088310, \ 0.3280848178088314, \ 0.0191707840803215, \ 0.6527443981108469, \ 0.4038255264164708, \ 0.2763615653108097, \ 0.3198129082727195, \ 0.3198129082727195, \ 0.2763615653108096, \ 0.4038255264164708, \ 0.8394322302943625, \ 0.0016411683438176, \ 0.1589266013618197, \ 0.1589266013618200, \ 0.0016411683438172, \ 0.8394322302943623, \ 0.7504008293814409, \ 0.0533231934213235, \ 0.1962759771972354, \ 0.1962759771972356, \ 0.0533231934213233, \ 0.7504008293814408, \ 0.4893390535628532, \ 0.0213218928742935, \ 0.4893390535628531, \ 0.6237289790086799, \ 0.0829288364011384, \ 0.2933421845901816, \ 0.2933421845901818, \ 0.0829288364011382, \ 0.6237289790086799, \ 0.9031781503497199, \ 0.0484109248251402, \ 0.0484109248251396, \ 0.8396809025040486, \ 0.0801595487479759, \ 0.0801595487479754, \ 0.8519536569694209, \ 0.0233190171491816, \ 0.1247273258813973, \ 0.1247273258813976, \ 0.0233190171491812, \ 0.8519536569694208, \ 0.5496936600973349, \ 0.1387130939593856, \ 0.3115932459432794, \ 0.3115932459432796, \ 0.1387130939593855, \ 0.5496936600973348, \ 0.4790902659592134, \ 0.0418194680815729, \ 0.4790902659592134, \ 0.4666424153484346, \ 0.0667151693031307, \ 0.4666424153484345, \ 0.8789179195599967, \ 0.0105406394081226, \ 0.1105414410318806, \ 0.1105414410318807, \ 0.0105406394081223, \ 0.8789179195599967, \ 0.6922355531565748, \ 0.0103472505675079, \ 0.2974171962759171, \ 0.2974171962759173, \ 0.0103472505675077, \ 0.6922355531565747, \ 0.6521500596889447, \ 0.0537818816587766, \ 0.2940680586522784, \ 0.2940680586522785, \ 0.0537818816587765, \ 0.6521500596889447, \ 0.8188384243732427, \ 0.0697603580204465, \ 0.1114012176063106, \ 0.1114012176063108, \ 0.0697603580204462, \ 0.8188384243732426, \ 0.5407542433571196, \ 0.0155023027792509, \ 0.4437434538636291, \ 0.4437434538636293, \ 0.0155023027792509, \ 0.5407542433571195, \ 0.5927417808117805, \ 0.0396225072588169, \ 0.3676357119294024, \ 0.3676357119294025, \ 0.0396225072588169, \ 0.5927417808117805, \ 0.9398058801827116, \ 0.0118107009236642, \ 0.0483834188936240, \ 0.0483834188936243, \ 0.0118107009236640, \ 0.9398058801827115, \ 0.5385135616187795, \ 0.0352878923463722, \ 0.4261985460348481, \ 0.4261985460348482, \ 0.0352878923463721, \ 0.5385135616187795, \ 0.5888811994896823, \ 0.0647150930019751, \ 0.3464037075083424, \ 0.3464037075083425, \ 0.0647150930019750, \ 0.5888811994896822, \ 0.9134087843531564, \ 0.0104225715676421, \ 0.0761686440792011, \ 0.0761686440792014, \ 0.0104225715676417, \ 0.9134087843531563, \ 0.4530392764801241, \ 0.2271049175306689, \ 0.3198558059892068, \ 0.3198558059892069, \ 0.2271049175306689, \ 0.4530392764801240, \ 0.8418683619431017, \ 0.0431548880805706, \ 0.1149767499763276, \ 0.1149767499763278, \ 0.0431548880805703, \ 0.8418683619431016, \ 0.7956838642952746, \ 0.0489749482183904, \ 0.1553411874863346, \ 0.1553411874863350, \ 0.0489749482183902, \ 0.7956838642952745, \ 0.8368813116799081, \ 0.0094545488420267, \ 0.1536641394780650, \ 0.1536641394780651, \ 0.0094545488420265, \ 0.8368813116799080, \ 0.9182518733490640, \ 0.0018943058791127, \ 0.0798538207718231, \ 0.0798538207718234, \ 0.0018943058791124, \ 0.9182518733490638, \ 0.9765908510657731, \ 0.0117045744671137, \ 0.0117045744671130, \ 0.7901115654677587, \ 0.0120283224036929, \ 0.1978601121285481, \ 0.1978601121285485, \ 0.0120283224036929, \ 0.7901115654677586, \ 0.6811801518412819, \ 0.0019044677779362, \ 0.3169153803807817, \ 0.3169153803807818, \ 0.0019044677779362, \ 0.6811801518412817, \ 0.8092307990442300, \ 0.0262052237923565, \ 0.1645639771634132, \ 0.1645639771634134, \ 0.0262052237923562, \ 0.8092307990442301, \ 0.5443992424960357, \ 0.0944709215240264, \ 0.3611298359799378, \ 0.3611298359799379, \ 0.0944709215240263, \ 0.5443992424960356, \ 0.4838506735119868, \ 0.0963233490337837, \ 0.4198259774542293, \ 0.4198259774542293, \ 0.0963233490337836, \ 0.4838506735119868, \ 0.7033344581619094, \ 0.0534903172634274, \ 0.2431752245746629, \ 0.2431752245746631, \ 0.0534903172634272, \ 0.7033344581619095, \ 0.7744922982855194, \ 0.0795244786008373, \ 0.1459832231136432, \ 0.1459832231136434, \ 0.0795244786008370, \ 0.7744922982855192, \ 0.9617299619505477, \ 0.0110307547814719, \ 0.0272392832679800, \ 0.0272392832679802, \ 0.0110307547814718, \ 0.9617299619505477, \ 0.7425000580712428, \ 0.0121862329639788, \ 0.2453137089647782, \ 0.2453137089647784, \ 0.0121862329639787, \ 0.7425000580712426, \ 0.4643069725776623, \ 0.2678465137111689, \ 0.2678465137111686, \ 0.8813325626640696, \ 0.0021132182624776, \ 0.1165542190734526, \ 0.1165542190734529, \ 0.0021132182624773, \ 0.8813325626640693, \ 0.9191953264718842, \ 0.0272189906580712, \ 0.0535856828700443, \ 0.0535856828700447, \ 0.0272189906580710, \ 0.9191953264718841, \ 0.8886082228375111, \ 0.0262562590124721, \ 0.0851355181500165, \ 0.0851355181500168, \ 0.0262562590124719, \ 0.8886082228375111, \ 0.5290322767639966, \ 0.0624750974503704, \ 0.4084926257856328, \ 0.4084926257856331, \ 0.0624750974503702, \ 0.5290322767639963, \ 0.4439727450289928, \ 0.1737762098761934, \ 0.3822510450948137, \ 0.3822510450948138, \ 0.1737762098761933, \ 0.4439727450289926, \ 0.9719768417503414, \ 0.0020491260430697, \ 0.0259740322065888, \ 0.0259740322065889, \ 0.0020491260430694, \ 0.9719768417503413, \ 0.5954207695783936, \ 0.0188900416615420, \ 0.3856891887600642, \ 0.3856891887600644, \ 0.0188900416615418, \ 0.5954207695783935, \ 0.7266345676228985, \ 0.0826189529456984, \ 0.1907464794314029, \ 0.1907464794314031, \ 0.0826189529456983, \ 0.7266345676228985, \ 0.9484053916083951, \ 0.0022799567867531, \ 0.0493146516048515, \ 0.0493146516048518, \ 0.0022799567867529, \ 0.9484053916083951, \ 0.5687452023816508, \ 0.0047722521203025, \ 0.4264825454980463, \ 0.4264825454980465, \ 0.0047722521203025, \ 0.5687452023816506, \ 0.7324328909178469, \ 0.1162023564115880, \ 0.1513647526705649, \ 0.1513647526705652, \ 0.1162023564115878, \ 0.7324328909178468, \ 0.6733891753666464, \ 0.0855252642423670, \ 0.2410855603909863, \ 0.2410855603909864, \ 0.0855252642423668, \ 0.6733891753666466, \ 0.7581870004717137, \ 0.0297767883228066, \ 0.2120362112054796, \ 0.2120362112054796, \ 0.0297767883228065, \ 0.7581870004717136, \ 0.8724044348798747, \ 0.0502535370358714, \ 0.0773420280842536, \ 0.0773420280842539, \ 0.0502535370358711, \ 0.8724044348798746, \ 0.5177727692431143, \ 0.2163002071023544, \ 0.2659270236545312, \ 0.2659270236545312, \ 0.2163002071023542, \ 0.5177727692431142, \ 0.5737234550396182, \ 0.2131382724801908, \ 0.2131382724801907, \ 0.9874036799114877, \ 0.0023182076844771, \ 0.0102781124040351, \ 0.0102781124040351, \ 0.0023182076844769, \ 0.9874036799114876, \ 0.4336266613666110, \ 0.1327466772667781, \ 0.4336266613666108, \ 0.6298211317204231, \ 0.0064301877897617, \ 0.3637486804898149, \ 0.3637486804898151, \ 0.0064301877897617, \ 0.6298211317204230, \ 0.4970686798278149, \ 0.1331111150654715, \ 0.3698202051067135, \ 0.3698202051067138, \ 0.1331111150654714, \ 0.4970686798278148, \ 0.6801981711189222, \ 0.1599009144405389, \ 0.1599009144405386, \ 0.9438726730146434, \ 0.0280636634926785, \ 0.0280636634926780, \ 0.5695106590028955, \ 0.1682524853715628, \ 0.2622368556255413, \ 0.2622368556255415, \ 0.1682524853715629, \ 0.5695106590028955, \ 0.7917570821001610, \ 0.0023776437008402, \ 0.2058652741989986, \ 0.2058652741989989, \ 0.0023776437008400, \ 0.7917570821001608, \ 0.4996635238460940, \ 0.1792751769147348, \ 0.3210612992391709, \ 0.3210612992391711, \ 0.1792751769147348, \ 0.4996635238460939, \ 0.7045277230351698, \ 0.0284633516120191, \ 0.2670089253528108, \ 0.2670089253528111, \ 0.0284633516120191, \ 0.7045277230351696, \ 0.7391689918977531, \ 0.0022264670918958, \ 0.2586045410103508, \ 0.2586045410103510, \ 0.0022264670918958, \ 0.7391689918977530, \ 0.6800108677503900, \ 0.1203643695722495, \ 0.1996247626773603, \ 0.1996247626773605, \ 0.1203643695722493, \ 0.6800108677503900, \ 0.6267746739288779, \ 0.1643344616867157, \ 0.2088908643844062, \ 0.2088908643844065, \ 0.1643344616867154, \ 0.6267746739288779, \ 0.7839057415153878, \ 0.1080471292423063, \ 0.1080471292423058, \ 0.6227789405605143, \ 0.1238874588376768, \ 0.2533336006018087, \ 0.2533336006018090, \ 0.1238874588376765, \ 0.6227789405605142, \ 0.4971756372384660, \ 0.0056487255230678, \ 0.4971756372384659, \ 0.5360438668640494, \ 0.0001600103893843, \ 0.4637961227465662, \ 0.4637961227465663, \ 0.0001600103893842, \ 0.5360438668640493, \ 0.6161736917477099, \ 0.0001085092017437, \ 0.3837177990505463, \ 0.3837177990505465, \ 0.0001085092017435, \ 0.6161736917477098 ] ) w = np.array ( [ \ 0.0043651387537827, \ 0.0043651387537827, \ 0.0043651387537827, \ 0.0037199314122967, \ 0.0037199314122967, \ 0.0037199314122967, \ 0.0037199314122967, \ 0.0037199314122967, \ 0.0037199314122967, \ 0.0030326109445702, \ 0.0030326109445702, \ 0.0030326109445702, \ 0.0030326109445702, \ 0.0030326109445702, \ 0.0030326109445702, \ 0.0018470108648335, \ 0.0018470108648335, \ 0.0018470108648335, \ 0.0018470108648335, \ 0.0018470108648335, \ 0.0018470108648335, \ 0.0039691750453026, \ 0.0039691750453026, \ 0.0039691750453026, \ 0.0000237729080849, \ 0.0000237729080849, \ 0.0000237729080849, \ 0.0000237729080849, \ 0.0000237729080849, \ 0.0000237729080849, \ 0.0015449674526410, \ 0.0015449674526410, \ 0.0015449674526410, \ 0.0015449674526410, \ 0.0015449674526410, \ 0.0015449674526410, \ 0.0050318869826994, \ 0.0050318869826994, \ 0.0050318869826994, \ 0.0050318869826994, \ 0.0050318869826994, \ 0.0050318869826994, \ 0.0003887357668010, \ 0.0003887357668010, \ 0.0003887357668010, \ 0.0003887357668010, \ 0.0003887357668010, \ 0.0003887357668010, \ 0.0022929693353195, \ 0.0022929693353195, \ 0.0022929693353195, \ 0.0022929693353195, \ 0.0022929693353195, \ 0.0022929693353195, \ 0.0018221145367845, \ 0.0018221145367845, \ 0.0018221145367845, \ 0.0032590081957709, \ 0.0032590081957709, \ 0.0032590081957709, \ 0.0032590081957709, \ 0.0032590081957709, \ 0.0032590081957709, \ 0.0012114472500650, \ 0.0012114472500650, \ 0.0012114472500650, \ 0.0019309544896271, \ 0.0019309544896271, \ 0.0019309544896271, \ 0.0012994343934015, \ 0.0012994343934015, \ 0.0012994343934015, \ 0.0012994343934015, \ 0.0012994343934015, \ 0.0012994343934015, \ 0.0040442317991415, \ 0.0040442317991415, \ 0.0040442317991415, \ 0.0040442317991415, \ 0.0040442317991415, \ 0.0040442317991415, \ 0.0026400243756411, \ 0.0026400243756411, \ 0.0026400243756411, \ 0.0032841920864061, \ 0.0032841920864061, \ 0.0032841920864061, \ 0.0008644791070945, \ 0.0008644791070945, \ 0.0008644791070945, \ 0.0008644791070945, \ 0.0008644791070945, \ 0.0008644791070945, \ 0.0012659714364757, \ 0.0012659714364757, \ 0.0012659714364757, \ 0.0012659714364757, \ 0.0012659714364757, \ 0.0012659714364757, \ 0.0027425885952415, \ 0.0027425885952415, \ 0.0027425885952415, \ 0.0027425885952415, \ 0.0027425885952415, \ 0.0027425885952415, \ 0.0021154075536657, \ 0.0021154075536657, \ 0.0021154075536657, \ 0.0021154075536657, \ 0.0021154075536657, \ 0.0021154075536657, \ 0.0016231545272857, \ 0.0016231545272857, \ 0.0016231545272857, \ 0.0016231545272857, \ 0.0016231545272857, \ 0.0016231545272857, \ 0.0025412737334053, \ 0.0025412737334053, \ 0.0025412737334053, \ 0.0025412737334053, \ 0.0025412737334053, \ 0.0025412737334053, \ 0.0006226354721122, \ 0.0006226354721122, \ 0.0006226354721122, \ 0.0006226354721122, \ 0.0006226354721122, \ 0.0006226354721122, \ 0.0026418403799763, \ 0.0026418403799763, \ 0.0026418403799763, \ 0.0026418403799763, \ 0.0026418403799763, \ 0.0026418403799763, \ 0.0032653171027574, \ 0.0032653171027574, \ 0.0032653171027574, \ 0.0032653171027574, \ 0.0032653171027574, \ 0.0032653171027574, \ 0.0007655145859224, \ 0.0007655145859224, \ 0.0007655145859224, \ 0.0007655145859224, \ 0.0007655145859224, \ 0.0007655145859224, \ 0.0051641360944715, \ 0.0051641360944715, \ 0.0051641360944715, \ 0.0051641360944715, \ 0.0051641360944715, \ 0.0051641360944715, \ 0.0018554389812758, \ 0.0018554389812758, \ 0.0018554389812758, \ 0.0018554389812758, \ 0.0018554389812758, \ 0.0018554389812758, \ 0.0022798100113623, \ 0.0022798100113623, \ 0.0022798100113623, \ 0.0022798100113623, \ 0.0022798100113623, \ 0.0022798100113623, \ 0.0010267946171961, \ 0.0010267946171961, \ 0.0010267946171961, \ 0.0010267946171961, \ 0.0010267946171961, \ 0.0010267946171961, \ 0.0003328431211266, \ 0.0003328431211266, \ 0.0003328431211266, \ 0.0003328431211266, \ 0.0003328431211266, \ 0.0003328431211266, \ 0.0003229449584348, \ 0.0003229449584348, \ 0.0003229449584348, \ 0.0012157493114517, \ 0.0012157493114517, \ 0.0012157493114517, \ 0.0012157493114517, \ 0.0012157493114517, \ 0.0012157493114517, \ 0.0005893115728957, \ 0.0005893115728957, \ 0.0005893115728957, \ 0.0005893115728957, \ 0.0005893115728957, \ 0.0005893115728957, \ 0.0017342658044949, \ 