#! /usr/bin/env python3 # def hexahedron_jaskowiec_rule_test ( ): #*****************************************************************************80 # ## hexahedron_jaskowiec_rule_test() tests hexahedron_jaskowiec_rule(). # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 17 July 2023 # # Author: # # John Burkardt. # import platform print ( '' ) print ( 'hexahedron_jaskowiec_rule_test():' ) print ( ' Python version: ' + platform.python_version ( ) ) print ( ' Test hexahedron_jaskowiec_rule().' ) p = 5 hexahedron_jaskowiec_rule_test01 ( p ) p = 5 hexahedron_jaskowiec_rule_test02 ( p ) p_lo = 0 p_hi = 21 hexahedron_jaskowiec_rule_test03 ( p_lo, p_hi ) # # Terminate. # print ( '' ) print ( 'hexahedron_jaskowiec_rule_test():' ) print ( ' Normal end of execution.' ) return def hexahedron_jaskowiec_rule_test01 ( p ): #*****************************************************************************80 # ## hexahedron_jaskowiec_rule_test01() prints a rule of precision P. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 24 May 2023 # # Author: # # John Burkardt. # import numpy as np print ( '' ) print ( 'hexahedron_jaskowiec_rule_test01():' ) print ( ' Quadrature rule for the unit hexahedron,' ) print ( ' Precision p =', p ) # # Retrieve the rule. # n, x, y, z, w = hexahedron_jaskowiec_rule ( p ) # # Print the rule. # print ( '' ) print ( ' I W X Y Z' ) print ( '' ) for i in range ( 0, n ): print ( ' %4d %10.6g %10.6g %10.6g %10.6g' \ % ( i, w[i], x[i], y[i], z[i] ) ) # # Verify that weights sum to 1. # w_sum = np.sum ( w ) print ( '' ) print ( ' Weight Sum ', w_sum ) return def hexahedron_jaskowiec_rule_test02 ( p ): #*****************************************************************************80 # ## hexahedron_jaskowiec_rule_test02() tests a rule of precision P. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 19 May 2023 # # Author: # # John Burkardt. # import numpy as np print ( '' ) print ( 'hexahedron_jaskowiec_rule_test02():' ) print ( ' Test the precision of a quadrature rule for the unit hexahedron.' ) dim_num = 3 # # Retrieve the rule. # n, x, y, z, w = hexahedron_jaskowiec_rule ( p ) # # Pack the x, y, z vectors as rows of an array. # xyz = np.transpose ( np.array ( [ x, y, z ] ) ) print ( '' ) print ( ' Stated precision of rule = ', p ) print ( ' Number of quadrature points = ', n ) print ( '' ) print ( ' Degree Maximum error' ) print ( '' ) for degree in range ( 0, p + 3 ): expon = np.zeros ( dim_num, dtype = int ) more = False h = 0 t = 0 max_error = 0.0 while ( True ): expon, more, h, t = comp_next ( degree, dim_num, expon, more, h, t ) v = monomial_value ( expon, xyz ) quad = hexahedron_unit_volume ( ) * np.dot ( w, v ) exact = hexahedron_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 hexahedron_jaskowiec_rule_test03 ( p_lo, p_hi ): #*****************************************************************************80 # ## hexahedron_jaskowiec_rule_test03() tests absolute and relative precision. # # Licensing: # # This code is distributed under the GNU GPL license. # # Modified: # # 17 July 2023 # # Author: # # John Burkardt. # import numpy as np print ( '' ) print ( 'hexahedron_jaskowiec_rule_test03():' ) print ( ' Test the precision of quadrature rules for the unit hexahedron.' ) print ( ' Check rules of precision p =', p_lo, 'through', p_hi ) print ( ' for error in approximating integrals of monomials.' ) dim_num = 3 print ( '' ) print ( ' maximum maximum' ) print ( ' p absolute relative' ) print ( ' error error' ) print ( '' ) for p in range ( p_lo, p_hi + 1 ): n, x, y, z, w = hexahedron_jaskowiec_rule ( p ) # # Pack the x, y, z vectors as rows of an array. # xyz = np.transpose ( np.array ( [ x, y, z ] ) ) max_abs = 0.0 max_rel = 0.0 for degree in range ( 0, p + 1 ): expon = np.zeros ( dim_num, dtype = int ) more = False h = 0 t = 0 while ( True ): expon, more, h, t = comp_next ( degree, dim_num, expon, more, h, t ) v = monomial_value ( expon, xyz ) quad = hexahedron_unit_volume ( ) * np.dot ( w, v ) exact = hexahedron_unit_monomial_integral ( expon ) quad_error = np.abs ( quad - exact ) max_abs = max ( max_abs, quad_error ) max_rel = max ( max_rel, quad_error / abs ( exact ) ) if ( not more ): break print ( ' %2d %24.16g %24.16g' % ( p, max_abs, max_rel ) ) return def comp_next ( n, k, a, more, h, t ): #*****************************************************************************80 # ## comp_next() computes the compositions of the integer N into K parts. # # Discussion: # # A composition of the integer N into K parts is an ordered sequence # of K nonnegative integers which sum to N. The compositions (1,2,1) # and (1,1,2) are considered to be distinct. # # The routine computes one composition on each call until there are no more. # For instance, one composition of 6 into 3 parts is # 3+2+1, another would be 6+0+0. # # On the first call to this routine, set MORE = FALSE. The routine # will compute the first element in the sequence of compositions, and # return it, as well as setting MORE = TRUE. If more compositions # are desired, call again, and again. Each time, the routine will # return with a new composition. # # However, when the LAST composition in the sequence is computed # and returned, the routine will reset MORE to FALSE, signaling that # the end of the sequence has been reached. # # This routine originally used a SAVE statement to maintain the # variables H and T. I have decided that it is safer # to pass these variables as arguments, even though the user should # never alter them. This allows this routine to safely shuffle # between several ongoing calculations. # # There are 28 compositions of 6 into three parts. This routine will # produce those compositions in the following order: # # I A # - --------- # 1 6 0 0 # 2 5 1 0 # 3 4 2 0 # 4 3 3 0 # 5 2 4 0 # 6 1 5 0 # 7 0 6 0 # 8 5 0 1 # 9 4 1 1 # 10 3 2 1 # 11 2 3 1 # 12 1 4 1 # 13 0 5 1 # 14 4 0 2 # 15 3 1 2 # 16 2 2 2 # 17 1 3 2 # 18 0 4 2 # 19 3 0 3 # 20 2 1 3 # 21 1 2 3 # 22 0 3 3 # 23 2 0 4 # 24 1 1 4 # 25 0 2 4 # 26 1 0 5 # 27 0 1 5 # 28 0 0 6 # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 20 May 2015 # # Author: # # John Burkardt. # # Reference: # # Albert Nijenhuis, Herbert Wilf, # Combinatorial Algorithms for Computers and Calculators, # Second Edition, # Academic Press, 1978, # ISBN: 0-12-519260-6, # LC: QA164.N54. # # Input: # # integer N, the integer whose compositions are desired. # # integer K, the number of parts in the composition. # # integer A(K), the previous composition. On the first call, # with MORE = FALSE, set A = []. Thereafter, A should be the # value of A output from the previous call. # # bool MORE. The input value of MORE on the first # call should be FALSE, which tells the program to initialize. # On subsequent calls, MORE should be TRUE, or simply the # output value of MORE from the previous call. # # integer H, T, two internal parameters needed for the # computation. The user may need to initialize these before the # very first call, but these initial values are not important. # The user should not alter these parameters once the computation # begins. # # Output: # # integer A(K), the next composition. # # bool MORE, will be TRUE unless the composition # that is being returned is the final one in the sequence. # # integer H, T, the updated values of the two internal # variables. # if ( k == 0 ): a = [] more = False t = n h = 0 return a, more, h, t if ( not more ): t = n h = 0 a[0] = n for i in range ( 1, k ): a[i] = 0 else: if ( 1 < t ): h = 0 t = a[h] a[h] = 0 a[0] = t - 1 a[h+1] = a[h+1] + 1 h = h + 1 more = ( a[k-1] != n ) return a, more, h, t def hexahedron_jaskowiec_rule ( p ): #*****************************************************************************80 # ## hexahedron_jaskowiec_rule() returns a hexahedron quadrature rule of given precision. # # Discussion: # # The unit hexahedron is defined as: # # 0 <= X <= 1 # 0 <= Y <= 1 # 0 <= Z <= 1. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 19 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and prisms, # International Journal of Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Input: # # integer p: the precision, 0 <= p <= 21. # # Output: # # integer n: the order of the rule. # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights. # if ( p < 0 ): raise Exception ( 'prism_jaskowiec_rule(): Input p < 0.' ) if ( 21 < p ): raise Exception ( 'prism_jaskowiec_rule(): Input 21 < p.' ) n = rule_order ( p ) if ( p <= 1 ): x, y, z, w = rule01 ( ) elif ( p <= 3 ): x, y, z, w = rule03 ( ) elif ( p <= 5 ): x, y, z, w = rule05 ( ) elif ( p <= 7 ): x, y, z, w = rule07 ( ) elif ( p <= 9 ): x, y, z, w = rule09 ( ) elif ( p <= 11 ): x, y, z, w = rule11 ( ) elif ( p <= 13 ): x, y, z, w = rule13 ( ) elif ( p <= 15 ): x, y, z, w = rule15 ( ) elif ( p <= 17 ): x, y, z, w = rule17 ( ) elif ( p <= 19 ): x, y, z, w = rule19 ( ) elif ( p <= 21 ): x, y, z, w = rule21 ( ) return n, x, y, z, w def hexahedron_unit_monomial_integral ( expon ): #*****************************************************************************80 # ## hexahedron_unit_monomial_integral(): monomial integral in a unit hexahedron. # # Discussion: # # This routine returns the integral of # # product ( 1 <= I <= 3 ) X(I)^EXPON(I) # # over the unit hexahedron. # # The unit hexahedron H is bounded by the vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1). # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 19 May 2023 # # Author: # # John Burkardt # # Input: # # integer EXPON(3): the exponents. # # Output: # # real VALUE: the integral of the monomial. # value = 1.0 / ( expon[0] + 1 ) \ * 1.0 / ( expon[1] + 1 ) \ * 1.0 / ( expon[2] + 1 ) return value def hexahedron_unit_volume ( ): #*****************************************************************************80 # ## hexahedron_unit_volume() returns the volume of a unit hexahedron. # # Discussion: # # The unit hexahedron has vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1). # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 01 May 2023 # # Author: # # John Burkardt # # Output: # # real value: the volume. # value = 1.0 return value 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 rule_order ( p ): #*****************************************************************************80 # ## rule_order() returns the order of a hexahedron quadrature rule of given precision. # # Discussion: # # The "order" of a quadrature rule is the number of points involved. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Input: # # integer p: the precision, 0 <= p <= 21. # # Output: # # integer order: the order of the rule. # import numpy as np if ( p < 0 ): raise Exception ( 'rule_order(): Input p < 0.' ) if ( 21 < p ): raise Exception ( 'rule_order(): Input 21 < p.' ) order_vec = np.array ( [ \ 1, \ 1, 6, 6, 14, 14, 34, 34, 58, 58, 90, \ 90, 154, 154, 256, 256, 346, 346, 454, 454, 580, \ 580 ] ) order = order_vec[p] return order def rule01 ( ): #*****************************************************************************80 # ## rule01() returns the hexahedron quadrature rule of precision 1. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.5000000000000000 ] ) y = np.array ( [ \ 0.5000000000000000 ] ) z = np.array ( [ \ 0.5000000000000000 ] ) w = np.array ( [ \ 1.0000000000000000 ] ) return x, y, z, w def rule03 ( ): #*****************************************************************************80 # ## rule03() returns the hexahedron quadrature rule of precision 3. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 1.0000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.0000000000000000, \ 0.5000000000000000, \ 0.5000000000000000 ] ) y = np.array ( [ \ 0.5000000000000000, \ 1.0000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.0000000000000000, \ 0.5000000000000000 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 1.0000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.0000000000000000 ] ) w = np.array ( [ \ 0.1666666666666667, \ 0.1666666666666667, \ 0.1666666666666667, \ 0.1666666666666667, \ 0.1666666666666667, \ 0.1666666666666667 ] ) return x, y, z, w def rule05 ( ): #*****************************************************************************80 # ## rule05() returns the hexahedron quadrature rule of precision 5. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.1020887871228893, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8979112128771107, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8793934553196641, \ 0.1206065446803359, \ 0.1206065446803359, \ 0.8793934553196641, \ 0.8793934553196641, \ 0.1206065446803359, \ 0.8793934553196641, \ 0.1206065446803359 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.1020887871228893, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8979112128771107, \ 0.5000000000000000, \ 0.8793934553196641, \ 0.1206065446803359, \ 0.8793934553196641, \ 0.1206065446803359, \ 0.8793934553196641, \ 0.1206065446803359, \ 0.1206065446803359, \ 0.8793934553196641 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1020887871228893, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8979112128771107, \ 0.8793934553196641, \ 0.1206065446803359, \ 0.8793934553196641, \ 0.8793934553196641, \ 0.1206065446803359, \ 0.8793934553196641, \ 0.1206065446803359, \ 0.1206065446803359 ] ) w = np.array ( [ \ 0.1108033240997230, \ 0.1108033240997230, \ 0.1108033240997230, \ 0.1108033240997230, \ 0.1108033240997230, \ 0.1108033240997230, \ 0.0418975069252078, \ 0.0418975069252078, \ 0.0418975069252078, \ 0.0418975069252078, \ 0.0418975069252078, \ 0.0418975069252078, \ 0.0418975069252078, \ 0.0418975069252078 ] ) return x, y, z, w def rule07 ( ): #*****************************************************************************80 # ## rule07() returns the hexahedron quadrature rule of precision 7. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.0305973139469912, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9694026860530087, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.1268331949935920, \ 0.8731668050064080, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.2949345508339928, \ 0.7050654491660072, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.9532303450614186, \ 0.5000000000000000, \ 0.9532303450614186, \ 0.0467696549385814, \ 0.5000000000000000, \ 0.0467696549385814, \ 0.9532303450614186, \ 0.5000000000000000, \ 0.9532303450614186, \ 0.0467696549385814, \ 0.5000000000000000, \ 0.0467696549385814 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.0305973139469912, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9694026860530087, \ 0.5000000000000000, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.1268331949935920, \ 0.8731668050064080, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.2949345508339928, \ 0.7050654491660072, \ 0.9532303450614186, \ 0.9532303450614186, \ 0.5000000000000000, \ 0.9532303450614186, \ 0.0467696549385814, \ 0.5000000000000000, \ 0.0467696549385814, \ 0.9532303450614186, \ 0.5000000000000000, \ 0.0467696549385814, \ 0.0467696549385814, \ 0.5000000000000000 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.0305973139469912, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9694026860530087, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.8731668050064080, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.8731668050064080, \ 0.1268331949935920, \ 0.1268331949935920, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.7050654491660072, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.7050654491660072, \ 0.2949345508339928, \ 0.2949345508339928, \ 0.5000000000000000, \ 0.9532303450614186, \ 0.9532303450614186, \ 0.5000000000000000, \ 0.9532303450614186, \ 0.9532303450614186, \ 0.5000000000000000, \ 0.0467696549385814, \ 0.0467696549385814, \ 0.5000000000000000, \ 0.0467696549385814, \ 0.0467696549385814 ] ) w = np.array ( [ \ 0.0340045847498003, \ 0.0340045847498003, \ 0.0340045847498003, \ 0.0340045847498003, \ 0.0340045847498003, \ 0.0340045847498003, \ 0.0252967244013519, \ 0.0252967244013519, \ 0.0252967244013519, \ 0.0252967244013519, \ 0.0252967244013519, \ 0.0252967244013519, \ 0.0252967244013519, \ 0.0252967244013519, \ 0.0541706353348564, \ 0.0541706353348564, \ 0.0541706353348564, \ 0.0541706353348564, \ 0.0541706353348564, \ 0.0541706353348564, \ 0.0541706353348564, \ 0.0541706353348564, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943, \ 0.0133528011342943 ] ) return x, y, z, w def rule09 ( ): #*****************************************************************************80 # ## rule09() returns the hexahedron quadrature rule of precision 9. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.1931592652041455, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8068407347958545, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.0649501076690120, \ 0.9350498923309880, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.2179445964899850, \ 0.7820554035100150, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.9388435616288391, \ 0.5000000000000000, \ 0.9388435616288391, \ 0.0611564383711609, \ 0.5000000000000000, \ 0.0611564383711609, \ 0.9388435616288391, \ 0.5000000000000000, \ 0.9388435616288391, \ 0.0611564383711609, \ 0.5000000000000000, \ 0.0611564383711609, \ 0.7161339513154311, \ 0.9692652109323359, \ 0.7161339513154311, \ 0.2838660486845689, \ 0.9692652109323359, \ 0.2838660486845689, \ 0.2838660486845689, \ 0.9692652109323359, \ 0.2838660486845689, \ 0.7161339513154311, \ 0.9692652109323359, \ 0.7161339513154311, \ 0.7161339513154311, \ 0.0307347890676641, \ 0.7161339513154311, \ 0.2838660486845689, \ 0.0307347890676641, \ 0.2838660486845689, \ 0.2838660486845689, \ 0.0307347890676641, \ 0.2838660486845689, \ 0.7161339513154311, \ 0.0307347890676641, \ 0.7161339513154311 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.1931592652041455, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8068407347958545, \ 0.5000000000000000, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.0649501076690120, \ 0.9350498923309880, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.2179445964899850, \ 0.7820554035100150, \ 0.9388435616288391, \ 0.9388435616288391, \ 0.5000000000000000, \ 0.9388435616288391, \ 0.0611564383711609, \ 0.5000000000000000, \ 0.0611564383711609, \ 0.9388435616288391, \ 0.5000000000000000, \ 0.0611564383711609, \ 0.0611564383711609, \ 0.5000000000000000, \ 0.9692652109323359, \ 0.7161339513154311, \ 0.7161339513154311, \ 0.9692652109323359, \ 0.2838660486845689, \ 0.7161339513154311, \ 0.9692652109323359, \ 0.2838660486845689, \ 0.2838660486845689, \ 0.9692652109323359, \ 0.7161339513154311, \ 0.2838660486845689, \ 0.0307347890676641, \ 0.7161339513154311, \ 0.7161339513154311, \ 0.0307347890676641, \ 0.2838660486845689, \ 0.7161339513154311, \ 0.0307347890676641, \ 0.2838660486845689, \ 0.2838660486845689, \ 0.0307347890676641, \ 0.7161339513154311, \ 0.2838660486845689 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1931592652041455, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8068407347958545, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.9350498923309880, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.9350498923309880, \ 0.0649501076690120, \ 0.0649501076690120, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.7820554035100150, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.7820554035100150, \ 0.2179445964899850, \ 0.2179445964899850, \ 0.5000000000000000, \ 0.9388435616288391, \ 0.9388435616288391, \ 0.5000000000000000, \ 0.9388435616288391, \ 0.9388435616288391, \ 0.5000000000000000, \ 0.0611564383711609, \ 0.0611564383711609, \ 0.5000000000000000, \ 0.0611564383711609, \ 0.0611564383711609, \ 0.7161339513154311, \ 0.7161339513154311, \ 0.9692652109323359, \ 0.7161339513154311, \ 0.7161339513154311, \ 0.9692652109323359, \ 0.2838660486845689, \ 0.2838660486845689, \ 0.9692652109323359, \ 0.2838660486845689, \ 0.2838660486845689, \ 0.9692652109323359, \ 0.7161339513154311, \ 0.7161339513154311, \ 0.0307347890676641, \ 0.7161339513154311, \ 0.7161339513154311, \ 0.0307347890676641, \ 0.2838660486845689, \ 0.2838660486845689, \ 0.0307347890676641, \ 0.2838660486845689, \ 0.2838660486845689, \ 0.0307347890676641 ] ) w = np.array ( [ \ 0.0541593744687068, \ 0.0541593744687068, \ 0.0541593744687068, \ 0.0541593744687068, \ 0.0541593744687068, \ 0.0541593744687068, \ 0.0062685994124186, \ 0.0062685994124186, \ 0.0062685994124186, \ 0.0062685994124186, \ 0.0062685994124186, \ 0.0062685994124186, \ 0.0062685994124186, \ 0.0062685994124186, \ 0.0248574797680029, \ 0.0248574797680029, \ 0.0248574797680029, \ 0.0248574797680029, \ 0.0248574797680029, \ 0.0248574797680029, \ 0.0248574797680029, \ 0.0248574797680029, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0114737257670222, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717, \ 0.0120146004391717 ] ) return x, y, z, w def rule11 ( ): #*****************************************************************************80 # ## rule11() returns the hexahedron quadrature rule of precision 11. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.8610665194372092, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1389334805627908, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.0952558990184506, \ 0.9047441009815494, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.7668270044402485, \ 0.2331729955597515, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.3596137066743628, \ 0.6403862933256372, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.9019667336076422, \ 0.5000000000000000, \ 0.9019667336076422, \ 0.0980332663923578, \ 0.5000000000000000, \ 0.0980332663923578, \ 0.9019667336076422, \ 0.5000000000000000, \ 0.9019667336076422, \ 0.0980332663923578, \ 0.5000000000000000, \ 0.0980332663923578, \ 0.9900497455045357, \ 0.2346080844030868, \ 0.9900497455045357, \ 0.0099502544954643, \ 0.2346080844030868, \ 0.0099502544954643, \ 0.0099502544954643, \ 0.2346080844030868, \ 0.0099502544954643, \ 0.9900497455045357, \ 0.2346080844030868, \ 0.9900497455045357, \ 0.9900497455045357, \ 0.7653919155969132, \ 0.9900497455045357, \ 0.0099502544954643, \ 0.7653919155969132, \ 0.0099502544954643, \ 0.0099502544954643, \ 0.7653919155969132, \ 0.0099502544954643, \ 0.9900497455045357, \ 0.7653919155969132, \ 0.9900497455045357, \ 0.7028429900975481, \ 0.9772916094647830, \ 0.7028429900975481, \ 0.2971570099024518, \ 0.9772916094647830, \ 0.2971570099024518, \ 0.2971570099024518, \ 0.9772916094647830, \ 0.2971570099024518, \ 0.7028429900975481, \ 0.9772916094647830, \ 0.7028429900975481, \ 0.7028429900975481, \ 0.0227083905352169, \ 0.7028429900975481, \ 0.2971570099024518, \ 0.0227083905352169, \ 0.2971570099024518, \ 0.2971570099024518, \ 0.0227083905352169, \ 0.2971570099024518, \ 0.7028429900975481, \ 0.0227083905352169, \ 0.7028429900975481 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.8610665194372092, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1389334805627908, \ 0.5000000000000000, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.0952558990184506, \ 0.9047441009815494, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.7668270044402485, \ 0.2331729955597515, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.3596137066743628, \ 0.6403862933256372, \ 0.9019667336076422, \ 0.9019667336076422, \ 0.5000000000000000, \ 0.9019667336076422, \ 0.0980332663923578, \ 0.5000000000000000, \ 0.0980332663923578, \ 0.9019667336076422, \ 0.5000000000000000, \ 0.0980332663923578, \ 0.0980332663923578, \ 0.5000000000000000, \ 0.2346080844030868, \ 0.9900497455045357, \ 0.9900497455045357, \ 0.2346080844030868, \ 0.0099502544954643, \ 0.9900497455045357, \ 0.2346080844030868, \ 0.0099502544954643, \ 0.0099502544954643, \ 0.2346080844030868, \ 0.9900497455045357, \ 0.0099502544954643, \ 0.7653919155969132, \ 0.9900497455045357, \ 0.9900497455045357, \ 0.7653919155969132, \ 0.0099502544954643, \ 0.9900497455045357, \ 0.7653919155969132, \ 0.0099502544954643, \ 0.0099502544954643, \ 0.7653919155969132, \ 0.9900497455045357, \ 0.0099502544954643, \ 0.9772916094647830, \ 0.7028429900975481, \ 0.7028429900975481, \ 0.9772916094647830, \ 0.2971570099024518, \ 0.7028429900975481, \ 0.9772916094647830, \ 0.2971570099024518, \ 0.2971570099024518, \ 0.9772916094647830, \ 0.7028429900975481, \ 0.2971570099024518, \ 0.0227083905352169, \ 0.7028429900975481, \ 0.7028429900975481, \ 0.0227083905352169, \ 0.2971570099024518, \ 0.7028429900975481, \ 0.0227083905352169, \ 0.2971570099024518, \ 0.2971570099024518, \ 0.0227083905352169, \ 0.7028429900975481, \ 0.2971570099024518 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8610665194372092, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1389334805627908, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.9047441009815494, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.9047441009815494, \ 0.0952558990184506, \ 0.0952558990184506, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.2331729955597515, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.2331729955597515, \ 0.7668270044402485, \ 0.7668270044402485, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.6403862933256372, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.6403862933256372, \ 0.3596137066743628, \ 0.3596137066743628, \ 0.5000000000000000, \ 0.9019667336076422, \ 0.9019667336076422, \ 0.5000000000000000, \ 0.9019667336076422, \ 0.9019667336076422, \ 0.5000000000000000, \ 0.0980332663923578, \ 0.0980332663923578, \ 0.5000000000000000, \ 0.0980332663923578, \ 0.0980332663923578, \ 0.9900497455045357, \ 0.9900497455045357, \ 0.2346080844030868, \ 0.9900497455045357, \ 0.9900497455045357, \ 0.2346080844030868, \ 0.0099502544954643, \ 0.0099502544954643, \ 0.2346080844030868, \ 0.0099502544954643, \ 0.0099502544954643, \ 0.2346080844030868, \ 0.9900497455045357, \ 0.9900497455045357, \ 0.7653919155969132, \ 0.9900497455045357, \ 0.9900497455045357, \ 0.7653919155969132, \ 0.0099502544954643, \ 0.0099502544954643, \ 0.7653919155969132, \ 0.0099502544954643, \ 0.0099502544954643, \ 0.7653919155969132, \ 0.7028429900975481, \ 0.7028429900975481, \ 0.9772916094647830, \ 0.7028429900975481, \ 0.7028429900975481, \ 0.9772916094647830, \ 0.2971570099024518, \ 0.2971570099024518, \ 0.9772916094647830, \ 0.2971570099024518, \ 0.2971570099024518, \ 0.9772916094647830, \ 0.7028429900975481, \ 0.7028429900975481, \ 0.0227083905352169, \ 0.7028429900975481, \ 0.7028429900975481, \ 0.0227083905352169, \ 0.2971570099024518, \ 0.2971570099024518, \ 0.0227083905352169, \ 0.2971570099024518, \ 0.2971570099024518, \ 0.0227083905352169 ] ) w = np.array ( [ \ 0.0296169245240206, \ 0.0296169245240206, \ 0.0296169245240206, \ 0.0296169245240206, \ 0.0296169245240206, \ 0.0296169245240206, \ 0.0077511837875231, \ 0.0077511837875231, \ 0.0077511837875231, \ 0.0077511837875231, \ 0.0077511837875231, \ 0.0077511837875231, \ 0.0077511837875231, \ 0.0077511837875231, \ 0.0222210081090505, \ 0.0222210081090505, \ 0.0222210081090505, \ 0.0222210081090505, \ 0.0222210081090505, \ 0.0222210081090505, \ 0.0222210081090505, \ 0.0222210081090505, \ 0.0169887021445520, \ 0.0169887021445520, \ 0.0169887021445520, \ 0.0169887021445520, \ 0.0169887021445520, \ 0.0169887021445520, \ 0.0169887021445520, \ 0.0169887021445520, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0160272817769356, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0016188211900323, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196, \ 0.0089763421101196 ] ) return x, y, z, w def rule13 ( ): #*****************************************************************************80 # ## rule13() returns the hexahedron quadrature rule of precision 13. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.1827950053146007, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8172049946853993, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.0460729760185823, \ 0.9539270239814177, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.6181026292258232, \ 0.3818973707741769, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.8687873171566183, \ 0.5000000000000000, \ 0.8687873171566183, \ 0.1312126828433817, \ 0.5000000000000000, \ 0.1312126828433817, \ 0.8687873171566183, \ 0.5000000000000000, \ 0.8687873171566183, \ 0.1312126828433817, \ 0.5000000000000000, \ 0.1312126828433817, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.9666726015054183, \ 0.0333273984945817, \ 0.0333273984945817, \ 0.9666726015054183, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9666726015054183, \ 0.0333273984945817, \ 0.0333273984945817, \ 0.9666726015054183, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6866920757899998, \ 0.8321081947965769, \ 0.6866920757899998, \ 0.3133079242100002, \ 0.8321081947965769, \ 0.3133079242100002, \ 0.3133079242100002, \ 0.8321081947965769, \ 0.3133079242100002, \ 0.6866920757899998, \ 0.8321081947965769, \ 0.6866920757899998, \ 0.6866920757899998, \ 0.1678918052034231, \ 0.6866920757899998, \ 0.3133079242100002, \ 0.1678918052034231, \ 0.3133079242100002, \ 0.3133079242100002, \ 0.1678918052034231, \ 0.3133079242100002, \ 0.6866920757899998, \ 0.1678918052034231, \ 0.6866920757899998, \ 0.9747555407321407, \ 0.6288381939284606, \ 0.9747555407321407, \ 0.0252444592678593, \ 0.6288381939284606, \ 0.0252444592678593, \ 0.0252444592678593, \ 0.6288381939284606, \ 0.0252444592678593, \ 0.9747555407321407, \ 0.6288381939284606, \ 0.9747555407321407, \ 0.9747555407321407, \ 0.3711618060715394, \ 0.9747555407321407, \ 0.0252444592678593, \ 0.3711618060715394, \ 0.0252444592678593, \ 0.0252444592678593, \ 0.3711618060715394, \ 0.0252444592678593, \ 0.9747555407321407, \ 0.3711618060715394, \ 0.9747555407321407, \ 0.8328347413800889, \ 0.9974350214009486, \ 0.8328347413800889, \ 0.1671652586199110, \ 0.9974350214009486, \ 0.1671652586199110, \ 0.1671652586199110, \ 0.9974350214009486, \ 0.1671652586199110, \ 0.8328347413800889, \ 0.9974350214009486, \ 0.8328347413800889, \ 0.8328347413800889, \ 0.0025649785990514, \ 0.8328347413800889, \ 0.1671652586199110, \ 0.0025649785990514, \ 0.1671652586199110, \ 0.1671652586199110, \ 0.0025649785990514, \ 0.1671652586199110, \ 0.8328347413800889, \ 0.0025649785990514, \ 0.8328347413800889, \ 0.0974495447483840, \ 0.2739297470225850, \ 0.0974495447483840, \ 0.9025504552516159, \ 0.2739297470225850, \ 0.9025504552516159, \ 0.9025504552516159, \ 0.2739297470225850, \ 0.9025504552516159, \ 0.0974495447483840, \ 0.2739297470225850, \ 0.0974495447483840, \ 0.0974495447483840, \ 0.7260702529774150, \ 0.0974495447483840, \ 0.9025504552516159, \ 0.7260702529774150, \ 0.9025504552516159, \ 0.9025504552516159, \ 0.7260702529774150, \ 0.9025504552516159, \ 0.0974495447483840, \ 0.7260702529774150, \ 0.0974495447483840 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.1827950053146007, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8172049946853993, \ 0.5000000000000000, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.0460729760185823, \ 0.9539270239814177, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.6181026292258232, \ 0.3818973707741769, \ 0.8687873171566183, \ 0.8687873171566183, \ 0.5000000000000000, \ 0.8687873171566183, \ 0.1312126828433817, \ 0.5000000000000000, \ 0.1312126828433817, \ 0.8687873171566183, \ 0.5000000000000000, \ 0.1312126828433817, \ 0.1312126828433817, \ 0.5000000000000000, \ 0.9666726015054183, \ 0.0333273984945817, \ 0.0333273984945817, \ 0.9666726015054183, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9666726015054183, \ 0.0333273984945817, \ 0.0333273984945817, \ 0.9666726015054183, \ 0.8321081947965769, \ 0.6866920757899998, \ 0.6866920757899998, \ 0.8321081947965769, \ 0.3133079242100002, \ 0.6866920757899998, \ 0.8321081947965769, \ 0.3133079242100002, \ 0.3133079242100002, \ 0.8321081947965769, \ 0.6866920757899998, \ 0.3133079242100002, \ 0.1678918052034231, \ 0.6866920757899998, \ 0.6866920757899998, \ 0.1678918052034231, \ 0.3133079242100002, \ 0.6866920757899998, \ 0.1678918052034231, \ 0.3133079242100002, \ 0.3133079242100002, \ 0.1678918052034231, \ 0.6866920757899998, \ 0.3133079242100002, \ 0.6288381939284606, \ 0.9747555407321407, \ 0.9747555407321407, \ 0.6288381939284606, \ 0.0252444592678593, \ 0.9747555407321407, \ 0.6288381939284606, \ 0.0252444592678593, \ 0.0252444592678593, \ 0.6288381939284606, \ 0.9747555407321407, \ 0.0252444592678593, \ 0.3711618060715394, \ 0.9747555407321407, \ 0.9747555407321407, \ 0.3711618060715394, \ 0.0252444592678593, \ 0.9747555407321407, \ 0.3711618060715394, \ 0.0252444592678593, \ 0.0252444592678593, \ 0.3711618060715394, \ 0.9747555407321407, \ 0.0252444592678593, \ 0.9974350214009486, \ 0.8328347413800889, \ 0.8328347413800889, \ 0.9974350214009486, \ 0.1671652586199110, \ 0.8328347413800889, \ 0.9974350214009486, \ 0.1671652586199110, \ 0.1671652586199110, \ 0.9974350214009486, \ 0.8328347413800889, \ 0.1671652586199110, \ 0.0025649785990514, \ 0.8328347413800889, \ 0.8328347413800889, \ 0.0025649785990514, \ 0.1671652586199110, \ 0.8328347413800889, \ 0.0025649785990514, \ 0.1671652586199110, \ 0.1671652586199110, \ 0.0025649785990514, \ 0.8328347413800889, \ 0.1671652586199110, \ 0.2739297470225850, \ 0.0974495447483840, \ 0.0974495447483840, \ 0.2739297470225850, \ 0.9025504552516159, \ 0.0974495447483840, \ 0.2739297470225850, \ 0.9025504552516159, \ 0.9025504552516159, \ 0.2739297470225850, \ 0.0974495447483840, \ 0.9025504552516159, \ 0.7260702529774150, \ 0.0974495447483840, \ 0.0974495447483840, \ 0.7260702529774150, \ 0.9025504552516159, \ 0.0974495447483840, \ 0.7260702529774150, \ 0.9025504552516159, \ 0.9025504552516159, \ 0.7260702529774150, \ 0.0974495447483840, \ 0.9025504552516159 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1827950053146007, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8172049946853993, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.9539270239814177, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.9539270239814177, \ 0.0460729760185823, \ 0.0460729760185823, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.3818973707741769, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.3818973707741769, \ 0.6181026292258232, \ 0.6181026292258232, \ 0.5000000000000000, \ 0.8687873171566183, \ 0.8687873171566183, \ 0.5000000000000000, \ 0.8687873171566183, \ 0.8687873171566183, \ 0.5000000000000000, \ 0.1312126828433817, \ 0.1312126828433817, \ 0.5000000000000000, \ 0.1312126828433817, \ 0.1312126828433817, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9666726015054183, \ 0.0333273984945817, \ 0.0333273984945817, \ 0.9666726015054183, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9666726015054183, \ 0.0333273984945817, \ 0.0333273984945817, \ 0.9666726015054183, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.7303580738482240, \ 0.2696419261517760, \ 0.6866920757899998, \ 0.6866920757899998, \ 0.8321081947965769, \ 0.6866920757899998, \ 0.6866920757899998, \ 0.8321081947965769, \ 0.3133079242100002, \ 0.3133079242100002, \ 0.8321081947965769, \ 0.3133079242100002, \ 0.3133079242100002, \ 0.8321081947965769, \ 0.6866920757899998, \ 0.6866920757899998, \ 0.1678918052034231, \ 0.6866920757899998, \ 0.6866920757899998, \ 0.1678918052034231, \ 0.3133079242100002, \ 0.3133079242100002, \ 0.1678918052034231, \ 0.3133079242100002, \ 0.3133079242100002, \ 0.1678918052034231, \ 0.9747555407321407, \ 0.9747555407321407, \ 0.6288381939284606, \ 0.9747555407321407, \ 0.9747555407321407, \ 0.6288381939284606, \ 0.0252444592678593, \ 0.0252444592678593, \ 0.6288381939284606, \ 0.0252444592678593, \ 0.0252444592678593, \ 0.6288381939284606, \ 0.9747555407321407, \ 0.9747555407321407, \ 0.3711618060715394, \ 0.9747555407321407, \ 0.9747555407321407, \ 0.3711618060715394, \ 0.0252444592678593, \ 0.0252444592678593, \ 0.3711618060715394, \ 0.0252444592678593, \ 0.0252444592678593, \ 0.3711618060715394, \ 0.8328347413800889, \ 0.8328347413800889, \ 0.9974350214009486, \ 0.8328347413800889, \ 0.8328347413800889, \ 0.9974350214009486, \ 0.1671652586199110, \ 0.1671652586199110, \ 0.9974350214009486, \ 0.1671652586199110, \ 0.1671652586199110, \ 0.9974350214009486, \ 0.8328347413800889, \ 0.8328347413800889, \ 0.0025649785990514, \ 0.8328347413800889, \ 0.8328347413800889, \ 0.0025649785990514, \ 0.1671652586199110, \ 0.1671652586199110, \ 0.0025649785990514, \ 0.1671652586199110, \ 0.1671652586199110, \ 0.0025649785990514, \ 0.0974495447483840, \ 0.0974495447483840, \ 0.2739297470225850, \ 0.0974495447483840, \ 0.0974495447483840, \ 0.2739297470225850, \ 0.9025504552516159, \ 0.9025504552516159, \ 0.2739297470225850, \ 0.9025504552516159, \ 0.9025504552516159, \ 0.2739297470225850, \ 0.0974495447483840, \ 0.0974495447483840, \ 0.7260702529774150, \ 0.0974495447483840, \ 0.0974495447483840, \ 0.7260702529774150, \ 0.9025504552516159, \ 0.9025504552516159, \ 0.7260702529774150, \ 0.9025504552516159, \ 0.9025504552516159, \ 0.7260702529774150 ] ) w = np.array ( [ \ 0.0173912824874704, \ 0.0173912824874704, \ 0.0173912824874704, \ 0.0173912824874704, \ 0.0173912824874704, \ 0.0173912824874704, \ 0.0018386577800611, \ 0.0018386577800611, \ 0.0018386577800611, \ 0.0018386577800611, \ 0.0018386577800611, \ 0.0018386577800611, \ 0.0018386577800611, \ 0.0018386577800611, \ 0.0112910248314292, \ 0.0112910248314292, \ 0.0112910248314292, \ 0.0112910248314292, \ 0.0112910248314292, \ 0.0112910248314292, \ 0.0112910248314292, \ 0.0112910248314292, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0059757596352895, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0086912315244171, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0106145587103426, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0016903589166661, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0022842405528399, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919, \ 0.0066740156523919 ] ) return x, y, z, w def rule15 ( ): #*****************************************************************************80 # ## rule15() returns the hexahedron quadrature rule of precision 15. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.9619577574752056, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.0380422425247944, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3913025693166751, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6086974306833248, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.3307634065252874, \ 0.6692365934747126, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.1034554344803311, \ 0.8965445655196689, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.8482759513633358, \ 0.5000000000000000, \ 0.8482759513633358, \ 0.1517240486366642, \ 0.5000000000000000, \ 0.1517240486366642, \ 0.8482759513633358, \ 0.5000000000000000, \ 0.8482759513633358, \ 0.1517240486366642, \ 0.5000000000000000, \ 0.1517240486366642, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.7924949743436622, \ 0.2075050256563378, \ 0.2075050256563378, \ 0.7924949743436622, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.7924949743436622, \ 0.2075050256563378, \ 0.2075050256563378, \ 0.7924949743436622, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.9914024363900886, \ 0.0085975636099114, \ 0.0085975636099114, \ 0.9914024363900886, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9914024363900886, \ 0.0085975636099114, \ 0.0085975636099114, \ 0.9914024363900886, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6360162945430453, \ 0.9390447038366581, \ 0.6360162945430453, \ 0.3639837054569547, \ 0.9390447038366581, \ 0.3639837054569547, \ 0.3639837054569547, \ 0.9390447038366581, \ 0.3639837054569547, \ 0.6360162945430453, \ 0.9390447038366581, \ 0.6360162945430453, \ 0.6360162945430453, \ 0.0609552961633420, \ 0.6360162945430453, \ 0.3639837054569547, \ 0.0609552961633420, \ 0.3639837054569547, \ 0.3639837054569547, \ 0.0609552961633420, \ 0.3639837054569547, \ 0.6360162945430453, \ 0.0609552961633420, \ 0.6360162945430453, \ 0.8093239300427761, \ 0.9699906676537717, \ 0.8093239300427761, \ 0.1906760699572239, \ 0.9699906676537717, \ 0.1906760699572239, \ 0.1906760699572239, \ 0.9699906676537717, \ 0.1906760699572239, \ 0.8093239300427761, \ 0.9699906676537717, \ 0.8093239300427761, \ 0.8093239300427761, \ 0.0300093323462282, \ 0.8093239300427761, \ 0.1906760699572239, \ 0.0300093323462282, \ 0.1906760699572239, \ 0.1906760699572239, \ 0.0300093323462282, \ 0.1906760699572239, \ 0.8093239300427761, \ 0.0300093323462282, \ 0.8093239300427761, \ 0.9315772312765189, \ 0.6521112975876302, \ 0.9315772312765189, \ 0.0684227687234810, \ 0.6521112975876302, \ 0.0684227687234810, \ 0.0684227687234810, \ 0.6521112975876302, \ 0.0684227687234810, \ 0.9315772312765189, \ 0.6521112975876302, \ 0.9315772312765189, \ 0.9315772312765189, \ 0.3478887024123698, \ 0.9315772312765189, \ 0.0684227687234810, \ 0.3478887024123698, \ 0.0684227687234810, \ 0.0684227687234810, \ 0.3478887024123698, \ 0.0684227687234810, \ 0.9315772312765189, \ 0.3478887024123698, \ 0.9315772312765189, \ 0.7308028863234025, \ 0.8685680591748091, \ 0.7308028863234025, \ 0.2691971136765975, \ 0.8685680591748091, \ 0.2691971136765975, \ 0.2691971136765975, \ 0.8685680591748091, \ 0.2691971136765975, \ 0.7308028863234025, \ 0.8685680591748091, \ 0.7308028863234025, \ 0.7308028863234025, \ 0.1314319408251909, \ 0.7308028863234025, \ 0.2691971136765975, \ 0.1314319408251909, \ 0.2691971136765975, \ 0.2691971136765975, \ 0.1314319408251909, \ 0.2691971136765975, \ 0.7308028863234025, \ 0.1314319408251909, \ 0.7308028863234025, \ 0.9801570902708128, \ 0.8835073040170505, \ 0.9801570902708128, \ 0.0198429097291872, \ 0.8835073040170505, \ 0.0198429097291872, \ 0.0198429097291872, \ 0.8835073040170505, \ 0.0198429097291872, \ 0.9801570902708128, \ 0.8835073040170505, \ 0.9801570902708128, \ 0.9801570902708128, \ 0.1164926959829496, \ 0.9801570902708128, \ 0.0198429097291872, \ 0.1164926959829496, \ 0.0198429097291872, \ 0.0198429097291872, \ 0.1164926959829496, \ 0.0198429097291872, \ 0.9801570902708128, \ 0.1164926959829496, \ 0.9801570902708128, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.9442969164789898, \ 0.9971300972924322, \ 0.9442969164789898, \ 0.9971300972924322, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.9442969164789898, \ 0.9971300972924322, \ 0.9442969164789898, \ 0.9971300972924322, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.0557030835210102, \ 0.9971300972924322, \ 0.0557030835210102, \ 0.9971300972924322, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.9442969164789898, \ 0.0028699027075679, \ 0.9442969164789898, \ 0.0028699027075679, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.0557030835210102, \ 0.9971300972924322, \ 0.0557030835210102, \ 0.9971300972924322, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.9442969164789898, \ 0.0028699027075679, \ 0.9442969164789898, \ 0.0028699027075679, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.0557030835210102, \ 0.0028699027075679, \ 0.0557030835210102, \ 0.0028699027075679, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.0557030835210102, \ 0.0028699027075679, \ 0.0557030835210102, \ 0.0028699027075679 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.9619577574752056, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.0380422425247944, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3913025693166751, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6086974306833248, \ 0.5000000000000000, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.3307634065252874, \ 0.6692365934747126, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.1034554344803311, \ 0.8965445655196689, \ 0.8482759513633358, \ 0.8482759513633358, \ 0.5000000000000000, \ 0.8482759513633358, \ 0.1517240486366642, \ 0.5000000000000000, \ 0.1517240486366642, \ 0.8482759513633358, \ 0.5000000000000000, \ 0.1517240486366642, \ 0.1517240486366642, \ 0.5000000000000000, \ 0.7924949743436622, \ 0.2075050256563378, \ 0.2075050256563378, \ 0.7924949743436622, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.7924949743436622, \ 0.2075050256563378, \ 0.2075050256563378, \ 0.7924949743436622, \ 0.9914024363900886, \ 0.0085975636099114, \ 0.0085975636099114, \ 0.9914024363900886, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9914024363900886, \ 0.0085975636099114, \ 0.0085975636099114, \ 0.9914024363900886, \ 0.9390447038366581, \ 0.6360162945430453, \ 0.6360162945430453, \ 0.9390447038366581, \ 0.3639837054569547, \ 0.6360162945430453, \ 0.9390447038366581, \ 0.3639837054569547, \ 0.3639837054569547, \ 0.9390447038366581, \ 0.6360162945430453, \ 0.3639837054569547, \ 0.0609552961633420, \ 0.6360162945430453, \ 0.6360162945430453, \ 0.0609552961633420, \ 0.3639837054569547, \ 0.6360162945430453, \ 0.0609552961633420, \ 0.3639837054569547, \ 0.3639837054569547, \ 0.0609552961633420, \ 0.6360162945430453, \ 0.3639837054569547, \ 0.9699906676537717, \ 0.8093239300427761, \ 0.8093239300427761, \ 0.9699906676537717, \ 0.1906760699572239, \ 0.8093239300427761, \ 0.9699906676537717, \ 0.1906760699572239, \ 0.1906760699572239, \ 0.9699906676537717, \ 0.8093239300427761, \ 0.1906760699572239, \ 0.0300093323462282, \ 0.8093239300427761, \ 0.8093239300427761, \ 0.0300093323462282, \ 0.1906760699572239, \ 0.8093239300427761, \ 0.0300093323462282, \ 0.1906760699572239, \ 0.1906760699572239, \ 0.0300093323462282, \ 0.8093239300427761, \ 0.1906760699572239, \ 0.6521112975876302, \ 0.9315772312765189, \ 0.9315772312765189, \ 0.6521112975876302, \ 0.0684227687234810, \ 0.9315772312765189, \ 0.6521112975876302, \ 0.0684227687234810, \ 0.0684227687234810, \ 0.6521112975876302, \ 0.9315772312765189, \ 0.0684227687234810, \ 0.3478887024123698, \ 0.9315772312765189, \ 0.9315772312765189, \ 0.3478887024123698, \ 0.0684227687234810, \ 0.9315772312765189, \ 0.3478887024123698, \ 0.0684227687234810, \ 0.0684227687234810, \ 0.3478887024123698, \ 0.9315772312765189, \ 0.0684227687234810, \ 0.8685680591748091, \ 0.7308028863234025, \ 0.7308028863234025, \ 0.8685680591748091, \ 0.2691971136765975, \ 0.7308028863234025, \ 0.8685680591748091, \ 0.2691971136765975, \ 0.2691971136765975, \ 0.8685680591748091, \ 0.7308028863234025, \ 0.2691971136765975, \ 0.1314319408251909, \ 0.7308028863234025, \ 0.7308028863234025, \ 0.1314319408251909, \ 0.2691971136765975, \ 0.7308028863234025, \ 0.1314319408251909, \ 0.2691971136765975, \ 0.2691971136765975, \ 0.1314319408251909, \ 0.7308028863234025, \ 0.2691971136765975, \ 0.8835073040170505, \ 0.9801570902708128, \ 0.9801570902708128, \ 0.8835073040170505, \ 0.0198429097291872, \ 0.9801570902708128, \ 0.8835073040170505, \ 0.0198429097291872, \ 0.0198429097291872, \ 0.8835073040170505, \ 0.9801570902708128, \ 0.0198429097291872, \ 0.1164926959829496, \ 0.9801570902708128, \ 0.9801570902708128, \ 0.1164926959829496, \ 0.0198429097291872, \ 0.9801570902708128, \ 0.1164926959829496, \ 0.0198429097291872, \ 0.0198429097291872, \ 0.1164926959829496, \ 0.9801570902708128, \ 0.0198429097291872, \ 0.9442969164789898, \ 0.9971300972924322, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.9971300972924322, \ 0.9442969164789898, \ 0.9442969164789898, \ 0.9971300972924322, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.9971300972924322, \ 0.9442969164789898, \ 0.0557030835210102, \ 0.9971300972924322, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.9971300972924322, \ 0.0557030835210102, \ 0.9442969164789898, \ 0.0028699027075679, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.0028699027075679, \ 0.9442969164789898, \ 0.0557030835210102, \ 0.9971300972924322, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.9971300972924322, \ 0.0557030835210102, \ 0.9442969164789898, \ 0.0028699027075679, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.0028699027075679, \ 0.9442969164789898, \ 0.0557030835210102, \ 0.0028699027075679, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.0028699027075679, \ 0.0557030835210102, \ 0.0557030835210102, \ 0.0028699027075679, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.0028699027075679, \ 0.0557030835210102 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9619577574752056, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.0380422425247944, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3913025693166751, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6086974306833248, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.6692365934747126, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.6692365934747126, \ 0.3307634065252874, \ 0.3307634065252874, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.8965445655196689, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.8965445655196689, \ 0.1034554344803311, \ 0.1034554344803311, \ 0.5000000000000000, \ 0.8482759513633358, \ 0.8482759513633358, \ 0.5000000000000000, \ 0.8482759513633358, \ 0.8482759513633358, \ 0.5000000000000000, \ 0.1517240486366642, \ 0.1517240486366642, \ 0.5000000000000000, \ 0.1517240486366642, \ 0.1517240486366642, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.7924949743436622, \ 0.2075050256563378, \ 0.2075050256563378, \ 0.7924949743436622, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.7924949743436622, \ 0.2075050256563378, \ 0.2075050256563378, \ 0.7924949743436622, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.6321333796314236, \ 0.3678666203685764, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9914024363900886, \ 0.0085975636099114, \ 0.0085975636099114, \ 0.9914024363900886, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9914024363900886, \ 0.0085975636099114, \ 0.0085975636099114, \ 0.9914024363900886, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.7764752956685337, \ 0.2235247043314663, \ 0.6360162945430453, \ 0.6360162945430453, \ 0.9390447038366581, \ 0.6360162945430453, \ 0.6360162945430453, \ 0.9390447038366581, \ 0.3639837054569547, \ 0.3639837054569547, \ 0.9390447038366581, \ 0.3639837054569547, \ 0.3639837054569547, \ 0.9390447038366581, \ 0.6360162945430453, \ 0.6360162945430453, \ 0.0609552961633420, \ 0.6360162945430453, \ 0.6360162945430453, \ 0.0609552961633420, \ 0.3639837054569547, \ 0.3639837054569547, \ 0.0609552961633420, \ 0.3639837054569547, \ 0.3639837054569547, \ 0.0609552961633420, \ 0.8093239300427761, \ 0.8093239300427761, \ 0.9699906676537717, \ 0.8093239300427761, \ 0.8093239300427761, \ 0.9699906676537717, \ 0.1906760699572239, \ 0.1906760699572239, \ 0.9699906676537717, \ 0.1906760699572239, \ 0.1906760699572239, \ 0.9699906676537717, \ 0.8093239300427761, \ 0.8093239300427761, \ 0.0300093323462282, \ 0.8093239300427761, \ 0.8093239300427761, \ 0.0300093323462282, \ 0.1906760699572239, \ 0.1906760699572239, \ 0.0300093323462282, \ 0.1906760699572239, \ 0.1906760699572239, \ 0.0300093323462282, \ 0.9315772312765189, \ 0.9315772312765189, \ 0.6521112975876302, \ 0.9315772312765189, \ 0.9315772312765189, \ 0.6521112975876302, \ 0.0684227687234810, \ 0.0684227687234810, \ 0.6521112975876302, \ 0.0684227687234810, \ 0.0684227687234810, \ 0.6521112975876302, \ 0.9315772312765189, \ 0.9315772312765189, \ 0.3478887024123698, \ 0.9315772312765189, \ 0.9315772312765189, \ 0.3478887024123698, \ 0.0684227687234810, \ 0.0684227687234810, \ 0.3478887024123698, \ 0.0684227687234810, \ 0.0684227687234810, \ 0.3478887024123698, \ 0.7308028863234025, \ 0.7308028863234025, \ 0.8685680591748091, \ 0.7308028863234025, \ 0.7308028863234025, \ 0.8685680591748091, \ 0.2691971136765975, \ 0.2691971136765975, \ 0.8685680591748091, \ 0.2691971136765975, \ 0.2691971136765975, \ 0.8685680591748091, \ 0.7308028863234025, \ 0.7308028863234025, \ 0.1314319408251909, \ 0.7308028863234025, \ 0.7308028863234025, \ 0.1314319408251909, \ 0.2691971136765975, \ 0.2691971136765975, \ 0.1314319408251909, \ 0.2691971136765975, \ 0.2691971136765975, \ 0.1314319408251909, \ 0.9801570902708128, \ 0.9801570902708128, \ 0.8835073040170505, \ 0.9801570902708128, \ 0.9801570902708128, \ 0.8835073040170505, \ 0.0198429097291872, \ 0.0198429097291872, \ 0.8835073040170505, \ 0.0198429097291872, \ 0.0198429097291872, \ 0.8835073040170505, \ 0.9801570902708128, \ 0.9801570902708128, \ 0.1164926959829496, \ 0.9801570902708128, \ 0.9801570902708128, \ 0.1164926959829496, \ 0.0198429097291872, \ 0.0198429097291872, \ 0.1164926959829496, \ 0.0198429097291872, \ 0.0198429097291872, \ 0.1164926959829496, \ 0.9971300972924322, \ 0.9442969164789898, \ 0.9971300972924322, \ 0.9442969164789898, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.9971300972924322, \ 0.9442969164789898, \ 0.9971300972924322, \ 0.9442969164789898, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.9971300972924322, \ 0.0557030835210102, \ 0.9971300972924322, \ 0.0557030835210102, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.0028699027075679, \ 0.9442969164789898, \ 0.0028699027075679, \ 0.9442969164789898, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.9971300972924322, \ 0.0557030835210102, \ 0.9971300972924322, \ 0.0557030835210102, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.0028699027075679, \ 0.9442969164789898, \ 0.0028699027075679, \ 0.9442969164789898, \ 0.3598740801041227, \ 0.3598740801041227, \ 0.0028699027075679, \ 0.0557030835210102, \ 0.0028699027075679, \ 0.0557030835210102, \ 0.6401259198958773, \ 0.6401259198958773, \ 0.0028699027075679, \ 0.0557030835210102, \ 0.0028699027075679, \ 0.0557030835210102, \ 0.3598740801041227, \ 0.3598740801041227 ] ) w = np.array ( [ \ 0.0033403050106945, \ 0.0033403050106945, \ 0.0033403050106945, \ 0.0033403050106945, \ 0.0033403050106945, \ 0.0033403050106945, \ 0.0050185523378773, \ 0.0050185523378773, \ 0.0050185523378773, \ 0.0050185523378773, \ 0.0050185523378773, \ 0.0050185523378773, \ 0.0090827588172248, \ 0.0090827588172248, \ 0.0090827588172248, \ 0.0090827588172248, \ 0.0090827588172248, \ 0.0090827588172248, \ 0.0090827588172248, \ 0.0090827588172248, \ 0.0029364087383876, \ 0.0029364087383876, \ 0.0029364087383876, \ 0.0029364087383876, \ 0.0029364087383876, \ 0.0029364087383876, \ 0.0029364087383876, \ 0.0029364087383876, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0093182386470488, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0069907862357511, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0028410057474906, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0053095740723308, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035708945365673, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0035058721795857, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0066651990511383, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0007781518386120, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597, \ 0.0006249800796597 ] ) return x, y, z, w def rule17 ( ): #*****************************************************************************80 # ## rule17() returns the hexahedron quadrature rule of precision 17. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.7426575151151338, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.2573424848848662, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.1296605920629508, \ 0.8703394079370492, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.0000002082088741, \ 0.9999997917911259, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.8773134026065881, \ 0.5000000000000000, \ 0.8773134026065881, \ 0.1226865973934119, \ 0.5000000000000000, \ 0.1226865973934119, \ 0.8773134026065881, \ 0.5000000000000000, \ 0.8773134026065881, \ 0.1226865973934119, \ 0.5000000000000000, \ 0.1226865973934119, \ 0.7748409070843456, \ 0.5000000000000000, \ 0.7748409070843456, \ 0.2251590929156544, \ 0.5000000000000000, \ 0.2251590929156544, \ 0.7748409070843456, \ 0.5000000000000000, \ 0.7748409070843456, \ 0.2251590929156544, \ 0.5000000000000000, \ 0.2251590929156544, \ 0.9998342518711405, \ 0.5000000000000000, \ 0.9998342518711405, \ 0.0001657481288594, \ 0.5000000000000000, \ 0.0001657481288594, \ 0.9998342518711405, \ 0.5000000000000000, \ 0.9998342518711405, \ 0.0001657481288594, \ 0.5000000000000000, \ 0.0001657481288594, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.9765209703524975, \ 0.0234790296475025, \ 0.0234790296475025, \ 0.9765209703524975, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9765209703524975, \ 0.0234790296475025, \ 0.0234790296475025, \ 0.9765209703524975, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.9085620340535459, \ 0.0914379659464542, \ 0.0914379659464542, \ 0.9085620340535459, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9085620340535459, \ 0.0914379659464542, \ 0.0914379659464542, \ 0.9085620340535459, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6276714770186411, \ 0.9848870223309694, \ 0.6276714770186411, \ 0.3723285229813589, \ 0.9848870223309694, \ 0.3723285229813589, \ 0.3723285229813589, \ 0.9848870223309694, \ 0.3723285229813589, \ 0.6276714770186411, \ 0.9848870223309694, \ 0.6276714770186411, \ 0.6276714770186411, \ 0.0151129776690307, \ 0.6276714770186411, \ 0.3723285229813589, \ 0.0151129776690307, \ 0.3723285229813589, \ 0.3723285229813589, \ 0.0151129776690307, \ 0.3723285229813589, \ 0.6276714770186411, \ 0.0151129776690307, \ 0.6276714770186411, \ 0.9676181924490221, \ 0.8733616537091691, \ 0.9676181924490221, \ 0.0323818075509779, \ 0.8733616537091691, \ 0.0323818075509779, \ 0.0323818075509779, \ 0.8733616537091691, \ 0.0323818075509779, \ 0.9676181924490221, \ 0.8733616537091691, \ 0.9676181924490221, \ 0.9676181924490221, \ 0.1266383462908310, \ 0.9676181924490221, \ 0.0323818075509779, \ 0.1266383462908310, \ 0.0323818075509779, \ 0.0323818075509779, \ 0.1266383462908310, \ 0.0323818075509779, \ 0.9676181924490221, \ 0.1266383462908310, \ 0.9676181924490221, \ 0.6715295730694326, \ 0.8093319789042792, \ 0.6715295730694326, \ 0.3284704269305673, \ 0.8093319789042792, \ 0.3284704269305673, \ 0.3284704269305673, \ 0.8093319789042792, \ 0.3284704269305673, \ 0.6715295730694326, \ 0.8093319789042792, \ 0.6715295730694326, \ 0.6715295730694326, \ 0.1906680210957207, \ 0.6715295730694326, \ 0.3284704269305673, \ 0.1906680210957207, \ 0.3284704269305673, \ 0.3284704269305673, \ 0.1906680210957207, \ 0.3284704269305673, \ 0.6715295730694326, \ 0.1906680210957207, \ 0.6715295730694326, \ 0.6277920800575361, \ 0.4229648752978111, \ 0.6277920800575361, \ 0.3722079199424639, \ 0.4229648752978111, \ 0.3722079199424639, \ 0.3722079199424639, \ 0.4229648752978111, \ 0.3722079199424639, \ 0.6277920800575361, \ 0.4229648752978111, \ 0.6277920800575361, \ 0.6277920800575361, \ 0.5770351247021889, \ 0.6277920800575361, \ 0.3722079199424639, \ 0.5770351247021889, \ 0.3722079199424639, \ 0.3722079199424639, \ 0.5770351247021889, \ 0.3722079199424639, \ 0.6277920800575361, \ 0.5770351247021889, \ 0.6277920800575361, \ 0.7708105708234440, \ 0.9478284758927406, \ 0.7708105708234440, \ 0.2291894291765560, \ 0.9478284758927406, \ 0.2291894291765560, \ 0.2291894291765560, \ 0.9478284758927406, \ 0.2291894291765560, \ 0.7708105708234440, \ 0.9478284758927406, \ 0.7708105708234440, \ 0.7708105708234440, \ 0.0521715241072594, \ 0.7708105708234440, \ 0.2291894291765560, \ 0.0521715241072594, \ 0.2291894291765560, \ 0.2291894291765560, \ 0.0521715241072594, \ 0.2291894291765560, \ 0.7708105708234440, \ 0.0521715241072594, \ 0.7708105708234440, \ 0.9437280545720244, \ 0.6207324889467394, \ 0.9437280545720244, \ 0.0562719454279757, \ 0.6207324889467394, \ 0.0562719454279757, \ 0.0562719454279757, \ 0.6207324889467394, \ 0.0562719454279757, \ 0.9437280545720244, \ 0.6207324889467394, \ 0.9437280545720244, \ 0.9437280545720244, \ 0.3792675110532606, \ 0.9437280545720244, \ 0.0562719454279757, \ 0.3792675110532606, \ 0.0562719454279757, \ 0.0562719454279757, \ 0.3792675110532606, \ 0.0562719454279757, \ 0.9437280545720244, \ 0.3792675110532606, \ 0.9437280545720244, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.9943923590724830, \ 0.7341796540172194, \ 0.9943923590724830, \ 0.7341796540172194, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.9943923590724830, \ 0.7341796540172194, \ 0.9943923590724830, \ 0.7341796540172194, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.0056076409275170, \ 0.7341796540172194, \ 0.0056076409275170, \ 0.7341796540172194, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.9943923590724830, \ 0.2658203459827806, \ 0.9943923590724830, \ 0.2658203459827806, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.0056076409275170, \ 0.7341796540172194, \ 0.0056076409275170, \ 0.7341796540172194, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.9943923590724830, \ 0.2658203459827806, \ 0.9943923590724830, \ 0.2658203459827806, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.0056076409275170, \ 0.2658203459827806, \ 0.0056076409275170, \ 0.2658203459827806, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.0056076409275170, \ 0.2658203459827806, \ 0.0056076409275170, \ 0.2658203459827806, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.8934115499715557, \ 0.6602554101905883, \ 0.8934115499715557, \ 0.6602554101905883, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.8934115499715557, \ 0.6602554101905883, \ 0.8934115499715557, \ 0.6602554101905883, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.1065884500284443, \ 0.6602554101905883, \ 0.1065884500284443, \ 0.6602554101905883, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.8934115499715557, \ 0.3397445898094117, \ 0.8934115499715557, \ 0.3397445898094117, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.1065884500284443, \ 0.6602554101905883, \ 0.1065884500284443, \ 0.6602554101905883, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.8934115499715557, \ 0.3397445898094117, \ 0.8934115499715557, \ 0.3397445898094117, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.1065884500284443, \ 0.3397445898094117, \ 0.1065884500284443, \ 0.3397445898094117, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.1065884500284443, \ 0.3397445898094117, \ 0.1065884500284443, \ 0.3397445898094117 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.7426575151151338, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.2573424848848662, \ 0.5000000000000000, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.1296605920629508, \ 0.8703394079370492, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.0000002082088741, \ 0.9999997917911259, \ 0.8773134026065881, \ 0.8773134026065881, \ 0.5000000000000000, \ 0.8773134026065881, \ 0.1226865973934119, \ 0.5000000000000000, \ 0.1226865973934119, \ 0.8773134026065881, \ 0.5000000000000000, \ 0.1226865973934119, \ 0.1226865973934119, \ 0.5000000000000000, \ 0.7748409070843456, \ 0.7748409070843456, \ 0.5000000000000000, \ 0.7748409070843456, \ 0.2251590929156544, \ 0.5000000000000000, \ 0.2251590929156544, \ 0.7748409070843456, \ 0.5000000000000000, \ 0.2251590929156544, \ 0.2251590929156544, \ 0.5000000000000000, \ 0.9998342518711405, \ 0.9998342518711405, \ 0.5000000000000000, \ 0.9998342518711405, \ 0.0001657481288594, \ 0.5000000000000000, \ 0.0001657481288594, \ 0.9998342518711405, \ 0.5000000000000000, \ 0.0001657481288594, \ 0.0001657481288594, \ 0.5000000000000000, \ 0.9765209703524975, \ 0.0234790296475025, \ 0.0234790296475025, \ 0.9765209703524975, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9765209703524975, \ 0.0234790296475025, \ 0.0234790296475025, \ 0.9765209703524975, \ 0.9085620340535459, \ 0.0914379659464542, \ 0.0914379659464542, \ 0.9085620340535459, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9085620340535459, \ 0.0914379659464542, \ 0.0914379659464542, \ 0.9085620340535459, \ 0.9848870223309694, \ 0.6276714770186411, \ 0.6276714770186411, \ 0.9848870223309694, \ 0.3723285229813589, \ 0.6276714770186411, \ 0.9848870223309694, \ 0.3723285229813589, \ 0.3723285229813589, \ 0.9848870223309694, \ 0.6276714770186411, \ 0.3723285229813589, \ 0.0151129776690307, \ 0.6276714770186411, \ 0.6276714770186411, \ 0.0151129776690307, \ 0.3723285229813589, \ 0.6276714770186411, \ 0.0151129776690307, \ 0.3723285229813589, \ 0.3723285229813589, \ 0.0151129776690307, \ 0.6276714770186411, \ 0.3723285229813589, \ 0.8733616537091691, \ 0.9676181924490221, \ 0.9676181924490221, \ 0.8733616537091691, \ 0.0323818075509779, \ 0.9676181924490221, \ 0.8733616537091691, \ 0.0323818075509779, \ 0.0323818075509779, \ 0.8733616537091691, \ 0.9676181924490221, \ 0.0323818075509779, \ 0.1266383462908310, \ 0.9676181924490221, \ 0.9676181924490221, \ 0.1266383462908310, \ 0.0323818075509779, \ 0.9676181924490221, \ 0.1266383462908310, \ 0.0323818075509779, \ 0.0323818075509779, \ 0.1266383462908310, \ 0.9676181924490221, \ 0.0323818075509779, \ 0.8093319789042792, \ 0.6715295730694326, \ 0.6715295730694326, \ 0.8093319789042792, \ 0.3284704269305673, \ 0.6715295730694326, \ 0.8093319789042792, \ 0.3284704269305673, \ 0.3284704269305673, \ 0.8093319789042792, \ 0.6715295730694326, \ 0.3284704269305673, \ 0.1906680210957207, \ 0.6715295730694326, \ 0.6715295730694326, \ 0.1906680210957207, \ 0.3284704269305673, \ 0.6715295730694326, \ 0.1906680210957207, \ 0.3284704269305673, \ 0.3284704269305673, \ 0.1906680210957207, \ 0.6715295730694326, \ 0.3284704269305673, \ 0.4229648752978111, \ 0.6277920800575361, \ 0.6277920800575361, \ 0.4229648752978111, \ 0.3722079199424639, \ 0.6277920800575361, \ 0.4229648752978111, \ 0.3722079199424639, \ 0.3722079199424639, \ 0.4229648752978111, \ 0.6277920800575361, \ 0.3722079199424639, \ 0.5770351247021889, \ 0.6277920800575361, \ 0.6277920800575361, \ 0.5770351247021889, \ 0.3722079199424639, \ 0.6277920800575361, \ 0.5770351247021889, \ 0.3722079199424639, \ 0.3722079199424639, \ 0.5770351247021889, \ 0.6277920800575361, \ 0.3722079199424639, \ 0.9478284758927406, \ 0.7708105708234440, \ 0.7708105708234440, \ 0.9478284758927406, \ 0.2291894291765560, \ 0.7708105708234440, \ 0.9478284758927406, \ 0.2291894291765560, \ 0.2291894291765560, \ 0.9478284758927406, \ 0.7708105708234440, \ 0.2291894291765560, \ 0.0521715241072594, \ 0.7708105708234440, \ 0.7708105708234440, \ 0.0521715241072594, \ 0.2291894291765560, \ 0.7708105708234440, \ 0.0521715241072594, \ 0.2291894291765560, \ 0.2291894291765560, \ 0.0521715241072594, \ 0.7708105708234440, \ 0.2291894291765560, \ 0.6207324889467394, \ 0.9437280545720244, \ 0.9437280545720244, \ 0.6207324889467394, \ 0.0562719454279757, \ 0.9437280545720244, \ 0.6207324889467394, \ 0.0562719454279757, \ 0.0562719454279757, \ 0.6207324889467394, \ 0.9437280545720244, \ 0.0562719454279757, \ 0.3792675110532606, \ 0.9437280545720244, \ 0.9437280545720244, \ 0.3792675110532606, \ 0.0562719454279757, \ 0.9437280545720244, \ 0.3792675110532606, \ 0.0562719454279757, \ 0.0562719454279757, \ 0.3792675110532606, \ 0.9437280545720244, \ 0.0562719454279757, \ 0.9943923590724830, \ 0.7341796540172194, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.7341796540172194, \ 0.9943923590724830, \ 0.9943923590724830, \ 0.7341796540172194, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.7341796540172194, \ 0.9943923590724830, \ 0.0056076409275170, \ 0.7341796540172194, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.7341796540172194, \ 0.0056076409275170, \ 0.9943923590724830, \ 0.2658203459827806, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.2658203459827806, \ 0.9943923590724830, \ 0.0056076409275170, \ 0.7341796540172194, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.7341796540172194, \ 0.0056076409275170, \ 0.9943923590724830, \ 0.2658203459827806, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.2658203459827806, \ 0.9943923590724830, \ 0.0056076409275170, \ 0.2658203459827806, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.2658203459827806, \ 0.0056076409275170, \ 0.0056076409275170, \ 0.2658203459827806, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.2658203459827806, \ 0.0056076409275170, \ 0.8934115499715557, \ 0.6602554101905883, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.6602554101905883, \ 0.8934115499715557, \ 0.8934115499715557, \ 0.6602554101905883, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.6602554101905883, \ 0.8934115499715557, \ 0.1065884500284443, \ 0.6602554101905883, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.6602554101905883, \ 0.1065884500284443, \ 0.8934115499715557, \ 0.3397445898094117, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.3397445898094117, \ 0.8934115499715557, \ 0.1065884500284443, \ 0.6602554101905883, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.6602554101905883, \ 0.1065884500284443, \ 0.8934115499715557, \ 0.3397445898094117, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.3397445898094117, \ 0.8934115499715557, \ 0.1065884500284443, \ 0.3397445898094117, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.3397445898094117, \ 0.1065884500284443, \ 0.1065884500284443, \ 0.3397445898094117, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.3397445898094117, \ 0.1065884500284443 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.7426575151151338, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.2573424848848662, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.8703394079370492, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.8703394079370492, \ 0.1296605920629508, \ 0.1296605920629508, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.9999997917911259, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.9999997917911259, \ 0.0000002082088741, \ 0.0000002082088741, \ 0.5000000000000000, \ 0.8773134026065881, \ 0.8773134026065881, \ 0.5000000000000000, \ 0.8773134026065881, \ 0.8773134026065881, \ 0.5000000000000000, \ 0.1226865973934119, \ 0.1226865973934119, \ 0.5000000000000000, \ 0.1226865973934119, \ 0.1226865973934119, \ 0.5000000000000000, \ 0.7748409070843456, \ 0.7748409070843456, \ 0.5000000000000000, \ 0.7748409070843456, \ 0.7748409070843456, \ 0.5000000000000000, \ 0.2251590929156544, \ 0.2251590929156544, \ 0.5000000000000000, \ 0.2251590929156544, \ 0.2251590929156544, \ 0.5000000000000000, \ 0.9998342518711405, \ 0.9998342518711405, \ 0.5000000000000000, \ 0.9998342518711405, \ 0.9998342518711405, \ 0.5000000000000000, \ 0.0001657481288594, \ 0.0001657481288594, \ 0.5000000000000000, \ 0.0001657481288594, \ 0.0001657481288594, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9765209703524975, \ 0.0234790296475025, \ 0.0234790296475025, \ 0.9765209703524975, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9765209703524975, \ 0.0234790296475025, \ 0.0234790296475025, \ 0.9765209703524975, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.8078645495842367, \ 0.1921354504157633, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9085620340535459, \ 0.0914379659464542, \ 0.0914379659464542, \ 0.9085620340535459, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9085620340535459, \ 0.0914379659464542, \ 0.0914379659464542, \ 0.9085620340535459, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6378406365996775, \ 0.3621593634003225, \ 0.6276714770186411, \ 0.6276714770186411, \ 0.9848870223309694, \ 0.6276714770186411, \ 0.6276714770186411, \ 0.9848870223309694, \ 0.3723285229813589, \ 0.3723285229813589, \ 0.9848870223309694, \ 0.3723285229813589, \ 0.3723285229813589, \ 0.9848870223309694, \ 0.6276714770186411, \ 0.6276714770186411, \ 0.0151129776690307, \ 0.6276714770186411, \ 0.6276714770186411, \ 0.0151129776690307, \ 0.3723285229813589, \ 0.3723285229813589, \ 0.0151129776690307, \ 0.3723285229813589, \ 0.3723285229813589, \ 0.0151129776690307, \ 0.9676181924490221, \ 0.9676181924490221, \ 0.8733616537091691, \ 0.9676181924490221, \ 0.9676181924490221, \ 0.8733616537091691, \ 0.0323818075509779, \ 0.0323818075509779, \ 0.8733616537091691, \ 0.0323818075509779, \ 0.0323818075509779, \ 0.8733616537091691, \ 0.9676181924490221, \ 0.9676181924490221, \ 0.1266383462908310, \ 0.9676181924490221, \ 0.9676181924490221, \ 0.1266383462908310, \ 0.0323818075509779, \ 0.0323818075509779, \ 0.1266383462908310, \ 0.0323818075509779, \ 0.0323818075509779, \ 0.1266383462908310, \ 0.6715295730694326, \ 0.6715295730694326, \ 0.8093319789042792, \ 0.6715295730694326, \ 0.6715295730694326, \ 0.8093319789042792, \ 0.3284704269305673, \ 0.3284704269305673, \ 0.8093319789042792, \ 0.3284704269305673, \ 0.3284704269305673, \ 0.8093319789042792, \ 0.6715295730694326, \ 0.6715295730694326, \ 0.1906680210957207, \ 0.6715295730694326, \ 0.6715295730694326, \ 0.1906680210957207, \ 0.3284704269305673, \ 0.3284704269305673, \ 0.1906680210957207, \ 0.3284704269305673, \ 0.3284704269305673, \ 0.1906680210957207, \ 0.6277920800575361, \ 0.6277920800575361, \ 0.4229648752978111, \ 0.6277920800575361, \ 0.6277920800575361, \ 0.4229648752978111, \ 0.3722079199424639, \ 0.3722079199424639, \ 0.4229648752978111, \ 0.3722079199424639, \ 0.3722079199424639, \ 0.4229648752978111, \ 0.6277920800575361, \ 0.6277920800575361, \ 0.5770351247021889, \ 0.6277920800575361, \ 0.6277920800575361, \ 0.5770351247021889, \ 0.3722079199424639, \ 0.3722079199424639, \ 0.5770351247021889, \ 0.3722079199424639, \ 0.3722079199424639, \ 0.5770351247021889, \ 0.7708105708234440, \ 0.7708105708234440, \ 0.9478284758927406, \ 0.7708105708234440, \ 0.7708105708234440, \ 0.9478284758927406, \ 0.2291894291765560, \ 0.2291894291765560, \ 0.9478284758927406, \ 0.2291894291765560, \ 0.2291894291765560, \ 0.9478284758927406, \ 0.7708105708234440, \ 0.7708105708234440, \ 0.0521715241072594, \ 0.7708105708234440, \ 0.7708105708234440, \ 0.0521715241072594, \ 0.2291894291765560, \ 0.2291894291765560, \ 0.0521715241072594, \ 0.2291894291765560, \ 0.2291894291765560, \ 0.0521715241072594, \ 0.9437280545720244, \ 0.9437280545720244, \ 0.6207324889467394, \ 0.9437280545720244, \ 0.9437280545720244, \ 0.6207324889467394, \ 0.0562719454279757, \ 0.0562719454279757, \ 0.6207324889467394, \ 0.0562719454279757, \ 0.0562719454279757, \ 0.6207324889467394, \ 0.9437280545720244, \ 0.9437280545720244, \ 0.3792675110532606, \ 0.9437280545720244, \ 0.9437280545720244, \ 0.3792675110532606, \ 0.0562719454279757, \ 0.0562719454279757, \ 0.3792675110532606, \ 0.0562719454279757, \ 0.0562719454279757, \ 0.3792675110532606, \ 0.7341796540172194, \ 0.9943923590724830, \ 0.7341796540172194, \ 0.9943923590724830, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.7341796540172194, \ 0.9943923590724830, \ 0.7341796540172194, \ 0.9943923590724830, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.7341796540172194, \ 0.0056076409275170, \ 0.7341796540172194, \ 0.0056076409275170, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.2658203459827806, \ 0.9943923590724830, \ 0.2658203459827806, \ 0.9943923590724830, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.7341796540172194, \ 0.0056076409275170, \ 0.7341796540172194, \ 0.0056076409275170, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.2658203459827806, \ 0.9943923590724830, \ 0.2658203459827806, \ 0.9943923590724830, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.2658203459827806, \ 0.0056076409275170, \ 0.2658203459827806, \ 0.0056076409275170, \ 0.9007366871015028, \ 0.9007366871015028, \ 0.2658203459827806, \ 0.0056076409275170, \ 0.2658203459827806, \ 0.0056076409275170, \ 0.0992633128984972, \ 0.0992633128984972, \ 0.6602554101905883, \ 0.8934115499715557, \ 0.6602554101905883, \ 0.8934115499715557, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.6602554101905883, \ 0.8934115499715557, \ 0.6602554101905883, \ 0.8934115499715557, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.6602554101905883, \ 0.1065884500284443, \ 0.6602554101905883, \ 0.1065884500284443, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.3397445898094117, \ 0.8934115499715557, \ 0.3397445898094117, \ 0.8934115499715557, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.6602554101905883, \ 0.1065884500284443, \ 0.6602554101905883, \ 0.1065884500284443, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.3397445898094117, \ 0.8934115499715557, \ 0.3397445898094117, \ 0.8934115499715557, \ 0.1950429669974847, \ 0.1950429669974847, \ 0.3397445898094117, \ 0.1065884500284443, \ 0.3397445898094117, \ 0.1065884500284443, \ 0.8049570330025153, \ 0.8049570330025153, \ 0.3397445898094117, \ 0.1065884500284443, \ 0.3397445898094117, \ 0.1065884500284443, \ 0.1950429669974847, \ 0.1950429669974847 ] ) w = np.array ( [ \ 0.0096145921289297, \ 0.0096145921289297, \ 0.0096145921289297, \ 0.0096145921289297, \ 0.0096145921289297, \ 0.0096145921289297, \ 0.0043938276021590, \ 0.0043938276021590, \ 0.0043938276021590, \ 0.0043938276021590, \ 0.0043938276021590, \ 0.0043938276021590, \ 0.0043938276021590, \ 0.0043938276021590, \ 0.0000496472519452, \ 0.0000496472519452, \ 0.0000496472519452, \ 0.0000496472519452, \ 0.0000496472519452, \ 0.0000496472519452, \ 0.0000496472519452, \ 0.0000496472519452, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0025062844648325, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0061332324820703, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0003052513689971, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0028254377330331, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0048177045987999, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0022831423389536, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0011774374872787, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0061840607506279, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0026746558375937, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0034191776775788, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0023346175566150, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0010527901648871, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639, \ 0.0027438309407639 ] ) return x, y, z, w def rule19 ( ): #*****************************************************************************80 # ## rule19() returns the hexahedron quadrature rule of precision 19. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 05 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.6178975194487687, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3821024805512313, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.0557524799779681, \ 0.9442475200220319, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.1654090765034974, \ 0.8345909234965025, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.9991488896425311, \ 0.0008511103574689, \ 0.0008511103574689, \ 0.9991488896425311, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9991488896425311, \ 0.0008511103574689, \ 0.0008511103574689, \ 0.9991488896425311, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.5860120647237821, \ 0.4139879352762179, \ 0.4139879352762179, \ 0.5860120647237821, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5860120647237821, \ 0.4139879352762179, \ 0.4139879352762179, \ 0.5860120647237821, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.2840454955532042, \ 0.7159545044467958, \ 0.7159545044467958, \ 0.2840454955532042, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.2840454955532042, \ 0.7159545044467958, \ 0.7159545044467958, \ 0.2840454955532042, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3449134012977228, \ 0.7705521820675761, \ 0.3449134012977228, \ 0.6550865987022771, \ 0.7705521820675761, \ 0.6550865987022771, \ 0.6550865987022771, \ 0.7705521820675761, \ 0.6550865987022771, \ 0.3449134012977228, \ 0.7705521820675761, \ 0.3449134012977228, \ 0.3449134012977228, \ 0.2294478179324239, \ 0.3449134012977228, \ 0.6550865987022771, \ 0.2294478179324239, \ 0.6550865987022771, \ 0.6550865987022771, \ 0.2294478179324239, \ 0.6550865987022771, \ 0.3449134012977228, \ 0.2294478179324239, \ 0.3449134012977228, \ 0.9920926274878630, \ 0.9103324974446185, \ 0.9920926274878630, \ 0.0079073725121370, \ 0.9103324974446185, \ 0.0079073725121370, \ 0.0079073725121370, \ 0.9103324974446185, \ 0.0079073725121370, \ 0.9920926274878630, \ 0.9103324974446185, \ 0.9920926274878630, \ 0.9920926274878630, \ 0.0896675025553814, \ 0.9920926274878630, \ 0.0079073725121370, \ 0.0896675025553814, \ 0.0079073725121370, \ 0.0079073725121370, \ 0.0896675025553814, \ 0.0079073725121370, \ 0.9920926274878630, \ 0.0896675025553814, \ 0.9920926274878630, \ 0.9221936167657927, \ 0.4263116836838957, \ 0.9221936167657927, \ 0.0778063832342073, \ 0.4263116836838957, \ 0.0778063832342073, \ 0.0778063832342073, \ 0.4263116836838957, \ 0.0778063832342073, \ 0.9221936167657927, \ 0.4263116836838957, \ 0.9221936167657927, \ 0.9221936167657927, \ 0.5736883163161043, \ 0.9221936167657927, \ 0.0778063832342073, \ 0.5736883163161043, \ 0.0778063832342073, \ 0.0778063832342073, \ 0.5736883163161043, \ 0.0778063832342073, \ 0.9221936167657927, \ 0.5736883163161043, \ 0.9221936167657927, \ 0.7437996999426106, \ 0.8837457372516819, \ 0.7437996999426106, \ 0.2562003000573894, \ 0.8837457372516819, \ 0.2562003000573894, \ 0.2562003000573894, \ 0.8837457372516819, \ 0.2562003000573894, \ 0.7437996999426106, \ 0.8837457372516819, \ 0.7437996999426106, \ 0.7437996999426106, \ 0.1162542627483181, \ 0.7437996999426106, \ 0.2562003000573894, \ 0.1162542627483181, \ 0.2562003000573894, \ 0.2562003000573894, \ 0.1162542627483181, \ 0.2562003000573894, \ 0.7437996999426106, \ 0.1162542627483181, \ 0.7437996999426106, \ 0.8820659248983722, \ 0.6931955182506035, \ 0.8820659248983722, \ 0.1179340751016278, \ 0.6931955182506035, \ 0.1179340751016278, \ 0.1179340751016278, \ 0.6931955182506035, \ 0.1179340751016278, \ 0.8820659248983722, \ 0.6931955182506035, \ 0.8820659248983722, \ 0.8820659248983722, \ 0.3068044817493964, \ 0.8820659248983722, \ 0.1179340751016278, \ 0.3068044817493964, \ 0.1179340751016278, \ 0.1179340751016278, \ 0.3068044817493964, \ 0.1179340751016278, \ 0.8820659248983722, \ 0.3068044817493964, \ 0.8820659248983722, \ 0.8556268694112152, \ 0.9516006474964566, \ 0.8556268694112152, \ 0.1443731305887847, \ 0.9516006474964566, \ 0.1443731305887847, \ 0.1443731305887847, \ 0.9516006474964566, \ 0.1443731305887847, \ 0.8556268694112152, \ 0.9516006474964566, \ 0.8556268694112152, \ 0.8556268694112152, \ 0.0483993525035434, \ 0.8556268694112152, \ 0.1443731305887847, \ 0.0483993525035434, \ 0.1443731305887847, \ 0.1443731305887847, \ 0.0483993525035434, \ 0.1443731305887847, \ 0.8556268694112152, \ 0.0483993525035434, \ 0.8556268694112152, \ 0.9775744747969544, \ 0.6113080322285057, \ 0.9775744747969544, \ 0.0224255252030456, \ 0.6113080322285057, \ 0.0224255252030456, \ 0.0224255252030456, \ 0.6113080322285057, \ 0.0224255252030456, \ 0.9775744747969544, \ 0.6113080322285057, \ 0.9775744747969544, \ 0.9775744747969544, \ 0.3886919677714943, \ 0.9775744747969544, \ 0.0224255252030456, \ 0.3886919677714943, \ 0.0224255252030456, \ 0.0224255252030456, \ 0.3886919677714943, \ 0.0224255252030456, \ 0.9775744747969544, \ 0.3886919677714943, \ 0.9775744747969544, \ 0.5848459901934986, \ 0.9825814337796190, \ 0.5848459901934986, \ 0.4151540098065015, \ 0.9825814337796190, \ 0.4151540098065015, \ 0.4151540098065015, \ 0.9825814337796190, \ 0.4151540098065015, \ 0.5848459901934986, \ 0.9825814337796190, \ 0.5848459901934986, \ 0.5848459901934986, \ 0.0174185662203810, \ 0.5848459901934986, \ 0.4151540098065015, \ 0.0174185662203810, \ 0.4151540098065015, \ 0.4151540098065015, \ 0.0174185662203810, \ 0.4151540098065015, \ 0.5848459901934986, \ 0.0174185662203810, \ 0.5848459901934986, \ 0.8042667629417029, \ 0.5470636340177077, \ 0.8042667629417029, \ 0.1957332370582971, \ 0.5470636340177077, \ 0.1957332370582971, \ 0.1957332370582971, \ 0.5470636340177077, \ 0.1957332370582971, \ 0.8042667629417029, \ 0.5470636340177077, \ 0.8042667629417029, \ 0.8042667629417029, \ 0.4529363659822923, \ 0.8042667629417029, \ 0.1957332370582971, \ 0.4529363659822923, \ 0.1957332370582971, \ 0.1957332370582971, \ 0.4529363659822923, \ 0.1957332370582971, \ 0.8042667629417029, \ 0.4529363659822923, \ 0.8042667629417029, \ 0.7132758893843609, \ 0.9892390565548020, \ 0.7132758893843609, \ 0.2867241106156391, \ 0.9892390565548020, \ 0.2867241106156391, \ 0.2867241106156391, \ 0.9892390565548020, \ 0.2867241106156391, \ 0.7132758893843609, \ 0.9892390565548020, \ 0.7132758893843609, \ 0.7132758893843609, \ 0.0107609434451980, \ 0.7132758893843609, \ 0.2867241106156391, \ 0.0107609434451980, \ 0.2867241106156391, \ 0.2867241106156391, \ 0.0107609434451980, \ 0.2867241106156391, \ 0.7132758893843609, \ 0.0107609434451980, \ 0.7132758893843609, \ 0.5918460351304471, \ 0.8728877113378553, \ 0.5918460351304471, \ 0.4081539648695529, \ 0.8728877113378553, \ 0.4081539648695529, \ 0.4081539648695529, \ 0.8728877113378553, \ 0.4081539648695529, \ 0.5918460351304471, \ 0.8728877113378553, \ 0.5918460351304471, \ 0.5918460351304471, \ 0.1271122886621447, \ 0.5918460351304471, \ 0.4081539648695529, \ 0.1271122886621447, \ 0.4081539648695529, \ 0.4081539648695529, \ 0.1271122886621447, \ 0.4081539648695529, \ 0.5918460351304471, \ 0.1271122886621447, \ 0.5918460351304471, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.9566761563025079, \ 0.6444314510393020, \ 0.9566761563025079, \ 0.6444314510393020, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.9566761563025079, \ 0.6444314510393020, \ 0.9566761563025079, \ 0.6444314510393020, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.0433238436974921, \ 0.6444314510393020, \ 0.0433238436974921, \ 0.6444314510393020, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.9566761563025079, \ 0.3555685489606980, \ 0.9566761563025079, \ 0.3555685489606980, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.0433238436974921, \ 0.6444314510393020, \ 0.0433238436974921, \ 0.6444314510393020, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.9566761563025079, \ 0.3555685489606980, \ 0.9566761563025079, \ 0.3555685489606980, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.0433238436974921, \ 0.3555685489606980, \ 0.0433238436974921, \ 0.3555685489606980, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.0433238436974921, \ 0.3555685489606980, \ 0.0433238436974921, \ 0.3555685489606980, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.9874241069713281, \ 0.7767138770406730, \ 0.9874241069713281, \ 0.7767138770406730, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.9874241069713281, \ 0.7767138770406730, \ 0.9874241069713281, \ 0.7767138770406730, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.0125758930286720, \ 0.7767138770406730, \ 0.0125758930286720, \ 0.7767138770406730, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.9874241069713281, \ 0.2232861229593271, \ 0.9874241069713281, \ 0.2232861229593271, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.0125758930286720, \ 0.7767138770406730, \ 0.0125758930286720, \ 0.7767138770406730, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.9874241069713281, \ 0.2232861229593271, \ 0.9874241069713281, \ 0.2232861229593271, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.0125758930286720, \ 0.2232861229593271, \ 0.0125758930286720, \ 0.2232861229593271, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.0125758930286720, \ 0.2232861229593271, \ 0.0125758930286720, \ 0.2232861229593271 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.6178975194487687, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3821024805512313, \ 0.5000000000000000, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.0557524799779681, \ 0.9442475200220319, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.1654090765034974, \ 0.8345909234965025, \ 0.9991488896425311, \ 0.0008511103574689, \ 0.0008511103574689, \ 0.9991488896425311, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9991488896425311, \ 0.0008511103574689, \ 0.0008511103574689, \ 0.9991488896425311, \ 0.5860120647237821, \ 0.4139879352762179, \ 0.4139879352762179, \ 0.5860120647237821, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5860120647237821, \ 0.4139879352762179, \ 0.4139879352762179, \ 0.5860120647237821, \ 0.2840454955532042, \ 0.7159545044467958, \ 0.7159545044467958, \ 0.2840454955532042, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.2840454955532042, \ 0.7159545044467958, \ 0.7159545044467958, \ 0.2840454955532042, \ 0.7705521820675761, \ 0.3449134012977228, \ 0.3449134012977228, \ 0.7705521820675761, \ 0.6550865987022771, \ 0.3449134012977228, \ 0.7705521820675761, \ 0.6550865987022771, \ 0.6550865987022771, \ 0.7705521820675761, \ 0.3449134012977228, \ 0.6550865987022771, \ 0.2294478179324239, \ 0.3449134012977228, \ 0.3449134012977228, \ 0.2294478179324239, \ 0.6550865987022771, \ 0.3449134012977228, \ 0.2294478179324239, \ 0.6550865987022771, \ 0.6550865987022771, \ 0.2294478179324239, \ 0.3449134012977228, \ 0.6550865987022771, \ 0.9103324974446185, \ 0.9920926274878630, \ 0.9920926274878630, \ 0.9103324974446185, \ 0.0079073725121370, \ 0.9920926274878630, \ 0.9103324974446185, \ 0.0079073725121370, \ 0.0079073725121370, \ 0.9103324974446185, \ 0.9920926274878630, \ 0.0079073725121370, \ 0.0896675025553814, \ 0.9920926274878630, \ 0.9920926274878630, \ 0.0896675025553814, \ 0.0079073725121370, \ 0.9920926274878630, \ 0.0896675025553814, \ 0.0079073725121370, \ 0.0079073725121370, \ 0.0896675025553814, \ 0.9920926274878630, \ 0.0079073725121370, \ 0.4263116836838957, \ 0.9221936167657927, \ 0.9221936167657927, \ 0.4263116836838957, \ 0.0778063832342073, \ 0.9221936167657927, \ 0.4263116836838957, \ 0.0778063832342073, \ 0.0778063832342073, \ 0.4263116836838957, \ 0.9221936167657927, \ 0.0778063832342073, \ 0.5736883163161043, \ 0.9221936167657927, \ 0.9221936167657927, \ 0.5736883163161043, \ 0.0778063832342073, \ 0.9221936167657927, \ 0.5736883163161043, \ 0.0778063832342073, \ 0.0778063832342073, \ 0.5736883163161043, \ 0.9221936167657927, \ 0.0778063832342073, \ 0.8837457372516819, \ 0.7437996999426106, \ 0.7437996999426106, \ 0.8837457372516819, \ 0.2562003000573894, \ 0.7437996999426106, \ 0.8837457372516819, \ 0.2562003000573894, \ 0.2562003000573894, \ 0.8837457372516819, \ 0.7437996999426106, \ 0.2562003000573894, \ 0.1162542627483181, \ 0.7437996999426106, \ 0.7437996999426106, \ 0.1162542627483181, \ 0.2562003000573894, \ 0.7437996999426106, \ 0.1162542627483181, \ 0.2562003000573894, \ 0.2562003000573894, \ 0.1162542627483181, \ 0.7437996999426106, \ 0.2562003000573894, \ 0.6931955182506035, \ 0.8820659248983722, \ 0.8820659248983722, \ 0.6931955182506035, \ 0.1179340751016278, \ 0.8820659248983722, \ 0.6931955182506035, \ 0.1179340751016278, \ 0.1179340751016278, \ 0.6931955182506035, \ 0.8820659248983722, \ 0.1179340751016278, \ 0.3068044817493964, \ 0.8820659248983722, \ 0.8820659248983722, \ 0.3068044817493964, \ 0.1179340751016278, \ 0.8820659248983722, \ 0.3068044817493964, \ 0.1179340751016278, \ 0.1179340751016278, \ 0.3068044817493964, \ 0.8820659248983722, \ 0.1179340751016278, \ 0.9516006474964566, \ 0.8556268694112152, \ 0.8556268694112152, \ 0.9516006474964566, \ 0.1443731305887847, \ 0.8556268694112152, \ 0.9516006474964566, \ 0.1443731305887847, \ 0.1443731305887847, \ 0.9516006474964566, \ 0.8556268694112152, \ 0.1443731305887847, \ 0.0483993525035434, \ 0.8556268694112152, \ 0.8556268694112152, \ 0.0483993525035434, \ 0.1443731305887847, \ 0.8556268694112152, \ 0.0483993525035434, \ 0.1443731305887847, \ 0.1443731305887847, \ 0.0483993525035434, \ 0.8556268694112152, \ 0.1443731305887847, \ 0.6113080322285057, \ 0.9775744747969544, \ 0.9775744747969544, \ 0.6113080322285057, \ 0.0224255252030456, \ 0.9775744747969544, \ 0.6113080322285057, \ 0.0224255252030456, \ 0.0224255252030456, \ 0.6113080322285057, \ 0.9775744747969544, \ 0.0224255252030456, \ 0.3886919677714943, \ 0.9775744747969544, \ 0.9775744747969544, \ 0.3886919677714943, \ 0.0224255252030456, \ 0.9775744747969544, \ 0.3886919677714943, \ 0.0224255252030456, \ 0.0224255252030456, \ 0.3886919677714943, \ 0.9775744747969544, \ 0.0224255252030456, \ 0.9825814337796190, \ 0.5848459901934986, \ 0.5848459901934986, \ 0.9825814337796190, \ 