0.0017342658044949, \ 0.0017342658044949, \ 0.0017342658044949, \ 0.0017342658044949, \ 0.0017342658044949, \ 0.0040498750757605, \ 0.0040498750757605, \ 0.0040498750757605, \ 0.0040498750757605, \ 0.0040498750757605, \ 0.0040498750757605, \ 0.0042742322977128, \ 0.0042742322977128, \ 0.0042742322977128, \ 0.0042742322977128, \ 0.0042742322977128, \ 0.0042742322977128, \ 0.0028335085475802, \ 0.0028335085475802, \ 0.0028335085475802, \ 0.0028335085475802, \ 0.0028335085475802, \ 0.0028335085475802, \ 0.0027438125458837, \ 0.0027438125458837, \ 0.0027438125458837, \ 0.0027438125458837, \ 0.0027438125458837, \ 0.0027438125458837, \ 0.0004730214563551, \ 0.0004730214563551, \ 0.0004730214563551, \ 0.0004730214563551, \ 0.0004730214563551, \ 0.0004730214563551, \ 0.0013733177441610, \ 0.0013733177441610, \ 0.0013733177441610, \ 0.0013733177441610, \ 0.0013733177441610, \ 0.0013733177441610, \ 0.0054310463039951, \ 0.0054310463039951, \ 0.0054310463039951, \ 0.0004233009914606, \ 0.0004233009914606, \ 0.0004233009914606, \ 0.0004233009914606, \ 0.0004233009914606, \ 0.0004233009914606, \ 0.0010664611871638, \ 0.0010664611871638, \ 0.0010664611871638, \ 0.0010664611871638, \ 0.0010664611871638, \ 0.0010664611871638, \ 0.0013824010733117, \ 0.0013824010733117, \ 0.0013824010733117, \ 0.0013824010733117, \ 0.0013824010733117, \ 0.0013824010733117, \ 0.0036585117930270, \ 0.0036585117930270, \ 0.0036585117930270, \ 0.0036585117930270, \ 0.0036585117930270, \ 0.0036585117930270, \ 0.0052100048548666, \ 0.0052100048548666, \ 0.0052100048548666, \ 0.0052100048548666, \ 0.0052100048548666, \ 0.0052100048548666, \ 0.0002073105605908, \ 0.0002073105605908, \ 0.0002073105605908, \ 0.0002073105605908, \ 0.0002073105605908, \ 0.0002073105605908, \ 0.0019583162868632, \ 0.0019583162868632, \ 0.0019583162868632, \ 0.0019583162868632, \ 0.0019583162868632, \ 0.0019583162868632, \ 0.0032089225299188, \ 0.0032089225299188, \ 0.0032089225299188, \ 0.0032089225299188, \ 0.0032089225299188, \ 0.0032089225299188, \ 0.0003144151546132, \ 0.0003144151546132, \ 0.0003144151546132, \ 0.0003144151546132, \ 0.0003144151546132, \ 0.0003144151546132, \ 0.0010785145551204, \ 0.0010785145551204, \ 0.0010785145551204, \ 0.0010785145551204, \ 0.0010785145551204, \ 0.0010785145551204, \ 0.0036004269766152, \ 0.0036004269766152, \ 0.0036004269766152, \ 0.0036004269766152, \ 0.0036004269766152, \ 0.0036004269766152, \ 0.0036611914178426, \ 0.0036611914178426, \ 0.0036611914178426, \ 0.0036611914178426, \ 0.0036611914178426, \ 0.0036611914178426, \ 0.0021617123138751, \ 0.0021617123138751, \ 0.0021617123138751, \ 0.0021617123138751, \ 0.0021617123138751, \ 0.0021617123138751, \ 0.0018010562763862, \ 0.0018010562763862, \ 0.0018010562763862, \ 0.0018010562763862, \ 0.0018010562763862, \ 0.0018010562763862, \ 0.0054475592942759, \ 0.0054475592942759, \ 0.0054475592942759, \ 0.0054475592942759, \ 0.0054475592942759, \ 0.0054475592942759, \ 0.0051525605444838, \ 0.0051525605444838, \ 0.0051525605444838, \ 0.0001397852015244, \ 0.0001397852015244, \ 0.0001397852015244, \ 0.0001397852015244, \ 0.0001397852015244, \ 0.0001397852015244, \ 0.0049930051499418, \ 0.0049930051499418, \ 0.0049930051499418, \ 0.0011962011851953, \ 0.0011962011851953, \ 0.0011962011851953, \ 0.0011962011851953, \ 0.0011962011851953, \ 0.0011962011851953, \ 0.0049525658235836, \ 0.0049525658235836, \ 0.0049525658235836, \ 0.0049525658235836, \ 0.0049525658235836, \ 0.0049525658235836, \ 0.0042434984918542, \ 0.0042434984918542, \ 0.0042434984918542, \ 0.0008876005610246, \ 0.0008876005610246, \ 0.0008876005610246, \ 0.0050552058738964, \ 0.0050552058738964, \ 0.0050552058738964, \ 0.0050552058738964, \ 0.0050552058738964, \ 0.0050552058738964, \ 0.0006055910618992, \ 0.0006055910618992, \ 0.0006055910618992, \ 0.0006055910618992, \ 0.0006055910618992, \ 0.0006055910618992, \ 0.0053577902109237, \ 0.0053577902109237, \ 0.0053577902109237, \ 0.0053577902109237, \ 0.0053577902109237, \ 0.0053577902109237, \ 0.0023655352245003, \ 0.0023655352245003, \ 0.0023655352245003, \ 0.0023655352245003, \ 0.0023655352245003, \ 0.0023655352245003, \ 0.0006361760556450, \ 0.0006361760556450, \ 0.0006361760556450, \ 0.0006361760556450, \ 0.0006361760556450, \ 0.0006361760556450, \ 0.0041167794317584, \ 0.0041167794317584, \ 0.0041167794317584, \ 0.0041167794317584, \ 0.0041167794317584, \ 0.0041167794317584, \ 0.0047435661701725, \ 0.0047435661701725, \ 0.0047435661701725, \ 0.0047435661701725, \ 0.0047435661701725, \ 0.0047435661701725, \ 0.0031739283489719, \ 0.0031739283489719, \ 0.0031739283489719, \ 0.0046022674251482, \ 0.0046022674251482, \ 0.0046022674251482, \ 0.0046022674251482, \ 0.0046022674251482, \ 0.0046022674251482, \ 0.0012950799113896, \ 0.0012950799113896, \ 0.0012950799113896, \ 0.0002350089224806, \ 0.0002350089224806, \ 0.0002350089224806, \ 0.0002350089224806, \ 0.0002350089224806, \ 0.0002350089224806, \ 0.0002398736789311, \ 0.0002398736789311, \ 0.0002398736789311, \ 0.0002398736789311, \ 0.0002398736789311, \ 0.0002398736789311 ] ) return a, b, c, w def rule49 ( ): #*****************************************************************************80 # ## rule49() returns the rule of precision 49. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.1747098543071731, \ 0.7852819906358907, \ 0.0400081550569363, \ 0.7852819906358907, \ 0.1747098543071732, \ 0.0400081550569361, \ 0.3869650571638262, \ 0.6043725256047221, \ 0.0086624172314518, \ 0.6043725256047220, \ 0.3869650571638262, \ 0.0086624172314517, \ 0.1260609334354054, \ 0.8726379574162407, \ 0.0013011091483540, \ 0.8726379574162407, \ 0.1260609334354055, \ 0.0013011091483536, \ 0.1783730162296315, \ 0.6432539675407367, \ 0.1783730162296319, \ 0.2839249520005005, \ 0.4704465426211537, \ 0.2456285053783458, \ 0.4704465426211537, \ 0.2839249520005004, \ 0.2456285053783457, \ 0.3302482693344623, \ 0.4190100944919284, \ 0.2507416361736092, \ 0.4190100944919285, \ 0.3302482693344623, \ 0.2507416361736091, \ 0.0728406536060113, \ 0.8543186927879770, \ 0.0728406536060117, \ 0.2560459410681578, \ 0.7424443214379617, \ 0.0015097374938804, \ 0.7424443214379618, \ 0.2560459410681578, \ 0.0015097374938802, \ 0.2603953161344762, \ 0.6306213036525985, \ 0.1089833802129252, \ 0.6306213036525986, \ 0.2603953161344763, \ 0.1089833802129251, \ 0.4289883556394070, \ 0.4289883556394070, \ 0.1420232887211859, \ 0.1707126963793420, \ 0.7273185867118819, \ 0.1019687169087761, \ 0.7273185867118819, \ 0.1707126963793419, \ 0.1019687169087760, \ 0.3746440580951249, \ 0.6055836533300153, \ 0.0197722885748599, \ 0.6055836533300152, \ 0.3746440580951250, \ 0.0197722885748598, \ 0.4351684572939831, \ 0.5634773574179233, \ 0.0013541852880936, \ 0.5634773574179233, \ 0.4351684572939831, \ 0.0013541852880936, \ 0.1390923912291039, \ 0.7732647562548985, \ 0.0876428525159975, \ 0.7732647562548985, \ 0.1390923912291041, \ 0.0876428525159973, \ 0.2801506543012279, \ 0.6414337667335724, \ 0.0784155789651995, \ 0.6414337667335726, \ 0.2801506543012280, \ 0.0784155789651994, \ 0.3463311874275595, \ 0.5909210399343486, \ 0.0627477726380918, \ 0.5909210399343486, \ 0.3463311874275596, \ 0.0627477726380916, \ 0.3811688378455703, \ 0.3811688378455702, \ 0.2376623243088594, \ 0.1142447933587818, \ 0.8786494761873791, \ 0.0071057304538392, \ 0.8786494761873791, \ 0.1142447933587818, \ 0.0071057304538389, \ 0.2601477827144039, \ 0.6989617430573259, \ 0.0408904742282701, \ 0.6989617430573259, \ 0.2601477827144039, \ 0.0408904742282700, \ 0.3385954503697221, \ 0.6289096666027175, \ 0.0324948830275603, \ 0.6289096666027175, \ 0.3385954503697222, \ 0.0324948830275602, \ 0.4405249471606921, \ 0.5507460085493718, \ 0.0087290442899361, \ 0.5507460085493717, \ 0.4405249471606921, \ 0.0087290442899361, \ 0.0857234837407636, \ 0.9127017575952171, \ 0.0015747586640192, \ 0.9127017575952172, \ 0.0857234837407637, \ 0.0015747586640189, \ 0.2007383675971185, \ 0.5985232648057627, \ 0.2007383675971187, \ 0.2859840866397785, \ 0.5124837078245130, \ 0.2015322055357083, \ 0.5124837078245130, \ 0.2859840866397785, \ 0.2015322055357083, \ 0.3022430648527080, \ 0.6463387716329330, \ 0.0514181635143590, \ 0.6463387716329331, \ 0.3022430648527081, \ 0.0514181635143589, \ 0.1145574257288858, \ 0.8664138254475557, \ 0.0190287488235586, \ 0.8664138254475557, \ 0.1145574257288858, \ 0.0190287488235582, \ 0.2122964300195307, \ 0.7469155107726292, \ 0.0407880592078402, \ 0.7469155107726291, \ 0.2122964300195309, \ 0.0407880592078400, \ 0.0462782231758691, \ 0.9074435536482615, \ 0.0462782231758695, \ 0.2971430888632479, \ 0.4057138222735041, \ 0.2971430888632479, \ 0.1465284297099020, \ 0.8249569583935215, \ 0.0285146118965767, \ 0.8249569583935213, \ 0.1465284297099020, \ 0.0285146118965764, \ 0.3740816461088270, \ 0.4722096952795328, \ 0.1537086586116402, \ 0.4722096952795327, \ 0.3740816461088270, \ 0.1537086586116402, \ 0.0817068303997551, \ 0.8936878492161561, \ 0.0246053203840890, \ 0.8936878492161561, \ 0.0817068303997551, \ 0.0246053203840887, \ 0.0108421217690070, \ 0.9783157564619855, \ 0.0108421217690075, \ 0.2941474788808447, \ 0.6823170191891728, \ 0.0235355019299825, \ 0.6823170191891728, \ 0.2941474788808447, \ 0.0235355019299824, \ 0.1750703694826515, \ 0.6872129092572276, \ 0.1377167212601208, \ 0.6872129092572277, \ 0.1750703694826515, \ 0.1377167212601206, \ 0.1028533816631290, \ 0.7942932366737417, \ 0.1028533816631293, \ 0.0476205378057730, \ 0.9414041521049951, \ 0.0109753100892320, \ 0.9414041521049952, \ 0.0476205378057731, \ 0.0109753100892315, \ 0.3175724815133269, \ 0.5219618612839483, \ 0.1604656572027248, \ 0.5219618612839483, \ 0.3175724815133269, \ 0.1604656572027247, \ 0.2881380539950774, \ 0.5789126782672228, \ 0.1329492677376997, \ 0.5789126782672228, \ 0.2881380539950775, \ 0.1329492677376996, \ 0.2679708893032962, \ 0.7232741594653924, \ 0.0087549512313114, \ 0.7232741594653924, \ 0.2679708893032962, \ 0.0087549512313113, \ 0.4841735634166949, \ 0.4841735634166949, \ 0.0316528731666102, \ 0.2393790592030269, \ 0.7398771788136165, \ 0.0207437619833566, \ 0.7398771788136166, \ 0.2393790592030269, \ 0.0207437619833564, \ 0.1918532715697031, \ 0.7883864387462218, \ 0.0197602896840751, \ 0.7883864387462219, \ 0.1918532715697031, \ 0.0197602896840748, \ 0.3873242425341850, \ 0.5697364716889479, \ 0.0429392857768670, \ 0.5697364716889479, \ 0.3873242425341850, \ 0.0429392857768670, \ 0.3535324158284108, \ 0.5285751660132987, \ 0.1178924181582904, \ 0.5285751660132987, \ 0.3535324158284108, \ 0.1178924181582903, \ 0.0521774890148561, \ 0.9224477815225601, \ 0.0253747294625839, \ 0.9224477815225601, \ 0.0521774890148562, \ 0.0253747294625835, \ 0.3237021161513139, \ 0.5827685017638400, \ 0.0935293820848460, \ 0.5827685017638401, \ 0.3237021161513140, \ 0.0935293820848459, \ 0.3720593606748486, \ 0.6259535358370784, \ 0.0019871034880730, \ 0.6259535358370782, \ 0.3720593606748486, \ 0.0019871034880730, \ 0.4136925346071049, \ 0.4776172690993892, \ 0.1086901962935059, \ 0.4776172690993891, \ 0.4136925346071050, \ 0.1086901962935058, \ 0.2508654436414371, \ 0.5742322222075992, \ 0.1749023341509636, \ 0.5742322222075992, \ 0.2508654436414372, \ 0.1749023341509635, \ 0.2368477035387836, \ 0.6961863830895678, \ 0.0669659133716486, \ 0.6961863830895679, \ 0.2368477035387836, \ 0.0669659133716483, \ 0.1099576830426482, \ 0.8490631831866196, \ 0.0409791337707323, \ 0.8490631831866197, \ 0.1099576830426484, \ 0.0409791337707320, \ 0.4297319028951815, \ 0.5458016820289727, \ 0.0244664150758457, \ 0.5458016820289727, \ 0.4297319028951816, \ 0.0244664150758457, \ 0.1437680374333725, \ 0.7995438742256191, \ 0.0566880883410085, \ 0.7995438742256191, \ 0.1437680374333726, \ 0.0566880883410082, \ 0.0774106779986908, \ 0.9129368386397628, \ 0.0096524833615466, \ 0.9129368386397629, \ 0.0774106779986908, \ 0.0096524833615462, \ 0.1557060056653469, \ 0.8331944267073318, \ 0.0110995676273212, \ 0.8331944267073320, \ 0.1557060056653469, \ 0.0110995676273209, \ 0.3128533024496512, \ 0.6851726257624122, \ 0.0019740717879365, \ 0.6851726257624123, \ 0.3128533024496513, \ 0.0019740717879363, \ 0.0260902661381798, \ 0.9628508665812467, \ 0.0110588672805734, \ 0.9628508665812469, \ 0.0260902661381799, \ 0.0110588672805730, \ 0.1656728608179916, \ 0.8318645947596423, \ 0.0024625444223663, \ 0.8318645947596421, \ 0.1656728608179916, \ 0.0024625444223660, \ 0.4932611955660527, \ 0.4932611955660527, \ 0.0134776088678945, \ 0.0742257546763114, \ 0.8793792323410512, \ 0.0463950129826375, \ 0.8793792323410513, \ 0.0742257546763114, \ 0.0463950129826371, \ 0.0288339172370140, \ 0.9690874828381117, \ 0.0020785999248743, \ 0.9690874828381117, \ 0.0288339172370142, \ 0.0020785999248739, \ 0.1868226606723151, \ 0.7448240425293629, \ 0.0683532967983221, \ 0.7448240425293629, \ 0.1868226606723152, \ 