0.4151540098065015, \ 0.5848459901934986, \ 0.9825814337796190, \ 0.4151540098065015, \ 0.4151540098065015, \ 0.9825814337796190, \ 0.5848459901934986, \ 0.4151540098065015, \ 0.0174185662203810, \ 0.5848459901934986, \ 0.5848459901934986, \ 0.0174185662203810, \ 0.4151540098065015, \ 0.5848459901934986, \ 0.0174185662203810, \ 0.4151540098065015, \ 0.4151540098065015, \ 0.0174185662203810, \ 0.5848459901934986, \ 0.4151540098065015, \ 0.5470636340177077, \ 0.8042667629417029, \ 0.8042667629417029, \ 0.5470636340177077, \ 0.1957332370582971, \ 0.8042667629417029, \ 0.5470636340177077, \ 0.1957332370582971, \ 0.1957332370582971, \ 0.5470636340177077, \ 0.8042667629417029, \ 0.1957332370582971, \ 0.4529363659822923, \ 0.8042667629417029, \ 0.8042667629417029, \ 0.4529363659822923, \ 0.1957332370582971, \ 0.8042667629417029, \ 0.4529363659822923, \ 0.1957332370582971, \ 0.1957332370582971, \ 0.4529363659822923, \ 0.8042667629417029, \ 0.1957332370582971, \ 0.9892390565548020, \ 0.7132758893843609, \ 0.7132758893843609, \ 0.9892390565548020, \ 0.2867241106156391, \ 0.7132758893843609, \ 0.9892390565548020, \ 0.2867241106156391, \ 0.2867241106156391, \ 0.9892390565548020, \ 0.7132758893843609, \ 0.2867241106156391, \ 0.0107609434451980, \ 0.7132758893843609, \ 0.7132758893843609, \ 0.0107609434451980, \ 0.2867241106156391, \ 0.7132758893843609, \ 0.0107609434451980, \ 0.2867241106156391, \ 0.2867241106156391, \ 0.0107609434451980, \ 0.7132758893843609, \ 0.2867241106156391, \ 0.8728877113378553, \ 0.5918460351304471, \ 0.5918460351304471, \ 0.8728877113378553, \ 0.4081539648695529, \ 0.5918460351304471, \ 0.8728877113378553, \ 0.4081539648695529, \ 0.4081539648695529, \ 0.8728877113378553, \ 0.5918460351304471, \ 0.4081539648695529, \ 0.1271122886621447, \ 0.5918460351304471, \ 0.5918460351304471, \ 0.1271122886621447, \ 0.4081539648695529, \ 0.5918460351304471, \ 0.1271122886621447, \ 0.4081539648695529, \ 0.4081539648695529, \ 0.1271122886621447, \ 0.5918460351304471, \ 0.4081539648695529, \ 0.9566761563025079, \ 0.6444314510393020, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.6444314510393020, \ 0.9566761563025079, \ 0.9566761563025079, \ 0.6444314510393020, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.6444314510393020, \ 0.9566761563025079, \ 0.0433238436974921, \ 0.6444314510393020, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.6444314510393020, \ 0.0433238436974921, \ 0.9566761563025079, \ 0.3555685489606980, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.3555685489606980, \ 0.9566761563025079, \ 0.0433238436974921, \ 0.6444314510393020, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.6444314510393020, \ 0.0433238436974921, \ 0.9566761563025079, \ 0.3555685489606980, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.3555685489606980, \ 0.9566761563025079, \ 0.0433238436974921, \ 0.3555685489606980, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.3555685489606980, \ 0.0433238436974921, \ 0.0433238436974921, \ 0.3555685489606980, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.3555685489606980, \ 0.0433238436974921, \ 0.9874241069713281, \ 0.7767138770406730, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.7767138770406730, \ 0.9874241069713281, \ 0.9874241069713281, \ 0.7767138770406730, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.7767138770406730, \ 0.9874241069713281, \ 0.0125758930286720, \ 0.7767138770406730, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.7767138770406730, \ 0.0125758930286720, \ 0.9874241069713281, \ 0.2232861229593271, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.2232861229593271, \ 0.9874241069713281, \ 0.0125758930286720, \ 0.7767138770406730, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.7767138770406730, \ 0.0125758930286720, \ 0.9874241069713281, \ 0.2232861229593271, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.2232861229593271, \ 0.9874241069713281, \ 0.0125758930286720, \ 0.2232861229593271, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.2232861229593271, \ 0.0125758930286720, \ 0.0125758930286720, \ 0.2232861229593271, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.2232861229593271, \ 0.0125758930286720 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6178975194487687, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3821024805512313, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.9442475200220319, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.9442475200220319, \ 0.0557524799779681, \ 0.0557524799779681, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.8345909234965025, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.8345909234965025, \ 0.1654090765034974, \ 0.1654090765034974, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9991488896425311, \ 0.0008511103574689, \ 0.0008511103574689, \ 0.9991488896425311, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9991488896425311, \ 0.0008511103574689, \ 0.0008511103574689, \ 0.9991488896425311, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.8561550198509273, \ 0.1438449801490727, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5860120647237821, \ 0.4139879352762179, \ 0.4139879352762179, \ 0.5860120647237821, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5860120647237821, \ 0.4139879352762179, \ 0.4139879352762179, \ 0.5860120647237821, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.6998570581371140, \ 0.3001429418628860, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.2840454955532042, \ 0.7159545044467958, \ 0.7159545044467958, \ 0.2840454955532042, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.2840454955532042, \ 0.7159545044467958, \ 0.7159545044467958, \ 0.2840454955532042, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.9382902632360840, \ 0.0617097367639160, \ 0.3449134012977228, \ 0.3449134012977228, \ 0.7705521820675761, \ 0.3449134012977228, \ 0.3449134012977228, \ 0.7705521820675761, \ 0.6550865987022771, \ 0.6550865987022771, \ 0.7705521820675761, \ 0.6550865987022771, \ 0.6550865987022771, \ 0.7705521820675761, \ 0.3449134012977228, \ 0.3449134012977228, \ 0.2294478179324239, \ 0.3449134012977228, \ 0.3449134012977228, \ 0.2294478179324239, \ 0.6550865987022771, \ 0.6550865987022771, \ 0.2294478179324239, \ 0.6550865987022771, \ 0.6550865987022771, \ 0.2294478179324239, \ 0.9920926274878630, \ 0.9920926274878630, \ 0.9103324974446185, \ 0.9920926274878630, \ 0.9920926274878630, \ 0.9103324974446185, \ 0.0079073725121370, \ 0.0079073725121370, \ 0.9103324974446185, \ 0.0079073725121370, \ 0.0079073725121370, \ 0.9103324974446185, \ 0.9920926274878630, \ 0.9920926274878630, \ 0.0896675025553814, \ 0.9920926274878630, \ 0.9920926274878630, \ 0.0896675025553814, \ 0.0079073725121370, \ 0.0079073725121370, \ 0.0896675025553814, \ 0.0079073725121370, \ 0.0079073725121370, \ 0.0896675025553814, \ 0.9221936167657927, \ 0.9221936167657927, \ 0.4263116836838957, \ 0.9221936167657927, \ 0.9221936167657927, \ 0.4263116836838957, \ 0.0778063832342073, \ 0.0778063832342073, \ 0.4263116836838957, \ 0.0778063832342073, \ 0.0778063832342073, \ 0.4263116836838957, \ 0.9221936167657927, \ 0.9221936167657927, \ 0.5736883163161043, \ 0.9221936167657927, \ 0.9221936167657927, \ 0.5736883163161043, \ 0.0778063832342073, \ 0.0778063832342073, \ 0.5736883163161043, \ 0.0778063832342073, \ 0.0778063832342073, \ 0.5736883163161043, \ 0.7437996999426106, \ 0.7437996999426106, \ 0.8837457372516819, \ 0.7437996999426106, \ 0.7437996999426106, \ 0.8837457372516819, \ 0.2562003000573894, \ 0.2562003000573894, \ 0.8837457372516819, \ 0.2562003000573894, \ 0.2562003000573894, \ 0.8837457372516819, \ 0.7437996999426106, \ 0.7437996999426106, \ 0.1162542627483181, \ 0.7437996999426106, \ 0.7437996999426106, \ 0.1162542627483181, \ 0.2562003000573894, \ 0.2562003000573894, \ 0.1162542627483181, \ 0.2562003000573894, \ 0.2562003000573894, \ 0.1162542627483181, \ 0.8820659248983722, \ 0.8820659248983722, \ 0.6931955182506035, \ 0.8820659248983722, \ 0.8820659248983722, \ 0.6931955182506035, \ 0.1179340751016278, \ 0.1179340751016278, \ 0.6931955182506035, \ 0.1179340751016278, \ 0.1179340751016278, \ 0.6931955182506035, \ 0.8820659248983722, \ 0.8820659248983722, \ 0.3068044817493964, \ 0.8820659248983722, \ 0.8820659248983722, \ 0.3068044817493964, \ 0.1179340751016278, \ 0.1179340751016278, \ 0.3068044817493964, \ 0.1179340751016278, \ 0.1179340751016278, \ 0.3068044817493964, \ 0.8556268694112152, \ 0.8556268694112152, \ 0.9516006474964566, \ 0.8556268694112152, \ 0.8556268694112152, \ 0.9516006474964566, \ 0.1443731305887847, \ 0.1443731305887847, \ 0.9516006474964566, \ 0.1443731305887847, \ 0.1443731305887847, \ 0.9516006474964566, \ 0.8556268694112152, \ 0.8556268694112152, \ 0.0483993525035434, \ 0.8556268694112152, \ 0.8556268694112152, \ 0.0483993525035434, \ 0.1443731305887847, \ 0.1443731305887847, \ 0.0483993525035434, \ 0.1443731305887847, \ 0.1443731305887847, \ 0.0483993525035434, \ 0.9775744747969544, \ 0.9775744747969544, \ 0.6113080322285057, \ 0.9775744747969544, \ 0.9775744747969544, \ 0.6113080322285057, \ 0.0224255252030456, \ 0.0224255252030456, \ 0.6113080322285057, \ 0.0224255252030456, \ 0.0224255252030456, \ 0.6113080322285057, \ 0.9775744747969544, \ 0.9775744747969544, \ 0.3886919677714943, \ 0.9775744747969544, \ 0.9775744747969544, \ 0.3886919677714943, \ 0.0224255252030456, \ 0.0224255252030456, \ 0.3886919677714943, \ 0.0224255252030456, \ 0.0224255252030456, \ 0.3886919677714943, \ 0.5848459901934986, \ 0.5848459901934986, \ 0.9825814337796190, \ 0.5848459901934986, \ 0.5848459901934986, \ 0.9825814337796190, \ 0.4151540098065015, \ 0.4151540098065015, \ 0.9825814337796190, \ 0.4151540098065015, \ 0.4151540098065015, \ 0.9825814337796190, \ 0.5848459901934986, \ 0.5848459901934986, \ 0.0174185662203810, \ 0.5848459901934986, \ 0.5848459901934986, \ 0.0174185662203810, \ 0.4151540098065015, \ 0.4151540098065015, \ 0.0174185662203810, \ 0.4151540098065015, \ 0.4151540098065015, \ 0.0174185662203810, \ 0.8042667629417029, \ 0.8042667629417029, \ 0.5470636340177077, \ 0.8042667629417029, \ 0.8042667629417029, \ 0.5470636340177077, \ 0.1957332370582971, \ 0.1957332370582971, \ 0.5470636340177077, \ 0.1957332370582971, \ 0.1957332370582971, \ 0.5470636340177077, \ 0.8042667629417029, \ 0.8042667629417029, \ 0.4529363659822923, \ 0.8042667629417029, \ 0.8042667629417029, \ 0.4529363659822923, \ 0.1957332370582971, \ 0.1957332370582971, \ 0.4529363659822923, \ 0.1957332370582971, \ 0.1957332370582971, \ 0.4529363659822923, \ 0.7132758893843609, \ 0.7132758893843609, \ 0.9892390565548020, \ 0.7132758893843609, \ 0.7132758893843609, \ 0.9892390565548020, \ 0.2867241106156391, \ 0.2867241106156391, \ 0.9892390565548020, \ 0.2867241106156391, \ 0.2867241106156391, \ 0.9892390565548020, \ 0.7132758893843609, \ 0.7132758893843609, \ 0.0107609434451980, \ 0.7132758893843609, \ 0.7132758893843609, \ 0.0107609434451980, \ 0.2867241106156391, \ 0.2867241106156391, \ 0.0107609434451980, \ 0.2867241106156391, \ 0.2867241106156391, \ 0.0107609434451980, \ 0.5918460351304471, \ 0.5918460351304471, \ 0.8728877113378553, \ 0.5918460351304471, \ 0.5918460351304471, \ 0.8728877113378553, \ 0.4081539648695529, \ 0.4081539648695529, \ 0.8728877113378553, \ 0.4081539648695529, \ 0.4081539648695529, \ 0.8728877113378553, \ 0.5918460351304471, \ 0.5918460351304471, \ 0.1271122886621447, \ 0.5918460351304471, \ 0.5918460351304471, \ 0.1271122886621447, \ 0.4081539648695529, \ 0.4081539648695529, \ 0.1271122886621447, \ 0.4081539648695529, \ 0.4081539648695529, \ 0.1271122886621447, \ 0.6444314510393020, \ 0.9566761563025079, \ 0.6444314510393020, \ 0.9566761563025079, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.6444314510393020, \ 0.9566761563025079, \ 0.6444314510393020, \ 0.9566761563025079, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.6444314510393020, \ 0.0433238436974921, \ 0.6444314510393020, \ 0.0433238436974921, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.3555685489606980, \ 0.9566761563025079, \ 0.3555685489606980, \ 0.9566761563025079, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.6444314510393020, \ 0.0433238436974921, \ 0.6444314510393020, \ 0.0433238436974921, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.3555685489606980, \ 0.9566761563025079, \ 0.3555685489606980, \ 0.9566761563025079, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.3555685489606980, \ 0.0433238436974921, \ 0.3555685489606980, \ 0.0433238436974921, \ 0.8267665443298317, \ 0.8267665443298317, \ 0.3555685489606980, \ 0.0433238436974921, \ 0.3555685489606980, \ 0.0433238436974921, \ 0.1732334556701683, \ 0.1732334556701683, \ 0.7767138770406730, \ 0.9874241069713281, \ 0.7767138770406730, \ 0.9874241069713281, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.7767138770406730, \ 0.9874241069713281, \ 0.7767138770406730, \ 0.9874241069713281, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.7767138770406730, \ 0.0125758930286720, \ 0.7767138770406730, \ 0.0125758930286720, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.2232861229593271, \ 0.9874241069713281, \ 0.2232861229593271, \ 0.9874241069713281, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.7767138770406730, \ 0.0125758930286720, \ 0.7767138770406730, \ 0.0125758930286720, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.2232861229593271, \ 0.9874241069713281, \ 0.2232861229593271, \ 0.9874241069713281, \ 0.0762182454507607, \ 0.0762182454507607, \ 0.2232861229593271, \ 0.0125758930286720, \ 0.2232861229593271, \ 0.0125758930286720, \ 0.9237817545492393, \ 0.9237817545492393, \ 0.2232861229593271, \ 0.0125758930286720, \ 0.2232861229593271, \ 0.0125758930286720, \ 0.0762182454507607, \ 0.0762182454507607 ] ) w = np.array ( [ \ 0.0020573710057311, \ 0.0020573710057311, \ 0.0020573710057311, \ 0.0020573710057311, \ 0.0020573710057311, \ 0.0020573710057311, \ 0.0009660877915728, \ 0.0009660877915728, \ 0.0009660877915728, \ 0.0009660877915728, \ 0.0009660877915728, \ 0.0009660877915728, \ 0.0009660877915728, \ 0.0009660877915728, \ 0.0016359014467992, \ 0.0016359014467992, \ 0.0016359014467992, \ 0.0016359014467992, \ 0.0016359014467992, \ 0.0016359014467992, \ 0.0016359014467992, \ 0.0016359014467992, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0008499912813105, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0035950037217364, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0038360634296226, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0050441284857989, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0001951830532879, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0017584548406612, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0038873202629322, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0018874010836757, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0016991651835215, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0007588378288378, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0014557629541032, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0040079050757571, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0013991860755843, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0040992807889267, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0019518612573850, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919, \ 0.0009537937942919 ] ) return x, y, z, w def rule21 ( ): #*****************************************************************************80 # ## rule21() returns the hexahedron quadrature rule of precision 21. # # Discussion: # # We suppose we are given a hexahedron H with vertices # (0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1), # We call a rule with n points, returning coordinates # x, y, z, and weights w. Then the integral I of f(x,y,z) over H is # approximated by Q as follows: # # Q = volume(H) * sum ( 1 <= i <= n ) w(i) * f(x(i),y(i),z(i)) # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 06 May 2023 # # Author: # # John Burkardt # # Reference: # # Jan Jaskowiec, Natarajan Sukumar, # High order symmetric cubature rules for tetrahedra and pyramids, # International Journal for Numerical Methods in Engineering, # Volume 122, Number 1, pages 148-171, 24 August 2020. # # Output: # # real x(n), y(n), z(n): the coordinates of quadrature points. # # real w(n): the quadrature weights, which add to 1. # import numpy as np x = np.array ( [ \ 0.1912521437383576, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8087478562616424, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3543162299281049, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6456837700718951, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.0688708408852879, \ 0.9311291591147122, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.2166600941952480, \ 0.7833399058047521, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.9999999935557286, \ 0.0000000064442714, \ 0.0000000064442714, \ 0.9999999935557286, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9999999935557286, \ 0.0000000064442714, \ 0.0000000064442714, \ 0.9999999935557286, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.6731903387258514, \ 0.3268096612741486, \ 0.3268096612741486, \ 0.6731903387258514, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6731903387258514, \ 0.3268096612741486, \ 0.3268096612741486, \ 0.6731903387258514, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.1873892499846415, \ 0.8126107500153585, \ 0.8126107500153585, \ 0.1873892499846415, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1873892499846415, \ 0.8126107500153585, \ 0.8126107500153585, \ 0.1873892499846415, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.2917727295202502, \ 0.9026740712514576, \ 0.2917727295202502, \ 0.7082272704797498, \ 0.9026740712514576, \ 0.7082272704797498, \ 0.7082272704797498, \ 0.9026740712514576, \ 0.7082272704797498, \ 0.2917727295202502, \ 0.9026740712514576, \ 0.2917727295202502, \ 0.2917727295202502, \ 0.0973259287485423, \ 0.2917727295202502, \ 0.7082272704797498, \ 0.0973259287485423, \ 0.7082272704797498, \ 0.7082272704797498, \ 0.0973259287485423, \ 0.7082272704797498, \ 0.2917727295202502, \ 0.0973259287485423, \ 0.2917727295202502, \ 0.9869259796545771, \ 0.9372501994187228, \ 0.9869259796545771, \ 0.0130740203454229, \ 0.9372501994187228, \ 0.0130740203454229, \ 