0.0683532967983218, \ 0.3270839281856873, \ 0.6622397675113322, \ 0.0106763043029805, \ 0.6622397675113322, \ 0.3270839281856875, \ 0.0106763043029803, \ 0.1038911034338268, \ 0.8269396131025599, \ 0.0691692834636134, \ 0.8269396131025599, \ 0.1038911034338268, \ 0.0691692834636131, \ 0.2155342882429546, \ 0.6837969023224015, \ 0.1006688094346437, \ 0.6837969023224016, \ 0.2155342882429546, \ 0.1006688094346435, \ 0.4057324719755224, \ 0.4057324719755224, \ 0.1885350560489550, \ 0.3431516130273899, \ 0.4556304494441659, \ 0.2012179375284442, \ 0.4556304494441658, \ 0.3431516130273899, \ 0.2012179375284441, \ 0.2224087587233254, \ 0.6341379927840377, \ 0.1434532484926369, \ 0.6341379927840377, \ 0.2224087587233254, \ 0.1434532484926367, \ 0.0534809769143942, \ 0.9443938625479114, \ 0.0021251605376946, \ 0.9443938625479115, \ 0.0534809769143944, \ 0.0021251605376941, \ 0.1304216449251314, \ 0.7391567101497368, \ 0.1304216449251318, \ 0.4387889688450269, \ 0.5097885287055710, \ 0.0514225024494020, \ 0.5097885287055710, \ 0.4387889688450270, \ 0.0514225024494020, \ 0.4614348056302963, \ 0.4614348056302963, \ 0.0771303887394074, \ 0.0275739602431112, \ 0.9448520795137773, \ 0.0275739602431116, \ 0.2318424453754739, \ 0.5363151092490520, \ 0.2318424453754740, \ 0.3517217766277714, \ 0.3517217766277714, \ 0.2965564467444570, \ 0.0022124213099818, \ 0.9955751573800362, \ 0.0022124213099822, \ 0.3919321013755558, \ 0.5299152656988659, \ 0.0781526329255782, \ 0.5299152656988659, \ 0.3919321013755558, \ 0.0781526329255781, \ 0.2110821798970346, \ 0.7824208956570436, \ 0.0064969244459219, \ 0.7824208956570435, \ 0.2110821798970346, \ 0.0064969244459216, \ 0.0117098573109518, \ 0.9861998362698954, \ 0.0020903064191530, \ 0.9861998362698954, \ 0.0117098573109518, \ 0.0020903064191526, \ 0.4987895646915128, \ 0.4987895646915129, \ 0.0024208706169742, \ 0.2063833537599898, \ 0.7934767827218625, \ 0.0001398635181475, \ 0.7934767827218626, \ 0.2063833537599898, \ 0.0001398635181473 ] ) b = np.array ( [ \ 0.0400081550569363, \ 0.1747098543071731, \ 0.7852819906358908, \ 0.0400081550569363, \ 0.7852819906358907, \ 0.1747098543071734, \ 0.0086624172314518, \ 0.3869650571638262, \ 0.6043725256047222, \ 0.0086624172314518, \ 0.6043725256047221, \ 0.3869650571638265, \ 0.0013011091483539, \ 0.1260609334354054, \ 0.8726379574162408, \ 0.0013011091483539, \ 0.8726379574162408, \ 0.1260609334354057, \ 0.1783730162296318, \ 0.1783730162296316, \ 0.6432539675407367, \ 0.2456285053783459, \ 0.2839249520005006, \ 0.4704465426211538, \ 0.2456285053783459, \ 0.4704465426211538, \ 0.2839249520005007, \ 0.2507416361736093, \ 0.3302482693344624, \ 0.4190100944919286, \ 0.2507416361736093, \ 0.4190100944919286, \ 0.3302482693344625, \ 0.0728406536060116, \ 0.0728406536060113, \ 0.8543186927879771, \ 0.0015097374938804, \ 0.2560459410681578, \ 0.7424443214379620, \ 0.0015097374938804, \ 0.7424443214379620, \ 0.2560459410681581, \ 0.1089833802129252, \ 0.2603953161344763, \ 0.6306213036525987, \ 0.1089833802129252, \ 0.6306213036525986, \ 0.2603953161344765, \ 0.1420232887211860, \ 0.4289883556394071, \ 0.4289883556394072, \ 0.1019687169087761, \ 0.1707126963793421, \ 0.7273185867118821, \ 0.1019687169087761, \ 0.7273185867118821, \ 0.1707126963793423, \ 0.0197722885748599, \ 0.3746440580951250, \ 0.6055836533300155, \ 0.0197722885748599, \ 0.6055836533300152, \ 0.3746440580951251, \ 0.0013541852880937, \ 0.4351684572939832, \ 0.5634773574179235, \ 0.0013541852880937, \ 0.5634773574179233, \ 0.4351684572939833, \ 0.0876428525159975, \ 0.1390923912291039, \ 0.7732647562548988, \ 0.0876428525159975, \ 0.7732647562548988, \ 0.1390923912291042, \ 0.0784155789651995, \ 0.2801506543012280, \ 0.6414337667335728, \ 0.0784155789651995, \ 0.6414337667335727, \ 0.2801506543012282, \ 0.0627477726380917, \ 0.3463311874275596, \ 0.5909210399343489, \ 0.0627477726380917, \ 0.5909210399343489, \ 0.3463311874275598, \ 0.2376623243088594, \ 0.3811688378455704, \ 0.3811688378455704, \ 0.0071057304538391, \ 0.1142447933587818, \ 0.8786494761873792, \ 0.0071057304538391, \ 0.8786494761873792, \ 0.1142447933587821, \ 0.0408904742282701, \ 0.2601477827144039, \ 0.6989617430573262, \ 0.0408904742282701, \ 0.6989617430573262, \ 0.2601477827144042, \ 0.0324948830275604, \ 0.3385954503697222, \ 0.6289096666027179, \ 0.0324948830275604, \ 0.6289096666027175, \ 0.3385954503697224, \ 0.0087290442899362, \ 0.4405249471606921, \ 0.5507460085493719, \ 0.0087290442899362, \ 0.5507460085493718, \ 0.4405249471606923, \ 0.0015747586640192, \ 0.0857234837407636, \ 0.9127017575952174, \ 0.0015747586640192, \ 0.9127017575952174, \ 0.0857234837407640, \ 0.2007383675971187, \ 0.2007383675971186, \ 0.5985232648057629, \ 0.2015322055357084, \ 0.2859840866397786, \ 0.5124837078245132, \ 0.2015322055357084, \ 0.5124837078245132, \ 0.2859840866397787, \ 0.0514181635143590, \ 0.3022430648527080, \ 0.6463387716329332, \ 0.0514181635143590, \ 0.6463387716329331, \ 0.3022430648527083, \ 0.0190287488235584, \ 0.1145574257288858, \ 0.8664138254475557, \ 0.0190287488235584, \ 0.8664138254475560, \ 0.1145574257288862, \ 0.0407880592078402, \ 0.2122964300195307, \ 0.7469155107726293, \ 0.0407880592078402, \ 0.7469155107726292, \ 0.2122964300195310, \ 0.0462782231758694, \ 0.0462782231758691, \ 0.9074435536482617, \ 0.2971430888632481, \ 0.2971430888632480, \ 0.4057138222735042, \ 0.0285146118965766, \ 0.1465284297099020, \ 0.8249569583935216, \ 0.0285146118965766, \ 0.8249569583935216, \ 0.1465284297099023, \ 0.1537086586116403, \ 0.3740816461088270, \ 0.4722096952795329, \ 0.1537086586116403, \ 0.4722096952795328, \ 0.3740816461088272, \ 0.0246053203840889, \ 0.0817068303997551, \ 0.8936878492161562, \ 0.0246053203840889, \ 0.8936878492161562, \ 0.0817068303997554, \ 0.0108421217690073, \ 0.0108421217690070, \ 0.9783157564619858, \ 0.0235355019299826, \ 0.2941474788808447, \ 0.6823170191891730, \ 0.0235355019299826, \ 0.6823170191891729, \ 0.2941474788808450, \ 0.1377167212601208, \ 0.1750703694826516, \ 0.6872129092572279, \ 0.1377167212601208, \ 0.6872129092572279, \ 0.1750703694826518, \ 0.1028533816631293, \ 0.1028533816631290, \ 0.7942932366737419, \ 0.0109753100892318, \ 0.0476205378057730, \ 0.9414041521049953, \ 0.0109753100892318, \ 0.9414041521049953, \ 0.0476205378057733, \ 0.1604656572027248, \ 0.3175724815133270, \ 0.5219618612839485, \ 0.1604656572027248, \ 0.5219618612839484, \ 0.3175724815133271, \ 0.1329492677376998, \ 0.2881380539950775, \ 0.5789126782672230, \ 0.1329492677376998, \ 0.5789126782672228, \ 0.2881380539950777, \ 0.0087549512313114, \ 0.2679708893032962, \ 0.7232741594653926, \ 0.0087549512313114, \ 0.7232741594653926, \ 0.2679708893032964, \ 0.0316528731666103, \ 0.4841735634166949, \ 0.4841735634166951, \ 0.0207437619833566, \ 0.2393790592030269, \ 0.7398771788136167, \ 0.0207437619833566, \ 0.7398771788136167, \ 0.2393790592030272, \ 0.0197602896840750, \ 0.1918532715697031, \ 0.7883864387462221, \ 0.0197602896840750, \ 0.7883864387462221, \ 0.1918532715697034, \ 0.0429392857768671, \ 0.3873242425341851, \ 0.5697364716889481, \ 0.0429392857768671, \ 0.5697364716889480, \ 0.3873242425341852, \ 0.1178924181582904, \ 0.3535324158284109, \ 0.5285751660132989, \ 0.1178924181582904, \ 0.5285751660132989, \ 0.3535324158284111, \ 0.0253747294625837, \ 0.0521774890148561, \ 0.9224477815225602, \ 0.0253747294625837, \ 0.9224477815225602, \ 0.0521774890148565, \ 0.0935293820848460, \ 0.3237021161513140, \ 0.5827685017638402, \ 0.0935293820848460, \ 0.5827685017638401, \ 0.3237021161513142, \ 0.0019871034880731, \ 0.3720593606748486, \ 0.6259535358370786, \ 0.0019871034880731, \ 0.6259535358370784, \ 0.3720593606748488, \ 0.1086901962935059, \ 0.4136925346071050, \ 0.4776172690993893, \ 0.1086901962935059, \ 0.4776172690993892, \ 0.4136925346071051, \ 0.1749023341509636, \ 0.2508654436414372, \ 0.5742322222075994, \ 0.1749023341509636, \ 0.5742322222075994, \ 0.2508654436414374, \ 0.0669659133716485, \ 0.2368477035387836, \ 0.6961863830895680, \ 0.0669659133716485, \ 0.6961863830895680, \ 0.2368477035387838, \ 0.0409791337707322, \ 0.1099576830426482, \ 0.8490631831866197, \ 0.0409791337707322, \ 0.8490631831866197, \ 0.1099576830426485, \ 0.0244664150758458, \ 0.4297319028951816, \ 0.5458016820289728, \ 0.0244664150758458, \ 0.5458016820289727, \ 0.4297319028951818, \ 0.0566880883410084, \ 0.1437680374333725, \ 0.7995438742256192, \ 0.0566880883410084, \ 0.7995438742256192, \ 0.1437680374333728, \ 0.0096524833615464, \ 0.0774106779986908, \ 0.9129368386397629, \ 0.0096524833615464, \ 0.9129368386397629, \ 0.0774106779986911, \ 0.0110995676273212, \ 0.1557060056653469, \ 0.8331944267073321, \ 0.0110995676273212, \ 0.8331944267073321, \ 0.1557060056653472, \ 0.0019740717879365, \ 0.3128533024496513, \ 0.6851726257624124, \ 0.0019740717879365, \ 0.6851726257624124, \ 0.3128533024496515, \ 0.0110588672805733, \ 0.0260902661381798, \ 0.9628508665812471, \ 0.0110588672805733, \ 0.9628508665812471, \ 0.0260902661381801, \ 0.0024625444223662, \ 0.1656728608179916, \ 0.8318645947596424, \ 0.0024625444223662, \ 0.8318645947596424, \ 0.1656728608179919, \ 0.0134776088678946, \ 0.4932611955660528, \ 0.4932611955660529, \ 0.0463950129826374, \ 0.0742257546763114, \ 0.8793792323410514, \ 0.0463950129826374, \ 0.8793792323410514, \ 0.0742257546763117, \ 0.0020785999248742, \ 0.0288339172370141, \ 0.9690874828381119, \ 0.0020785999248742, \ 0.9690874828381119, \ 0.0288339172370144, \ 0.0683532967983220, \ 0.1868226606723151, \ 0.7448240425293630, \ 0.0683532967983220, \ 0.7448240425293630, \ 0.1868226606723153, \ 0.0106763043029805, \ 0.3270839281856874, \ 0.6622397675113323, \ 0.0106763043029805, \ 0.6622397675113322, \ 0.3270839281856877, \ 0.0691692834636133, \ 0.1038911034338268, \ 0.8269396131025600, \ 0.0691692834636133, \ 0.8269396131025600, \ 0.1038911034338271, \ 0.1006688094346437, \ 0.2155342882429546, \ 0.6837969023224019, \ 0.1006688094346437, \ 0.6837969023224019, \ 0.2155342882429548, \ 0.1885350560489551, \ 0.4057324719755226, \ 0.4057324719755226, \ 0.2012179375284443, \ 0.3431516130273900, \ 0.4556304494441660, \ 0.2012179375284443, \ 0.4556304494441659, \ 0.3431516130273902, \ 0.1434532484926369, \ 0.2224087587233255, \ 0.6341379927840379, \ 0.1434532484926369, \ 0.6341379927840379, \ 0.2224087587233256, \ 0.0021251605376943, \ 0.0534809769143942, \ 0.9443938625479115, \ 0.0021251605376943, \ 0.9443938625479115, \ 0.0534809769143946, \ 0.1304216449251317, \ 0.1304216449251314, \ 0.7391567101497369, \ 0.0514225024494020, \ 0.4387889688450270, \ 0.5097885287055712, \ 0.0514225024494020, \ 0.5097885287055710, \ 0.4387889688450272, \ 0.0771303887394075, \ 0.4614348056302963, \ 0.4614348056302964, \ 0.0275739602431115, \ 0.0275739602431112, \ 0.9448520795137775, \ 0.2318424453754741, \ 0.2318424453754740, \ 0.5363151092490521, \ 0.2965564467444571, \ 0.3517217766277715, \ 0.3517217766277716, \ 0.0022124213099821, \ 0.0022124213099817, \ 0.9955751573800363, \ 0.0781526329255783, \ 0.3919321013755560, \ 0.5299152656988662, \ 0.0781526329255783, \ 0.5299152656988660, \ 0.3919321013755561, \ 0.0064969244459218, \ 0.2110821798970346, \ 0.7824208956570438, \ 0.0064969244459218, \ 0.7824208956570438, \ 0.2110821798970349, \ 0.0020903064191529, \ 0.0117098573109518, \ 0.9861998362698955, \ 0.0020903064191529, \ 0.9861998362698955, \ 0.0117098573109521, \ 0.0024208706169743, \ 0.4987895646915129, \ 0.4987895646915131, \ 0.0001398635181475, \ 0.2063833537599899, \ 0.7934767827218628, \ 0.0001398635181475, \ 0.7934767827218628, \ 0.2063833537599901 ] ) c = np.array ( [ \ 0.7852819906358905, \ 0.0400081550569363, \ 0.1747098543071729, \ 0.1747098543071730, \ 0.0400081550569361, \ 0.7852819906358905, \ 0.6043725256047220, \ 0.0086624172314517, \ 0.3869650571638260, \ 0.3869650571638262, \ 0.0086624172314517, \ 0.6043725256047218, \ 0.8726379574162407, \ 0.0013011091483539, \ 0.1260609334354051, \ 0.1260609334354054, \ 0.0013011091483537, \ 0.8726379574162407, \ 0.6432539675407367, \ 0.1783730162296317, \ 0.1783730162296314, \ 0.4704465426211537, \ 0.2456285053783457, \ 0.2839249520005004, \ 0.2839249520005004, \ 0.2456285053783457, \ 0.4704465426211537, \ 0.4190100944919284, \ 0.2507416361736092, \ 0.3302482693344622, \ 0.3302482693344622, \ 0.2507416361736092, \ 0.4190100944919284, \ 0.8543186927879770, \ 0.0728406536060116, \ 0.0728406536060112, \ 0.7424443214379618, \ 0.0015097374938805, \ 0.2560459410681576, \ 0.2560459410681578, \ 0.0015097374938803, \ 0.7424443214379617, \ 0.6306213036525986, \ 0.1089833802129253, \ 0.2603953161344761, \ 0.2603953161344762, \ 0.1089833802129251, \ 0.6306213036525985, \ 0.4289883556394071, \ 0.1420232887211860, \ 0.4289883556394070, \ 0.7273185867118819, \ 0.1019687169087761, \ 0.1707126963793417, \ 0.1707126963793420, \ 0.1019687169087760, \ 0.7273185867118818, \ 0.6055836533300152, \ 0.0197722885748597, \ 0.3746440580951246, \ 0.3746440580951249, \ 0.0197722885748598, \ 0.6055836533300151, \ 0.5634773574179232, \ 0.0013541852880936, \ 0.4351684572939829, \ 0.4351684572939831, \ 0.0013541852880936, \ 0.5634773574179230, \ 0.7732647562548985, \ 0.0876428525159975, \ 0.1390923912291037, \ 0.1390923912291040, \ 0.0876428525159972, \ 0.7732647562548985, \ 0.6414337667335724, \ 0.0784155789651995, \ 0.2801506543012278, \ 0.2801506543012279, \ 0.0784155789651994, \ 0.6414337667335724, \ 0.5909210399343487, \ 0.0627477726380918, \ 0.3463311874275593, \ 0.3463311874275596, \ 0.0627477726380915, \ 0.5909210399343485, \ 0.3811688378455703, \ 0.2376623243088594, \ 0.3811688378455702, \ 0.8786494761873791, \ 0.0071057304538391, \ 0.1142447933587816, \ 0.1142447933587818, \ 0.0071057304538390, \ 0.8786494761873790, \ 0.6989617430573259, \ 0.0408904742282701, \ 0.2601477827144038, \ 0.2601477827144039, \ 0.0408904742282700, \ 0.6989617430573258, \ 0.6289096666027175, \ 0.0324948830275603, \ 0.3385954503697218, \ 0.3385954503697221, \ 0.0324948830275603, \ 0.6289096666027174, \ 0.5507460085493718, \ 0.0087290442899360, \ 0.4405249471606919, \ 0.4405249471606921, \ 0.0087290442899360, \ 0.5507460085493715, \ 0.9127017575952171, \ 0.0015747586640193, \ 0.0857234837407633, \ 0.0857234837407636, \ 0.0015747586640189, \ 0.9127017575952171, \ 0.5985232648057627, \ 0.2007383675971187, \ 0.2007383675971185, \ 0.5124837078245131, \ 0.2015322055357084, \ 0.2859840866397785, \ 0.2859840866397786, \ 0.2015322055357083, \ 0.5124837078245130, \ 0.6463387716329331, \ 0.0514181635143590, \ 0.3022430648527078, \ 0.3022430648527079, \ 0.0514181635143588, \ 0.6463387716329327, \ 0.8664138254475557, \ 0.0190287488235584, \ 0.1145574257288857, \ 0.1145574257288858, \ 0.0190287488235582, \ 0.8664138254475556, \ 0.7469155107726292, \ 0.0407880592078401, \ 0.2122964300195305, \ 0.2122964300195307, \ 0.0407880592078399, \ 0.7469155107726290, \ 0.9074435536482616, \ 0.0462782231758695, \ 0.0462782231758688, \ 0.4057138222735040, \ 0.2971430888632479, \ 0.2971430888632479, \ 0.8249569583935215, \ 0.0285146118965766, \ 0.1465284297099018, \ 0.1465284297099021, \ 0.0285146118965763, \ 0.8249569583935213, \ 0.4722096952795327, \ 0.1537086586116401, \ 0.3740816461088269, \ 0.3740816461088270, \ 0.1537086586116402, \ 0.4722096952795326, \ 0.8936878492161561, \ 0.0246053203840889, \ 0.0817068303997548, \ 0.0817068303997550, \ 0.0246053203840887, \ 0.8936878492161560, \ 0.9783157564619857, \ 0.0108421217690075, \ 0.0108421217690068, \ 0.6823170191891728, \ 0.0235355019299825, \ 0.2941474788808445, \ 0.2941474788808447, \ 0.0235355019299824, \ 0.6823170191891725, \ 0.6872129092572277, \ 0.1377167212601209, \ 0.1750703694826513, \ 0.1750703694826515, \ 0.1377167212601206, \ 0.6872129092572276, \ 0.7942932366737416, \ 0.1028533816631292, \ 0.1028533816631289, \ 0.9414041521049952, \ 0.0109753100892319, \ 0.0476205378057727, \ 0.0476205378057730, \ 0.0109753100892317, \ 0.9414041521049951, \ 0.5219618612839482, \ 0.1604656572027248, \ 0.3175724815133267, \ 0.3175724815133268, \ 0.1604656572027247, \ 0.5219618612839482, \ 0.5789126782672228, \ 0.1329492677376997, \ 0.2881380539950772, \ 0.2881380539950774, \ 0.1329492677376997, \ 0.5789126782672227, \ 0.7232741594653924, \ 0.0087549512313114, \ 0.2679708893032959, \ 0.2679708893032962, \ 0.0087549512313112, \ 0.7232741594653922, \ 0.4841735634166949, \ 0.0316528731666103, \ 0.4841735634166947, \ 0.7398771788136165, \ 0.0207437619833566, \ 0.2393790592030267, \ 0.2393790592030269, \ 0.0207437619833564, \ 0.7398771788136165, \ 0.7883864387462219, \ 0.0197602896840751, \ 0.1918532715697029, \ 0.1918532715697031, \ 0.0197602896840748, \ 0.7883864387462218, \ 0.5697364716889479, \ 0.0429392857768670, \ 0.3873242425341848, \ 0.3873242425341850, \ 0.0429392857768670, \ 0.5697364716889477, \ 0.5285751660132988, \ 0.1178924181582904, \ 0.3535324158284107, \ 0.3535324158284109, \ 0.1178924181582903, \ 0.5285751660132987, \ 0.9224477815225602, \ 0.0253747294625838, \ 0.0521774890148559, \ 0.0521774890148561, \ 0.0253747294625836, \ 0.9224477815225601, \ 0.5827685017638400, \ 0.0935293820848460, \ 0.3237021161513138, \ 0.3237021161513139, \ 0.0935293820848458, \ 0.5827685017638400, \ 0.6259535358370784, \ 0.0019871034880730, \ 0.3720593606748485, \ 0.3720593606748486, \ 0.0019871034880731, \ 0.6259535358370780, \ 0.4776172690993891, \ 0.1086901962935058, \ 0.4136925346071049, \ 0.4136925346071049, \ 0.1086901962935058, \ 0.4776172690993891, \ 0.5742322222075993, \ 0.1749023341509636, \ 0.2508654436414369, \ 0.2508654436414372, \ 0.1749023341509633, \ 0.5742322222075992, \ 0.6961863830895679, \ 0.0669659133716486, \ 0.2368477035387834, \ 0.2368477035387836, \ 0.0669659133716484, \ 0.6961863830895679, \ 0.8490631831866196, \ 0.0409791337707322, \ 0.1099576830426480, \ 0.1099576830426481, \ 0.0409791337707320, \ 0.8490631831866196, \ 0.5458016820289726, \ 0.0244664150758456, \ 0.4297319028951814, \ 0.4297319028951815, \ 0.0244664150758457, \ 0.5458016820289725, \ 0.7995438742256191, \ 0.0566880883410084, \ 0.1437680374333722, \ 0.1437680374333725, \ 0.0566880883410082, \ 0.7995438742256189, \ 0.9129368386397629, \ 0.0096524833615464, \ 0.0774106779986905, \ 0.0774106779986907, \ 0.0096524833615462, \ 0.9129368386397628, \ 0.8331944267073319, \ 0.0110995676273213, \ 0.1557060056653466, \ 0.1557060056653468, \ 0.0110995676273210, \ 0.8331944267073319, \ 0.6851726257624123, \ 0.0019740717879365, \ 0.3128533024496510, \ 0.3128533024496512, \ 0.0019740717879363, \ 0.6851726257624122, \ 0.9628508665812470, \ 0.0110588672805735, \ 0.0260902661381796, \ 0.0260902661381799, \ 0.0110588672805730, \ 0.9628508665812469, \ 0.8318645947596423, \ 0.0024625444223662, \ 0.1656728608179914, \ 0.1656728608179917, \ 0.0024625444223660, \ 0.8318645947596420, \ 0.4932611955660528, \ 0.0134776088678945, \ 0.4932611955660526, \ 0.8793792323410513, \ 0.0463950129826374, \ 0.0742257546763111, \ 0.0742257546763113, \ 0.0463950129826372, \ 0.8793792323410512, \ 0.9690874828381117, \ 0.0020785999248742, \ 0.0288339172370139, \ 0.0288339172370141, \ 0.0020785999248739, \ 0.9690874828381117, \ 0.7448240425293629, \ 0.0683532967983221, \ 0.1868226606723149, \ 0.1868226606723151, \ 0.0683532967983219, \ 0.7448240425293629, \ 0.6622397675113322, \ 0.0106763043029804, \ 0.3270839281856872, \ 0.3270839281856874, \ 0.0106763043029804, \ 0.6622397675113321, \ 0.8269396131025599, \ 0.0691692834636133, \ 0.1038911034338266, \ 0.1038911034338268, \ 0.0691692834636132, \ 0.8269396131025599, \ 0.6837969023224016, \ 0.1006688094346438, \ 0.2155342882429544, \ 0.2155342882429546, \ 0.1006688094346436, \ 0.6837969023224016, \ 0.4057324719755225, \ 0.1885350560489550, \ 0.4057324719755224, \ 0.4556304494441658, \ 0.2012179375284441, \ 0.3431516130273898, \ 0.3431516130273898, \ 0.2012179375284442, \ 0.4556304494441656, \ 0.6341379927840377, \ 0.1434532484926368, \ 0.2224087587233252, \ 0.2224087587233254, \ 0.1434532484926366, \ 0.6341379927840376, \ 0.9443938625479115, \ 0.0021251605376944, \ 0.0534809769143939, \ 0.0534809769143942, \ 0.0021251605376941, \ 0.9443938625479114, \ 0.7391567101497369, \ 0.1304216449251317, \ 0.1304216449251313, \ 0.5097885287055710, \ 0.0514225024494020, \ 0.4387889688450268, \ 0.4387889688450269, \ 0.0514225024494019, \ 0.5097885287055708, \ 0.4614348056302962, \ 0.0771303887394074, \ 0.4614348056302961, \ 0.9448520795137773, \ 0.0275739602431116, \ 0.0275739602431110, \ 0.5363151092490519, \ 0.2318424453754740, \ 0.2318424453754738, \ 0.3517217766277715, \ 0.2965564467444571, \ 0.3517217766277714, \ 0.9955751573800361, \ 0.0022124213099820, \ 0.0022124213099816, \ 0.5299152656988658, \ 0.0781526329255781, \ 0.3919321013755557, \ 0.3919321013755558, \ 0.0781526329255781, \ 0.5299152656988657, \ 0.7824208956570436, \ 0.0064969244459218, \ 0.2110821798970344, \ 0.2110821798970347, \ 0.0064969244459216, \ 0.7824208956570435, \ 0.9861998362698954, \ 0.0020903064191529, \ 0.0117098573109514, \ 0.0117098573109518, \ 0.0020903064191528, \ 0.9861998362698953, \ 0.4987895646915129, \ 0.0024208706169743, \ 0.4987895646915126, \ 0.7934767827218626, \ 0.0001398635181476, \ 0.2063833537599896, \ 0.2063833537599898, \ 0.0001398635181474, \ 0.7934767827218625 ] ) w = np.array ( [ \ 0.0015179493827508, \ 0.0015179493827508, \ 0.0015179493827508, \ 0.0015179493827508, \ 0.0015179493827508, \ 0.0015179493827508, \ 0.0009640363088870, \ 0.0009640363088870, \ 0.0009640363088870, \ 0.0009640363088870, \ 0.0009640363088870, \ 0.0009640363088870, \ 0.0002813503665322, \ 0.0002813503665322, \ 0.0002813503665322, \ 0.0002813503665322, \ 0.0002813503665322, \ 0.0002813503665322, \ 0.0032298776744525, \ 0.0032298776744525, \ 0.0032298776744525, \ 0.0046862213374651, \ 0.0046862213374651, \ 0.0046862213374651, \ 0.0046862213374651, \ 0.0046862213374651, \ 0.0046862213374651, \ 0.0045178989983832, \ 0.0045178989983832, \ 0.0045178989983832, \ 0.0045178989983832, \ 0.0045178989983832, \ 0.0045178989983832, \ 0.0015790917860184, \ 0.0015790917860184, \ 0.0015790917860184, \ 0.0004264134812992, \ 0.0004264134812992, \ 0.0004264134812992, \ 0.0004264134812992, \ 0.0004264134812992, \ 0.0004264134812992, \ 0.0032468366301052, \ 0.0032468366301052, \ 0.0032468366301052, \ 0.0032468366301052, \ 0.0032468366301052, \ 0.0032468366301052, \ 0.0039309054788202, \ 0.0039309054788202, \ 0.0039309054788202, \ 0.0027113498937414, \ 0.0027113498937414, \ 0.0027113498937414, \ 0.0027113498937414, \ 0.0027113498937414, \ 0.0027113498937414, \ 0.0016327582269425, \ 0.0016327582269425, \ 0.0016327582269425, \ 0.0016327582269425, \ 0.0016327582269425, \ 0.0016327582269425, \ 0.0004790301761790, \ 0.0004790301761790, \ 0.0004790301761790, \ 0.0004790301761790, \ 0.0004790301761790, \ 0.0004790301761790, \ 0.0026002718294388, \ 0.0026002718294388, \ 0.0026002718294388, \ 0.0026002718294388, \ 0.0026002718294388, \ 0.0026002718294388, \ 0.0030738076620057, \ 0.0030738076620057, \ 0.0030738076620057, \ 0.0030738076620057, \ 0.0030738076620057, \ 0.0030738076620057, \ 0.0029878198502273, \ 0.0029878198502273, \ 0.0029878198502273, \ 0.0029878198502273, \ 0.0029878198502273, \ 0.0029878198502273, \ 0.0049958592249662, \ 0.0049958592249662, \ 0.0049958592249662, \ 0.0006925913496786, \ 0.0006925913496786, \ 0.0006925913496786, \ 0.0006925913496786, \ 0.0006925913496786, \ 0.0006925913496786, \ 0.0022641894958966, \ 0.0022641894958966, \ 0.0022641894958966, \ 0.0022641894958966, \ 0.0022641894958966, \ 0.0022641894958966, \ 0.0021683619372714, \ 0.0021683619372714, \ 0.0021683619372714, \ 0.0021683619372714, \ 0.0021683619372714, \ 0.0021683619372714, \ 0.0012603344824756, \ 0.0012603344824756, \ 0.0012603344824756, \ 0.0012603344824756, \ 0.0012603344824756, \ 0.0012603344824756, \ 0.0003019280054420, \ 0.0003019280054420, \ 0.0003019280054420, \ 0.0003019280054420, \ 0.0003019280054420, \ 0.0003019280054420, \ 0.0040779189028797, \ 0.0040779189028797, \ 0.0040779189028797, \ 0.0045616230274563, \ 0.0045616230274563, \ 0.0045616230274563, \ 0.0045616230274563, \ 0.0045616230274563, \ 0.0045616230274563, \ 0.0026431427639031, \ 0.0026431427639031, \ 0.0026431427639031, \ 0.0026431427639031, \ 0.0026431427639031, \ 0.0026431427639031, \ 0.0011314599292834, \ 0.0011314599292834, \ 0.0011314599292834, \ 0.0011314599292834, \ 0.0011314599292834, \ 0.0011314599292834, \ 0.0021088731883819, \ 0.0021088731883819, \ 0.0021088731883819, \ 0.0021088731883819, \ 0.0021088731883819, \ 0.0021088731883819, \ 0.0011717865482745, \ 0.0011717865482745, \ 0.0011717865482745, \ 0.0050840537579920, \ 0.0050840537579920, \ 0.0050840537579920, \ 0.0015608187011213, \ 0.0015608187011213, \ 0.0015608187011213, \ 0.0015608187011213, \ 0.0015608187011213, \ 0.0015608187011213, \ 0.0046308511124104, \ 0.0046308511124104, \ 0.0046308511124104, \ 0.0046308511124104, \ 0.0046308511124104, \ 0.0046308511124104, \ 0.0011648378245234, \ 0.0011648378245234, \ 0.0011648378245234, \ 0.0011648378245234, \ 0.0011648378245234, \ 0.0011648378245234, \ 0.0002909934397913, \ 0.0002909934397913, \ 0.0002909934397913, \ 0.0019078475871128, \ 0.0019078475871128, \ 0.0019078475871128, \ 0.0019078475871128, \ 0.0019078475871128, \ 0.0019078475871128, \ 0.0036207359330354, \ 0.0036207359330354, \ 0.0036207359330354, \ 0.0036207359330354, \ 0.0036207359330354, \ 0.0036207359330354, \ 0.0024679826387392, \ 0.0024679826387392, \ 0.0024679826387392, \ 0.0006047059166113, \ 0.0006047059166113, \ 0.0006047059166113, \ 0.0006047059166113, \ 0.0006047059166113, \ 0.0006047059166113, \ 0.0044715780288226, \ 0.0044715780288226, \ 0.0044715780288226, \ 0.0044715780288226, \ 0.0044715780288226, \ 0.0044715780288226, \ 0.0043217865559446, \ 0.0043217865559446, \ 0.0043217865559446, \ 