0.0130740203454229, \ 0.9372501994187228, \ 0.0130740203454229, \ 0.9869259796545771, \ 0.9372501994187228, \ 0.9869259796545771, \ 0.9869259796545771, \ 0.0627498005812772, \ 0.9869259796545771, \ 0.0130740203454229, \ 0.0627498005812772, \ 0.0130740203454229, \ 0.0130740203454229, \ 0.0627498005812772, \ 0.0130740203454229, \ 0.9869259796545771, \ 0.0627498005812772, \ 0.9869259796545771, \ 0.8645117252804405, \ 0.6225837716647646, \ 0.8645117252804405, \ 0.1354882747195595, \ 0.6225837716647646, \ 0.1354882747195595, \ 0.1354882747195595, \ 0.6225837716647646, \ 0.1354882747195595, \ 0.8645117252804405, \ 0.6225837716647646, \ 0.8645117252804405, \ 0.8645117252804405, \ 0.3774162283352354, \ 0.8645117252804405, \ 0.1354882747195595, \ 0.3774162283352354, \ 0.1354882747195595, \ 0.1354882747195595, \ 0.3774162283352354, \ 0.1354882747195595, \ 0.8645117252804405, \ 0.3774162283352354, \ 0.8645117252804405, \ 0.8248058551406905, \ 0.9220515632141263, \ 0.8248058551406905, \ 0.1751941448593096, \ 0.9220515632141263, \ 0.1751941448593096, \ 0.1751941448593096, \ 0.9220515632141263, \ 0.1751941448593096, \ 0.8248058551406905, \ 0.9220515632141263, \ 0.8248058551406905, \ 0.8248058551406905, \ 0.0779484367858737, \ 0.8248058551406905, \ 0.1751941448593096, \ 0.0779484367858737, \ 0.1751941448593096, \ 0.1751941448593096, \ 0.0779484367858737, \ 0.1751941448593096, \ 0.8248058551406905, \ 0.0779484367858737, \ 0.8248058551406905, \ 0.9459853758476011, \ 0.5650967942783419, \ 0.9459853758476011, \ 0.0540146241523989, \ 0.5650967942783419, \ 0.0540146241523989, \ 0.0540146241523989, \ 0.5650967942783419, \ 0.0540146241523989, \ 0.9459853758476011, \ 0.5650967942783419, \ 0.9459853758476011, \ 0.9459853758476011, \ 0.4349032057216580, \ 0.9459853758476011, \ 0.0540146241523989, \ 0.4349032057216580, \ 0.0540146241523989, \ 0.0540146241523989, \ 0.4349032057216580, \ 0.0540146241523989, \ 0.9459853758476011, \ 0.4349032057216580, \ 0.9459853758476011, \ 0.8916635718645309, \ 0.9766093536267083, \ 0.8916635718645309, \ 0.1083364281354691, \ 0.9766093536267083, \ 0.1083364281354691, \ 0.1083364281354691, \ 0.9766093536267083, \ 0.1083364281354691, \ 0.8916635718645309, \ 0.9766093536267083, \ 0.8916635718645309, \ 0.8916635718645309, \ 0.0233906463732917, \ 0.8916635718645309, \ 0.1083364281354691, \ 0.0233906463732917, \ 0.1083364281354691, \ 0.1083364281354691, \ 0.0233906463732917, \ 0.1083364281354691, \ 0.8916635718645309, \ 0.0233906463732917, \ 0.8916635718645309, \ 0.9849705936644424, \ 0.6355079664366210, \ 0.9849705936644424, \ 0.0150294063355575, \ 0.6355079664366210, \ 0.0150294063355575, \ 0.0150294063355575, \ 0.6355079664366210, \ 0.0150294063355575, \ 0.9849705936644424, \ 0.6355079664366210, \ 0.9849705936644424, \ 0.9849705936644424, \ 0.3644920335633790, \ 0.9849705936644424, \ 0.0150294063355575, \ 0.3644920335633790, \ 0.0150294063355575, \ 0.0150294063355575, \ 0.3644920335633790, \ 0.0150294063355575, \ 0.9849705936644424, \ 0.3644920335633790, \ 0.9849705936644424, \ 0.5860169886103869, \ 0.9923845018898745, \ 0.5860169886103869, \ 0.4139830113896131, \ 0.9923845018898745, \ 0.4139830113896131, \ 0.4139830113896131, \ 0.9923845018898745, \ 0.4139830113896131, \ 0.5860169886103869, \ 0.9923845018898745, \ 0.5860169886103869, \ 0.5860169886103869, \ 0.0076154981101255, \ 0.5860169886103869, \ 0.4139830113896131, \ 0.0076154981101255, \ 0.4139830113896131, \ 0.4139830113896131, \ 0.0076154981101255, \ 0.4139830113896131, \ 0.5860169886103869, \ 0.0076154981101255, \ 0.5860169886103869, \ 0.7690492963095925, \ 0.3896184326892077, \ 0.7690492963095925, \ 0.2309507036904074, \ 0.3896184326892077, \ 0.2309507036904074, \ 0.2309507036904074, \ 0.3896184326892077, \ 0.2309507036904074, \ 0.7690492963095925, \ 0.3896184326892077, \ 0.7690492963095925, \ 0.7690492963095925, \ 0.6103815673107923, \ 0.7690492963095925, \ 0.2309507036904074, \ 0.6103815673107923, \ 0.2309507036904074, \ 0.2309507036904074, \ 0.6103815673107923, \ 0.2309507036904074, \ 0.7690492963095925, \ 0.6103815673107923, \ 0.7690492963095925, \ 0.7768424517946938, \ 0.9994864489115713, \ 0.7768424517946938, \ 0.2231575482053062, \ 0.9994864489115713, \ 0.2231575482053062, \ 0.2231575482053062, \ 0.9994864489115713, \ 0.2231575482053062, \ 0.7768424517946938, \ 0.9994864489115713, \ 0.7768424517946938, \ 0.7768424517946938, \ 0.0005135510884287, \ 0.7768424517946938, \ 0.2231575482053062, \ 0.0005135510884287, \ 0.2231575482053062, \ 0.2231575482053062, \ 0.0005135510884287, \ 0.2231575482053062, \ 0.7768424517946938, \ 0.0005135510884287, \ 0.7768424517946938, \ 0.6117790069755276, \ 0.7209288728023533, \ 0.6117790069755276, \ 0.3882209930244724, \ 0.7209288728023533, \ 0.3882209930244724, \ 0.3882209930244724, \ 0.7209288728023533, \ 0.3882209930244724, \ 0.6117790069755276, \ 0.7209288728023533, \ 0.6117790069755276, \ 0.6117790069755276, \ 0.2790711271976467, \ 0.6117790069755276, \ 0.3882209930244724, \ 0.2790711271976467, \ 0.3882209930244724, \ 0.3882209930244724, \ 0.2790711271976467, \ 0.3882209930244724, \ 0.6117790069755276, \ 0.2790711271976467, \ 0.6117790069755276, \ 0.9350312907963207, \ 0.7494073604468848, \ 0.9350312907963207, \ 0.0649687092036792, \ 0.7494073604468848, \ 0.0649687092036792, \ 0.0649687092036792, \ 0.7494073604468848, \ 0.0649687092036792, \ 0.9350312907963207, \ 0.7494073604468848, \ 0.9350312907963207, \ 0.9350312907963207, \ 0.2505926395531152, \ 0.9350312907963207, \ 0.0649687092036792, \ 0.2505926395531152, \ 0.0649687092036792, \ 0.0649687092036792, \ 0.2505926395531152, \ 0.0649687092036792, \ 0.9350312907963207, \ 0.2505926395531152, \ 0.9350312907963207, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.9719926774632096, \ 0.6986057011288138, \ 0.9719926774632096, \ 0.6986057011288138, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.9719926774632096, \ 0.6986057011288138, \ 0.9719926774632096, \ 0.6986057011288138, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.0280073225367904, \ 0.6986057011288138, \ 0.0280073225367904, \ 0.6986057011288138, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.9719926774632096, \ 0.3013942988711862, \ 0.9719926774632096, \ 0.3013942988711862, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.0280073225367904, \ 0.6986057011288138, \ 0.0280073225367904, \ 0.6986057011288138, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.9719926774632096, \ 0.3013942988711862, \ 0.9719926774632096, \ 0.3013942988711862, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.0280073225367904, \ 0.3013942988711862, \ 0.0280073225367904, \ 0.3013942988711862, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.0280073225367904, \ 0.3013942988711862, \ 0.0280073225367904, \ 0.3013942988711862, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.9923118941018740, \ 0.8153563222457214, \ 0.9923118941018740, \ 0.8153563222457214, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.9923118941018740, \ 0.8153563222457214, \ 0.9923118941018740, \ 0.8153563222457214, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.0076881058981259, \ 0.8153563222457214, \ 0.0076881058981259, \ 0.8153563222457214, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.9923118941018740, \ 0.1846436777542786, \ 0.9923118941018740, \ 0.1846436777542786, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.0076881058981259, \ 0.8153563222457214, \ 0.0076881058981259, \ 0.8153563222457214, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.9923118941018740, \ 0.1846436777542786, \ 0.9923118941018740, \ 0.1846436777542786, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.0076881058981259, \ 0.1846436777542786, \ 0.0076881058981259, \ 0.1846436777542786, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.0076881058981259, \ 0.1846436777542786, \ 0.0076881058981259, \ 0.1846436777542786, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.5491142465864416, \ 0.9360994289291793, \ 0.5491142465864416, \ 0.9360994289291793, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.5491142465864416, \ 0.9360994289291793, \ 0.5491142465864416, \ 0.9360994289291793, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.4508857534135584, \ 0.9360994289291793, \ 0.4508857534135584, \ 0.9360994289291793, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.5491142465864416, \ 0.0639005710708208, \ 0.5491142465864416, \ 0.0639005710708208, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.4508857534135584, \ 0.9360994289291793, \ 0.4508857534135584, \ 0.9360994289291793, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.5491142465864416, \ 0.0639005710708208, \ 0.5491142465864416, \ 0.0639005710708208, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.4508857534135584, \ 0.0639005710708208, \ 0.4508857534135584, \ 0.0639005710708208, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.4508857534135584, \ 0.0639005710708208, \ 0.4508857534135584, \ 0.0639005710708208, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.6040696445748173, \ 0.7479204633014319, \ 0.6040696445748173, \ 0.7479204633014319, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.6040696445748173, \ 0.7479204633014319, \ 0.6040696445748173, \ 0.7479204633014319, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.3959303554251827, \ 0.7479204633014319, \ 0.3959303554251827, \ 0.7479204633014319, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.6040696445748173, \ 0.2520795366985681, \ 0.6040696445748173, \ 0.2520795366985681, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.3959303554251827, \ 0.7479204633014319, \ 0.3959303554251827, \ 0.7479204633014319, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.6040696445748173, \ 0.2520795366985681, \ 0.6040696445748173, \ 0.2520795366985681, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.3959303554251827, \ 0.2520795366985681, \ 0.3959303554251827, \ 0.2520795366985681, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.3959303554251827, \ 0.2520795366985681, \ 0.3959303554251827, \ 0.2520795366985681 ] ) y = np.array ( [ \ 0.5000000000000000, \ 0.1912521437383576, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8087478562616424, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3543162299281049, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6456837700718951, \ 0.5000000000000000, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.0688708408852879, \ 0.9311291591147122, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.2166600941952480, \ 0.7833399058047521, \ 0.9999999935557286, \ 0.0000000064442714, \ 0.0000000064442714, \ 0.9999999935557286, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9999999935557286, \ 0.0000000064442714, \ 0.0000000064442714, \ 0.9999999935557286, \ 0.6731903387258514, \ 0.3268096612741486, \ 0.3268096612741486, \ 0.6731903387258514, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6731903387258514, \ 0.3268096612741486, \ 0.3268096612741486, \ 0.6731903387258514, \ 0.1873892499846415, \ 0.8126107500153585, \ 0.8126107500153585, \ 0.1873892499846415, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1873892499846415, \ 0.8126107500153585, \ 0.8126107500153585, \ 0.1873892499846415, \ 0.9026740712514576, \ 0.2917727295202502, \ 0.2917727295202502, \ 0.9026740712514576, \ 0.7082272704797498, \ 0.2917727295202502, \ 0.9026740712514576, \ 0.7082272704797498, \ 0.7082272704797498, \ 0.9026740712514576, \ 0.2917727295202502, \ 0.7082272704797498, \ 0.0973259287485423, \ 0.2917727295202502, \ 0.2917727295202502, \ 0.0973259287485423, \ 0.7082272704797498, \ 0.2917727295202502, \ 0.0973259287485423, \ 0.7082272704797498, \ 0.7082272704797498, \ 0.0973259287485423, \ 0.2917727295202502, \ 0.7082272704797498, \ 0.9372501994187228, \ 0.9869259796545771, \ 0.9869259796545771, \ 0.9372501994187228, \ 0.0130740203454229, \ 0.9869259796545771, \ 0.9372501994187228, \ 0.0130740203454229, \ 0.0130740203454229, \ 0.9372501994187228, \ 0.9869259796545771, \ 0.0130740203454229, \ 0.0627498005812772, \ 0.9869259796545771, \ 0.9869259796545771, \ 0.0627498005812772, \ 0.0130740203454229, \ 0.9869259796545771, \ 0.0627498005812772, \ 0.0130740203454229, \ 0.0130740203454229, \ 0.0627498005812772, \ 0.9869259796545771, \ 0.0130740203454229, \ 0.6225837716647646, \ 0.8645117252804405, \ 0.8645117252804405, \ 0.6225837716647646, \ 0.1354882747195595, \ 0.8645117252804405, \ 0.6225837716647646, \ 0.1354882747195595, \ 0.1354882747195595, \ 0.6225837716647646, \ 0.8645117252804405, \ 0.1354882747195595, \ 0.3774162283352354, \ 0.8645117252804405, \ 0.8645117252804405, \ 0.3774162283352354, \ 0.1354882747195595, \ 0.8645117252804405, \ 0.3774162283352354, \ 0.1354882747195595, \ 0.1354882747195595, \ 0.3774162283352354, \ 0.8645117252804405, \ 0.1354882747195595, \ 0.9220515632141263, \ 0.8248058551406905, \ 0.8248058551406905, \ 0.9220515632141263, \ 0.1751941448593096, \ 0.8248058551406905, \ 0.9220515632141263, \ 0.1751941448593096, \ 0.1751941448593096, \ 0.9220515632141263, \ 0.8248058551406905, \ 0.1751941448593096, \ 0.0779484367858737, \ 0.8248058551406905, \ 0.8248058551406905, \ 0.0779484367858737, \ 0.1751941448593096, \ 0.8248058551406905, \ 0.0779484367858737, \ 0.1751941448593096, \ 0.1751941448593096, \ 0.0779484367858737, \ 0.8248058551406905, \ 0.1751941448593096, \ 0.5650967942783419, \ 0.9459853758476011, \ 0.9459853758476011, \ 0.5650967942783419, \ 0.0540146241523989, \ 0.9459853758476011, \ 0.5650967942783419, \ 0.0540146241523989, \ 0.0540146241523989, \ 0.5650967942783419, \ 0.9459853758476011, \ 0.0540146241523989, \ 0.4349032057216580, \ 0.9459853758476011, \ 0.9459853758476011, \ 0.4349032057216580, \ 0.0540146241523989, \ 0.9459853758476011, \ 0.4349032057216580, \ 0.0540146241523989, \ 0.0540146241523989, \ 0.4349032057216580, \ 0.9459853758476011, \ 0.0540146241523989, \ 0.9766093536267083, \ 0.8916635718645309, \ 0.8916635718645309, \ 0.9766093536267083, \ 0.1083364281354691, \ 0.8916635718645309, \ 0.9766093536267083, \ 0.1083364281354691, \ 0.1083364281354691, \ 0.9766093536267083, \ 0.8916635718645309, \ 0.1083364281354691, \ 0.0233906463732917, \ 0.8916635718645309, \ 0.8916635718645309, \ 0.0233906463732917, \ 0.1083364281354691, \ 0.8916635718645309, \ 0.0233906463732917, \ 0.1083364281354691, \ 0.1083364281354691, \ 0.0233906463732917, \ 0.8916635718645309, \ 0.1083364281354691, \ 0.6355079664366210, \ 0.9849705936644424, \ 0.9849705936644424, \ 0.6355079664366210, \ 0.0150294063355575, \ 0.9849705936644424, \ 0.6355079664366210, \ 0.0150294063355575, \ 0.0150294063355575, \ 0.6355079664366210, \ 0.9849705936644424, \ 0.0150294063355575, \ 0.3644920335633790, \ 0.9849705936644424, \ 0.9849705936644424, \ 0.3644920335633790, \ 0.0150294063355575, \ 0.9849705936644424, \ 0.3644920335633790, \ 0.0150294063355575, \ 0.0150294063355575, \ 0.3644920335633790, \ 0.9849705936644424, \ 0.0150294063355575, \ 0.9923845018898745, \ 0.5860169886103869, \ 0.5860169886103869, \ 0.9923845018898745, \ 0.4139830113896131, \ 0.5860169886103869, \ 0.9923845018898745, \ 0.4139830113896131, \ 0.4139830113896131, \ 0.9923845018898745, \ 0.5860169886103869, \ 0.4139830113896131, \ 0.0076154981101255, \ 0.5860169886103869, \ 0.5860169886103869, \ 0.0076154981101255, \ 0.4139830113896131, \ 0.5860169886103869, \ 0.0076154981101255, \ 0.4139830113896131, \ 0.4139830113896131, \ 0.0076154981101255, \ 0.5860169886103869, \ 0.4139830113896131, \ 0.3896184326892077, \ 0.7690492963095925, \ 0.7690492963095925, \ 0.3896184326892077, \ 0.2309507036904074, \ 0.7690492963095925, \ 0.3896184326892077, \ 0.2309507036904074, \ 0.2309507036904074, \ 0.3896184326892077, \ 0.7690492963095925, \ 0.2309507036904074, \ 0.6103815673107923, \ 0.7690492963095925, \ 0.7690492963095925, \ 0.6103815673107923, \ 0.2309507036904074, \ 0.7690492963095925, \ 0.6103815673107923, \ 0.2309507036904074, \ 0.2309507036904074, \ 0.6103815673107923, \ 0.7690492963095925, \ 0.2309507036904074, \ 0.9994864489115713, \ 0.7768424517946938, \ 0.7768424517946938, \ 0.9994864489115713, \ 0.2231575482053062, \ 0.7768424517946938, \ 0.9994864489115713, \ 0.2231575482053062, \ 0.2231575482053062, \ 0.9994864489115713, \ 0.7768424517946938, \ 0.2231575482053062, \ 0.0005135510884287, \ 0.7768424517946938, \ 0.7768424517946938, \ 0.0005135510884287, \ 0.2231575482053062, \ 0.7768424517946938, \ 0.0005135510884287, \ 0.2231575482053062, \ 0.2231575482053062, \ 0.0005135510884287, \ 0.7768424517946938, \ 0.2231575482053062, \ 0.7209288728023533, \ 0.6117790069755276, \ 0.6117790069755276, \ 0.7209288728023533, \ 0.3882209930244724, \ 0.6117790069755276, \ 0.7209288728023533, \ 0.3882209930244724, \ 0.3882209930244724, \ 0.7209288728023533, \ 0.6117790069755276, \ 0.3882209930244724, \ 0.2790711271976467, \ 0.6117790069755276, \ 0.6117790069755276, \ 0.2790711271976467, \ 0.3882209930244724, \ 0.6117790069755276, \ 0.2790711271976467, \ 0.3882209930244724, \ 0.3882209930244724, \ 0.2790711271976467, \ 0.6117790069755276, \ 0.3882209930244724, \ 0.7494073604468848, \ 0.9350312907963207, \ 0.9350312907963207, \ 0.7494073604468848, \ 0.0649687092036792, \ 0.9350312907963207, \ 0.7494073604468848, \ 0.0649687092036792, \ 0.0649687092036792, \ 0.7494073604468848, \ 0.9350312907963207, \ 0.0649687092036792, \ 0.2505926395531152, \ 0.9350312907963207, \ 0.9350312907963207, \ 0.2505926395531152, \ 0.0649687092036792, \ 0.9350312907963207, \ 0.2505926395531152, \ 0.0649687092036792, \ 0.0649687092036792, \ 0.2505926395531152, \ 0.9350312907963207, \ 0.0649687092036792, \ 0.9719926774632096, \ 0.6986057011288138, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.6986057011288138, \ 0.9719926774632096, \ 0.9719926774632096, \ 0.6986057011288138, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.6986057011288138, \ 0.9719926774632096, \ 0.0280073225367904, \ 0.6986057011288138, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.6986057011288138, \ 0.0280073225367904, \ 0.9719926774632096, \ 0.3013942988711862, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.3013942988711862, \ 0.9719926774632096, \ 0.0280073225367904, \ 0.6986057011288138, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.6986057011288138, \ 0.0280073225367904, \ 0.9719926774632096, \ 0.3013942988711862, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.3013942988711862, \ 0.9719926774632096, \ 0.0280073225367904, \ 