0.0043217865559446, \ 0.0043217865559446, \ 0.0043217865559446, \ 0.0011834459680029, \ 0.0011834459680029, \ 0.0011834459680029, \ 0.0011834459680029, \ 0.0011834459680029, \ 0.0011834459680029, \ 0.0024475548918752, \ 0.0024475548918752, \ 0.0024475548918752, \ 0.0017098461192591, \ 0.0017098461192591, \ 0.0017098461192591, \ 0.0017098461192591, \ 0.0017098461192591, \ 0.0017098461192591, \ 0.0015260667775320, \ 0.0015260667775320, \ 0.0015260667775320, \ 0.0015260667775320, \ 0.0015260667775320, \ 0.0015260667775320, \ 0.0027529020694636, \ 0.0027529020694636, \ 0.0027529020694636, \ 0.0027529020694636, \ 0.0027529020694636, \ 0.0027529020694636, \ 0.0043632272367912, \ 0.0043632272367912, \ 0.0043632272367912, \ 0.0043632272367912, \ 0.0043632272367912, \ 0.0043632272367912, \ 0.0009662853562326, \ 0.0009662853562326, \ 0.0009662853562326, \ 0.0009662853562326, \ 0.0009662853562326, \ 0.0009662853562326, \ 0.0037815526680686, \ 0.0037815526680686, \ 0.0037815526680686, \ 0.0037815526680686, \ 0.0037815526680686, \ 0.0037815526680686, \ 0.0006035693127469, \ 0.0006035693127469, \ 0.0006035693127469, \ 0.0006035693127469, \ 0.0006035693127469, \ 0.0006035693127469, \ 0.0042551639608390, \ 0.0042551639608390, \ 0.0042551639608390, \ 0.0042551639608390, \ 0.0042551639608390, \ 0.0042551639608390, \ 0.0048490533224092, \ 0.0048490533224092, \ 0.0048490533224092, \ 0.0048490533224092, \ 0.0048490533224092, \ 0.0048490533224092, \ 0.0030254918153352, \ 0.0030254918153352, \ 0.0030254918153352, \ 0.0030254918153352, \ 0.0030254918153352, \ 0.0030254918153352, \ 0.0018302659109492, \ 0.0018302659109492, \ 0.0018302659109492, \ 0.0018302659109492, \ 0.0018302659109492, \ 0.0018302659109492, \ 0.0023112911452725, \ 0.0023112911452725, \ 0.0023112911452725, \ 0.0023112911452725, \ 0.0023112911452725, \ 0.0023112911452725, \ 0.0022976181282931, \ 0.0022976181282931, \ 0.0022976181282931, \ 0.0022976181282931, \ 0.0022976181282931, \ 0.0022976181282931, \ 0.0007737426014553, \ 0.0007737426014553, \ 0.0007737426014553, \ 0.0007737426014553, \ 0.0007737426014553, \ 0.0007737426014553, \ 0.0011091107906633, \ 0.0011091107906633, \ 0.0011091107906633, \ 0.0011091107906633, \ 0.0011091107906633, \ 0.0011091107906633, \ 0.0005917280070787, \ 0.0005917280070787, \ 0.0005917280070787, \ 0.0005917280070787, \ 0.0005917280070787, \ 0.0005917280070787, \ 0.0004663290783398, \ 0.0004663290783398, \ 0.0004663290783398, \ 0.0004663290783398, \ 0.0004663290783398, \ 0.0004663290783398, \ 0.0005060545142142, \ 0.0005060545142142, \ 0.0005060545142142, \ 0.0005060545142142, \ 0.0005060545142142, \ 0.0005060545142142, \ 0.0016834711767858, \ 0.0016834711767858, \ 0.0016834711767858, \ 0.0015462052435902, \ 0.0015462052435902, \ 0.0015462052435902, \ 0.0015462052435902, \ 0.0015462052435902, \ 0.0015462052435902, \ 0.0002238167725271, \ 0.0002238167725271, \ 0.0002238167725271, \ 0.0002238167725271, \ 0.0002238167725271, \ 0.0002238167725271, \ 0.0029561851838940, \ 0.0029561851838940, \ 0.0029561851838940, \ 0.0029561851838940, \ 0.0029561851838940, \ 0.0029561851838940, \ 0.0014290418491702, \ 0.0014290418491702, \ 0.0014290418491702, \ 0.0014290418491702, \ 0.0014290418491702, \ 0.0014290418491702, \ 0.0021458693484176, \ 0.0021458693484176, \ 0.0021458693484176, \ 0.0021458693484176, \ 0.0021458693484176, \ 0.0021458693484176, \ 0.0035847674194570, \ 0.0035847674194570, \ 0.0035847674194570, \ 0.0035847674194570, \ 0.0035847674194570, \ 0.0035847674194570, \ 0.0053654225406028, \ 0.0053654225406028, \ 0.0053654225406028, \ 0.0054527357782272, \ 0.0054527357782272, \ 0.0054527357782272, \ 0.0054527357782272, \ 0.0054527357782272, \ 0.0054527357782272, \ 0.0043816657756572, \ 0.0043816657756572, \ 0.0043816657756572, \ 0.0043816657756572, \ 0.0043816657756572, \ 0.0043816657756572, \ 0.0003071745359645, \ 0.0003071745359645, \ 0.0003071745359645, \ 0.0003071745359645, \ 0.0003071745359645, \ 0.0003071745359645, \ 0.0034992680317617, \ 0.0034992680317617, \ 0.0034992680317617, \ 0.0032381770164589, \ 0.0032381770164589, \ 0.0032381770164589, \ 0.0032381770164589, \ 0.0032381770164589, \ 0.0032381770164589, \ 0.0039600197915087, \ 0.0039600197915087, \ 0.0039600197915087, \ 0.0008319508889038, \ 0.0008319508889038, \ 0.0008319508889038, \ 0.0053644090708949, \ 0.0053644090708949, \ 0.0053644090708949, \ 0.0061267736075541, \ 0.0061267736075541, \ 0.0061267736075541, \ 0.0000646114299085, \ 0.0000646114299085, \ 0.0000646114299085, \ 0.0041053828589275, \ 0.0041053828589275, \ 0.0041053828589275, \ 0.0041053828589275, \ 0.0041053828589275, \ 0.0041053828589275, \ 0.0010683587323421, \ 0.0010683587323421, \ 0.0010683587323421, \ 0.0010683587323421, \ 0.0010683587323421, \ 0.0010683587323421, \ 0.0001423198916150, \ 0.0001423198916150, \ 0.0001423198916150, \ 0.0001423198916150, \ 0.0001423198916150, \ 0.0001423198916150, \ 0.0007885551654533, \ 0.0007885551654533, \ 0.0007885551654533, \ 0.0001605584705522, \ 0.0001605584705522, \ 0.0001605584705522, \ 0.0001605584705522, \ 0.0001605584705522, \ 0.0001605584705522 ] ) return a, b, c, w def rule50 ( ): #*****************************************************************************80 # ## rule50() returns the rule of precision 50. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 10 July 2023 # # Author: # # John Burkardt # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient # quadrature rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Output: # # real a(n), b(n), c(n): the barycentric coordinates of quadrature points. # # real w(n): the quadrature weights. # import numpy as np a = np.array ( [ \ 0.2563558633847908, \ 0.4872882732304182, \ 0.2563558633847909, \ 0.4433230868583420, \ 0.5557544570355875, \ 0.0009224561060704, \ 0.5557544570355875, \ 0.4433230868583420, \ 0.0009224561060704, \ 0.0259368938757904, \ 0.9516251148618965, \ 0.0224379912623133, \ 0.9516251148618965, \ 0.0259368938757906, \ 0.0224379912623128, \ 0.2401441052632695, \ 0.5370651664429976, \ 0.2227907282937328, \ 0.5370651664429976, \ 0.2401441052632695, \ 0.2227907282937327, \ 0.1345526180266427, \ 0.8423271680031109, \ 0.0231202139702464, \ 0.8423271680031110, \ 0.1345526180266427, \ 0.0231202139702461, \ 0.0450355724673314, \ 0.9541076477376595, \ 0.0008567797950091, \ 0.9541076477376597, \ 0.0450355724673315, \ 0.0008567797950087, \ 0.4087145665677719, \ 0.5864767957713561, \ 0.0048086376608720, \ 0.5864767957713561, \ 0.4087145665677719, \ 0.0048086376608719, \ 0.1714634577399832, \ 0.8050435299005781, \ 0.0234930123594386, \ 0.8050435299005783, \ 0.1714634577399832, \ 0.0234930123594384, \ 0.0016305781421460, \ 0.9967388437157076, \ 0.0016305781421465, \ 0.2101059247050331, \ 0.6964974281656032, \ 0.0933966471293636, \ 0.6964974281656033, \ 0.2101059247050331, \ 0.0933966471293634, \ 0.1392968201185850, \ 0.8189065432302668, \ 0.0417966366511482, \ 0.8189065432302668, \ 0.1392968201185851, \ 0.0417966366511480, \ 0.0703820539127592, \ 0.8802606341943795, \ 0.0493573118928615, \ 0.8802606341943796, \ 0.0703820539127593, \ 0.0493573118928611, \ 0.4903268692484512, \ 0.4903268692484513, \ 0.0193462615030975, \ 0.3726064881564940, \ 0.4745794048313449, \ 0.1528141070121611, \ 0.4745794048313449, \ 0.3726064881564940, \ 0.1528141070121610, \ 0.1479157172776441, \ 0.7869688527917342, \ 0.0651154299306216, \ 0.7869688527917343, \ 0.1479157172776442, \ 0.0651154299306213, \ 0.2140246435816437, \ 0.7625132132423355, \ 0.0234621431760209, \ 0.7625132132423355, \ 0.2140246435816437, \ 0.0234621431760206, \ 0.3302674030581440, \ 0.6177003187074449, \ 0.0520322782344111, \ 0.6177003187074449, \ 0.3302674030581441, \ 0.0520322782344110, \ 0.3699848635444039, \ 0.6285206173500637, \ 0.0014945191055323, \ 0.6285206173500638, \ 0.3699848635444039, \ 0.0014945191055322, \ 0.0675115690433361, \ 0.9204446840218713, \ 0.0120437469347927, \ 0.9204446840218714, \ 0.0675115690433362, \ 0.0120437469347923, \ 0.4370988411800967, \ 0.5062163732764420, \ 0.0566847855434612, \ 0.5062163732764420, \ 0.4370988411800968, \ 0.0566847855434611, \ 0.4225871685075206, \ 0.4225871685075206, \ 0.1548256629849586, \ 0.4145122211577853, \ 0.4706276367973991, \ 0.1148601420448156, \ 0.4706276367973991, \ 0.4145122211577853, \ 0.1148601420448156, \ 0.3623805122689274, \ 0.6063546515443636, \ 0.0312648361867088, \ 0.6063546515443636, \ 0.3623805122689275, \ 0.0312648361867088, \ 0.3122512855112035, \ 0.5855020743432547, \ 0.1022466401455417, \ 0.5855020743432547, \ 0.3122512855112035, \ 0.1022466401455416, \ 0.4805756764340300, \ 0.4805756764340301, \ 0.0388486471319398, \ 0.3926893217036879, \ 0.5589613764232392, \ 0.0483493018730729, \ 0.5589613764232392, \ 0.3926893217036880, \ 0.0483493018730728, \ 0.0260638541622880, \ 0.9639565689080692, \ 0.0099795769296427, \ 0.9639565689080694, \ 0.0260638541622881, \ 0.0099795769296424, \ 0.3983909958449554, \ 0.5176960633851162, \ 0.0839129407699283, \ 0.5176960633851162, \ 0.3983909958449555, \ 0.0839129407699283, \ 0.0458803913209149, \ 0.9473914769778008, \ 0.0067281317012844, \ 0.9473914769778008, \ 0.0458803913209150, \ 0.0067281317012840, \ 0.2510983078651668, \ 0.5715936673024646, \ 0.1773080248323685, \ 0.5715936673024647, \ 0.2510983078651668, \ 0.1773080248323682, \ 0.1831369339346112, \ 0.7741789783303032, \ 0.0426840877350856, \ 0.7741789783303031, \ 0.1831369339346113, \ 0.0426840877350855, \ 0.3540463032783623, \ 0.5715609286815995, \ 0.0743927680400381, \ 0.5715609286815995, \ 0.3540463032783623, \ 0.0743927680400380, \ 0.2992109871101671, \ 0.4572200650927965, \ 0.2435689477970363, \ 0.4572200650927966, \ 0.2992109871101671, \ 0.2435689477970362, \ 0.2908392329854116, \ 0.6327691972686006, \ 0.0763915697459878, \ 0.6327691972686005, \ 0.2908392329854118, \ 0.0763915697459877, \ 0.1861461318533070, \ 0.6896292784778069, \ 0.1242245896688862, \ 0.6896292784778069, \ 0.1861461318533070, \ 0.1242245896688860, \ 0.1336271749712246, \ 0.8565938166582099, \ 0.0097790083705656, \ 0.8565938166582099, \ 0.1336271749712248, \ 0.0097790083705652, \ 0.0689763351482116, \ 0.9030804628036242, \ 0.0279432020481643, \ 0.9030804628036242, \ 0.0689763351482117, \ 0.0279432020481639, \ 0.2614910192698080, \ 0.7137007122193398, \ 0.0248082685108522, \ 0.7137007122193398, \ 0.2614910192698081, \ 0.0248082685108520, \ 0.0439794560591168, \ 0.9348945435129993, \ 0.0211260004278840, \ 0.9348945435129993, \ 0.0439794560591169, \ 0.0211260004278836, \ 0.2469572317073108, \ 0.6848928980386439, \ 0.0681498702540453, \ 0.6848928980386439, \ 0.2469572317073108, \ 0.0681498702540452, \ 0.1916073029798411, \ 0.7395973901197243, \ 0.0687953069004347, \ 0.7395973901197241, \ 0.1916073029798412, \ 0.0687953069004345, \ 0.3173959823085313, \ 0.5262505405714473, \ 0.1563534771200214, \ 0.5262505405714473, \ 0.3173959823085312, \ 0.1563534771200213, \ 0.3938393062998427, \ 0.5903719225644825, \ 0.0157887711356747, \ 0.5903719225644825, \ 0.3938393062998428, \ 0.0157887711356747, \ 0.3181446682127857, \ 0.6584089238199839, \ 0.0234464079672303, \ 0.6584089238199841, \ 0.3181446682127858, \ 0.0234464079672302, \ 0.2803644875579968, \ 0.5837056989706170, \ 0.1359298134713862, \ 0.5837056989706170, \ 0.2803644875579968, \ 0.1359298134713861, \ 0.2299757300841567, \ 0.7253286729028012, \ 0.0446955970130422, \ 0.7253286729028012, \ 0.2299757300841567, \ 0.0446955970130419, \ 0.3494881250371351, \ 0.4044556242737054, \ 0.2460562506891595, \ 0.4044556242737053, \ 0.3494881250371351, \ 0.2460562506891595, \ 0.0964083579062225, \ 0.8928281693560606, \ 0.0107634727377169, \ 0.8928281693560607, \ 0.0964083579062225, \ 0.0107634727377166, \ 0.1003380079665996, \ 0.8728642223074309, \ 0.0267977697259696, \ 0.8728642223074310, \ 0.1003380079665996, \ 0.0267977697259692, \ 0.2894378430839789, \ 0.5106605002764818, \ 0.1999016566395393, \ 0.5106605002764818, \ 0.2894378430839789, \ 0.1999016566395392, \ 0.4595867718244119, \ 0.4595867718244119, \ 0.0808264563511762, \ 0.1786164539550919, \ 0.8117237531973031, \ 0.0096597928476050, \ 0.8117237531973032, \ 0.1786164539550919, \ 0.0096597928476048, \ 0.1133332341350742, \ 0.7733335317298511, \ 0.1133332341350746, \ 0.2861539226312519, \ 0.6702297883431256, \ 0.0436162890256225, \ 0.6702297883431256, \ 0.2861539226312521, \ 0.0436162890256222, \ 0.2293288959608979, \ 0.7610373084893327, \ 0.0096337955497694, \ 0.7610373084893327, \ 0.2293288959608979, \ 0.0096337955497692, \ 0.3542128961664716, \ 0.5293301016817759, \ 0.1164570021517525, \ 0.5293301016817759, \ 0.3542128961664716, \ 0.1164570021517524, \ 0.3449444915449854, \ 0.6455786313059102, \ 0.0094768771491044, \ 0.6455786313059101, \ 0.3449444915449854, \ 0.0094768771491043, \ 0.4316732308235539, \ 0.5403601528804488, \ 0.0279666162959972, \ 0.5403601528804488, \ 0.4316732308235539, \ 0.0279666162959972, \ 0.2207972237518396, \ 0.6319369320513635, \ 0.1472658441967969, \ 0.6319369320513635, \ 0.2207972237518397, \ 0.1472658441967967, \ 0.0109390130646629, \ 0.9781219738706738, \ 0.0109390130646634, \ 0.1531728350976843, \ 0.8449565979912814, \ 0.0018705669110343, \ 0.8449565979912815, \ 0.1531728350976843, \ 0.0018705669110340, \ 0.0786463619513997, \ 0.8427072760972003, \ 0.0786463619514000, \ 0.0091986167658109, \ 0.9887342430556623, \ 0.0020671401785269, \ 0.9887342430556624, \ 0.0091986167658110, \ 0.0020671401785264, \ 0.0235452342574103, \ 0.9744483849005658, \ 0.0020063808420239, \ 0.9744483849005658, \ 0.0235452342574104, \ 0.0020063808420235, \ 0.3457284797184662, \ 0.4576795280020015, \ 0.1965919922795323, \ 0.4576795280020015, \ 0.3457284797184662, \ 0.1965919922795323, \ 0.2501693088121573, \ 0.6423518250856121, \ 0.1074788661022307, \ 0.6423518250856121, \ 0.2501693088121574, \ 0.1074788661022305, \ 0.2555498626016329, \ 0.7425883280451013, \ 0.0018618093532657, \ 0.7425883280451014, \ 0.2555498626016329, \ 0.0018618093532655, \ 0.1032934352626250, \ 0.8464992721458153, \ 0.0502072925915598, \ 0.8464992721458153, \ 0.1032934352626251, \ 0.0502072925915595, \ 0.1702588823641313, \ 0.6594822352717371, \ 0.1702588823641316, \ 0.1134827791905402, \ 0.8074184540525852, \ 0.0790987667568747, \ 0.8074184540525853, \ 0.1134827791905403, \ 0.0790987667568744, \ 0.2020015191395728, \ 0.7961696111804121, \ 0.0018288696800152, \ 0.7961696111804121, \ 0.2020015191395729, \ 0.0018288696800149, \ 0.1996334593368171, \ 0.6007330813263655, \ 0.1996334593368173, \ 0.1554072933416661, \ 0.7470942459833944, \ 0.0974984606749396, \ 0.7470942459833944, \ 0.1554072933416663, \ 0.0974984606749393, \ 0.2837331258499088, \ 0.7059958314121547, \ 0.0102710427379366, \ 0.7059958314121546, \ 0.2837331258499087, \ 0.0102710427379364, \ 0.4006689325488300, \ 0.4006689325488300, \ 0.1986621349023399, \ 0.1406138740563841, \ 0.7187722518872315, \ 0.1406138740563844, \ 0.1101376107119611, \ 0.8879173225135152, \ 0.0019450667745238, \ 0.8879173225135152, \ 0.1101376107119612, \ 0.0019450667745234, \ 0.3511903644454155, \ 0.3511903644454155, \ 0.2976192711091689, \ 0.0422503625151380, \ 0.9154992749697237, \ 0.0422503625151384, \ 0.3116269863962924, \ 0.6863602986744455, \ 0.0020127149292622, \ 0.6863602986744455, \ 0.3116269863962924, \ 0.0020127149292620, \ 0.4986838983120579, \ 0.4986838983120579, \ 0.0026322033758840, \ 0.4560656275499566, \ 0.5340545482354229, \ 0.0098798242146205, \ 0.5340545482354229, \ 0.4560656275499566, \ 0.0098798242146206, \ 0.2964798675129709, \ 0.4070402649740581, \ 0.2964798675129710, \ 0.0740590746798509, \ 0.9237147727731391, \ 0.0022261525470102, \ 0.9237147727731391, \ 0.0740590746798510, \ 0.0022261525470098 ] ) b = np.array ( [ \ 0.2563558633847910, \ 0.2563558633847909, \ 0.4872882732304183, \ 0.0009224561060705, \ 0.4433230868583421, \ 0.5557544570355878, \ 0.0009224561060705, \ 0.5557544570355876, \ 0.4433230868583423, \ 0.0224379912623131, \ 0.0259368938757903, \ 0.9516251148618966, \ 0.0224379912623131, \ 0.9516251148618966, \ 0.0259368938757907, \ 0.2227907282937329, \ 0.2401441052632695, \ 0.5370651664429978, \ 0.2227907282937329, \ 0.5370651664429978, \ 0.2401441052632697, \ 0.0231202139702463, \ 0.1345526180266427, \ 0.8423271680031111, \ 0.0231202139702463, \ 0.8423271680031111, \ 0.1345526180266430, \ 0.0008567797950090, \ 0.0450355724673314, \ 0.9541076477376597, \ 0.0008567797950090, \ 0.9541076477376597, \ 0.0450355724673318, \ 0.0048086376608720, \ 0.4087145665677719, \ 0.5864767957713563, \ 0.0048086376608720, \ 0.5864767957713561, \ 0.4087145665677722, \ 0.0234930123594386, \ 0.1714634577399832, \ 0.8050435299005784, \ 0.0234930123594386, \ 0.8050435299005784, \ 0.1714634577399836, \ 0.0016305781421463, \ 0.0016305781421460, \ 0.9967388437157076, \ 0.0933966471293636, \ 0.2101059247050332, \ 0.6964974281656034, \ 0.0933966471293636, \ 0.6964974281656034, \ 0.2101059247050334, \ 0.0417966366511482, \ 0.1392968201185851, \ 0.8189065432302669, \ 0.0417966366511482, \ 0.8189065432302669, \ 0.1392968201185854, \ 0.0493573118928613, \ 0.0703820539127592, \ 0.8802606341943795, \ 0.0493573118928613, \ 0.8802606341943796, \ 0.0703820539127595, \ 0.0193462615030976, \ 0.4903268692484513, \ 0.4903268692484514, \ 0.1528141070121611, \ 0.3726064881564941, \ 0.4745794048313450, \ 0.1528141070121611, \ 0.4745794048313449, \ 0.3726064881564942, \ 0.0651154299306216, \ 0.1479157172776441, \ 0.7869688527917345, \ 0.0651154299306216, \ 0.7869688527917345, \ 0.1479157172776444, \ 0.0234621431760208, \ 0.2140246435816437, \ 0.7625132132423356, \ 0.0234621431760208, \ 0.7625132132423356, \ 0.2140246435816440, \ 0.0520322782344111, \ 0.3302674030581440, \ 0.6177003187074451, \ 0.0520322782344111, \ 0.6177003187074450, \ 0.3302674030581442, \ 0.0014945191055323, \ 0.3699848635444040, \ 0.6285206173500639, \ 0.0014945191055323, \ 0.6285206173500638, \ 0.3699848635444041, \ 0.0120437469347925, \ 0.0675115690433361, \ 0.9204446840218714, \ 0.0120437469347925, \ 0.9204446840218714, \ 0.0675115690433364, \ 0.0566847855434612, \ 0.4370988411800968, \ 0.5062163732764422, \ 0.0566847855434612, \ 0.5062163732764421, \ 0.4370988411800970, \ 0.1548256629849588, \ 0.4225871685075207, \ 0.4225871685075208, \ 0.1148601420448157, \ 0.4145122211577854, \ 0.4706276367973992, \ 0.1148601420448157, \ 0.4706276367973991, \ 0.4145122211577855, \ 0.0312648361867089, \ 0.3623805122689275, \ 0.6063546515443639, \ 0.0312648361867089, \ 0.6063546515443637, \ 0.3623805122689277, \ 0.1022466401455418, \ 0.3122512855112036, \ 0.5855020743432550, \ 0.1022466401455418, \ 0.5855020743432549, \ 0.3122512855112037, \ 0.0388486471319399, \ 0.4805756764340301, \ 0.4805756764340303, \ 0.0483493018730729, \ 0.3926893217036880, \ 0.5589613764232394, \ 0.0483493018730729, \ 0.5589613764232393, \ 0.3926893217036881, \ 0.0099795769296427, \ 0.0260638541622880, \ 0.9639565689080695, \ 0.0099795769296427, \ 0.9639565689080695, \ 0.0260638541622883, \ 0.0839129407699284, \ 0.3983909958449555, \ 0.5176960633851163, \ 0.0839129407699284, \ 0.5176960633851163, \ 0.3983909958449556, \ 0.0067281317012843, \ 0.0458803913209149, \ 0.9473914769778009, \ 0.0067281317012843, \ 0.9473914769778009, \ 0.0458803913209153, \ 0.1773080248323685, \ 0.2510983078651669, \ 0.5715936673024649, \ 0.1773080248323685, \ 0.5715936673024649, \ 0.2510983078651671, \ 0.0426840877350856, \ 0.1831369339346113, \ 0.7741789783303034, \ 0.0426840877350856, \ 0.7741789783303031, \ 0.1831369339346115, \ 0.0743927680400382, \ 0.3540463032783624, \ 0.5715609286815998, \ 0.0743927680400382, \ 0.5715609286815997, \ 0.3540463032783625, \ 0.2435689477970363, \ 0.2992109871101672, \ 0.4572200650927967, \ 0.2435689477970363, \ 0.4572200650927967, \ 0.2992109871101673, \ 0.0763915697459878, \ 0.2908392329854117, \ 0.6327691972686007, \ 0.0763915697459878, \ 0.6327691972686006, \ 0.2908392329854119, \ 0.1242245896688861, \ 0.1861461318533070, \ 0.6896292784778070, \ 0.1242245896688861, \ 0.6896292784778070, \ 0.1861461318533073, \ 0.0097790083705655, \ 0.1336271749712246, \ 0.8565938166582100, \ 0.0097790083705655, \ 0.8565938166582099, \ 0.1336271749712250, \ 0.0279432020481641, \ 0.0689763351482116, \ 0.9030804628036244, \ 0.0279432020481641, \ 0.9030804628036244, \ 0.0689763351482120, \ 0.0248082685108521, \ 0.2614910192698081, \ 0.7137007122193399, \ 0.0248082685108521, \ 0.7137007122193399, \ 0.2614910192698083, \ 0.0211260004278839, \ 0.0439794560591167, \ 0.9348945435129995, \ 0.0211260004278839, \ 0.9348945435129995, \ 0.0439794560591171, \ 0.0681498702540453, \ 0.2469572317073107, \ 0.6848928980386442, \ 0.0681498702540453, \ 0.6848928980386441, \ 0.2469572317073110, \ 0.0687953069004347, \ 0.1916073029798411, \ 0.7395973901197244, \ 0.0687953069004347, \ 0.7395973901197243, \ 0.1916073029798415, \ 0.1563534771200215, \ 0.3173959823085313, \ 0.5262505405714475, \ 0.1563534771200215, \ 0.5262505405714474, \ 0.3173959823085315, \ 0.0157887711356748, \ 0.3938393062998428, \ 0.5903719225644827, \ 0.0157887711356748, \ 0.5903719225644826, \ 0.3938393062998430, \ 0.0234464079672303, \ 0.3181446682127858, \ 0.6584089238199842, \ 0.0234464079672303, \ 0.6584089238199841, \ 0.3181446682127860, \ 0.1359298134713862, \ 0.2803644875579969, \ 0.5837056989706172, \ 0.1359298134713862, \ 0.5837056989706172, \ 0.2803644875579970, \ 0.0446955970130421, \ 0.2299757300841567, \ 0.7253286729028013, \ 0.0446955970130421, \ 0.7253286729028013, \ 0.2299757300841569, \ 0.2460562506891596, \ 0.3494881250371351, \ 0.4044556242737055, \ 0.2460562506891596, \ 0.4044556242737055, \ 0.3494881250371352, \ 0.0107634727377169, \ 0.0964083579062225, \ 0.8928281693560609, \ 0.0107634727377169, \ 0.8928281693560609, \ 0.0964083579062228, \ 0.0267977697259695, \ 0.1003380079665996, \ 0.8728642223074310, \ 0.0267977697259695, \ 0.8728642223074310, \ 0.1003380079665999, \ 0.1999016566395393, \ 0.2894378430839790, \ 0.5106605002764819, \ 0.1999016566395393, \ 0.5106605002764819, \ 0.2894378430839791, \ 0.0808264563511763, \ 0.4595867718244119, \ 0.4595867718244120, \ 0.0096597928476050, \ 0.1786164539550919, \ 0.8117237531973033, \ 0.0096597928476050, \ 0.8117237531973033, \ 0.1786164539550922, \ 0.1133332341350745, \ 0.1133332341350743, \ 0.7733335317298513, \ 0.0436162890256224, \ 0.2861539226312520, \ 0.6702297883431257, \ 0.0436162890256224, \ 0.6702297883431256, \ 0.2861539226312523, \ 0.0096337955497694, \ 0.2293288959608979, \ 0.7610373084893329, \ 0.0096337955497694, \ 0.7610373084893329, \ 0.2293288959608982, \ 0.1164570021517526, \ 0.3542128961664717, \ 0.5293301016817761, \ 0.1164570021517526, \ 0.5293301016817760, \ 0.3542128961664718, \ 0.0094768771491045, \ 0.3449444915449854, \ 0.6455786313059104, \ 0.0094768771491045, \ 0.6455786313059102, \ 0.3449444915449857, \ 0.0279666162959973, \ 0.4316732308235540, \ 0.5403601528804491, \ 0.0279666162959973, \ 0.5403601528804489, \ 0.4316732308235541, \ 0.1472658441967969, \ 0.2207972237518397, \ 0.6319369320513636, \ 0.1472658441967969, \ 0.6319369320513636, \ 0.2207972237518398, \ 0.0109390130646632, \ 0.0109390130646629, \ 0.9781219738706741, \ 0.0018705669110342, \ 0.1531728350976843, \ 0.8449565979912816, \ 0.0018705669110342, \ 0.8449565979912816, \ 0.1531728350976846, \ 0.0786463619514000, \ 0.0786463619513997, \ 0.8427072760972005, \ 0.0020671401785267, \ 0.0091986167658108, \ 0.9887342430556626, \ 0.0020671401785267, \ 0.9887342430556626, \ 0.0091986167658113, \ 0.0020063808420238, \ 0.0235452342574103, \ 0.9744483849005661, \ 0.0020063808420238, \ 0.9744483849005661, \ 0.0235452342574107, \ 0.1965919922795324, \ 0.3457284797184662, \ 0.4576795280020016, \ 0.1965919922795324, \ 0.4576795280020016, \ 0.3457284797184664, \ 0.1074788661022307, \ 0.2501693088121573, \ 0.6423518250856122, \ 0.1074788661022307, \ 0.6423518250856121, \ 0.2501693088121575, \ 0.0018618093532657, \ 0.2555498626016329, \ 0.7425883280451016, \ 0.0018618093532657, \ 0.7425883280451016, \ 0.2555498626016332, \ 0.0502072925915597, \ 0.1032934352626250, \ 0.8464992721458154, \ 0.0502072925915597, \ 0.8464992721458154, \ 0.1032934352626254, \ 0.1702588823641316, \ 0.1702588823641314, \ 0.6594822352717372, \ 0.0790987667568746, \ 0.1134827791905402, \ 0.8074184540525853, \ 0.0790987667568746, \ 0.8074184540525853, \ 0.1134827791905405, \ 0.0018288696800151, \ 0.2020015191395728, \ 0.7961696111804121, \ 0.0018288696800151, \ 0.7961696111804121, \ 0.2020015191395731, \ 0.1996334593368174, \ 0.1996334593368172, \ 0.6007330813263656, \ 0.0974984606749395, \ 0.1554072933416662, \ 0.7470942459833945, \ 0.0974984606749395, \ 0.7470942459833945, \ 0.1554072933416664, \ 0.0102710427379366, \ 0.2837331258499088, \ 0.7059958314121549, \ 0.0102710427379366, \ 0.7059958314121548, \ 0.2837331258499091, \ 0.1986621349023400, \ 0.4006689325488301, \ 0.4006689325488302, \ 0.1406138740563844, \ 0.1406138740563842, \ 0.7187722518872316, \ 0.0019450667745237, \ 0.1101376107119611, \ 0.8879173225135153, \ 0.0019450667745237, \ 0.8879173225135153, \ 0.1101376107119614, \ 0.2976192711091690, \ 0.3511903644454157, \ 0.3511903644454157, \ 0.0422503625151383, \ 0.0422503625151379, \ 0.9154992749697239, \ 0.0020127149292621, \ 0.3116269863962924, \ 0.6863602986744456, \ 0.0020127149292621, \ 0.6863602986744456, \ 0.3116269863962926, \ 0.0026322033758842, \ 0.4986838983120580, \ 0.4986838983120582, \ 0.0098798242146206, \ 0.4560656275499567, \ 0.5340545482354231, \ 0.0098798242146206, \ 0.5340545482354230, \ 0.4560656275499568, \ 0.2964798675129711, \ 0.2964798675129710, \ 0.4070402649740582, \ 0.0022261525470101, \ 0.0740590746798509, \ 0.9237147727731391, \ 0.0022261525470101, \ 0.9237147727731391, \ 0.0740590746798513 ] ) c = np.array ( [ \ 0.4872882732304181, \ 0.2563558633847908, \ 0.2563558633847908, \ 0.5557544570355876, \ 