0.3013942988711862, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.3013942988711862, \ 0.0280073225367904, \ 0.0280073225367904, \ 0.3013942988711862, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.3013942988711862, \ 0.0280073225367904, \ 0.9923118941018740, \ 0.8153563222457214, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.8153563222457214, \ 0.9923118941018740, \ 0.9923118941018740, \ 0.8153563222457214, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.8153563222457214, \ 0.9923118941018740, \ 0.0076881058981259, \ 0.8153563222457214, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.8153563222457214, \ 0.0076881058981259, \ 0.9923118941018740, \ 0.1846436777542786, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.1846436777542786, \ 0.9923118941018740, \ 0.0076881058981259, \ 0.8153563222457214, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.8153563222457214, \ 0.0076881058981259, \ 0.9923118941018740, \ 0.1846436777542786, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.1846436777542786, \ 0.9923118941018740, \ 0.0076881058981259, \ 0.1846436777542786, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.1846436777542786, \ 0.0076881058981259, \ 0.0076881058981259, \ 0.1846436777542786, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.1846436777542786, \ 0.0076881058981259, \ 0.5491142465864416, \ 0.9360994289291793, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.9360994289291793, \ 0.5491142465864416, \ 0.5491142465864416, \ 0.9360994289291793, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.9360994289291793, \ 0.5491142465864416, \ 0.4508857534135584, \ 0.9360994289291793, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.9360994289291793, \ 0.4508857534135584, \ 0.5491142465864416, \ 0.0639005710708208, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.0639005710708208, \ 0.5491142465864416, \ 0.4508857534135584, \ 0.9360994289291793, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.9360994289291793, \ 0.4508857534135584, \ 0.5491142465864416, \ 0.0639005710708208, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.0639005710708208, \ 0.5491142465864416, \ 0.4508857534135584, \ 0.0639005710708208, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.0639005710708208, \ 0.4508857534135584, \ 0.4508857534135584, \ 0.0639005710708208, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.0639005710708208, \ 0.4508857534135584, \ 0.6040696445748173, \ 0.7479204633014319, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.7479204633014319, \ 0.6040696445748173, \ 0.6040696445748173, \ 0.7479204633014319, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.7479204633014319, \ 0.6040696445748173, \ 0.3959303554251827, \ 0.7479204633014319, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.7479204633014319, \ 0.3959303554251827, \ 0.6040696445748173, \ 0.2520795366985681, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.2520795366985681, \ 0.6040696445748173, \ 0.3959303554251827, \ 0.7479204633014319, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.7479204633014319, \ 0.3959303554251827, \ 0.6040696445748173, \ 0.2520795366985681, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.2520795366985681, \ 0.6040696445748173, \ 0.3959303554251827, \ 0.2520795366985681, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.2520795366985681, \ 0.3959303554251827, \ 0.3959303554251827, \ 0.2520795366985681, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.2520795366985681, \ 0.3959303554251827 ] ) z = np.array ( [ \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1912521437383576, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.8087478562616424, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.3543162299281049, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6456837700718951, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.9311291591147122, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.9311291591147122, \ 0.0688708408852879, \ 0.0688708408852879, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.7833399058047521, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.7833399058047521, \ 0.2166600941952480, \ 0.2166600941952480, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9999999935557286, \ 0.0000000064442714, \ 0.0000000064442714, \ 0.9999999935557286, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.9999999935557286, \ 0.0000000064442714, \ 0.0000000064442714, \ 0.9999999935557286, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.8981144288438190, \ 0.1018855711561810, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6731903387258514, \ 0.3268096612741486, \ 0.3268096612741486, \ 0.6731903387258514, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.6731903387258514, \ 0.3268096612741486, \ 0.3268096612741486, \ 0.6731903387258514, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.8467830886160004, \ 0.1532169113839996, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1873892499846415, \ 0.8126107500153585, \ 0.8126107500153585, \ 0.1873892499846415, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.5000000000000000, \ 0.1873892499846415, \ 0.8126107500153585, \ 0.8126107500153585, \ 0.1873892499846415, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.9359181010210101, \ 0.0640818989789899, \ 0.2917727295202502, \ 0.2917727295202502, \ 0.9026740712514576, \ 0.2917727295202502, \ 0.2917727295202502, \ 0.9026740712514576, \ 0.7082272704797498, \ 0.7082272704797498, \ 0.9026740712514576, \ 0.7082272704797498, \ 0.7082272704797498, \ 0.9026740712514576, \ 0.2917727295202502, \ 0.2917727295202502, \ 0.0973259287485423, \ 0.2917727295202502, \ 0.2917727295202502, \ 0.0973259287485423, \ 0.7082272704797498, \ 0.7082272704797498, \ 0.0973259287485423, \ 0.7082272704797498, \ 0.7082272704797498, \ 0.0973259287485423, \ 0.9869259796545771, \ 0.9869259796545771, \ 0.9372501994187228, \ 0.9869259796545771, \ 0.9869259796545771, \ 0.9372501994187228, \ 0.0130740203454229, \ 0.0130740203454229, \ 0.9372501994187228, \ 0.0130740203454229, \ 0.0130740203454229, \ 0.9372501994187228, \ 0.9869259796545771, \ 0.9869259796545771, \ 0.0627498005812772, \ 0.9869259796545771, \ 0.9869259796545771, \ 0.0627498005812772, \ 0.0130740203454229, \ 0.0130740203454229, \ 0.0627498005812772, \ 0.0130740203454229, \ 0.0130740203454229, \ 0.0627498005812772, \ 0.8645117252804405, \ 0.8645117252804405, \ 0.6225837716647646, \ 0.8645117252804405, \ 0.8645117252804405, \ 0.6225837716647646, \ 0.1354882747195595, \ 0.1354882747195595, \ 0.6225837716647646, \ 0.1354882747195595, \ 0.1354882747195595, \ 0.6225837716647646, \ 0.8645117252804405, \ 0.8645117252804405, \ 0.3774162283352354, \ 0.8645117252804405, \ 0.8645117252804405, \ 0.3774162283352354, \ 0.1354882747195595, \ 0.1354882747195595, \ 0.3774162283352354, \ 0.1354882747195595, \ 0.1354882747195595, \ 0.3774162283352354, \ 0.8248058551406905, \ 0.8248058551406905, \ 0.9220515632141263, \ 0.8248058551406905, \ 0.8248058551406905, \ 0.9220515632141263, \ 0.1751941448593096, \ 0.1751941448593096, \ 0.9220515632141263, \ 0.1751941448593096, \ 0.1751941448593096, \ 0.9220515632141263, \ 0.8248058551406905, \ 0.8248058551406905, \ 0.0779484367858737, \ 0.8248058551406905, \ 0.8248058551406905, \ 0.0779484367858737, \ 0.1751941448593096, \ 0.1751941448593096, \ 0.0779484367858737, \ 0.1751941448593096, \ 0.1751941448593096, \ 0.0779484367858737, \ 0.9459853758476011, \ 0.9459853758476011, \ 0.5650967942783419, \ 0.9459853758476011, \ 0.9459853758476011, \ 0.5650967942783419, \ 0.0540146241523989, \ 0.0540146241523989, \ 0.5650967942783419, \ 0.0540146241523989, \ 0.0540146241523989, \ 0.5650967942783419, \ 0.9459853758476011, \ 0.9459853758476011, \ 0.4349032057216580, \ 0.9459853758476011, \ 0.9459853758476011, \ 0.4349032057216580, \ 0.0540146241523989, \ 0.0540146241523989, \ 0.4349032057216580, \ 0.0540146241523989, \ 0.0540146241523989, \ 0.4349032057216580, \ 0.8916635718645309, \ 0.8916635718645309, \ 0.9766093536267083, \ 0.8916635718645309, \ 0.8916635718645309, \ 0.9766093536267083, \ 0.1083364281354691, \ 0.1083364281354691, \ 0.9766093536267083, \ 0.1083364281354691, \ 0.1083364281354691, \ 0.9766093536267083, \ 0.8916635718645309, \ 0.8916635718645309, \ 0.0233906463732917, \ 0.8916635718645309, \ 0.8916635718645309, \ 0.0233906463732917, \ 0.1083364281354691, \ 0.1083364281354691, \ 0.0233906463732917, \ 0.1083364281354691, \ 0.1083364281354691, \ 0.0233906463732917, \ 0.9849705936644424, \ 0.9849705936644424, \ 0.6355079664366210, \ 0.9849705936644424, \ 0.9849705936644424, \ 0.6355079664366210, \ 0.0150294063355575, \ 0.0150294063355575, \ 0.6355079664366210, \ 0.0150294063355575, \ 0.0150294063355575, \ 0.6355079664366210, \ 0.9849705936644424, \ 0.9849705936644424, \ 0.3644920335633790, \ 0.9849705936644424, \ 0.9849705936644424, \ 0.3644920335633790, \ 0.0150294063355575, \ 0.0150294063355575, \ 0.3644920335633790, \ 0.0150294063355575, \ 0.0150294063355575, \ 0.3644920335633790, \ 0.5860169886103869, \ 0.5860169886103869, \ 0.9923845018898745, \ 0.5860169886103869, \ 0.5860169886103869, \ 0.9923845018898745, \ 0.4139830113896131, \ 0.4139830113896131, \ 0.9923845018898745, \ 0.4139830113896131, \ 0.4139830113896131, \ 0.9923845018898745, \ 0.5860169886103869, \ 0.5860169886103869, \ 0.0076154981101255, \ 0.5860169886103869, \ 0.5860169886103869, \ 0.0076154981101255, \ 0.4139830113896131, \ 0.4139830113896131, \ 0.0076154981101255, \ 0.4139830113896131, \ 0.4139830113896131, \ 0.0076154981101255, \ 0.7690492963095925, \ 0.7690492963095925, \ 0.3896184326892077, \ 0.7690492963095925, \ 0.7690492963095925, \ 0.3896184326892077, \ 0.2309507036904074, \ 0.2309507036904074, \ 0.3896184326892077, \ 0.2309507036904074, \ 0.2309507036904074, \ 0.3896184326892077, \ 0.7690492963095925, \ 0.7690492963095925, \ 0.6103815673107923, \ 0.7690492963095925, \ 0.7690492963095925, \ 0.6103815673107923, \ 0.2309507036904074, \ 0.2309507036904074, \ 0.6103815673107923, \ 0.2309507036904074, \ 0.2309507036904074, \ 0.6103815673107923, \ 0.7768424517946938, \ 0.7768424517946938, \ 0.9994864489115713, \ 0.7768424517946938, \ 0.7768424517946938, \ 0.9994864489115713, \ 0.2231575482053062, \ 0.2231575482053062, \ 0.9994864489115713, \ 0.2231575482053062, \ 0.2231575482053062, \ 0.9994864489115713, \ 0.7768424517946938, \ 0.7768424517946938, \ 0.0005135510884287, \ 0.7768424517946938, \ 0.7768424517946938, \ 0.0005135510884287, \ 0.2231575482053062, \ 0.2231575482053062, \ 0.0005135510884287, \ 0.2231575482053062, \ 0.2231575482053062, \ 0.0005135510884287, \ 0.6117790069755276, \ 0.6117790069755276, \ 0.7209288728023533, \ 0.6117790069755276, \ 0.6117790069755276, \ 0.7209288728023533, \ 0.3882209930244724, \ 0.3882209930244724, \ 0.7209288728023533, \ 0.3882209930244724, \ 0.3882209930244724, \ 0.7209288728023533, \ 0.6117790069755276, \ 0.6117790069755276, \ 0.2790711271976467, \ 0.6117790069755276, \ 0.6117790069755276, \ 0.2790711271976467, \ 0.3882209930244724, \ 0.3882209930244724, \ 0.2790711271976467, \ 0.3882209930244724, \ 0.3882209930244724, \ 0.2790711271976467, \ 0.9350312907963207, \ 0.9350312907963207, \ 0.7494073604468848, \ 0.9350312907963207, \ 0.9350312907963207, \ 0.7494073604468848, \ 0.0649687092036792, \ 0.0649687092036792, \ 0.7494073604468848, \ 0.0649687092036792, \ 0.0649687092036792, \ 0.7494073604468848, \ 0.9350312907963207, \ 0.9350312907963207, \ 0.2505926395531152, \ 0.9350312907963207, \ 0.9350312907963207, \ 0.2505926395531152, \ 0.0649687092036792, \ 0.0649687092036792, \ 0.2505926395531152, \ 0.0649687092036792, \ 0.0649687092036792, \ 0.2505926395531152, \ 0.6986057011288138, \ 0.9719926774632096, \ 0.6986057011288138, \ 0.9719926774632096, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.6986057011288138, \ 0.9719926774632096, \ 0.6986057011288138, \ 0.9719926774632096, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.6986057011288138, \ 0.0280073225367904, \ 0.6986057011288138, \ 0.0280073225367904, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.3013942988711862, \ 0.9719926774632096, \ 0.3013942988711862, \ 0.9719926774632096, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.6986057011288138, \ 0.0280073225367904, \ 0.6986057011288138, \ 0.0280073225367904, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.3013942988711862, \ 0.9719926774632096, \ 0.3013942988711862, \ 0.9719926774632096, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.3013942988711862, \ 0.0280073225367904, \ 0.3013942988711862, \ 0.0280073225367904, \ 0.8750719993006615, \ 0.8750719993006615, \ 0.3013942988711862, \ 0.0280073225367904, \ 0.3013942988711862, \ 0.0280073225367904, \ 0.1249280006993386, \ 0.1249280006993386, \ 0.8153563222457214, \ 0.9923118941018740, \ 0.8153563222457214, \ 0.9923118941018740, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.8153563222457214, \ 0.9923118941018740, \ 0.8153563222457214, \ 0.9923118941018740, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.8153563222457214, \ 0.0076881058981259, \ 0.8153563222457214, \ 0.0076881058981259, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.1846436777542786, \ 0.9923118941018740, \ 0.1846436777542786, \ 0.9923118941018740, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.8153563222457214, \ 0.0076881058981259, \ 0.8153563222457214, \ 0.0076881058981259, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.1846436777542786, \ 0.9923118941018740, \ 0.1846436777542786, \ 0.9923118941018740, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.1846436777542786, \ 0.0076881058981259, \ 0.1846436777542786, \ 0.0076881058981259, \ 0.9512929061479376, \ 0.9512929061479376, \ 0.1846436777542786, \ 0.0076881058981259, \ 0.1846436777542786, \ 0.0076881058981259, \ 0.0487070938520624, \ 0.0487070938520624, \ 0.9360994289291793, \ 0.5491142465864416, \ 0.9360994289291793, \ 0.5491142465864416, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.9360994289291793, \ 0.5491142465864416, \ 0.9360994289291793, \ 0.5491142465864416, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.9360994289291793, \ 0.4508857534135584, \ 0.9360994289291793, \ 0.4508857534135584, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.0639005710708208, \ 0.5491142465864416, \ 0.0639005710708208, \ 0.5491142465864416, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.9360994289291793, \ 0.4508857534135584, \ 0.9360994289291793, \ 0.4508857534135584, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.0639005710708208, \ 0.5491142465864416, \ 0.0639005710708208, \ 0.5491142465864416, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.0639005710708208, \ 0.4508857534135584, \ 0.0639005710708208, \ 0.4508857534135584, \ 0.6108897298239304, \ 0.6108897298239304, \ 0.0639005710708208, \ 0.4508857534135584, \ 0.0639005710708208, \ 0.4508857534135584, \ 0.3891102701760696, \ 0.3891102701760696, \ 0.7479204633014319, \ 0.6040696445748173, \ 0.7479204633014319, \ 0.6040696445748173, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.7479204633014319, \ 0.6040696445748173, \ 0.7479204633014319, \ 0.6040696445748173, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.7479204633014319, \ 0.3959303554251827, \ 0.7479204633014319, \ 0.3959303554251827, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.2520795366985681, \ 0.6040696445748173, \ 0.2520795366985681, \ 0.6040696445748173, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.7479204633014319, \ 0.3959303554251827, \ 0.7479204633014319, \ 0.3959303554251827, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.2520795366985681, \ 0.6040696445748173, \ 0.2520795366985681, \ 0.6040696445748173, \ 0.0215788718228733, \ 0.0215788718228733, \ 0.2520795366985681, \ 0.3959303554251827, \ 0.2520795366985681, \ 0.3959303554251827, \ 0.9784211281771267, \ 0.9784211281771267, \ 0.2520795366985681, \ 0.3959303554251827, \ 0.2520795366985681, \ 0.3959303554251827, \ 0.0215788718228733, \ 0.0215788718228733 ] ) w = np.array ( [ \ 0.0030079175616226, \ 0.0030079175616226, \ 0.0030079175616226, \ 0.0030079175616226, \ 0.0030079175616226, \ 0.0030079175616226, \ 0.0061575518559863, \ 0.0061575518559863, \ 0.0061575518559863, \ 0.0061575518559863, \ 0.0061575518559863, \ 0.0061575518559863, \ 0.0007451864938265, \ 0.0007451864938265, \ 0.0007451864938265, \ 0.0007451864938265, \ 0.0007451864938265, \ 0.0007451864938265, \ 0.0007451864938265, \ 0.0007451864938265, \ 0.0034736498758246, \ 0.0034736498758246, \ 0.0034736498758246, \ 0.0034736498758246, \ 0.0034736498758246, \ 0.0034736498758246, \ 0.0034736498758246, \ 0.0034736498758246, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0005231065457280, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0047212614224319, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0023372223737635, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0038417548985660, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0001507767719634, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0032140794095183, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0022454466226130, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0010413676731518, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0005920000965024, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0004100172337698, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0007465850926621, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0037432896839704, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0004534357504253, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0041828675781781, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0007389797381823, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0013712825533878, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0003675472168789, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0012580194835158, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946, \ 0.0015165655616946 ] ) return x, y, z, w def timestamp ( ): #*****************************************************************************80 # ## timestamp() prints the date as a timestamp. # # Licensing: # # This code is distributed under the MIT license. # # Modified: # # 21 August 2019 # # Author: # # John Burkardt # import time t = time.time ( ) print ( time.ctime ( t ) ) return if ( __name__ == '__main__' ): timestamp ( ) hexahedron_jaskowiec_rule_test ( ) timestamp ( )