0.0009224561060704, \ 0.4433230868583419, \ 0.4433230868583421, \ 0.0009224561060704, \ 0.5557544570355873, \ 0.9516251148618966, \ 0.0224379912623132, \ 0.0259368938757901, \ 0.0259368938757904, \ 0.0224379912623128, \ 0.9516251148618964, \ 0.5370651664429976, \ 0.2227907282937328, \ 0.2401441052632693, \ 0.2401441052632695, \ 0.2227907282937326, \ 0.5370651664429976, \ 0.8423271680031109, \ 0.0231202139702464, \ 0.1345526180266424, \ 0.1345526180266427, \ 0.0231202139702461, \ 0.8423271680031108, \ 0.9541076477376595, \ 0.0008567797950090, \ 0.0450355724673311, \ 0.0450355724673314, \ 0.0008567797950089, \ 0.9541076477376594, \ 0.5864767957713561, \ 0.0048086376608720, \ 0.4087145665677717, \ 0.4087145665677718, \ 0.0048086376608719, \ 0.5864767957713560, \ 0.8050435299005783, \ 0.0234930123594386, \ 0.1714634577399831, \ 0.1714634577399832, \ 0.0234930123594385, \ 0.8050435299005780, \ 0.9967388437157076, \ 0.0016305781421463, \ 0.0016305781421458, \ 0.6964974281656032, \ 0.0933966471293636, \ 0.2101059247050330, \ 0.2101059247050331, \ 0.0933966471293634, \ 0.6964974281656032, \ 0.8189065432302668, \ 0.0417966366511481, \ 0.1392968201185849, \ 0.1392968201185850, \ 0.0417966366511480, \ 0.8189065432302667, \ 0.8802606341943795, \ 0.0493573118928613, \ 0.0703820539127590, \ 0.0703820539127591, \ 0.0493573118928611, \ 0.8802606341943794, \ 0.4903268692484512, \ 0.0193462615030974, \ 0.4903268692484511, \ 0.4745794048313449, \ 0.1528141070121611, \ 0.3726064881564939, \ 0.3726064881564940, \ 0.1528141070121611, \ 0.4745794048313448, \ 0.7869688527917343, \ 0.0651154299306217, \ 0.1479157172776440, \ 0.1479157172776441, \ 0.0651154299306214, \ 0.7869688527917342, \ 0.7625132132423355, \ 0.0234621431760209, \ 0.2140246435816435, \ 0.2140246435816437, \ 0.0234621431760207, \ 0.7625132132423355, \ 0.6177003187074449, \ 0.0520322782344111, \ 0.3302674030581437, \ 0.3302674030581440, \ 0.0520322782344109, \ 0.6177003187074448, \ 0.6285206173500638, \ 0.0014945191055323, \ 0.3699848635444037, \ 0.3699848635444039, \ 0.0014945191055323, \ 0.6285206173500637, \ 0.9204446840218714, \ 0.0120437469347926, \ 0.0675115690433359, \ 0.0675115690433361, \ 0.0120437469347924, \ 0.9204446840218713, \ 0.5062163732764421, \ 0.0566847855434612, \ 0.4370988411800966, \ 0.4370988411800968, \ 0.0566847855434610, \ 0.5062163732764419, \ 0.4225871685075206, \ 0.1548256629849586, \ 0.4225871685075206, \ 0.4706276367973990, \ 0.1148601420448155, \ 0.4145122211577852, \ 0.4145122211577852, \ 0.1148601420448156, \ 0.4706276367973988, \ 0.6063546515443636, \ 0.0312648361867088, \ 0.3623805122689273, \ 0.3623805122689275, \ 0.0312648361867088, \ 0.6063546515443634, \ 0.5855020743432547, \ 0.1022466401455417, \ 0.3122512855112033, \ 0.3122512855112035, \ 0.1022466401455416, \ 0.5855020743432546, \ 0.4805756764340300, \ 0.0388486471319398, \ 0.4805756764340299, \ 0.5589613764232392, \ 0.0483493018730728, \ 0.3926893217036876, \ 0.3926893217036879, \ 0.0483493018730727, \ 0.5589613764232391, \ 0.9639565689080692, \ 0.0099795769296427, \ 0.0260638541622878, \ 0.0260638541622880, \ 0.0099795769296424, \ 0.9639565689080694, \ 0.5176960633851162, \ 0.0839129407699283, \ 0.3983909958449553, \ 0.3983909958449554, \ 0.0839129407699283, \ 0.5176960633851161, \ 0.9473914769778008, \ 0.0067281317012843, \ 0.0458803913209147, \ 0.0458803913209149, \ 0.0067281317012841, \ 0.9473914769778008, \ 0.5715936673024646, \ 0.1773080248323685, \ 0.2510983078651667, \ 0.2510983078651668, \ 0.1773080248323683, \ 0.5715936673024647, \ 0.7741789783303032, \ 0.0426840877350855, \ 0.1831369339346111, \ 0.1831369339346113, \ 0.0426840877350855, \ 0.7741789783303030, \ 0.5715609286815996, \ 0.0743927680400381, \ 0.3540463032783622, \ 0.3540463032783624, \ 0.0743927680400380, \ 0.5715609286815995, \ 0.4572200650927966, \ 0.2435689477970363, \ 0.2992109871101671, \ 0.2992109871101670, \ 0.2435689477970362, \ 0.4572200650927965, \ 0.6327691972686005, \ 0.0763915697459877, \ 0.2908392329854115, \ 0.2908392329854117, \ 0.0763915697459877, \ 0.6327691972686005, \ 0.6896292784778069, \ 0.1242245896688861, \ 0.1861461318533069, \ 0.1861461318533070, \ 0.1242245896688859, \ 0.6896292784778068, \ 0.8565938166582099, \ 0.0097790083705655, \ 0.1336271749712244, \ 0.1336271749712246, \ 0.0097790083705653, \ 0.8565938166582098, \ 0.9030804628036243, \ 0.0279432020481642, \ 0.0689763351482113, \ 0.0689763351482117, \ 0.0279432020481639, \ 0.9030804628036241, \ 0.7137007122193398, \ 0.0248082685108521, \ 0.2614910192698079, \ 0.2614910192698081, \ 0.0248082685108519, \ 0.7137007122193397, \ 0.9348945435129993, \ 0.0211260004278840, \ 0.0439794560591165, \ 0.0439794560591169, \ 0.0211260004278836, \ 0.9348945435129994, \ 0.6848928980386439, \ 0.0681498702540453, \ 0.2469572317073105, \ 0.2469572317073108, \ 0.0681498702540452, \ 0.6848928980386438, \ 0.7395973901197243, \ 0.0687953069004346, \ 0.1916073029798410, \ 0.1916073029798412, \ 0.0687953069004344, \ 0.7395973901197241, \ 0.5262505405714473, \ 0.1563534771200214, \ 0.3173959823085311, \ 0.3173959823085313, \ 0.1563534771200213, \ 0.5262505405714472, \ 0.5903719225644826, \ 0.0157887711356747, \ 0.3938393062998425, \ 0.3938393062998428, \ 0.0157887711356747, \ 0.5903719225644823, \ 0.6584089238199839, \ 0.0234464079672303, \ 0.3181446682127855, \ 0.3181446682127856, \ 0.0234464079672302, \ 0.6584089238199838, \ 0.5837056989706170, \ 0.1359298134713862, \ 0.2803644875579966, \ 0.2803644875579968, \ 0.1359298134713861, \ 0.5837056989706170, \ 0.7253286729028012, \ 0.0446955970130421, \ 0.2299757300841565, \ 0.2299757300841567, \ 0.0446955970130419, \ 0.7253286729028011, \ 0.4044556242737053, \ 0.2460562506891595, \ 0.3494881250371350, \ 0.3494881250371350, \ 0.2460562506891594, \ 0.4044556242737053, \ 0.8928281693560607, \ 0.0107634727377169, \ 0.0964083579062222, \ 0.0964083579062225, \ 0.0107634727377166, \ 0.8928281693560606, \ 0.8728642223074309, \ 0.0267977697259695, \ 0.1003380079665994, \ 0.1003380079665995, \ 0.0267977697259694, \ 0.8728642223074308, \ 0.5106605002764818, \ 0.1999016566395392, \ 0.2894378430839788, \ 0.2894378430839789, \ 0.1999016566395392, \ 0.5106605002764817, \ 0.4595867718244118, \ 0.0808264563511762, \ 0.4595867718244117, \ 0.8117237531973032, \ 0.0096597928476050, \ 0.1786164539550917, \ 0.1786164539550919, \ 0.0096597928476049, \ 0.8117237531973031, \ 0.7733335317298512, \ 0.1133332341350746, \ 0.1133332341350741, \ 0.6702297883431256, \ 0.0436162890256224, \ 0.2861539226312518, \ 0.2861539226312519, \ 0.0436162890256223, \ 0.6702297883431255, \ 0.7610373084893327, \ 0.0096337955497694, \ 0.2293288959608977, \ 0.2293288959608979, \ 0.0096337955497692, \ 0.7610373084893326, \ 0.5293301016817759, \ 0.1164570021517525, \ 0.3542128961664713, \ 0.3542128961664716, \ 0.1164570021517525, \ 0.5293301016817757, \ 0.6455786313059102, \ 0.0094768771491044, \ 0.3449444915449851, \ 0.3449444915449855, \ 0.0094768771491044, \ 0.6455786313059100, \ 0.5403601528804489, \ 0.0279666162959972, \ 0.4316732308235537, \ 0.4316732308235539, \ 0.0279666162959972, \ 0.5403601528804487, \ 0.6319369320513635, \ 0.1472658441967969, \ 0.2207972237518395, \ 0.2207972237518396, \ 0.1472658441967968, \ 0.6319369320513635, \ 0.9781219738706739, \ 0.0109390130646633, \ 0.0109390130646625, \ 0.8449565979912814, \ 0.0018705669110343, \ 0.1531728350976840, \ 0.1531728350976842, \ 0.0018705669110340, \ 0.8449565979912813, \ 0.8427072760972004, \ 0.0786463619514000, \ 0.0786463619513995, \ 0.9887342430556624, \ 0.0020671401785269, \ 0.0091986167658106, \ 0.0091986167658109, \ 0.0020671401785265, \ 0.9887342430556624, \ 0.9744483849005660, \ 0.0020063808420239, \ 0.0235452342574101, \ 0.0235452342574104, \ 0.0020063808420235, \ 0.9744483849005658, \ 0.4576795280020015, \ 0.1965919922795324, \ 0.3457284797184662, \ 0.3457284797184662, \ 0.1965919922795322, \ 0.4576795280020013, \ 0.6423518250856121, \ 0.1074788661022306, \ 0.2501693088121572, \ 0.2501693088121573, \ 0.1074788661022305, \ 0.6423518250856119, \ 0.7425883280451014, \ 0.0018618093532657, \ 0.2555498626016327, \ 0.2555498626016329, \ 0.0018618093532655, \ 0.7425883280451013, \ 0.8464992721458153, \ 0.0502072925915597, \ 0.1032934352626248, \ 0.1032934352626250, \ 0.0502072925915594, \ 0.8464992721458152, \ 0.6594822352717371, \ 0.1702588823641315, \ 0.1702588823641312, \ 0.8074184540525853, \ 0.0790987667568746, \ 0.1134827791905400, \ 0.1134827791905401, \ 0.0790987667568744, \ 0.8074184540525852, \ 0.7961696111804120, \ 0.0018288696800151, \ 0.2020015191395726, \ 0.2020015191395728, \ 0.0018288696800149, \ 0.7961696111804120, \ 0.6007330813263656, \ 0.1996334593368173, \ 0.1996334593368171, \ 0.7470942459833944, \ 0.0974984606749394, \ 0.1554072933416659, \ 0.1554072933416661, \ 0.0974984606749393, \ 0.7470942459833942, \ 0.7059958314121547, \ 0.0102710427379365, \ 0.2837331258499085, \ 0.2837331258499088, \ 0.0102710427379364, \ 0.7059958314121545, \ 0.4006689325488301, \ 0.1986621349023399, \ 0.4006689325488300, \ 0.7187722518872315, \ 0.1406138740563843, \ 0.1406138740563839, \ 0.8879173225135152, \ 0.0019450667745237, \ 0.1101376107119609, \ 0.1101376107119611, \ 0.0019450667745236, \ 0.8879173225135152, \ 0.3511903644454155, \ 0.2976192711091688, \ 0.3511903644454155, \ 0.9154992749697237, \ 0.0422503625151383, \ 0.0422503625151377, \ 0.6863602986744455, \ 0.0020127149292621, \ 0.3116269863962923, \ 0.3116269863962924, \ 0.0020127149292620, \ 0.6863602986744454, \ 0.4986838983120579, \ 0.0026322033758840, \ 0.4986838983120577, \ 0.5340545482354228, \ 0.0098798242146205, \ 0.4560656275499564, \ 0.4560656275499565, \ 0.0098798242146204, \ 0.5340545482354226, \ 0.4070402649740580, \ 0.2964798675129709, \ 0.2964798675129709, \ 0.9237147727731390, \ 0.0022261525470100, \ 0.0740590746798507, \ 0.0740590746798509, \ 0.0022261525470099, \ 0.9237147727731388 ] ) w = np.array ( [ \ 0.0033286951747132, \ 0.0033286951747132, \ 0.0033286951747132, \ 0.0003473281594925, \ 0.0003473281594925, \ 0.0003473281594925, \ 0.0003473281594925, \ 0.0003473281594925, \ 0.0003473281594925, \ 0.0003000501019099, \ 0.0003000501019099, \ 0.0003000501019099, \ 0.0003000501019099, \ 0.0003000501019099, \ 0.0003000501019099, \ 0.0027304020592298, \ 0.0027304020592298, \ 0.0027304020592298, \ 0.0027304020592298, \ 0.0027304020592298, \ 0.0027304020592298, \ 0.0011329714517846, \ 0.0011329714517846, \ 0.0011329714517846, \ 0.0011329714517846, \ 0.0011329714517846, \ 0.0011329714517846, \ 0.0001365218409967, \ 0.0001365218409967, \ 0.0001365218409967, \ 0.0001365218409967, \ 0.0001365218409967, \ 0.0001365218409967, \ 0.0007693760667843, \ 0.0007693760667843, \ 0.0007693760667843, \ 0.0007693760667843, \ 0.0007693760667843, \ 0.0007693760667843, \ 0.0012969731946121, \ 0.0012969731946121, \ 0.0012969731946121, \ 0.0012969731946121, \ 0.0012969731946121, \ 0.0012969731946121, \ 0.0000365932242464, \ 0.0000365932242464, \ 0.0000365932242464, \ 0.0028058551621104, \ 0.0028058551621104, \ 0.0028058551621104, \ 0.0028058551621104, \ 0.0028058551621104, \ 0.0028058551621104, \ 0.0017088242229934, \ 0.0017088242229934, \ 0.0017088242229934, \ 0.0017088242229934, \ 0.0017088242229934, \ 0.0017088242229934, \ 0.0014835269432187, \ 0.0014835269432187, \ 0.0014835269432187, \ 0.0014835269432187, \ 0.0014835269432187, \ 0.0014835269432187, \ 0.0016513963572791, \ 0.0016513963572791, \ 0.0016513963572791, \ 0.0042541944332406, \ 0.0042541944332406, \ 0.0042541944332406, \ 0.0042541944332406, \ 0.0042541944332406, \ 0.0042541944332406, \ 0.0021977995867184, \ 0.0021977995867184, \ 0.0021977995867184, \ 0.0021977995867184, \ 0.0021977995867184, \ 0.0021977995867184, \ 0.0015485819478916, \ 0.0015485819478916, \ 0.0015485819478916, \ 0.0015485819478916, \ 0.0015485819478916, \ 0.0015485819478916, \ 0.0026032805301536, \ 0.0026032805301536, \ 0.0026032805301536, \ 0.0026032805301536, \ 0.0026032805301536, \ 0.0026032805301536, \ 0.0004661702641033, \ 0.0004661702641033, \ 0.0004661702641033, \ 0.0004661702641033, \ 0.0004661702641033, \ 0.0004661702641033, \ 0.0006575771563735, \ 0.0006575771563735, \ 0.0006575771563735, \ 0.0006575771563735, \ 0.0006575771563735, \ 0.0006575771563735, \ 0.0027864654094994, \ 0.0027864654094994, \ 0.0027864654094994, \ 0.0027864654094994, \ 0.0027864654094994, \ 0.0027864654094994, \ 0.0042590966781915, \ 0.0042590966781915, \ 0.0042590966781915, \ 0.0041296569531417, \ 0.0041296569531417, \ 0.0041296569531417, \ 0.0041296569531417, \ 0.0041296569531417, \ 0.0041296569531417, \ 0.0021542829173275, \ 0.0021542829173275, \ 0.0021542829173275, \ 0.0021542829173275, \ 0.0021542829173275, \ 0.0021542829173275, \ 0.0034759522016711, \ 0.0034759522016711, \ 0.0034759522016711, \ 0.0034759522016711, \ 0.0034759522016711, \ 0.0034759522016711, \ 0.0024242799574099, \ 0.0024242799574099, \ 0.0024242799574099, \ 0.0027066142543971, \ 0.0027066142543971, \ 0.0027066142543971, \ 0.0027066142543971, \ 0.0027066142543971, \ 0.0027066142543971, \ 0.0003857792869821, \ 0.0003857792869821, \ 0.0003857792869821, \ 0.0003857792869821, \ 0.0003857792869821, \ 0.0003857792869821, \ 0.0034396664292256, \ 0.0034396664292256, \ 0.0034396664292256, \ 0.0034396664292256, \ 0.0034396664292256, \ 0.0034396664292256, \ 0.0004380269370904, \ 0.0004380269370904, \ 0.0004380269370904, \ 0.0004380269370904, \ 0.0004380269370904, \ 0.0004380269370904, \ 0.0044060145278103, \ 0.0044060145278103, \ 0.0044060145278103, \ 0.0044060145278103, \ 0.0044060145278103, \ 0.0044060145278103, \ 0.0020175008084554, \ 0.0020175008084554, \ 0.0020175008084554, \ 0.0020175008084554, \ 0.0020175008084554, \ 0.0020175008084554, \ 0.0032382786045497, \ 0.0032382786045497, \ 0.0032382786045497, \ 0.0032382786045497, \ 0.0032382786045497, \ 0.0032382786045497, \ 0.0046662107991940, \ 0.0046662107991940, \ 0.0046662107991940, \ 0.0046662107991940, \ 0.0046662107991940, \ 0.0046662107991940, \ 0.0031592258177549, \ 0.0031592258177549, \ 0.0031592258177549, \ 0.0031592258177549, \ 0.0031592258177549, \ 0.0031592258177549, \ 0.0034735845184462, \ 0.0034735845184462, \ 0.0034735845184462, \ 0.0034735845184462, \ 0.0034735845184462, \ 0.0034735845184462, \ 0.0008953928804098, \ 0.0008953928804098, \ 0.0008953928804098, \ 0.0008953928804098, \ 0.0008953928804098, \ 0.0008953928804098, \ 0.0010804784836254, \ 0.0010804784836254, \ 0.0010804784836254, \ 0.0010804784836254, \ 0.0010804784836254, \ 0.0010804784836254, \ 0.0018129744491099, \ 0.0018129744491099, \ 0.0018129744491099, \ 0.0018129744491099, \ 0.0018129744491099, \ 0.0018129744491099, \ 0.0007651571304863, \ 0.0007651571304863, \ 0.0007651571304863, \ 0.0007651571304863, \ 0.0007651571304863, \ 0.0007651571304863, \ 0.0028576817042790, \ 0.0028576817042790, \ 0.0028576817042790, \ 0.0028576817042790, \ 0.0028576817042790, \ 0.0028576817042790, \ 0.0026558120905517, \ 0.0026558120905517, \ 0.0026558120905517, \ 0.0026558120905517, \ 0.0026558120905517, \ 0.0026558120905517, \ 0.0044774376211065, \ 0.0044774376211065, \ 0.0044774376211065, \ 0.0044774376211065, \ 0.0044774376211065, \ 0.0044774376211065, \ 0.0016535172612734, \ 0.0016535172612734, \ 0.0016535172612734, \ 0.0016535172612734, \ 0.0016535172612734, \ 0.0016535172612734, \ 0.0019449896357145, \ 0.0019449896357145, \ 0.0019449896357145, \ 0.0019449896357145, \ 0.0019449896357145, \ 0.0019449896357145, \ 0.0040545175807175, \ 0.0040545175807175, \ 0.0040545175807175, \ 0.0040545175807175, \ 0.0040545175807175, \ 0.0040545175807175, \ 0.0023471970098679, \ 0.0023471970098679, \ 0.0023471970098679, \ 0.0023471970098679, \ 0.0023471970098679, \ 0.0023471970098679, \ 0.0054197966818915, \ 0.0054197966818915, \ 0.0054197966818915, \ 0.0054197966818915, \ 0.0054197966818915, \ 0.0054197966818915, \ 0.0008214191155562, \ 0.0008214191155562, \ 0.0008214191155562, \ 0.0008214191155562, \ 0.0008214191155562, \ 0.0008214191155562, \ 0.0013331230747820, \ 0.0013331230747820, \ 0.0013331230747820, \ 0.0013331230747820, \ 0.0013331230747820, \ 0.0013331230747820, \ 0.0046726023038407, \ 0.0046726023038407, \ 0.0046726023038407, \ 0.0046726023038407, \ 0.0046726023038407, \ 0.0046726023038407, \ 0.0035827112110621, \ 0.0035827112110621, \ 0.0035827112110621, \ 0.0010473492443510, \ 0.0010473492443510, \ 0.0010473492443510, \ 0.0010473492443510, \ 0.0010473492443510, \ 0.0010473492443510, \ 0.0027795988004447, \ 0.0027795988004447, \ 0.0027795988004447, \ 0.0025570128208941, \ 0.0025570128208941, \ 0.0025570128208941, \ 0.0025570128208941, \ 0.0025570128208941, \ 0.0025570128208941, \ 0.0011537659281314, \ 0.0011537659281314, \ 0.0011537659281314, \ 0.0011537659281314, \ 0.0011537659281314, \ 0.0011537659281314, \ 0.0042237575830891, \ 0.0042237575830891, \ 0.0042237575830891, \ 0.0042237575830891, \ 0.0042237575830891, \ 0.0042237575830891, \ 0.0013374175145031, \ 0.0013374175145031, \ 0.0013374175145031, \ 0.0013374175145031, \ 0.0013374175145031, \ 0.0013374175145031, \ 0.0023814233045742, \ 0.0023814233045742, \ 0.0023814233045742, \ 0.0023814233045742, \ 0.0023814233045742, \ 0.0023814233045742, \ 0.0042828524520190, \ 0.0042828524520190, \ 0.0042828524520190, \ 0.0042828524520190, \ 0.0042828524520190, \ 0.0042828524520190, \ 0.0002999521869148, \ 0.0002999521869148, \ 0.0002999521869148, \ 0.0004406939585376, \ 0.0004406939585376, \ 0.0004406939585376, \ 0.0004406939585376, \ 0.0004406939585376, \ 0.0004406939585376, \ 0.0020678716670798, \ 0.0020678716670798, \ 0.0020678716670798, \ 0.0001156452577508, \ 0.0001156452577508, \ 0.0001156452577508, \ 0.0001156452577508, \ 0.0001156452577508, \ 0.0001156452577508, \ 0.0001824251018040, \ 0.0001824251018040, \ 0.0001824251018040, \ 0.0001824251018040, \ 0.0001824251018040, \ 0.0001824251018040, \ 0.0051351158472688, \ 0.0051351158472688, \ 0.0051351158472688, \ 0.0051351158472688, \ 0.0051351158472688, \ 0.0051351158472688, \ 0.0039050557101547, \ 0.0039050557101547, \ 0.0039050557101547, \ 0.0039050557101547, \ 0.0039050557101547, \ 0.0039050557101547, \ 0.0005282175598339, \ 0.0005282175598339, \ 0.0005282175598339, \ 0.0005282175598339, \ 0.0005282175598339, \ 0.0005282175598339, \ 0.0018990634758471, \ 0.0018990634758471, \ 0.0018990634758471, \ 0.0018990634758471, \ 0.0018990634758471, \ 0.0018990634758471, \ 0.0040277109885183, \ 0.0040277109885183, \ 0.0040277109885183, \ 0.0023340593121637, \ 0.0023340593121637, \ 0.0023340593121637, \ 0.0023340593121637, \ 0.0023340593121637, \ 0.0023340593121637, \ 0.0004826706779797, \ 0.0004826706779797, \ 0.0004826706779797, \ 0.0004826706779797, \ 0.0004826706779797, \ 0.0004826706779797, \ 0.0045706738891262, \ 0.0045706738891262, \ 0.0045706738891262, \ 0.0032490194493214, \ 0.0032490194493214, \ 0.0032490194493214, \ 0.0032490194493214, \ 0.0032490194493214, \ 0.0032490194493214, \ 0.0013197669167677, \ 0.0013197669167677, \ 0.0013197669167677, \ 0.0013197669167677, \ 0.0013197669167677, \ 0.0013197669167677, \ 0.0051653559274539, \ 0.0051653559274539, \ 0.0051653559274539, \ 0.0034852633534527, \ 0.0034852633534527, \ 0.0034852633534527, \ 0.0003967292610444, \ 0.0003967292610444, \ 0.0003967292610444, \ 0.0003967292610444, \ 0.0003967292610444, \ 0.0003967292610444, \ 0.0058568144539184, \ 0.0058568144539184, \ 0.0058568144539184, \ 0.0011989487838384, \ 0.0011989487838384, \ 0.0011989487838384, \ 0.0005855934410211, \ 0.0005855934410211, \ 0.0005855934410211, \ 0.0005855934410211, \ 0.0005855934410211, \ 0.0005855934410211, \ 0.0007493220541052, \ 0.0007493220541052, \ 0.0007493220541052, \ 0.0014007748847512, \ 0.0014007748847512, \ 0.0014007748847512, \ 0.0014007748847512, \ 0.0014007748847512, \ 0.0014007748847512, \ 0.0057736389035923, \ 0.0057736389035923, \ 0.0057736389035923, \ 0.0003705055488142, \ 0.0003705055488142, \ 0.0003705055488142, \ 0.0003705055488142, \ 0.0003705055488142, \ 0.0003705055488142 ] ) return a, b, c, w def rule_order ( p ): #*****************************************************************************80 # ## rule_order() returns the order of the requested quadrature rule. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 10 June 2023 # # Author: # # John Burkardt. # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient quadrature # rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Input: # # integer p: the precision of the quadrature. 1 <= p <= 50. # # Output: # # integer n: the number of nodes in the full rule. # import numpy as np nnodes = np.array ( [ \ 1, \ 1, 3, 6, 6, 7, 12, 15, 16, 19, 25, \ 28, 33, 37, 42, 49, 55, 60, 67, 73, 79, \ 87, 96, 103, 112, 120, 130, 141, 150, 159, 171, \ 181, 193, 204, 214, 228, 243, 252, 267, 282, 295, \ 309, 324, 339, 354, 370, 385, 399, 423, 435, 453 ] ) if ( 0 <= p and p <= 50 ): n = nnodes[p] else: print ( '' ) print ( 'rule_order(): Fatal error!' ) print ( ' Precision p must be between 0 and 50.' ) raise Exception ( 'rule_order(): Fatal error!' ) return n 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 def triangle_symq_rule ( p ): #*****************************************************************************80 # ## triangle_symq_rule() returns the requested quadrature rule. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 10 June 2023 # # Author: # # Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas. # This version by John Burkardt. # # Reference: # # Hong Xiao, Zydrunas Gimbutas, # A numerical algorithm for the construction of efficient quadrature # rules in two and higher dimensions, # Computers and Mathematics with Applications, # Volume 59, 2010, pages 663-676. # # Input: # # integer p: the precision of the quadrature. 0 <= p <= 50. # # Output: # # integer n: the number of nodes. # # real a(n), b(n), c(n): the barycentric coordinates of the nodes. # # real w(n): the weights. # n = rule_order ( p ) # # Copy the arrays defining the compressed rule. # if ( p == 0 ): a, b, c, w = rule00 ( ) elif ( p == 1 ): a, b, c, w = rule01 ( ) elif ( p == 2 ): a, b, c, w = rule02 ( ) elif ( p == 3 ): a, b, c, w = rule03 ( ) elif ( p == 4 ): a, b, c, w = rule04 ( ) elif ( p == 5 ): a, b, c, w = rule05 ( ) elif ( p == 6 ): a, b, c, w = rule06 ( ) elif ( p == 7 ): a, b, c, w = rule07 ( ) elif ( p == 8 ): a, b, c, w = rule08 ( ) elif ( p == 9 ): a, b, c, w = rule09 ( ) elif ( p == 10 ): a, b, c, w = rule10 ( ) elif ( p == 11 ): a, b, c, w = rule11 ( ) elif ( p == 12 ): a, b, c, w = rule12 ( ) elif ( p == 13 ): a, b, c, w = rule13 ( ) elif ( p == 14 ): a, b, c, w = rule14 ( ) elif ( p == 15 ): a, b, c, w = rule15 ( ) elif ( p == 16 ): a, b, c, w = rule16 ( ) elif ( p == 17 ): a, b, c, w = rule17 ( ) elif ( p == 18 ): a, b, c, w = rule18 ( ) elif ( p == 19 ): a, b, c, w = rule19 ( ) elif ( p == 20 ): a, b, c, w = rule20 ( ) elif ( p == 21 ): a, b, c, w = rule21 ( ) elif ( p == 22 ): a, b, c, w = rule22 ( ) elif ( p == 23 ): a, b, c, w = rule23 ( ) elif ( p == 24 ): a, b, c, w = rule24 ( ) elif ( p == 25 ): a, b, c, w = rule25 ( ) elif ( p == 26 ): a, b, c, w = rule26 ( ) elif ( p == 27 ): a, b, c, w = rule27 ( ) elif ( p == 28 ): a, b, c, w = rule28 ( ) elif ( p == 29 ): a, b, c, w = rule29 ( ) elif ( p == 30 ): a, b, c, w = rule30 ( ) elif ( p == 31 ): a, b, c, w = rule31 ( ) elif ( p == 32 ): a, b, c, w = rule32 ( ) elif ( p == 33 ): a, b, c, w = rule33 ( ) elif ( p == 34 ): a, b, c, w = rule34 ( ) elif ( p == 35 ): a, b, c, w = rule35 ( ) elif ( p == 36 ): a, b, c, w = rule36 ( ) elif ( p == 37 ): a, b, c, w = rule37 ( ) elif ( p == 38 ): a, b, c, w = rule38 ( ) elif ( p == 39 ): a, b, c, w = rule39 ( ) elif ( p == 40 ): a, b, c, w = rule40 ( ) elif ( p == 41 ): a, b, c, w = rule41 ( ) elif ( p == 42 ): a, b, c, w = rule42 ( ) elif ( p == 43 ): a, b, c, w = rule43 ( ) elif ( p == 44 ): a, b, c, w = rule44 ( ) elif ( p == 45 ): a, b, c, w = rule45 ( ) elif ( p == 46 ): a, b, c, w = rule46 ( ) elif ( p == 47 ): a, b, c, w = rule47 ( ) elif ( p == 48 ): a, b, c, w = rule48 ( ) elif ( p == 49 ): a, b, c, w = rule49 ( ) elif ( p == 50 ): a, b, c, w = rule50 ( ) else: print ( '' ) print ( 'triangle_symq_rule(): Fatal error!' ) print ( ' Illegal input value of p.' ) print ( ' 0 <= p <= 50 required.' ) raise Exception ( 'triangle_symq_rule(): Fatal error!' ) return n, a, b, c, w def triangle_unit_area ( ): #*****************************************************************************80 # ## triangle_unit_area() returns the area of a unit triangle. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 24 May 2023 # # Author: # # John Burkardt. # # Output: # # real area: the area of the unit triangle. # area = 0.5 return area def triangle_unit_monomial_integral ( expon ): #*****************************************************************************80 # ## triangle_unit_monomial_integral(): integral of a monomial over unit triangle. # # Discussion: # # This routine evaluates a monomial of the form # # product ( 1 <= dim <= dim_num ) x(dim)^expon(dim) # # where the exponents are nonnegative integers. Note that # if the combination 0^0 is encountered, it should be treated # as 1. # # Integral ( over unit triangle ) x^m y^n dx dy = m! * n! / ( m + n + 2 )! # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 03 July 2007 # # Author: # # John Burkardt # # Input: # # integer DIM_NUM, the spatial dimension. # # integer EXPON(DIM_NUM), the exponents. # # Output: # # real VALUE, the value of the integral of the monomial. # # # The first computation ends with VALUE = 1.0 # value = 1.0 k = 0 for i in range ( 1, expon[0] + 1 ): k = k + 1 # value = value * i / k for i in range ( 1, expon[1] + 1 ): k = k + 1 value = value * i / k k = k + 1 value = value / k k = k + 1 value = value / k return value if ( __name__ == '__main__' ): timestamp ( ) triangle_symq_rule_test ( ) timestamp ( )