# include # include # include # include # include # include "triangle_symq_rule.h" /******************************************************************************/ void comp_next ( int n, int k, int a[], int *more, int *h, int *t ) /******************************************************************************/ /* Purpose: 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 STATIC statement to maintain the variables H and T. I have decided (based on an wasting an entire morning trying to track down a problem) 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: 02 July 2008 Author: Original FORTRAN77 version by Albert Nijenhuis, Herbert Wilf. C version by 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. Parameters: Input, int N, the integer whose compositions are desired. Input, int K, the number of parts in the composition. Input/output, int A[K], the parts of the composition. Input/output, int *MORE. Set MORE = FALSE on first call. It will be reset to TRUE on return with a new composition. Each new call returns another composition until MORE is set to FALSE when the last composition has been computed and returned. Input/output, int *H, *T, two internal parameters needed for the computation. The user should allocate space for these in the calling program, include them in the calling sequence, but never alter them! */ { int i; if ( !( *more ) ) { *t = n; *h = 0; a[0] = n; for ( i = 1; i < k; i++ ) { a[i] = 0; } } else { if ( 1 < *t ) { *h = 0; } *h = *h + 1; *t = a[*h-1]; a[*h-1] = 0; a[0] = *t - 1; a[*h] = a[*h] + 1; } *more = ( a[k-1] != n ); return; } /******************************************************************************/ double *monomial_value ( int m, int n, int e[], double x[] ) /******************************************************************************/ /* Purpose: 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 is encountered is treated as 1.0. Licensing: This code is distributed under the MIT license. Modified: 17 August 2014 Author: John Burkardt Input: int M, the spatial dimension. int N, the number of evaluation points. int E[M], the exponents. double X[M*N], the point coordinates. Output: double MONOMIAL_VALUE[N], the monomial values. */ { int i; int j; double *v; v = ( double * ) malloc ( n * sizeof ( double ) ); for ( j = 0; j < n; j++ ) { v[j] = 1.0; } for ( i = 0; i < m; i++ ) { if ( 0 != e[i] ) { for ( j = 0; j < n; j++ ) { v[j] = v[j] * pow ( x[i+j*m], e[i] ); } } } return v; } /******************************************************************************/ void r8vec_copy ( int n, double a1[], double a2[] ) /******************************************************************************/ /* Purpose: r8vec_copy() copies an R8VEC. Discussion: An R8VEC is a vector of R8's. Licensing: This code is distributed under the MIT license. Modified: 03 July 2005 Author: John Burkardt Input: int N, the number of entries in the vectors. double A1[N], the vector to be copied. Output: double A2[N], the copy of A1. */ { int i; for ( i = 0; i < n; i++ ) { a2[i] = a1[i]; } return; } /******************************************************************************/ double r8vec_sum ( int n, double a[] ) /******************************************************************************/ /* Purpose: r8vec_sum() returns the sum of an R8VEC. Discussion: An R8VEC is a vector of R8's. Licensing: This code is distributed under the MIT license. Modified: 26 August 2008 Author: John Burkardt Input: int N, the number of entries in the vector. double A[N], the vector. Output: double R8VEC_SUM, the sum of the vector. */ { int i; double value; value = 0.0; for ( i = 0; i < n; i++ ) { value = value + a[i]; } return value; } /******************************************************************************/ int rule_order ( int p ) /******************************************************************************/ /* Purpose: rule_order() returns the number of points in the requested rule. Licensing: This code is distributed under the GNU GPL license. Modified: 11 June 2023 Author: Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas. This version by John Burkardt. Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int p: the precision of the quadrature rule. 0 <= p <= 50. Output: int rule_order: the number of nodes in the full rule. */ { int n; const int nnodes[51] = { 1, 1, 3, 6, 6, 7, 12, 15, 16, 19, 25, 28, 33, 37, 42, 49, 55, 60, 67, 73, 79, 87, 96, 103, 112, 120, 130, 141, 150, 159, 171, 181, 193, 204, 214, 228, 243, 252, 267, 282, 295, 309, 324, 339, 354, 370, 385, 399, 423, 435, 453 }; if ( 0 <= p && p <= 50 ) { n = nnodes[p]; } else { fprintf ( stderr, "\n" ); fprintf ( stderr, "rule_order(): Fatal error!\n" ); fprintf ( stderr, " Degree p must be between 0 and 50.\n" ); exit ( 1 ); } return n; } void rule00 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule00() returns the rule of precision 0. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3333333333333333 }; static double b_save[] = { 0.3333333333333334 }; static double c_save[] = { 0.3333333333333333 }; static double w_save[] = { 1.0000000000000000 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule01 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule01() returns the rule of precision 1. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3333333333333333 }; static double b_save[] = { 0.3333333333333334 }; static double c_save[] = { 0.3333333333333333 }; static double w_save[] = { 1.0000000000000000 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule02 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule02() returns the rule of precision 2. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1666666666666666, 0.6666666666666665, 0.1666666666666669 }; static double b_save[] = { 0.1666666666666668, 0.1666666666666667, 0.6666666666666667 }; static double c_save[] = { 0.6666666666666665, 0.1666666666666668, 0.1666666666666664 }; static double w_save[] = { 0.3333333333333333, 0.3333333333333333, 0.3333333333333333 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule03 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule03() returns the rule of precision 3. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4459484909159648, 0.4459484909159649, 0.1081030181680702, 0.0915762135097707, 0.8168475729804584, 0.0915762135097710 }; static double b_save[] = { 0.1081030181680703, 0.4459484909159649, 0.4459484909159651, 0.0915762135097709, 0.0915762135097707, 0.8168475729804585 }; static double c_save[] = { 0.4459484909159649, 0.1081030181680702, 0.4459484909159647, 0.8168475729804585, 0.0915762135097709, 0.0915762135097705 }; static double w_save[] = { 0.2233815896780115, 0.2233815896780115, 0.2233815896780115, 0.1099517436553219, 0.1099517436553219, 0.1099517436553219 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule04 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule04() returns the rule of precision 4. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4459484909159648, 0.4459484909159649, 0.1081030181680702, 0.0915762135097707, 0.8168475729804584, 0.0915762135097710 }; static double b_save[] = { 0.1081030181680703, 0.4459484909159649, 0.4459484909159651, 0.0915762135097709, 0.0915762135097707, 0.8168475729804585 }; static double c_save[] = { 0.4459484909159649, 0.1081030181680702, 0.4459484909159647, 0.8168475729804585, 0.0915762135097709, 0.0915762135097705 }; static double w_save[] = { 0.2233815896780115, 0.2233815896780115, 0.2233815896780115, 0.1099517436553219, 0.1099517436553219, 0.1099517436553219 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule05 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule05() returns the rule of precision 5. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1012865073234563, 0.7974269853530872, 0.1012865073234565, 0.4701420641051151, 0.4701420641051151, 0.0597158717897698, 0.3333333333333333 }; static double b_save[] = { 0.1012865073234565, 0.1012865073234562, 0.7974269853530874, 0.0597158717897699, 0.4701420641051151, 0.4701420641051153, 0.3333333333333334 }; static double c_save[] = { 0.7974269853530873, 0.1012865073234566, 0.1012865073234560, 0.4701420641051151, 0.0597158717897698, 0.4701420641051149, 0.3333333333333333 }; static double w_save[] = { 0.1259391805448272, 0.1259391805448272, 0.1259391805448272, 0.1323941527885062, 0.1323941527885062, 0.1323941527885062, 0.2250000000000000 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule06 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule06() returns the rule of precision 6. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.2194299825497829, 0.5611400349004340, 0.2194299825497830, 0.4801379641122150, 0.4801379641122151, 0.0397240717755699, 0.1416190159239681, 0.8390092597147910, 0.0193717243612410, 0.8390092597147911, 0.1416190159239681, 0.0193717243612406 }; static double b_save[] = { 0.2194299825497831, 0.2194299825497830, 0.5611400349004342, 0.0397240717755700, 0.4801379641122150, 0.4801379641122153, 0.0193717243612408, 0.1416190159239681, 0.8390092597147911, 0.0193717243612408, 0.8390092597147912, 0.1416190159239684 }; static double c_save[] = { 0.5611400349004340, 0.2194299825497831, 0.2194299825497829, 0.4801379641122150, 0.0397240717755699, 0.4801379641122148, 0.8390092597147911, 0.0193717243612409, 0.1416190159239679, 0.1416190159239681, 0.0193717243612407, 0.8390092597147910 }; static double w_save[] = { 0.1713331241529810, 0.1713331241529810, 0.1713331241529810, 0.0807310895930310, 0.0807310895930310, 0.0807310895930310, 0.0406345597936607, 0.0406345597936607, 0.0406345597936607, 0.0406345597936607, 0.0406345597936607, 0.0406345597936607 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule07 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule07() returns the rule of precision 7. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4731956536892510, 0.4731956536892510, 0.0536086926214978, 0.0577976400545063, 0.8844047198909870, 0.0577976400545066, 0.2593390118657857, 0.6936897820041288, 0.0469712061300856, 0.6936897820041288, 0.2593390118657857, 0.0469712061300854, 0.2416636063972473, 0.5166727872055051, 0.2416636063972475 }; static double b_save[] = { 0.0536086926214979, 0.4731956536892511, 0.4731956536892513, 0.0577976400545066, 0.0577976400545063, 0.8844047198909872, 0.0469712061300856, 0.2593390118657857, 0.6936897820041289, 0.0469712061300856, 0.6936897820041289, 0.2593390118657859, 0.2416636063972475, 0.2416636063972474, 0.5166727872055052 }; static double c_save[] = { 0.4731956536892511, 0.0536086926214979, 0.4731956536892509, 0.8844047198909871, 0.0577976400545067, 0.0577976400545062, 0.6936897820041288, 0.0469712061300855, 0.2593390118657856, 0.2593390118657857, 0.0469712061300854, 0.6936897820041287, 0.5166727872055050, 0.2416636063972475, 0.2416636063972473 }; static double w_save[] = { 0.0531808332967605, 0.0531808332967605, 0.0531808332967605, 0.0409181703940569, 0.0409181703940569, 0.0409181703940569, 0.0557545405406911, 0.0557545405406911, 0.0557545405406911, 0.0557545405406911, 0.0557545405406911, 0.0557545405406911, 0.1277252485611338, 0.1277252485611338, 0.1277252485611338 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule08 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule08() returns the rule of precision 8. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1705693077517601, 0.6588613844964795, 0.1705693077517604, 0.4592925882927231, 0.4592925882927231, 0.0814148234145537, 0.3333333333333333, 0.0505472283170309, 0.8989055433659379, 0.0505472283170313, 0.2631128296346381, 0.7284923929554042, 0.0083947774099577, 0.7284923929554042, 0.2631128296346381, 0.0083947774099575 }; static double b_save[] = { 0.1705693077517604, 0.1705693077517602, 0.6588613844964796, 0.0814148234145537, 0.4592925882927232, 0.4592925882927233, 0.3333333333333334, 0.0505472283170312, 0.0505472283170309, 0.8989055433659381, 0.0083947774099577, 0.2631128296346381, 0.7284923929554045, 0.0083947774099577, 0.7284923929554044, 0.2631128296346383 }; static double c_save[] = { 0.6588613844964796, 0.1705693077517604, 0.1705693077517599, 0.4592925882927231, 0.0814148234145537, 0.4592925882927231, 0.3333333333333333, 0.8989055433659380, 0.0505472283170313, 0.0505472283170306, 0.7284923929554042, 0.0083947774099577, 0.2631128296346378, 0.2631128296346381, 0.0083947774099575, 0.7284923929554041 }; static double w_save[] = { 0.1032173705347182, 0.1032173705347182, 0.1032173705347182, 0.0950916342672846, 0.0950916342672846, 0.0950916342672846, 0.1443156076777872, 0.0324584976231981, 0.0324584976231981, 0.0324584976231981, 0.0272303141744350, 0.0272303141744350, 0.0272303141744350, 0.0272303141744350, 0.0272303141744350, 0.0272303141744350 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule09 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule09() returns the rule of precision 9. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4896825191987376, 0.4896825191987376, 0.0206349616025247, 0.3333333333333333, 0.1882035356190326, 0.6235929287619344, 0.1882035356190329, 0.2219629891607657, 0.7411985987844980, 0.0368384120547364, 0.7411985987844980, 0.2219629891607658, 0.0368384120547361, 0.4370895914929366, 0.4370895914929366, 0.1258208170141267, 0.0447295133944526, 0.9105409732110945, 0.0447295133944530 }; static double b_save[] = { 0.0206349616025248, 0.4896825191987377, 0.4896825191987378, 0.3333333333333334, 0.1882035356190329, 0.1882035356190327, 0.6235929287619346, 0.0368384120547363, 0.2219629891607657, 0.7411985987844981, 0.0368384120547363, 0.7411985987844981, 0.2219629891607660, 0.1258208170141268, 0.4370895914929367, 0.4370895914929368, 0.0447295133944529, 0.0447295133944525, 0.9105409732110946 }; static double c_save[] = { 0.4896825191987376, 0.0206349616025246, 0.4896825191987374, 0.3333333333333333, 0.6235929287619345, 0.1882035356190329, 0.1882035356190325, 0.7411985987844980, 0.0368384120547363, 0.2219629891607655, 0.2219629891607657, 0.0368384120547361, 0.7411985987844979, 0.4370895914929366, 0.1258208170141267, 0.4370895914929366, 0.9105409732110946, 0.0447295133944530, 0.0447295133944524 }; static double w_save[] = { 0.0313347002271391, 0.0313347002271391, 0.0313347002271391, 0.0971357962827989, 0.0796477389272103, 0.0796477389272103, 0.0796477389272103, 0.0432835393772894, 0.0432835393772894, 0.0432835393772894, 0.0432835393772894, 0.0432835393772894, 0.0432835393772894, 0.0778275410047743, 0.0778275410047743, 0.0778275410047743, 0.0255776756586980, 0.0255776756586980, 0.0255776756586980 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule10 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule10() returns the rule of precision 10. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4951734598011704, 0.4951734598011704, 0.0096530803976590, 0.0191394152428411, 0.9617211695143175, 0.0191394152428416, 0.1337347551008691, 0.8315416244168033, 0.0347236204823275, 0.8315416244168033, 0.1337347551008692, 0.0347236204823273, 0.3333333333333333, 0.3266931362813369, 0.6357241363774715, 0.0375827273411917, 0.6357241363774714, 0.3266931362813369, 0.0375827273411916, 0.1844850126852464, 0.6310299746295069, 0.1844850126852466, 0.4282348209437188, 0.4282348209437188, 0.1435303581125623 }; static double b_save[] = { 0.0096530803976591, 0.4951734598011706, 0.4951734598011707, 0.0191394152428414, 0.0191394152428411, 0.9617211695143175, 0.0347236204823275, 0.1337347551008691, 0.8315416244168037, 0.0347236204823275, 0.8315416244168035, 0.1337347551008694, 0.3333333333333334, 0.0375827273411917, 0.3266931362813369, 0.6357241363774715, 0.0375827273411917, 0.6357241363774715, 0.3266931362813372, 0.1844850126852466, 0.1844850126852465, 0.6310299746295072, 0.1435303581125623, 0.4282348209437189, 0.4282348209437190 }; static double c_save[] = { 0.4951734598011705, 0.0096530803976590, 0.4951734598011703, 0.9617211695143174, 0.0191394152428414, 0.0191394152428409, 0.8315416244168033, 0.0347236204823275, 0.1337347551008689, 0.1337347551008692, 0.0347236204823274, 0.8315416244168033, 0.3333333333333333, 0.6357241363774714, 0.0375827273411916, 0.3266931362813368, 0.3266931362813369, 0.0375827273411916, 0.6357241363774713, 0.6310299746295069, 0.1844850126852466, 0.1844850126852462, 0.4282348209437189, 0.1435303581125623, 0.4282348209437188 }; static double w_save[] = { 0.0097925904984183, 0.0097925904984183, 0.0097925904984183, 0.0063853592301187, 0.0063853592301187, 0.0063853592301187, 0.0289622814632563, 0.0289622814632563, 0.0289622814632563, 0.0289622814632563, 0.0289622814632563, 0.0289622814632563, 0.0836148743739739, 0.0387390490860189, 0.0387390490860189, 0.0387390490860189, 0.0387390490860189, 0.0387390490860189, 0.0387390490860189, 0.0786337697463773, 0.0786337697463773, 0.0786337697463773, 0.0752473279685440, 0.0752473279685440, 0.0752473279685440 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule11 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule11() returns the rule of precision 11. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.0308468956355879, 0.9383062087288239, 0.0308468956355883, 0.4987801651784607, 0.4987801651784607, 0.0024396696430784, 0.1593036198376935, 0.8263297175927509, 0.0143666625695557, 0.8263297175927509, 0.1593036198376935, 0.0143666625695554, 0.3333333333333333, 0.1132078272866939, 0.7735843454266120, 0.1132078272866941, 0.4366550163931761, 0.4366550163931761, 0.1266899672136477, 0.2144834586192693, 0.5710330827614613, 0.2144834586192694, 0.3106312163134631, 0.6417047167143861, 0.0476640669721508, 0.6417047167143860, 0.3106312163134631, 0.0476640669721507 }; static double b_save[] = { 0.0308468956355882, 0.0308468956355879, 0.9383062087288241, 0.0024396696430785, 0.4987801651784608, 0.4987801651784610, 0.0143666625695556, 0.1593036198376935, 0.8263297175927511, 0.0143666625695556, 0.8263297175927511, 0.1593036198376938, 0.3333333333333334, 0.1132078272866941, 0.1132078272866939, 0.7735843454266123, 0.1266899672136478, 0.4366550163931761, 0.4366550163931763, 0.2144834586192694, 0.2144834586192693, 0.5710330827614615, 0.0476640669721508, 0.3106312163134631, 0.6417047167143863, 0.0476640669721508, 0.6417047167143861, 0.3106312163134634 }; static double c_save[] = { 0.9383062087288240, 0.0308468956355883, 0.0308468956355876, 0.4987801651784608, 0.0024396696430785, 0.4987801651784606, 0.8263297175927509, 0.0143666625695556, 0.1593036198376933, 0.1593036198376935, 0.0143666625695554, 0.8263297175927509, 0.3333333333333333, 0.7735843454266120, 0.1132078272866941, 0.1132078272866937, 0.4366550163931761, 0.1266899672136478, 0.4366550163931761, 0.5710330827614614, 0.2144834586192694, 0.2144834586192691, 0.6417047167143861, 0.0476640669721508, 0.3106312163134629, 0.3106312163134632, 0.0476640669721508, 0.6417047167143859 }; static double w_save[] = { 0.0122492969507080, 0.0122492969507080, 0.0122492969507080, 0.0124654918738814, 0.0124654918738814, 0.0124654918738814, 0.0145576233378092, 0.0145576233378092, 0.0145576233378092, 0.0145576233378092, 0.0145576233378092, 0.0145576233378092, 0.0814451347093513, 0.0401292423813083, 0.0401292423813083, 0.0401292423813083, 0.0630948721598987, 0.0630948721598987, 0.0630948721598987, 0.0678451077436951, 0.0678451077436951, 0.0678451077436951, 0.0406428486558865, 0.0406428486558865, 0.0406428486558865, 0.0406428486558865, 0.0406428486558865, 0.0406428486558865 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule12 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule12() returns the rule of precision 12. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.2714625070149260, 0.4570749859701477, 0.2714625070149261, 0.1092578276593542, 0.7814843446812912, 0.1092578276593545, 0.4401116486585931, 0.4401116486585931, 0.1197767026828138, 0.2554542286385173, 0.6282497516835561, 0.1162960196779266, 0.6282497516835561, 0.2554542286385174, 0.1162960196779265, 0.1272797172335894, 0.8513377925102400, 0.0213824902561707, 0.8513377925102400, 0.1272797172335894, 0.0213824902561704, 0.2916556797383409, 0.6853101639063919, 0.0230341563552672, 0.6853101639063919, 0.2916556797383410, 0.0230341563552670, 0.4882037509455415, 0.4882037509455415, 0.0235924981089169, 0.0246463634363355, 0.9507072731273287, 0.0246463634363359 }; static double b_save[] = { 0.2714625070149262, 0.2714625070149261, 0.4570749859701479, 0.1092578276593545, 0.1092578276593542, 0.7814843446812915, 0.1197767026828138, 0.4401116486585931, 0.4401116486585933, 0.1162960196779266, 0.2554542286385174, 0.6282497516835562, 0.1162960196779266, 0.6282497516835562, 0.2554542286385176, 0.0213824902561706, 0.1272797172335893, 0.8513377925102402, 0.0213824902561706, 0.8513377925102402, 0.1272797172335897, 0.0230341563552672, 0.2916556797383410, 0.6853101639063921, 0.0230341563552672, 0.6853101639063920, 0.2916556797383412, 0.0235924981089169, 0.4882037509455416, 0.4882037509455417, 0.0246463634363358, 0.0246463634363355, 0.9507072731273288 }; static double c_save[] = { 0.4570749859701478, 0.2714625070149261, 0.2714625070149260, 0.7814843446812914, 0.1092578276593545, 0.1092578276593540, 0.4401116486585931, 0.1197767026828138, 0.4401116486585929, 0.6282497516835560, 0.1162960196779265, 0.2554542286385172, 0.2554542286385172, 0.1162960196779265, 0.6282497516835559, 0.8513377925102400, 0.0213824902561707, 0.1272797172335890, 0.1272797172335894, 0.0213824902561704, 0.8513377925102400, 0.6853101639063919, 0.0230341563552671, 0.2916556797383407, 0.2916556797383409, 0.0230341563552671, 0.6853101639063917, 0.4882037509455416, 0.0235924981089169, 0.4882037509455414, 0.9507072731273288, 0.0246463634363358, 0.0246463634363353 }; static double w_save[] = { 0.0625412131959027, 0.0625412131959027, 0.0625412131959027, 0.0284860520688775, 0.0284860520688775, 0.0284860520688775, 0.0499183349280609, 0.0499183349280609, 0.0499183349280609, 0.0432273636594142, 0.0432273636594142, 0.0432273636594142, 0.0432273636594142, 0.0432273636594142, 0.0432273636594142, 0.0150836775765114, 0.0150836775765114, 0.0150836775765114, 0.0150836775765114, 0.0150836775765114, 0.0150836775765114, 0.0217835850386075, 0.0217835850386075, 0.0217835850386075, 0.0217835850386075, 0.0217835850386075, 0.0217835850386075, 0.0242668380814520, 0.0242668380814520, 0.0242668380814520, 0.0079316425099736, 0.0079316425099736, 0.0079316425099736 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule13 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule13() returns the rule of precision 13. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4961358947410461, 0.4961358947410460, 0.0077282105179078, 0.4696086896534919, 0.4696086896534918, 0.0607826206930162, 0.2311102849490822, 0.5377794301018355, 0.2311102849490823, 0.2920786885766364, 0.6889333070396045, 0.0189880043837591, 0.6889333070396045, 0.2920786885766364, 0.0189880043837589, 0.3333333333333333, 0.2667452533103511, 0.6355187156236324, 0.0977360310660165, 0.6355187156236323, 0.2667452533103513, 0.0977360310660164, 0.4144775702790545, 0.4144775702790545, 0.1710448594418908, 0.1135599125721331, 0.7728801748557336, 0.1135599125721334, 0.1267997757838373, 0.8512338800096334, 0.0219663442065294, 0.8512338800096334, 0.1267997757838374, 0.0219663442065290, 0.0248959314912162, 0.9502081370175671, 0.0248959314912167 }; static double b_save[] = { 0.0077282105179079, 0.4961358947410461, 0.4961358947410462, 0.0607826206930162, 0.4696086896534920, 0.4696086896534921, 0.2311102849490824, 0.2311102849490823, 0.5377794301018356, 0.0189880043837590, 0.2920786885766364, 0.6889333070396048, 0.0189880043837590, 0.6889333070396046, 0.2920786885766367, 0.3333333333333334, 0.0977360310660166, 0.2667452533103512, 0.6355187156236326, 0.0977360310660166, 0.6355187156236323, 0.2667452533103514, 0.1710448594418909, 0.4144775702790546, 0.4144775702790547, 0.1135599125721333, 0.1135599125721331, 0.7728801748557337, 0.0219663442065293, 0.1267997757838373, 0.8512338800096335, 0.0219663442065293, 0.8512338800096335, 0.1267997757838377, 0.0248959314912165, 0.0248959314912162, 0.9502081370175673 }; static double c_save[] = { 0.4961358947410460, 0.0077282105179078, 0.4961358947410459, 0.4696086896534919, 0.0607826206930161, 0.4696086896534917, 0.5377794301018354, 0.2311102849490823, 0.2311102849490821, 0.6889333070396045, 0.0189880043837590, 0.2920786885766361, 0.2920786885766364, 0.0189880043837589, 0.6889333070396044, 0.3333333333333333, 0.6355187156236323, 0.0977360310660164, 0.2667452533103509, 0.2667452533103511, 0.0977360310660164, 0.6355187156236322, 0.4144775702790546, 0.1710448594418909, 0.4144775702790545, 0.7728801748557337, 0.1135599125721334, 0.1135599125721329, 0.8512338800096335, 0.0219663442065293, 0.1267997757838371, 0.1267997757838373, 0.0219663442065291, 0.8512338800096333, 0.9502081370175672, 0.0248959314912166, 0.0248959314912159 }; static double w_save[] = { 0.0099414763610726, 0.0099414763610726, 0.0099414763610726, 0.0327812416037230, 0.0327812416037230, 0.0327812416037230, 0.0460624095927782, 0.0460624095927782, 0.0460624095927782, 0.0181254986462009, 0.0181254986462009, 0.0181254986462009, 0.0181254986462009, 0.0181254986462009, 0.0181254986462009, 0.0516226466642908, 0.0372119604572615, 0.0372119604572615, 0.0372119604572615, 0.0372119604572615, 0.0372119604572615, 0.0372119604572615, 0.0469470955421552, 0.0469470955421552, 0.0469470955421552, 0.0309030979757598, 0.0309030979757598, 0.0309030979757598, 0.0153930726837822, 0.0153930726837822, 0.0153930726837822, 0.0153930726837822, 0.0153930726837822, 0.0153930726837822, 0.0080293997952584, 0.0080293997952584, 0.0080293997952584 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule14 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule14() returns the rule of precision 14. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4176447193404539, 0.4176447193404539, 0.1647105613190921, 0.2983728821362577, 0.6869801678080878, 0.0146469500556545, 0.6869801678080878, 0.2983728821362577, 0.0146469500556543, 0.0617998830908725, 0.8764002338182547, 0.0617998830908729, 0.3368614597963450, 0.5702222908466831, 0.0929162493569718, 0.5702222908466831, 0.3368614597963450, 0.0929162493569718, 0.2734775283088386, 0.4530449433823227, 0.2734775283088388, 0.1772055324125434, 0.6455889351749130, 0.1772055324125437, 0.0193909612487009, 0.9612180775025979, 0.0193909612487014, 0.4889639103621786, 0.4889639103621787, 0.0220721792756427, 0.1722666878213555, 0.7706085547749963, 0.0571247574036480, 0.7706085547749965, 0.1722666878213556, 0.0571247574036478, 0.1189744976969568, 0.8797571713701711, 0.0012683309328722, 0.8797571713701712, 0.1189744976969569, 0.0012683309328719 }; static double b_save[] = { 0.1647105613190922, 0.4176447193404541, 0.4176447193404541, 0.0146469500556545, 0.2983728821362578, 0.6869801678080880, 0.0146469500556545, 0.6869801678080880, 0.2983728821362580, 0.0617998830908728, 0.0617998830908724, 0.8764002338182548, 0.0929162493569719, 0.3368614597963451, 0.5702222908466833, 0.0929162493569719, 0.5702222908466833, 0.3368614597963452, 0.2734775283088388, 0.2734775283088387, 0.4530449433823228, 0.1772055324125436, 0.1772055324125434, 0.6455889351749131, 0.0193909612487012, 0.0193909612487009, 0.9612180775025979, 0.0220721792756428, 0.4889639103621786, 0.4889639103621788, 0.0571247574036480, 0.1722666878213556, 0.7706085547749967, 0.0571247574036480, 0.7706085547749966, 0.1722666878213558, 0.0012683309328721, 0.1189744976969568, 0.8797571713701712, 0.0012683309328721, 0.8797571713701712, 0.1189744976969572 }; static double c_save[] = { 0.4176447193404539, 0.1647105613190921, 0.4176447193404539, 0.6869801678080878, 0.0146469500556544, 0.2983728821362575, 0.2983728821362577, 0.0146469500556543, 0.6869801678080877, 0.8764002338182547, 0.0617998830908728, 0.0617998830908723, 0.5702222908466831, 0.0929162493569718, 0.3368614597963449, 0.3368614597963450, 0.0929162493569716, 0.5702222908466831, 0.4530449433823226, 0.2734775283088386, 0.2734775283088385, 0.6455889351749130, 0.1772055324125436, 0.1772055324125432, 0.9612180775025979, 0.0193909612487012, 0.0193909612487008, 0.4889639103621786, 0.0220721792756427, 0.4889639103621784, 0.7706085547749965, 0.0571247574036481, 0.1722666878213553, 0.1722666878213555, 0.0571247574036479, 0.7706085547749963, 0.8797571713701712, 0.0012683309328721, 0.1189744976969566, 0.1189744976969567, 0.0012683309328719, 0.8797571713701708 }; static double w_save[] = { 0.0327883535441254, 0.0327883535441254, 0.0327883535441254, 0.0144363081135338, 0.0144363081135338, 0.0144363081135338, 0.0144363081135338, 0.0144363081135338, 0.0144363081135338, 0.0144336996697767, 0.0144336996697767, 0.0144336996697767, 0.0385715107870607, 0.0385715107870607, 0.0385715107870607, 0.0385715107870607, 0.0385715107870607, 0.0385715107870607, 0.0517741045072916, 0.0517741045072916, 0.0517741045072916, 0.0421625887369930, 0.0421625887369930, 0.0421625887369930, 0.0049234036024001, 0.0049234036024001, 0.0049234036024001, 0.0218835813694289, 0.0218835813694289, 0.0218835813694289, 0.0246657532125637, 0.0246657532125637, 0.0246657532125637, 0.0246657532125637, 0.0246657532125637, 0.0246657532125637, 0.0050102288385007, 0.0050102288385007, 0.0050102288385007, 0.0050102288385007, 0.0050102288385007, 0.0050102288385007 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule15 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule15() returns the rule of precision 15. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1299782299330778, 0.7400435401338442, 0.1299782299330779, 0.3333333333333333, 0.4600769492970597, 0.4600769492970597, 0.0798461014058805, 0.1823217834071913, 0.7330839951106168, 0.0845942214821919, 0.7330839951106169, 0.1823217834071914, 0.0845942214821916, 0.1502003840652387, 0.8337725261484157, 0.0160270897863456, 0.8337725261484158, 0.1502003840652388, 0.0160270897863453, 0.3231113151637127, 0.5792382424060449, 0.0976504424302423, 0.5792382424060449, 0.3231113151637127, 0.0976504424302423, 0.4916858166302972, 0.4916858166302972, 0.0166283667394055, 0.2215323407951419, 0.5569353184097160, 0.2215323407951421, 0.3969337374090606, 0.3969337374090606, 0.2061325251818788, 0.3079476814836729, 0.6735980666116939, 0.0184542519046332, 0.6735980666116940, 0.3079476814836729, 0.0184542519046331, 0.0563419176961000, 0.8873161646077997, 0.0563419176961004, 0.0380352293011093, 0.9608512354248769, 0.0011135352740139, 0.9608512354248770, 0.0380352293011093, 0.0011135352740135 }; static double b_save[] = { 0.1299782299330780, 0.1299782299330778, 0.7400435401338445, 0.3333333333333334, 0.0798461014058806, 0.4600769492970598, 0.4600769492970599, 0.0845942214821918, 0.1823217834071913, 0.7330839951106169, 0.0845942214821918, 0.7330839951106171, 0.1823217834071916, 0.0160270897863455, 0.1502003840652387, 0.8337725261484159, 0.0160270897863455, 0.8337725261484159, 0.1502003840652391, 0.0976504424302424, 0.3231113151637127, 0.5792382424060452, 0.0976504424302424, 0.5792382424060450, 0.3231113151637129, 0.0166283667394056, 0.4916858166302973, 0.4916858166302975, 0.2215323407951421, 0.2215323407951420, 0.5569353184097161, 0.2061325251818789, 0.3969337374090606, 0.3969337374090607, 0.0184542519046332, 0.3079476814836729, 0.6735980666116942, 0.0184542519046332, 0.6735980666116941, 0.3079476814836731, 0.0563419176961003, 0.0563419176960999, 0.8873161646077998, 0.0011135352740137, 0.0380352293011093, 0.9608512354248772, 0.0011135352740137, 0.9608512354248772, 0.0380352293011096 }; static double c_save[] = { 0.7400435401338443, 0.1299782299330780, 0.1299782299330775, 0.3333333333333333, 0.4600769492970597, 0.0798461014058806, 0.4600769492970595, 0.7330839951106168, 0.0845942214821918, 0.1823217834071911, 0.1823217834071912, 0.0845942214821916, 0.7330839951106169, 0.8337725261484158, 0.0160270897863456, 0.1502003840652385, 0.1502003840652387, 0.0160270897863453, 0.8337725261484157, 0.5792382424060450, 0.0976504424302423, 0.3231113151637125, 0.3231113151637127, 0.0976504424302423, 0.5792382424060449, 0.4916858166302972, 0.0166283667394055, 0.4916858166302970, 0.5569353184097159, 0.2215323407951420, 0.2215323407951418, 0.3969337374090605, 0.2061325251818788, 0.3969337374090605, 0.6735980666116940, 0.0184542519046332, 0.3079476814836727, 0.3079476814836729, 0.0184542519046330, 0.6735980666116937, 0.8873161646077997, 0.0563419176961003, 0.0563419176960998, 0.9608512354248770, 0.0011135352740138, 0.0380352293011089, 0.0380352293011092, 0.0011135352740136, 0.9608512354248769 }; static double w_save[] = { 0.0073975040670461, 0.0073975040670461, 0.0073975040670461, 0.0297304197480713, 0.0215940879364384, 0.0215940879364384, 0.0215940879364384, 0.0242300087831256, 0.0242300087831256, 0.0242300087831256, 0.0242300087831256, 0.0242300087831256, 0.0242300087831256, 0.0112285042988781, 0.0112285042988781, 0.0112285042988781, 0.0112285042988781, 0.0112285042988781, 0.0112285042988781, 0.0310752204705109, 0.0310752204705109, 0.0310752204705109, 0.0310752204705109, 0.0310752204705109, 0.0310752204705109, 0.0158322763500218, 0.0158322763500218, 0.0158322763500218, 0.0462872861051981, 0.0462872861051981, 0.0462872861051981, 0.0463360413912072, 0.0463360413912072, 0.0463360413912072, 0.0164367620928279, 0.0164367620928279, 0.0164367620928279, 0.0164367620928279, 0.0164367620928279, 0.0164367620928279, 0.0150844742475971, 0.0150844742475971, 0.0150844742475971, 0.0024752660145579, 0.0024752660145579, 0.0024752660145579, 0.0024752660145579, 0.0024752660145579, 0.0024752660145579 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule16 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule16() returns the rule of precision 16. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4137694858270852, 0.5765655597692547, 0.0096649544036603, 0.5765655597692546, 0.4137694858270852, 0.0096649544036602, 0.3041794482294797, 0.6655146084153339, 0.0303059433551864, 0.6655146084153339, 0.3041794482294798, 0.0303059433551863, 0.0666744722402382, 0.8666510555195234, 0.0666744722402385, 0.0896090890227058, 0.8995779382011904, 0.0108129727761038, 0.8995779382011904, 0.0896090890227059, 0.0108129727761035, 0.2966153724003829, 0.5967314670634685, 0.1066531605361485, 0.5967314670634686, 0.2966153724003830, 0.1066531605361483, 0.2413216807013783, 0.5173566385972432, 0.2413216807013784, 0.4127980959552237, 0.4127980959552237, 0.1744038080895526, 0.1697633551502897, 0.7788823295056971, 0.0513543153440132, 0.7788823295056972, 0.1697633551502898, 0.0513543153440130, 0.1500637365870350, 0.6998725268259297, 0.1500637365870353, 0.2140487799258473, 0.7822542773667971, 0.0036969427073556, 0.7822542773667971, 0.2140487799258473, 0.0036969427073554, 0.4695480309966850, 0.4695480309966850, 0.0609039380066300, 0.3333333333333333, 0.0170416294057183, 0.9659167411885631, 0.0170416294057187 }; static double b_save[] = { 0.0096649544036603, 0.4137694858270852, 0.5765655597692547, 0.0096649544036603, 0.5765655597692547, 0.4137694858270854, 0.0303059433551864, 0.3041794482294797, 0.6655146084153342, 0.0303059433551864, 0.6655146084153339, 0.3041794482294800, 0.0666744722402385, 0.0666744722402381, 0.8666510555195236, 0.0108129727761038, 0.0896090890227058, 0.8995779382011906, 0.0108129727761038, 0.8995779382011906, 0.0896090890227062, 0.1066531605361485, 0.2966153724003830, 0.5967314670634687, 0.1066531605361485, 0.5967314670634686, 0.2966153724003832, 0.2413216807013785, 0.2413216807013784, 0.5173566385972433, 0.1744038080895527, 0.4127980959552238, 0.4127980959552238, 0.0513543153440131, 0.1697633551502898, 0.7788823295056972, 0.0513543153440131, 0.7788823295056971, 0.1697633551502900, 0.1500637365870353, 0.1500637365870350, 0.6998725268259298, 0.0036969427073556, 0.2140487799258473, 0.7822542773667974, 0.0036969427073556, 0.7822542773667972, 0.2140487799258476, 0.0609039380066301, 0.4695480309966850, 0.4695480309966852, 0.3333333333333334, 0.0170416294057186, 0.0170416294057182, 0.9659167411885633 }; static double c_save[] = { 0.5765655597692546, 0.0096649544036601, 0.4137694858270851, 0.4137694858270851, 0.0096649544036601, 0.5765655597692544, 0.6655146084153339, 0.0303059433551863, 0.3041794482294794, 0.3041794482294797, 0.0303059433551863, 0.6655146084153338, 0.8666510555195234, 0.0666744722402385, 0.0666744722402378, 0.8995779382011905, 0.0108129727761038, 0.0896090890227056, 0.0896090890227059, 0.0108129727761035, 0.8995779382011904, 0.5967314670634686, 0.1066531605361485, 0.2966153724003828, 0.2966153724003829, 0.1066531605361484, 0.5967314670634685, 0.5173566385972432, 0.2413216807013784, 0.2413216807013782, 0.4127980959552237, 0.1744038080895526, 0.4127980959552236, 0.7788823295056971, 0.0513543153440131, 0.1697633551502895, 0.1697633551502896, 0.0513543153440131, 0.7788823295056969, 0.6998725268259297, 0.1500637365870353, 0.1500637365870349, 0.7822542773667971, 0.0036969427073556, 0.2140487799258469, 0.2140487799258473, 0.0036969427073555, 0.7822542773667970, 0.4695480309966850, 0.0609039380066300, 0.4695480309966847, 0.3333333333333333, 0.9659167411885632, 0.0170416294057187, 0.0170416294057180 }; static double w_save[] = { 0.0081822105532221, 0.0081822105532221, 0.0081822105532221, 0.0081822105532221, 0.0081822105532221, 0.0081822105532221, 0.0139836071246536, 0.0139836071246536, 0.0139836071246536, 0.0139836071246536, 0.0139836071246536, 0.0139836071246536, 0.0124254255955610, 0.0124254255955610, 0.0124254255955610, 0.0057518699704972, 0.0057518699704972, 0.0057518699704972, 0.0057518699704972, 0.0057518699704972, 0.0057518699704972, 0.0316460616819832, 0.0316460616819832, 0.0316460616819832, 0.0316460616819832, 0.0316460616819832, 0.0316460616819832, 0.0411840410697925, 0.0411840410697925, 0.0411840410697925, 0.0409852197868154, 0.0409852197868154, 0.0409852197868154, 0.0176530810471033, 0.0176530810471033, 0.0176530810471033, 0.0176530810471033, 0.0176530810471033, 0.0176530810471033, 0.0287834967027489, 0.0287834967027489, 0.0287834967027489, 0.0046146906397291, 0.0046146906397291, 0.0046146906397291, 0.0046146906397291, 0.0046146906397291, 0.0046146906397291, 0.0270936694677105, 0.0270936694677105, 0.0270936694677105, 0.0462279103141913, 0.0037891352382642, 0.0037891352382642, 0.0037891352382642 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule17 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule17() returns the rule of precision 17. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4171034443615992, 0.4171034443615992, 0.1657931112768016, 0.0725054707990024, 0.9159193532978169, 0.0115751759031809, 0.9159193532978169, 0.0725054707990024, 0.0115751759031804, 0.1803581162663705, 0.6392837674672587, 0.1803581162663708, 0.4154754592952291, 0.5712948679446841, 0.0132296727600869, 0.5712948679446841, 0.4154754592952290, 0.0132296727600868, 0.2717918700553548, 0.7150722591106424, 0.0131358708340029, 0.7150722591106424, 0.2717918700553550, 0.0131358708340026, 0.2992189424769703, 0.5432755795961597, 0.1575054779268699, 0.5432755795961597, 0.2992189424769702, 0.1575054779268698, 0.2857065024365866, 0.4285869951268267, 0.2857065024365867, 0.3062815917461865, 0.6263690303864522, 0.0673493778673613, 0.6263690303864522, 0.3062815917461865, 0.0673493778673612, 0.1687225134952594, 0.7532351459364581, 0.0780423405682825, 0.7532351459364581, 0.1687225134952594, 0.0780423405682823, 0.0666540634795968, 0.8666918730408060, 0.0666540634795971, 0.1591922874727927, 0.8247900701650880, 0.0160176423621194, 0.8247900701650880, 0.1591922874727927, 0.0160176423621192, 0.0147554916607538, 0.9704890166784920, 0.0147554916607542, 0.4655978716188903, 0.4655978716188902, 0.0688042567622194 }; static double b_save[] = { 0.1657931112768017, 0.4171034443615993, 0.4171034443615994, 0.0115751759031807, 0.0725054707990024, 0.9159193532978170, 0.0115751759031807, 0.9159193532978170, 0.0725054707990027, 0.1803581162663707, 0.1803581162663706, 0.6392837674672588, 0.0132296727600870, 0.4154754592952291, 0.5712948679446843, 0.0132296727600870, 0.5712948679446841, 0.4154754592952293, 0.0131358708340028, 0.2717918700553549, 0.7150722591106425, 0.0131358708340028, 0.7150722591106424, 0.2717918700553552, 0.1575054779268700, 0.2992189424769703, 0.5432755795961599, 0.1575054779268700, 0.5432755795961599, 0.2992189424769705, 0.2857065024365867, 0.2857065024365867, 0.4285869951268269, 0.0673493778673613, 0.3062815917461865, 0.6263690303864524, 0.0673493778673613, 0.6263690303864524, 0.3062815917461867, 0.0780423405682825, 0.1687225134952594, 0.7532351459364584, 0.0780423405682825, 0.7532351459364582, 0.1687225134952597, 0.0666540634795971, 0.0666540634795968, 0.8666918730408062, 0.0160176423621193, 0.1591922874727927, 0.8247900701650882, 0.0160176423621193, 0.8247900701650882, 0.1591922874727930, 0.0147554916607541, 0.0147554916607538, 0.9704890166784922, 0.0688042567622194, 0.4655978716188904, 0.4655978716188905 }; static double c_save[] = { 0.4171034443615991, 0.1657931112768015, 0.4171034443615990, 0.9159193532978169, 0.0115751759031807, 0.0725054707990022, 0.0725054707990024, 0.0115751759031805, 0.9159193532978168, 0.6392837674672587, 0.1803581162663707, 0.1803581162663704, 0.5712948679446841, 0.0132296727600869, 0.4154754592952288, 0.4154754592952289, 0.0132296727600869, 0.5712948679446839, 0.7150722591106424, 0.0131358708340027, 0.2717918700553547, 0.2717918700553548, 0.0131358708340026, 0.7150722591106422, 0.5432755795961598, 0.1575054779268700, 0.2992189424769702, 0.2992189424769703, 0.1575054779268699, 0.5432755795961597, 0.4285869951268267, 0.2857065024365867, 0.2857065024365865, 0.6263690303864522, 0.0673493778673613, 0.3062815917461863, 0.3062815917461865, 0.0673493778673611, 0.6263690303864521, 0.7532351459364580, 0.0780423405682825, 0.1687225134952591, 0.1687225134952594, 0.0780423405682823, 0.7532351459364579, 0.8666918730408061, 0.0666540634795972, 0.0666540634795967, 0.8247900701650880, 0.0160176423621193, 0.1591922874727923, 0.1591922874727927, 0.0160176423621191, 0.8247900701650878, 0.9704890166784921, 0.0147554916607542, 0.0147554916607536, 0.4655978716188903, 0.0688042567622194, 0.4655978716188902 }; static double w_save[] = { 0.0273109265281021, 0.0273109265281021, 0.0273109265281021, 0.0045843484017359, 0.0045843484017359, 0.0045843484017359, 0.0045843484017359, 0.0045843484017359, 0.0045843484017359, 0.0263126305880180, 0.0263126305880180, 0.0263126305880180, 0.0103984399558395, 0.0103984399558395, 0.0103984399558395, 0.0103984399558395, 0.0103984399558395, 0.0103984399558395, 0.0086922145010012, 0.0086922145010012, 0.0086922145010012, 0.0086922145010012, 0.0086922145010012, 0.0086922145010012, 0.0261716259353370, 0.0261716259353370, 0.0261716259353370, 0.0261716259353370, 0.0261716259353370, 0.0261716259353370, 0.0377162371527953, 0.0377162371527953, 0.0377162371527953, 0.0224877725466911, 0.0224877725466911, 0.0224877725466911, 0.0224877725466911, 0.0224877725466911, 0.0224877725466911, 0.0205578983204545, 0.0205578983204545, 0.0205578983204545, 0.0205578983204545, 0.0205578983204545, 0.0205578983204545, 0.0124590008023054, 0.0124590008023054, 0.0124590008023054, 0.0079783002059296, 0.0079783002059296, 0.0079783002059296, 0.0079783002059296, 0.0079783002059296, 0.0079783002059296, 0.0027738875776376, 0.0027738875776376, 0.0027738875776376, 0.0250194509504974, 0.0250194509504974, 0.0250194509504974 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule18 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule18() returns the rule of precision 18. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3850440344131636, 0.5245289252324958, 0.0904270403543406, 0.5245289252324957, 0.3850440344131637, 0.0904270403543405, 0.4749182113240457, 0.4749182113240458, 0.0501635773519085, 0.1516385069726047, 0.6967229860547902, 0.1516385069726050, 0.0472761418326517, 0.9402249256838527, 0.0124989324834957, 0.9402249256838527, 0.0472761418326518, 0.0124989324834952, 0.3333333333333333, 0.3020619577128708, 0.6439263069481050, 0.0540117353390243, 0.6439263069481049, 0.3020619577128708, 0.0540117353390241, 0.2565061597742415, 0.7329888214065164, 0.0105050188192420, 0.7329888214065166, 0.2565061597742415, 0.0105050188192418, 0.4110671018759194, 0.4110671018759194, 0.1778657962481610, 0.1784791255658876, 0.7553984164057089, 0.0661224580284036, 0.7553984164057089, 0.1784791255658877, 0.0661224580284032, 0.2656146099053742, 0.4687707801892516, 0.2656146099053743, 0.0037589443410682, 0.9924821113178632, 0.0037589443410687, 0.2685733063960138, 0.5823597834782123, 0.1490669101257739, 0.5823597834782123, 0.2685733063960138, 0.1490669101257737, 0.4110656686746184, 0.5772425066507145, 0.0116918246746671, 0.5772425066507145, 0.4110656686746185, 0.0116918246746671, 0.1327788302713893, 0.8528896449496687, 0.0143315247789422, 0.8528896449496688, 0.1327788302713893, 0.0143315247789417, 0.0724387055673328, 0.8551225888653341, 0.0724387055673332 }; static double b_save[] = { 0.0904270403543407, 0.3850440344131637, 0.5245289252324959, 0.0904270403543407, 0.5245289252324958, 0.3850440344131639, 0.0501635773519086, 0.4749182113240458, 0.4749182113240459, 0.1516385069726050, 0.1516385069726048, 0.6967229860547904, 0.0124989324834955, 0.0472761418326518, 0.9402249256838529, 0.0124989324834955, 0.9402249256838529, 0.0472761418326521, 0.3333333333333334, 0.0540117353390243, 0.3020619577128708, 0.6439263069481052, 0.0540117353390243, 0.6439263069481049, 0.3020619577128710, 0.0105050188192420, 0.2565061597742415, 0.7329888214065168, 0.0105050188192420, 0.7329888214065168, 0.2565061597742418, 0.1778657962481611, 0.4110671018759195, 0.4110671018759197, 0.0661224580284034, 0.1784791255658876, 0.7553984164057090, 0.0661224580284034, 0.7553984164057090, 0.1784791255658879, 0.2656146099053743, 0.2656146099053742, 0.4687707801892517, 0.0037589443410685, 0.0037589443410682, 0.9924821113178633, 0.1490669101257739, 0.2685733063960138, 0.5823597834782125, 0.1490669101257739, 0.5823597834782125, 0.2685733063960140, 0.0116918246746672, 0.4110656686746184, 0.5772425066507147, 0.0116918246746672, 0.5772425066507145, 0.4110656686746186, 0.0143315247789420, 0.1327788302713893, 0.8528896449496687, 0.0143315247789420, 0.8528896449496690, 0.1327788302713896, 0.0724387055673330, 0.0724387055673327, 0.8551225888653343 }; static double c_save[] = { 0.5245289252324957, 0.0904270403543405, 0.3850440344131635, 0.3850440344131636, 0.0904270403543405, 0.5245289252324956, 0.4749182113240457, 0.0501635773519085, 0.4749182113240456, 0.6967229860547902, 0.1516385069726050, 0.1516385069726046, 0.9402249256838529, 0.0124989324834955, 0.0472761418326515, 0.0472761418326518, 0.0124989324834953, 0.9402249256838527, 0.3333333333333333, 0.6439263069481050, 0.0540117353390242, 0.3020619577128706, 0.3020619577128708, 0.0540117353390243, 0.6439263069481048, 0.7329888214065166, 0.0105050188192420, 0.2565061597742413, 0.2565061597742415, 0.0105050188192417, 0.7329888214065164, 0.4110671018759195, 0.1778657962481610, 0.4110671018759194, 0.7553984164057089, 0.0661224580284035, 0.1784791255658874, 0.1784791255658876, 0.0661224580284032, 0.7553984164057088, 0.4687707801892514, 0.2656146099053742, 0.2656146099053741, 0.9924821113178633, 0.0037589443410686, 0.0037589443410680, 0.5823597834782123, 0.1490669101257739, 0.2685733063960136, 0.2685733063960138, 0.1490669101257737, 0.5823597834782122, 0.5772425066507145, 0.0116918246746671, 0.4110656686746181, 0.4110656686746183, 0.0116918246746670, 0.5772425066507143, 0.8528896449496688, 0.0143315247789421, 0.1327788302713891, 0.1327788302713892, 0.0143315247789417, 0.8528896449496687, 0.8551225888653342, 0.0724387055673332, 0.0724387055673325 }; static double w_save[] = { 0.0153282581945531, 0.0153282581945531, 0.0153282581945531, 0.0153282581945531, 0.0153282581945531, 0.0153282581945531, 0.0131070274917388, 0.0131070274917388, 0.0131070274917388, 0.0203183388454584, 0.0203183388454584, 0.0203183388454584, 0.0042175167747444, 0.0042175167747444, 0.0042175167747444, 0.0042175167747444, 0.0042175167747444, 0.0042175167747444, 0.0307485212391159, 0.0163659084139866, 0.0163659084139866, 0.0163659084139866, 0.0163659084139866, 0.0163659084139866, 0.0163659084139866, 0.0077298352800062, 0.0077298352800062, 0.0077298352800062, 0.0077298352800062, 0.0077298352800062, 0.0077298352800062, 0.0334719940598479, 0.0334719940598479, 0.0334719940598479, 0.0169116539174801, 0.0169116539174801, 0.0169116539174801, 0.0169116539174801, 0.0169116539174801, 0.0169116539174801, 0.0311163966020061, 0.0311163966020061, 0.0311163966020061, 0.0005320056169478, 0.0005320056169478, 0.0005320056169478, 0.0275928864885795, 0.0275928864885795, 0.0275928864885795, 0.0275928864885795, 0.0275928864885795, 0.0275928864885795, 0.0095861244743615, 0.0095861244743615, 0.0095861244743615, 0.0095861244743615, 0.0095861244743615, 0.0095861244743615, 0.0076417049727196, 0.0076417049727196, 0.0076417049727196, 0.0076417049727196, 0.0076417049727196, 0.0076417049727196, 0.0137902866047669, 0.0137902866047669, 0.0137902866047669 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule19 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule19() returns the rule of precision 19. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1424222825711269, 0.8525725750765226, 0.0050051423523504, 0.8525725750765226, 0.1424222825711269, 0.0050051423523502, 0.0525262798541034, 0.8949474402917929, 0.0525262798541039, 0.0600838999627024, 0.9301390385986208, 0.0097770614386771, 0.9301390385986208, 0.0600838999627025, 0.0097770614386767, 0.1307006699605345, 0.8301568806048565, 0.0391424494346090, 0.8301568806048566, 0.1307006699605346, 0.0391424494346087, 0.3113183832239869, 0.5593688070080342, 0.1293128097679790, 0.5593688070080342, 0.3113183832239869, 0.1293128097679789, 0.1114480557169985, 0.7771038885660025, 0.1114480557169988, 0.0116390273279224, 0.9767219453441548, 0.0116390273279229, 0.2551621331531247, 0.4896757336937503, 0.2551621331531249, 0.2214339418891134, 0.7040048688065315, 0.0745611893043552, 0.7040048688065313, 0.2214339418891134, 0.0745611893043550, 0.4039697179663860, 0.4039697179663860, 0.1920605640672278, 0.3540259269997119, 0.6050857585353100, 0.0408883144649781, 0.6050857585353100, 0.3540259269997119, 0.0408883144649780, 0.1781710060796274, 0.6436579878407451, 0.1781710060796276, 0.4591943889568276, 0.4591943889568276, 0.0816112220863447, 0.3333333333333333, 0.4925124498658742, 0.4925124498658742, 0.0149751002682516, 0.2418941040068926, 0.7431822570856689, 0.0149236389074385, 0.7431822570856689, 0.2418941040068927, 0.0149236389074383, 0.3646204143387100, 0.6333104818121875, 0.0020691038491024, 0.6333104818121876, 0.3646204143387101, 0.0020691038491022 }; static double b_save[] = { 0.0050051423523504, 0.1424222825711269, 0.8525725750765228, 0.0050051423523504, 0.8525725750765228, 0.1424222825711273, 0.0525262798541037, 0.0525262798541034, 0.8949474402917930, 0.0097770614386769, 0.0600838999627023, 0.9301390385986208, 0.0097770614386769, 0.9301390385986208, 0.0600838999627027, 0.0391424494346089, 0.1307006699605346, 0.8301568806048567, 0.0391424494346089, 0.8301568806048567, 0.1307006699605348, 0.1293128097679790, 0.3113183832239869, 0.5593688070080343, 0.1293128097679790, 0.5593688070080343, 0.3113183832239870, 0.1114480557169988, 0.1114480557169985, 0.7771038885660028, 0.0116390273279228, 0.0116390273279224, 0.9767219453441548, 0.2551621331531249, 0.2551621331531249, 0.4896757336937504, 0.0745611893043552, 0.2214339418891134, 0.7040048688065317, 0.0745611893043552, 0.7040048688065317, 0.2214339418891137, 0.1920605640672279, 0.4039697179663861, 0.4039697179663862, 0.0408883144649781, 0.3540259269997119, 0.6050857585353102, 0.0408883144649781, 0.6050857585353101, 0.3540259269997121, 0.1781710060796276, 0.1781710060796274, 0.6436579878407452, 0.0816112220863448, 0.4591943889568277, 0.4591943889568278, 0.3333333333333334, 0.0149751002682516, 0.4925124498658743, 0.4925124498658744, 0.0149236389074385, 0.2418941040068926, 0.7431822570856692, 0.0149236389074385, 0.7431822570856690, 0.2418941040068929, 0.0020691038491024, 0.3646204143387101, 0.6333104818121877, 0.0020691038491024, 0.6333104818121877, 0.3646204143387103 }; static double c_save[] = { 0.8525725750765227, 0.0050051423523504, 0.1424222825711267, 0.1424222825711269, 0.0050051423523502, 0.8525725750765225, 0.8949474402917929, 0.0525262798541037, 0.0525262798541032, 0.9301390385986208, 0.0097770614386769, 0.0600838999627021, 0.0600838999627024, 0.0097770614386767, 0.9301390385986207, 0.8301568806048566, 0.0391424494346090, 0.1307006699605343, 0.1307006699605345, 0.0391424494346087, 0.8301568806048565, 0.5593688070080340, 0.1293128097679789, 0.3113183832239867, 0.3113183832239868, 0.1293128097679789, 0.5593688070080340, 0.7771038885660027, 0.1114480557169989, 0.1114480557169985, 0.9767219453441548, 0.0116390273279228, 0.0116390273279222, 0.4896757336937503, 0.2551621331531249, 0.2551621331531247, 0.7040048688065315, 0.0745611893043551, 0.2214339418891131, 0.2214339418891135, 0.0745611893043550, 0.7040048688065313, 0.4039697179663861, 0.1920605640672278, 0.4039697179663860, 0.6050857585353100, 0.0408883144649781, 0.3540259269997117, 0.3540259269997119, 0.0408883144649780, 0.6050857585353098, 0.6436579878407449, 0.1781710060796274, 0.1781710060796272, 0.4591943889568276, 0.0816112220863447, 0.4591943889568275, 0.3333333333333333, 0.4925124498658742, 0.0149751002682516, 0.4925124498658741, 0.7431822570856689, 0.0149236389074385, 0.2418941040068923, 0.2418941040068927, 0.0149236389074383, 0.7431822570856688, 0.6333104818121876, 0.0020691038491024, 0.3646204143387098, 0.3646204143387100, 0.0020691038491022, 0.6333104818121874 }; static double w_save[] = { 0.0029256924878801, 0.0029256924878801, 0.0029256924878801, 0.0029256924878801, 0.0029256924878801, 0.0029256924878801, 0.0071093936227949, 0.0071093936227949, 0.0071093936227949, 0.0033273888405939, 0.0033273888405939, 0.0033273888405939, 0.0033273888405939, 0.0033273888405939, 0.0033273888405939, 0.0096955190816242, 0.0096955190816242, 0.0096955190816242, 0.0096955190816242, 0.0096955190816242, 0.0096955190816242, 0.0263462647074454, 0.0263462647074454, 0.0263462647074454, 0.0263462647074454, 0.0263462647074454, 0.0263462647074454, 0.0152349565170048, 0.0152349565170048, 0.0152349565170048, 0.0017651924183085, 0.0017651924183085, 0.0017651924183085, 0.0317528545875300, 0.0317528545875300, 0.0317528545875300, 0.0181080745904305, 0.0181080745904305, 0.0181080745904305, 0.0181080745904305, 0.0181080745904305, 0.0181080745904305, 0.0315373586452396, 0.0315373586452396, 0.0315373586452396, 0.0161022094609394, 0.0161022094609394, 0.0161022094609394, 0.0161022094609394, 0.0161022094609394, 0.0161022094609394, 0.0246519810535848, 0.0246519810535848, 0.0246519810535848, 0.0229835709771232, 0.0229835709771232, 0.0229835709771232, 0.0344691608509053, 0.0103218821824189, 0.0103218821824189, 0.0103218821824189, 0.0084559248390935, 0.0084559248390935, 0.0084559248390935, 0.0084559248390935, 0.0084559248390935, 0.0084559248390935, 0.0032821375148397, 0.0032821375148397, 0.0032821375148397, 0.0032821375148397, 0.0032821375148397, 0.0032821375148397 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule20 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule20() returns the rule of precision 20. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1862949977445409, 0.6274100045109180, 0.1862949977445411, 0.0373108805988846, 0.9253782388022305, 0.0373108805988850, 0.4762456115404990, 0.4762456115404990, 0.0475087769190019, 0.0640905856084340, 0.9310544767839422, 0.0048549376076240, 0.9310544767839422, 0.0640905856084341, 0.0048549376076235, 0.2156070573900944, 0.6781657378896355, 0.1062272047202701, 0.6781657378896355, 0.2156070573900943, 0.1062272047202699, 0.4455510569559248, 0.4455510569559248, 0.1088978860881503, 0.1591337076570672, 0.8332955118382362, 0.0075707805046966, 0.8332955118382362, 0.1591337076570672, 0.0075707805046964, 0.3178601238357719, 0.5423318041724280, 0.1398080719918000, 0.5423318041724280, 0.3178601238357719, 0.1398080719917999, 0.2545792676733390, 0.4908414646533217, 0.2545792676733392, 0.3333333333333333, 0.1985181322287882, 0.7549215028635475, 0.0465603649076644, 0.7549215028635474, 0.1985181322287882, 0.0465603649076642, 0.3934253478170998, 0.3934253478170998, 0.2131493043658002, 0.0999522962881386, 0.8616840189364867, 0.0383636847753748, 0.8616840189364866, 0.0999522962881387, 0.0383636847753744, 0.4200237588162241, 0.5701446928909734, 0.0098315482928025, 0.5701446928909734, 0.4200237588162241, 0.0098315482928025, 0.3331348173095874, 0.6118777035474257, 0.0549874791429869, 0.6118777035474257, 0.3331348173095874, 0.0549874791429867, 0.2805814114236652, 0.7086813757203236, 0.0107372128560111, 0.7086813757203237, 0.2805814114236653, 0.0107372128560110, 0.0109761410283976, 0.9780477179432044, 0.0109761410283981, 0.1093835967117145, 0.7812328065765708, 0.1093835967117148 }; static double b_save[] = { 0.1862949977445411, 0.1862949977445409, 0.6274100045109182, 0.0373108805988849, 0.0373108805988846, 0.9253782388022306, 0.0475087769190020, 0.4762456115404990, 0.4762456115404993, 0.0048549376076238, 0.0640905856084340, 0.9310544767839423, 0.0048549376076238, 0.9310544767839423, 0.0640905856084343, 0.1062272047202701, 0.2156070573900944, 0.6781657378896357, 0.1062272047202701, 0.6781657378896357, 0.2156070573900946, 0.1088978860881504, 0.4455510569559249, 0.4455510569559250, 0.0075707805046966, 0.1591337076570672, 0.8332955118382365, 0.0075707805046966, 0.8332955118382364, 0.1591337076570676, 0.1398080719918000, 0.3178601238357721, 0.5423318041724282, 0.1398080719918000, 0.5423318041724282, 0.3178601238357722, 0.2545792676733392, 0.2545792676733392, 0.4908414646533218, 0.3333333333333334, 0.0465603649076644, 0.1985181322287882, 0.7549215028635476, 0.0465603649076644, 0.7549215028635476, 0.1985181322287885, 0.2131493043658003, 0.3934253478171000, 0.3934253478171000, 0.0383636847753747, 0.0999522962881386, 0.8616840189364868, 0.0383636847753747, 0.8616840189364868, 0.0999522962881389, 0.0098315482928026, 0.4200237588162241, 0.5701446928909736, 0.0098315482928026, 0.5701446928909735, 0.4200237588162243, 0.0549874791429869, 0.3331348173095875, 0.6118777035474259, 0.0549874791429869, 0.6118777035474258, 0.3331348173095877, 0.0107372128560111, 0.2805814114236653, 0.7086813757203239, 0.0107372128560111, 0.7086813757203237, 0.2805814114236655, 0.0109761410283979, 0.0109761410283976, 0.9780477179432047, 0.1093835967117148, 0.1093835967117145, 0.7812328065765709 }; static double c_save[] = { 0.6274100045109180, 0.1862949977445411, 0.1862949977445406, 0.9253782388022306, 0.0373108805988850, 0.0373108805988843, 0.4762456115404990, 0.0475087769190020, 0.4762456115404988, 0.9310544767839422, 0.0048549376076238, 0.0640905856084338, 0.0640905856084340, 0.0048549376076236, 0.9310544767839422, 0.6781657378896355, 0.1062272047202700, 0.2156070573900941, 0.2156070573900944, 0.1062272047202699, 0.6781657378896354, 0.4455510569559248, 0.1088978860881503, 0.4455510569559247, 0.8332955118382361, 0.0075707805046965, 0.1591337076570670, 0.1591337076570672, 0.0075707805046964, 0.8332955118382360, 0.5423318041724281, 0.1398080719918000, 0.3178601238357718, 0.3178601238357720, 0.1398080719917999, 0.5423318041724279, 0.4908414646533217, 0.2545792676733392, 0.2545792676733390, 0.3333333333333333, 0.7549215028635475, 0.0465603649076643, 0.1985181322287879, 0.1985181322287882, 0.0465603649076641, 0.7549215028635474, 0.3934253478170998, 0.2131493043658002, 0.3934253478170998, 0.8616840189364867, 0.0383636847753747, 0.0999522962881384, 0.0999522962881387, 0.0383636847753744, 0.8616840189364866, 0.5701446928909732, 0.0098315482928025, 0.4200237588162239, 0.4200237588162241, 0.0098315482928024, 0.5701446928909732, 0.6118777035474258, 0.0549874791429869, 0.3331348173095873, 0.3331348173095875, 0.0549874791429869, 0.6118777035474255, 0.7086813757203236, 0.0107372128560111, 0.2805814114236650, 0.2805814114236652, 0.0107372128560109, 0.7086813757203236, 0.9780477179432044, 0.0109761410283980, 0.0109761410283972, 0.7812328065765708, 0.1093835967117147, 0.1093835967117144 }; static double w_save[] = { 0.0183469259485058, 0.0183469259485058, 0.0183469259485058, 0.0043225508213312, 0.0043225508213312, 0.0043225508213312, 0.0142036506068169, 0.0142036506068169, 0.0142036506068169, 0.0022597392042517, 0.0022597392042517, 0.0022597392042517, 0.0022597392042517, 0.0022597392042517, 0.0022597392042517, 0.0154452156441985, 0.0154452156441985, 0.0154452156441985, 0.0154452156441985, 0.0154452156441985, 0.0154452156441985, 0.0189047998664649, 0.0189047998664649, 0.0189047998664649, 0.0044057948371170, 0.0044057948371170, 0.0044057948371170, 0.0044057948371170, 0.0044057948371170, 0.0044057948371170, 0.0233834914636555, 0.0233834914636555, 0.0233834914636555, 0.0233834914636555, 0.0233834914636555, 0.0233834914636555, 0.0281664026150405, 0.0281664026150405, 0.0281664026150405, 0.0278202214029062, 0.0119727971579094, 0.0119727971579094, 0.0119727971579094, 0.0119727971579094, 0.0119727971579094, 0.0119727971579094, 0.0275761012581409, 0.0275761012581409, 0.0275761012581409, 0.0082914230552277, 0.0082914230552277, 0.0082914230552277, 0.0082914230552277, 0.0082914230552277, 0.0082914230552277, 0.0073913630005106, 0.0073913630005106, 0.0073913630005106, 0.0073913630005106, 0.0073913630005106, 0.0073913630005106, 0.0173344511344387, 0.0173344511344387, 0.0173344511344387, 0.0173344511344387, 0.0173344511344387, 0.0173344511344387, 0.0071564004769154, 0.0071564004769154, 0.0071564004769154, 0.0071564004769154, 0.0071564004769154, 0.0071564004769154, 0.0015976815821332, 0.0015976815821332, 0.0015976815821332, 0.0156604615521491, 0.0156604615521491, 0.0156604615521491 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule21 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule21() returns the rule of precision 21. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.2989362353149825, 0.4021275293700348, 0.2989362353149825, 0.2891894960785947, 0.5055149445862437, 0.2052955593351616, 0.5055149445862437, 0.2891894960785947, 0.2052955593351615, 0.4970078754686856, 0.4970078754686856, 0.0059842490626288, 0.2378733825979940, 0.7551948083705379, 0.0069318090314683, 0.7551948083705379, 0.2378733825979941, 0.0069318090314680, 0.4036175865463851, 0.4036175865463851, 0.1927648269072297, 0.3188653107948282, 0.5573552887996790, 0.1237794004054928, 0.5573552887996790, 0.3188653107948283, 0.1237794004054926, 0.2318736253704010, 0.7291350120063786, 0.0389913626232204, 0.7291350120063788, 0.2318736253704010, 0.0389913626232202, 0.1331671229413703, 0.8572966295289191, 0.0095362475297107, 0.8572966295289192, 0.1331671229413703, 0.0095362475297104, 0.3468079798099110, 0.6001398284888722, 0.0530521917012168, 0.6001398284888722, 0.3468079798099111, 0.0530521917012167, 0.1189885776227193, 0.7620228447545612, 0.1189885776227196, 0.1902887180912784, 0.6194225638174430, 0.1902887180912786, 0.2165996231899825, 0.6829423567359030, 0.1004580200741146, 0.6829423567359030, 0.2165996231899825, 0.1004580200741143, 0.4815978686532166, 0.4815978686532166, 0.0368042626935668, 0.4498127917753624, 0.4498127917753624, 0.1003744164492752, 0.1288298079620515, 0.8217191264694078, 0.0494510655685407, 0.8217191264694079, 0.1288298079620517, 0.0494510655685403, 0.0536275755461449, 0.8927448489077100, 0.0536275755461453, 0.3609534080189222, 0.6287919561081534, 0.0102546358729245, 0.6287919561081533, 0.3609534080189222, 0.0102546358729244, 0.0107424564328283, 0.9785150871343431, 0.0107424564328287, 0.0557195650723719, 0.9339785312842042, 0.0103019036434240, 0.9339785312842040, 0.0557195650723720, 0.0103019036434236 }; static double b_save[] = { 0.2989362353149826, 0.2989362353149826, 0.4021275293700349, 0.2052955593351616, 0.2891894960785948, 0.5055149445862438, 0.2052955593351616, 0.5055149445862438, 0.2891894960785949, 0.0059842490626289, 0.4970078754686856, 0.4970078754686857, 0.0069318090314681, 0.2378733825979940, 0.7551948083705379, 0.0069318090314681, 0.7551948083705379, 0.2378733825979943, 0.1927648269072298, 0.4036175865463852, 0.4036175865463852, 0.1237794004054928, 0.3188653107948283, 0.5573552887996791, 0.1237794004054928, 0.5573552887996791, 0.3188653107948285, 0.0389913626232203, 0.2318736253704010, 0.7291350120063789, 0.0389913626232203, 0.7291350120063789, 0.2318736253704013, 0.0095362475297106, 0.1331671229413703, 0.8572966295289193, 0.0095362475297106, 0.8572966295289193, 0.1331671229413706, 0.0530521917012168, 0.3468079798099111, 0.6001398284888723, 0.0530521917012168, 0.6001398284888722, 0.3468079798099113, 0.1189885776227196, 0.1189885776227193, 0.7620228447545613, 0.1902887180912786, 0.1902887180912785, 0.6194225638174431, 0.1004580200741145, 0.2165996231899825, 0.6829423567359031, 0.1004580200741145, 0.6829423567359032, 0.2165996231899828, 0.0368042626935668, 0.4815978686532166, 0.4815978686532168, 0.1003744164492753, 0.4498127917753625, 0.4498127917753625, 0.0494510655685406, 0.1288298079620515, 0.8217191264694079, 0.0494510655685406, 0.8217191264694079, 0.1288298079620518, 0.0536275755461451, 0.0536275755461448, 0.8927448489077101, 0.0102546358729245, 0.3609534080189222, 0.6287919561081535, 0.0102546358729245, 0.6287919561081534, 0.3609534080189224, 0.0107424564328286, 0.0107424564328283, 0.9785150871343433, 0.0103019036434239, 0.0557195650723719, 0.9339785312842044, 0.0103019036434239, 0.9339785312842044, 0.0557195650723723 }; static double c_save[] = { 0.4021275293700349, 0.2989362353149825, 0.2989362353149826, 0.5055149445862437, 0.2052955593351615, 0.2891894960785947, 0.2891894960785947, 0.2052955593351614, 0.5055149445862436, 0.4970078754686856, 0.0059842490626288, 0.4970078754686854, 0.7551948083705379, 0.0069318090314681, 0.2378733825979938, 0.2378733825979940, 0.0069318090314680, 0.7551948083705377, 0.4036175865463850, 0.1927648269072297, 0.4036175865463850, 0.5573552887996789, 0.1237794004054927, 0.3188653107948280, 0.3188653107948282, 0.1237794004054926, 0.5573552887996789, 0.7291350120063786, 0.0389913626232204, 0.2318736253704008, 0.2318736253704009, 0.0389913626232201, 0.7291350120063785, 0.8572966295289192, 0.0095362475297107, 0.1331671229413700, 0.1331671229413702, 0.0095362475297104, 0.8572966295289191, 0.6001398284888720, 0.0530521917012167, 0.3468079798099110, 0.3468079798099110, 0.0530521917012168, 0.6001398284888719, 0.7620228447545612, 0.1189885776227195, 0.1189885776227192, 0.6194225638174429, 0.1902887180912785, 0.1902887180912783, 0.6829423567359030, 0.1004580200741145, 0.2165996231899824, 0.2165996231899825, 0.1004580200741143, 0.6829423567359030, 0.4815978686532166, 0.0368042626935668, 0.4815978686532165, 0.4498127917753624, 0.1003744164492751, 0.4498127917753622, 0.8217191264694078, 0.0494510655685407, 0.1288298079620513, 0.1288298079620515, 0.0494510655685404, 0.8217191264694079, 0.8927448489077100, 0.0536275755461452, 0.0536275755461446, 0.6287919561081533, 0.0102546358729244, 0.3609534080189220, 0.3609534080189222, 0.0102546358729244, 0.6287919561081532, 0.9785150871343432, 0.0107424564328287, 0.0107424564328280, 0.9339785312842042, 0.0103019036434239, 0.0557195650723716, 0.0557195650723720, 0.0103019036434236, 0.9339785312842040 }; static double w_save[] = { 0.0214511219291323, 0.0214511219291323, 0.0214511219291323, 0.0174954161557631, 0.0174954161557631, 0.0174954161557631, 0.0174954161557631, 0.0174954161557631, 0.0174954161557631, 0.0044378296970659, 0.0044378296970659, 0.0044378296970659, 0.0042061202881497, 0.0042061202881497, 0.0042061202881497, 0.0042061202881497, 0.0042061202881497, 0.0042061202881497, 0.0230007046532839, 0.0230007046532839, 0.0230007046532839, 0.0184474848479328, 0.0184474848479328, 0.0184474848479328, 0.0184474848479328, 0.0184474848479328, 0.0184474848479328, 0.0104699041853248, 0.0104699041853248, 0.0104699041853248, 0.0104699041853248, 0.0104699041853248, 0.0104699041853248, 0.0044808131219015, 0.0044808131219015, 0.0044808131219015, 0.0044808131219015, 0.0044808131219015, 0.0044808131219015, 0.0145003059189710, 0.0145003059189710, 0.0145003059189710, 0.0145003059189710, 0.0145003059189710, 0.0145003059189710, 0.0136560324522302, 0.0136560324522302, 0.0136560324522302, 0.0194552418607507, 0.0194552418607507, 0.0194552418607507, 0.0159040367054280, 0.0159040367054280, 0.0159040367054280, 0.0159040367054280, 0.0159040367054280, 0.0159040367054280, 0.0122144101633844, 0.0122144101633844, 0.0122144101633844, 0.0196144752278240, 0.0196144752278240, 0.0196144752278240, 0.0098119718225504, 0.0098119718225504, 0.0098119718225504, 0.0098119718225504, 0.0098119718225504, 0.0098119718225504, 0.0071520851012837, 0.0071520851012837, 0.0071520851012837, 0.0068398848579343, 0.0068398848579343, 0.0068398848579343, 0.0068398848579343, 0.0068398848579343, 0.0068398848579343, 0.0015086992723787, 0.0015086992723787, 0.0015086992723787, 0.0032654285840441, 0.0032654285840441, 0.0032654285840441, 0.0032654285840441, 0.0032654285840441, 0.0032654285840441 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule22 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule22() returns the rule of precision 22. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3851845246273021, 0.3851845246273021, 0.2296309507453957, 0.4577694113676721, 0.4577694113676721, 0.0844611772646559, 0.0698421694674436, 0.9222815483109740, 0.0078762822215824, 0.9222815483109740, 0.0698421694674436, 0.0078762822215821, 0.2945582590299500, 0.4108834819400997, 0.2945582590299501, 0.1885105236302838, 0.6229789527394320, 0.1885105236302841, 0.4219818887935349, 0.4219818887935349, 0.1560362224129301, 0.0903988311664077, 0.8648488844852564, 0.0447522843483360, 0.8648488844852564, 0.0903988311664079, 0.0447522843483357, 0.4113417640205587, 0.5503830012785774, 0.0382752347008638, 0.5503830012785774, 0.4113417640205588, 0.0382752347008637, 0.3321061050074464, 0.5651468190056221, 0.1027470759869314, 0.5651468190056222, 0.3321061050074463, 0.1027470759869313, 0.3625762804324673, 0.6300234783328220, 0.0074002412347108, 0.6300234783328220, 0.3625762804324673, 0.0074002412347107, 0.2900668241166688, 0.5188518779166110, 0.1910812979667201, 0.5188518779166110, 0.2900668241166688, 0.1910812979667200, 0.4961611784097086, 0.4961611784097086, 0.0076776431805827, 0.2879318028241718, 0.6680765517823724, 0.0439916453934559, 0.6680765517823722, 0.2879318028241718, 0.0439916453934557, 0.2167869333649411, 0.6745231247723867, 0.1086899418626721, 0.6745231247723867, 0.2167869333649412, 0.1086899418626718, 0.1458737198735252, 0.8449815687515108, 0.0091447113749641, 0.8449815687515108, 0.1458737198735252, 0.0091447113749638, 0.1762974348245001, 0.7754476410608585, 0.0482549241146414, 0.7754476410608585, 0.1762974348245001, 0.0482549241146412, 0.2439906460394931, 0.7468454447123216, 0.0091639092481853, 0.7468454447123217, 0.2439906460394931, 0.0091639092481851, 0.0291084706708074, 0.9417830586583850, 0.0291084706708079, 0.1154315382192049, 0.7691369235615900, 0.1154315382192052, 0.0179343210529390, 0.9802672139581126, 0.0017984649889486, 0.9802672139581127, 0.0179343210529391, 0.0017984649889481 }; static double b_save[] = { 0.2296309507453958, 0.3851845246273022, 0.3851845246273022, 0.0844611772646559, 0.4577694113676721, 0.4577694113676722, 0.0078762822215824, 0.0698421694674436, 0.9222815483109743, 0.0078762822215824, 0.9222815483109743, 0.0698421694674439, 0.2945582590299502, 0.2945582590299502, 0.4108834819400998, 0.1885105236302840, 0.1885105236302839, 0.6229789527394323, 0.1560362224129302, 0.4219818887935350, 0.4219818887935351, 0.0447522843483359, 0.0903988311664078, 0.8648488844852564, 0.0447522843483359, 0.8648488844852564, 0.0903988311664081, 0.0382752347008638, 0.4113417640205588, 0.5503830012785776, 0.0382752347008638, 0.5503830012785775, 0.4113417640205590, 0.1027470759869314, 0.3321061050074464, 0.5651468190056224, 0.1027470759869314, 0.5651468190056224, 0.3321061050074466, 0.0074002412347108, 0.3625762804324673, 0.6300234783328221, 0.0074002412347108, 0.6300234783328221, 0.3625762804324675, 0.1910812979667202, 0.2900668241166688, 0.5188518779166111, 0.1910812979667202, 0.5188518779166111, 0.2900668241166690, 0.0076776431805828, 0.4961611784097087, 0.4961611784097089, 0.0439916453934559, 0.2879318028241719, 0.6680765517823725, 0.0439916453934559, 0.6680765517823725, 0.2879318028241721, 0.1086899418626720, 0.2167869333649412, 0.6745231247723870, 0.1086899418626720, 0.6745231247723870, 0.2167869333649414, 0.0091447113749641, 0.1458737198735252, 0.8449815687515109, 0.0091447113749641, 0.8449815687515109, 0.1458737198735255, 0.0482549241146414, 0.1762974348245001, 0.7754476410608587, 0.0482549241146414, 0.7754476410608587, 0.1762974348245004, 0.0091639092481852, 0.2439906460394931, 0.7468454447123218, 0.0091639092481852, 0.7468454447123218, 0.2439906460394934, 0.0291084706708077, 0.0291084706708073, 0.9417830586583850, 0.1154315382192051, 0.1154315382192049, 0.7691369235615901, 0.0017984649889484, 0.0179343210529390, 0.9802672139581127, 0.0017984649889484, 0.9802672139581129, 0.0179343210529393 }; static double c_save[] = { 0.3851845246273021, 0.2296309507453957, 0.3851845246273020, 0.4577694113676721, 0.0844611772646559, 0.4577694113676719, 0.9222815483109740, 0.0078762822215824, 0.0698421694674433, 0.0698421694674436, 0.0078762822215821, 0.9222815483109740, 0.4108834819400998, 0.2945582590299501, 0.2945582590299501, 0.6229789527394320, 0.1885105236302841, 0.1885105236302836, 0.4219818887935349, 0.1560362224129300, 0.4219818887935349, 0.8648488844852564, 0.0447522843483358, 0.0903988311664076, 0.0903988311664077, 0.0447522843483357, 0.8648488844852562, 0.5503830012785774, 0.0382752347008638, 0.4113417640205586, 0.4113417640205587, 0.0382752347008637, 0.5503830012785773, 0.5651468190056222, 0.1027470759869314, 0.3321061050074462, 0.3321061050074463, 0.1027470759869313, 0.5651468190056220, 0.6300234783328220, 0.0074002412347107, 0.3625762804324671, 0.3625762804324672, 0.0074002412347106, 0.6300234783328218, 0.5188518779166110, 0.1910812979667201, 0.2900668241166687, 0.2900668241166688, 0.1910812979667200, 0.5188518779166110, 0.4961611784097086, 0.0076776431805827, 0.4961611784097084, 0.6680765517823724, 0.0439916453934558, 0.2879318028241716, 0.2879318028241719, 0.0439916453934558, 0.6680765517823722, 0.6745231247723869, 0.1086899418626721, 0.2167869333649409, 0.2167869333649412, 0.1086899418626718, 0.6745231247723867, 0.8449815687515108, 0.0091447113749641, 0.1458737198735250, 0.1458737198735252, 0.0091447113749640, 0.8449815687515108, 0.7754476410608585, 0.0482549241146414, 0.1762974348244998, 0.1762974348245001, 0.0482549241146412, 0.7754476410608585, 0.7468454447123217, 0.0091639092481853, 0.2439906460394928, 0.2439906460394931, 0.0091639092481851, 0.7468454447123216, 0.9417830586583850, 0.0291084706708077, 0.0291084706708072, 0.7691369235615899, 0.1154315382192051, 0.1154315382192047, 0.9802672139581126, 0.0017984649889485, 0.0179343210529387, 0.0179343210529390, 0.0017984649889481, 0.9802672139581127 }; static double w_save[] = { 0.0134930838836107, 0.0134930838836107, 0.0134930838836107, 0.0138613995242342, 0.0138613995242342, 0.0138613995242342, 0.0025954384742313, 0.0025954384742313, 0.0025954384742313, 0.0025954384742313, 0.0025954384742313, 0.0025954384742313, 0.0210757639574522, 0.0210757639574522, 0.0210757639574522, 0.0160212991251489, 0.0160212991251489, 0.0160212991251489, 0.0188530925538413, 0.0188530925538413, 0.0188530925538413, 0.0075175778177884, 0.0075175778177884, 0.0075175778177884, 0.0075175778177884, 0.0075175778177884, 0.0075175778177884, 0.0111973134719628, 0.0111973134719628, 0.0111973134719628, 0.0111973134719628, 0.0111973134719628, 0.0111973134719628, 0.0177190934895102, 0.0177190934895102, 0.0177190934895102, 0.0177190934895102, 0.0177190934895102, 0.0177190934895102, 0.0049042603975570, 0.0049042603975570, 0.0049042603975570, 0.0049042603975570, 0.0049042603975570, 0.0049042603975570, 0.0217064195555090, 0.0217064195555090, 0.0217064195555090, 0.0217064195555090, 0.0217064195555090, 0.0217064195555090, 0.0052893396659844, 0.0052893396659844, 0.0052893396659844, 0.0116622228673430, 0.0116622228673430, 0.0116622228673430, 0.0116622228673430, 0.0116622228673430, 0.0116622228673430, 0.0157101626225703, 0.0157101626225703, 0.0157101626225703, 0.0157101626225703, 0.0157101626225703, 0.0157101626225703, 0.0041066870715756, 0.0041066870715756, 0.0041066870715756, 0.0041066870715756, 0.0041066870715756, 0.0041066870715756, 0.0105635849677469, 0.0105635849677469, 0.0105635849677469, 0.0105635849677469, 0.0105635849677469, 0.0105635849677469, 0.0050540768975846, 0.0050540768975846, 0.0050540768975846, 0.0050540768975846, 0.0050540768975846, 0.0050540768975846, 0.0035691091658564, 0.0035691091658564, 0.0035691091658564, 0.0144157131281046, 0.0144157131281046, 0.0144157131281046, 0.0006404285311714, 0.0006404285311714, 0.0006404285311714, 0.0006404285311714, 0.0006404285311714, 0.0006404285311714 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule23 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule23() returns the rule of precision 23. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1595037989247572, 0.8166259474208891, 0.0238702536543537, 0.8166259474208892, 0.1595037989247573, 0.0238702536543534, 0.1141013603223645, 0.8807088179167908, 0.0051898217608446, 0.8807088179167909, 0.1141013603223646, 0.0051898217608443, 0.0390072687570320, 0.9219854624859357, 0.0390072687570324, 0.0955398781717349, 0.8717190926395586, 0.0327410291887065, 0.8717190926395587, 0.0955398781717349, 0.0327410291887062, 0.3111622680517019, 0.6863901320923316, 0.0024475998559664, 0.6863901320923317, 0.3111622680517019, 0.0024475998559662, 0.2056172320580521, 0.7856574783566395, 0.0087252895853085, 0.7856574783566393, 0.2056172320580521, 0.0087252895853083, 0.0472616294497253, 0.9455758306400303, 0.0071625399102447, 0.9455758306400303, 0.0472616294497255, 0.0071625399102442, 0.3585095935696251, 0.5729634522431619, 0.0685269541872131, 0.5729634522431619, 0.3585095935696250, 0.0685269541872129, 0.4803288773373085, 0.4803288773373085, 0.0393422453253830, 0.2404827720350127, 0.6577888986377031, 0.1017283293272843, 0.6577888986377032, 0.2404827720350126, 0.1017283293272841, 0.0868410482076331, 0.8263179035847337, 0.0868410482076334, 0.3943235060115415, 0.3943235060115415, 0.2113529879769169, 0.2662513178772472, 0.4674973642455053, 0.2662513178772474, 0.1729323031292240, 0.7687161216332605, 0.0583515752375156, 0.7687161216332605, 0.1729323031292240, 0.0583515752375153, 0.3163043076538381, 0.5288655369406456, 0.1548301554055163, 0.5288655369406456, 0.3163043076538382, 0.1548301554055161, 0.1371293873116475, 0.7257412253767047, 0.1371293873116478, 0.4989594312095863, 0.4989594312095863, 0.0020811375808273, 0.3977585768030076, 0.5874824534670471, 0.0147589697299451, 0.5874824534670471, 0.3977585768030076, 0.0147589697299450, 0.4446924421277275, 0.4446924421277275, 0.1106151157445449, 0.1987498063965361, 0.6025003872069274, 0.1987498063965363, 0.2787941698141023, 0.6882121219933649, 0.0329937081925328, 0.6882121219933649, 0.2787941698141023, 0.0329937081925327, 0.0090164402055982, 0.9819671195888033, 0.0090164402055986, 0.3333333333333333 }; static double b_save[] = { 0.0238702536543536, 0.1595037989247572, 0.8166259474208892, 0.0238702536543536, 0.8166259474208892, 0.1595037989247576, 0.0051898217608445, 0.1141013603223645, 0.8807088179167911, 0.0051898217608445, 0.8807088179167911, 0.1141013603223648, 0.0390072687570323, 0.0390072687570320, 0.9219854624859359, 0.0327410291887064, 0.0955398781717349, 0.8717190926395588, 0.0327410291887064, 0.8717190926395588, 0.0955398781717352, 0.0024475998559664, 0.3111622680517020, 0.6863901320923319, 0.0024475998559664, 0.6863901320923319, 0.3111622680517022, 0.0087252895853085, 0.2056172320580521, 0.7856574783566396, 0.0087252895853085, 0.7856574783566396, 0.2056172320580524, 0.0071625399102445, 0.0472616294497253, 0.9455758306400303, 0.0071625399102445, 0.9455758306400303, 0.0472616294497257, 0.0685269541872130, 0.3585095935696251, 0.5729634522431620, 0.0685269541872130, 0.5729634522431620, 0.3585095935696253, 0.0393422453253830, 0.4803288773373086, 0.4803288773373087, 0.1017283293272843, 0.2404827720350127, 0.6577888986377033, 0.1017283293272843, 0.6577888986377033, 0.2404827720350129, 0.0868410482076333, 0.0868410482076330, 0.8263179035847338, 0.2113529879769170, 0.3943235060115416, 0.3943235060115416, 0.2662513178772474, 0.2662513178772473, 0.4674973642455055, 0.0583515752375155, 0.1729323031292239, 0.7687161216332608, 0.0583515752375155, 0.7687161216332608, 0.1729323031292242, 0.1548301554055163, 0.3163043076538382, 0.5288655369406458, 0.1548301554055163, 0.5288655369406458, 0.3163043076538383, 0.1371293873116478, 0.1371293873116475, 0.7257412253767048, 0.0020811375808274, 0.4989594312095864, 0.4989594312095865, 0.0147589697299452, 0.3977585768030077, 0.5874824534670474, 0.0147589697299452, 0.5874824534670473, 0.3977585768030079, 0.1106151157445450, 0.4446924421277276, 0.4446924421277277, 0.1987498063965364, 0.1987498063965362, 0.6025003872069277, 0.0329937081925328, 0.2787941698141023, 0.6882121219933651, 0.0329937081925328, 0.6882121219933650, 0.2787941698141025, 0.0090164402055985, 0.0090164402055982, 0.9819671195888034, 0.3333333333333334 }; static double c_save[] = { 0.8166259474208892, 0.0238702536543536, 0.1595037989247570, 0.1595037989247572, 0.0238702536543535, 0.8166259474208891, 0.8807088179167910, 0.0051898217608447, 0.1141013603223643, 0.1141013603223646, 0.0051898217608443, 0.8807088179167908, 0.9219854624859357, 0.0390072687570323, 0.0390072687570316, 0.8717190926395586, 0.0327410291887065, 0.0955398781717347, 0.0955398781717349, 0.0327410291887062, 0.8717190926395585, 0.6863901320923317, 0.0024475998559664, 0.3111622680517018, 0.3111622680517019, 0.0024475998559662, 0.6863901320923316, 0.7856574783566395, 0.0087252895853084, 0.2056172320580519, 0.2056172320580521, 0.0087252895853084, 0.7856574783566393, 0.9455758306400301, 0.0071625399102445, 0.0472616294497251, 0.0472616294497253, 0.0071625399102443, 0.9455758306400301, 0.5729634522431619, 0.0685269541872129, 0.3585095935696249, 0.3585095935696251, 0.0685269541872130, 0.5729634522431618, 0.4803288773373085, 0.0393422453253830, 0.4803288773373083, 0.6577888986377031, 0.1017283293272842, 0.2404827720350124, 0.2404827720350126, 0.1017283293272840, 0.6577888986377031, 0.8263179035847337, 0.0868410482076333, 0.0868410482076328, 0.3943235060115415, 0.2113529879769168, 0.3943235060115414, 0.4674973642455054, 0.2662513178772473, 0.2662513178772471, 0.7687161216332605, 0.0583515752375155, 0.1729323031292237, 0.1729323031292240, 0.0583515752375152, 0.7687161216332604, 0.5288655369406456, 0.1548301554055162, 0.3163043076538380, 0.3163043076538381, 0.1548301554055161, 0.5288655369406455, 0.7257412253767047, 0.1371293873116478, 0.1371293873116474, 0.4989594312095863, 0.0020811375808273, 0.4989594312095861, 0.5874824534670472, 0.0147589697299452, 0.3977585768030075, 0.3977585768030077, 0.0147589697299451, 0.5874824534670471, 0.4446924421277275, 0.1106151157445449, 0.4446924421277273, 0.6025003872069276, 0.1987498063965363, 0.1987498063965361, 0.6882121219933649, 0.0329937081925328, 0.2787941698141020, 0.2787941698141023, 0.0329937081925327, 0.6882121219933648, 0.9819671195888033, 0.0090164402055985, 0.0090164402055980, 0.3333333333333333 }; static double w_save[] = { 0.0025281660553823, 0.0025281660553823, 0.0025281660553823, 0.0025281660553823, 0.0025281660553823, 0.0025281660553823, 0.0022250197297245, 0.0022250197297245, 0.0022250197297245, 0.0022250197297245, 0.0022250197297245, 0.0022250197297245, 0.0039157402590329, 0.0039157402590329, 0.0039157402590329, 0.0053280304311948, 0.0053280304311948, 0.0053280304311948, 0.0053280304311948, 0.0053280304311948, 0.0053280304311948, 0.0022811036762558, 0.0022811036762558, 0.0022811036762558, 0.0022811036762558, 0.0022811036762558, 0.0022811036762558, 0.0041147503444161, 0.0041147503444161, 0.0041147503444161, 0.0041147503444161, 0.0041147503444161, 0.0041147503444161, 0.0019525913278907, 0.0019525913278907, 0.0019525913278907, 0.0019525913278907, 0.0019525913278907, 0.0019525913278907, 0.0149811133931992, 0.0149811133931992, 0.0149811133931992, 0.0149811133931992, 0.0149811133931992, 0.0149811133931992, 0.0113978892678008, 0.0113978892678008, 0.0113978892678008, 0.0161212416370172, 0.0161212416370172, 0.0161212416370172, 0.0161212416370172, 0.0161212416370172, 0.0161212416370172, 0.0089599170255135, 0.0089599170255135, 0.0089599170255135, 0.0236746084631280, 0.0236746084631280, 0.0236746084631280, 0.0238078628874998, 0.0238078628874998, 0.0238078628874998, 0.0104702564931301, 0.0104702564931301, 0.0104702564931301, 0.0104702564931301, 0.0104702564931301, 0.0104702564931301, 0.0208443958589688, 0.0208443958589688, 0.0208443958589688, 0.0208443958589688, 0.0208443958589688, 0.0208443958589688, 0.0145594493927417, 0.0145594493927417, 0.0145594493927417, 0.0024075446041814, 0.0024075446041814, 0.0024075446041814, 0.0070977788345218, 0.0070977788345218, 0.0070977788345218, 0.0070977788345218, 0.0070977788345218, 0.0070977788345218, 0.0189519506693389, 0.0189519506693389, 0.0189519506693389, 0.0199352778801050, 0.0199352778801050, 0.0199352778801050, 0.0101755746567070, 0.0101755746567070, 0.0101755746567070, 0.0101755746567070, 0.0101755746567070, 0.0101755746567070, 0.0010653612328293, 0.0010653612328293, 0.0010653612328293, 0.0252530603230362 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule24 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule24() returns the rule of precision 24. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3333333333333333, 0.4188909749106027, 0.4188909749106027, 0.1622180501787944, 0.1623606337169263, 0.6752787325661472, 0.1623606337169265, 0.2414797600735940, 0.5881529574639622, 0.1703672824624437, 0.5881529574639622, 0.2414797600735940, 0.1703672824624436, 0.3289758089242263, 0.5012643952150375, 0.1697597958607360, 0.5012643952150376, 0.3289758089242264, 0.1697597958607359, 0.0409856290011169, 0.9180287419977657, 0.0409856290011174, 0.0067312708878883, 0.9865374582242232, 0.0067312708878887, 0.0931674097798811, 0.8685143643990995, 0.0383182258210195, 0.8685143643990995, 0.0931674097798812, 0.0383182258210191, 0.3945202798001943, 0.5128232386790481, 0.0926564815207574, 0.5128232386790481, 0.3945202798001944, 0.0926564815207574, 0.1626774163944774, 0.7961338693570472, 0.0411887142484756, 0.7961338693570472, 0.1626774163944775, 0.0411887142484752, 0.2535890142188795, 0.7068400808109625, 0.0395709049701581, 0.7068400808109625, 0.2535890142188795, 0.0395709049701579, 0.3622522413177913, 0.5991550585073127, 0.0385927001748961, 0.5991550585073125, 0.3622522413177913, 0.0385927001748960, 0.2816225777061608, 0.6238424605572400, 0.0945349617365990, 0.6238424605572401, 0.2816225777061608, 0.0945349617365988, 0.3832726649926592, 0.6093393403750466, 0.0073879946322942, 0.6093393403750464, 0.3832726649926592, 0.0073879946322941, 0.2737503525162605, 0.7187036443214266, 0.0075460031623129, 0.7187036443214266, 0.2737503525162606, 0.0075460031623126, 0.4962552776757351, 0.4962552776757351, 0.0074894446485297, 0.0941213427973660, 0.8986440987448518, 0.0072345584577822, 0.8986440987448518, 0.0941213427973661, 0.0072345584577819, 0.2642313154382725, 0.4715373691234548, 0.2642313154382727, 0.1803961518867657, 0.7240375785858689, 0.0955662695273654, 0.7240375785858689, 0.1803961518867657, 0.0955662695273650, 0.4806125617925032, 0.4806125617925033, 0.0387748764149934, 0.1747373462828057, 0.8172747318363464, 0.0079879218808480, 0.8172747318363462, 0.1747373462828057, 0.0079879218808478, 0.0963284955992151, 0.8073430088015696, 0.0963284955992154, 0.0372914720512912, 0.9546336170785000, 0.0080749108702090, 0.9546336170785000, 0.0372914720512914, 0.0080749108702085, 0.3753529267020863, 0.3753529267020863, 0.2492941465958274 }; static double b_save[] = { 0.3333333333333334, 0.1622180501787945, 0.4188909749106028, 0.4188909749106029, 0.1623606337169265, 0.1623606337169263, 0.6752787325661475, 0.1703672824624437, 0.2414797600735941, 0.5881529574639625, 0.1703672824624437, 0.5881529574639625, 0.2414797600735942, 0.1697597958607361, 0.3289758089242264, 0.5012643952150377, 0.1697597958607361, 0.5012643952150377, 0.3289758089242266, 0.0409856290011173, 0.0409856290011169, 0.9180287419977659, 0.0067312708878885, 0.0067312708878882, 0.9865374582242232, 0.0383182258210194, 0.0931674097798812, 0.8685143643990996, 0.0383182258210194, 0.8685143643990996, 0.0931674097798815, 0.0926564815207575, 0.3945202798001944, 0.5128232386790483, 0.0926564815207575, 0.5128232386790482, 0.3945202798001946, 0.0411887142484754, 0.1626774163944774, 0.7961338693570472, 0.0411887142484754, 0.7961338693570472, 0.1626774163944777, 0.0395709049701581, 0.2535890142188795, 0.7068400808109626, 0.0395709049701581, 0.7068400808109626, 0.2535890142188797, 0.0385927001748961, 0.3622522413177914, 0.5991550585073128, 0.0385927001748961, 0.5991550585073127, 0.3622522413177915, 0.0945349617365990, 0.2816225777061609, 0.6238424605572404, 0.0945349617365990, 0.6238424605572404, 0.2816225777061611, 0.0073879946322942, 0.3832726649926593, 0.6093393403750468, 0.0073879946322942, 0.6093393403750467, 0.3832726649926595, 0.0075460031623128, 0.2737503525162605, 0.7187036443214270, 0.0075460031623128, 0.7187036443214267, 0.2737503525162608, 0.0074894446485298, 0.4962552776757352, 0.4962552776757354, 0.0072345584577821, 0.0941213427973660, 0.8986440987448521, 0.0072345584577821, 0.8986440987448520, 0.0941213427973664, 0.2642313154382727, 0.2642313154382726, 0.4715373691234549, 0.0955662695273653, 0.1803961518867657, 0.7240375785858691, 0.0955662695273653, 0.7240375785858693, 0.1803961518867660, 0.0387748764149935, 0.4806125617925033, 0.4806125617925034, 0.0079879218808480, 0.1747373462828057, 0.8172747318363466, 0.0079879218808480, 0.8172747318363466, 0.1747373462828060, 0.0963284955992153, 0.0963284955992151, 0.8073430088015697, 0.0080749108702088, 0.0372914720512912, 0.9546336170785000, 0.0080749108702088, 0.9546336170785000, 0.0372914720512916, 0.2492941465958275, 0.3753529267020864, 0.3753529267020864 }; static double c_save[] = { 0.3333333333333333, 0.4188909749106028, 0.1622180501787945, 0.4188909749106027, 0.6752787325661472, 0.1623606337169265, 0.1623606337169260, 0.5881529574639622, 0.1703672824624437, 0.2414797600735938, 0.2414797600735940, 0.1703672824624435, 0.5881529574639621, 0.5012643952150376, 0.1697597958607361, 0.3289758089242263, 0.3289758089242263, 0.1697597958607359, 0.5012643952150375, 0.9180287419977659, 0.0409856290011173, 0.0409856290011167, 0.9865374582242232, 0.0067312708878886, 0.0067312708878881, 0.8685143643990995, 0.0383182258210194, 0.0931674097798809, 0.0931674097798811, 0.0383182258210192, 0.8685143643990995, 0.5128232386790481, 0.0926564815207574, 0.3945202798001942, 0.3945202798001943, 0.0926564815207574, 0.5128232386790480, 0.7961338693570472, 0.0411887142484754, 0.1626774163944772, 0.1626774163944774, 0.0411887142484753, 0.7961338693570471, 0.7068400808109625, 0.0395709049701580, 0.2535890142188794, 0.2535890142188795, 0.0395709049701579, 0.7068400808109623, 0.5991550585073125, 0.0385927001748960, 0.3622522413177912, 0.3622522413177913, 0.0385927001748960, 0.5991550585073124, 0.6238424605572401, 0.0945349617365990, 0.2816225777061607, 0.2816225777061608, 0.0945349617365988, 0.6238424605572401, 0.6093393403750466, 0.0073879946322942, 0.3832726649926591, 0.3832726649926593, 0.0073879946322941, 0.6093393403750464, 0.7187036443214266, 0.0075460031623129, 0.2737503525162601, 0.2737503525162606, 0.0075460031623127, 0.7187036443214266, 0.4962552776757350, 0.0074894446485297, 0.4962552776757349, 0.8986440987448518, 0.0072345584577821, 0.0941213427973657, 0.0941213427973660, 0.0072345584577819, 0.8986440987448517, 0.4715373691234548, 0.2642313154382726, 0.2642313154382724, 0.7240375785858690, 0.0955662695273653, 0.1803961518867655, 0.1803961518867658, 0.0955662695273650, 0.7240375785858690, 0.4806125617925033, 0.0387748764149934, 0.4806125617925031, 0.8172747318363464, 0.0079879218808480, 0.1747373462828054, 0.1747373462828058, 0.0079879218808477, 0.8172747318363462, 0.8073430088015696, 0.0963284955992153, 0.0963284955992149, 0.9546336170785000, 0.0080749108702088, 0.0372914720512910, 0.0372914720512912, 0.0080749108702086, 0.9546336170784999, 0.3753529267020862, 0.2492941465958273, 0.3753529267020862 }; static double w_save[] = { 0.0125456898456003, 0.0131105327018852, 0.0131105327018852, 0.0131105327018852, 0.0103790160564002, 0.0103790160564002, 0.0103790160564002, 0.0141450458064848, 0.0141450458064848, 0.0141450458064848, 0.0141450458064848, 0.0141450458064848, 0.0141450458064848, 0.0152744426013246, 0.0152744426013246, 0.0152744426013246, 0.0152744426013246, 0.0152744426013246, 0.0152744426013246, 0.0038336997309292, 0.0038336997309292, 0.0038336997309292, 0.0006172545054966, 0.0006172545054966, 0.0006172545054966, 0.0053662714541678, 0.0053662714541678, 0.0053662714541678, 0.0053662714541678, 0.0053662714541678, 0.0053662714541678, 0.0150318543497413, 0.0150318543497413, 0.0150318543497413, 0.0150318543497413, 0.0150318543497413, 0.0150318543497413, 0.0072041341747974, 0.0072041341747974, 0.0072041341747974, 0.0072041341747974, 0.0072041341747974, 0.0072041341747974, 0.0089048769281636, 0.0089048769281636, 0.0089048769281636, 0.0089048769281636, 0.0089048769281636, 0.0089048769281636, 0.0099472518756824, 0.0099472518756824, 0.0099472518756824, 0.0099472518756824, 0.0099472518756824, 0.0099472518756824, 0.0143523515781575, 0.0143523515781575, 0.0143523515781575, 0.0143523515781575, 0.0143523515781575, 0.0143523515781575, 0.0042421492668038, 0.0042421492668038, 0.0042421492668038, 0.0042421492668038, 0.0042421492668038, 0.0042421492668038, 0.0040812750771165, 0.0040812750771165, 0.0040812750771165, 0.0040812750771165, 0.0040812750771165, 0.0040812750771165, 0.0043432467221707, 0.0043432467221707, 0.0043432467221707, 0.0025892123823980, 0.0025892123823980, 0.0025892123823980, 0.0025892123823980, 0.0025892123823980, 0.0025892123823980, 0.0205200086715098, 0.0205200086715098, 0.0205200086715098, 0.0118435621425431, 0.0118435621425431, 0.0118435621425431, 0.0118435621425431, 0.0118435621425431, 0.0118435621425431, 0.0103524947708526, 0.0103524947708526, 0.0103524947708526, 0.0037072267642463, 0.0037072267642463, 0.0037072267642463, 0.0037072267642463, 0.0037072267642463, 0.0037072267642463, 0.0100273930673889, 0.0100273930673889, 0.0100273930673889, 0.0017969475854466, 0.0017969475854466, 0.0017969475854466, 0.0017969475854466, 0.0017969475854466, 0.0017969475854466, 0.0189945865173527, 0.0189945865173527, 0.0189945865173527 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule25 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule25() returns the rule of precision 25. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3876420304045634, 0.3876420304045634, 0.2247159391908731, 0.2110045080614966, 0.5779909838770066, 0.2110045080614967, 0.4404169274793433, 0.5577642058863823, 0.0018188666342743, 0.5577642058863823, 0.4404169274793434, 0.0018188666342743, 0.2994923158045084, 0.4010153683909830, 0.2994923158045084, 0.1590079061973279, 0.8040319522230005, 0.0369601415796716, 0.8040319522230007, 0.1590079061973279, 0.0369601415796713, 0.0372229259924406, 0.9255541480151184, 0.0372229259924410, 0.1773537967572529, 0.7437881352371117, 0.0788580680056354, 0.7437881352371118, 0.1773537967572530, 0.0788580680056351, 0.1451092435745002, 0.7097815128509992, 0.1451092435745006, 0.2700667358209594, 0.6610857347475426, 0.0688475294314979, 0.6610857347475427, 0.2700667358209594, 0.0688475294314977, 0.3413910330211499, 0.5426091593378899, 0.1159998076409602, 0.5426091593378899, 0.3413910330211499, 0.1159998076409601, 0.3739379797195844, 0.5777445859930386, 0.0483174342873769, 0.5777445859930387, 0.3739379797195845, 0.0483174342873768, 0.0991330633416822, 0.8937386221570603, 0.0071283145012576, 0.8937386221570603, 0.0991330633416823, 0.0071283145012572, 0.2995064186296745, 0.4968006707860745, 0.2036929105842510, 0.4968006707860745, 0.2995064186296745, 0.2036929105842509, 0.4247593045405747, 0.4247593045405746, 0.1504813909188505, 0.1786298486036162, 0.8141339896484356, 0.0072361617479482, 0.8141339896484356, 0.1786298486036164, 0.0072361617479479, 0.3620688018959720, 0.6250173148539955, 0.0129138832500325, 0.6250173148539954, 0.3620688018959721, 0.0129138832500325, 0.0887929154893665, 0.8735191347263743, 0.0376879497842592, 0.8735191347263743, 0.0887929154893666, 0.0376879497842588, 0.2336228101417152, 0.6293704957712137, 0.1370066940870710, 0.6293704957712138, 0.2336228101417152, 0.1370066940870708, 0.4622087087487061, 0.4622087087487061, 0.0755825825025877, 0.2565954097090198, 0.7188645300434557, 0.0245400602475245, 0.7188645300434559, 0.2565954097090199, 0.0245400602475242, 0.0929497017007698, 0.8141005965984600, 0.0929497017007701, 0.0410688191117846, 0.9517423526265223, 0.0071888282616933, 0.9517423526265224, 0.0410688191117848, 0.0071888282616928, 0.0078353442826036, 0.9843293114347924, 0.0078353442826041, 0.4890393696603955, 0.4890393696603955, 0.0219212606792090, 0.2794161886492607, 0.7196923470332411, 0.0008914643174981, 0.7196923470332411, 0.2794161886492608, 0.0008914643174980 }; static double b_save[] = { 0.2247159391908732, 0.3876420304045635, 0.3876420304045636, 0.2110045080614968, 0.2110045080614966, 0.5779909838770069, 0.0018188666342744, 0.4404169274793434, 0.5577642058863825, 0.0018188666342744, 0.5577642058863823, 0.4404169274793436, 0.2994923158045086, 0.2994923158045085, 0.4010153683909831, 0.0369601415796715, 0.1590079061973279, 0.8040319522230007, 0.0369601415796715, 0.8040319522230007, 0.1590079061973282, 0.0372229259924409, 0.0372229259924406, 0.9255541480151186, 0.0788580680056353, 0.1773537967572529, 0.7437881352371120, 0.0788580680056353, 0.7437881352371120, 0.1773537967572532, 0.1451092435745005, 0.1451092435745003, 0.7097815128509993, 0.0688475294314979, 0.2700667358209594, 0.6610857347475428, 0.0688475294314979, 0.6610857347475428, 0.2700667358209596, 0.1159998076409602, 0.3413910330211499, 0.5426091593378901, 0.1159998076409602, 0.5426091593378900, 0.3413910330211500, 0.0483174342873770, 0.3739379797195844, 0.5777445859930388, 0.0483174342873770, 0.5777445859930387, 0.3739379797195846, 0.0071283145012574, 0.0991330633416822, 0.8937386221570605, 0.0071283145012574, 0.8937386221570605, 0.0991330633416825, 0.2036929105842510, 0.2995064186296746, 0.4968006707860746, 0.2036929105842510, 0.4968006707860746, 0.2995064186296747, 0.1504813909188506, 0.4247593045405748, 0.4247593045405749, 0.0072361617479482, 0.1786298486036162, 0.8141339896484358, 0.0072361617479482, 0.8141339896484358, 0.1786298486036166, 0.0129138832500325, 0.3620688018959721, 0.6250173148539957, 0.0129138832500325, 0.6250173148539956, 0.3620688018959722, 0.0376879497842591, 0.0887929154893666, 0.8735191347263744, 0.0376879497842591, 0.8735191347263744, 0.0887929154893669, 0.1370066940870710, 0.2336228101417153, 0.6293704957712140, 0.1370066940870710, 0.6293704957712140, 0.2336228101417155, 0.0755825825025878, 0.4622087087487062, 0.4622087087487063, 0.0245400602475244, 0.2565954097090198, 0.7188645300434559, 0.0245400602475244, 0.7188645300434559, 0.2565954097090201, 0.0929497017007700, 0.0929497017007698, 0.8141005965984602, 0.0071888282616930, 0.0410688191117846, 0.9517423526265224, 0.0071888282616930, 0.9517423526265224, 0.0410688191117850, 0.0078353442826039, 0.0078353442826036, 0.9843293114347926, 0.0219212606792091, 0.4890393696603955, 0.4890393696603957, 0.0008914643174981, 0.2794161886492607, 0.7196923470332415, 0.0008914643174981, 0.7196923470332413, 0.2794161886492610 }; static double c_save[] = { 0.3876420304045634, 0.2247159391908732, 0.3876420304045634, 0.5779909838770066, 0.2110045080614967, 0.2110045080614965, 0.5577642058863823, 0.0018188666342743, 0.4404169274793431, 0.4404169274793433, 0.0018188666342743, 0.5577642058863822, 0.4010153683909830, 0.2994923158045085, 0.2994923158045085, 0.8040319522230006, 0.0369601415796716, 0.1590079061973276, 0.1590079061973278, 0.0369601415796713, 0.8040319522230005, 0.9255541480151185, 0.0372229259924410, 0.0372229259924404, 0.7437881352371117, 0.0788580680056354, 0.1773537967572526, 0.1773537967572529, 0.0788580680056351, 0.7437881352371117, 0.7097815128509992, 0.1451092435745005, 0.1451092435745002, 0.6610857347475426, 0.0688475294314980, 0.2700667358209593, 0.2700667358209593, 0.0688475294314977, 0.6610857347475426, 0.5426091593378900, 0.1159998076409602, 0.3413910330211497, 0.3413910330211499, 0.1159998076409602, 0.5426091593378899, 0.5777445859930387, 0.0483174342873770, 0.3739379797195843, 0.3739379797195844, 0.0483174342873768, 0.5777445859930385, 0.8937386221570605, 0.0071283145012575, 0.0991330633416820, 0.0991330633416822, 0.0071283145012573, 0.8937386221570603, 0.4968006707860744, 0.2036929105842509, 0.2995064186296744, 0.2995064186296745, 0.2036929105842509, 0.4968006707860744, 0.4247593045405748, 0.1504813909188505, 0.4247593045405746, 0.8141339896484356, 0.0072361617479481, 0.1786298486036161, 0.1786298486036162, 0.0072361617479478, 0.8141339896484355, 0.6250173148539955, 0.0129138832500325, 0.3620688018959718, 0.3620688018959721, 0.0129138832500323, 0.6250173148539954, 0.8735191347263744, 0.0376879497842591, 0.0887929154893663, 0.0887929154893666, 0.0376879497842589, 0.8735191347263743, 0.6293704957712137, 0.1370066940870710, 0.2336228101417150, 0.2336228101417152, 0.1370066940870708, 0.6293704957712137, 0.4622087087487061, 0.0755825825025877, 0.4622087087487059, 0.7188645300434559, 0.0245400602475244, 0.2565954097090196, 0.2565954097090197, 0.0245400602475242, 0.7188645300434557, 0.8141005965984602, 0.0929497017007702, 0.0929497017007697, 0.9517423526265223, 0.0071888282616931, 0.0410688191117844, 0.0410688191117846, 0.0071888282616929, 0.9517423526265223, 0.9843293114347924, 0.0078353442826040, 0.0078353442826032, 0.4890393696603955, 0.0219212606792091, 0.4890393696603952, 0.7196923470332411, 0.0008914643174981, 0.2794161886492604, 0.2794161886492607, 0.0008914643174980, 0.7196923470332410 }; static double w_save[] = { 0.0136898515482722, 0.0136898515482722, 0.0136898515482722, 0.0115872632360106, 0.0115872632360106, 0.0115872632360106, 0.0016748178319347, 0.0016748178319347, 0.0016748178319347, 0.0016748178319347, 0.0016748178319347, 0.0016748178319347, 0.0180176407017015, 0.0180176407017015, 0.0180176407017015, 0.0063114780247593, 0.0063114780247593, 0.0063114780247593, 0.0063114780247593, 0.0063114780247593, 0.0063114780247593, 0.0033972977219047, 0.0033972977219047, 0.0033972977219047, 0.0095150215674558, 0.0095150215674558, 0.0095150215674558, 0.0095150215674558, 0.0095150215674558, 0.0095150215674558, 0.0114915258625648, 0.0114915258625648, 0.0114915258625648, 0.0108843936124369, 0.0108843936124369, 0.0108843936124369, 0.0108843936124369, 0.0108843936124369, 0.0108843936124369, 0.0158403522878984, 0.0158403522878984, 0.0158403522878984, 0.0158403522878984, 0.0158403522878984, 0.0158403522878984, 0.0106401706955088, 0.0106401706955088, 0.0106401706955088, 0.0106401706955088, 0.0106401706955088, 0.0106401706955088, 0.0025452716253490, 0.0025452716253490, 0.0025452716253490, 0.0025452716253490, 0.0025452716253490, 0.0025452716253490, 0.0179138208922761, 0.0179138208922761, 0.0179138208922761, 0.0179138208922761, 0.0179138208922761, 0.0179138208922761, 0.0159113101374584, 0.0159113101374584, 0.0159113101374584, 0.0032637396820492, 0.0032637396820492, 0.0032637396820492, 0.0032637396820492, 0.0032637396820492, 0.0032637396820492, 0.0054546383679744, 0.0054546383679744, 0.0054546383679744, 0.0054546383679744, 0.0054546383679744, 0.0054546383679744, 0.0052725619214294, 0.0052725619214294, 0.0052725619214294, 0.0052725619214294, 0.0052725619214294, 0.0052725619214294, 0.0137400825920226, 0.0137400825920226, 0.0137400825920226, 0.0137400825920226, 0.0137400825920226, 0.0137400825920226, 0.0136542751875280, 0.0136542751875280, 0.0136542751875280, 0.0073143409079328, 0.0073143409079328, 0.0073143409079328, 0.0073143409079328, 0.0073143409079328, 0.0073143409079328, 0.0091828212598200, 0.0091828212598200, 0.0091828212598200, 0.0016929836341273, 0.0016929836341273, 0.0016929836341273, 0.0016929836341273, 0.0016929836341273, 0.0016929836341273, 0.0008065102883246, 0.0008065102883246, 0.0008065102883246, 0.0084440859465211, 0.0084440859465211, 0.0084440859465211, 0.0015117020784589, 0.0015117020784589, 0.0015117020784589, 0.0015117020784589, 0.0015117020784589, 0.0015117020784589 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule26 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule26() returns the rule of precision 26. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.0800716549403165, 0.9151336840842468, 0.0047946609754368, 0.9151336840842468, 0.0800716549403166, 0.0047946609754365, 0.0316436115715308, 0.9392011922216335, 0.0291551962068360, 0.9392011922216333, 0.0316436115715308, 0.0291551962068356, 0.0667371225764661, 0.8665257548470675, 0.0667371225764665, 0.0753800475153987, 0.8984105884621026, 0.0262093640224987, 0.8984105884621026, 0.0753800475153986, 0.0262093640224984, 0.0331000343360323, 0.9612018477470925, 0.0056981179168754, 0.9612018477470925, 0.0331000343360324, 0.0056981179168749, 0.0063401164920767, 0.9873197670158463, 0.0063401164920771, 0.1324861896145673, 0.8257890876433117, 0.0417247227421210, 0.8257890876433117, 0.1324861896145674, 0.0417247227421207, 0.1086871329144021, 0.7912672079790702, 0.1000456591065276, 0.7912672079790704, 0.1086871329144022, 0.1000456591065273, 0.4937530328963848, 0.4937530328963847, 0.0124939342072304, 0.2502723132905265, 0.6291132845042245, 0.1206144022052490, 0.6291132845042245, 0.2502723132905265, 0.1206144022052489, 0.3890220620427617, 0.5814399954403304, 0.0295379425169078, 0.5814399954403304, 0.3890220620427618, 0.0295379425169077, 0.3585092964276616, 0.5541122384084940, 0.0873784651638445, 0.5541122384084940, 0.3585092964276616, 0.0873784651638444, 0.3887874971075940, 0.3887874971075940, 0.2224250057848119, 0.1868691794762216, 0.7368189190108190, 0.0763119015129595, 0.7368189190108190, 0.1868691794762216, 0.0763119015129592, 0.2731471009290787, 0.4537057981418425, 0.2731471009290788, 0.4147059095903063, 0.5832365594443230, 0.0020575309653708, 0.5832365594443230, 0.4147059095903063, 0.0020575309653707, 0.3194153053834387, 0.5101059661193124, 0.1704787284972489, 0.5101059661193124, 0.3194153053834387, 0.1704787284972488, 0.1437376261997640, 0.8482627657087517, 0.0079996080914844, 0.8482627657087517, 0.1437376261997642, 0.0079996080914840, 0.4718285633211660, 0.4718285633211661, 0.0563428733576679, 0.1542014303645442, 0.6915971392709114, 0.1542014303645444, 0.2837881388594704, 0.6650459874553918, 0.0511658736851378, 0.6650459874553918, 0.2837881388594705, 0.0511658736851376, 0.2120431633022055, 0.5759136733955887, 0.2120431633022057, 0.4359854193843832, 0.4359854193843832, 0.1280291612312335, 0.2165466664734771, 0.7606687342756272, 0.0227845992508957, 0.7606687342756272, 0.2165466664734772, 0.0227845992508955, 0.3333333333333333, 0.3128985030748800, 0.6776281990129065, 0.0094732979122136, 0.6776281990129064, 0.3128985030748800, 0.0094732979122134, 0.2264347974077175, 0.7731011948601069, 0.0004640077321757, 0.7731011948601069, 0.2264347974077175, 0.0004640077321755 }; static double b_save[] = { 0.0047946609754367, 0.0800716549403165, 0.9151336840842469, 0.0047946609754367, 0.9151336840842469, 0.0800716549403169, 0.0291551962068358, 0.0316436115715307, 0.9392011922216336, 0.0291551962068358, 0.9392011922216336, 0.0316436115715311, 0.0667371225764664, 0.0667371225764660, 0.8665257548470677, 0.0262093640224987, 0.0753800475153986, 0.8984105884621029, 0.0262093640224987, 0.8984105884621030, 0.0753800475153990, 0.0056981179168752, 0.0331000343360323, 0.9612018477470927, 0.0056981179168752, 0.9612018477470927, 0.0331000343360326, 0.0063401164920770, 0.0063401164920766, 0.9873197670158466, 0.0417247227421209, 0.1324861896145673, 0.8257890876433118, 0.0417247227421209, 0.8257890876433118, 0.1324861896145676, 0.1000456591065276, 0.1086871329144021, 0.7912672079790705, 0.1000456591065276, 0.7912672079790705, 0.1086871329144024, 0.0124939342072305, 0.4937530328963848, 0.4937530328963849, 0.1206144022052490, 0.2502723132905265, 0.6291132845042247, 0.1206144022052490, 0.6291132845042245, 0.2502723132905267, 0.0295379425169078, 0.3890220620427618, 0.5814399954403305, 0.0295379425169078, 0.5814399954403304, 0.3890220620427621, 0.0873784651638445, 0.3585092964276616, 0.5541122384084942, 0.0873784651638445, 0.5541122384084941, 0.3585092964276618, 0.2224250057848120, 0.3887874971075941, 0.3887874971075941, 0.0763119015129594, 0.1868691794762216, 0.7368189190108192, 0.0763119015129594, 0.7368189190108192, 0.1868691794762219, 0.2731471009290788, 0.2731471009290788, 0.4537057981418426, 0.0020575309653709, 0.4147059095903063, 0.5832365594443231, 0.0020575309653709, 0.5832365594443230, 0.4147059095903066, 0.1704787284972490, 0.3194153053834388, 0.5101059661193126, 0.1704787284972490, 0.5101059661193125, 0.3194153053834389, 0.0079996080914843, 0.1437376261997640, 0.8482627657087518, 0.0079996080914843, 0.8482627657087518, 0.1437376261997644, 0.0563428733576680, 0.4718285633211661, 0.4718285633211662, 0.1542014303645444, 0.1542014303645442, 0.6915971392709116, 0.0511658736851378, 0.2837881388594705, 0.6650459874553920, 0.0511658736851378, 0.6650459874553919, 0.2837881388594707, 0.2120431633022057, 0.2120431633022056, 0.5759136733955889, 0.1280291612312336, 0.4359854193843832, 0.4359854193843834, 0.0227845992508957, 0.2165466664734771, 0.7606687342756275, 0.0227845992508957, 0.7606687342756273, 0.2165466664734774, 0.3333333333333334, 0.0094732979122136, 0.3128985030748800, 0.6776281990129066, 0.0094732979122136, 0.6776281990129066, 0.3128985030748803, 0.0004640077321757, 0.2264347974077175, 0.7731011948601070, 0.0004640077321757, 0.7731011948601070, 0.2264347974077178 }; static double c_save[] = { 0.9151336840842468, 0.0047946609754367, 0.0800716549403163, 0.0800716549403165, 0.0047946609754365, 0.9151336840842467, 0.9392011922216335, 0.0291551962068358, 0.0316436115715305, 0.0316436115715308, 0.0291551962068356, 0.9392011922216333, 0.8665257548470676, 0.0667371225764665, 0.0667371225764658, 0.8984105884621028, 0.0262093640224987, 0.0753800475153984, 0.0753800475153987, 0.0262093640224984, 0.8984105884621026, 0.9612018477470925, 0.0056981179168753, 0.0331000343360319, 0.0331000343360323, 0.0056981179168749, 0.9612018477470925, 0.9873197670158463, 0.0063401164920770, 0.0063401164920763, 0.8257890876433118, 0.0417247227421210, 0.1324861896145672, 0.1324861896145673, 0.0417247227421208, 0.8257890876433117, 0.7912672079790704, 0.1000456591065276, 0.1086871329144019, 0.1086871329144021, 0.1000456591065274, 0.7912672079790702, 0.4937530328963847, 0.0124939342072304, 0.4937530328963846, 0.6291132845042245, 0.1206144022052490, 0.2502723132905263, 0.2502723132905264, 0.1206144022052490, 0.6291132845042244, 0.5814399954403303, 0.0295379425169078, 0.3890220620427617, 0.3890220620427617, 0.0295379425169078, 0.5814399954403302, 0.5541122384084940, 0.0873784651638444, 0.3585092964276613, 0.3585092964276615, 0.0873784651638444, 0.5541122384084938, 0.3887874971075940, 0.2224250057848119, 0.3887874971075939, 0.7368189190108190, 0.0763119015129595, 0.1868691794762213, 0.1868691794762216, 0.0763119015129592, 0.7368189190108190, 0.4537057981418425, 0.2731471009290788, 0.2731471009290786, 0.5832365594443228, 0.0020575309653708, 0.4147059095903062, 0.4147059095903062, 0.0020575309653708, 0.5832365594443227, 0.5101059661193122, 0.1704787284972489, 0.3194153053834385, 0.3194153053834387, 0.1704787284972488, 0.5101059661193122, 0.8482627657087517, 0.0079996080914843, 0.1437376261997638, 0.1437376261997640, 0.0079996080914840, 0.8482627657087516, 0.4718285633211660, 0.0563428733576679, 0.4718285633211659, 0.6915971392709115, 0.1542014303645444, 0.1542014303645439, 0.6650459874553918, 0.0511658736851378, 0.2837881388594703, 0.2837881388594704, 0.0511658736851376, 0.6650459874553916, 0.5759136733955887, 0.2120431633022057, 0.2120431633022054, 0.4359854193843832, 0.1280291612312336, 0.4359854193843831, 0.7606687342756272, 0.0227845992508957, 0.2165466664734768, 0.2165466664734771, 0.0227845992508955, 0.7606687342756271, 0.3333333333333333, 0.6776281990129065, 0.0094732979122135, 0.3128985030748798, 0.3128985030748800, 0.0094732979122133, 0.6776281990129063, 0.7731011948601068, 0.0004640077321756, 0.2264347974077173, 0.2264347974077175, 0.0004640077321755, 0.7731011948601068 }; static double w_save[] = { 0.0013985264481603, 0.0013985264481603, 0.0013985264481603, 0.0013985264481603, 0.0013985264481603, 0.0013985264481603, 0.0012055647737169, 0.0012055647737169, 0.0012055647737169, 0.0012055647737169, 0.0012055647737169, 0.0012055647737169, 0.0049138253029660, 0.0049138253029660, 0.0049138253029660, 0.0033055447129677, 0.0033055447129677, 0.0033055447129677, 0.0033055447129677, 0.0033055447129677, 0.0033055447129677, 0.0010857073429968, 0.0010857073429968, 0.0010857073429968, 0.0010857073429968, 0.0010857073429968, 0.0010857073429968, 0.0005269531166819, 0.0005269531166819, 0.0005269531166819, 0.0064035978997128, 0.0064035978997128, 0.0064035978997128, 0.0064035978997128, 0.0064035978997128, 0.0064035978997128, 0.0046142110763783, 0.0046142110763783, 0.0046142110763783, 0.0046142110763783, 0.0046142110763783, 0.0046142110763783, 0.0053021591818673, 0.0053021591818673, 0.0053021591818673, 0.0143794732275987, 0.0143794732275987, 0.0143794732275987, 0.0143794732275987, 0.0143794732275987, 0.0143794732275987, 0.0082597672170868, 0.0082597672170868, 0.0082597672170868, 0.0082597672170868, 0.0082597672170868, 0.0082597672170868, 0.0137279582160857, 0.0137279582160857, 0.0137279582160857, 0.0137279582160857, 0.0137279582160857, 0.0137279582160857, 0.0194680678371829, 0.0194680678371829, 0.0194680678371829, 0.0103976455281743, 0.0103976455281743, 0.0103976455281743, 0.0103976455281743, 0.0103976455281743, 0.0103976455281743, 0.0195356469232475, 0.0195356469232475, 0.0195356469232475, 0.0018571474709981, 0.0018571474709981, 0.0018571474709981, 0.0018571474709981, 0.0018571474709981, 0.0018571474709981, 0.0175991671806952, 0.0175991671806952, 0.0175991671806952, 0.0175991671806952, 0.0175991671806952, 0.0175991671806952, 0.0029667616626565, 0.0029667616626565, 0.0029667616626565, 0.0029667616626565, 0.0029667616626565, 0.0029667616626565, 0.0115285036346569, 0.0115285036346569, 0.0115285036346569, 0.0132552594485453, 0.0132552594485453, 0.0132552594485453, 0.0101071244320887, 0.0101071244320887, 0.0101071244320887, 0.0101071244320887, 0.0101071244320887, 0.0101071244320887, 0.0169443450785281, 0.0169443450785281, 0.0169443450785281, 0.0164124006025879, 0.0164124006025879, 0.0164124006025879, 0.0062693378460806, 0.0062693378460806, 0.0062693378460806, 0.0062693378460806, 0.0062693378460806, 0.0062693378460806, 0.0204866625892232, 0.0045915583873986, 0.0045915583873986, 0.0045915583873986, 0.0045915583873986, 0.0045915583873986, 0.0045915583873986, 0.0011395489158682, 0.0011395489158682, 0.0011395489158682, 0.0011395489158682, 0.0011395489158682, 0.0011395489158682 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule27 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule27() returns the rule of precision 27. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3807140211811871, 0.3807140211811871, 0.2385719576376256, 0.4466678037038646, 0.4466678037038646, 0.1066643925922708, 0.4161413788054121, 0.4161413788054121, 0.1677172423891756, 0.0803046477884383, 0.8393907044231230, 0.0803046477884388, 0.2870421965934966, 0.6822271986792305, 0.0307306047272730, 0.6822271986792305, 0.2870421965934966, 0.0307306047272727, 0.3450878417155684, 0.5257595182209819, 0.1291526400634497, 0.5257595182209819, 0.3450878417155684, 0.1291526400634496, 0.2334004066698710, 0.5331991866602577, 0.2334004066698712, 0.3759301570486618, 0.5960363568560882, 0.0280334860952500, 0.5960363568560882, 0.3759301570486618, 0.0280334860952499, 0.3011654651665091, 0.3976690696669817, 0.3011654651665091, 0.1747799663549000, 0.6504400672901998, 0.1747799663549002, 0.3169455889331320, 0.4739234899291993, 0.2091309211376687, 0.4739234899291992, 0.3169455889331320, 0.2091309211376686, 0.4072283930427198, 0.5267326941075414, 0.0660389128497386, 0.5267326941075414, 0.4072283930427199, 0.0660389128497386, 0.2135535984578239, 0.7454158247229943, 0.0410305768191818, 0.7454158247229943, 0.2135535984578240, 0.0410305768191816, 0.3288528780688926, 0.6658474815593083, 0.0052996403717991, 0.6658474815593083, 0.3288528780688927, 0.0052996403717989, 0.4855650541851628, 0.4855650541851628, 0.0288698916296744, 0.1392953061421487, 0.7976306984429004, 0.0630739954149511, 0.7976306984429004, 0.1392953061421489, 0.0630739954149507, 0.0325715201801815, 0.9348569596396367, 0.0325715201801819, 0.2552462546969780, 0.5957908943647818, 0.1489628509382402, 0.5957908943647818, 0.2552462546969780, 0.1489628509382400, 0.2083760156003741, 0.6969269019664952, 0.0946970824331307, 0.6969269019664952, 0.2083760156003741, 0.0946970824331305, 0.4400105519462155, 0.5544087310385245, 0.0055807170152600, 0.5544087310385244, 0.4400105519462155, 0.0055807170152600, 0.1275709019046775, 0.7448581961906449, 0.1275709019046778, 0.3022209412278211, 0.6227021563389826, 0.0750769024331963, 0.6227021563389826, 0.3022209412278211, 0.0750769024331961, 0.0819468025835337, 0.9110706680920073, 0.0069825293244591, 0.9110706680920073, 0.0819468025835338, 0.0069825293244588, 0.0343649699121420, 0.9595414606840931, 0.0060935694037650, 0.9595414606840931, 0.0343649699121421, 0.0060935694037646, 0.0801120738471011, 0.8848535036252014, 0.0350344225276975, 0.8848535036252014, 0.0801120738471012, 0.0350344225276972, 0.0066392191809586, 0.9867215616380824, 0.0066392191809590, 0.1472134318989225, 0.8334345667830385, 0.0193520013180390, 0.8334345667830385, 0.1472134318989225, 0.0193520013180388, 0.2297196532578432, 0.7629478741931164, 0.0073324725490405, 0.7629478741931163, 0.2297196532578433, 0.0073324725490403, 0.1476555211198698, 0.8518541504366672, 0.0004903284434630, 0.8518541504366672, 0.1476555211198698, 0.0004903284434627 }; static double b_save[] = { 0.2385719576376257, 0.3807140211811872, 0.3807140211811873, 0.1066643925922709, 0.4466678037038647, 0.4466678037038648, 0.1677172423891757, 0.4161413788054122, 0.4161413788054124, 0.0803046477884386, 0.0803046477884383, 0.8393907044231231, 0.0307306047272729, 0.2870421965934966, 0.6822271986792307, 0.0307306047272729, 0.6822271986792307, 0.2870421965934968, 0.1291526400634497, 0.3450878417155684, 0.5257595182209820, 0.1291526400634497, 0.5257595182209820, 0.3450878417155686, 0.2334004066698712, 0.2334004066698711, 0.5331991866602579, 0.0280334860952500, 0.3759301570486618, 0.5960363568560885, 0.0280334860952500, 0.5960363568560882, 0.3759301570486621, 0.3011654651665093, 0.3011654651665092, 0.3976690696669818, 0.1747799663549002, 0.1747799663549000, 0.6504400672902000, 0.2091309211376688, 0.3169455889331320, 0.4739234899291995, 0.2091309211376688, 0.4739234899291995, 0.3169455889331322, 0.0660389128497387, 0.4072283930427200, 0.5267326941075416, 0.0660389128497387, 0.5267326941075415, 0.4072283930427201, 0.0410305768191818, 0.2135535984578240, 0.7454158247229945, 0.0410305768191818, 0.7454158247229945, 0.2135535984578242, 0.0052996403717990, 0.3288528780688927, 0.6658474815593085, 0.0052996403717990, 0.6658474815593083, 0.3288528780688930, 0.0288698916296745, 0.4855650541851628, 0.4855650541851630, 0.0630739954149509, 0.1392953061421487, 0.7976306984429004, 0.0630739954149509, 0.7976306984429004, 0.1392953061421490, 0.0325715201801818, 0.0325715201801814, 0.9348569596396370, 0.1489628509382402, 0.2552462546969780, 0.5957908943647819, 0.1489628509382402, 0.5957908943647819, 0.2552462546969783, 0.0946970824331307, 0.2083760156003741, 0.6969269019664954, 0.0946970824331307, 0.6969269019664954, 0.2083760156003744, 0.0055807170152601, 0.4400105519462155, 0.5544087310385247, 0.0055807170152601, 0.5544087310385245, 0.4400105519462157, 0.1275709019046777, 0.1275709019046775, 0.7448581961906449, 0.0750769024331962, 0.3022209412278212, 0.6227021563389828, 0.0750769024331962, 0.6227021563389828, 0.3022209412278213, 0.0069825293244590, 0.0819468025835337, 0.9110706680920074, 0.0069825293244590, 0.9110706680920074, 0.0819468025835340, 0.0060935694037648, 0.0343649699121420, 0.9595414606840932, 0.0060935694037648, 0.9595414606840934, 0.0343649699121423, 0.0350344225276974, 0.0801120738471011, 0.8848535036252017, 0.0350344225276974, 0.8848535036252017, 0.0801120738471014, 0.0066392191809589, 0.0066392191809586, 0.9867215616380827, 0.0193520013180390, 0.1472134318989225, 0.8334345667830388, 0.0193520013180390, 0.8334345667830388, 0.1472134318989227, 0.0073324725490405, 0.2297196532578432, 0.7629478741931165, 0.0073324725490405, 0.7629478741931164, 0.2297196532578435, 0.0004903284434630, 0.1476555211198698, 0.8518541504366673, 0.0004903284434630, 0.8518541504366673, 0.1476555211198702 }; static double c_save[] = { 0.3807140211811872, 0.2385719576376256, 0.3807140211811871, 0.4466678037038647, 0.1066643925922707, 0.4466678037038644, 0.4161413788054121, 0.1677172423891756, 0.4161413788054120, 0.8393907044231231, 0.0803046477884387, 0.0803046477884380, 0.6822271986792305, 0.0307306047272728, 0.2870421965934964, 0.2870421965934966, 0.0307306047272727, 0.6822271986792304, 0.5257595182209819, 0.1291526400634497, 0.3450878417155683, 0.3450878417155684, 0.1291526400634496, 0.5257595182209819, 0.5331991866602578, 0.2334004066698712, 0.2334004066698709, 0.5960363568560882, 0.0280334860952499, 0.3759301570486615, 0.3759301570486617, 0.0280334860952499, 0.5960363568560880, 0.3976690696669816, 0.3011654651665091, 0.3011654651665091, 0.6504400672901998, 0.1747799663549002, 0.1747799663548998, 0.4739234899291993, 0.2091309211376687, 0.3169455889331319, 0.3169455889331320, 0.2091309211376686, 0.4739234899291992, 0.5267326941075414, 0.0660389128497386, 0.4072283930427197, 0.4072283930427199, 0.0660389128497386, 0.5267326941075413, 0.7454158247229942, 0.0410305768191818, 0.2135535984578236, 0.2135535984578239, 0.0410305768191815, 0.7454158247229942, 0.6658474815593083, 0.0052996403717990, 0.3288528780688924, 0.3288528780688927, 0.0052996403717990, 0.6658474815593081, 0.4855650541851627, 0.0288698916296743, 0.4855650541851627, 0.7976306984429005, 0.0630739954149509, 0.1392953061421486, 0.1392953061421487, 0.0630739954149507, 0.7976306984429002, 0.9348569596396368, 0.0325715201801819, 0.0325715201801811, 0.5957908943647818, 0.1489628509382401, 0.2552462546969779, 0.2552462546969780, 0.1489628509382400, 0.5957908943647817, 0.6969269019664953, 0.0946970824331307, 0.2083760156003739, 0.2083760156003741, 0.0946970824331305, 0.6969269019664952, 0.5544087310385245, 0.0055807170152600, 0.4400105519462153, 0.4400105519462155, 0.0055807170152601, 0.5544087310385244, 0.7448581961906449, 0.1275709019046777, 0.1275709019046773, 0.6227021563389826, 0.0750769024331962, 0.3022209412278208, 0.3022209412278211, 0.0750769024331960, 0.6227021563389825, 0.9110706680920073, 0.0069825293244590, 0.0819468025835334, 0.0819468025835337, 0.0069825293244589, 0.9110706680920072, 0.9595414606840932, 0.0060935694037649, 0.0343649699121418, 0.0343649699121421, 0.0060935694037646, 0.9595414606840931, 0.8848535036252015, 0.0350344225276975, 0.0801120738471008, 0.0801120738471012, 0.0350344225276972, 0.8848535036252014, 0.9867215616380826, 0.0066392191809590, 0.0066392191809583, 0.8334345667830386, 0.0193520013180390, 0.1472134318989221, 0.1472134318989225, 0.0193520013180387, 0.8334345667830384, 0.7629478741931164, 0.0073324725490404, 0.2297196532578430, 0.2297196532578433, 0.0073324725490403, 0.7629478741931163, 0.8518541504366672, 0.0004903284434630, 0.1476555211198697, 0.1476555211198698, 0.0004903284434629, 0.8518541504366671 }; static double w_save[] = { 0.0095600849674599, 0.0095600849674599, 0.0095600849674599, 0.0094101598094542, 0.0094101598094542, 0.0094101598094542, 0.0120502270241504, 0.0120502270241504, 0.0120502270241504, 0.0052126218728019, 0.0052126218728019, 0.0052126218728019, 0.0055317948337667, 0.0055317948337667, 0.0055317948337667, 0.0055317948337667, 0.0055317948337667, 0.0055317948337667, 0.0125574362040365, 0.0125574362040365, 0.0125574362040365, 0.0125574362040365, 0.0125574362040365, 0.0125574362040365, 0.0134713153980494, 0.0134713153980494, 0.0134713153980494, 0.0063951526994544, 0.0063951526994544, 0.0063951526994544, 0.0063951526994544, 0.0063951526994544, 0.0063951526994544, 0.0157479657813627, 0.0157479657813627, 0.0157479657813627, 0.0112824425446984, 0.0112824425446984, 0.0112824425446984, 0.0137153932305508, 0.0137153932305508, 0.0137153932305508, 0.0137153932305508, 0.0137153932305508, 0.0137153932305508, 0.0098622701189896, 0.0098622701189896, 0.0098622701189896, 0.0098622701189896, 0.0098622701189896, 0.0098622701189896, 0.0064553729049297, 0.0064553729049297, 0.0064553729049297, 0.0064553729049297, 0.0064553729049297, 0.0064553729049297, 0.0029278263617991, 0.0029278263617991, 0.0029278263617991, 0.0029278263617991, 0.0029278263617991, 0.0029278263617991, 0.0071172374128746, 0.0071172374128746, 0.0071172374128746, 0.0071306353104870, 0.0071306353104870, 0.0071306353104870, 0.0071306353104870, 0.0071306353104870, 0.0071306353104870, 0.0027773395289542, 0.0027773395289542, 0.0027773395289542, 0.0123476631308614, 0.0123476631308614, 0.0123476631308614, 0.0123476631308614, 0.0123476631308614, 0.0123476631308614, 0.0106937005896163, 0.0106937005896163, 0.0106937005896163, 0.0106937005896163, 0.0106937005896163, 0.0106937005896163, 0.0032424675976393, 0.0032424675976393, 0.0032424675976393, 0.0032424675976393, 0.0032424675976393, 0.0032424675976393, 0.0097432449228177, 0.0097432449228177, 0.0097432449228177, 0.0109306110929133, 0.0109306110929133, 0.0109306110929133, 0.0109306110929133, 0.0109306110929133, 0.0109306110929133, 0.0020151231272897, 0.0020151231272897, 0.0020151231272897, 0.0020151231272897, 0.0020151231272897, 0.0020151231272897, 0.0011967736084732, 0.0011967736084732, 0.0011967736084732, 0.0011967736084732, 0.0011967736084732, 0.0011967736084732, 0.0043271580353607, 0.0043271580353607, 0.0043271580353607, 0.0043271580353607, 0.0043271580353607, 0.0043271580353607, 0.0005754424056705, 0.0005754424056705, 0.0005754424056705, 0.0046223871117811, 0.0046223871117811, 0.0046223871117811, 0.0046223871117811, 0.0046223871117811, 0.0046223871117811, 0.0033942537388070, 0.0033942537388070, 0.0033942537388070, 0.0033942537388070, 0.0033942537388070, 0.0033942537388070, 0.0008466061357639, 0.0008466061357639, 0.0008466061357639, 0.0008466061357639, 0.0008466061357639, 0.0008466061357639 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule28 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule28() returns the rule of precision 28. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3039829225164841, 0.3920341549670316, 0.3039829225164841, 0.0455054005583464, 0.9329702140721974, 0.0215243853694563, 0.9329702140721974, 0.0455054005583465, 0.0215243853694558, 0.2133944547670873, 0.7375358758753532, 0.0490696693575595, 0.7375358758753532, 0.2133944547670873, 0.0490696693575593, 0.0048041261966579, 0.9903917476066839, 0.0048041261966584, 0.4582799042404119, 0.4582799042404120, 0.0834401915191761, 0.2421025119193196, 0.5802390377843101, 0.1776584502963703, 0.5802390377843101, 0.2421025119193198, 0.1776584502963702, 0.3862679735700421, 0.3862679735700420, 0.2274640528599158, 0.3271907320191700, 0.4829969116880932, 0.1898123562927368, 0.4829969116880932, 0.3271907320191700, 0.1898123562927368, 0.1419981669331742, 0.8535434510435363, 0.0044583820232894, 0.8535434510435365, 0.1419981669331742, 0.0044583820232890, 0.1753963931914617, 0.7369256303241862, 0.0876779764843521, 0.7369256303241862, 0.1753963931914618, 0.0876779764843519, 0.3921396133344145, 0.5446800590311748, 0.0631803276344107, 0.5446800590311748, 0.3921396133344145, 0.0631803276344106, 0.2582640721504621, 0.4834718556990756, 0.2582640721504622, 0.3341456150359213, 0.6617049208301551, 0.0041494641339236, 0.6617049208301550, 0.3341456150359213, 0.0041494641339235, 0.1741461960511821, 0.8030589990229017, 0.0227948049259163, 0.8030589990229016, 0.1741461960511822, 0.0227948049259160, 0.2758390080718242, 0.7014601475563789, 0.0227008443717971, 0.7014601475563788, 0.2758390080718242, 0.0227008443717968, 0.0262226671646523, 0.9676276842926838, 0.0061496485426642, 0.9676276842926838, 0.0262226671646523, 0.0061496485426637, 0.2430472023659261, 0.6449191682918028, 0.1120336293422710, 0.6449191682918028, 0.2430472023659263, 0.1120336293422708, 0.2299929840579072, 0.7652255261691058, 0.0047814897729871, 0.7652255261691057, 0.2299929840579072, 0.0047814897729869, 0.1058958441786275, 0.7882083116427446, 0.1058958441786279, 0.4295522021188993, 0.4295522021188993, 0.1408955957622013, 0.2956082808724017, 0.6419429769479655, 0.0624487421796328, 0.6419429769479654, 0.2956082808724017, 0.0624487421796327, 0.1213934507540912, 0.8283953633324806, 0.0502111859134282, 0.8283953633324806, 0.1213934507540914, 0.0502111859134279, 0.3738238003102096, 0.6004482009469115, 0.0257279987428787, 0.6004482009469116, 0.3738238003102097, 0.0257279987428786, 0.4427834065202436, 0.5515700274862902, 0.0056465659934661, 0.5515700274862904, 0.4427834065202436, 0.0056465659934661, 0.3377986632005823, 0.5441122670843226, 0.1180890697150950, 0.5441122670843226, 0.3377986632005823, 0.1180890697150949, 0.0922291891952822, 0.8895285197924230, 0.0182422910122948, 0.8895285197924231, 0.0922291891952822, 0.0182422910122945, 0.4848411325625894, 0.4848411325625895, 0.0303177348748211, 0.1586376888630596, 0.6827246222738805, 0.1586376888630599, 0.0608391923927586, 0.8783216152144825, 0.0608391923927590, 0.0702907404781327, 0.9285090039203800, 0.0012002556014873, 0.9285090039203802, 0.0702907404781328, 0.0012002556014869 }; static double b_save[] = { 0.3039829225164842, 0.3039829225164842, 0.3920341549670319, 0.0215243853694561, 0.0455054005583464, 0.9329702140721976, 0.0215243853694561, 0.9329702140721976, 0.0455054005583467, 0.0490696693575595, 0.2133944547670873, 0.7375358758753534, 0.0490696693575595, 0.7375358758753533, 0.2133944547670876, 0.0048041261966582, 0.0048041261966579, 0.9903917476066839, 0.0834401915191761, 0.4582799042404120, 0.4582799042404122, 0.1776584502963703, 0.2421025119193198, 0.5802390377843101, 0.1776584502963703, 0.5802390377843101, 0.2421025119193199, 0.2274640528599159, 0.3862679735700422, 0.3862679735700422, 0.1898123562927369, 0.3271907320191700, 0.4829969116880933, 0.1898123562927369, 0.4829969116880933, 0.3271907320191702, 0.0044583820232893, 0.1419981669331742, 0.8535434510435367, 0.0044583820232893, 0.8535434510435367, 0.1419981669331745, 0.0876779764843520, 0.1753963931914617, 0.7369256303241863, 0.0876779764843520, 0.7369256303241863, 0.1753963931914620, 0.0631803276344107, 0.3921396133344145, 0.5446800590311750, 0.0631803276344107, 0.5446800590311749, 0.3921396133344148, 0.2582640721504623, 0.2582640721504622, 0.4834718556990758, 0.0041494641339237, 0.3341456150359213, 0.6617049208301553, 0.0041494641339237, 0.6617049208301551, 0.3341456150359216, 0.0227948049259162, 0.1741461960511821, 0.8030589990229018, 0.0227948049259162, 0.8030589990229018, 0.1741461960511825, 0.0227008443717970, 0.2758390080718242, 0.7014601475563790, 0.0227008443717970, 0.7014601475563790, 0.2758390080718244, 0.0061496485426640, 0.0262226671646522, 0.9676276842926838, 0.0061496485426640, 0.9676276842926840, 0.0262226671646526, 0.1120336293422710, 0.2430472023659262, 0.6449191682918030, 0.1120336293422710, 0.6449191682918030, 0.2430472023659264, 0.0047814897729871, 0.2299929840579072, 0.7652255261691059, 0.0047814897729871, 0.7652255261691059, 0.2299929840579075, 0.1058958441786278, 0.1058958441786275, 0.7882083116427449, 0.1408955957622014, 0.4295522021188994, 0.4295522021188995, 0.0624487421796329, 0.2956082808724017, 0.6419429769479658, 0.0624487421796329, 0.6419429769479655, 0.2956082808724020, 0.0502111859134281, 0.1213934507540912, 0.8283953633324808, 0.0502111859134281, 0.8283953633324808, 0.1213934507540915, 0.0257279987428787, 0.3738238003102097, 0.6004482009469118, 0.0257279987428787, 0.6004482009469116, 0.3738238003102100, 0.0056465659934662, 0.4427834065202436, 0.5515700274862906, 0.0056465659934662, 0.5515700274862904, 0.4427834065202438, 0.1180890697150951, 0.3377986632005824, 0.5441122670843228, 0.1180890697150951, 0.5441122670843228, 0.3377986632005825, 0.0182422910122947, 0.0922291891952822, 0.8895285197924232, 0.0182422910122947, 0.8895285197924232, 0.0922291891952825, 0.0303177348748211, 0.4848411325625895, 0.4848411325625896, 0.1586376888630598, 0.1586376888630597, 0.6827246222738806, 0.0608391923927589, 0.0608391923927586, 0.8783216152144826, 0.0012002556014872, 0.0702907404781327, 0.9285090039203803, 0.0012002556014872, 0.9285090039203803, 0.0702907404781331 }; static double c_save[] = { 0.3920341549670317, 0.3039829225164841, 0.3039829225164841, 0.9329702140721975, 0.0215243853694563, 0.0455054005583461, 0.0455054005583465, 0.0215243853694559, 0.9329702140721975, 0.7375358758753532, 0.0490696693575595, 0.2133944547670871, 0.2133944547670873, 0.0490696693575593, 0.7375358758753531, 0.9903917476066840, 0.0048041261966582, 0.0048041261966577, 0.4582799042404119, 0.0834401915191760, 0.4582799042404118, 0.5802390377843101, 0.1776584502963702, 0.2421025119193196, 0.2421025119193196, 0.1776584502963702, 0.5802390377843100, 0.3862679735700420, 0.2274640528599158, 0.3862679735700420, 0.4829969116880931, 0.1898123562927367, 0.3271907320191699, 0.3271907320191699, 0.1898123562927367, 0.4829969116880931, 0.8535434510435365, 0.0044583820232895, 0.1419981669331739, 0.1419981669331742, 0.0044583820232891, 0.8535434510435363, 0.7369256303241862, 0.0876779764843520, 0.1753963931914616, 0.1753963931914617, 0.0876779764843519, 0.7369256303241862, 0.5446800590311749, 0.0631803276344107, 0.3921396133344143, 0.3921396133344145, 0.0631803276344106, 0.5446800590311747, 0.4834718556990756, 0.2582640721504622, 0.2582640721504620, 0.6617049208301550, 0.0041494641339236, 0.3341456150359210, 0.3341456150359213, 0.0041494641339236, 0.6617049208301549, 0.8030589990229017, 0.0227948049259162, 0.1741461960511819, 0.1741461960511822, 0.0227948049259160, 0.8030589990229016, 0.7014601475563788, 0.0227008443717970, 0.2758390080718239, 0.2758390080718242, 0.0227008443717968, 0.7014601475563786, 0.9676276842926838, 0.0061496485426640, 0.0262226671646520, 0.0262226671646523, 0.0061496485426636, 0.9676276842926838, 0.6449191682918028, 0.1120336293422710, 0.2430472023659260, 0.2430472023659262, 0.1120336293422708, 0.6449191682918027, 0.7652255261691058, 0.0047814897729870, 0.2299929840579069, 0.2299929840579072, 0.0047814897729869, 0.7652255261691057, 0.7882083116427447, 0.1058958441786279, 0.1058958441786272, 0.4295522021188993, 0.1408955957622013, 0.4295522021188992, 0.6419429769479654, 0.0624487421796328, 0.2956082808724014, 0.2956082808724017, 0.0624487421796328, 0.6419429769479653, 0.8283953633324806, 0.0502111859134282, 0.1213934507540910, 0.1213934507540912, 0.0502111859134279, 0.8283953633324806, 0.6004482009469115, 0.0257279987428788, 0.3738238003102096, 0.3738238003102096, 0.0257279987428787, 0.6004482009469114, 0.5515700274862902, 0.0056465659934662, 0.4427834065202433, 0.4427834065202435, 0.0056465659934660, 0.5515700274862902, 0.5441122670843227, 0.1180890697150950, 0.3377986632005822, 0.3377986632005823, 0.1180890697150949, 0.5441122670843226, 0.8895285197924231, 0.0182422910122948, 0.0922291891952820, 0.0922291891952822, 0.0182422910122946, 0.8895285197924230, 0.4848411325625894, 0.0303177348748210, 0.4848411325625892, 0.6827246222738805, 0.1586376888630598, 0.1586376888630595, 0.8783216152144825, 0.0608391923927590, 0.0608391923927584, 0.9285090039203800, 0.0012002556014872, 0.0702907404781324, 0.0702907404781327, 0.0012002556014870, 0.9285090039203799 }; static double w_save[] = { 0.0143624663006461, 0.0143624663006461, 0.0143624663006461, 0.0021175395576809, 0.0021175395576809, 0.0021175395576809, 0.0021175395576809, 0.0021175395576809, 0.0021175395576809, 0.0058956722345142, 0.0058956722345142, 0.0058956722345142, 0.0058956722345142, 0.0058956722345142, 0.0058956722345142, 0.0003111352086815, 0.0003111352086815, 0.0003111352086815, 0.0088517050108932, 0.0088517050108932, 0.0088517050108932, 0.0125572562166769, 0.0125572562166769, 0.0125572562166769, 0.0125572562166769, 0.0125572562166769, 0.0125572562166769, 0.0142105863904482, 0.0142105863904482, 0.0142105863904482, 0.0131061141240994, 0.0131061141240994, 0.0131061141240994, 0.0131061141240994, 0.0131061141240994, 0.0131061141240994, 0.0017788954192555, 0.0017788954192555, 0.0017788954192555, 0.0017788954192555, 0.0017788954192555, 0.0017788954192555, 0.0080119292866950, 0.0080119292866950, 0.0080119292866950, 0.0080119292866950, 0.0080119292866950, 0.0080119292866950, 0.0084646957342766, 0.0084646957342766, 0.0084646957342766, 0.0084646957342766, 0.0084646957342766, 0.0084646957342766, 0.0130927485890890, 0.0130927485890890, 0.0130927485890890, 0.0023767642676878, 0.0023767642676878, 0.0023767642676878, 0.0023767642676878, 0.0023767642676878, 0.0023767642676878, 0.0042769423350179, 0.0042769423350179, 0.0042769423350179, 0.0042769423350179, 0.0042769423350179, 0.0042769423350179, 0.0051312773820373, 0.0051312773820373, 0.0051312773820373, 0.0051312773820373, 0.0051312773820373, 0.0051312773820373, 0.0009485404258894, 0.0009485404258894, 0.0009485404258894, 0.0009485404258894, 0.0009485404258894, 0.0009485404258894, 0.0102459865617042, 0.0102459865617042, 0.0102459865617042, 0.0102459865617042, 0.0102459865617042, 0.0102459865617042, 0.0023245453644640, 0.0023245453644640, 0.0023245453644640, 0.0023245453644640, 0.0023245453644640, 0.0023245453644640, 0.0078099433710863, 0.0078099433710863, 0.0078099433710863, 0.0135475956033255, 0.0135475956033255, 0.0135475956033255, 0.0089251161402765, 0.0089251161402765, 0.0089251161402765, 0.0089251161402765, 0.0089251161402765, 0.0089251161402765, 0.0059178837723539, 0.0059178837723539, 0.0059178837723539, 0.0059178837723539, 0.0059178837723539, 0.0059178837723539, 0.0062605346429685, 0.0062605346429685, 0.0062605346429685, 0.0062605346429685, 0.0062605346429685, 0.0062605346429685, 0.0031401776434880, 0.0031401776434880, 0.0031401776434880, 0.0031401776434880, 0.0031401776434880, 0.0031401776434880, 0.0127871384229558, 0.0127871384229558, 0.0127871384229558, 0.0127871384229558, 0.0127871384229558, 0.0127871384229558, 0.0032049161907930, 0.0032049161907930, 0.0032049161907930, 0.0032049161907930, 0.0032049161907930, 0.0032049161907930, 0.0076821105785950, 0.0076821105785950, 0.0076821105785950, 0.0119426696402482, 0.0119426696402482, 0.0119426696402482, 0.0051282520046781, 0.0051282520046781, 0.0051282520046781, 0.0007251345949861, 0.0007251345949861, 0.0007251345949861, 0.0007251345949861, 0.0007251345949861, 0.0007251345949861 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule29 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule29() returns the rule of precision 29. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.0589421088402292, 0.9383291479118497, 0.0027287432479212, 0.9383291479118497, 0.0589421088402293, 0.0027287432479208, 0.3497880100093318, 0.4930342901234747, 0.1571776998671934, 0.4930342901234748, 0.3497880100093319, 0.1571776998671934, 0.3230018235435502, 0.6748972098116223, 0.0021009666448276, 0.6748972098116223, 0.3230018235435501, 0.0021009666448274, 0.4989148246376862, 0.4989148246376862, 0.0021703507246276, 0.1581458542495161, 0.7736883369367373, 0.0681658088137465, 0.7736883369367374, 0.1581458542495162, 0.0681658088137463, 0.0295494682613534, 0.9596195731350373, 0.0108309586036096, 0.9596195731350373, 0.0295494682613534, 0.0108309586036091, 0.2918191734265371, 0.4892484845932904, 0.2189323419801725, 0.4892484845932904, 0.2918191734265371, 0.2189323419801724, 0.0755221785129958, 0.9031909252462709, 0.0212868962407334, 0.9031909252462710, 0.0755221785129958, 0.0212868962407330, 0.1171166695088989, 0.8420361139149987, 0.0408472165761026, 0.8420361139149987, 0.1171166695088989, 0.0408472165761022, 0.0111662181081692, 0.9872302853957871, 0.0016034964960439, 0.9872302853957869, 0.0111662181081692, 0.0016034964960435, 0.4343804267617306, 0.4343804267617307, 0.1312391464765387, 0.0410973356271179, 0.9178053287457638, 0.0410973356271184, 0.2080456492790871, 0.6904083654940788, 0.1015459852268340, 0.6904083654940788, 0.2080456492790871, 0.1015459852268338, 0.3922101149804348, 0.5662628237507425, 0.0415270612688227, 0.5662628237507424, 0.3922101149804348, 0.0415270612688226, 0.3597112755099758, 0.5464396833448917, 0.0938490411451324, 0.5464396833448917, 0.3597112755099759, 0.0938490411451323, 0.2458746994828754, 0.7454392707127403, 0.0086860298043842, 0.7454392707127405, 0.2458746994828755, 0.0086860298043840, 0.1670027381749231, 0.8154081377810313, 0.0175891240440457, 0.8154081377810313, 0.1670027381749231, 0.0175891240440454, 0.2084053051324008, 0.5831893897351982, 0.2084053051324009, 0.1150085986319464, 0.8794678768558409, 0.0055235245122127, 0.8794678768558410, 0.1150085986319465, 0.0055235245122124, 0.1607458844319635, 0.6785082311360726, 0.1607458844319638, 0.3153953981173191, 0.6607456749400253, 0.0238589269426557, 0.6607456749400252, 0.3153953981173192, 0.0238589269426554, 0.2232226502248206, 0.7364820152304076, 0.0402953345447719, 0.7364820152304076, 0.2232226502248207, 0.0402953345447716, 0.2883958599187324, 0.6437257357698205, 0.0678784043114471, 0.6437257357698205, 0.2883958599187324, 0.0678784043114470, 0.4884016029326027, 0.4884016029326027, 0.0231967941347945, 0.2673663502727756, 0.5930980425461417, 0.1395356071810827, 0.5930980425461417, 0.2673663502727755, 0.1395356071810825, 0.3023864112151284, 0.3952271775697430, 0.3023864112151284, 0.4057653952988916, 0.5861680189969418, 0.0080665857041666, 0.5861680189969418, 0.4057653952988916, 0.0080665857041665, 0.1144268129944254, 0.7711463740111488, 0.1144268129944257, 0.4647624310807389, 0.4647624310807389, 0.0704751378385221, 0.0737218813900997, 0.8525562372198003, 0.0737218813901001, 0.3906191787832637, 0.3906191787832638, 0.2187616424334725, 0.1863207276753595, 0.8135558255123531, 0.0001234468122875, 0.8135558255123529, 0.1863207276753596, 0.0001234468122872 }; static double b_save[] = { 0.0027287432479211, 0.0589421088402292, 0.9383291479118498, 0.0027287432479211, 0.9383291479118498, 0.0589421088402295, 0.1571776998671935, 0.3497880100093319, 0.4930342901234749, 0.1571776998671935, 0.4930342901234748, 0.3497880100093320, 0.0021009666448276, 0.3230018235435502, 0.6748972098116225, 0.0021009666448276, 0.6748972098116225, 0.3230018235435504, 0.0021703507246276, 0.4989148246376863, 0.4989148246376864, 0.0681658088137464, 0.1581458542495161, 0.7736883369367377, 0.0681658088137464, 0.7736883369367376, 0.1581458542495164, 0.0108309586036094, 0.0295494682613534, 0.9596195731350372, 0.0108309586036094, 0.9596195731350375, 0.0295494682613537, 0.2189323419801726, 0.2918191734265372, 0.4892484845932905, 0.2189323419801726, 0.4892484845932905, 0.2918191734265372, 0.0212868962407333, 0.0755221785129958, 0.9031909252462711, 0.0212868962407333, 0.9031909252462711, 0.0755221785129961, 0.0408472165761025, 0.1171166695088989, 0.8420361139149987, 0.0408472165761025, 0.8420361139149989, 0.1171166695088992, 0.0016034964960438, 0.0111662181081691, 0.9872302853957873, 0.0016034964960438, 0.9872302853957873, 0.0111662181081695, 0.1312391464765388, 0.4343804267617307, 0.4343804267617308, 0.0410973356271182, 0.0410973356271179, 0.9178053287457639, 0.1015459852268340, 0.2080456492790872, 0.6904083654940790, 0.1015459852268340, 0.6904083654940790, 0.2080456492790874, 0.0415270612688227, 0.3922101149804349, 0.5662628237507427, 0.0415270612688227, 0.5662628237507425, 0.3922101149804351, 0.0938490411451324, 0.3597112755099759, 0.5464396833448918, 0.0938490411451324, 0.5464396833448918, 0.3597112755099761, 0.0086860298043841, 0.2458746994828755, 0.7454392707127405, 0.0086860298043841, 0.7454392707127405, 0.2458746994828757, 0.0175891240440456, 0.1670027381749231, 0.8154081377810315, 0.0175891240440456, 0.8154081377810315, 0.1670027381749234, 0.2084053051324010, 0.2084053051324008, 0.5831893897351984, 0.0055235245122126, 0.1150085986319464, 0.8794678768558412, 0.0055235245122126, 0.8794678768558412, 0.1150085986319467, 0.1607458844319638, 0.1607458844319636, 0.6785082311360728, 0.0238589269426556, 0.3153953981173191, 0.6607456749400253, 0.0238589269426556, 0.6607456749400253, 0.3153953981173194, 0.0402953345447718, 0.2232226502248206, 0.7364820152304077, 0.0402953345447718, 0.7364820152304077, 0.2232226502248209, 0.0678784043114471, 0.2883958599187324, 0.6437257357698207, 0.0678784043114471, 0.6437257357698207, 0.2883958599187327, 0.0231967941347945, 0.4884016029326028, 0.4884016029326029, 0.1395356071810827, 0.2673663502727756, 0.5930980425461420, 0.1395356071810827, 0.5930980425461420, 0.2673663502727758, 0.3023864112151286, 0.3023864112151285, 0.3952271775697432, 0.0080665857041666, 0.4057653952988916, 0.5861680189969420, 0.0080665857041666, 0.5861680189969419, 0.4057653952988918, 0.1144268129944257, 0.1144268129944254, 0.7711463740111490, 0.0704751378385222, 0.4647624310807390, 0.4647624310807391, 0.0737218813901000, 0.0737218813900997, 0.8525562372198006, 0.2187616424334726, 0.3906191787832639, 0.3906191787832639, 0.0001234468122874, 0.1863207276753596, 0.8135558255123532, 0.0001234468122874, 0.8135558255123531, 0.1863207276753599 }; static double c_save[] = { 0.9383291479118497, 0.0027287432479211, 0.0589421088402289, 0.0589421088402292, 0.0027287432479208, 0.9383291479118496, 0.4930342901234747, 0.1571776998671933, 0.3497880100093317, 0.3497880100093317, 0.1571776998671933, 0.4930342901234746, 0.6748972098116224, 0.0021009666448276, 0.3230018235435500, 0.3230018235435502, 0.0021009666448274, 0.6748972098116222, 0.4989148246376862, 0.0021703507246275, 0.4989148246376860, 0.7736883369367374, 0.0681658088137465, 0.1581458542495159, 0.1581458542495161, 0.0681658088137462, 0.7736883369367373, 0.9596195731350372, 0.0108309586036093, 0.0295494682613533, 0.0295494682613533, 0.0108309586036092, 0.9596195731350372, 0.4892484845932904, 0.2189323419801724, 0.2918191734265370, 0.2918191734265371, 0.2189323419801725, 0.4892484845932903, 0.9031909252462710, 0.0212868962407334, 0.0755221785129956, 0.0755221785129958, 0.0212868962407331, 0.9031909252462709, 0.8420361139149987, 0.0408472165761025, 0.1171166695088987, 0.1171166695088989, 0.0408472165761021, 0.8420361139149986, 0.9872302853957871, 0.0016034964960438, 0.0111662181081689, 0.0111662181081693, 0.0016034964960435, 0.9872302853957871, 0.4343804267617306, 0.1312391464765387, 0.4343804267617306, 0.9178053287457638, 0.0410973356271183, 0.0410973356271177, 0.6904083654940788, 0.1015459852268340, 0.2080456492790870, 0.2080456492790872, 0.1015459852268338, 0.6904083654940787, 0.5662628237507424, 0.0415270612688226, 0.3922101149804347, 0.3922101149804349, 0.0415270612688227, 0.5662628237507423, 0.5464396833448917, 0.0938490411451324, 0.3597112755099757, 0.3597112755099759, 0.0938490411451324, 0.5464396833448915, 0.7454392707127404, 0.0086860298043842, 0.2458746994828752, 0.2458746994828754, 0.0086860298043839, 0.7454392707127404, 0.8154081377810312, 0.0175891240440456, 0.1670027381749228, 0.1670027381749231, 0.0175891240440454, 0.8154081377810313, 0.5831893897351982, 0.2084053051324010, 0.2084053051324007, 0.8794678768558409, 0.0055235245122126, 0.1150085986319461, 0.1150085986319464, 0.0055235245122124, 0.8794678768558408, 0.6785082311360726, 0.1607458844319638, 0.1607458844319634, 0.6607456749400252, 0.0238589269426556, 0.3153953981173190, 0.3153953981173191, 0.0238589269426555, 0.6607456749400251, 0.7364820152304076, 0.0402953345447718, 0.2232226502248205, 0.2232226502248206, 0.0402953345447716, 0.7364820152304075, 0.6437257357698205, 0.0678784043114471, 0.2883958599187322, 0.2883958599187324, 0.0678784043114469, 0.6437257357698203, 0.4884016029326028, 0.0231967941347945, 0.4884016029326026, 0.5930980425461418, 0.1395356071810827, 0.2673663502727753, 0.2673663502727756, 0.1395356071810826, 0.5930980425461417, 0.3952271775697430, 0.3023864112151285, 0.3023864112151284, 0.5861680189969418, 0.0080665857041666, 0.4057653952988913, 0.4057653952988916, 0.0080665857041665, 0.5861680189969416, 0.7711463740111488, 0.1144268129944257, 0.1144268129944253, 0.4647624310807389, 0.0704751378385221, 0.4647624310807388, 0.8525562372198005, 0.0737218813901000, 0.0737218813900994, 0.3906191787832637, 0.2187616424334723, 0.3906191787832637, 0.8135558255123531, 0.0001234468122874, 0.1863207276753593, 0.1863207276753596, 0.0001234468122874, 0.8135558255123528 }; static double w_save[] = { 0.0007692529714762, 0.0007692529714762, 0.0007692529714762, 0.0007692529714762, 0.0007692529714762, 0.0007692529714762, 0.0104522146969224, 0.0104522146969224, 0.0104522146969224, 0.0104522146969224, 0.0104522146969224, 0.0104522146969224, 0.0013528239492524, 0.0013528239492524, 0.0013528239492524, 0.0013528239492524, 0.0013528239492524, 0.0013528239492524, 0.0015164621031569, 0.0015164621031569, 0.0015164621031569, 0.0064391367075338, 0.0064391367075338, 0.0064391367075338, 0.0064391367075338, 0.0064391367075338, 0.0064391367075338, 0.0012721944371716, 0.0012721944371716, 0.0012721944371716, 0.0012721944371716, 0.0012721944371716, 0.0012721944371716, 0.0135452465720076, 0.0135452465720076, 0.0135452465720076, 0.0135452465720076, 0.0135452465720076, 0.0135452465720076, 0.0027615307495904, 0.0027615307495904, 0.0027615307495904, 0.0027615307495904, 0.0027615307495904, 0.0027615307495904, 0.0045126868454873, 0.0045126868454873, 0.0045126868454873, 0.0045126868454873, 0.0045126868454873, 0.0045126868454873, 0.0002694922318587, 0.0002694922318587, 0.0002694922318587, 0.0002694922318587, 0.0002694922318587, 0.0002694922318587, 0.0111711002951679, 0.0111711002951679, 0.0111711002951679, 0.0028604915061569, 0.0028604915061569, 0.0028604915061569, 0.0093863306762837, 0.0093863306762837, 0.0093863306762837, 0.0093863306762837, 0.0093863306762837, 0.0093863306762837, 0.0078229184583065, 0.0078229184583065, 0.0078229184583065, 0.0078229184583065, 0.0078229184583065, 0.0078229184583065, 0.0106303963631966, 0.0106303963631966, 0.0106303963631966, 0.0106303963631966, 0.0106303963631966, 0.0106303963631966, 0.0030512388233452, 0.0030512388233452, 0.0030512388233452, 0.0030512388233452, 0.0030512388233452, 0.0030512388233452, 0.0038253666717300, 0.0038253666717300, 0.0038253666717300, 0.0038253666717300, 0.0038253666717300, 0.0038253666717300, 0.0125392034426232, 0.0125392034426232, 0.0125392034426232, 0.0017416952313017, 0.0017416952313017, 0.0017416952313017, 0.0017416952313017, 0.0017416952313017, 0.0017416952313017, 0.0105714178582276, 0.0105714178582276, 0.0105714178582276, 0.0056691534816655, 0.0056691534816655, 0.0056691534816655, 0.0056691534816655, 0.0056691534816655, 0.0056691534816655, 0.0065819977638522, 0.0065819977638522, 0.0065819977638522, 0.0065819977638522, 0.0065819977638522, 0.0065819977638522, 0.0091789241649276, 0.0091789241649276, 0.0091789241649276, 0.0091789241649276, 0.0091789241649276, 0.0091789241649276, 0.0061344011647189, 0.0061344011647189, 0.0061344011647189, 0.0125183664988344, 0.0125183664988344, 0.0125183664988344, 0.0125183664988344, 0.0125183664988344, 0.0125183664988344, 0.0163102388077432, 0.0163102388077432, 0.0163102388077432, 0.0036413404112807, 0.0036413404112807, 0.0036413404112807, 0.0036413404112807, 0.0036413404112807, 0.0036413404112807, 0.0081728784412271, 0.0081728784412271, 0.0081728784412271, 0.0103131166352585, 0.0103131166352585, 0.0103131166352585, 0.0056088471328313, 0.0056088471328313, 0.0056088471328313, 0.0159132152840889, 0.0159132152840889, 0.0159132152840889, 0.0006886726250418, 0.0006886726250418, 0.0006886726250418, 0.0006886726250418, 0.0006886726250418, 0.0006886726250418 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule30 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule30() returns the rule of precision 30. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.2590538845210674, 0.6931109923381602, 0.0478351231407726, 0.6931109923381601, 0.2590538845210674, 0.0478351231407724, 0.0033187249366444, 0.9933625501267108, 0.0033187249366448, 0.3915721882912563, 0.5287682847771430, 0.0796595269316006, 0.5287682847771430, 0.3915721882912564, 0.0796595269316005, 0.3561402832962335, 0.5861663154298922, 0.0576934012738742, 0.5861663154298922, 0.3561402832962335, 0.0576934012738741, 0.0723724072246778, 0.8552551855506439, 0.0723724072246782, 0.2830124973495888, 0.6397260650735270, 0.0772614375768841, 0.6397260650735271, 0.2830124973495887, 0.0772614375768839, 0.0471579102421718, 0.9056841795156562, 0.0471579102421721, 0.2416137624515244, 0.7356278532534756, 0.0227583842950001, 0.7356278532534756, 0.2416137624515244, 0.0227583842949999, 0.2527812471879329, 0.6234067740413924, 0.1238119787706746, 0.6234067740413924, 0.2527812471879329, 0.1238119787706745, 0.1849061063839171, 0.6992119263799822, 0.1158819672361006, 0.6992119263799822, 0.1849061063839172, 0.1158819672361004, 0.4680301736511254, 0.4680301736511254, 0.0639396526977491, 0.0126866046744676, 0.9746267906510645, 0.0126866046744680, 0.1937043771536401, 0.7397781780644782, 0.0665174447818817, 0.7397781780644782, 0.1937043771536401, 0.0665174447818814, 0.0764012484393875, 0.9191599701835511, 0.0044387813770616, 0.9191599701835510, 0.0764012484393877, 0.0044387813770611, 0.1215915082227279, 0.7568169835545440, 0.1215915082227282, 0.2090480874526896, 0.7862883331546218, 0.0046635793926887, 0.7862883331546218, 0.2090480874526897, 0.0046635793926884, 0.2985429940592427, 0.6967533241762803, 0.0047036817644771, 0.6967533241762803, 0.2985429940592427, 0.0047036817644769, 0.3343790400340311, 0.6404388932621004, 0.0251820667038687, 0.6404388932621002, 0.3343790400340311, 0.0251820667038686, 0.1232308023806951, 0.8109926237945619, 0.0657765738247430, 0.8109926237945619, 0.1232308023806952, 0.0657765738247426, 0.3385141624298457, 0.5353617425851648, 0.1261240949849894, 0.5353617425851648, 0.3385141624298457, 0.1261240949849893, 0.3544036021806874, 0.4507254468957941, 0.1948709509235184, 0.4507254468957941, 0.3544036021806874, 0.1948709509235184, 0.2630682977578083, 0.5459302776699086, 0.1910014245722831, 0.5459302776699086, 0.2630682977578084, 0.1910014245722829, 0.1824095615174529, 0.6351808769650940, 0.1824095615174532, 0.4345661739646696, 0.5379004199107804, 0.0275334061245499, 0.5379004199107805, 0.4345661739646697, 0.0275334061245498, 0.1640709870698783, 0.8078650909487486, 0.0280639219813731, 0.8078650909487487, 0.1640709870698785, 0.0280639219813727, 0.3622872793529498, 0.3622872793529498, 0.2754254412941003, 0.0426819997060804, 0.9414155840249848, 0.0159024162689350, 0.9414155840249848, 0.0426819997060806, 0.0159024162689344, 0.0939597946527299, 0.8787459746951742, 0.0272942306520959, 0.8787459746951743, 0.0939597946527300, 0.0272942306520955, 0.1354088535199345, 0.8588999350346495, 0.0056912114454161, 0.8588999350346495, 0.1354088535199345, 0.0056912114454159, 0.4367432485484602, 0.4367432485484602, 0.1265135029030796, 0.2724280407839282, 0.4551439184321434, 0.2724280407839283, 0.3962215147396591, 0.5986161382437196, 0.0051623470166213, 0.5986161382437196, 0.3962215147396591, 0.0051623470166212, 0.4973193390003086, 0.4973193390003087, 0.0053613219993828, 0.0294840425976739, 0.9699822487416315, 0.0005337086606946, 0.9699822487416316, 0.0294840425976741, 0.0005337086606942 }; static double b_save[] = { 0.0478351231407726, 0.2590538845210673, 0.6931109923381603, 0.0478351231407726, 0.6931109923381602, 0.2590538845210676, 0.0033187249366447, 0.0033187249366444, 0.9933625501267112, 0.0796595269316007, 0.3915721882912564, 0.5287682847771432, 0.0796595269316007, 0.5287682847771431, 0.3915721882912566, 0.0576934012738742, 0.3561402832962335, 0.5861663154298924, 0.0576934012738742, 0.5861663154298923, 0.3561402832962338, 0.0723724072246781, 0.0723724072246778, 0.8552551855506442, 0.0772614375768841, 0.2830124973495888, 0.6397260650735274, 0.0772614375768841, 0.6397260650735274, 0.2830124973495890, 0.0471579102421721, 0.0471579102421717, 0.9056841795156564, 0.0227583842950001, 0.2416137624515244, 0.7356278532534757, 0.0227583842950001, 0.7356278532534757, 0.2416137624515247, 0.1238119787706747, 0.2527812471879330, 0.6234067740413927, 0.1238119787706747, 0.6234067740413927, 0.2527812471879332, 0.1158819672361006, 0.1849061063839172, 0.6992119263799824, 0.1158819672361006, 0.6992119263799824, 0.1849061063839174, 0.0639396526977492, 0.4680301736511254, 0.4680301736511256, 0.0126866046744679, 0.0126866046744676, 0.9746267906510646, 0.0665174447818816, 0.1937043771536401, 0.7397781780644784, 0.0665174447818816, 0.7397781780644784, 0.1937043771536404, 0.0044387813770614, 0.0764012484393875, 0.9191599701835511, 0.0044387813770614, 0.9191599701835511, 0.0764012484393879, 0.1215915082227282, 0.1215915082227279, 0.7568169835545441, 0.0046635793926886, 0.2090480874526896, 0.7862883331546219, 0.0046635793926886, 0.7862883331546219, 0.2090480874526899, 0.0047036817644770, 0.2985429940592426, 0.6967533241762806, 0.0047036817644770, 0.6967533241762803, 0.2985429940592429, 0.0251820667038687, 0.3343790400340311, 0.6404388932621005, 0.0251820667038687, 0.6404388932621004, 0.3343790400340313, 0.0657765738247429, 0.1232308023806951, 0.8109926237945622, 0.0657765738247429, 0.8109926237945622, 0.1232308023806954, 0.1261240949849895, 0.3385141624298458, 0.5353617425851650, 0.1261240949849895, 0.5353617425851650, 0.3385141624298459, 0.1948709509235185, 0.3544036021806876, 0.4507254468957942, 0.1948709509235185, 0.4507254468957941, 0.3544036021806876, 0.1910014245722831, 0.2630682977578084, 0.5459302776699086, 0.1910014245722831, 0.5459302776699086, 0.2630682977578085, 0.1824095615174531, 0.1824095615174529, 0.6351808769650941, 0.0275334061245499, 0.4345661739646697, 0.5379004199107807, 0.0275334061245499, 0.5379004199107805, 0.4345661739646698, 0.0280639219813730, 0.1640709870698784, 0.8078650909487487, 0.0280639219813730, 0.8078650909487487, 0.1640709870698787, 0.2754254412941004, 0.3622872793529499, 0.3622872793529500, 0.0159024162689347, 0.0426819997060803, 0.9414155840249849, 0.0159024162689347, 0.9414155840249849, 0.0426819997060808, 0.0272942306520958, 0.0939597946527299, 0.8787459746951745, 0.0272942306520958, 0.8787459746951745, 0.0939597946527302, 0.0056912114454161, 0.1354088535199344, 0.8588999350346497, 0.0056912114454161, 0.8588999350346497, 0.1354088535199348, 0.1265135029030796, 0.4367432485484603, 0.4367432485484604, 0.2724280407839283, 0.2724280407839283, 0.4551439184321436, 0.0051623470166213, 0.3962215147396591, 0.5986161382437198, 0.0051623470166213, 0.5986161382437197, 0.3962215147396594, 0.0053613219993829, 0.4973193390003086, 0.4973193390003088, 0.0005337086606945, 0.0294840425976739, 0.9699822487416317, 0.0005337086606945, 0.9699822487416317, 0.0294840425976742 }; static double c_save[] = { 0.6931109923381601, 0.0478351231407725, 0.2590538845210671, 0.2590538845210673, 0.0478351231407724, 0.6931109923381600, 0.9933625501267110, 0.0033187249366448, 0.0033187249366441, 0.5287682847771430, 0.0796595269316006, 0.3915721882912562, 0.3915721882912563, 0.0796595269316005, 0.5287682847771429, 0.5861663154298923, 0.0576934012738743, 0.3561402832962334, 0.3561402832962336, 0.0576934012738742, 0.5861663154298921, 0.8552551855506441, 0.0723724072246782, 0.0723724072246775, 0.6397260650735271, 0.0772614375768842, 0.2830124973495886, 0.2830124973495887, 0.0772614375768840, 0.6397260650735271, 0.9056841795156562, 0.0471579102421721, 0.0471579102421714, 0.7356278532534755, 0.0227583842950000, 0.2416137624515242, 0.2416137624515244, 0.0227583842949999, 0.7356278532534755, 0.6234067740413924, 0.1238119787706746, 0.2527812471879327, 0.2527812471879329, 0.1238119787706744, 0.6234067740413923, 0.6992119263799823, 0.1158819672361006, 0.1849061063839169, 0.1849061063839172, 0.1158819672361003, 0.6992119263799823, 0.4680301736511254, 0.0639396526977491, 0.4680301736511252, 0.9746267906510645, 0.0126866046744679, 0.0126866046744674, 0.7397781780644782, 0.0665174447818817, 0.1937043771536399, 0.1937043771536402, 0.0665174447818814, 0.7397781780644782, 0.9191599701835511, 0.0044387813770613, 0.0764012484393873, 0.0764012484393876, 0.0044387813770612, 0.9191599701835510, 0.7568169835545440, 0.1215915082227281, 0.1215915082227278, 0.7862883331546218, 0.0046635793926886, 0.2090480874526894, 0.2090480874526896, 0.0046635793926885, 0.7862883331546215, 0.6967533241762803, 0.0047036817644771, 0.2985429940592425, 0.2985429940592426, 0.0047036817644769, 0.6967533241762802, 0.6404388932621002, 0.0251820667038686, 0.3343790400340308, 0.3343790400340311, 0.0251820667038686, 0.6404388932621001, 0.8109926237945619, 0.0657765738247430, 0.1232308023806948, 0.1232308023806952, 0.0657765738247427, 0.8109926237945619, 0.5353617425851648, 0.1261240949849894, 0.3385141624298456, 0.3385141624298458, 0.1261240949849892, 0.5353617425851648, 0.4507254468957941, 0.1948709509235184, 0.3544036021806874, 0.3544036021806874, 0.1948709509235184, 0.4507254468957940, 0.5459302776699086, 0.1910014245722830, 0.2630682977578083, 0.2630682977578082, 0.1910014245722830, 0.5459302776699084, 0.6351808769650941, 0.1824095615174531, 0.1824095615174527, 0.5379004199107805, 0.0275334061245499, 0.4345661739646695, 0.4345661739646696, 0.0275334061245497, 0.5379004199107804, 0.8078650909487487, 0.0280639219813731, 0.1640709870698781, 0.1640709870698783, 0.0280639219813729, 0.8078650909487486, 0.3622872793529498, 0.2754254412941003, 0.3622872793529497, 0.9414155840249848, 0.0159024162689349, 0.0426819997060801, 0.0426819997060805, 0.0159024162689345, 0.9414155840249848, 0.8787459746951743, 0.0272942306520959, 0.0939597946527296, 0.0939597946527299, 0.0272942306520956, 0.8787459746951742, 0.8588999350346495, 0.0056912114454161, 0.1354088535199341, 0.1354088535199345, 0.0056912114454158, 0.8588999350346493, 0.4367432485484603, 0.1265135029030796, 0.4367432485484601, 0.4551439184321435, 0.2724280407839283, 0.2724280407839281, 0.5986161382437196, 0.0051623470166213, 0.3962215147396588, 0.3962215147396591, 0.0051623470166212, 0.5986161382437194, 0.4973193390003086, 0.0053613219993827, 0.4973193390003083, 0.9699822487416316, 0.0005337086606946, 0.0294840425976736, 0.0294840425976739, 0.0005337086606941, 0.9699822487416315 }; static double w_save[] = { 0.0042147584639124, 0.0042147584639124, 0.0042147584639124, 0.0042147584639124, 0.0042147584639124, 0.0042147584639124, 0.0001717299013710, 0.0001717299013710, 0.0001717299013710, 0.0059249227450920, 0.0059249227450920, 0.0059249227450920, 0.0059249227450920, 0.0059249227450920, 0.0059249227450920, 0.0059442201844245, 0.0059442201844245, 0.0059442201844245, 0.0059442201844245, 0.0059442201844245, 0.0059442201844245, 0.0038019326684155, 0.0038019326684155, 0.0038019326684155, 0.0068771843875359, 0.0068771843875359, 0.0068771843875359, 0.0068771843875359, 0.0068771843875359, 0.0068771843875359, 0.0028444336676875, 0.0028444336676875, 0.0028444336676875, 0.0040924989683472, 0.0040924989683472, 0.0040924989683472, 0.0040924989683472, 0.0040924989683472, 0.0040924989683472, 0.0088726545060173, 0.0088726545060173, 0.0088726545060173, 0.0088726545060173, 0.0088726545060173, 0.0088726545060173, 0.0075343229295465, 0.0075343229295465, 0.0075343229295465, 0.0075343229295465, 0.0075343229295465, 0.0075343229295465, 0.0077841287323308, 0.0077841287323308, 0.0077841287323308, 0.0008465501453289, 0.0008465501453289, 0.0008465501453289, 0.0068040067561019, 0.0068040067561019, 0.0068040067561019, 0.0068040067561019, 0.0068040067561019, 0.0068040067561019, 0.0012066965685421, 0.0012066965685421, 0.0012066965685421, 0.0012066965685421, 0.0012066965685421, 0.0012066965685421, 0.0073869118349143, 0.0073869118349143, 0.0073869118349143, 0.0019589485778932, 0.0019589485778932, 0.0019589485778932, 0.0019589485778932, 0.0019589485778932, 0.0019589485778932, 0.0022744459009987, 0.0022744459009987, 0.0022744459009987, 0.0022744459009987, 0.0022744459009987, 0.0022744459009987, 0.0053646848461863, 0.0053646848461863, 0.0053646848461863, 0.0053646848461863, 0.0053646848461863, 0.0053646848461863, 0.0058700698030655, 0.0058700698030655, 0.0058700698030655, 0.0058700698030655, 0.0058700698030655, 0.0058700698030655, 0.0113030235429375, 0.0113030235429375, 0.0113030235429375, 0.0113030235429375, 0.0113030235429375, 0.0113030235429375, 0.0143164852696676, 0.0143164852696676, 0.0143164852696676, 0.0143164852696676, 0.0143164852696676, 0.0143164852696676, 0.0129260234501183, 0.0129260234501183, 0.0129260234501183, 0.0129260234501183, 0.0129260234501183, 0.0129260234501183, 0.0107528509654328, 0.0107528509654328, 0.0107528509654328, 0.0062815965808917, 0.0062815965808917, 0.0062815965808917, 0.0062815965808917, 0.0062815965808917, 0.0062815965808917, 0.0047019369941060, 0.0047019369941060, 0.0047019369941060, 0.0047019369941060, 0.0047019369941060, 0.0047019369941060, 0.0155960913258258, 0.0155960913258258, 0.0155960913258258, 0.0018305068761488, 0.0018305068761488, 0.0018305068761488, 0.0018305068761488, 0.0018305068761488, 0.0018305068761488, 0.0038218805470950, 0.0038218805470950, 0.0038218805470950, 0.0038218805470950, 0.0038218805470950, 0.0038218805470950, 0.0019198805574689, 0.0019198805574689, 0.0019198805574689, 0.0019198805574689, 0.0019198805574689, 0.0019198805574689, 0.0124049590281460, 0.0124049590281460, 0.0124049590281460, 0.0149145507626858, 0.0149145507626858, 0.0149145507626858, 0.0026425679231633, 0.0026425679231633, 0.0026425679231633, 0.0026425679231633, 0.0026425679231633, 0.0026425679231633, 0.0027913181197408, 0.0027913181197408, 0.0027913181197408, 0.0003356217114664, 0.0003356217114664, 0.0003356217114664, 0.0003356217114664, 0.0003356217114664, 0.0003356217114664 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule31 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule31() returns the rule of precision 31. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3333333333333333, 0.4861524679130598, 0.4861524679130598, 0.0276950641738803, 0.1390906284720946, 0.7542396906638279, 0.1066696808640776, 0.7542396906638279, 0.1390906284720947, 0.1066696808640773, 0.4195880808642605, 0.4195880808642605, 0.1608238382714789, 0.1972331307896530, 0.7995057135466186, 0.0032611556637284, 0.7995057135466186, 0.1972331307896531, 0.0032611556637281, 0.2385241509843100, 0.7483360311752862, 0.0131398178404037, 0.7483360311752864, 0.2385241509843100, 0.0131398178404035, 0.0792067965066985, 0.8415864069866026, 0.0792067965066989, 0.0297507293859900, 0.9679050494853231, 0.0023442211286871, 0.9679050494853232, 0.0297507293859901, 0.0023442211286867, 0.0177313492497139, 0.9645373015005718, 0.0177313492497143, 0.3957839332968854, 0.6022546663332196, 0.0019614003698950, 0.6022546663332196, 0.3957839332968854, 0.0019614003698949, 0.3516800587760809, 0.4956833754486993, 0.1526365657752197, 0.4956833754486993, 0.3516800587760809, 0.1526365657752196, 0.2024821942617583, 0.6840925273907388, 0.1134252783475029, 0.6840925273907387, 0.2024821942617585, 0.1134252783475028, 0.4225539552222151, 0.5229246603331018, 0.0545213844446831, 0.5229246603331018, 0.4225539552222151, 0.0545213844446831, 0.1246805088474440, 0.8147145619917838, 0.0606049291607723, 0.8147145619917838, 0.1246805088474441, 0.0606049291607719, 0.2555462364028573, 0.7068648114396249, 0.0375889521575178, 0.7068648114396250, 0.2555462364028574, 0.0375889521575175, 0.0745031299353863, 0.9211105398945520, 0.0043863301700618, 0.9211105398945520, 0.0745031299353864, 0.0043863301700614, 0.4168072755236505, 0.5659193101514124, 0.0172734143249371, 0.5659193101514123, 0.4168072755236506, 0.0172734143249370, 0.1928717230061985, 0.7445502549794906, 0.0625780220143110, 0.7445502549794907, 0.1928717230061984, 0.0625780220143108, 0.0473478189395525, 0.9342442340291646, 0.0184079470312831, 0.9342442340291646, 0.0473478189395526, 0.0184079470312826, 0.2184364967909280, 0.5631270064181437, 0.2184364967909281, 0.1724507871838860, 0.6550984256322278, 0.1724507871838863, 0.0510951808223813, 0.8978096383552372, 0.0510951808223817, 0.3419050053475277, 0.6151917857097009, 0.0429032089427714, 0.6151917857097009, 0.3419050053475278, 0.0429032089427713, 0.3258139530575097, 0.6609969631634746, 0.0131890837790157, 0.6609969631634747, 0.3258139530575097, 0.0131890837790155, 0.2894259487571373, 0.7093771696121531, 0.0011968816307096, 0.7093771696121531, 0.2894259487571372, 0.0011968816307094, 0.2987897956760133, 0.4820774428938099, 0.2191327614301768, 0.4820774428938098, 0.2987897956760134, 0.2191327614301767, 0.2744757477427950, 0.6443943606878740, 0.0811298915693310, 0.6443943606878740, 0.2744757477427950, 0.0811298915693308, 0.3532298738914156, 0.5514920116265676, 0.0952781144820168, 0.5514920116265676, 0.3532298738914156, 0.0952781144820166, 0.4977486206264703, 0.4977486206264703, 0.0045027587470594, 0.2663678824750718, 0.5867434095228163, 0.1468887080021118, 0.5867434095228162, 0.2663678824750718, 0.1468887080021118, 0.3851684692456800, 0.3851684692456801, 0.2296630615086398, 0.2974914903679928, 0.4050170192640142, 0.2974914903679928, 0.0960481521010511, 0.8764212178203614, 0.0275306300785876, 0.8764212178203614, 0.0960481521010512, 0.0275306300785873, 0.0050828094627277, 0.9898343810745441, 0.0050828094627282, 0.1674078247783561, 0.8067170670017056, 0.0258751082199382, 0.8067170670017058, 0.1674078247783561, 0.0258751082199379, 0.4503409417390182, 0.4503409417390182, 0.0993181165219635, 0.1306776337702883, 0.8635250475449717, 0.0057973186847399, 0.8635250475449718, 0.1306776337702885, 0.0057973186847396 }; static double b_save[] = { 0.3333333333333334, 0.0276950641738804, 0.4861524679130599, 0.4861524679130600, 0.1066696808640776, 0.1390906284720946, 0.7542396906638279, 0.1066696808640776, 0.7542396906638279, 0.1390906284720949, 0.1608238382714791, 0.4195880808642605, 0.4195880808642607, 0.0032611556637283, 0.1972331307896530, 0.7995057135466188, 0.0032611556637283, 0.7995057135466188, 0.1972331307896533, 0.0131398178404037, 0.2385241509843100, 0.7483360311752866, 0.0131398178404037, 0.7483360311752866, 0.2385241509843103, 0.0792067965066988, 0.0792067965066985, 0.8415864069866028, 0.0023442211286869, 0.0297507293859899, 0.9679050494853232, 0.0023442211286869, 0.9679050494853232, 0.0297507293859903, 0.0177313492497142, 0.0177313492497139, 0.9645373015005720, 0.0019614003698950, 0.3957839332968854, 0.6022546663332198, 0.0019614003698950, 0.6022546663332197, 0.3957839332968856, 0.1526365657752198, 0.3516800587760810, 0.4956833754486996, 0.1526365657752198, 0.4956833754486994, 0.3516800587760812, 0.1134252783475029, 0.2024821942617584, 0.6840925273907389, 0.1134252783475029, 0.6840925273907389, 0.2024821942617586, 0.0545213844446831, 0.4225539552222151, 0.5229246603331020, 0.0545213844446831, 0.5229246603331019, 0.4225539552222153, 0.0606049291607722, 0.1246805088474439, 0.8147145619917839, 0.0606049291607722, 0.8147145619917839, 0.1246805088474443, 0.0375889521575178, 0.2555462364028573, 0.7068648114396252, 0.0375889521575178, 0.7068648114396251, 0.2555462364028576, 0.0043863301700617, 0.0745031299353863, 0.9211105398945522, 0.0043863301700617, 0.9211105398945522, 0.0745031299353866, 0.0172734143249371, 0.4168072755236506, 0.5659193101514125, 0.0172734143249371, 0.5659193101514124, 0.4168072755236508, 0.0625780220143109, 0.1928717230061985, 0.7445502549794908, 0.0625780220143109, 0.7445502549794908, 0.1928717230061987, 0.0184079470312829, 0.0473478189395524, 0.9342442340291647, 0.0184079470312829, 0.9342442340291647, 0.0473478189395528, 0.2184364967909282, 0.2184364967909281, 0.5631270064181439, 0.1724507871838862, 0.1724507871838861, 0.6550984256322279, 0.0510951808223816, 0.0510951808223813, 0.8978096383552373, 0.0429032089427714, 0.3419050053475277, 0.6151917857097011, 0.0429032089427714, 0.6151917857097009, 0.3419050053475279, 0.0131890837790157, 0.3258139530575097, 0.6609969631634748, 0.0131890837790157, 0.6609969631634748, 0.3258139530575100, 0.0011968816307096, 0.2894259487571373, 0.7093771696121534, 0.0011968816307096, 0.7093771696121534, 0.2894259487571375, 0.2191327614301768, 0.2987897956760134, 0.4820774428938099, 0.2191327614301768, 0.4820774428938099, 0.2987897956760135, 0.0811298915693310, 0.2744757477427950, 0.6443943606878743, 0.0811298915693310, 0.6443943606878741, 0.2744757477427952, 0.0952781144820168, 0.3532298738914157, 0.5514920116265677, 0.0952781144820168, 0.5514920116265677, 0.3532298738914159, 0.0045027587470595, 0.4977486206264704, 0.4977486206264705, 0.1468887080021119, 0.2663678824750718, 0.5867434095228166, 0.1468887080021119, 0.5867434095228163, 0.2663678824750720, 0.2296630615086399, 0.3851684692456802, 0.3851684692456802, 0.2974914903679930, 0.2974914903679929, 0.4050170192640143, 0.0275306300785875, 0.0960481521010511, 0.8764212178203615, 0.0275306300785875, 0.8764212178203615, 0.0960481521010514, 0.0050828094627280, 0.0050828094627277, 0.9898343810745442, 0.0258751082199382, 0.1674078247783561, 0.8067170670017060, 0.0258751082199382, 0.8067170670017060, 0.1674078247783564, 0.0993181165219637, 0.4503409417390183, 0.4503409417390184, 0.0057973186847398, 0.1306776337702883, 0.8635250475449719, 0.0057973186847398, 0.8635250475449719, 0.1306776337702887 }; static double c_save[] = { 0.3333333333333333, 0.4861524679130598, 0.0276950641738803, 0.4861524679130597, 0.7542396906638279, 0.1066696808640775, 0.1390906284720944, 0.1390906284720945, 0.1066696808640774, 0.7542396906638278, 0.4195880808642605, 0.1608238382714790, 0.4195880808642604, 0.7995057135466186, 0.0032611556637284, 0.1972331307896529, 0.1972331307896531, 0.0032611556637281, 0.7995057135466186, 0.7483360311752864, 0.0131398178404037, 0.2385241509843098, 0.2385241509843100, 0.0131398178404035, 0.7483360311752864, 0.8415864069866027, 0.0792067965066989, 0.0792067965066983, 0.9679050494853231, 0.0023442211286870, 0.0297507293859898, 0.0297507293859899, 0.0023442211286867, 0.9679050494853230, 0.9645373015005719, 0.0177313492497143, 0.0177313492497136, 0.6022546663332197, 0.0019614003698950, 0.3957839332968852, 0.3957839332968854, 0.0019614003698950, 0.6022546663332196, 0.4956833754486993, 0.1526365657752197, 0.3516800587760808, 0.3516800587760809, 0.1526365657752197, 0.4956833754486992, 0.6840925273907388, 0.1134252783475028, 0.2024821942617582, 0.2024821942617584, 0.1134252783475026, 0.6840925273907387, 0.5229246603331018, 0.0545213844446831, 0.4225539552222149, 0.4225539552222151, 0.0545213844446830, 0.5229246603331017, 0.8147145619917838, 0.0606049291607722, 0.1246805088474437, 0.1246805088474440, 0.0606049291607720, 0.8147145619917837, 0.7068648114396249, 0.0375889521575178, 0.2555462364028570, 0.2555462364028572, 0.0375889521575176, 0.7068648114396248, 0.9211105398945520, 0.0043863301700617, 0.0745031299353861, 0.0745031299353863, 0.0043863301700614, 0.9211105398945519, 0.5659193101514124, 0.0172734143249370, 0.4168072755236504, 0.4168072755236506, 0.0172734143249370, 0.5659193101514122, 0.7445502549794906, 0.0625780220143110, 0.1928717230061983, 0.1928717230061984, 0.0625780220143107, 0.7445502549794906, 0.9342442340291647, 0.0184079470312830, 0.0473478189395523, 0.0473478189395525, 0.0184079470312827, 0.9342442340291645, 0.5631270064181437, 0.2184364967909282, 0.2184364967909279, 0.6550984256322278, 0.1724507871838862, 0.1724507871838858, 0.8978096383552372, 0.0510951808223815, 0.0510951808223811, 0.6151917857097009, 0.0429032089427714, 0.3419050053475274, 0.3419050053475277, 0.0429032089427713, 0.6151917857097007, 0.6609969631634746, 0.0131890837790157, 0.3258139530575095, 0.3258139530575096, 0.0131890837790155, 0.6609969631634744, 0.7093771696121530, 0.0011968816307096, 0.2894259487571371, 0.2894259487571373, 0.0011968816307094, 0.7093771696121531, 0.4820774428938099, 0.2191327614301767, 0.2987897956760133, 0.2987897956760133, 0.2191327614301767, 0.4820774428938098, 0.6443943606878740, 0.0811298915693309, 0.2744757477427947, 0.2744757477427950, 0.0811298915693308, 0.6443943606878739, 0.5514920116265676, 0.0952781144820167, 0.3532298738914156, 0.3532298738914156, 0.0952781144820166, 0.5514920116265676, 0.4977486206264702, 0.0045027587470594, 0.4977486206264701, 0.5867434095228163, 0.1468887080021118, 0.2663678824750716, 0.2663678824750719, 0.1468887080021118, 0.5867434095228162, 0.3851684692456800, 0.2296630615086398, 0.3851684692456800, 0.4050170192640142, 0.2974914903679929, 0.2974914903679928, 0.8764212178203614, 0.0275306300785875, 0.0960481521010509, 0.0960481521010511, 0.0275306300785872, 0.8764212178203613, 0.9898343810745441, 0.0050828094627281, 0.0050828094627275, 0.8067170670017058, 0.0258751082199383, 0.1674078247783558, 0.1674078247783561, 0.0258751082199379, 0.8067170670017056, 0.4503409417390182, 0.0993181165219635, 0.4503409417390181, 0.8635250475449718, 0.0057973186847400, 0.1306776337702881, 0.1306776337702883, 0.0057973186847396, 0.8635250475449716 }; static double w_save[] = { 0.0083431208138864, 0.0040439883965194, 0.0040439883965194, 0.0040439883965194, 0.0058062932483637, 0.0058062932483637, 0.0058062932483637, 0.0058062932483637, 0.0058062932483637, 0.0058062932483637, 0.0088430826430883, 0.0088430826430883, 0.0088430826430883, 0.0012838516987697, 0.0012838516987697, 0.0012838516987697, 0.0012838516987697, 0.0012838516987697, 0.0012838516987697, 0.0028265142759277, 0.0028265142759277, 0.0028265142759277, 0.0028265142759277, 0.0028265142759277, 0.0028265142759277, 0.0042237298511032, 0.0042237298511032, 0.0042237298511032, 0.0005055090468723, 0.0005055090468723, 0.0005055090468723, 0.0005055090468723, 0.0005055090468723, 0.0005055090468723, 0.0009868661450271, 0.0009868661450271, 0.0009868661450271, 0.0013026954489735, 0.0013026954489735, 0.0013026954489735, 0.0013026954489735, 0.0013026954489735, 0.0013026954489735, 0.0101925794443413, 0.0101925794443413, 0.0101925794443413, 0.0101925794443413, 0.0101925794443413, 0.0101925794443413, 0.0078668704957381, 0.0078668704957381, 0.0078668704957381, 0.0078668704957381, 0.0078668704957381, 0.0078668704957381, 0.0071208092414188, 0.0071208092414188, 0.0071208092414188, 0.0071208092414188, 0.0071208092414188, 0.0071208092414188, 0.0049641144765077, 0.0049641144765077, 0.0049641144765077, 0.0049641144765077, 0.0049641144765077, 0.0049641144765077, 0.0054364374730136, 0.0054364374730136, 0.0054364374730136, 0.0054364374730136, 0.0054364374730136, 0.0054364374730136, 0.0011525829400843, 0.0011525829400843, 0.0011525829400843, 0.0011525829400843, 0.0011525829400843, 0.0011525829400843, 0.0041783326918215, 0.0041783326918215, 0.0041783326918215, 0.0041783326918215, 0.0041783326918215, 0.0041783326918215, 0.0063624230528669, 0.0063624230528669, 0.0063624230528669, 0.0063624230528669, 0.0063624230528669, 0.0063624230528669, 0.0018127692882839, 0.0018127692882839, 0.0018127692882839, 0.0018127692882839, 0.0018127692882839, 0.0018127692882839, 0.0112370035080132, 0.0112370035080132, 0.0112370035080132, 0.0095591959667284, 0.0095591959667284, 0.0095591959667284, 0.0032590866501858, 0.0032590866501858, 0.0032590866501858, 0.0066899592450456, 0.0066899592450456, 0.0066899592450456, 0.0066899592450456, 0.0066899592450456, 0.0066899592450456, 0.0036397134849474, 0.0036397134849474, 0.0036397134849474, 0.0036397134849474, 0.0036397134849474, 0.0036397134849474, 0.0009293703376931, 0.0009293703376931, 0.0009293703376931, 0.0009293703376931, 0.0009293703376931, 0.0009293703376931, 0.0128955867879842, 0.0128955867879842, 0.0128955867879842, 0.0128955867879842, 0.0128955867879842, 0.0128955867879842, 0.0084758977171366, 0.0084758977171366, 0.0084758977171366, 0.0084758977171366, 0.0084758977171366, 0.0084758977171366, 0.0096222755316967, 0.0096222755316967, 0.0096222755316967, 0.0096222755316967, 0.0096222755316967, 0.0096222755316967, 0.0023276606420564, 0.0023276606420564, 0.0023276606420564, 0.0115996690313856, 0.0115996690313856, 0.0115996690313856, 0.0115996690313856, 0.0115996690313856, 0.0115996690313856, 0.0137393951965683, 0.0137393951965683, 0.0137393951965683, 0.0123590405093469, 0.0123590405093469, 0.0123590405093469, 0.0036665867049268, 0.0036665867049268, 0.0036665867049268, 0.0036665867049268, 0.0036665867049268, 0.0036665867049268, 0.0003444013792726, 0.0003444013792726, 0.0003444013792726, 0.0044453379912524, 0.0044453379912524, 0.0044453379912524, 0.0044453379912524, 0.0044453379912524, 0.0044453379912524, 0.0104339772957806, 0.0104339772957806, 0.0104339772957806, 0.0018212527841225, 0.0018212527841225, 0.0018212527841225, 0.0018212527841225, 0.0018212527841225, 0.0018212527841225 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule32 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule32() returns the rule of precision 32. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.0014574454623699, 0.9970851090752599, 0.0014574454623703, 0.2068316863159020, 0.6343003724550512, 0.1588679412290467, 0.6343003724550512, 0.2068316863159020, 0.1588679412290465, 0.4467614265331670, 0.5384721310359784, 0.0147664424308546, 0.5384721310359784, 0.4467614265331671, 0.0147664424308546, 0.4986508935788473, 0.4986508935788473, 0.0026982128423053, 0.2324662076463787, 0.7161026651133882, 0.0514311272402331, 0.7161026651133883, 0.2324662076463787, 0.0514311272402328, 0.1168349267069579, 0.8636053329284497, 0.0195597403645925, 0.8636053329284497, 0.1168349267069580, 0.0195597403645921, 0.3282405458449340, 0.6591408874049088, 0.0126185667501573, 0.6591408874049087, 0.3282405458449340, 0.0126185667501570, 0.2593509320031201, 0.7195869113212406, 0.0210621566756393, 0.7195869113212405, 0.2593509320031203, 0.0210621566756391, 0.1654639982373495, 0.7169924925083024, 0.1175435092543480, 0.7169924925083024, 0.1654639982373496, 0.1175435092543477, 0.3824649073809372, 0.5882362420785776, 0.0292988505404852, 0.5882362420785775, 0.3824649073809373, 0.0292988505404851, 0.3978170726467208, 0.5987401057010048, 0.0034428216522743, 0.5987401057010048, 0.3978170726467208, 0.0034428216522742, 0.4811681159958368, 0.4811681159958369, 0.0376637680083264, 0.3254174696466901, 0.5842122492084456, 0.0903702811448643, 0.5842122492084456, 0.3254174696466901, 0.0903702811448641, 0.4522857565116005, 0.4522857565116005, 0.0954284869767989, 0.1133391914876031, 0.8359631725856564, 0.0506976359267406, 0.8359631725856566, 0.1133391914876031, 0.0506976359267403, 0.3110416328276417, 0.6410138882567965, 0.0479444789155618, 0.6410138882567965, 0.3110416328276417, 0.0479444789155617, 0.2988371353889130, 0.6998862072308072, 0.0012766573802799, 0.6998862072308072, 0.2988371353889130, 0.0012766573802797, 0.3763287580479190, 0.3763287580479190, 0.2473424839041620, 0.1521122809437838, 0.8436251556411046, 0.0042625634151116, 0.8436251556411045, 0.1521122809437838, 0.0042625634151113, 0.0886617050339115, 0.9074857829773694, 0.0038525119887192, 0.9074857829773694, 0.0886617050339115, 0.0038525119887188, 0.2830182798495732, 0.4339634403008535, 0.2830182798495733, 0.3191525805930605, 0.4789472707744628, 0.2019001486324766, 0.4789472707744628, 0.3191525805930605, 0.2019001486324766, 0.4136797843254134, 0.4136797843254134, 0.1726404313491732, 0.1667556935821333, 0.7655339131965976, 0.0677103932212692, 0.7655339131965975, 0.1667556935821334, 0.0677103932212689, 0.0302691910404442, 0.9394616179191112, 0.0302691910404446, 0.0128101964801118, 0.9743796070397761, 0.0128101964801123, 0.2421379240194328, 0.6622896588699126, 0.0955724171106545, 0.6622896588699126, 0.2421379240194329, 0.0955724171106544, 0.2798617479978297, 0.5697673874287119, 0.1503708645734583, 0.5697673874287120, 0.2798617479978297, 0.1503708645734581, 0.0673984002072567, 0.9082517491081563, 0.0243498506845873, 0.9082517491081562, 0.0673984002072567, 0.0243498506845868, 0.3716879666934204, 0.4989241659396562, 0.1293878673669234, 0.4989241659396562, 0.3716879666934203, 0.1293878673669233, 0.4056281490658828, 0.5311444304776159, 0.0632274204565012, 0.5311444304776159, 0.4056281490658829, 0.0632274204565011, 0.3333333333333333, 0.0620106498262642, 0.8759787003474712, 0.0620106498262646, 0.2219801657374810, 0.7727532012417533, 0.0052666330207657, 0.7727532012417532, 0.2219801657374811, 0.0052666330207656, 0.1783256820378629, 0.7955154359824860, 0.0261588819796511, 0.7955154359824860, 0.1783256820378630, 0.0261588819796509, 0.0426221905914095, 0.9518230415381582, 0.0055547678704324, 0.9518230415381583, 0.0426221905914095, 0.0055547678704320, 0.2292779969280699, 0.5414440061438599, 0.2292779969280701, 0.1019588269002696, 0.7960823461994605, 0.1019588269002699, 0.0143443003792804, 0.9850326016003745, 0.0006230980203453, 0.9850326016003746, 0.0143443003792806, 0.0006230980203448 }; static double b_save[] = { 0.0014574454623702, 0.0014574454623698, 0.9970851090752600, 0.1588679412290467, 0.2068316863159021, 0.6343003724550514, 0.1588679412290467, 0.6343003724550514, 0.2068316863159023, 0.0147664424308547, 0.4467614265331671, 0.5384721310359786, 0.0147664424308547, 0.5384721310359784, 0.4467614265331673, 0.0026982128423054, 0.4986508935788474, 0.4986508935788476, 0.0514311272402331, 0.2324662076463787, 0.7161026651133885, 0.0514311272402331, 0.7161026651133884, 0.2324662076463790, 0.0195597403645924, 0.1168349267069579, 0.8636053329284498, 0.0195597403645924, 0.8636053329284498, 0.1168349267069583, 0.0126185667501572, 0.3282405458449341, 0.6591408874049089, 0.0126185667501572, 0.6591408874049089, 0.3282405458449343, 0.0210621566756392, 0.2593509320031202, 0.7195869113212408, 0.0210621566756392, 0.7195869113212406, 0.2593509320031205, 0.1175435092543480, 0.1654639982373496, 0.7169924925083025, 0.1175435092543480, 0.7169924925083027, 0.1654639982373498, 0.0292988505404852, 0.3824649073809372, 0.5882362420785777, 0.0292988505404852, 0.5882362420785776, 0.3824649073809375, 0.0034428216522744, 0.3978170726467209, 0.5987401057010050, 0.0034428216522744, 0.5987401057010049, 0.3978170726467211, 0.0376637680083265, 0.4811681159958368, 0.4811681159958370, 0.0903702811448643, 0.3254174696466902, 0.5842122492084457, 0.0903702811448643, 0.5842122492084457, 0.3254174696466903, 0.0954284869767990, 0.4522857565116006, 0.4522857565116007, 0.0506976359267405, 0.1133391914876030, 0.8359631725856566, 0.0506976359267405, 0.8359631725856566, 0.1133391914876034, 0.0479444789155618, 0.3110416328276418, 0.6410138882567966, 0.0479444789155618, 0.6410138882567966, 0.3110416328276420, 0.0012766573802798, 0.2988371353889130, 0.6998862072308073, 0.0012766573802798, 0.6998862072308073, 0.2988371353889133, 0.2473424839041621, 0.3763287580479191, 0.3763287580479191, 0.0042625634151116, 0.1521122809437838, 0.8436251556411049, 0.0042625634151116, 0.8436251556411049, 0.1521122809437842, 0.0038525119887191, 0.0886617050339115, 0.9074857829773696, 0.0038525119887191, 0.9074857829773696, 0.0886617050339118, 0.2830182798495733, 0.2830182798495732, 0.4339634403008537, 0.2019001486324767, 0.3191525805930606, 0.4789472707744629, 0.2019001486324767, 0.4789472707744629, 0.3191525805930607, 0.1726404313491733, 0.4136797843254134, 0.4136797843254136, 0.0677103932212692, 0.1667556935821333, 0.7655339131965977, 0.0677103932212692, 0.7655339131965977, 0.1667556935821336, 0.0302691910404445, 0.0302691910404442, 0.9394616179191115, 0.0128101964801121, 0.0128101964801118, 0.9743796070397761, 0.0955724171106545, 0.2421379240194328, 0.6622896588699130, 0.0955724171106545, 0.6622896588699128, 0.2421379240194330, 0.1503708645734583, 0.2798617479978298, 0.5697673874287121, 0.1503708645734583, 0.5697673874287121, 0.2798617479978299, 0.0243498506845871, 0.0673984002072566, 0.9082517491081563, 0.0243498506845871, 0.9082517491081563, 0.0673984002072569, 0.1293878673669234, 0.3716879666934204, 0.4989241659396564, 0.1293878673669234, 0.4989241659396564, 0.3716879666934205, 0.0632274204565012, 0.4056281490658829, 0.5311444304776161, 0.0632274204565012, 0.5311444304776159, 0.4056281490658831, 0.3333333333333334, 0.0620106498262645, 0.0620106498262642, 0.8759787003474714, 0.0052666330207658, 0.2219801657374810, 0.7727532012417535, 0.0052666330207658, 0.7727532012417533, 0.2219801657374814, 0.0261588819796510, 0.1783256820378630, 0.7955154359824862, 0.0261588819796510, 0.7955154359824862, 0.1783256820378632, 0.0055547678704322, 0.0426221905914095, 0.9518230415381584, 0.0055547678704322, 0.9518230415381584, 0.0426221905914099, 0.2292779969280701, 0.2292779969280700, 0.5414440061438600, 0.1019588269002698, 0.1019588269002696, 0.7960823461994607, 0.0006230980203451, 0.0143443003792804, 0.9850326016003745, 0.0006230980203451, 0.9850326016003745, 0.0143443003792807 }; static double c_save[] = { 0.9970851090752600, 0.0014574454623702, 0.0014574454623696, 0.6343003724550513, 0.1588679412290467, 0.2068316863159019, 0.2068316863159020, 0.1588679412290465, 0.6343003724550511, 0.5384721310359784, 0.0147664424308546, 0.4467614265331668, 0.4467614265331670, 0.0147664424308546, 0.5384721310359781, 0.4986508935788472, 0.0026982128423053, 0.4986508935788471, 0.7161026651133883, 0.0514311272402331, 0.2324662076463785, 0.2324662076463787, 0.0514311272402329, 0.7161026651133883, 0.8636053329284497, 0.0195597403645924, 0.1168349267069578, 0.1168349267069580, 0.0195597403645923, 0.8636053329284495, 0.6591408874049088, 0.0126185667501571, 0.3282405458449338, 0.3282405458449341, 0.0126185667501570, 0.6591408874049086, 0.7195869113212405, 0.0210621566756392, 0.2593509320031200, 0.2593509320031203, 0.0210621566756392, 0.7195869113212403, 0.7169924925083024, 0.1175435092543480, 0.1654639982373495, 0.1654639982373496, 0.1175435092543478, 0.7169924925083024, 0.5882362420785776, 0.0292988505404851, 0.3824649073809371, 0.3824649073809373, 0.0292988505404851, 0.5882362420785774, 0.5987401057010048, 0.0034428216522743, 0.3978170726467206, 0.3978170726467209, 0.0034428216522743, 0.5987401057010047, 0.4811681159958368, 0.0376637680083263, 0.4811681159958366, 0.5842122492084457, 0.0903702811448642, 0.3254174696466899, 0.3254174696466902, 0.0903702811448642, 0.5842122492084456, 0.4522857565116005, 0.0954284869767989, 0.4522857565116003, 0.8359631725856564, 0.0506976359267405, 0.1133391914876029, 0.1133391914876030, 0.0506976359267403, 0.8359631725856563, 0.6410138882567965, 0.0479444789155617, 0.3110416328276415, 0.3110416328276417, 0.0479444789155616, 0.6410138882567964, 0.6998862072308072, 0.0012766573802798, 0.2988371353889129, 0.2988371353889130, 0.0012766573802797, 0.6998862072308070, 0.3763287580479189, 0.2473424839041619, 0.3763287580479189, 0.8436251556411046, 0.0042625634151116, 0.1521122809437835, 0.1521122809437839, 0.0042625634151113, 0.8436251556411045, 0.9074857829773694, 0.0038525119887192, 0.0886617050339112, 0.0886617050339116, 0.0038525119887188, 0.9074857829773694, 0.4339634403008535, 0.2830182798495732, 0.2830182798495731, 0.4789472707744628, 0.2019001486324766, 0.3191525805930605, 0.3191525805930606, 0.2019001486324766, 0.4789472707744628, 0.4136797843254133, 0.1726404313491732, 0.4136797843254132, 0.7655339131965976, 0.0677103932212691, 0.1667556935821330, 0.1667556935821334, 0.0677103932212689, 0.7655339131965975, 0.9394616179191114, 0.0302691910404446, 0.0302691910404439, 0.9743796070397761, 0.0128101964801121, 0.0128101964801116, 0.6622896588699126, 0.0955724171106545, 0.2421379240194326, 0.2421379240194328, 0.0955724171106543, 0.6622896588699126, 0.5697673874287120, 0.1503708645734583, 0.2798617479978296, 0.2798617479978297, 0.1503708645734582, 0.5697673874287120, 0.9082517491081562, 0.0243498506845871, 0.0673984002072564, 0.0673984002072567, 0.0243498506845869, 0.9082517491081562, 0.4989241659396563, 0.1293878673669234, 0.3716879666934201, 0.3716879666934204, 0.1293878673669233, 0.4989241659396562, 0.5311444304776159, 0.0632274204565011, 0.4056281490658827, 0.4056281490658828, 0.0632274204565012, 0.5311444304776158, 0.3333333333333333, 0.8759787003474713, 0.0620106498262646, 0.0620106498262639, 0.7727532012417532, 0.0052666330207657, 0.2219801657374807, 0.2219801657374811, 0.0052666330207656, 0.7727532012417531, 0.7955154359824861, 0.0261588819796510, 0.1783256820378627, 0.1783256820378630, 0.0261588819796509, 0.7955154359824859, 0.9518230415381583, 0.0055547678704323, 0.0426221905914091, 0.0426221905914094, 0.0055547678704321, 0.9518230415381582, 0.5414440061438600, 0.2292779969280701, 0.2292779969280699, 0.7960823461994606, 0.1019588269002699, 0.1019588269002695, 0.9850326016003745, 0.0006230980203451, 0.0143443003792801, 0.0143443003792803, 0.0006230980203449, 0.9850326016003745 }; static double w_save[] = { 0.0000533239023334, 0.0000533239023334, 0.0000533239023334, 0.0083492191295379, 0.0083492191295379, 0.0083492191295379, 0.0083492191295379, 0.0083492191295379, 0.0083492191295379, 0.0030406522577730, 0.0030406522577730, 0.0030406522577730, 0.0030406522577730, 0.0030406522577730, 0.0030406522577730, 0.0014146272476628, 0.0014146272476628, 0.0014146272476628, 0.0052860436025325, 0.0052860436025325, 0.0052860436025325, 0.0052860436025325, 0.0052860436025325, 0.0052860436025325, 0.0024932699246691, 0.0024932699246691, 0.0024932699246691, 0.0024932699246691, 0.0024932699246691, 0.0024932699246691, 0.0030205810567136, 0.0030205810567136, 0.0030205810567136, 0.0030205810567136, 0.0030205810567136, 0.0030205810567136, 0.0036441755768762, 0.0036441755768762, 0.0036441755768762, 0.0036441755768762, 0.0036441755768762, 0.0036441755768762, 0.0074810896991602, 0.0074810896991602, 0.0074810896991602, 0.0074810896991602, 0.0074810896991602, 0.0074810896991602, 0.0045681541355720, 0.0045681541355720, 0.0045681541355720, 0.0045681541355720, 0.0045681541355720, 0.0045681541355720, 0.0016852036405343, 0.0016852036405343, 0.0016852036405343, 0.0016852036405343, 0.0016852036405343, 0.0016852036405343, 0.0055800151424133, 0.0055800151424133, 0.0055800151424133, 0.0082092066464793, 0.0082092066464793, 0.0082092066464793, 0.0082092066464793, 0.0082092066464793, 0.0082092066464793, 0.0083785907041262, 0.0083785907041262, 0.0083785907041262, 0.0044656768476199, 0.0044656768476199, 0.0044656768476199, 0.0044656768476199, 0.0044656768476199, 0.0044656768476199, 0.0062028347215228, 0.0062028347215228, 0.0062028347215228, 0.0062028347215228, 0.0062028347215228, 0.0062028347215228, 0.0008888925431519, 0.0008888925431519, 0.0008888925431519, 0.0008888925431519, 0.0008888925431519, 0.0008888925431519, 0.0126612945604860, 0.0126612945604860, 0.0126612945604860, 0.0014852293291852, 0.0014852293291852, 0.0014852293291852, 0.0014852293291852, 0.0014852293291852, 0.0014852293291852, 0.0011127063455906, 0.0011127063455906, 0.0011127063455906, 0.0011127063455906, 0.0011127063455906, 0.0011127063455906, 0.0128827331771754, 0.0128827331771754, 0.0128827331771754, 0.0119733591024828, 0.0119733591024828, 0.0119733591024828, 0.0119733591024828, 0.0119733591024828, 0.0119733591024828, 0.0108804660269342, 0.0108804660269342, 0.0108804660269342, 0.0058823160628199, 0.0058823160628199, 0.0058823160628199, 0.0058823160628199, 0.0058823160628199, 0.0058823160628199, 0.0018592782531939, 0.0018592782531939, 0.0018592782531939, 0.0008017410516731, 0.0008017410516731, 0.0008017410516731, 0.0084487434719511, 0.0084487434719511, 0.0084487434719511, 0.0084487434719511, 0.0084487434719511, 0.0084487434719511, 0.0102114559163661, 0.0102114559163661, 0.0102114559163661, 0.0102114559163661, 0.0102114559163661, 0.0102114559163661, 0.0024899591532165, 0.0024899591532165, 0.0024899591532165, 0.0024899591532165, 0.0024899591532165, 0.0024899591532165, 0.0098885056550223, 0.0098885056550223, 0.0098885056550223, 0.0098885056550223, 0.0098885056550223, 0.0098885056550223, 0.0074091131429365, 0.0074091131429365, 0.0074091131429365, 0.0074091131429365, 0.0074091131429365, 0.0074091131429365, 0.0130300709957626, 0.0039763485949254, 0.0039763485949254, 0.0039763485949254, 0.0019455932409831, 0.0019455932409831, 0.0019455932409831, 0.0019455932409831, 0.0019455932409831, 0.0019455932409831, 0.0042608365965002, 0.0042608365965002, 0.0042608365965002, 0.0042608365965002, 0.0042608365965002, 0.0042608365965002, 0.0010553743696176, 0.0010553743696176, 0.0010553743696176, 0.0010553743696176, 0.0010553743696176, 0.0010553743696176, 0.0125355977256489, 0.0125355977256489, 0.0125355977256489, 0.0066293991150592, 0.0066293991150592, 0.0066293991150592, 0.0001700882477425, 0.0001700882477425, 0.0001700882477425, 0.0001700882477425, 0.0001700882477425, 0.0001700882477425 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule33 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule33() returns the rule of precision 33. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.0866842399345696, 0.8266315201308605, 0.0866842399345699, 0.4094279608026433, 0.4094279608026433, 0.1811440783947132, 0.2581529287895067, 0.6549184352472063, 0.0869286359632870, 0.6549184352472063, 0.2581529287895068, 0.0869286359632869, 0.2849624019720829, 0.6009455627050857, 0.1140920353228314, 0.6009455627050857, 0.2849624019720829, 0.1140920353228312, 0.3783335382962427, 0.3783335382962427, 0.2433329234075145, 0.4989797178600512, 0.4989797178600512, 0.0020405642798976, 0.1340676338419341, 0.7742670347180146, 0.0916653314400512, 0.7742670347180146, 0.1340676338419342, 0.0916653314400510, 0.3269137502096716, 0.4571468585469127, 0.2159393912434156, 0.4571468585469128, 0.3269137502096715, 0.2159393912434155, 0.2596606680087211, 0.4806786639825575, 0.2596606680087213, 0.1008457159827756, 0.8767639677306408, 0.0223903162865836, 0.8767639677306409, 0.1008457159827757, 0.0223903162865833, 0.3552328254047640, 0.5455252367072077, 0.0992419378880283, 0.5455252367072078, 0.3552328254047640, 0.0992419378880282, 0.1584027341957248, 0.8211535906601003, 0.0204436751441749, 0.8211535906601004, 0.1584027341957248, 0.0204436751441747, 0.4785119732563822, 0.4785119732563822, 0.0429760534872356, 0.4012397484580547, 0.5401481330852944, 0.0586121184566509, 0.5401481330852945, 0.4012397484580547, 0.0586121184566507, 0.2273220131649666, 0.7532530766694563, 0.0194249101655773, 0.7532530766694562, 0.2273220131649666, 0.0194249101655771, 0.1040040001314270, 0.8451258076748079, 0.0508701921937651, 0.8451258076748080, 0.1040040001314272, 0.0508701921937648, 0.2516190193630367, 0.7445747285081441, 0.0038062521288191, 0.7445747285081442, 0.2516190193630368, 0.0038062521288190, 0.1946715273720462, 0.7113747622583637, 0.0939537103695900, 0.7113747622583638, 0.1946715273720463, 0.0939537103695898, 0.1756396314580331, 0.8206933909179547, 0.0036669776240122, 0.8206933909179547, 0.1756396314580332, 0.0036669776240119, 0.1654225039506263, 0.7841517925433079, 0.0504257035060658, 0.7841517925433079, 0.1654225039506264, 0.0504257035060656, 0.0604829240909603, 0.9354049276280985, 0.0041121482809413, 0.9354049276280986, 0.0604829240909603, 0.0041121482809409, 0.3321035653575233, 0.6635597637774838, 0.0043366708649930, 0.6635597637774838, 0.3321035653575233, 0.0043366708649928, 0.3794132168456387, 0.4768226069138183, 0.1437641762405430, 0.4768226069138183, 0.3794132168456387, 0.1437641762405429, 0.0235174430579130, 0.9529651138841736, 0.0235174430579135, 0.0565688972489456, 0.9215652847226834, 0.0218658180283709, 0.9215652847226835, 0.0565688972489457, 0.0218658180283706, 0.3060238617603606, 0.3879522764792787, 0.3060238617603606, 0.1464890507166427, 0.7070218985667143, 0.1464890507166430, 0.0543792032794963, 0.8912415934410072, 0.0543792032794967, 0.2909849162693301, 0.5407077523881676, 0.1683073313425023, 0.5407077523881676, 0.2909849162693300, 0.1683073313425022, 0.2368453944831515, 0.7146406256116400, 0.0485139799052084, 0.7146406256116401, 0.2368453944831516, 0.0485139799052082, 0.4145491529764430, 0.5807136071426248, 0.0047372398809322, 0.5807136071426248, 0.4145491529764430, 0.0047372398809321, 0.3075361882409410, 0.6703285978516907, 0.0221352139073682, 0.6703285978516907, 0.3075361882409411, 0.0221352139073681, 0.1109266644334704, 0.8846799404570630, 0.0043933951094668, 0.8846799404570630, 0.1109266644334704, 0.0043933951094664, 0.2181920158632539, 0.5636159682734920, 0.2181920158632540, 0.3188631220563678, 0.6259766725873849, 0.0551602053562473, 0.6259766725873848, 0.3188631220563678, 0.0551602053562472, 0.4919913444565532, 0.4919913444565532, 0.0160173110868935, 0.3953677591013828, 0.5802323524289785, 0.0243998884696386, 0.5802323524289785, 0.3953677591013828, 0.0243998884696386, 0.4533999616178053, 0.4533999616178053, 0.0932000767643894, 0.2137578302973531, 0.6356072278734608, 0.1506349418291862, 0.6356072278734608, 0.2137578302973531, 0.1506349418291860, 0.0047266605105680, 0.9905466789788636, 0.0047266605105684, 0.0247793702175406, 0.9707182444941620, 0.0045023852882976, 0.9707182444941620, 0.0247793702175407, 0.0045023852882971 }; static double b_save[] = { 0.0866842399345699, 0.0866842399345696, 0.8266315201308606, 0.1811440783947133, 0.4094279608026434, 0.4094279608026435, 0.0869286359632870, 0.2581529287895068, 0.6549184352472064, 0.0869286359632870, 0.6549184352472064, 0.2581529287895070, 0.1140920353228314, 0.2849624019720829, 0.6009455627050859, 0.1140920353228314, 0.6009455627050859, 0.2849624019720831, 0.2433329234075146, 0.3783335382962428, 0.3783335382962429, 0.0020405642798976, 0.4989797178600513, 0.4989797178600514, 0.0916653314400512, 0.1340676338419342, 0.7742670347180148, 0.0916653314400512, 0.7742670347180148, 0.1340676338419345, 0.2159393912434157, 0.3269137502096717, 0.4571468585469129, 0.2159393912434157, 0.4571468585469129, 0.3269137502096717, 0.2596606680087213, 0.2596606680087212, 0.4806786639825577, 0.0223903162865835, 0.1008457159827756, 0.8767639677306410, 0.0223903162865835, 0.8767639677306409, 0.1008457159827759, 0.0992419378880283, 0.3552328254047640, 0.5455252367072079, 0.0992419378880283, 0.5455252367072079, 0.3552328254047642, 0.0204436751441748, 0.1584027341957248, 0.8211535906601005, 0.0204436751441748, 0.8211535906601006, 0.1584027341957251, 0.0429760534872357, 0.4785119732563822, 0.4785119732563824, 0.0586121184566509, 0.4012397484580547, 0.5401481330852946, 0.0586121184566509, 0.5401481330852945, 0.4012397484580549, 0.0194249101655772, 0.2273220131649666, 0.7532530766694563, 0.0194249101655772, 0.7532530766694563, 0.2273220131649669, 0.0508701921937650, 0.1040040001314270, 0.8451258076748080, 0.0508701921937650, 0.8451258076748080, 0.1040040001314274, 0.0038062521288191, 0.2516190193630367, 0.7445747285081444, 0.0038062521288191, 0.7445747285081442, 0.2516190193630370, 0.0939537103695900, 0.1946715273720463, 0.7113747622583638, 0.0939537103695900, 0.7113747622583639, 0.1946715273720465, 0.0036669776240121, 0.1756396314580332, 0.8206933909179549, 0.0036669776240121, 0.8206933909179549, 0.1756396314580335, 0.0504257035060658, 0.1654225039506263, 0.7841517925433081, 0.0504257035060658, 0.7841517925433080, 0.1654225039506266, 0.0041121482809412, 0.0604829240909602, 0.9354049276280987, 0.0041121482809412, 0.9354049276280987, 0.0604829240909606, 0.0043366708649929, 0.3321035653575233, 0.6635597637774840, 0.0043366708649929, 0.6635597637774838, 0.3321035653575235, 0.1437641762405430, 0.3794132168456388, 0.4768226069138184, 0.1437641762405430, 0.4768226069138183, 0.3794132168456389, 0.0235174430579133, 0.0235174430579130, 0.9529651138841736, 0.0218658180283708, 0.0565688972489457, 0.9215652847226837, 0.0218658180283708, 0.9215652847226837, 0.0565688972489460, 0.3060238617603607, 0.3060238617603607, 0.3879522764792788, 0.1464890507166429, 0.1464890507166427, 0.7070218985667144, 0.0543792032794966, 0.0543792032794963, 0.8912415934410073, 0.1683073313425024, 0.2909849162693301, 0.5407077523881677, 0.1683073313425024, 0.5407077523881677, 0.2909849162693303, 0.0485139799052084, 0.2368453944831516, 0.7146406256116403, 0.0485139799052084, 0.7146406256116402, 0.2368453944831518, 0.0047372398809322, 0.4145491529764431, 0.5807136071426250, 0.0047372398809322, 0.5807136071426249, 0.4145491529764432, 0.0221352139073682, 0.3075361882409411, 0.6703285978516910, 0.0221352139073682, 0.6703285978516909, 0.3075361882409413, 0.0043933951094667, 0.1109266644334704, 0.8846799404570631, 0.0043933951094667, 0.8846799404570631, 0.1109266644334707, 0.2181920158632541, 0.2181920158632540, 0.5636159682734921, 0.0551602053562474, 0.3188631220563678, 0.6259766725873851, 0.0551602053562474, 0.6259766725873850, 0.3188631220563680, 0.0160173110868935, 0.4919913444565533, 0.4919913444565535, 0.0243998884696387, 0.3953677591013828, 0.5802323524289787, 0.0243998884696387, 0.5802323524289786, 0.3953677591013830, 0.0932000767643895, 0.4533999616178053, 0.4533999616178054, 0.1506349418291862, 0.2137578302973531, 0.6356072278734609, 0.1506349418291862, 0.6356072278734609, 0.2137578302973533, 0.0047266605105683, 0.0047266605105680, 0.9905466789788638, 0.0045023852882974, 0.0247793702175406, 0.9707182444941621, 0.0045023852882974, 0.9707182444941621, 0.0247793702175410 }; static double c_save[] = { 0.8266315201308605, 0.0866842399345699, 0.0866842399345694, 0.4094279608026433, 0.1811440783947132, 0.4094279608026433, 0.6549184352472062, 0.0869286359632869, 0.2581529287895066, 0.2581529287895067, 0.0869286359632868, 0.6549184352472062, 0.6009455627050857, 0.1140920353228314, 0.2849624019720827, 0.2849624019720829, 0.1140920353228312, 0.6009455627050857, 0.3783335382962427, 0.2433329234075144, 0.3783335382962427, 0.4989797178600511, 0.0020405642798975, 0.4989797178600510, 0.7742670347180147, 0.0916653314400512, 0.1340676338419339, 0.1340676338419342, 0.0916653314400510, 0.7742670347180146, 0.4571468585469128, 0.2159393912434156, 0.3269137502096715, 0.3269137502096716, 0.2159393912434156, 0.4571468585469127, 0.4806786639825576, 0.2596606680087212, 0.2596606680087211, 0.8767639677306409, 0.0223903162865836, 0.1008457159827754, 0.1008457159827755, 0.0223903162865834, 0.8767639677306408, 0.5455252367072078, 0.0992419378880283, 0.3552328254047639, 0.3552328254047640, 0.0992419378880282, 0.5455252367072077, 0.8211535906601003, 0.0204436751441749, 0.1584027341957245, 0.1584027341957248, 0.0204436751441746, 0.8211535906601003, 0.4785119732563821, 0.0429760534872355, 0.4785119732563820, 0.5401481330852944, 0.0586121184566509, 0.4012397484580545, 0.4012397484580545, 0.0586121184566507, 0.5401481330852944, 0.7532530766694562, 0.0194249101655771, 0.2273220131649664, 0.2273220131649666, 0.0194249101655771, 0.7532530766694561, 0.8451258076748079, 0.0508701921937651, 0.1040040001314269, 0.1040040001314270, 0.0508701921937648, 0.8451258076748078, 0.7445747285081442, 0.0038062521288192, 0.2516190193630364, 0.2516190193630367, 0.0038062521288190, 0.7445747285081441, 0.7113747622583637, 0.0939537103695900, 0.1946715273720462, 0.1946715273720462, 0.0939537103695898, 0.7113747622583637, 0.8206933909179548, 0.0036669776240122, 0.1756396314580330, 0.1756396314580332, 0.0036669776240118, 0.8206933909179546, 0.7841517925433079, 0.0504257035060658, 0.1654225039506261, 0.1654225039506262, 0.0504257035060657, 0.7841517925433077, 0.9354049276280986, 0.0041121482809413, 0.0604829240909600, 0.0604829240909602, 0.0041121482809410, 0.9354049276280985, 0.6635597637774838, 0.0043366708649929, 0.3321035653575229, 0.3321035653575233, 0.0043366708649929, 0.6635597637774837, 0.4768226069138182, 0.1437641762405429, 0.3794132168456386, 0.3794132168456387, 0.1437641762405430, 0.4768226069138181, 0.9529651138841736, 0.0235174430579134, 0.0235174430579129, 0.9215652847226835, 0.0218658180283709, 0.0565688972489454, 0.0565688972489456, 0.0218658180283705, 0.9215652847226834, 0.3879522764792787, 0.3060238617603607, 0.3060238617603606, 0.7070218985667143, 0.1464890507166430, 0.1464890507166426, 0.8912415934410072, 0.0543792032794966, 0.0543792032794960, 0.5407077523881676, 0.1683073313425023, 0.2909849162693300, 0.2909849162693300, 0.1683073313425022, 0.5407077523881675, 0.7146406256116400, 0.0485139799052084, 0.2368453944831513, 0.2368453944831515, 0.0485139799052082, 0.7146406256116400, 0.5807136071426249, 0.0047372398809322, 0.4145491529764428, 0.4145491529764431, 0.0047372398809321, 0.5807136071426248, 0.6703285978516907, 0.0221352139073682, 0.3075361882409408, 0.3075361882409410, 0.0221352139073681, 0.6703285978516906, 0.8846799404570629, 0.0043933951094666, 0.1109266644334701, 0.1109266644334703, 0.0043933951094665, 0.8846799404570630, 0.5636159682734920, 0.2181920158632540, 0.2181920158632539, 0.6259766725873849, 0.0551602053562473, 0.3188631220563676, 0.3188631220563679, 0.0551602053562472, 0.6259766725873848, 0.4919913444565532, 0.0160173110868935, 0.4919913444565530, 0.5802323524289785, 0.0243998884696386, 0.3953677591013827, 0.3953677591013828, 0.0243998884696385, 0.5802323524289784, 0.4533999616178052, 0.0932000767643894, 0.4533999616178051, 0.6356072278734608, 0.1506349418291861, 0.2137578302973530, 0.2137578302973530, 0.1506349418291860, 0.6356072278734608, 0.9905466789788637, 0.0047266605105684, 0.0047266605105677, 0.9707182444941620, 0.0045023852882974, 0.0247793702175404, 0.0247793702175406, 0.0045023852882972, 0.9707182444941619 }; static double w_save[] = { 0.0032023640124142, 0.0032023640124142, 0.0032023640124142, 0.0068346799344681, 0.0068346799344681, 0.0068346799344681, 0.0050108234565749, 0.0050108234565749, 0.0050108234565749, 0.0050108234565749, 0.0050108234565749, 0.0050108234565749, 0.0062666715145980, 0.0062666715145980, 0.0062666715145980, 0.0062666715145980, 0.0062666715145980, 0.0062666715145980, 0.0089341618081367, 0.0089341618081367, 0.0089341618081367, 0.0010410912372864, 0.0010410912372864, 0.0010410912372864, 0.0051060923018633, 0.0051060923018633, 0.0051060923018633, 0.0051060923018633, 0.0051060923018633, 0.0051060923018633, 0.0096392468588408, 0.0096392468588408, 0.0096392468588408, 0.0096392468588408, 0.0096392468588408, 0.0096392468588408, 0.0097388572366854, 0.0097388572366854, 0.0097388572366854, 0.0024212380388685, 0.0024212380388685, 0.0024212380388685, 0.0024212380388685, 0.0024212380388685, 0.0024212380388685, 0.0076973467270549, 0.0076973467270549, 0.0076973467270549, 0.0076973467270549, 0.0076973467270549, 0.0076973467270549, 0.0029882446919490, 0.0029882446919490, 0.0029882446919490, 0.0029882446919490, 0.0029882446919490, 0.0029882446919490, 0.0054643256840460, 0.0054643256840460, 0.0054643256840460, 0.0061988540259434, 0.0061988540259434, 0.0061988540259434, 0.0061988540259434, 0.0061988540259434, 0.0061988540259434, 0.0033169972939131, 0.0033169972939131, 0.0033169972939131, 0.0033169972939131, 0.0033169972939131, 0.0033169972939131, 0.0037089296125893, 0.0037089296125893, 0.0037089296125893, 0.0037089296125893, 0.0037089296125893, 0.0037089296125893, 0.0015426465184706, 0.0015426465184706, 0.0015426465184706, 0.0015426465184706, 0.0015426465184706, 0.0015426465184706, 0.0066121724110684, 0.0066121724110684, 0.0066121724110684, 0.0066121724110684, 0.0066121724110684, 0.0066121724110684, 0.0013551781957506, 0.0013551781957506, 0.0013551781957506, 0.0013551781957506, 0.0013551781957506, 0.0013551781957506, 0.0049036283435529, 0.0049036283435529, 0.0049036283435529, 0.0049036283435529, 0.0049036283435529, 0.0049036283435529, 0.0009157661571810, 0.0009157661571810, 0.0009157661571810, 0.0009157661571810, 0.0009157661571810, 0.0009157661571810, 0.0018218162644265, 0.0018218162644265, 0.0018218162644265, 0.0018218162644265, 0.0018218162644265, 0.0018218162644265, 0.0092423799017096, 0.0092423799017096, 0.0092423799017096, 0.0092423799017096, 0.0092423799017096, 0.0092423799017096, 0.0013813690630279, 0.0013813690630279, 0.0013813690630279, 0.0019606312336932, 0.0019606312336932, 0.0019606312336932, 0.0019606312336932, 0.0019606312336932, 0.0019606312336932, 0.0120887399809166, 0.0120887399809166, 0.0120887399809166, 0.0073774464967342, 0.0073774464967342, 0.0073774464967342, 0.0032093504439416, 0.0032093504439416, 0.0032093504439416, 0.0102099177863965, 0.0102099177863965, 0.0102099177863965, 0.0102099177863965, 0.0102099177863965, 0.0102099177863965, 0.0054637704373722, 0.0054637704373722, 0.0054637704373722, 0.0054637704373722, 0.0054637704373722, 0.0054637704373722, 0.0020111020097847, 0.0020111020097847, 0.0020111020097847, 0.0020111020097847, 0.0020111020097847, 0.0020111020097847, 0.0042683347026345, 0.0042683347026345, 0.0042683347026345, 0.0042683347026345, 0.0042683347026345, 0.0042683347026345, 0.0012878764088954, 0.0012878764088954, 0.0012878764088954, 0.0012878764088954, 0.0012878764088954, 0.0012878764088954, 0.0099263761795442, 0.0099263761795442, 0.0099263761795442, 0.0065998833272568, 0.0065998833272568, 0.0065998833272568, 0.0065998833272568, 0.0065998833272568, 0.0065998833272568, 0.0038623620299660, 0.0038623620299660, 0.0038623620299660, 0.0049474328088082, 0.0049474328088082, 0.0049474328088082, 0.0049474328088082, 0.0049474328088082, 0.0049474328088082, 0.0093337977696466, 0.0093337977696466, 0.0093337977696466, 0.0091814815579271, 0.0091814815579271, 0.0091814815579271, 0.0091814815579271, 0.0091814815579271, 0.0091814815579271, 0.0002934827335780, 0.0002934827335780, 0.0002934827335780, 0.0006440017743474, 0.0006440017743474, 0.0006440017743474, 0.0006440017743474, 0.0006440017743474, 0.0006440017743474 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule34 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule34() returns the rule of precision 34. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3851262518382810, 0.5937769878916170, 0.0210967602701019, 0.5937769878916170, 0.3851262518382810, 0.0210967602701018, 0.0528200673454988, 0.9437918205041110, 0.0033881121503903, 0.9437918205041111, 0.0528200673454988, 0.0033881121503898, 0.0459825951541271, 0.9080348096917454, 0.0459825951541276, 0.0508987652831316, 0.9308929059173959, 0.0182083287994725, 0.9308929059173960, 0.0508987652831318, 0.0182083287994721, 0.0208387475149684, 0.9583225049700629, 0.0208387475149688, 0.1291243720726085, 0.8103648572840793, 0.0605107706433124, 0.8103648572840793, 0.1291243720726087, 0.0605107706433121, 0.0878179027775245, 0.8762622058588977, 0.0359198913635778, 0.8762622058588977, 0.0878179027775245, 0.0359198913635776, 0.0757621741867908, 0.8484756516264180, 0.0757621741867912, 0.3766019805175457, 0.3766019805175457, 0.2467960389649085, 0.2735537380248192, 0.5623852333049681, 0.1640610286702127, 0.5623852333049681, 0.2735537380248192, 0.1640610286702125, 0.0944770656323742, 0.8948396708440374, 0.0106832635235886, 0.8948396708440374, 0.0944770656323743, 0.0106832635235882, 0.2873558398221649, 0.4252883203556701, 0.2873558398221651, 0.4111522333036005, 0.5577150863900258, 0.0311326803063737, 0.5577150863900259, 0.4111522333036006, 0.0311326803063736, 0.3594475694982553, 0.5073598072800389, 0.1331926232217058, 0.5073598072800389, 0.3594475694982553, 0.1331926232217057, 0.3884100853304371, 0.5372925954322688, 0.0742973192372942, 0.5372925954322687, 0.3884100853304370, 0.0742973192372941, 0.3253550433420577, 0.4694784588431804, 0.2051664978147619, 0.4694784588431803, 0.3253550433420578, 0.2051664978147618, 0.1747804794810684, 0.7349999143937561, 0.0902196061251755, 0.7349999143937561, 0.1747804794810685, 0.0902196061251753, 0.1941646181495633, 0.7619195089459252, 0.0439158729045115, 0.7619195089459252, 0.1941646181495633, 0.0439158729045113, 0.4744124989028456, 0.4744124989028456, 0.0511750021943088, 0.2483278734045790, 0.6827082966308193, 0.0689638299646018, 0.6827082966308193, 0.2483278734045790, 0.0689638299646015, 0.2229920412612009, 0.6518261605959125, 0.1251817981428867, 0.6518261605959125, 0.2229920412612009, 0.1251817981428865, 0.1496044235489511, 0.8457252778897656, 0.0046702985612834, 0.8457252778897657, 0.1496044235489512, 0.0046702985612830, 0.1111727012858456, 0.7776545974283084, 0.1111727012858459, 0.4918649619576897, 0.4918649619576897, 0.0162700760846206, 0.3283914136921266, 0.6226826638040091, 0.0489259225038643, 0.6226826638040089, 0.3283914136921267, 0.0489259225038643, 0.1508877227628729, 0.6982245544742539, 0.1508877227628732, 0.1423855003245428, 0.8329562498972498, 0.0246582497782074, 0.8329562498972499, 0.1423855003245429, 0.0246582497782072, 0.4238402997203689, 0.5701997570298869, 0.0059599432497442, 0.5701997570298869, 0.4238402997203689, 0.0059599432497442, 0.0041579573923189, 0.9916840852153618, 0.0041579573923194, 0.2404349104138168, 0.5191301791723664, 0.2404349104138169, 0.2676904193443056, 0.7037908578134091, 0.0285187228422855, 0.7037908578134090, 0.2676904193443056, 0.0285187228422852, 0.4155115967448372, 0.4155115967448372, 0.1689768065103256, 0.4995421826615118, 0.4995421826615117, 0.0009156346769764, 0.3454113789529011, 0.6390259777460834, 0.0155626433010154, 0.6390259777460834, 0.3454113789529011, 0.0155626433010154, 0.3534495196576637, 0.6456247621084024, 0.0009257182339338, 0.6456247621084025, 0.3534495196576638, 0.0009257182339337, 0.4485642658787082, 0.4485642658787082, 0.1028714682425834, 0.3033356394717892, 0.5973781489096254, 0.0992862116185854, 0.5973781489096254, 0.3033356394717892, 0.0992862116185853, 0.0217555603201839, 0.9742699338072974, 0.0039745058725186, 0.9742699338072975, 0.0217555603201841, 0.0039745058725182, 0.3333333333333333, 0.2075468682735205, 0.7786734923211107, 0.0137796394053689, 0.7786734923211107, 0.2075468682735205, 0.0137796394053686, 0.1943865435789661, 0.6112269128420674, 0.1943865435789664, 0.2135602395179478, 0.7856676213617251, 0.0007721391203271, 0.7856676213617252, 0.2135602395179479, 0.0007721391203269, 0.2793864317822237, 0.7151517773234828, 0.0054617908942934, 0.7151517773234828, 0.2793864317822238, 0.0054617908942933, 0.0968669225755472, 0.9031283677334342, 0.0000047096910187, 0.9031283677334343, 0.0968669225755472, 0.0000047096910183 }; static double b_save[] = { 0.0210967602701019, 0.3851262518382811, 0.5937769878916171, 0.0210967602701019, 0.5937769878916171, 0.3851262518382813, 0.0033881121503900, 0.0528200673454988, 0.9437918205041111, 0.0033881121503900, 0.9437918205041114, 0.0528200673454991, 0.0459825951541274, 0.0459825951541271, 0.9080348096917455, 0.0182083287994724, 0.0508987652831316, 0.9308929059173960, 0.0182083287994724, 0.9308929059173960, 0.0508987652831320, 0.0208387475149687, 0.0208387475149684, 0.9583225049700631, 0.0605107706433123, 0.1291243720726085, 0.8103648572840793, 0.0605107706433123, 0.8103648572840793, 0.1291243720726088, 0.0359198913635778, 0.0878179027775245, 0.8762622058588979, 0.0359198913635778, 0.8762622058588979, 0.0878179027775248, 0.0757621741867911, 0.0757621741867908, 0.8484756516264182, 0.2467960389649086, 0.3766019805175458, 0.3766019805175458, 0.1640610286702127, 0.2735537380248192, 0.5623852333049683, 0.1640610286702127, 0.5623852333049683, 0.2735537380248194, 0.0106832635235884, 0.0944770656323742, 0.8948396708440375, 0.0106832635235884, 0.8948396708440375, 0.0944770656323745, 0.2873558398221651, 0.2873558398221650, 0.4252883203556702, 0.0311326803063737, 0.4111522333036006, 0.5577150863900260, 0.0311326803063737, 0.5577150863900259, 0.4111522333036007, 0.1331926232217058, 0.3594475694982554, 0.5073598072800390, 0.1331926232217058, 0.5073598072800389, 0.3594475694982555, 0.0742973192372942, 0.3884100853304371, 0.5372925954322689, 0.0742973192372942, 0.5372925954322688, 0.3884100853304373, 0.2051664978147620, 0.3253550433420578, 0.4694784588431805, 0.2051664978147620, 0.4694784588431805, 0.3253550433420579, 0.0902196061251755, 0.1747804794810684, 0.7349999143937562, 0.0902196061251755, 0.7349999143937561, 0.1747804794810687, 0.0439158729045114, 0.1941646181495633, 0.7619195089459254, 0.0439158729045114, 0.7619195089459254, 0.1941646181495635, 0.0511750021943088, 0.4744124989028456, 0.4744124989028458, 0.0689638299646017, 0.2483278734045790, 0.6827082966308194, 0.0689638299646017, 0.6827082966308194, 0.2483278734045792, 0.1251817981428867, 0.2229920412612009, 0.6518261605959126, 0.1251817981428867, 0.6518261605959126, 0.2229920412612011, 0.0046702985612833, 0.1496044235489511, 0.8457252778897658, 0.0046702985612833, 0.8457252778897657, 0.1496044235489514, 0.1111727012858459, 0.1111727012858457, 0.7776545974283087, 0.0162700760846207, 0.4918649619576898, 0.4918649619576899, 0.0489259225038644, 0.3283914136921267, 0.6226826638040092, 0.0489259225038644, 0.6226826638040091, 0.3283914136921268, 0.1508877227628732, 0.1508877227628729, 0.6982245544742540, 0.0246582497782073, 0.1423855003245428, 0.8329562498972500, 0.0246582497782073, 0.8329562498972499, 0.1423855003245431, 0.0059599432497443, 0.4238402997203689, 0.5701997570298871, 0.0059599432497443, 0.5701997570298870, 0.4238402997203691, 0.0041579573923192, 0.0041579573923189, 0.9916840852153619, 0.2404349104138169, 0.2404349104138168, 0.5191301791723665, 0.0285187228422854, 0.2676904193443056, 0.7037908578134091, 0.0285187228422854, 0.7037908578134091, 0.2676904193443059, 0.1689768065103257, 0.4155115967448372, 0.4155115967448373, 0.0009156346769765, 0.4995421826615118, 0.4995421826615120, 0.0155626433010155, 0.3454113789529012, 0.6390259777460836, 0.0155626433010155, 0.6390259777460835, 0.3454113789529014, 0.0009257182339338, 0.3534495196576638, 0.6456247621084026, 0.0009257182339338, 0.6456247621084026, 0.3534495196576640, 0.1028714682425835, 0.4485642658787083, 0.4485642658787085, 0.0992862116185854, 0.3033356394717893, 0.5973781489096255, 0.0992862116185854, 0.5973781489096255, 0.3033356394717894, 0.0039745058725185, 0.0217555603201839, 0.9742699338072977, 0.0039745058725185, 0.9742699338072977, 0.0217555603201842, 0.3333333333333334, 0.0137796394053688, 0.2075468682735205, 0.7786734923211108, 0.0137796394053688, 0.7786734923211108, 0.2075468682735207, 0.1943865435789664, 0.1943865435789662, 0.6112269128420676, 0.0007721391203270, 0.2135602395179478, 0.7856676213617252, 0.0007721391203270, 0.7856676213617252, 0.2135602395179481, 0.0054617908942934, 0.2793864317822238, 0.7151517773234830, 0.0054617908942934, 0.7151517773234830, 0.2793864317822241, 0.0000047096910185, 0.0968669225755471, 0.9031283677334344, 0.0000047096910185, 0.9031283677334344, 0.0968669225755475 }; static double c_save[] = { 0.5937769878916170, 0.0210967602701019, 0.3851262518382809, 0.3851262518382810, 0.0210967602701019, 0.5937769878916168, 0.9437918205041113, 0.0033881121503902, 0.0528200673454986, 0.0528200673454988, 0.0033881121503898, 0.9437918205041110, 0.9080348096917454, 0.0459825951541274, 0.0459825951541269, 0.9308929059173959, 0.0182083287994725, 0.0508987652831314, 0.0508987652831316, 0.0182083287994722, 0.9308929059173959, 0.9583225049700629, 0.0208387475149687, 0.0208387475149682, 0.8103648572840793, 0.0605107706433123, 0.1291243720726084, 0.1291243720726085, 0.0605107706433120, 0.8103648572840791, 0.8762622058588978, 0.0359198913635778, 0.0878179027775242, 0.0878179027775245, 0.0359198913635775, 0.8762622058588976, 0.8484756516264181, 0.0757621741867912, 0.0757621741867905, 0.3766019805175457, 0.2467960389649085, 0.3766019805175456, 0.5623852333049681, 0.1640610286702126, 0.2735537380248191, 0.2735537380248192, 0.1640610286702125, 0.5623852333049681, 0.8948396708440375, 0.0106832635235885, 0.0944770656323740, 0.0944770656323742, 0.0106832635235882, 0.8948396708440374, 0.4252883203556700, 0.2873558398221649, 0.2873558398221648, 0.5577150863900258, 0.0311326803063737, 0.4111522333036004, 0.4111522333036004, 0.0311326803063735, 0.5577150863900256, 0.5073598072800389, 0.1331926232217057, 0.3594475694982552, 0.3594475694982552, 0.1331926232217058, 0.5073598072800387, 0.5372925954322687, 0.0742973192372940, 0.3884100853304369, 0.3884100853304371, 0.0742973192372941, 0.5372925954322686, 0.4694784588431803, 0.2051664978147618, 0.3253550433420577, 0.3253550433420577, 0.2051664978147618, 0.4694784588431803, 0.7349999143937561, 0.0902196061251755, 0.1747804794810682, 0.1747804794810684, 0.0902196061251753, 0.7349999143937560, 0.7619195089459252, 0.0439158729045115, 0.1941646181495631, 0.1941646181495634, 0.0439158729045113, 0.7619195089459252, 0.4744124989028456, 0.0511750021943088, 0.4744124989028454, 0.6827082966308193, 0.0689638299646017, 0.2483278734045787, 0.2483278734045790, 0.0689638299646015, 0.6827082966308193, 0.6518261605959125, 0.1251817981428866, 0.2229920412612008, 0.2229920412612009, 0.1251817981428865, 0.6518261605959124, 0.8457252778897656, 0.0046702985612833, 0.1496044235489508, 0.1496044235489510, 0.0046702985612831, 0.8457252778897656, 0.7776545974283084, 0.1111727012858459, 0.1111727012858454, 0.4918649619576896, 0.0162700760846206, 0.4918649619576895, 0.6226826638040089, 0.0489259225038643, 0.3283914136921265, 0.3283914136921267, 0.0489259225038643, 0.6226826638040088, 0.6982245544742540, 0.1508877227628732, 0.1508877227628728, 0.8329562498972499, 0.0246582497782074, 0.1423855003245426, 0.1423855003245427, 0.0246582497782072, 0.8329562498972497, 0.5701997570298869, 0.0059599432497442, 0.4238402997203686, 0.4238402997203689, 0.0059599432497440, 0.5701997570298867, 0.9916840852153619, 0.0041579573923193, 0.0041579573923187, 0.5191301791723663, 0.2404349104138168, 0.2404349104138167, 0.7037908578134090, 0.0285187228422853, 0.2676904193443054, 0.2676904193443056, 0.0285187228422853, 0.7037908578134089, 0.4155115967448372, 0.1689768065103256, 0.4155115967448370, 0.4995421826615117, 0.0009156346769764, 0.4995421826615116, 0.6390259777460833, 0.0155626433010154, 0.3454113789529010, 0.3454113789529011, 0.0155626433010153, 0.6390259777460832, 0.6456247621084025, 0.0009257182339338, 0.3534495196576636, 0.3534495196576637, 0.0009257182339336, 0.6456247621084023, 0.4485642658787082, 0.1028714682425834, 0.4485642658787081, 0.5973781489096254, 0.0992862116185854, 0.3033356394717891, 0.3033356394717892, 0.0992862116185853, 0.5973781489096253, 0.9742699338072977, 0.0039745058725186, 0.0217555603201837, 0.0217555603201840, 0.0039745058725184, 0.9742699338072975, 0.3333333333333333, 0.7786734923211107, 0.0137796394053688, 0.2075468682735203, 0.2075468682735205, 0.0137796394053687, 0.7786734923211107, 0.6112269128420675, 0.1943865435789664, 0.1943865435789659, 0.7856676213617251, 0.0007721391203271, 0.2135602395179477, 0.2135602395179478, 0.0007721391203269, 0.7856676213617251, 0.7151517773234829, 0.0054617908942934, 0.2793864317822236, 0.2793864317822238, 0.0054617908942932, 0.7151517773234826, 0.9031283677334343, 0.0000047096910187, 0.0968669225755469, 0.0968669225755472, 0.0000047096910184, 0.9031283677334342 }; static double w_save[] = { 0.0001016859723671, 0.0001016859723671, 0.0001016859723671, 0.0001016859723671, 0.0001016859723671, 0.0001016859723671, 0.0006540479665875, 0.0006540479665875, 0.0006540479665875, 0.0006540479665875, 0.0006540479665875, 0.0006540479665875, 0.0022989665688091, 0.0022989665688091, 0.0022989665688091, 0.0015198116582616, 0.0015198116582616, 0.0015198116582616, 0.0015198116582616, 0.0015198116582616, 0.0015198116582616, 0.0010996805664632, 0.0010996805664632, 0.0010996805664632, 0.0046696376839459, 0.0046696376839459, 0.0046696376839459, 0.0046696376839459, 0.0046696376839459, 0.0046696376839459, 0.0029521156305622, 0.0029521156305622, 0.0029521156305622, 0.0029521156305622, 0.0029521156305622, 0.0029521156305622, 0.0039973734536493, 0.0039973734536493, 0.0039973734536493, 0.0117400065912576, 0.0117400065912576, 0.0117400065912576, 0.0098609303129047, 0.0098609303129047, 0.0098609303129047, 0.0098609303129047, 0.0098609303129047, 0.0098609303129047, 0.0017262732588417, 0.0017262732588417, 0.0017262732588417, 0.0017262732588417, 0.0017262732588417, 0.0017262732588417, 0.0117612076394136, 0.0117612076394136, 0.0117612076394136, 0.0050361825013339, 0.0050361825013339, 0.0050361825013339, 0.0050361825013339, 0.0050361825013339, 0.0050361825013339, 0.0096578802294468, 0.0096578802294468, 0.0096578802294468, 0.0096578802294468, 0.0096578802294468, 0.0096578802294468, 0.0076119150208859, 0.0076119150208859, 0.0076119150208859, 0.0076119150208859, 0.0076119150208859, 0.0076119150208859, 0.0110658638875991, 0.0110658638875991, 0.0110658638875991, 0.0110658638875991, 0.0110658638875991, 0.0110658638875991, 0.0065038397126497, 0.0065038397126497, 0.0065038397126497, 0.0065038397126497, 0.0065038397126497, 0.0065038397126497, 0.0048326872534851, 0.0048326872534851, 0.0048326872534851, 0.0048326872534851, 0.0048326872534851, 0.0048326872534851, 0.0064842252138385, 0.0064842252138385, 0.0064842252138385, 0.0065935144677494, 0.0065935144677494, 0.0065935144677494, 0.0065935144677494, 0.0065935144677494, 0.0065935144677494, 0.0082852665131007, 0.0082852665131007, 0.0082852665131007, 0.0082852665131007, 0.0082852665131007, 0.0082852665131007, 0.0013994293854031, 0.0013994293854031, 0.0013994293854031, 0.0013994293854031, 0.0013994293854031, 0.0013994293854031, 0.0058334336795542, 0.0058334336795542, 0.0058334336795542, 0.0037293709434182, 0.0037293709434182, 0.0037293709434182, 0.0060952640324883, 0.0060952640324883, 0.0060952640324883, 0.0060952640324883, 0.0060952640324883, 0.0060952640324883, 0.0076873106859637, 0.0076873106859637, 0.0076873106859637, 0.0031432061481593, 0.0031432061481593, 0.0031432061481593, 0.0031432061481593, 0.0031432061481593, 0.0031432061481593, 0.0022313317933533, 0.0022313317933533, 0.0022313317933533, 0.0022313317933533, 0.0022313317933533, 0.0022313317933533, 0.0002269613567709, 0.0002269613567709, 0.0002269613567709, 0.0108136993162696, 0.0108136993162696, 0.0108136993162696, 0.0044357309734420, 0.0044357309734420, 0.0044357309734420, 0.0044357309734420, 0.0044357309734420, 0.0044357309734420, 0.0106474448424889, 0.0106474448424889, 0.0106474448424889, 0.0007609261662181, 0.0007609261662181, 0.0007609261662181, 0.0034883273457438, 0.0034883273457438, 0.0034883273457438, 0.0034883273457438, 0.0034883273457438, 0.0034883273457438, 0.0007318458736701, 0.0007318458736701, 0.0007318458736701, 0.0007318458736701, 0.0007318458736701, 0.0007318458736701, 0.0088609393001530, 0.0088609393001530, 0.0088609393001530, 0.0082507974307530, 0.0082507974307530, 0.0082507974307530, 0.0082507974307530, 0.0082507974307530, 0.0082507974307530, 0.0004979675731971, 0.0004979675731971, 0.0004979675731971, 0.0004979675731971, 0.0004979675731971, 0.0004979675731971, 0.0121009649301711, 0.0028058181373137, 0.0028058181373137, 0.0028058181373137, 0.0028058181373137, 0.0028058181373137, 0.0028058181373137, 0.0094001410371984, 0.0094001410371984, 0.0094001410371984, 0.0005776505742348, 0.0005776505742348, 0.0005776505742348, 0.0005776505742348, 0.0005776505742348, 0.0005776505742348, 0.0019626288054833, 0.0019626288054833, 0.0019626288054833, 0.0019626288054833, 0.0019626288054833, 0.0019626288054833, 0.0002873453546081, 0.0002873453546081, 0.0002873453546081, 0.0002873453546081, 0.0002873453546081, 0.0002873453546081 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule35 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule35() returns the rule of precision 35. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3014351686173180, 0.3971296627653639, 0.3014351686173180, 0.4916414039828907, 0.4916414039828907, 0.0167171920342186, 0.3577931357985971, 0.3577931357985971, 0.2844137284028057, 0.0550454796915316, 0.9428863000930624, 0.0020682202154061, 0.9428863000930625, 0.0550454796915318, 0.0020682202154057, 0.4453764649152975, 0.5457185408985746, 0.0089049941861278, 0.5457185408985746, 0.4453764649152976, 0.0089049941861277, 0.1523840025243152, 0.8455000199126449, 0.0021159775630399, 0.8455000199126449, 0.1523840025243154, 0.0021159775630396, 0.2624139601093454, 0.4751720797813089, 0.2624139601093456, 0.3975166100282313, 0.5992221165426375, 0.0032612734291312, 0.5992221165426374, 0.3975166100282314, 0.0032612734291311, 0.4028164505857819, 0.4028164505857819, 0.1943670988284362, 0.1560787694034761, 0.7987533357833951, 0.0451678948131288, 0.7987533357833952, 0.1560787694034762, 0.0451678948131284, 0.4730889655006641, 0.4730889655006641, 0.0538220689986716, 0.1972956762765587, 0.7940983020176844, 0.0086060217057569, 0.7940983020176845, 0.1972956762765588, 0.0086060217057566, 0.0500938368999262, 0.9359318098485054, 0.0139743532515686, 0.9359318098485054, 0.0500938368999261, 0.0139743532515681, 0.2988590630143191, 0.5136696044857865, 0.1874713324998944, 0.5136696044857865, 0.2988590630143191, 0.1874713324998943, 0.0628680490440657, 0.8742639019118683, 0.0628680490440661, 0.4415974337549303, 0.4415974337549303, 0.1168051324901392, 0.0196271599834707, 0.9607456800330582, 0.0196271599834711, 0.3347633432653314, 0.4325143126587202, 0.2327223440759484, 0.4325143126587202, 0.3347633432653314, 0.2327223440759484, 0.2093728249763754, 0.7616252904089401, 0.0290018846146846, 0.7616252904089401, 0.2093728249763754, 0.0290018846146844, 0.1065647448613834, 0.8398677722708630, 0.0535674828677536, 0.8398677722708631, 0.1065647448613836, 0.0535674828677533, 0.3213626276695433, 0.6751411779813131, 0.0034961943491436, 0.6751411779813131, 0.3213626276695434, 0.0034961943491434, 0.2415870263479875, 0.7572369308551706, 0.0011760427968418, 0.7572369308551707, 0.2415870263479876, 0.0011760427968416, 0.3331530997207648, 0.5528929715350868, 0.1139539287441483, 0.5528929715350868, 0.3331530997207648, 0.1139539287441482, 0.1551165548133034, 0.7599448456751416, 0.0849385995115551, 0.7599448456751415, 0.1551165548133034, 0.0849385995115548, 0.3710141516774619, 0.4764206619753218, 0.1525651863472163, 0.4764206619753217, 0.3710141516774620, 0.1525651863472163, 0.0402868688301934, 0.9194262623396129, 0.0402868688301939, 0.2708836618077721, 0.7154976600831513, 0.0136186781090767, 0.7154976600831513, 0.2708836618077720, 0.0136186781090765, 0.3525067484154665, 0.5912668641409812, 0.0562263874435524, 0.5912668641409811, 0.3525067484154665, 0.0562263874435522, 0.4057201327781905, 0.5125263777821213, 0.0817534894396881, 0.5125263777821213, 0.4057201327781905, 0.0817534894396881, 0.2189496810149983, 0.7174078887952542, 0.0636424301897475, 0.7174078887952543, 0.2189496810149983, 0.0636424301897472, 0.2067092480855645, 0.6778965310783613, 0.1153942208360741, 0.6778965310783613, 0.2067092480855646, 0.1153942208360739, 0.0985261546687924, 0.8029476906624150, 0.0985261546687927, 0.2566010878790922, 0.5952117958375970, 0.1481871162833107, 0.5952117958375971, 0.2566010878790923, 0.1481871162833105, 0.1382062952112500, 0.8431958337273686, 0.0185978710613815, 0.8431958337273686, 0.1382062952112501, 0.0185978710613812, 0.1395344629893073, 0.7209310740213852, 0.1395344629893076, 0.2215360105096920, 0.5569279789806159, 0.2215360105096921, 0.4258102085854810, 0.5412187714875727, 0.0329710199269463, 0.5412187714875726, 0.4258102085854810, 0.0329710199269463, 0.1807503221352996, 0.6384993557294008, 0.1807503221352998, 0.2797259269522402, 0.6348945214748060, 0.0853795515729538, 0.6348945214748060, 0.2797259269522402, 0.0853795515729537, 0.0224666835802112, 0.9739002605768547, 0.0036330558429342, 0.9739002605768547, 0.0224666835802113, 0.0036330558429336, 0.0838622585244554, 0.8901176638131806, 0.0260200776623640, 0.8901176638131806, 0.0838622585244554, 0.0260200776623637, 0.2848003464144683, 0.6757427274290935, 0.0394569261564381, 0.6757427274290936, 0.2848003464144683, 0.0394569261564380, 0.3565941035365738, 0.6236351787590180, 0.0197707177044082, 0.6236351787590180, 0.3565941035365738, 0.0197707177044081, 0.0974242311151380, 0.8975470714692345, 0.0050286974156275, 0.8975470714692346, 0.0974242311151381, 0.0050286974156271, 0.0042772072684830, 0.9914455854630337, 0.0042772072684834, 0.4999132224862251, 0.4999132224862251, 0.0001735550275497 }; static double b_save[] = { 0.3014351686173181, 0.3014351686173181, 0.3971296627653640, 0.0167171920342186, 0.4916414039828907, 0.4916414039828909, 0.2844137284028058, 0.3577931357985972, 0.3577931357985973, 0.0020682202154059, 0.0550454796915316, 0.9428863000930624, 0.0020682202154059, 0.9428863000930624, 0.0550454796915320, 0.0089049941861278, 0.4453764649152975, 0.5457185408985749, 0.0089049941861278, 0.5457185408985747, 0.4453764649152978, 0.0021159775630399, 0.1523840025243152, 0.8455000199126450, 0.0021159775630399, 0.8455000199126450, 0.1523840025243156, 0.2624139601093456, 0.2624139601093455, 0.4751720797813091, 0.0032612734291312, 0.3975166100282314, 0.5992221165426377, 0.0032612734291312, 0.5992221165426375, 0.3975166100282316, 0.1943670988284363, 0.4028164505857819, 0.4028164505857820, 0.0451678948131287, 0.1560787694034761, 0.7987533357833954, 0.0451678948131287, 0.7987533357833954, 0.1560787694034764, 0.0538220689986717, 0.4730889655006642, 0.4730889655006644, 0.0086060217057568, 0.1972956762765587, 0.7940983020176846, 0.0086060217057568, 0.7940983020176846, 0.1972956762765590, 0.0139743532515684, 0.0500938368999262, 0.9359318098485054, 0.0139743532515684, 0.9359318098485058, 0.0500938368999265, 0.1874713324998945, 0.2988590630143192, 0.5136696044857866, 0.1874713324998945, 0.5136696044857866, 0.2988590630143193, 0.0628680490440660, 0.0628680490440657, 0.8742639019118684, 0.1168051324901393, 0.4415974337549304, 0.4415974337549305, 0.0196271599834710, 0.0196271599834707, 0.9607456800330584, 0.2327223440759485, 0.3347633432653315, 0.4325143126587203, 0.2327223440759485, 0.4325143126587202, 0.3347633432653315, 0.0290018846146845, 0.2093728249763754, 0.7616252904089403, 0.0290018846146845, 0.7616252904089402, 0.2093728249763756, 0.0535674828677535, 0.1065647448613835, 0.8398677722708632, 0.0535674828677535, 0.8398677722708632, 0.1065647448613838, 0.0034961943491435, 0.3213626276695434, 0.6751411779813132, 0.0034961943491435, 0.6751411779813132, 0.3213626276695436, 0.0011760427968418, 0.2415870263479876, 0.7572369308551709, 0.0011760427968418, 0.7572369308551709, 0.2415870263479878, 0.1139539287441484, 0.3331530997207649, 0.5528929715350870, 0.1139539287441484, 0.5528929715350869, 0.3331530997207651, 0.0849385995115550, 0.1551165548133034, 0.7599448456751416, 0.0849385995115550, 0.7599448456751416, 0.1551165548133037, 0.1525651863472164, 0.3710141516774620, 0.4764206619753220, 0.1525651863472164, 0.4764206619753218, 0.3710141516774621, 0.0402868688301937, 0.0402868688301934, 0.9194262623396129, 0.0136186781090766, 0.2708836618077721, 0.7154976600831515, 0.0136186781090766, 0.7154976600831515, 0.2708836618077723, 0.0562263874435524, 0.3525067484154665, 0.5912668641409813, 0.0562263874435524, 0.5912668641409812, 0.3525067484154668, 0.0817534894396882, 0.4057201327781905, 0.5125263777821215, 0.0817534894396882, 0.5125263777821214, 0.4057201327781906, 0.0636424301897474, 0.2189496810149984, 0.7174078887952544, 0.0636424301897474, 0.7174078887952544, 0.2189496810149986, 0.1153942208360741, 0.2067092480855645, 0.6778965310783615, 0.1153942208360741, 0.6778965310783615, 0.2067092480855648, 0.0985261546687926, 0.0985261546687924, 0.8029476906624151, 0.1481871162833107, 0.2566010878790924, 0.5952117958375971, 0.1481871162833107, 0.5952117958375971, 0.2566010878790925, 0.0185978710613814, 0.1382062952112499, 0.8431958337273687, 0.0185978710613814, 0.8431958337273687, 0.1382062952112503, 0.1395344629893075, 0.1395344629893073, 0.7209310740213853, 0.2215360105096922, 0.2215360105096921, 0.5569279789806160, 0.0329710199269464, 0.4258102085854810, 0.5412187714875728, 0.0329710199269464, 0.5412187714875727, 0.4258102085854812, 0.1807503221352998, 0.1807503221352996, 0.6384993557294009, 0.0853795515729539, 0.2797259269522402, 0.6348945214748062, 0.0853795515729539, 0.6348945214748061, 0.2797259269522404, 0.0036330558429340, 0.0224666835802112, 0.9739002605768550, 0.0036330558429340, 0.9739002605768550, 0.0224666835802115, 0.0260200776623640, 0.0838622585244554, 0.8901176638131808, 0.0260200776623640, 0.8901176638131808, 0.0838622585244558, 0.0394569261564381, 0.2848003464144683, 0.6757427274290937, 0.0394569261564381, 0.6757427274290937, 0.2848003464144686, 0.0197707177044082, 0.3565941035365738, 0.6236351787590181, 0.0197707177044082, 0.6236351787590181, 0.3565941035365741, 0.0050286974156274, 0.0974242311151380, 0.8975470714692347, 0.0050286974156274, 0.8975470714692347, 0.0974242311151384, 0.0042772072684833, 0.0042772072684829, 0.9914455854630339, 0.0001735550275498, 0.4999132224862252, 0.4999132224862253 }; static double c_save[] = { 0.3971296627653639, 0.3014351686173179, 0.3014351686173180, 0.4916414039828907, 0.0167171920342186, 0.4916414039828905, 0.3577931357985971, 0.2844137284028057, 0.3577931357985971, 0.9428863000930624, 0.0020682202154060, 0.0550454796915315, 0.0550454796915315, 0.0020682202154058, 0.9428863000930622, 0.5457185408985747, 0.0089049941861278, 0.4453764649152973, 0.4453764649152975, 0.0089049941861277, 0.5457185408985745, 0.8455000199126449, 0.0021159775630399, 0.1523840025243151, 0.1523840025243152, 0.0021159775630396, 0.8455000199126448, 0.4751720797813090, 0.2624139601093455, 0.2624139601093453, 0.5992221165426375, 0.0032612734291312, 0.3975166100282311, 0.3975166100282314, 0.0032612734291312, 0.5992221165426372, 0.4028164505857818, 0.1943670988284362, 0.4028164505857818, 0.7987533357833952, 0.0451678948131287, 0.1560787694034759, 0.1560787694034761, 0.0451678948131284, 0.7987533357833951, 0.4730889655006641, 0.0538220689986716, 0.4730889655006639, 0.7940983020176844, 0.0086060217057569, 0.1972956762765585, 0.1972956762765587, 0.0086060217057566, 0.7940983020176844, 0.9359318098485054, 0.0139743532515684, 0.0500938368999260, 0.0500938368999262, 0.0139743532515680, 0.9359318098485053, 0.5136696044857865, 0.1874713324998943, 0.2988590630143190, 0.2988590630143190, 0.1874713324998943, 0.5136696044857864, 0.8742639019118683, 0.0628680490440660, 0.0628680490440655, 0.4415974337549304, 0.1168051324901392, 0.4415974337549302, 0.9607456800330582, 0.0196271599834711, 0.0196271599834704, 0.4325143126587201, 0.2327223440759483, 0.3347633432653313, 0.3347633432653313, 0.2327223440759484, 0.4325143126587201, 0.7616252904089401, 0.0290018846146845, 0.2093728249763751, 0.2093728249763754, 0.0290018846146843, 0.7616252904089400, 0.8398677722708631, 0.0535674828677536, 0.1065647448613832, 0.1065647448613834, 0.0535674828677533, 0.8398677722708630, 0.6751411779813131, 0.0034961943491435, 0.3213626276695432, 0.3213626276695434, 0.0034961943491434, 0.6751411779813130, 0.7572369308551706, 0.0011760427968418, 0.2415870263479873, 0.2415870263479875, 0.0011760427968416, 0.7572369308551705, 0.5528929715350869, 0.1139539287441483, 0.3331530997207647, 0.3331530997207648, 0.1139539287441483, 0.5528929715350867, 0.7599448456751415, 0.0849385995115549, 0.1551165548133032, 0.1551165548133034, 0.0849385995115549, 0.7599448456751414, 0.4764206619753217, 0.1525651863472163, 0.3710141516774618, 0.3710141516774619, 0.1525651863472162, 0.4764206619753216, 0.9194262623396129, 0.0402868688301937, 0.0402868688301933, 0.7154976600831513, 0.0136186781090766, 0.2708836618077718, 0.2708836618077721, 0.0136186781090765, 0.7154976600831512, 0.5912668641409812, 0.0562263874435523, 0.3525067484154663, 0.3525067484154665, 0.0562263874435524, 0.5912668641409811, 0.5125263777821213, 0.0817534894396882, 0.4057201327781904, 0.4057201327781905, 0.0817534894396881, 0.5125263777821213, 0.7174078887952543, 0.0636424301897474, 0.2189496810149981, 0.2189496810149983, 0.0636424301897472, 0.7174078887952542, 0.6778965310783613, 0.1153942208360741, 0.2067092480855645, 0.2067092480855646, 0.1153942208360740, 0.6778965310783613, 0.8029476906624151, 0.0985261546687926, 0.0985261546687922, 0.5952117958375970, 0.1481871162833107, 0.2566010878790922, 0.2566010878790922, 0.1481871162833106, 0.5952117958375969, 0.8431958337273686, 0.0185978710613814, 0.1382062952112498, 0.1382062952112500, 0.0185978710613811, 0.8431958337273685, 0.7209310740213852, 0.1395344629893075, 0.1395344629893071, 0.5569279789806159, 0.2215360105096921, 0.2215360105096918, 0.5412187714875726, 0.0329710199269463, 0.4258102085854808, 0.4258102085854810, 0.0329710199269463, 0.5412187714875725, 0.6384993557294008, 0.1807503221352997, 0.1807503221352994, 0.6348945214748060, 0.0853795515729538, 0.2797259269522400, 0.2797259269522402, 0.0853795515729537, 0.6348945214748060, 0.9739002605768549, 0.0036330558429341, 0.0224666835802109, 0.0224666835802113, 0.0036330558429337, 0.9739002605768549, 0.8901176638131807, 0.0260200776623640, 0.0838622585244552, 0.0838622585244555, 0.0260200776623637, 0.8901176638131805, 0.6757427274290936, 0.0394569261564382, 0.2848003464144682, 0.2848003464144683, 0.0394569261564380, 0.6757427274290935, 0.6236351787590180, 0.0197707177044082, 0.3565941035365737, 0.3565941035365738, 0.0197707177044081, 0.6236351787590179, 0.8975470714692345, 0.0050286974156274, 0.0974242311151378, 0.0974242311151380, 0.0050286974156272, 0.8975470714692345, 0.9914455854630339, 0.0042772072684833, 0.0042772072684828, 0.4999132224862252, 0.0001735550275497, 0.4999132224862250 }; static double w_save[] = { 0.0057479340296702, 0.0057479340296702, 0.0057479340296702, 0.0022963680920994, 0.0022963680920994, 0.0022963680920994, 0.0079953508418643, 0.0079953508418643, 0.0079953508418643, 0.0004541993823754, 0.0004541993823754, 0.0004541993823754, 0.0004541993823754, 0.0004541993823754, 0.0004541993823754, 0.0019717493309842, 0.0019717493309842, 0.0019717493309842, 0.0019717493309842, 0.0019717493309842, 0.0019717493309842, 0.0007826663054394, 0.0007826663054394, 0.0007826663054394, 0.0007826663054394, 0.0007826663054394, 0.0007826663054394, 0.0087901858933278, 0.0087901858933278, 0.0087901858933278, 0.0012646931023972, 0.0012646931023972, 0.0012646931023972, 0.0012646931023972, 0.0012646931023972, 0.0012646931023972, 0.0083203666123256, 0.0083203666123256, 0.0083203666123256, 0.0035572562609095, 0.0035572562609095, 0.0035572562609095, 0.0035572562609095, 0.0035572562609095, 0.0035572562609095, 0.0052751882851615, 0.0052751882851615, 0.0052751882851615, 0.0018428326631755, 0.0018428326631755, 0.0018428326631755, 0.0018428326631755, 0.0018428326631755, 0.0018428326631755, 0.0013289799356542, 0.0013289799356542, 0.0013289799356542, 0.0013289799356542, 0.0013289799356542, 0.0013289799356542, 0.0090234128551062, 0.0090234128551062, 0.0090234128551062, 0.0090234128551062, 0.0090234128551062, 0.0090234128551062, 0.0029682066390516, 0.0029682066390516, 0.0029682066390516, 0.0076051825305364, 0.0076051825305364, 0.0076051825305364, 0.0010131210327381, 0.0010131210327381, 0.0010131210327381, 0.0086055044940838, 0.0086055044940838, 0.0086055044940838, 0.0086055044940838, 0.0086055044940838, 0.0086055044940838, 0.0036104679969938, 0.0036104679969938, 0.0036104679969938, 0.0036104679969938, 0.0036104679969938, 0.0036104679969938, 0.0035235607672108, 0.0035235607672108, 0.0035235607672108, 0.0035235607672108, 0.0035235607672108, 0.0035235607672108, 0.0013780765220064, 0.0013780765220064, 0.0013780765220064, 0.0013780765220064, 0.0013780765220064, 0.0013780765220064, 0.0006950295859519, 0.0006950295859519, 0.0006950295859519, 0.0006950295859519, 0.0006950295859519, 0.0006950295859519, 0.0081297205980780, 0.0081297205980780, 0.0081297205980780, 0.0081297205980780, 0.0081297205980780, 0.0081297205980780, 0.0054896563598667, 0.0054896563598667, 0.0054896563598667, 0.0054896563598667, 0.0054896563598667, 0.0054896563598667, 0.0082359873228582, 0.0082359873228582, 0.0082359873228582, 0.0082359873228582, 0.0082359873228582, 0.0082359873228582, 0.0020648356265983, 0.0020648356265983, 0.0020648356265983, 0.0027797735193626, 0.0027797735193626, 0.0027797735193626, 0.0027797735193626, 0.0027797735193626, 0.0027797735193626, 0.0063317818814834, 0.0063317818814834, 0.0063317818814834, 0.0063317818814834, 0.0063317818814834, 0.0063317818814834, 0.0069457107199416, 0.0069457107199416, 0.0069457107199416, 0.0069457107199416, 0.0069457107199416, 0.0069457107199416, 0.0055659411156861, 0.0055659411156861, 0.0055659411156861, 0.0055659411156861, 0.0055659411156861, 0.0055659411156861, 0.0073376101567627, 0.0073376101567627, 0.0073376101567627, 0.0073376101567627, 0.0073376101567627, 0.0073376101567627, 0.0050036396155573, 0.0050036396155573, 0.0050036396155573, 0.0087114266235609, 0.0087114266235609, 0.0087114266235609, 0.0087114266235609, 0.0087114266235609, 0.0087114266235609, 0.0027367494327220, 0.0027367494327220, 0.0027367494327220, 0.0027367494327220, 0.0027367494327220, 0.0027367494327220, 0.0067190798124174, 0.0067190798124174, 0.0067190798124174, 0.0091619089409373, 0.0091619089409373, 0.0091619089409373, 0.0047016575809322, 0.0047016575809322, 0.0047016575809322, 0.0047016575809322, 0.0047016575809322, 0.0047016575809322, 0.0083719066370130, 0.0083719066370130, 0.0083719066370130, 0.0071750089599327, 0.0071750089599327, 0.0071750089599327, 0.0071750089599327, 0.0071750089599327, 0.0071750089599327, 0.0004732469738005, 0.0004732469738005, 0.0004732469738005, 0.0004732469738005, 0.0004732469738005, 0.0004732469738005, 0.0025346621113678, 0.0025346621113678, 0.0025346621113678, 0.0025346621113678, 0.0025346621113678, 0.0025346621113678, 0.0050701573000114, 0.0050701573000114, 0.0050701573000114, 0.0050701573000114, 0.0050701573000114, 0.0050701573000114, 0.0040540720868840, 0.0040540720868840, 0.0040540720868840, 0.0040540720868840, 0.0040540720868840, 0.0040540720868840, 0.0012544783872410, 0.0012544783872410, 0.0012544783872410, 0.0012544783872410, 0.0012544783872410, 0.0012544783872410, 0.0002403337374048, 0.0002403337374048, 0.0002403337374048, 0.0006275843410706, 0.0006275843410706, 0.0006275843410706 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule36 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule36() returns the rule of precision 36. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.2550023360754195, 0.7127053999508112, 0.0322922639737694, 0.7127053999508112, 0.2550023360754196, 0.0322922639737692, 0.2711215136033400, 0.6347382765922519, 0.0941402098044082, 0.6347382765922519, 0.2711215136033400, 0.0941402098044080, 0.0926886044848755, 0.8423177234108842, 0.0649936721042403, 0.8423177234108843, 0.0926886044848757, 0.0649936721042400, 0.3294543765845505, 0.5968319589620307, 0.0737136644534188, 0.5968319589620307, 0.3294543765845505, 0.0737136644534187, 0.2883788411304420, 0.6615561707226660, 0.0500649881468920, 0.6615561707226659, 0.2883788411304421, 0.0500649881468918, 0.3921724164051739, 0.5419312451199315, 0.0658963384748946, 0.5419312451199314, 0.3921724164051738, 0.0658963384748946, 0.0076222500155876, 0.9911436314566491, 0.0012341185277635, 0.9911436314566491, 0.0076222500155876, 0.0012341185277630, 0.4123573403136303, 0.4123573403136303, 0.1752853193727393, 0.1782079366279757, 0.7160962360444145, 0.1056958273276099, 0.7160962360444145, 0.1782079366279757, 0.1056958273276097, 0.3102489314599136, 0.5658793981445355, 0.1238716703955509, 0.5658793981445355, 0.3102489314599136, 0.1238716703955508, 0.4390483832458435, 0.4390483832458435, 0.1219032335083129, 0.0829157021331252, 0.9142769002483087, 0.0028073976185662, 0.9142769002483088, 0.0829157021331253, 0.0028073976185659, 0.3796386793469431, 0.5096715423270356, 0.1106897783260212, 0.5096715423270356, 0.3796386793469431, 0.1106897783260211, 0.2350523254582137, 0.5298953490835725, 0.2350523254582138, 0.1980682921145434, 0.7991752852717510, 0.0027564226137057, 0.7991752852717511, 0.1980682921145434, 0.0027564226137055, 0.1479479453220730, 0.7800003555819109, 0.0720516990960159, 0.7800003555819111, 0.1479479453220731, 0.0720516990960157, 0.2292027665534673, 0.7563686218758484, 0.0144286115706843, 0.7563686218758484, 0.2292027665534674, 0.0144286115706841, 0.3574738503443845, 0.6397835829582036, 0.0027425666974119, 0.6397835829582036, 0.3574738503443844, 0.0027425666974117, 0.1252496722294377, 0.8357259979283462, 0.0390243298422160, 0.8357259979283463, 0.1252496722294378, 0.0390243298422157, 0.0209805646004062, 0.9715447719336604, 0.0074746634659335, 0.9715447719336604, 0.0209805646004063, 0.0074746634659331, 0.2691316117440097, 0.5552966096544709, 0.1755717786015192, 0.5552966096544710, 0.2691316117440098, 0.1755717786015191, 0.1508217347798915, 0.6983565304402166, 0.1508217347798919, 0.3462198724218936, 0.4825533687273535, 0.1712267588507529, 0.4825533687273536, 0.3462198724218935, 0.1712267588507528, 0.4423877426580685, 0.5233061138878379, 0.0343061434540937, 0.5233061138878379, 0.4423877426580686, 0.0343061434540936, 0.2746338837226588, 0.7223364807654942, 0.0030296355118472, 0.7223364807654941, 0.2746338837226588, 0.0030296355118469, 0.2237012846551441, 0.7038117568892118, 0.0724869584556441, 0.7038117568892117, 0.2237012846551442, 0.0724869584556440, 0.2264729475116298, 0.6397100291477062, 0.1338170233406640, 0.6397100291477064, 0.2264729475116297, 0.1338170233406638, 0.1633619668293704, 0.8189638129323793, 0.0176742202382503, 0.8189638129323793, 0.1633619668293705, 0.0176742202382500, 0.1907912728543789, 0.7670005101060391, 0.0422082170395822, 0.7670005101060390, 0.1907912728543789, 0.0422082170395819, 0.3581658706314307, 0.6074178089715797, 0.0344163203969896, 0.6074178089715797, 0.3581658706314307, 0.0344163203969895, 0.0993849892050522, 0.8831620205339272, 0.0174529902610207, 0.8831620205339273, 0.0993849892050523, 0.0174529902610203, 0.4502328978916524, 0.5485392672636246, 0.0012278348447230, 0.5485392672636246, 0.4502328978916525, 0.0012278348447230, 0.4642737776346700, 0.4642737776346701, 0.0714524447306599, 0.3048602929866793, 0.4588765169470121, 0.2362631900663086, 0.4588765169470121, 0.3048602929866793, 0.2362631900663085, 0.3135836062706951, 0.6708934652005731, 0.0155229285287318, 0.6708934652005731, 0.3135836062706952, 0.0155229285287316, 0.1348062882666829, 0.8613456659624720, 0.0038480457708451, 0.8613456659624721, 0.1348062882666830, 0.0038480457708449, 0.1911613618773089, 0.6176772762453819, 0.1911613618773091, 0.0658281924328199, 0.8960993382441670, 0.0380724693230132, 0.8960993382441671, 0.0658281924328200, 0.0380724693230129, 0.0293500490934269, 0.9412999018131458, 0.0293500490934273, 0.3081452189910933, 0.3837095620178134, 0.3081452189910933, 0.0531928439194577, 0.9346369019266020, 0.0121702541539404, 0.9346369019266021, 0.0531928439194579, 0.0121702541539399, 0.1111782647883809, 0.7776434704232379, 0.1111782647883812, 0.0406479626359586, 0.9584934783193574, 0.0008585590446841, 0.9584934783193575, 0.0406479626359587, 0.0008585590446836, 0.4064475672122849, 0.5812165949773879, 0.0123358378103273, 0.5812165949773879, 0.4064475672122848, 0.0123358378103271, 0.3810023496034419, 0.3810023496034418, 0.2379953007931161, 0.4944809967477004, 0.4944809967477005, 0.0110380065045990 }; static double b_save[] = { 0.0322922639737694, 0.2550023360754195, 0.7127053999508113, 0.0322922639737694, 0.7127053999508113, 0.2550023360754198, 0.0941402098044082, 0.2711215136033400, 0.6347382765922520, 0.0941402098044082, 0.6347382765922520, 0.2711215136033402, 0.0649936721042402, 0.0926886044848756, 0.8423177234108843, 0.0649936721042402, 0.8423177234108843, 0.0926886044848759, 0.0737136644534188, 0.3294543765845505, 0.5968319589620309, 0.0737136644534188, 0.5968319589620308, 0.3294543765845507, 0.0500649881468919, 0.2883788411304421, 0.6615561707226660, 0.0500649881468919, 0.6615561707226660, 0.2883788411304423, 0.0658963384748947, 0.3921724164051739, 0.5419312451199317, 0.0658963384748947, 0.5419312451199316, 0.3921724164051740, 0.0012341185277633, 0.0076222500155876, 0.9911436314566491, 0.0012341185277633, 0.9911436314566494, 0.0076222500155880, 0.1752853193727394, 0.4123573403136304, 0.4123573403136305, 0.1056958273276099, 0.1782079366279757, 0.7160962360444146, 0.1056958273276099, 0.7160962360444146, 0.1782079366279760, 0.1238716703955509, 0.3102489314599137, 0.5658793981445357, 0.1238716703955509, 0.5658793981445357, 0.3102489314599138, 0.1219032335083130, 0.4390483832458436, 0.4390483832458437, 0.0028073976185661, 0.0829157021331252, 0.9142769002483089, 0.0028073976185661, 0.9142769002483089, 0.0829157021331255, 0.1106897783260212, 0.3796386793469432, 0.5096715423270358, 0.1106897783260212, 0.5096715423270358, 0.3796386793469433, 0.2350523254582139, 0.2350523254582138, 0.5298953490835726, 0.0027564226137057, 0.1980682921145434, 0.7991752852717512, 0.0027564226137057, 0.7991752852717511, 0.1980682921145436, 0.0720516990960159, 0.1479479453220730, 0.7800003555819113, 0.0720516990960159, 0.7800003555819113, 0.1479479453220733, 0.0144286115706843, 0.2292027665534674, 0.7563686218758485, 0.0144286115706843, 0.7563686218758484, 0.2292027665534676, 0.0027425666974119, 0.3574738503443846, 0.6397835829582038, 0.0027425666974119, 0.6397835829582038, 0.3574738503443848, 0.0390243298422159, 0.1252496722294378, 0.8357259979283465, 0.0390243298422159, 0.8357259979283465, 0.1252496722294380, 0.0074746634659333, 0.0209805646004062, 0.9715447719336605, 0.0074746634659333, 0.9715447719336605, 0.0209805646004066, 0.1755717786015193, 0.2691316117440098, 0.5552966096544713, 0.1755717786015193, 0.5552966096544711, 0.2691316117440100, 0.1508217347798918, 0.1508217347798916, 0.6983565304402167, 0.1712267588507529, 0.3462198724218936, 0.4825533687273537, 0.1712267588507529, 0.4825533687273537, 0.3462198724218937, 0.0343061434540937, 0.4423877426580686, 0.5233061138878380, 0.0343061434540937, 0.5233061138878379, 0.4423877426580687, 0.0030296355118471, 0.2746338837226588, 0.7223364807654942, 0.0030296355118471, 0.7223364807654942, 0.2746338837226592, 0.0724869584556441, 0.2237012846551441, 0.7038117568892120, 0.0724869584556441, 0.7038117568892119, 0.2237012846551444, 0.1338170233406639, 0.2264729475116298, 0.6397100291477065, 0.1338170233406639, 0.6397100291477065, 0.2264729475116300, 0.0176742202382503, 0.1633619668293704, 0.8189638129323794, 0.0176742202382503, 0.8189638129323794, 0.1633619668293707, 0.0422082170395821, 0.1907912728543789, 0.7670005101060392, 0.0422082170395821, 0.7670005101060391, 0.1907912728543791, 0.0344163203969896, 0.3581658706314307, 0.6074178089715798, 0.0344163203969896, 0.6074178089715798, 0.3581658706314309, 0.0174529902610205, 0.0993849892050522, 0.8831620205339273, 0.0174529902610205, 0.8831620205339273, 0.0993849892050526, 0.0012278348447231, 0.4502328978916525, 0.5485392672636248, 0.0012278348447231, 0.5485392672636246, 0.4502328978916527, 0.0714524447306600, 0.4642737776346700, 0.4642737776346703, 0.2362631900663087, 0.3048602929866794, 0.4588765169470122, 0.2362631900663087, 0.4588765169470121, 0.3048602929866794, 0.0155229285287317, 0.3135836062706952, 0.6708934652005732, 0.0155229285287317, 0.6708934652005732, 0.3135836062706954, 0.0038480457708451, 0.1348062882666829, 0.8613456659624722, 0.0038480457708451, 0.8613456659624722, 0.1348062882666833, 0.1911613618773092, 0.1911613618773090, 0.6176772762453820, 0.0380724693230131, 0.0658281924328199, 0.8960993382441672, 0.0380724693230131, 0.8960993382441672, 0.0658281924328202, 0.0293500490934272, 0.0293500490934269, 0.9412999018131460, 0.3081452189910934, 0.3081452189910934, 0.3837095620178135, 0.0121702541539402, 0.0531928439194577, 0.9346369019266021, 0.0121702541539402, 0.9346369019266021, 0.0531928439194581, 0.1111782647883812, 0.1111782647883809, 0.7776434704232381, 0.0008585590446839, 0.0406479626359585, 0.9584934783193576, 0.0008585590446839, 0.9584934783193576, 0.0406479626359589, 0.0123358378103272, 0.4064475672122849, 0.5812165949773881, 0.0123358378103272, 0.5812165949773881, 0.4064475672122851, 0.2379953007931163, 0.3810023496034420, 0.3810023496034420, 0.0110380065045991, 0.4944809967477005, 0.4944809967477007 }; static double c_save[] = { 0.7127053999508112, 0.0322922639737693, 0.2550023360754192, 0.2550023360754194, 0.0322922639737692, 0.7127053999508109, 0.6347382765922518, 0.0941402098044081, 0.2711215136033398, 0.2711215136033399, 0.0941402098044080, 0.6347382765922518, 0.8423177234108842, 0.0649936721042403, 0.0926886044848754, 0.0926886044848755, 0.0649936721042400, 0.8423177234108841, 0.5968319589620307, 0.0737136644534188, 0.3294543765845502, 0.3294543765845506, 0.0737136644534188, 0.5968319589620306, 0.6615561707226660, 0.0500649881468919, 0.2883788411304420, 0.2883788411304422, 0.0500649881468919, 0.6615561707226659, 0.5419312451199314, 0.0658963384748946, 0.3921724164051736, 0.3921724164051739, 0.0658963384748946, 0.5419312451199314, 0.9911436314566492, 0.0012341185277633, 0.0076222500155874, 0.0076222500155877, 0.0012341185277630, 0.9911436314566491, 0.4123573403136304, 0.1752853193727394, 0.4123573403136302, 0.7160962360444145, 0.1056958273276098, 0.1782079366279755, 0.1782079366279756, 0.1056958273276097, 0.7160962360444144, 0.5658793981445355, 0.1238716703955509, 0.3102489314599134, 0.3102489314599136, 0.1238716703955508, 0.5658793981445354, 0.4390483832458435, 0.1219032335083129, 0.4390483832458434, 0.9142769002483087, 0.0028073976185661, 0.0829157021331249, 0.0829157021331251, 0.0028073976185659, 0.9142769002483084, 0.5096715423270357, 0.1106897783260212, 0.3796386793469430, 0.3796386793469432, 0.1106897783260211, 0.5096715423270355, 0.5298953490835724, 0.2350523254582137, 0.2350523254582136, 0.7991752852717510, 0.0027564226137057, 0.1980682921145430, 0.1980682921145433, 0.0027564226137056, 0.7991752852717509, 0.7800003555819111, 0.0720516990960160, 0.1479479453220728, 0.1479479453220731, 0.0720516990960156, 0.7800003555819111, 0.7563686218758484, 0.0144286115706842, 0.2292027665534672, 0.2292027665534673, 0.0144286115706841, 0.7563686218758482, 0.6397835829582036, 0.0027425666974119, 0.3574738503443843, 0.3574738503443846, 0.0027425666974118, 0.6397835829582035, 0.8357259979283463, 0.0390243298422160, 0.1252496722294375, 0.1252496722294377, 0.0390243298422157, 0.8357259979283462, 0.9715447719336605, 0.0074746634659334, 0.0209805646004060, 0.0209805646004063, 0.0074746634659332, 0.9715447719336603, 0.5552966096544710, 0.1755717786015193, 0.2691316117440096, 0.2691316117440097, 0.1755717786015191, 0.5552966096544709, 0.6983565304402167, 0.1508217347798918, 0.1508217347798914, 0.4825533687273535, 0.1712267588507528, 0.3462198724218934, 0.3462198724218936, 0.1712267588507529, 0.4825533687273535, 0.5233061138878379, 0.0343061434540936, 0.4423877426580684, 0.4423877426580685, 0.0343061434540936, 0.5233061138878377, 0.7223364807654941, 0.0030296355118470, 0.2746338837226586, 0.2746338837226588, 0.0030296355118470, 0.7223364807654939, 0.7038117568892118, 0.0724869584556440, 0.2237012846551438, 0.2237012846551442, 0.0724869584556439, 0.7038117568892116, 0.6397100291477062, 0.1338170233406640, 0.2264729475116296, 0.2264729475116297, 0.1338170233406638, 0.6397100291477062, 0.8189638129323793, 0.0176742202382503, 0.1633619668293703, 0.1633619668293704, 0.0176742202382502, 0.8189638129323793, 0.7670005101060391, 0.0422082170395821, 0.1907912728543787, 0.1907912728543789, 0.0422082170395820, 0.7670005101060390, 0.6074178089715797, 0.0344163203969896, 0.3581658706314306, 0.3581658706314307, 0.0344163203969895, 0.6074178089715796, 0.8831620205339272, 0.0174529902610206, 0.0993849892050520, 0.0993849892050521, 0.0174529902610204, 0.8831620205339271, 0.5485392672636246, 0.0012278348447229, 0.4502328978916522, 0.4502328978916524, 0.0012278348447229, 0.5485392672636243, 0.4642737776346700, 0.0714524447306598, 0.4642737776346698, 0.4588765169470120, 0.2362631900663085, 0.3048602929866792, 0.3048602929866792, 0.2362631900663086, 0.4588765169470121, 0.6708934652005731, 0.0155229285287317, 0.3135836062706950, 0.3135836062706951, 0.0155229285287316, 0.6708934652005729, 0.8613456659624720, 0.0038480457708451, 0.1348062882666826, 0.1348062882666829, 0.0038480457708449, 0.8613456659624719, 0.6176772762453819, 0.1911613618773091, 0.1911613618773088, 0.8960993382441670, 0.0380724693230132, 0.0658281924328196, 0.0658281924328198, 0.0380724693230129, 0.8960993382441669, 0.9412999018131459, 0.0293500490934273, 0.0293500490934266, 0.3837095620178134, 0.3081452189910933, 0.3081452189910932, 0.9346369019266020, 0.0121702541539403, 0.0531928439194576, 0.0531928439194577, 0.0121702541539400, 0.9346369019266020, 0.7776434704232380, 0.1111782647883812, 0.1111782647883807, 0.9584934783193575, 0.0008585590446841, 0.0406479626359583, 0.0406479626359586, 0.0008585590446838, 0.9584934783193574, 0.5812165949773879, 0.0123358378103273, 0.4064475672122846, 0.4064475672122849, 0.0123358378103272, 0.5812165949773878, 0.3810023496034419, 0.2379953007931162, 0.3810023496034418, 0.4944809967477005, 0.0110380065045990, 0.4944809967477002 }; static double w_save[] = { 0.0030616831670682, 0.0030616831670682, 0.0030616831670682, 0.0030616831670682, 0.0030616831670682, 0.0030616831670682, 0.0049232719752900, 0.0049232719752900, 0.0049232719752900, 0.0049232719752900, 0.0049232719752900, 0.0049232719752900, 0.0033237208433952, 0.0033237208433952, 0.0033237208433952, 0.0033237208433952, 0.0033237208433952, 0.0033237208433952, 0.0047427364930338, 0.0047427364930338, 0.0047427364930338, 0.0047427364930338, 0.0047427364930338, 0.0047427364930338, 0.0041138012926497, 0.0041138012926497, 0.0041138012926497, 0.0041138012926497, 0.0041138012926497, 0.0041138012926497, 0.0052353425228938, 0.0052353425228938, 0.0052353425228938, 0.0052353425228938, 0.0052353425228938, 0.0052353425228938, 0.0001303399284527, 0.0001303399284527, 0.0001303399284527, 0.0001303399284527, 0.0001303399284527, 0.0001303399284527, 0.0076704945179086, 0.0076704945179086, 0.0076704945179086, 0.0052277042839384, 0.0052277042839384, 0.0052277042839384, 0.0052277042839384, 0.0052277042839384, 0.0052277042839384, 0.0066311375415485, 0.0066311375415485, 0.0066311375415485, 0.0066311375415485, 0.0066311375415485, 0.0066311375415485, 0.0068762957093961, 0.0068762957093961, 0.0068762957093961, 0.0006952346397171, 0.0006952346397171, 0.0006952346397171, 0.0006952346397171, 0.0006952346397171, 0.0006952346397171, 0.0069183724873925, 0.0069183724873925, 0.0069183724873925, 0.0069183724873925, 0.0069183724873925, 0.0069183724873925, 0.0080679977166382, 0.0080679977166382, 0.0080679977166382, 0.0010177068493549, 0.0010177068493549, 0.0010177068493549, 0.0010177068493549, 0.0010177068493549, 0.0010177068493549, 0.0045309912970645, 0.0045309912970645, 0.0045309912970645, 0.0045309912970645, 0.0045309912970645, 0.0045309912970645, 0.0023792804956386, 0.0023792804956386, 0.0023792804956386, 0.0023792804956386, 0.0023792804956386, 0.0023792804956386, 0.0012168791097054, 0.0012168791097054, 0.0012168791097054, 0.0012168791097054, 0.0012168791097054, 0.0012168791097054, 0.0031130272403783, 0.0031130272403783, 0.0031130272403783, 0.0031130272403783, 0.0031130272403783, 0.0031130272403783, 0.0006481853328131, 0.0006481853328131, 0.0006481853328131, 0.0006481853328131, 0.0006481853328131, 0.0006481853328131, 0.0083451647460546, 0.0083451647460546, 0.0083451647460546, 0.0083451647460546, 0.0083451647460546, 0.0083451647460546, 0.0061710606814515, 0.0061710606814515, 0.0061710606814515, 0.0089038028492518, 0.0089038028492518, 0.0089038028492518, 0.0089038028492518, 0.0089038028492518, 0.0089038028492518, 0.0047638139693883, 0.0047638139693883, 0.0047638139693883, 0.0047638139693883, 0.0047638139693883, 0.0047638139693883, 0.0012331434914374, 0.0012331434914374, 0.0012331434914374, 0.0012331434914374, 0.0012331434914374, 0.0012331434914374, 0.0052810362353661, 0.0052810362353661, 0.0052810362353661, 0.0052810362353661, 0.0052810362353661, 0.0052810362353661, 0.0072039581630510, 0.0072039581630510, 0.0072039581630510, 0.0072039581630510, 0.0072039581630510, 0.0072039581630510, 0.0025500464663513, 0.0025500464663513, 0.0025500464663513, 0.0025500464663513, 0.0025500464663513, 0.0025500464663513, 0.0040931211574027, 0.0040931211574027, 0.0040931211574027, 0.0040931211574027, 0.0040931211574027, 0.0040931211574027, 0.0044693917436126, 0.0044693917436126, 0.0044693917436126, 0.0044693917436126, 0.0044693917436126, 0.0044693917436126, 0.0021012224230352, 0.0021012224230352, 0.0021012224230352, 0.0021012224230352, 0.0021012224230352, 0.0021012224230352, 0.0008220891073142, 0.0008220891073142, 0.0008220891073142, 0.0008220891073142, 0.0008220891073142, 0.0008220891073142, 0.0066612336212475, 0.0066612336212475, 0.0066612336212475, 0.0102133456155291, 0.0102133456155291, 0.0102133456155291, 0.0102133456155291, 0.0102133456155291, 0.0102133456155291, 0.0030402213548301, 0.0030402213548301, 0.0030402213548301, 0.0030402213548301, 0.0030402213548301, 0.0030402213548301, 0.0011096101536171, 0.0011096101536171, 0.0011096101536171, 0.0011096101536171, 0.0011096101536171, 0.0011096101536171, 0.0080932250756891, 0.0080932250756891, 0.0080932250756891, 0.0026669011660035, 0.0026669011660035, 0.0026669011660035, 0.0026669011660035, 0.0026669011660035, 0.0026669011660035, 0.0015674237111509, 0.0015674237111509, 0.0015674237111509, 0.0110082761617136, 0.0110082761617136, 0.0110082761617136, 0.0013356087640650, 0.0013356087640650, 0.0013356087640650, 0.0013356087640650, 0.0013356087640650, 0.0013356087640650, 0.0054235489241326, 0.0054235489241326, 0.0054235489241326, 0.0002661778238934, 0.0002661778238934, 0.0002661778238934, 0.0002661778238934, 0.0002661778238934, 0.0002661778238934, 0.0028876869913215, 0.0028876869913215, 0.0028876869913215, 0.0028876869913215, 0.0028876869913215, 0.0028876869913215, 0.0105063460068171, 0.0105063460068171, 0.0105063460068171, 0.0028959157634686, 0.0028959157634686, 0.0028959157634686 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule37 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule37() returns the rule of precision 37. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1023039321577603, 0.7953921356844791, 0.1023039321577607, 0.3160240964966399, 0.6501468128206388, 0.0338290906827213, 0.6501468128206388, 0.3160240964966400, 0.0338290906827212, 0.0350202358754684, 0.9299595282490629, 0.0350202358754688, 0.1053594119602819, 0.8614945984835296, 0.0331459895561886, 0.8614945984835296, 0.1053594119602819, 0.0331459895561881, 0.0749810217841138, 0.9229855021397688, 0.0020334760761175, 0.9229855021397688, 0.0749810217841139, 0.0020334760761171, 0.1194865933803552, 0.8250030034571860, 0.0555104031624590, 0.8250030034571859, 0.1194865933803553, 0.0555104031624586, 0.3192351650459891, 0.4427039878369861, 0.2380608471170247, 0.4427039878369861, 0.3192351650459891, 0.2380608471170247, 0.3917882577236701, 0.5329411933388201, 0.0752705489375098, 0.5329411933388201, 0.3917882577236701, 0.0752705489375098, 0.2592434904565495, 0.4815130190869007, 0.2592434904565497, 0.3175434072141983, 0.6288357611566886, 0.0536208316291132, 0.6288357611566886, 0.3175434072141983, 0.0536208316291130, 0.3267645245927318, 0.5819407083122254, 0.0912947670950428, 0.5819407083122254, 0.3267645245927318, 0.0912947670950427, 0.3187496668271801, 0.5461345841025351, 0.1351157490702847, 0.5461345841025351, 0.3187496668271802, 0.1351157490702846, 0.0674578790813868, 0.8917719971619344, 0.0407701237566788, 0.8917719971619346, 0.0674578790813870, 0.0407701237566784, 0.0183794409210812, 0.9786302812023548, 0.0029902778765640, 0.9786302812023550, 0.0183794409210812, 0.0029902778765637, 0.0476569358622159, 0.9350921036839764, 0.0172509604538077, 0.9350921036839764, 0.0476569358622161, 0.0172509604538073, 0.3357227870380101, 0.4831608037664580, 0.1811164091955319, 0.4831608037664580, 0.3357227870380101, 0.1811164091955318, 0.1394412358722927, 0.7211175282554143, 0.1394412358722930, 0.4611684588908100, 0.4611684588908100, 0.0776630822183799, 0.1356716079161176, 0.7741981202355922, 0.0901302718482901, 0.7741981202355922, 0.1356716079161178, 0.0901302718482899, 0.0417693614359698, 0.9542135414767989, 0.0040170970872315, 0.9542135414767989, 0.0417693614359699, 0.0040170970872310, 0.3791537179550378, 0.3791537179550378, 0.2416925640899243, 0.1912637374380762, 0.7277709423326696, 0.0809653202292542, 0.7277709423326697, 0.1912637374380762, 0.0809653202292539, 0.4489203299566428, 0.5341982115332263, 0.0168814585101307, 0.5341982115332264, 0.4489203299566429, 0.0168814585101307, 0.3970833791349885, 0.5614399423313745, 0.0414766785336368, 0.5614399423313746, 0.3970833791349885, 0.0414766785336368, 0.0862263440628872, 0.9000390697749006, 0.0137345861622123, 0.9000390697749007, 0.0862263440628872, 0.0137345861622120, 0.0173411753639024, 0.9653176492721949, 0.0173411753639029, 0.2814879599422820, 0.7005934357274263, 0.0179186043302919, 0.7005934357274262, 0.2814879599422819, 0.0179186043302916, 0.1923768347442593, 0.6791517751989478, 0.1284713900567929, 0.6791517751989478, 0.1923768347442593, 0.1284713900567927, 0.2517942475174331, 0.6108845927509712, 0.1373211597315956, 0.6108845927509713, 0.2517942475174332, 0.1373211597315955, 0.0779889301806426, 0.8440221396387144, 0.0779889301806430, 0.3650347949363280, 0.6175233785692882, 0.0174418264943838, 0.6175233785692882, 0.3650347949363280, 0.0174418264943837, 0.4792449355569203, 0.4792449355569204, 0.0415101288861593, 0.4120614054796895, 0.4120614054796895, 0.1758771890406210, 0.2571566355502535, 0.6566451941716462, 0.0861981702781003, 0.6566451941716462, 0.2571566355502535, 0.0861981702781001, 0.4984105744139570, 0.4984105744139570, 0.0031788511720860, 0.3091259486853505, 0.3817481026292989, 0.3091259486853505, 0.1241816119341110, 0.8724071202650543, 0.0034112678008348, 0.8724071202650543, 0.1241816119341111, 0.0034112678008344, 0.1716507278093692, 0.7837937554788413, 0.0445555167117896, 0.7837937554788413, 0.1716507278093692, 0.0445555167117893, 0.3977231091982856, 0.4801793419171518, 0.1220975488845627, 0.4801793419171518, 0.3977231091982856, 0.1220975488845626, 0.0036715668219831, 0.9926568663560335, 0.0036715668219836, 0.2578966456698565, 0.5463929830937153, 0.1957103712364281, 0.5463929830937154, 0.2578966456698565, 0.1957103712364280, 0.1441500744811936, 0.8375385335389723, 0.0183113919798341, 0.8375385335389725, 0.1441500744811937, 0.0183113919798338, 0.4122595610017910, 0.5844781809630051, 0.0032622580352039, 0.5844781809630052, 0.4122595610017911, 0.0032622580352037, 0.2524284647914363, 0.7440960937012480, 0.0034754415073158, 0.7440960937012480, 0.2524284647914364, 0.0034754415073155, 0.3293669274857745, 0.6670942824316437, 0.0035387900825819, 0.6670942824316437, 0.3293669274857746, 0.0035387900825817, 0.2095814817005154, 0.7715735792437323, 0.0188449390557522, 0.7715735792437323, 0.2095814817005155, 0.0188449390557521, 0.1836401694462322, 0.8127217284450714, 0.0036381021086965, 0.8127217284450714, 0.1836401694462323, 0.0036381021086962, 0.2416962324693375, 0.7125504805693451, 0.0457532869613175, 0.7125504805693450, 0.2416962324693376, 0.0457532869613173, 0.1893642612001962, 0.6212714775996074, 0.1893642612001963 }; static double b_save[] = { 0.1023039321577605, 0.1023039321577603, 0.7953921356844793, 0.0338290906827213, 0.3160240964966399, 0.6501468128206390, 0.0338290906827213, 0.6501468128206389, 0.3160240964966402, 0.0350202358754687, 0.0350202358754684, 0.9299595282490630, 0.0331459895561884, 0.1053594119602819, 0.8614945984835296, 0.0331459895561884, 0.8614945984835299, 0.1053594119602822, 0.0020334760761173, 0.0749810217841138, 0.9229855021397689, 0.0020334760761173, 0.9229855021397689, 0.0749810217841142, 0.0555104031624589, 0.1194865933803552, 0.8250030034571860, 0.0555104031624589, 0.8250030034571860, 0.1194865933803555, 0.2380608471170249, 0.3192351650459893, 0.4427039878369862, 0.2380608471170249, 0.4427039878369862, 0.3192351650459893, 0.0752705489375098, 0.3917882577236702, 0.5329411933388202, 0.0752705489375098, 0.5329411933388202, 0.3917882577236704, 0.2592434904565497, 0.2592434904565497, 0.4815130190869009, 0.0536208316291131, 0.3175434072141983, 0.6288357611566887, 0.0536208316291131, 0.6288357611566887, 0.3175434072141985, 0.0912947670950428, 0.3267645245927318, 0.5819407083122257, 0.0912947670950428, 0.5819407083122256, 0.3267645245927320, 0.1351157490702847, 0.3187496668271802, 0.5461345841025353, 0.1351157490702847, 0.5461345841025353, 0.3187496668271803, 0.0407701237566787, 0.0674578790813868, 0.8917719971619346, 0.0407701237566787, 0.8917719971619346, 0.0674578790813871, 0.0029902778765639, 0.0183794409210811, 0.9786302812023551, 0.0029902778765639, 0.9786302812023551, 0.0183794409210815, 0.0172509604538075, 0.0476569358622160, 0.9350921036839765, 0.0172509604538075, 0.9350921036839765, 0.0476569358622163, 0.1811164091955320, 0.3357227870380101, 0.4831608037664581, 0.1811164091955320, 0.4831608037664581, 0.3357227870380102, 0.1394412358722930, 0.1394412358722927, 0.7211175282554145, 0.0776630822183800, 0.4611684588908101, 0.4611684588908102, 0.0901302718482901, 0.1356716079161177, 0.7741981202355923, 0.0901302718482901, 0.7741981202355923, 0.1356716079161179, 0.0040170970872313, 0.0417693614359697, 0.9542135414767990, 0.0040170970872313, 0.9542135414767990, 0.0417693614359701, 0.2416925640899244, 0.3791537179550379, 0.3791537179550379, 0.0809653202292541, 0.1912637374380763, 0.7277709423326698, 0.0809653202292541, 0.7277709423326699, 0.1912637374380765, 0.0168814585101308, 0.4489203299566429, 0.5341982115332266, 0.0168814585101308, 0.5341982115332264, 0.4489203299566431, 0.0414766785336369, 0.3970833791349886, 0.5614399423313748, 0.0414766785336369, 0.5614399423313746, 0.3970833791349888, 0.0137345861622122, 0.0862263440628872, 0.9000390697749008, 0.0137345861622122, 0.9000390697749008, 0.0862263440628875, 0.0173411753639027, 0.0173411753639024, 0.9653176492721949, 0.0179186043302918, 0.2814879599422820, 0.7005934357274264, 0.0179186043302918, 0.7005934357274264, 0.2814879599422823, 0.1284713900567929, 0.1923768347442593, 0.6791517751989480, 0.1284713900567929, 0.6791517751989480, 0.1923768347442595, 0.1373211597315956, 0.2517942475174332, 0.6108845927509714, 0.1373211597315956, 0.6108845927509713, 0.2517942475174334, 0.0779889301806429, 0.0779889301806426, 0.8440221396387146, 0.0174418264943838, 0.3650347949363281, 0.6175233785692883, 0.0174418264943838, 0.6175233785692883, 0.3650347949363282, 0.0415101288861593, 0.4792449355569204, 0.4792449355569205, 0.1758771890406211, 0.4120614054796896, 0.4120614054796897, 0.0861981702781003, 0.2571566355502535, 0.6566451941716464, 0.0861981702781003, 0.6566451941716464, 0.2571566355502538, 0.0031788511720861, 0.4984105744139570, 0.4984105744139572, 0.3091259486853506, 0.3091259486853506, 0.3817481026292990, 0.0034112678008347, 0.1241816119341110, 0.8724071202650543, 0.0034112678008347, 0.8724071202650543, 0.1241816119341114, 0.0445555167117895, 0.1716507278093692, 0.7837937554788414, 0.0445555167117895, 0.7837937554788414, 0.1716507278093694, 0.1220975488845627, 0.3977231091982856, 0.4801793419171519, 0.1220975488845627, 0.4801793419171518, 0.3977231091982857, 0.0036715668219834, 0.0036715668219831, 0.9926568663560336, 0.1957103712364281, 0.2578966456698565, 0.5463929830937155, 0.1957103712364281, 0.5463929830937155, 0.2578966456698567, 0.0183113919798340, 0.1441500744811936, 0.8375385335389725, 0.0183113919798340, 0.8375385335389725, 0.1441500744811939, 0.0032622580352038, 0.4122595610017911, 0.5844781809630053, 0.0032622580352038, 0.5844781809630052, 0.4122595610017913, 0.0034754415073157, 0.2524284647914364, 0.7440960937012481, 0.0034754415073157, 0.7440960937012481, 0.2524284647914367, 0.0035387900825818, 0.3293669274857746, 0.6670942824316438, 0.0035387900825818, 0.6670942824316437, 0.3293669274857748, 0.0188449390557523, 0.2095814817005154, 0.7715735792437326, 0.0188449390557523, 0.7715735792437324, 0.2095814817005157, 0.0036381021086963, 0.1836401694462322, 0.8127217284450715, 0.0036381021086963, 0.8127217284450715, 0.1836401694462325, 0.0457532869613174, 0.2416962324693375, 0.7125504805693452, 0.0457532869613174, 0.7125504805693452, 0.2416962324693378, 0.1893642612001964, 0.1893642612001962, 0.6212714775996077 }; static double c_save[] = { 0.7953921356844791, 0.1023039321577606, 0.1023039321577600, 0.6501468128206388, 0.0338290906827213, 0.3160240964966398, 0.3160240964966399, 0.0338290906827211, 0.6501468128206387, 0.9299595282490629, 0.0350202358754687, 0.0350202358754682, 0.8614945984835297, 0.0331459895561885, 0.1053594119602818, 0.1053594119602820, 0.0331459895561882, 0.8614945984835297, 0.9229855021397688, 0.0020334760761174, 0.0749810217841136, 0.0749810217841139, 0.0020334760761173, 0.9229855021397688, 0.8250030034571860, 0.0555104031624588, 0.1194865933803551, 0.1194865933803552, 0.0555104031624587, 0.8250030034571859, 0.4427039878369860, 0.2380608471170247, 0.3192351650459891, 0.3192351650459891, 0.2380608471170248, 0.4427039878369860, 0.5329411933388201, 0.0752705489375098, 0.3917882577236700, 0.3917882577236701, 0.0752705489375097, 0.5329411933388200, 0.4815130190869008, 0.2592434904565497, 0.2592434904565494, 0.6288357611566886, 0.0536208316291131, 0.3175434072141982, 0.3175434072141983, 0.0536208316291130, 0.6288357611566884, 0.5819407083122254, 0.0912947670950428, 0.3267645245927315, 0.3267645245927318, 0.0912947670950427, 0.5819407083122253, 0.5461345841025352, 0.1351157490702847, 0.3187496668271800, 0.3187496668271802, 0.1351157490702845, 0.5461345841025351, 0.8917719971619346, 0.0407701237566787, 0.0674578790813867, 0.0674578790813868, 0.0407701237566785, 0.8917719971619344, 0.9786302812023550, 0.0029902778765640, 0.0183794409210809, 0.0183794409210811, 0.0029902778765637, 0.9786302812023547, 0.9350921036839765, 0.0172509604538076, 0.0476569358622158, 0.0476569358622160, 0.0172509604538074, 0.9350921036839764, 0.4831608037664580, 0.1811164091955319, 0.3357227870380099, 0.3357227870380101, 0.1811164091955318, 0.4831608037664579, 0.7211175282554143, 0.1394412358722930, 0.1394412358722925, 0.4611684588908100, 0.0776630822183799, 0.4611684588908099, 0.7741981202355923, 0.0901302718482901, 0.1356716079161175, 0.1356716079161177, 0.0901302718482899, 0.7741981202355923, 0.9542135414767989, 0.0040170970872313, 0.0417693614359694, 0.0417693614359698, 0.0040170970872310, 0.9542135414767989, 0.3791537179550378, 0.2416925640899242, 0.3791537179550377, 0.7277709423326697, 0.0809653202292542, 0.1912637374380760, 0.1912637374380762, 0.0809653202292538, 0.7277709423326697, 0.5341982115332263, 0.0168814585101308, 0.4489203299566428, 0.4489203299566428, 0.0168814585101307, 0.5341982115332262, 0.5614399423313746, 0.0414766785336369, 0.3970833791349883, 0.3970833791349885, 0.0414766785336368, 0.5614399423313745, 0.9000390697749007, 0.0137345861622123, 0.0862263440628869, 0.0862263440628872, 0.0137345861622120, 0.9000390697749004, 0.9653176492721949, 0.0173411753639027, 0.0173411753639022, 0.7005934357274263, 0.0179186043302917, 0.2814879599422817, 0.2814879599422820, 0.0179186043302917, 0.7005934357274261, 0.6791517751989478, 0.1284713900567929, 0.1923768347442592, 0.1923768347442593, 0.1284713900567928, 0.6791517751989478, 0.6108845927509713, 0.1373211597315956, 0.2517942475174331, 0.2517942475174331, 0.1373211597315954, 0.6108845927509711, 0.8440221396387144, 0.0779889301806430, 0.0779889301806423, 0.6175233785692882, 0.0174418264943837, 0.3650347949363278, 0.3650347949363280, 0.0174418264943837, 0.6175233785692880, 0.4792449355569203, 0.0415101288861592, 0.4792449355569202, 0.4120614054796894, 0.1758771890406209, 0.4120614054796893, 0.6566451941716462, 0.0861981702781002, 0.2571566355502534, 0.2571566355502534, 0.0861981702781002, 0.6566451941716460, 0.4984105744139569, 0.0031788511720860, 0.4984105744139568, 0.3817481026292989, 0.3091259486853504, 0.3091259486853505, 0.8724071202650543, 0.0034112678008347, 0.1241816119341108, 0.1241816119341110, 0.0034112678008346, 0.8724071202650542, 0.7837937554788413, 0.0445555167117895, 0.1716507278093690, 0.1716507278093692, 0.0445555167117894, 0.7837937554788413, 0.4801793419171517, 0.1220975488845625, 0.3977231091982854, 0.3977231091982855, 0.1220975488845626, 0.4801793419171517, 0.9926568663560335, 0.0036715668219834, 0.0036715668219829, 0.5463929830937153, 0.1957103712364281, 0.2578966456698564, 0.2578966456698564, 0.1957103712364280, 0.5463929830937153, 0.8375385335389723, 0.0183113919798340, 0.1441500744811934, 0.1441500744811935, 0.0183113919798339, 0.8375385335389723, 0.5844781809630052, 0.0032622580352038, 0.4122595610017908, 0.4122595610017910, 0.0032622580352036, 0.5844781809630050, 0.7440960937012480, 0.0034754415073157, 0.2524284647914362, 0.2524284647914363, 0.0034754415073156, 0.7440960937012479, 0.6670942824316437, 0.0035387900825817, 0.3293669274857743, 0.3293669274857745, 0.0035387900825817, 0.6670942824316435, 0.7715735792437323, 0.0188449390557523, 0.2095814817005152, 0.2095814817005154, 0.0188449390557521, 0.7715735792437322, 0.8127217284450715, 0.0036381021086964, 0.1836401694462321, 0.1836401694462323, 0.0036381021086961, 0.8127217284450713, 0.7125504805693451, 0.0457532869613174, 0.2416962324693372, 0.2416962324693376, 0.0457532869613172, 0.7125504805693449, 0.6212714775996074, 0.1893642612001964, 0.1893642612001961 }; static double w_save[] = { 0.0015139897718580, 0.0015139897718580, 0.0015139897718580, 0.0020991920973495, 0.0020991920973495, 0.0020991920973495, 0.0020991920973495, 0.0020991920973495, 0.0020991920973495, 0.0011046836690446, 0.0011046836690446, 0.0011046836690446, 0.0019226251721821, 0.0019226251721821, 0.0019226251721821, 0.0019226251721821, 0.0019226251721821, 0.0019226251721821, 0.0004804430100019, 0.0004804430100019, 0.0004804430100019, 0.0004804430100019, 0.0004804430100019, 0.0004804430100019, 0.0030325474600895, 0.0030325474600895, 0.0030325474600895, 0.0030325474600895, 0.0030325474600895, 0.0030325474600895, 0.0073189063292417, 0.0073189063292417, 0.0073189063292417, 0.0073189063292417, 0.0073189063292417, 0.0073189063292417, 0.0053883188429810, 0.0053883188429810, 0.0053883188429810, 0.0053883188429810, 0.0053883188429810, 0.0053883188429810, 0.0075850923563705, 0.0075850923563705, 0.0075850923563705, 0.0045692159189815, 0.0045692159189815, 0.0045692159189815, 0.0045692159189815, 0.0045692159189815, 0.0045692159189815, 0.0057203599064585, 0.0057203599064585, 0.0057203599064585, 0.0057203599064585, 0.0057203599064585, 0.0057203599064585, 0.0067120048490857, 0.0067120048490857, 0.0067120048490857, 0.0067120048490857, 0.0067120048490857, 0.0067120048490857, 0.0023170775093131, 0.0023170775093131, 0.0023170775093131, 0.0023170775093131, 0.0023170775093131, 0.0023170775093131, 0.0003086692619705, 0.0003086692619705, 0.0003086692619705, 0.0003086692619705, 0.0003086692619705, 0.0003086692619705, 0.0012047027694411, 0.0012047027694411, 0.0012047027694411, 0.0012047027694411, 0.0012047027694411, 0.0012047027694411, 0.0081637462521436, 0.0081637462521436, 0.0081637462521436, 0.0081637462521436, 0.0081637462521436, 0.0081637462521436, 0.0052500601543288, 0.0052500601543288, 0.0052500601543288, 0.0058808346792778, 0.0058808346792778, 0.0058808346792778, 0.0043645240281899, 0.0043645240281899, 0.0043645240281899, 0.0043645240281899, 0.0043645240281899, 0.0043645240281899, 0.0005497965506473, 0.0005497965506473, 0.0005497965506473, 0.0005497965506473, 0.0005497965506473, 0.0005497965506473, 0.0086445565740853, 0.0086445565740853, 0.0086445565740853, 0.0052464381586922, 0.0052464381586922, 0.0052464381586922, 0.0052464381586922, 0.0052464381586922, 0.0052464381586922, 0.0032584894563913, 0.0032584894563913, 0.0032584894563913, 0.0032584894563913, 0.0032584894563913, 0.0032584894563913, 0.0047812349883804, 0.0047812349883804, 0.0047812349883804, 0.0047812349883804, 0.0047812349883804, 0.0047812349883804, 0.0016087719028869, 0.0016087719028869, 0.0016087719028869, 0.0016087719028869, 0.0016087719028869, 0.0016087719028869, 0.0008775872521508, 0.0008775872521508, 0.0008775872521508, 0.0029825665052993, 0.0029825665052993, 0.0029825665052993, 0.0029825665052993, 0.0029825665052993, 0.0029825665052993, 0.0060939488435529, 0.0060939488435529, 0.0060939488435529, 0.0060939488435529, 0.0060939488435529, 0.0060939488435529, 0.0070873407460566, 0.0070873407460566, 0.0070873407460566, 0.0070873407460566, 0.0070873407460566, 0.0070873407460566, 0.0035862336027497, 0.0035862336027497, 0.0035862336027497, 0.0031497526280812, 0.0031497526280812, 0.0031497526280812, 0.0031497526280812, 0.0031497526280812, 0.0031497526280812, 0.0049992428284758, 0.0049992428284758, 0.0049992428284758, 0.0090788425055397, 0.0090788425055397, 0.0090788425055397, 0.0062518699531210, 0.0062518699531210, 0.0062518699531210, 0.0062518699531210, 0.0062518699531210, 0.0062518699531210, 0.0014156781091945, 0.0014156781091945, 0.0014156781091945, 0.0102066366491736, 0.0102066366491736, 0.0102066366491736, 0.0009493053225472, 0.0009493053225472, 0.0009493053225472, 0.0009493053225472, 0.0009493053225472, 0.0009493053225472, 0.0040312520842928, 0.0040312520842928, 0.0040312520842928, 0.0040312520842928, 0.0040312520842928, 0.0040312520842928, 0.0081722175482304, 0.0081722175482304, 0.0081722175482304, 0.0081722175482304, 0.0081722175482304, 0.0081722175482304, 0.0001732953357809, 0.0001732953357809, 0.0001732953357809, 0.0089586590287218, 0.0089586590287218, 0.0089586590287218, 0.0089586590287218, 0.0089586590287218, 0.0089586590287218, 0.0024620987414923, 0.0024620987414923, 0.0024620987414923, 0.0024620987414923, 0.0024620987414923, 0.0024620987414923, 0.0014212929213219, 0.0014212929213219, 0.0014212929213219, 0.0014212929213219, 0.0014212929213219, 0.0014212929213219, 0.0013051564959187, 0.0013051564959187, 0.0013051564959187, 0.0013051564959187, 0.0013051564959187, 0.0013051564959187, 0.0014459095277887, 0.0014459095277887, 0.0014459095277887, 0.0014459095277887, 0.0014459095277887, 0.0014459095277887, 0.0029345950580795, 0.0029345950580795, 0.0029345950580795, 0.0029345950580795, 0.0029345950580795, 0.0029345950580795, 0.0011964590052698, 0.0011964590052698, 0.0011964590052698, 0.0011964590052698, 0.0011964590052698, 0.0011964590052698, 0.0048735044199229, 0.0048735044199229, 0.0048735044199229, 0.0048735044199229, 0.0048735044199229, 0.0048735044199229, 0.0082906132570537, 0.0082906132570537, 0.0082906132570537 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule38 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule38() returns the rule of precision 38. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4590721360317646, 0.4590721360317646, 0.0818557279364708, 0.2837655147017407, 0.6639373713962480, 0.0522971139020114, 0.6639373713962479, 0.2837655147017407, 0.0522971139020114, 0.3932680062553601, 0.3932680062553601, 0.2134639874892798, 0.1285165649696939, 0.7724036723284647, 0.0990797627018414, 0.7724036723284647, 0.1285165649696941, 0.0990797627018411, 0.4681825892069357, 0.4681825892069357, 0.0636348215861285, 0.0413075041428614, 0.9566280907078333, 0.0020644051493054, 0.9566280907078334, 0.0413075041428616, 0.0020644051493049, 0.0892719800534145, 0.8739978442972371, 0.0367301756493484, 0.8739978442972371, 0.0892719800534145, 0.0367301756493481, 0.3372052923179872, 0.4368488831942271, 0.2259458244877856, 0.4368488831942271, 0.3372052923179872, 0.2259458244877856, 0.2738513741241787, 0.6934474438857674, 0.0327011819900538, 0.6934474438857675, 0.2738513741241788, 0.0327011819900536, 0.0399162626294194, 0.9470142283262505, 0.0130695090443302, 0.9470142283262506, 0.0399162626294196, 0.0130695090443297, 0.0175045040462673, 0.9649909919074650, 0.0175045040462677, 0.3081068327593843, 0.6181755526695998, 0.0737176145710159, 0.6181755526695998, 0.3081068327593843, 0.0737176145710158, 0.1454801146528607, 0.7090397706942783, 0.1454801146528609, 0.2196247131384356, 0.7776714046470208, 0.0027038822145437, 0.7776714046470208, 0.2196247131384357, 0.0027038822145434, 0.2734646071142814, 0.5073771294396898, 0.2191582634460287, 0.5073771294396898, 0.2734646071142814, 0.2191582634460286, 0.0686830028555527, 0.9105941852629332, 0.0207228118815142, 0.9105941852629332, 0.0686830028555528, 0.0207228118815138, 0.1830135998401795, 0.7163646792677445, 0.1006217208920760, 0.7163646792677445, 0.1830135998401795, 0.1006217208920759, 0.0030471742663605, 0.9939056514672787, 0.0030471742663609, 0.2287994832299253, 0.7017106989365653, 0.0694898178335093, 0.7017106989365655, 0.2287994832299252, 0.0694898178335091, 0.0587361601120220, 0.8825276797759557, 0.0587361601120223, 0.1018827114869391, 0.8297399330905469, 0.0683773554225139, 0.8297399330905471, 0.1018827114869392, 0.0683773554225136, 0.2435636733958171, 0.7421158852408665, 0.0143204413633164, 0.7421158852408665, 0.2435636733958172, 0.0143204413633164, 0.2058877165179012, 0.7551444267398045, 0.0389678567422944, 0.7551444267398045, 0.2058877165179013, 0.0389678567422941, 0.2018695088876031, 0.6487340291944527, 0.1493964619179441, 0.6487340291944528, 0.2018695088876032, 0.1493964619179440, 0.1591160210105452, 0.7786557671705014, 0.0622282118189533, 0.7786557671705016, 0.1591160210105452, 0.0622282118189531, 0.1779476358555918, 0.8044331226739222, 0.0176192414704860, 0.8044331226739222, 0.1779476358555919, 0.0176192414704858, 0.1620367479496921, 0.8340155243850955, 0.0039477276652125, 0.8340155243850954, 0.1620367479496921, 0.0039477276652123, 0.2918549838585246, 0.7052138362553024, 0.0029311798861729, 0.7052138362553025, 0.2918549838585245, 0.0029311798861727, 0.3718786917495892, 0.6253433272679723, 0.0027779809824385, 0.6253433272679723, 0.3718786917495892, 0.0027779809824384, 0.1349693726524653, 0.8307084415116845, 0.0343221858358503, 0.8307084415116845, 0.1349693726524654, 0.0343221858358500, 0.0373835575017465, 0.9252328849965067, 0.0373835575017469, 0.2855047782912640, 0.4289904434174718, 0.2855047782912640, 0.2524534299064219, 0.6388225307516531, 0.1087240393419249, 0.6388225307516532, 0.2524534299064219, 0.1087240393419247, 0.4203335017700142, 0.4203335017700143, 0.1593329964599715, 0.3242351641083045, 0.6608157279836501, 0.0149491079080454, 0.6608157279836501, 0.3242351641083045, 0.0149491079080453, 0.2076894216538629, 0.5846211566922740, 0.2076894216538630, 0.4921962729553108, 0.4921962729553108, 0.0156074540893784, 0.4374161906466257, 0.5252597321941108, 0.0373240771592634, 0.5252597321941108, 0.4374161906466257, 0.0373240771592634, 0.4559988036612093, 0.5410379244071537, 0.0029632719316369, 0.5410379244071537, 0.4559988036612093, 0.0029632719316369, 0.0754872857005683, 0.9203097361386582, 0.0042029781607736, 0.9203097361386582, 0.0754872857005683, 0.0042029781607733, 0.3260541266529466, 0.5596716859665990, 0.1142741873804544, 0.5596716859665990, 0.3260541266529467, 0.1142741873804543, 0.4011995885054882, 0.4859123261815903, 0.1128880853129214, 0.4859123261815903, 0.4011995885054881, 0.1128880853129214, 0.2687606603412640, 0.5710426617589802, 0.1601966778997558, 0.5710426617589801, 0.2687606603412641, 0.1601966778997558, 0.4060147025738772, 0.5788301687858335, 0.0151551286402894, 0.5788301687858335, 0.4060147025738773, 0.0151551286402893, 0.3565655939830261, 0.3565655939830261, 0.2868688120339477, 0.3835103468343402, 0.5464474716652220, 0.0700421815004378, 0.5464474716652219, 0.3835103468343402, 0.0700421815004378, 0.0164470646369432, 0.9801099468614760, 0.0034429885015809, 0.9801099468614760, 0.0164470646369433, 0.0034429885015805, 0.3542977861626948, 0.6080345993586279, 0.0376676144786774, 0.6080345993586279, 0.3542977861626948, 0.0376676144786772, 0.3419951757983160, 0.4920063975249682, 0.1659984266767156, 0.4920063975249683, 0.3419951757983161, 0.1659984266767155, 0.1152888910792784, 0.8726785778095564, 0.0120325311111653, 0.8726785778095565, 0.1152888910792785, 0.0120325311111650, 0.1165281018124025, 0.8831736765060774, 0.0002982216815202, 0.8831736765060774, 0.1165281018124027, 0.0002982216815200 }; static double b_save[] = { 0.0818557279364709, 0.4590721360317646, 0.4590721360317648, 0.0522971139020114, 0.2837655147017407, 0.6639373713962481, 0.0522971139020114, 0.6639373713962480, 0.2837655147017409, 0.2134639874892799, 0.3932680062553601, 0.3932680062553602, 0.0990797627018413, 0.1285165649696940, 0.7724036723284649, 0.0990797627018413, 0.7724036723284649, 0.1285165649696943, 0.0636348215861286, 0.4681825892069358, 0.4681825892069360, 0.0020644051493052, 0.0413075041428614, 0.9566280907078335, 0.0020644051493052, 0.9566280907078335, 0.0413075041428617, 0.0367301756493483, 0.0892719800534144, 0.8739978442972374, 0.0367301756493483, 0.8739978442972374, 0.0892719800534148, 0.2259458244877857, 0.3372052923179873, 0.4368488831942272, 0.2259458244877857, 0.4368488831942272, 0.3372052923179874, 0.0327011819900538, 0.2738513741241788, 0.6934474438857677, 0.0327011819900538, 0.6934474438857677, 0.2738513741241790, 0.0130695090443300, 0.0399162626294194, 0.9470142283262506, 0.0130695090443300, 0.9470142283262506, 0.0399162626294198, 0.0175045040462676, 0.0175045040462673, 0.9649909919074653, 0.0737176145710159, 0.3081068327593843, 0.6181755526695999, 0.0737176145710159, 0.6181755526695998, 0.3081068327593845, 0.1454801146528609, 0.1454801146528608, 0.7090397706942786, 0.0027038822145435, 0.2196247131384356, 0.7776714046470209, 0.0027038822145435, 0.7776714046470209, 0.2196247131384359, 0.2191582634460288, 0.2734646071142815, 0.5073771294396899, 0.2191582634460288, 0.5073771294396899, 0.2734646071142816, 0.0207228118815140, 0.0686830028555526, 0.9105941852629333, 0.0207228118815140, 0.9105941852629333, 0.0686830028555530, 0.1006217208920761, 0.1830135998401795, 0.7163646792677447, 0.1006217208920761, 0.7163646792677446, 0.1830135998401798, 0.0030471742663608, 0.0030471742663604, 0.9939056514672788, 0.0694898178335093, 0.2287994832299253, 0.7017106989365657, 0.0694898178335093, 0.7017106989365657, 0.2287994832299255, 0.0587361601120223, 0.0587361601120220, 0.8825276797759559, 0.0683773554225139, 0.1018827114869391, 0.8297399330905472, 0.0683773554225139, 0.8297399330905472, 0.1018827114869394, 0.0143204413633165, 0.2435636733958171, 0.7421158852408667, 0.0143204413633165, 0.7421158852408665, 0.2435636733958174, 0.0389678567422943, 0.2058877165179012, 0.7551444267398046, 0.0389678567422943, 0.7551444267398046, 0.2058877165179015, 0.1493964619179442, 0.2018695088876032, 0.6487340291944529, 0.1493964619179442, 0.6487340291944529, 0.2018695088876034, 0.0622282118189533, 0.1591160210105452, 0.7786557671705017, 0.0622282118189533, 0.7786557671705017, 0.1591160210105455, 0.0176192414704860, 0.1779476358555918, 0.8044331226739224, 0.0176192414704860, 0.8044331226739224, 0.1779476358555921, 0.0039477276652125, 0.1620367479496921, 0.8340155243850956, 0.0039477276652125, 0.8340155243850956, 0.1620367479496924, 0.0029311798861729, 0.2918549838585247, 0.7052138362553028, 0.0029311798861729, 0.7052138362553028, 0.2918549838585249, 0.0027779809824386, 0.3718786917495892, 0.6253433272679726, 0.0027779809824386, 0.6253433272679724, 0.3718786917495893, 0.0343221858358502, 0.1349693726524653, 0.8307084415116845, 0.0343221858358502, 0.8307084415116845, 0.1349693726524656, 0.0373835575017468, 0.0373835575017464, 0.9252328849965068, 0.2855047782912642, 0.2855047782912641, 0.4289904434174719, 0.1087240393419249, 0.2524534299064219, 0.6388225307516533, 0.1087240393419249, 0.6388225307516533, 0.2524534299064221, 0.1593329964599716, 0.4203335017700143, 0.4203335017700144, 0.0149491079080454, 0.3242351641083045, 0.6608157279836503, 0.0149491079080454, 0.6608157279836503, 0.3242351641083048, 0.2076894216538631, 0.2076894216538630, 0.5846211566922742, 0.0156074540893784, 0.4921962729553109, 0.4921962729553110, 0.0373240771592635, 0.4374161906466258, 0.5252597321941110, 0.0373240771592635, 0.5252597321941109, 0.4374161906466259, 0.0029632719316370, 0.4559988036612094, 0.5410379244071539, 0.0029632719316370, 0.5410379244071538, 0.4559988036612095, 0.0042029781607735, 0.0754872857005682, 0.9203097361386584, 0.0042029781607735, 0.9203097361386584, 0.0754872857005686, 0.1142741873804544, 0.3260541266529467, 0.5596716859665991, 0.1142741873804544, 0.5596716859665990, 0.3260541266529468, 0.1128880853129215, 0.4011995885054883, 0.4859123261815905, 0.1128880853129215, 0.4859123261815904, 0.4011995885054884, 0.1601966778997559, 0.2687606603412641, 0.5710426617589803, 0.1601966778997559, 0.5710426617589802, 0.2687606603412642, 0.0151551286402894, 0.4060147025738772, 0.5788301687858336, 0.0151551286402894, 0.5788301687858335, 0.4060147025738775, 0.2868688120339477, 0.3565655939830263, 0.3565655939830263, 0.0700421815004379, 0.3835103468343402, 0.5464474716652222, 0.0700421815004379, 0.5464474716652220, 0.3835103468343404, 0.0034429885015808, 0.0164470646369432, 0.9801099468614761, 0.0034429885015808, 0.9801099468614761, 0.0164470646369435, 0.0376676144786773, 0.3542977861626948, 0.6080345993586280, 0.0376676144786773, 0.6080345993586280, 0.3542977861626950, 0.1659984266767157, 0.3419951757983162, 0.4920063975249684, 0.1659984266767157, 0.4920063975249684, 0.3419951757983163, 0.0120325311111652, 0.1152888910792784, 0.8726785778095566, 0.0120325311111652, 0.8726785778095566, 0.1152888910792787, 0.0002982216815201, 0.1165281018124025, 0.8831736765060775, 0.0002982216815201, 0.8831736765060774, 0.1165281018124029 }; static double c_save[] = { 0.4590721360317646, 0.0818557279364708, 0.4590721360317643, 0.6639373713962479, 0.0522971139020113, 0.2837655147017405, 0.2837655147017407, 0.0522971139020113, 0.6639373713962476, 0.3932680062553600, 0.2134639874892798, 0.3932680062553600, 0.7724036723284647, 0.0990797627018413, 0.1285165649696938, 0.1285165649696940, 0.0990797627018410, 0.7724036723284646, 0.4681825892069357, 0.0636348215861285, 0.4681825892069355, 0.9566280907078334, 0.0020644051493053, 0.0413075041428611, 0.0413075041428614, 0.0020644051493049, 0.9566280907078334, 0.8739978442972371, 0.0367301756493484, 0.0892719800534142, 0.0892719800534145, 0.0367301756493481, 0.8739978442972371, 0.4368488831942270, 0.2259458244877856, 0.3372052923179872, 0.3372052923179872, 0.2259458244877856, 0.4368488831942270, 0.6934474438857675, 0.0327011819900538, 0.2738513741241785, 0.2738513741241787, 0.0327011819900535, 0.6934474438857674, 0.9470142283262506, 0.0130695090443301, 0.0399162626294192, 0.0399162626294194, 0.0130695090443298, 0.9470142283262505, 0.9649909919074652, 0.0175045040462678, 0.0175045040462670, 0.6181755526695998, 0.0737176145710159, 0.3081068327593842, 0.3081068327593843, 0.0737176145710159, 0.6181755526695998, 0.7090397706942784, 0.1454801146528610, 0.1454801146528605, 0.7776714046470208, 0.0027038822145436, 0.2196247131384355, 0.2196247131384357, 0.0027038822145434, 0.7776714046470208, 0.5073771294396898, 0.2191582634460287, 0.2734646071142813, 0.2734646071142814, 0.2191582634460286, 0.5073771294396898, 0.9105941852629332, 0.0207228118815141, 0.0686830028555525, 0.0686830028555527, 0.0207228118815138, 0.9105941852629332, 0.7163646792677445, 0.1006217208920760, 0.1830135998401792, 0.1830135998401794, 0.1006217208920760, 0.7163646792677443, 0.9939056514672787, 0.0030471742663608, 0.0030471742663603, 0.7017106989365655, 0.0694898178335094, 0.2287994832299250, 0.2287994832299253, 0.0694898178335092, 0.7017106989365653, 0.8825276797759557, 0.0587361601120223, 0.0587361601120219, 0.8297399330905469, 0.0683773554225139, 0.1018827114869388, 0.1018827114869391, 0.0683773554225137, 0.8297399330905468, 0.7421158852408665, 0.0143204413633164, 0.2435636733958169, 0.2435636733958171, 0.0143204413633163, 0.7421158852408662, 0.7551444267398045, 0.0389678567422943, 0.2058877165179009, 0.2058877165179012, 0.0389678567422941, 0.7551444267398044, 0.6487340291944528, 0.1493964619179442, 0.2018695088876029, 0.2018695088876030, 0.1493964619179439, 0.6487340291944527, 0.7786557671705016, 0.0622282118189533, 0.1591160210105450, 0.1591160210105451, 0.0622282118189531, 0.7786557671705014, 0.8044331226739222, 0.0176192414704860, 0.1779476358555916, 0.1779476358555918, 0.0176192414704858, 0.8044331226739220, 0.8340155243850955, 0.0039477276652124, 0.1620367479496919, 0.1620367479496921, 0.0039477276652123, 0.8340155243850953, 0.7052138362553025, 0.0029311798861729, 0.2918549838585244, 0.2918549838585245, 0.0029311798861728, 0.7052138362553024, 0.6253433272679724, 0.0027779809824385, 0.3718786917495890, 0.3718786917495892, 0.0027779809824385, 0.6253433272679723, 0.8307084415116845, 0.0343221858358502, 0.1349693726524651, 0.1349693726524652, 0.0343221858358500, 0.8307084415116844, 0.9252328849965067, 0.0373835575017469, 0.0373835575017463, 0.4289904434174717, 0.2855047782912640, 0.2855047782912640, 0.6388225307516532, 0.1087240393419250, 0.2524534299064218, 0.2524534299064219, 0.1087240393419248, 0.6388225307516531, 0.4203335017700142, 0.1593329964599714, 0.4203335017700142, 0.6608157279836501, 0.0149491079080454, 0.3242351641083042, 0.3242351641083045, 0.0149491079080452, 0.6608157279836500, 0.5846211566922739, 0.2076894216538630, 0.2076894216538628, 0.4921962729553108, 0.0156074540893784, 0.4921962729553107, 0.5252597321941109, 0.0373240771592634, 0.4374161906466255, 0.4374161906466257, 0.0373240771592634, 0.5252597321941106, 0.5410379244071538, 0.0029632719316369, 0.4559988036612092, 0.4559988036612093, 0.0029632719316369, 0.5410379244071535, 0.9203097361386582, 0.0042029781607736, 0.0754872857005680, 0.0754872857005683, 0.0042029781607732, 0.9203097361386581, 0.5596716859665989, 0.1142741873804543, 0.3260541266529464, 0.3260541266529466, 0.1142741873804544, 0.5596716859665989, 0.4859123261815903, 0.1128880853129214, 0.4011995885054880, 0.4011995885054882, 0.1128880853129214, 0.4859123261815902, 0.5710426617589801, 0.1601966778997557, 0.2687606603412638, 0.2687606603412640, 0.1601966778997558, 0.5710426617589801, 0.5788301687858334, 0.0151551286402893, 0.4060147025738771, 0.4060147025738771, 0.0151551286402892, 0.5788301687858333, 0.3565655939830262, 0.2868688120339476, 0.3565655939830261, 0.5464474716652219, 0.0700421815004378, 0.3835103468343400, 0.3835103468343402, 0.0700421815004378, 0.5464474716652218, 0.9801099468614761, 0.0034429885015808, 0.0164470646369429, 0.0164470646369432, 0.0034429885015806, 0.9801099468614759, 0.6080345993586279, 0.0376676144786773, 0.3542977861626946, 0.3542977861626948, 0.0376676144786772, 0.6080345993586278, 0.4920063975249683, 0.1659984266767156, 0.3419951757983160, 0.3419951757983161, 0.1659984266767155, 0.4920063975249681, 0.8726785778095564, 0.0120325311111653, 0.1152888910792781, 0.1152888910792783, 0.0120325311111650, 0.8726785778095563, 0.8831736765060773, 0.0002982216815201, 0.1165281018124024, 0.1165281018124025, 0.0002982216815199, 0.8831736765060771 }; static double w_save[] = { 0.0031639644402839, 0.0031639644402839, 0.0031639644402839, 0.0024850052311427, 0.0024850052311427, 0.0024850052311427, 0.0024850052311427, 0.0024850052311427, 0.0024850052311427, 0.0058616582191086, 0.0058616582191086, 0.0058616582191086, 0.0036964891607068, 0.0036964891607068, 0.0036964891607068, 0.0036964891607068, 0.0036964891607068, 0.0036964891607068, 0.0039302169037011, 0.0039302169037011, 0.0039302169037011, 0.0003477043989937, 0.0003477043989937, 0.0003477043989937, 0.0003477043989937, 0.0003477043989937, 0.0003477043989937, 0.0020738268739408, 0.0020738268739408, 0.0020738268739408, 0.0020738268739408, 0.0020738268739408, 0.0020738268739408, 0.0073710410900113, 0.0073710410900113, 0.0073710410900113, 0.0073710410900113, 0.0073710410900113, 0.0073710410900113, 0.0031253981144399, 0.0031253981144399, 0.0031253981144399, 0.0031253981144399, 0.0031253981144399, 0.0031253981144399, 0.0009061762144521, 0.0009061762144521, 0.0009061762144521, 0.0009061762144521, 0.0009061762144521, 0.0009061762144521, 0.0006994697673296, 0.0006994697673296, 0.0006994697673296, 0.0049956277697467, 0.0049956277697467, 0.0049956277697467, 0.0049956277697467, 0.0049956277697467, 0.0049956277697467, 0.0052024225110439, 0.0052024225110439, 0.0052024225110439, 0.0009256681988499, 0.0009256681988499, 0.0009256681988499, 0.0009256681988499, 0.0009256681988499, 0.0009256681988499, 0.0082821664626930, 0.0082821664626930, 0.0082821664626930, 0.0082821664626930, 0.0082821664626930, 0.0082821664626930, 0.0015368424658073, 0.0015368424658073, 0.0015368424658073, 0.0015368424658073, 0.0015368424658073, 0.0015368424658073, 0.0052227407388144, 0.0052227407388144, 0.0052227407388144, 0.0052227407388144, 0.0052227407388144, 0.0052227407388144, 0.0001240466626531, 0.0001240466626531, 0.0001240466626531, 0.0047183927884199, 0.0047183927884199, 0.0047183927884199, 0.0047183927884199, 0.0047183927884199, 0.0047183927884199, 0.0025063822165145, 0.0025063822165145, 0.0025063822165145, 0.0036021170049529, 0.0036021170049529, 0.0036021170049529, 0.0036021170049529, 0.0036021170049529, 0.0036021170049529, 0.0023702904673934, 0.0023702904673934, 0.0023702904673934, 0.0023702904673934, 0.0023702904673934, 0.0023702904673934, 0.0036104898333758, 0.0036104898333758, 0.0036104898333758, 0.0036104898333758, 0.0036104898333758, 0.0036104898333758, 0.0065404545307455, 0.0065404545307455, 0.0065404545307455, 0.0065404545307455, 0.0065404545307455, 0.0065404545307455, 0.0040792214803126, 0.0040792214803126, 0.0040792214803126, 0.0040792214803126, 0.0040792214803126, 0.0040792214803126, 0.0023256389181058, 0.0023256389181058, 0.0023256389181058, 0.0023256389181058, 0.0023256389181058, 0.0023256389181058, 0.0010057440220833, 0.0010057440220833, 0.0010057440220833, 0.0010057440220833, 0.0010057440220833, 0.0010057440220833, 0.0011431617714117, 0.0011431617714117, 0.0011431617714117, 0.0011431617714117, 0.0011431617714117, 0.0011431617714117, 0.0011884613225083, 0.0011884613225083, 0.0011884613225083, 0.0011884613225083, 0.0011884613225083, 0.0011884613225083, 0.0029052189452109, 0.0029052189452109, 0.0029052189452109, 0.0029052189452109, 0.0029052189452109, 0.0029052189452109, 0.0017075502039157, 0.0017075502039157, 0.0017075502039157, 0.0089856095188050, 0.0089856095188050, 0.0089856095188050, 0.0063267151975866, 0.0063267151975866, 0.0063267151975866, 0.0063267151975866, 0.0063267151975866, 0.0063267151975866, 0.0079377042751205, 0.0079377042751205, 0.0079377042751205, 0.0027256862207201, 0.0027256862207201, 0.0027256862207201, 0.0027256862207201, 0.0027256862207201, 0.0027256862207201, 0.0077485531926675, 0.0077485531926675, 0.0077485531926675, 0.0030358975545344, 0.0030358975545344, 0.0030358975545344, 0.0045215915998052, 0.0045215915998052, 0.0045215915998052, 0.0045215915998052, 0.0045215915998052, 0.0045215915998052, 0.0012891742774294, 0.0012891742774294, 0.0012891742774294, 0.0012891742774294, 0.0012891742774294, 0.0012891742774294, 0.0008166839181728, 0.0008166839181728, 0.0008166839181728, 0.0008166839181728, 0.0008166839181728, 0.0008166839181728, 0.0069477793235522, 0.0069477793235522, 0.0069477793235522, 0.0069477793235522, 0.0069477793235522, 0.0069477793235522, 0.0070986179394903, 0.0070986179394903, 0.0070986179394903, 0.0070986179394903, 0.0070986179394903, 0.0070986179394903, 0.0076919203485779, 0.0076919203485779, 0.0076919203485779, 0.0076919203485779, 0.0076919203485779, 0.0076919203485779, 0.0029252190187241, 0.0029252190187241, 0.0029252190187241, 0.0029252190187241, 0.0029252190187241, 0.0029252190187241, 0.0099759936103826, 0.0099759936103826, 0.0099759936103826, 0.0060566969964858, 0.0060566969964858, 0.0060566969964858, 0.0060566969964858, 0.0060566969964858, 0.0060566969964858, 0.0003337056331188, 0.0003337056331188, 0.0003337056331188, 0.0003337056331188, 0.0003337056331188, 0.0003337056331188, 0.0045294689209488, 0.0045294689209488, 0.0045294689209488, 0.0045294689209488, 0.0045294689209488, 0.0045294689209488, 0.0084025374143198, 0.0084025374143198, 0.0084025374143198, 0.0084025374143198, 0.0084025374143198, 0.0084025374143198, 0.0018109718524034, 0.0018109718524034, 0.0018109718524034, 0.0018109718524034, 0.0018109718524034, 0.0018109718524034, 0.0002922856631828, 0.0002922856631828, 0.0002922856631828, 0.0002922856631828, 0.0002922856631828, 0.0002922856631828 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule39 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule39() returns the rule of precision 39. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.2382752085845570, 0.7573503089771818, 0.0043744824382613, 0.7573503089771818, 0.2382752085845571, 0.0043744824382611, 0.5022902013149184, 0.2662727227960811, 0.2314370758890004, 0.2662727227960811, 0.5022902013149184, 0.2314370758890005, 0.3506827341571583, 0.4132178184063219, 0.2360994474365198, 0.4132178184063219, 0.3506827341571582, 0.2360994474365199, 0.2778089177192840, 0.7195287425328243, 0.0026623397478918, 0.7195287425328242, 0.2778089177192840, 0.0026623397478915, 0.4724094821505567, 0.4724094821505566, 0.0551810356988866, 0.3212034826826168, 0.4713569053824377, 0.2074396119349455, 0.4713569053824377, 0.3212034826826168, 0.2074396119349454, 0.4575079686738243, 0.4575079686738243, 0.0849840626523514, 0.4574242168529821, 0.5306666306702293, 0.0119091524767885, 0.5306666306702292, 0.4574242168529821, 0.0119091524767886, 0.1910383428521846, 0.8068046948089155, 0.0021569623388999, 0.8068046948089155, 0.1910383428521847, 0.0021569623388998, 0.3538472919168833, 0.3538472919168833, 0.2923054161662332, 0.4991061498602990, 0.4991061498602990, 0.0017877002794020, 0.2063519407328363, 0.6863905655155179, 0.1072574937516458, 0.6863905655155178, 0.2063519407328364, 0.1072574937516456, 0.2612383827874719, 0.6263232239210454, 0.1124383932914825, 0.6263232239210456, 0.2612383827874720, 0.1124383932914823, 0.1133316581963653, 0.7733366836072691, 0.1133316581963656, 0.1593888996231203, 0.7265207753801600, 0.1140903249967197, 0.7265207753801599, 0.1593888996231204, 0.1140903249967195, 0.3988695132240669, 0.5391856448598707, 0.0619448419160624, 0.5391856448598707, 0.3988695132240669, 0.0619448419160624, 0.3122725792733609, 0.5657645375013545, 0.1219628832252846, 0.5657645375013546, 0.3122725792733608, 0.1219628832252845, 0.3644362623584764, 0.5969189412939834, 0.0386447963475403, 0.5969189412939834, 0.3644362623584764, 0.0386447963475401, 0.2305648342404432, 0.7522011939909903, 0.0172339717685666, 0.7522011939909903, 0.2305648342404432, 0.0172339717685664, 0.0157787047228343, 0.9684425905543310, 0.0157787047228348, 0.0392682833818940, 0.9461693463150468, 0.0145623703030595, 0.9461693463150468, 0.0392682833818942, 0.0145623703030590, 0.3582577335477227, 0.4875811564549278, 0.1541611099973494, 0.4875811564549278, 0.3582577335477227, 0.1541611099973493, 0.3805078825483125, 0.5183519867727387, 0.1011401306789488, 0.5183519867727387, 0.3805078825483125, 0.1011401306789487, 0.1318865755866089, 0.7948276077652688, 0.0732858166481222, 0.7948276077652688, 0.1318865755866089, 0.0732858166481220, 0.1726302550688860, 0.8138522815338993, 0.0135174633972147, 0.8138522815338993, 0.1726302550688861, 0.0135174633972144, 0.0707756358900086, 0.8860757177287693, 0.0431486463812223, 0.8860757177287693, 0.0707756358900087, 0.0431486463812219, 0.0473824731204699, 0.9497691880411768, 0.0028483388383533, 0.9497691880411769, 0.0473824731204700, 0.0028483388383529, 0.1640091847666056, 0.6719816304667885, 0.1640091847666059, 0.4084715607291340, 0.4084715607291340, 0.1830568785417320, 0.2971932482957449, 0.6624092975072737, 0.0403974541969814, 0.6624092975072737, 0.2971932482957449, 0.0403974541969812, 0.4437652399535983, 0.5252322117028740, 0.0310025483435276, 0.5252322117028740, 0.4437652399535983, 0.0310025483435276, 0.2298548902498229, 0.7308596458500963, 0.0392854639000808, 0.7308596458500963, 0.2298548902498229, 0.0392854639000805, 0.4365416551079566, 0.4365416551079566, 0.1269166897840867, 0.2515254271389071, 0.6769104408114252, 0.0715641320496676, 0.6769104408114253, 0.2515254271389073, 0.0715641320496676, 0.2206287919327525, 0.6249766162864728, 0.1543945917807746, 0.6249766162864728, 0.2206287919327525, 0.1543945917807745, 0.0370326513393936, 0.9259346973212126, 0.0370326513393939, 0.4164031820468178, 0.5808233445804072, 0.0027734733727750, 0.5808233445804072, 0.4164031820468178, 0.0027734733727749, 0.2780372435840275, 0.5501168873807294, 0.1718458690352431, 0.5501168873807294, 0.2780372435840275, 0.1718458690352429, 0.3420758322145085, 0.6546717575274422, 0.0032524102580493, 0.6546717575274422, 0.3420758322145085, 0.0032524102580491, 0.2117317495651855, 0.5765365008696287, 0.2117317495651856, 0.3766515227420243, 0.6072672777807482, 0.0160811994772276, 0.6072672777807481, 0.3766515227420243, 0.0160811994772275, 0.1122979167412356, 0.8440428845538768, 0.0436591987048877, 0.8440428845538769, 0.1122979167412357, 0.0436591987048873, 0.1861411558417737, 0.7455631517971735, 0.0682956923610529, 0.7455631517971736, 0.1861411558417738, 0.0682956923610526, 0.3217033982751871, 0.6035740986139331, 0.0747225031108797, 0.6035740986139331, 0.3217033982751872, 0.0747225031108797, 0.1660126851788667, 0.7978319404567993, 0.0361553743643340, 0.7978319404567994, 0.1660126851788668, 0.0361553743643337, 0.0193576952354285, 0.9778092140653304, 0.0028330906992414, 0.9778092140653304, 0.0193576952354286, 0.0028330906992409, 0.0719904092251254, 0.9100597072441559, 0.0179498835307189, 0.9100597072441557, 0.0719904092251255, 0.0179498835307185, 0.2869572884590686, 0.4260854230818626, 0.2869572884590688, 0.1333327168798979, 0.8634747432495302, 0.0031925398705718, 0.8634747432495303, 0.1333327168798978, 0.0031925398705716, 0.2994455291729939, 0.6842620134079914, 0.0162924574190148, 0.6842620134079914, 0.2994455291729938, 0.0162924574190146, 0.1171078851891533, 0.8649767156294978, 0.0179153991813488, 0.8649767156294980, 0.1171078851891534, 0.0179153991813485, 0.0806765828829425, 0.8386468342341147, 0.0806765828829429, 0.0853676016562655, 0.9110651490396003, 0.0035672493041343, 0.9110651490396005, 0.0853676016562656, 0.0035672493041339, 0.0036432199207299, 0.9927135601585398, 0.0036432199207303 }; static double b_save[] = { 0.0043744824382613, 0.2382752085845570, 0.7573503089771819, 0.0043744824382613, 0.7573503089771818, 0.2382752085845573, 0.2314370758890006, 0.5022902013149185, 0.2662727227960813, 0.2314370758890006, 0.2662727227960812, 0.5022902013149185, 0.2360994474365199, 0.3506827341571583, 0.4132178184063220, 0.2360994474365199, 0.4132178184063219, 0.3506827341571584, 0.0026623397478917, 0.2778089177192841, 0.7195287425328244, 0.0026623397478917, 0.7195287425328244, 0.2778089177192843, 0.0551810356988867, 0.4724094821505568, 0.4724094821505569, 0.2074396119349455, 0.3212034826826168, 0.4713569053824378, 0.2074396119349455, 0.4713569053824377, 0.3212034826826170, 0.0849840626523515, 0.4575079686738243, 0.4575079686738245, 0.0119091524767886, 0.4574242168529821, 0.5306666306702296, 0.0119091524767886, 0.5306666306702293, 0.4574242168529823, 0.0021569623388999, 0.1910383428521846, 0.8068046948089157, 0.0021569623388999, 0.8068046948089155, 0.1910383428521849, 0.2923054161662334, 0.3538472919168835, 0.3538472919168835, 0.0017877002794021, 0.4991061498602991, 0.4991061498602992, 0.1072574937516458, 0.2063519407328363, 0.6863905655155180, 0.1072574937516458, 0.6863905655155180, 0.2063519407328365, 0.1124383932914825, 0.2612383827874720, 0.6263232239210457, 0.1124383932914825, 0.6263232239210456, 0.2612383827874722, 0.1133316581963656, 0.1133316581963653, 0.7733366836072691, 0.1140903249967197, 0.1593888996231203, 0.7265207753801601, 0.1140903249967197, 0.7265207753801601, 0.1593888996231206, 0.0619448419160625, 0.3988695132240669, 0.5391856448598709, 0.0619448419160625, 0.5391856448598707, 0.3988695132240671, 0.1219628832252846, 0.3122725792733609, 0.5657645375013547, 0.1219628832252846, 0.5657645375013547, 0.3122725792733611, 0.0386447963475402, 0.3644362623584764, 0.5969189412939835, 0.0386447963475402, 0.5969189412939835, 0.3644362623584766, 0.0172339717685666, 0.2305648342404432, 0.7522011939909904, 0.0172339717685666, 0.7522011939909904, 0.2305648342404434, 0.0157787047228346, 0.0157787047228343, 0.9684425905543311, 0.0145623703030592, 0.0392682833818940, 0.9461693463150468, 0.0145623703030592, 0.9461693463150468, 0.0392682833818944, 0.1541611099973495, 0.3582577335477228, 0.4875811564549280, 0.1541611099973495, 0.4875811564549279, 0.3582577335477229, 0.1011401306789488, 0.3805078825483126, 0.5183519867727389, 0.1011401306789488, 0.5183519867727387, 0.3805078825483127, 0.0732858166481222, 0.1318865755866089, 0.7948276077652691, 0.0732858166481222, 0.7948276077652691, 0.1318865755866092, 0.0135174633972146, 0.1726302550688860, 0.8138522815338995, 0.0135174633972146, 0.8138522815338995, 0.1726302550688863, 0.0431486463812222, 0.0707756358900086, 0.8860757177287693, 0.0431486463812222, 0.8860757177287693, 0.0707756358900089, 0.0028483388383532, 0.0473824731204699, 0.9497691880411770, 0.0028483388383532, 0.9497691880411770, 0.0473824731204703, 0.1640091847666058, 0.1640091847666057, 0.6719816304667886, 0.1830568785417320, 0.4084715607291341, 0.4084715607291342, 0.0403974541969814, 0.2971932482957449, 0.6624092975072738, 0.0403974541969814, 0.6624092975072738, 0.2971932482957452, 0.0310025483435277, 0.4437652399535983, 0.5252322117028743, 0.0310025483435277, 0.5252322117028742, 0.4437652399535986, 0.0392854639000807, 0.2298548902498229, 0.7308596458500966, 0.0392854639000807, 0.7308596458500966, 0.2298548902498232, 0.1269166897840868, 0.4365416551079567, 0.4365416551079568, 0.0715641320496677, 0.2515254271389071, 0.6769104408114255, 0.0715641320496677, 0.6769104408114252, 0.2515254271389074, 0.1543945917807747, 0.2206287919327525, 0.6249766162864731, 0.1543945917807747, 0.6249766162864731, 0.2206287919327527, 0.0370326513393939, 0.0370326513393935, 0.9259346973212128, 0.0027734733727750, 0.4164031820468178, 0.5808233445804074, 0.0027734733727750, 0.5808233445804073, 0.4164031820468180, 0.1718458690352430, 0.2780372435840276, 0.5501168873807295, 0.1718458690352430, 0.5501168873807295, 0.2780372435840278, 0.0032524102580493, 0.3420758322145085, 0.6546717575274423, 0.0032524102580493, 0.6546717575274423, 0.3420758322145088, 0.2117317495651857, 0.2117317495651856, 0.5765365008696289, 0.0160811994772277, 0.3766515227420243, 0.6072672777807483, 0.0160811994772277, 0.6072672777807482, 0.3766515227420245, 0.0436591987048876, 0.1122979167412356, 0.8440428845538770, 0.0436591987048876, 0.8440428845538770, 0.1122979167412359, 0.0682956923610528, 0.1861411558417737, 0.7455631517971736, 0.0682956923610528, 0.7455631517971735, 0.1861411558417740, 0.0747225031108798, 0.3217033982751872, 0.6035740986139333, 0.0747225031108798, 0.6035740986139331, 0.3217033982751874, 0.0361553743643339, 0.1660126851788667, 0.7978319404567995, 0.0361553743643339, 0.7978319404567995, 0.1660126851788670, 0.0028330906992412, 0.0193576952354285, 0.9778092140653304, 0.0028330906992412, 0.9778092140653306, 0.0193576952354288, 0.0179498835307188, 0.0719904092251254, 0.9100597072441560, 0.0179498835307188, 0.9100597072441560, 0.0719904092251257, 0.2869572884590688, 0.2869572884590687, 0.4260854230818627, 0.0031925398705718, 0.1333327168798978, 0.8634747432495306, 0.0031925398705718, 0.8634747432495306, 0.1333327168798982, 0.0162924574190147, 0.2994455291729939, 0.6842620134079915, 0.0162924574190147, 0.6842620134079915, 0.2994455291729942, 0.0179153991813487, 0.1171078851891533, 0.8649767156294981, 0.0179153991813487, 0.8649767156294981, 0.1171078851891536, 0.0806765828829428, 0.0806765828829425, 0.8386468342341149, 0.0035672493041342, 0.0853676016562654, 0.9110651490396005, 0.0035672493041342, 0.9110651490396005, 0.0853676016562658, 0.0036432199207302, 0.0036432199207299, 0.9927135601585401 }; static double c_save[] = { 0.7573503089771818, 0.0043744824382612, 0.2382752085845569, 0.2382752085845569, 0.0043744824382611, 0.7573503089771817, 0.2662727227960810, 0.2314370758890004, 0.5022902013149183, 0.5022902013149184, 0.2314370758890004, 0.2662727227960809, 0.4132178184063218, 0.2360994474365198, 0.3506827341571581, 0.3506827341571582, 0.2360994474365198, 0.4132178184063217, 0.7195287425328243, 0.0026623397478917, 0.2778089177192838, 0.2778089177192841, 0.0026623397478917, 0.7195287425328241, 0.4724094821505567, 0.0551810356988865, 0.4724094821505564, 0.4713569053824377, 0.2074396119349455, 0.3212034826826167, 0.3212034826826168, 0.2074396119349455, 0.4713569053824377, 0.4575079686738243, 0.0849840626523514, 0.4575079686738240, 0.5306666306702292, 0.0119091524767885, 0.4574242168529820, 0.4574242168529821, 0.0119091524767886, 0.5306666306702290, 0.8068046948089155, 0.0021569623388999, 0.1910383428521844, 0.1910383428521846, 0.0021569623388998, 0.8068046948089154, 0.3538472919168832, 0.2923054161662332, 0.3538472919168832, 0.4991061498602989, 0.0017877002794019, 0.4991061498602988, 0.6863905655155179, 0.1072574937516458, 0.2063519407328361, 0.2063519407328364, 0.1072574937516456, 0.6863905655155178, 0.6263232239210456, 0.1124383932914826, 0.2612383827874718, 0.2612383827874719, 0.1124383932914824, 0.6263232239210454, 0.7733366836072691, 0.1133316581963655, 0.1133316581963651, 0.7265207753801600, 0.1140903249967197, 0.1593888996231201, 0.1593888996231204, 0.1140903249967194, 0.7265207753801600, 0.5391856448598706, 0.0619448419160623, 0.3988695132240667, 0.3988695132240668, 0.0619448419160623, 0.5391856448598705, 0.5657645375013545, 0.1219628832252846, 0.3122725792733607, 0.3122725792733608, 0.1219628832252845, 0.5657645375013545, 0.5969189412939834, 0.0386447963475402, 0.3644362623584763, 0.3644362623584764, 0.0386447963475401, 0.5969189412939833, 0.7522011939909903, 0.0172339717685665, 0.2305648342404431, 0.2305648342404432, 0.0172339717685664, 0.7522011939909903, 0.9684425905543311, 0.0157787047228347, 0.0157787047228340, 0.9461693463150469, 0.0145623703030592, 0.0392682833818937, 0.0392682833818940, 0.0145623703030590, 0.9461693463150466, 0.4875811564549278, 0.1541611099973494, 0.3582577335477226, 0.3582577335477227, 0.1541611099973494, 0.4875811564549277, 0.5183519867727386, 0.1011401306789487, 0.3805078825483124, 0.3805078825483125, 0.1011401306789487, 0.5183519867727385, 0.7948276077652688, 0.0732858166481222, 0.1318865755866087, 0.1318865755866090, 0.0732858166481219, 0.7948276077652687, 0.8138522815338993, 0.0135174633972147, 0.1726302550688857, 0.1726302550688860, 0.0135174633972144, 0.8138522815338993, 0.8860757177287693, 0.0431486463812222, 0.0707756358900085, 0.0707756358900086, 0.0431486463812221, 0.8860757177287691, 0.9497691880411768, 0.0028483388383533, 0.0473824731204696, 0.0473824731204699, 0.0028483388383530, 0.9497691880411768, 0.6719816304667885, 0.1640091847666058, 0.1640091847666055, 0.4084715607291339, 0.1830568785417319, 0.4084715607291339, 0.6624092975072737, 0.0403974541969814, 0.2971932482957448, 0.2971932482957449, 0.0403974541969813, 0.6624092975072735, 0.5252322117028740, 0.0310025483435276, 0.4437652399535981, 0.4437652399535983, 0.0310025483435276, 0.5252322117028738, 0.7308596458500963, 0.0392854639000808, 0.2298548902498226, 0.2298548902498230, 0.0392854639000805, 0.7308596458500963, 0.4365416551079566, 0.1269166897840867, 0.4365416551079564, 0.6769104408114252, 0.0715641320496677, 0.2515254271389069, 0.2515254271389070, 0.0715641320496675, 0.6769104408114250, 0.6249766162864728, 0.1543945917807746, 0.2206287919327523, 0.2206287919327525, 0.1543945917807744, 0.6249766162864727, 0.9259346973212126, 0.0370326513393939, 0.0370326513393933, 0.5808233445804073, 0.0027734733727750, 0.4164031820468176, 0.4164031820468178, 0.0027734733727750, 0.5808233445804071, 0.5501168873807295, 0.1718458690352430, 0.2780372435840274, 0.2780372435840276, 0.1718458690352430, 0.5501168873807294, 0.6546717575274421, 0.0032524102580492, 0.3420758322145083, 0.3420758322145085, 0.0032524102580491, 0.6546717575274421, 0.5765365008696287, 0.2117317495651857, 0.2117317495651855, 0.6072672777807481, 0.0160811994772275, 0.3766515227420241, 0.3766515227420243, 0.0160811994772275, 0.6072672777807480, 0.8440428845538769, 0.0436591987048877, 0.1122979167412353, 0.1122979167412356, 0.0436591987048873, 0.8440428845538768, 0.7455631517971735, 0.0682956923610528, 0.1861411558417735, 0.1861411558417736, 0.0682956923610527, 0.7455631517971734, 0.6035740986139331, 0.0747225031108797, 0.3217033982751869, 0.3217033982751871, 0.0747225031108797, 0.6035740986139329, 0.7978319404567993, 0.0361553743643340, 0.1660126851788665, 0.1660126851788667, 0.0361553743643337, 0.7978319404567993, 0.9778092140653303, 0.0028330906992411, 0.0193576952354283, 0.0193576952354284, 0.0028330906992408, 0.9778092140653303, 0.9100597072441557, 0.0179498835307187, 0.0719904092251252, 0.0719904092251255, 0.0179498835307185, 0.9100597072441557, 0.4260854230818627, 0.2869572884590687, 0.2869572884590685, 0.8634747432495303, 0.0031925398705719, 0.1333327168798976, 0.1333327168798979, 0.0031925398705716, 0.8634747432495302, 0.6842620134079914, 0.0162924574190147, 0.2994455291729936, 0.2994455291729938, 0.0162924574190146, 0.6842620134079912, 0.8649767156294980, 0.0179153991813489, 0.1171078851891532, 0.1171078851891533, 0.0179153991813485, 0.8649767156294980, 0.8386468342341147, 0.0806765828829429, 0.0806765828829422, 0.9110651490396003, 0.0035672493041342, 0.0853676016562652, 0.0853676016562654, 0.0035672493041340, 0.9110651490396003, 0.9927135601585400, 0.0036432199207303, 0.0036432199207296 }; static double w_save[] = { 0.0007824030328396, 0.0007824030328396, 0.0007824030328396, 0.0007824030328396, 0.0007824030328396, 0.0007824030328396, 0.0054259258789525, 0.0054259258789525, 0.0054259258789525, 0.0054259258789525, 0.0054259258789525, 0.0054259258789525, 0.0064335649832209, 0.0064335649832209, 0.0064335649832209, 0.0064335649832209, 0.0064335649832209, 0.0064335649832209, 0.0007645106376317, 0.0007645106376317, 0.0007645106376317, 0.0007645106376317, 0.0007645106376317, 0.0007645106376317, 0.0038004729776007, 0.0038004729776007, 0.0038004729776007, 0.0062594886810264, 0.0062594886810264, 0.0062594886810264, 0.0062594886810264, 0.0062594886810264, 0.0062594886810264, 0.0048090357401686, 0.0048090357401686, 0.0048090357401686, 0.0021620874068945, 0.0021620874068945, 0.0021620874068945, 0.0021620874068945, 0.0021620874068945, 0.0021620874068945, 0.0006908539783223, 0.0006908539783223, 0.0006908539783223, 0.0006908539783223, 0.0006908539783223, 0.0006908539783223, 0.0080789945453473, 0.0080789945453473, 0.0080789945453473, 0.0008384766818292, 0.0008384766818292, 0.0008384766818292, 0.0043810960857082, 0.0043810960857082, 0.0043810960857082, 0.0043810960857082, 0.0043810960857082, 0.0043810960857082, 0.0048977390707915, 0.0048977390707915, 0.0048977390707915, 0.0048977390707915, 0.0048977390707915, 0.0048977390707915, 0.0037089356213762, 0.0037089356213762, 0.0037089356213762, 0.0044309896508941, 0.0044309896508941, 0.0044309896508941, 0.0044309896508941, 0.0044309896508941, 0.0044309896508941, 0.0046998784286279, 0.0046998784286279, 0.0046998784286279, 0.0046998784286279, 0.0046998784286279, 0.0046998784286279, 0.0056949471589669, 0.0056949471589669, 0.0056949471589669, 0.0056949471589669, 0.0056949471589669, 0.0056949471589669, 0.0037232299887488, 0.0037232299887488, 0.0037232299887488, 0.0037232299887488, 0.0037232299887488, 0.0037232299887488, 0.0022711066220262, 0.0022711066220262, 0.0022711066220262, 0.0022711066220262, 0.0022711066220262, 0.0022711066220262, 0.0006686069116893, 0.0006686069116893, 0.0006686069116893, 0.0009501856551478, 0.0009501856551478, 0.0009501856551478, 0.0009501856551478, 0.0009501856551478, 0.0009501856551478, 0.0074331006305706, 0.0074331006305706, 0.0074331006305706, 0.0074331006305706, 0.0074331006305706, 0.0074331006305706, 0.0061864305337419, 0.0061864305337419, 0.0061864305337419, 0.0061864305337419, 0.0061864305337419, 0.0061864305337419, 0.0038374222817439, 0.0038374222817439, 0.0038374222817439, 0.0038374222817439, 0.0038374222817439, 0.0038374222817439, 0.0018958729657531, 0.0018958729657531, 0.0018958729657531, 0.0018958729657531, 0.0018958729657531, 0.0018958729657531, 0.0023158771686324, 0.0023158771686324, 0.0023158771686324, 0.0023158771686324, 0.0023158771686324, 0.0023158771686324, 0.0004882707622038, 0.0004882707622038, 0.0004882707622038, 0.0004882707622038, 0.0004882707622038, 0.0004882707622038, 0.0058035379196036, 0.0058035379196036, 0.0058035379196036, 0.0076992066322763, 0.0076992066322763, 0.0076992066322763, 0.0039332470075349, 0.0039332470075349, 0.0039332470075349, 0.0039332470075349, 0.0039332470075349, 0.0039332470075349, 0.0037369831874343, 0.0037369831874343, 0.0037369831874343, 0.0037369831874343, 0.0037369831874343, 0.0037369831874343, 0.0035306268703356, 0.0035306268703356, 0.0035306268703356, 0.0035306268703356, 0.0035306268703356, 0.0035306268703356, 0.0067765032180855, 0.0067765032180855, 0.0067765032180855, 0.0048733014906139, 0.0048733014906139, 0.0048733014906139, 0.0048733014906139, 0.0048733014906139, 0.0048733014906139, 0.0060696924219261, 0.0060696924219261, 0.0060696924219261, 0.0060696924219261, 0.0060696924219261, 0.0060696924219261, 0.0015920496320693, 0.0015920496320693, 0.0015920496320693, 0.0011017635807508, 0.0011017635807508, 0.0011017635807508, 0.0011017635807508, 0.0011017635807508, 0.0011017635807508, 0.0073091828155223, 0.0073091828155223, 0.0073091828155223, 0.0073091828155223, 0.0073091828155223, 0.0073091828155223, 0.0011736195277390, 0.0011736195277390, 0.0011736195277390, 0.0011736195277390, 0.0011736195277390, 0.0011736195277390, 0.0071255638341493, 0.0071255638341493, 0.0071255638341493, 0.0028277464204102, 0.0028277464204102, 0.0028277464204102, 0.0028277464204102, 0.0028277464204102, 0.0028277464204102, 0.0028118195580629, 0.0028118195580629, 0.0028118195580629, 0.0028118195580629, 0.0028118195580629, 0.0028118195580629, 0.0043776217728844, 0.0043776217728844, 0.0043776217728844, 0.0043776217728844, 0.0043776217728844, 0.0043776217728844, 0.0057797851749689, 0.0057797851749689, 0.0057797851749689, 0.0057797851749689, 0.0057797851749689, 0.0057797851749689, 0.0033216883150331, 0.0033216883150331, 0.0033216883150331, 0.0033216883150331, 0.0033216883150331, 0.0033216883150331, 0.0003234214385767, 0.0003234214385767, 0.0003234214385767, 0.0003234214385767, 0.0003234214385767, 0.0003234214385767, 0.0015599585117589, 0.0015599585117589, 0.0015599585117589, 0.0015599585117589, 0.0015599585117589, 0.0015599585117589, 0.0087287285098108, 0.0087287285098108, 0.0087287285098108, 0.0008684596573017, 0.0008684596573017, 0.0008684596573017, 0.0008684596573017, 0.0008684596573017, 0.0008684596573017, 0.0027516782565965, 0.0027516782565965, 0.0027516782565965, 0.0027516782565965, 0.0027516782565965, 0.0027516782565965, 0.0020505862443132, 0.0020505862443132, 0.0020505862443132, 0.0020505862443132, 0.0020505862443132, 0.0020505862443132, 0.0037076853680653, 0.0037076853680653, 0.0037076853680653, 0.0007841501256460, 0.0007841501256460, 0.0007841501256460, 0.0007841501256460, 0.0007841501256460, 0.0007841501256460, 0.0001749077815533, 0.0001749077815533, 0.0001749077815533 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule40 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule40() returns the rule of precision 40. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1671778383557105, 0.8312942125952762, 0.0015279490490133, 0.8312942125952764, 0.1671778383557105, 0.0015279490490130, 0.3714780994452375, 0.6135500780826215, 0.0149718224721411, 0.6135500780826214, 0.3714780994452375, 0.0149718224721410, 0.1590238847123736, 0.8341718564884986, 0.0068042587991279, 0.8341718564884986, 0.1590238847123738, 0.0068042587991276, 0.0462179329282665, 0.9184680923701788, 0.0353139747015547, 0.9184680923701789, 0.0462179329282665, 0.0353139747015544, 0.1148651673800807, 0.8835508461723146, 0.0015839864476049, 0.8835508461723147, 0.1148651673800808, 0.0015839864476045, 0.3342460081847144, 0.6442373197308038, 0.0215166720844818, 0.6442373197308038, 0.3342460081847144, 0.0215166720844817, 0.0723711649483900, 0.9256035733590469, 0.0020252616925632, 0.9256035733590469, 0.0723711649483901, 0.0020252616925628, 0.2236842466647887, 0.7609545495861244, 0.0153612037490869, 0.7609545495861244, 0.2236842466647888, 0.0153612037490867, 0.1111290169905849, 0.8787050390615000, 0.0101659439479151, 0.8787050390615001, 0.1111290169905850, 0.0101659439479147, 0.2764445418077909, 0.6935416044083799, 0.0300138537838293, 0.6935416044083799, 0.2764445418077908, 0.0300138537838291, 0.1692633554656758, 0.8117666018943027, 0.0189700426400217, 0.8117666018943026, 0.1692633554656758, 0.0189700426400213, 0.1196509552487583, 0.8536082605291146, 0.0267407842221271, 0.8536082605291146, 0.1196509552487584, 0.0267407842221267, 0.2830190971292686, 0.7161270841771937, 0.0008538186935376, 0.7161270841771938, 0.2830190971292687, 0.0008538186935374, 0.0704045501511468, 0.9173369798048715, 0.0122584700439818, 0.9173369798048715, 0.0704045501511468, 0.0122584700439815, 0.2164720987514121, 0.7463578541350908, 0.0371700471134971, 0.7463578541350909, 0.2164720987514122, 0.0371700471134968, 0.0769268815632591, 0.8908789177732704, 0.0321942006634706, 0.8908789177732706, 0.0769268815632591, 0.0321942006634703, 0.4292227320385513, 0.5618451152501334, 0.0089321527113154, 0.5618451152501333, 0.4292227320385513, 0.0089321527113153, 0.0157037453637930, 0.9685925092724137, 0.0157037453637935, 0.2938899628974431, 0.4122200742051138, 0.2938899628974431, 0.3701028684237416, 0.3701028684237416, 0.2597942631525166, 0.3251479248852048, 0.4508068598872954, 0.2240452152274997, 0.4508068598872955, 0.3251479248852048, 0.2240452152274996, 0.2782727102869363, 0.5341010727223879, 0.1876262169906756, 0.5341010727223879, 0.2782727102869363, 0.1876262169906754, 0.2852102535187100, 0.7050312251574219, 0.0097585213238682, 0.7050312251574219, 0.2852102535187100, 0.0097585213238680, 0.2727256318298310, 0.6685680775484955, 0.0587062906216736, 0.6685680775484953, 0.2727256318298311, 0.0587062906216735, 0.4154695947712394, 0.5537884055426003, 0.0307419996861603, 0.5537884055426003, 0.4154695947712395, 0.0307419996861602, 0.2205774465337091, 0.7761657998291807, 0.0032567536371101, 0.7761657998291808, 0.2205774465337091, 0.0032567536371099, 0.3428856203943587, 0.6119267566451521, 0.0451876229604891, 0.6119267566451522, 0.3428856203943588, 0.0451876229604890, 0.2315038606116803, 0.6176776291642629, 0.1508185102240567, 0.6176776291642631, 0.2315038606116803, 0.1508185102240566, 0.0381017129649182, 0.9452246129976019, 0.0166736740374801, 0.9452246129976020, 0.0381017129649182, 0.0166736740374796, 0.3528911085101677, 0.4850036493442883, 0.1621052421455439, 0.4850036493442883, 0.3528911085101677, 0.1621052421455439, 0.4000760699195811, 0.5353980699804886, 0.0645258600999303, 0.5353980699804887, 0.4000760699195811, 0.0645258600999302, 0.1877843415465376, 0.6978359629848933, 0.1143796954685691, 0.6978359629848933, 0.1877843415465377, 0.1143796954685689, 0.2073769376903412, 0.7230510664568768, 0.0695719958527821, 0.7230510664568768, 0.2073769376903412, 0.0695719958527819, 0.1078038302263755, 0.8361618100730819, 0.0560343597005427, 0.8361618100730819, 0.1078038302263756, 0.0560343597005424, 0.1479014660731261, 0.7705088681427068, 0.0815896657841672, 0.7705088681427068, 0.1479014660731260, 0.0815896657841669, 0.1600426684113588, 0.7953280578174164, 0.0446292737712248, 0.7953280578174164, 0.1600426684113588, 0.0446292737712245, 0.3778766696887720, 0.5133314537120106, 0.1087918765992173, 0.5133314537120106, 0.3778766696887720, 0.1087918765992173, 0.2526963148522067, 0.4946073702955864, 0.2526963148522068, 0.0392233696648084, 0.9575704817506674, 0.0032061485845244, 0.9575704817506674, 0.0392233696648085, 0.0032061485845240, 0.3243044450771381, 0.5927190068639427, 0.0829765480589191, 0.5927190068639427, 0.3243044450771381, 0.0829765480589190, 0.2105771295148042, 0.5788457409703914, 0.2105771295148043, 0.0030575106285418, 0.9938849787429160, 0.0030575106285423, 0.4032922222742628, 0.4032922222742628, 0.1934155554514743, 0.4767516468002929, 0.4767516468002928, 0.0464967063994142, 0.3509848476225047, 0.6454944173675070, 0.0035207350099882, 0.6454944173675071, 0.3509848476225048, 0.0035207350099881, 0.0648562451597025, 0.8702875096805947, 0.0648562451597030, 0.1688963797829617, 0.6622072404340762, 0.1688963797829621, 0.3333333333333333, 0.4208708276256937, 0.5785308776456697, 0.0005982947286367, 0.5785308776456696, 0.4208708276256937, 0.0005982947286367, 0.0962980341591576, 0.8074039316816845, 0.0962980341591579, 0.2526560385602647, 0.6476602419795359, 0.0996837194601995, 0.6476602419795359, 0.2526560385602647, 0.0996837194601994, 0.4907015691302040, 0.4907015691302040, 0.0185968617395920, 0.4984645792365976, 0.4984645792365976, 0.0030708415268047, 0.3016703335605275, 0.5675057520644238, 0.1308239143750486, 0.5675057520644238, 0.3016703335605276, 0.1308239143750485, 0.4322719776068064, 0.4322719776068064, 0.1354560447863873, 0.1302416069902091, 0.7395167860195814, 0.1302416069902094, 0.4568717371543228, 0.4568717371543228, 0.0862565256913544, 0.0160613879667907, 0.9809430242931965, 0.0029955877400129, 0.9809430242931966, 0.0160613879667909, 0.0029955877400125 }; static double b_save[] = { 0.0015279490490132, 0.1671778383557105, 0.8312942125952765, 0.0015279490490132, 0.8312942125952765, 0.1671778383557108, 0.0149718224721411, 0.3714780994452375, 0.6135500780826216, 0.0149718224721411, 0.6135500780826215, 0.3714780994452377, 0.0068042587991278, 0.1590238847123736, 0.8341718564884987, 0.0068042587991278, 0.8341718564884987, 0.1590238847123739, 0.0353139747015546, 0.0462179329282665, 0.9184680923701790, 0.0353139747015546, 0.9184680923701790, 0.0462179329282669, 0.0015839864476047, 0.1148651673800806, 0.8835508461723147, 0.0015839864476047, 0.8835508461723147, 0.1148651673800810, 0.0215166720844818, 0.3342460081847145, 0.6442373197308039, 0.0215166720844818, 0.6442373197308039, 0.3342460081847147, 0.0020252616925631, 0.0723711649483900, 0.9256035733590470, 0.0020252616925631, 0.9256035733590470, 0.0723711649483903, 0.0153612037490869, 0.2236842466647887, 0.7609545495861246, 0.0153612037490869, 0.7609545495861246, 0.2236842466647890, 0.0101659439479150, 0.1111290169905849, 0.8787050390615002, 0.0101659439479150, 0.8787050390615003, 0.1111290169905853, 0.0300138537838293, 0.2764445418077909, 0.6935416044083801, 0.0300138537838293, 0.6935416044083801, 0.2764445418077912, 0.0189700426400216, 0.1692633554656758, 0.8117666018943028, 0.0189700426400216, 0.8117666018943028, 0.1692633554656761, 0.0267407842221270, 0.1196509552487583, 0.8536082605291148, 0.0267407842221270, 0.8536082605291149, 0.1196509552487586, 0.0008538186935375, 0.2830190971292687, 0.7161270841771940, 0.0008538186935375, 0.7161270841771940, 0.2830190971292690, 0.0122584700439817, 0.0704045501511468, 0.9173369798048717, 0.0122584700439817, 0.9173369798048717, 0.0704045501511471, 0.0371700471134970, 0.2164720987514121, 0.7463578541350910, 0.0371700471134970, 0.7463578541350910, 0.2164720987514124, 0.0321942006634705, 0.0769268815632591, 0.8908789177732706, 0.0321942006634705, 0.8908789177732707, 0.0769268815632594, 0.0089321527113154, 0.4292227320385513, 0.5618451152501336, 0.0089321527113154, 0.5618451152501334, 0.4292227320385515, 0.0157037453637933, 0.0157037453637930, 0.9685925092724137, 0.2938899628974431, 0.2938899628974431, 0.4122200742051139, 0.2597942631525167, 0.3701028684237417, 0.3701028684237418, 0.2240452152274997, 0.3251479248852049, 0.4508068598872956, 0.2240452152274997, 0.4508068598872956, 0.3251479248852050, 0.1876262169906757, 0.2782727102869364, 0.5341010727223882, 0.1876262169906757, 0.5341010727223882, 0.2782727102869366, 0.0097585213238681, 0.2852102535187100, 0.7050312251574220, 0.0097585213238681, 0.7050312251574220, 0.2852102535187103, 0.0587062906216736, 0.2727256318298311, 0.6685680775484956, 0.0587062906216736, 0.6685680775484956, 0.2727256318298313, 0.0307419996861603, 0.4154695947712395, 0.5537884055426004, 0.0307419996861603, 0.5537884055426003, 0.4154695947712397, 0.0032567536371102, 0.2205774465337091, 0.7761657998291810, 0.0032567536371102, 0.7761657998291810, 0.2205774465337094, 0.0451876229604891, 0.3428856203943588, 0.6119267566451523, 0.0451876229604891, 0.6119267566451522, 0.3428856203943590, 0.1508185102240568, 0.2315038606116803, 0.6176776291642632, 0.1508185102240568, 0.6176776291642631, 0.2315038606116805, 0.0166736740374799, 0.0381017129649183, 0.9452246129976019, 0.0166736740374799, 0.9452246129976022, 0.0381017129649186, 0.1621052421455440, 0.3528911085101678, 0.4850036493442885, 0.1621052421455440, 0.4850036493442884, 0.3528911085101679, 0.0645258600999304, 0.4000760699195811, 0.5353980699804888, 0.0645258600999304, 0.5353980699804887, 0.4000760699195813, 0.1143796954685691, 0.1877843415465376, 0.6978359629848935, 0.1143796954685691, 0.6978359629848934, 0.1877843415465379, 0.0695719958527821, 0.2073769376903412, 0.7230510664568770, 0.0695719958527821, 0.7230510664568770, 0.2073769376903414, 0.0560343597005426, 0.1078038302263755, 0.8361618100730821, 0.0560343597005426, 0.8361618100730820, 0.1078038302263758, 0.0815896657841671, 0.1479014660731261, 0.7705088681427070, 0.0815896657841671, 0.7705088681427070, 0.1479014660731263, 0.0446292737712247, 0.1600426684113588, 0.7953280578174167, 0.0446292737712247, 0.7953280578174167, 0.1600426684113591, 0.1087918765992174, 0.3778766696887721, 0.5133314537120108, 0.1087918765992174, 0.5133314537120107, 0.3778766696887723, 0.2526963148522068, 0.2526963148522067, 0.4946073702955866, 0.0032061485845242, 0.0392233696648084, 0.9575704817506674, 0.0032061485845242, 0.9575704817506674, 0.0392233696648088, 0.0829765480589191, 0.3243044450771382, 0.5927190068639430, 0.0829765480589191, 0.5927190068639429, 0.3243044450771383, 0.2105771295148044, 0.2105771295148043, 0.5788457409703917, 0.0030575106285422, 0.0030575106285418, 0.9938849787429160, 0.1934155554514744, 0.4032922222742629, 0.4032922222742630, 0.0464967063994142, 0.4767516468002930, 0.4767516468002931, 0.0035207350099882, 0.3509848476225048, 0.6454944173675073, 0.0035207350099882, 0.6454944173675070, 0.3509848476225050, 0.0648562451597028, 0.0648562451597025, 0.8702875096805948, 0.1688963797829620, 0.1688963797829618, 0.6622072404340763, 0.3333333333333334, 0.0005982947286368, 0.4208708276256937, 0.5785308776456698, 0.0005982947286368, 0.5785308776456696, 0.4208708276256939, 0.0962980341591579, 0.0962980341591576, 0.8074039316816847, 0.0996837194601995, 0.2526560385602647, 0.6476602419795360, 0.0996837194601995, 0.6476602419795360, 0.2526560385602649, 0.0185968617395921, 0.4907015691302040, 0.4907015691302042, 0.0030708415268048, 0.4984645792365977, 0.4984645792365979, 0.1308239143750487, 0.3016703335605276, 0.5675057520644240, 0.1308239143750487, 0.5675057520644239, 0.3016703335605278, 0.1354560447863873, 0.4322719776068065, 0.4322719776068065, 0.1302416069902094, 0.1302416069902092, 0.7395167860195816, 0.0862565256913544, 0.4568717371543228, 0.4568717371543230, 0.0029955877400127, 0.0160613879667907, 0.9809430242931966, 0.0029955877400127, 0.9809430242931966, 0.0160613879667911 }; static double c_save[] = { 0.8312942125952764, 0.0015279490490133, 0.1671778383557102, 0.1671778383557104, 0.0015279490490130, 0.8312942125952762, 0.6135500780826214, 0.0149718224721410, 0.3714780994452372, 0.3714780994452375, 0.0149718224721410, 0.6135500780826213, 0.8341718564884986, 0.0068042587991278, 0.1590238847123734, 0.1590238847123737, 0.0068042587991276, 0.8341718564884986, 0.9184680923701788, 0.0353139747015547, 0.0462179329282663, 0.0462179329282665, 0.0353139747015544, 0.9184680923701787, 0.8835508461723147, 0.0015839864476048, 0.1148651673800805, 0.1148651673800806, 0.0015839864476045, 0.8835508461723145, 0.6442373197308037, 0.0215166720844817, 0.3342460081847143, 0.3342460081847144, 0.0215166720844816, 0.6442373197308036, 0.9256035733590469, 0.0020252616925631, 0.0723711649483898, 0.0723711649483900, 0.0020252616925630, 0.9256035733590467, 0.7609545495861244, 0.0153612037490869, 0.2236842466647885, 0.2236842466647887, 0.0153612037490866, 0.7609545495861243, 0.8787050390615000, 0.0101659439479151, 0.1111290169905846, 0.1111290169905849, 0.0101659439479147, 0.8787050390615000, 0.6935416044083799, 0.0300138537838292, 0.2764445418077907, 0.2764445418077909, 0.0300138537838291, 0.6935416044083798, 0.8117666018943027, 0.0189700426400215, 0.1692633554656755, 0.1692633554656758, 0.0189700426400213, 0.8117666018943026, 0.8536082605291146, 0.0267407842221270, 0.1196509552487581, 0.1196509552487584, 0.0267407842221268, 0.8536082605291145, 0.7161270841771938, 0.0008538186935376, 0.2830190971292684, 0.2830190971292686, 0.0008538186935373, 0.7161270841771936, 0.9173369798048715, 0.0122584700439817, 0.0704045501511464, 0.0704045501511468, 0.0122584700439815, 0.9173369798048714, 0.7463578541350908, 0.0371700471134971, 0.2164720987514119, 0.2164720987514120, 0.0371700471134968, 0.7463578541350908, 0.8908789177732704, 0.0321942006634705, 0.0769268815632589, 0.0769268815632590, 0.0321942006634702, 0.8908789177732704, 0.5618451152501333, 0.0089321527113153, 0.4292227320385511, 0.4292227320385513, 0.0089321527113153, 0.5618451152501331, 0.9685925092724137, 0.0157037453637933, 0.0157037453637928, 0.4122200742051138, 0.2938899628974431, 0.2938899628974430, 0.3701028684237416, 0.2597942631525166, 0.3701028684237416, 0.4508068598872954, 0.2240452152274997, 0.3251479248852048, 0.3251479248852048, 0.2240452152274996, 0.4508068598872954, 0.5341010727223880, 0.1876262169906757, 0.2782727102869362, 0.2782727102869364, 0.1876262169906756, 0.5341010727223879, 0.7050312251574219, 0.0097585213238681, 0.2852102535187098, 0.2852102535187100, 0.0097585213238680, 0.7050312251574217, 0.6685680775484953, 0.0587062906216735, 0.2727256318298309, 0.2727256318298311, 0.0587062906216734, 0.6685680775484952, 0.5537884055426002, 0.0307419996861601, 0.4154695947712393, 0.4154695947712394, 0.0307419996861602, 0.5537884055426001, 0.7761657998291807, 0.0032567536371102, 0.2205774465337088, 0.2205774465337091, 0.0032567536371099, 0.7761657998291808, 0.6119267566451522, 0.0451876229604891, 0.3428856203943587, 0.3428856203943587, 0.0451876229604889, 0.6119267566451519, 0.6176776291642629, 0.1508185102240568, 0.2315038606116802, 0.2315038606116802, 0.1508185102240566, 0.6176776291642629, 0.9452246129976020, 0.0166736740374799, 0.0381017129649180, 0.0381017129649182, 0.0166736740374797, 0.9452246129976017, 0.4850036493442883, 0.1621052421455439, 0.3528911085101676, 0.3528911085101677, 0.1621052421455439, 0.4850036493442882, 0.5353980699804886, 0.0645258600999303, 0.4000760699195809, 0.4000760699195810, 0.0645258600999302, 0.5353980699804886, 0.6978359629848934, 0.1143796954685691, 0.1877843415465373, 0.1877843415465376, 0.1143796954685690, 0.6978359629848931, 0.7230510664568768, 0.0695719958527820, 0.2073769376903409, 0.2073769376903412, 0.0695719958527818, 0.7230510664568766, 0.8361618100730819, 0.0560343597005426, 0.1078038302263753, 0.1078038302263755, 0.0560343597005425, 0.8361618100730819, 0.7705088681427068, 0.0815896657841671, 0.1479014660731258, 0.1479014660731261, 0.0815896657841669, 0.7705088681427068, 0.7953280578174166, 0.0446292737712247, 0.1600426684113585, 0.1600426684113588, 0.0446292737712245, 0.7953280578174164, 0.5133314537120105, 0.1087918765992172, 0.3778766696887719, 0.3778766696887720, 0.1087918765992172, 0.5133314537120104, 0.4946073702955865, 0.2526963148522068, 0.2526963148522066, 0.9575704817506674, 0.0032061485845242, 0.0392233696648082, 0.0392233696648084, 0.0032061485845241, 0.9575704817506673, 0.5927190068639426, 0.0829765480589191, 0.3243044450771380, 0.3243044450771381, 0.0829765480589190, 0.5927190068639427, 0.5788457409703913, 0.2105771295148043, 0.2105771295148041, 0.9938849787429159, 0.0030575106285421, 0.0030575106285416, 0.4032922222742629, 0.1934155554514743, 0.4032922222742628, 0.4767516468002930, 0.0464967063994142, 0.4767516468002927, 0.6454944173675070, 0.0035207350099882, 0.3509848476225045, 0.3509848476225046, 0.0035207350099882, 0.6454944173675068, 0.8702875096805947, 0.0648562451597028, 0.0648562451597022, 0.6622072404340763, 0.1688963797829620, 0.1688963797829616, 0.3333333333333333, 0.5785308776456696, 0.0005982947286366, 0.4208708276256935, 0.4208708276256937, 0.0005982947286368, 0.5785308776456694, 0.8074039316816846, 0.0962980341591579, 0.0962980341591574, 0.6476602419795358, 0.0996837194601994, 0.2526560385602645, 0.2526560385602646, 0.0996837194601993, 0.6476602419795356, 0.4907015691302040, 0.0185968617395921, 0.4907015691302037, 0.4984645792365976, 0.0030708415268047, 0.4984645792365974, 0.5675057520644238, 0.1308239143750486, 0.3016703335605274, 0.3016703335605275, 0.1308239143750486, 0.5675057520644238, 0.4322719776068064, 0.1354560447863872, 0.4322719776068062, 0.7395167860195815, 0.1302416069902095, 0.1302416069902089, 0.4568717371543228, 0.0862565256913544, 0.4568717371543227, 0.9809430242931965, 0.0029955877400128, 0.0160613879667905, 0.0160613879667907, 0.0029955877400126, 0.9809430242931964 }; static double w_save[] = { 0.0003775523678536, 0.0003775523678536, 0.0003775523678536, 0.0003775523678536, 0.0003775523678536, 0.0003775523678536, 0.0015516849698550, 0.0015516849698550, 0.0015516849698550, 0.0015516849698550, 0.0015516849698550, 0.0015516849698550, 0.0008644145607466, 0.0008644145607466, 0.0008644145607466, 0.0008644145607466, 0.0008644145607466, 0.0008644145607466, 0.0009971849318732, 0.0009971849318732, 0.0009971849318732, 0.0009971849318732, 0.0009971849318732, 0.0009971849318732, 0.0004090770312980, 0.0004090770312980, 0.0004090770312980, 0.0004090770312980, 0.0004090770312980, 0.0004090770312980, 0.0020436671600844, 0.0020436671600844, 0.0020436671600844, 0.0020436671600844, 0.0020436671600844, 0.0020436671600844, 0.0004126443326276, 0.0004126443326276, 0.0004126443326276, 0.0004126443326276, 0.0004126443326276, 0.0004126443326276, 0.0019146967543968, 0.0019146967543968, 0.0019146967543968, 0.0019146967543968, 0.0019146967543968, 0.0019146967543968, 0.0011640031359899, 0.0011640031359899, 0.0011640031359899, 0.0011640031359899, 0.0011640031359899, 0.0011640031359899, 0.0029186737106524, 0.0029186737106524, 0.0029186737106524, 0.0029186737106524, 0.0029186737106524, 0.0029186737106524, 0.0019423381723224, 0.0019423381723224, 0.0019423381723224, 0.0019423381723224, 0.0019423381723224, 0.0019423381723224, 0.0020437160642330, 0.0020437160642330, 0.0020437160642330, 0.0020437160642330, 0.0020437160642330, 0.0020437160642330, 0.0004561788584349, 0.0004561788584349, 0.0004561788584349, 0.0004561788584349, 0.0004561788584349, 0.0004561788584349, 0.0011181526506985, 0.0011181526506985, 0.0011181526506985, 0.0011181526506985, 0.0011181526506985, 0.0011181526506985, 0.0030364724116124, 0.0030364724116124, 0.0030364724116124, 0.0030364724116124, 0.0030364724116124, 0.0030364724116124, 0.0019401856791114, 0.0019401856791114, 0.0019401856791114, 0.0019401856791114, 0.0019401856791114, 0.0019401856791114, 0.0019149234843930, 0.0019149234843930, 0.0019149234843930, 0.0019149234843930, 0.0019149234843930, 0.0019149234843930, 0.0006256066196749, 0.0006256066196749, 0.0006256066196749, 0.0085945289589868, 0.0085945289589868, 0.0085945289589868, 0.0085993323415620, 0.0085993323415620, 0.0085993323415620, 0.0082321340562276, 0.0082321340562276, 0.0082321340562276, 0.0082321340562276, 0.0082321340562276, 0.0082321340562276, 0.0075395204858702, 0.0075395204858702, 0.0075395204858702, 0.0075395204858702, 0.0075395204858702, 0.0075395204858702, 0.0018551746248727, 0.0018551746248727, 0.0018551746248727, 0.0018551746248727, 0.0018551746248727, 0.0018551746248727, 0.0044048213741681, 0.0044048213741681, 0.0044048213741681, 0.0044048213741681, 0.0044048213741681, 0.0044048213741681, 0.0038072050061859, 0.0038072050061859, 0.0038072050061859, 0.0038072050061859, 0.0038072050061859, 0.0038072050061859, 0.0009694445790545, 0.0009694445790545, 0.0009694445790545, 0.0009694445790545, 0.0009694445790545, 0.0009694445790545, 0.0042240803334808, 0.0042240803334808, 0.0042240803334808, 0.0042240803334808, 0.0042240803334808, 0.0042240803334808, 0.0066193255529404, 0.0066193255529404, 0.0066193255529404, 0.0066193255529404, 0.0066193255529404, 0.0066193255529404, 0.0010014072888268, 0.0010014072888268, 0.0010014072888268, 0.0010014072888268, 0.0010014072888268, 0.0010014072888268, 0.0075563110745215, 0.0075563110745215, 0.0075563110745215, 0.0075563110745215, 0.0075563110745215, 0.0075563110745215, 0.0052987050439936, 0.0052987050439936, 0.0052987050439936, 0.0052987050439936, 0.0052987050439936, 0.0052987050439936, 0.0055546897961284, 0.0055546897961284, 0.0055546897961284, 0.0055546897961284, 0.0055546897961284, 0.0055546897961284, 0.0045059845609494, 0.0045059845609494, 0.0045059845609494, 0.0045059845609494, 0.0045059845609494, 0.0045059845609494, 0.0031131351389203, 0.0031131351389203, 0.0031131351389203, 0.0031131351389203, 0.0031131351389203, 0.0031131351389203, 0.0043898382162027, 0.0043898382162027, 0.0043898382162027, 0.0043898382162027, 0.0043898382162027, 0.0043898382162027, 0.0032385523720829, 0.0032385523720829, 0.0032385523720829, 0.0032385523720829, 0.0032385523720829, 0.0032385523720829, 0.0065742981116095, 0.0065742981116095, 0.0065742981116095, 0.0065742981116095, 0.0065742981116095, 0.0065742981116095, 0.0080391355993214, 0.0080391355993214, 0.0080391355993214, 0.0004619375803747, 0.0004619375803747, 0.0004619375803747, 0.0004619375803747, 0.0004619375803747, 0.0004619375803747, 0.0056203298622696, 0.0056203298622696, 0.0056203298622696, 0.0056203298622696, 0.0056203298622696, 0.0056203298622696, 0.0072118235949089, 0.0072118235949089, 0.0072118235949089, 0.0001229638851333, 0.0001229638851333, 0.0001229638851333, 0.0080668049674519, 0.0080668049674519, 0.0080668049674519, 0.0046789762284529, 0.0046789762284529, 0.0046789762284529, 0.0012327695569297, 0.0012327695569297, 0.0012327695569297, 0.0012327695569297, 0.0012327695569297, 0.0012327695569297, 0.0027172985719248, 0.0027172985719248, 0.0027172985719248, 0.0062399420305303, 0.0062399420305303, 0.0062399420305303, 0.0087854844528631, 0.0004490102381961, 0.0004490102381961, 0.0004490102381961, 0.0004490102381961, 0.0004490102381961, 0.0004490102381961, 0.0038909093796050, 0.0038909093796050, 0.0038909093796050, 0.0056881832653567, 0.0056881832653567, 0.0056881832653567, 0.0056881832653567, 0.0056881832653567, 0.0056881832653567, 0.0030289691062773, 0.0030289691062773, 0.0030289691062773, 0.0012050280622555, 0.0012050280622555, 0.0012050280622555, 0.0067479088961223, 0.0067479088961223, 0.0067479088961223, 0.0067479088961223, 0.0067479088961223, 0.0067479088961223, 0.0072248857349589, 0.0072248857349589, 0.0072248857349589, 0.0051363917261404, 0.0051363917261404, 0.0051363917261404, 0.0060844538754953, 0.0060844538754953, 0.0060844538754953, 0.0002785606250486, 0.0002785606250486, 0.0002785606250486, 0.0002785606250486, 0.0002785606250486, 0.0002785606250486 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule41 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule41() returns the rule of precision 41. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.0018100550930815, 0.9963798898138365, 0.0018100550930819, 0.3146077513838778, 0.3707844972322443, 0.3146077513838778, 0.3718324578394357, 0.3718324578394359, 0.2563350843211283, 0.9338478958692606, 0.0393793019220240, 0.0267728022087153, 0.0393793019220239, 0.9338478958692605, 0.0267728022087157, 0.0708749727266859, 0.9076576411610010, 0.0214673861123131, 0.9076576411610010, 0.0708749727266859, 0.0214673861123128, 0.0227676589099524, 0.9652472298472927, 0.0119851112427549, 0.9652472298472928, 0.0227676589099525, 0.0119851112427545, 0.2127026585190979, 0.6908861388566330, 0.0964112026242691, 0.6908861388566331, 0.2127026585190979, 0.0964112026242688, 0.1970799949415202, 0.6749417822120469, 0.1279782228464328, 0.6749417822120470, 0.1970799949415203, 0.1279782228464326, 0.4818489601758344, 0.4818489601758343, 0.0363020796483312, 0.0639130414360007, 0.8936878519528431, 0.0423991066111563, 0.8936878519528432, 0.0639130414360007, 0.0423991066111560, 0.0916254632757577, 0.8966875393230677, 0.0116869974011748, 0.8966875393230677, 0.0916254632757578, 0.0116869974011745, 0.0889175403557380, 0.8478409267056788, 0.0632415329385833, 0.8478409267056788, 0.0889175403557381, 0.0632415329385829, 0.4592305589036990, 0.5259284962555215, 0.0148409448407795, 0.5259284962555214, 0.4592305589036990, 0.0148409448407795, 0.0338843822348439, 0.9642755781495430, 0.0018400396156133, 0.9642755781495431, 0.0338843822348439, 0.0018400396156128, 0.3200752104066154, 0.4218676758535129, 0.2580571137398716, 0.4218676758535129, 0.3200752104066154, 0.2580571137398715, 0.1422819983084207, 0.7154360033831583, 0.1422819983084210, 0.4220684925318889, 0.5417122820340925, 0.0362192254340186, 0.5417122820340925, 0.4220684925318889, 0.0362192254340186, 0.0478764410729284, 0.9415795928827051, 0.0105439660443666, 0.9415795928827051, 0.0478764410729285, 0.0105439660443662, 0.1746336148663416, 0.6507327702673166, 0.1746336148663419, 0.4251980784151399, 0.4251980784151399, 0.1496038431697200, 0.3617990227060762, 0.4871740897943582, 0.1510268874995655, 0.4871740897943583, 0.3617990227060763, 0.1510268874995655, 0.2099773723379177, 0.5800452553241643, 0.2099773723379179, 0.0684569430922210, 0.9290609960060465, 0.0024820609017325, 0.9290609960060466, 0.0684569430922210, 0.0024820609017321, 0.2362884725964560, 0.6087537603815811, 0.1549577670219628, 0.6087537603815811, 0.2362884725964560, 0.1549577670219627, 0.2978954189850496, 0.5501430273498515, 0.1519615536650988, 0.5501430273498515, 0.2978954189850496, 0.1519615536650987, 0.1125572515239218, 0.8850652027457061, 0.0023775457303723, 0.8850652027457061, 0.1125572515239218, 0.0023775457303719, 0.0120658629713076, 0.9848848989428542, 0.0030492380858384, 0.9848848989428541, 0.0120658629713077, 0.0030492380858379, 0.3906530970863169, 0.5942714371631589, 0.0150754657505243, 0.5942714371631588, 0.3906530970863170, 0.0150754657505242, 0.4274107273739702, 0.5697047185184613, 0.0028845541075684, 0.5697047185184614, 0.4274107273739702, 0.0028845541075684, 0.2627399736253427, 0.4745200527493144, 0.2627399736253428, 0.4118455220977197, 0.4833893401764346, 0.1047651377258456, 0.4833893401764346, 0.4118455220977197, 0.1047651377258456, 0.4986036392311143, 0.4986036392311143, 0.0027927215377713, 0.3222211945168437, 0.6629470379075842, 0.0148317675755723, 0.6629470379075841, 0.3222211945168438, 0.0148317675755720, 0.3545249016308813, 0.6087299048044915, 0.0367451935646271, 0.6087299048044915, 0.3545249016308814, 0.0367451935646270, 0.3320276172987797, 0.4651394056449660, 0.2028329770562542, 0.4651394056449660, 0.3320276172987797, 0.2028329770562542, 0.2530297390847723, 0.6813809432255311, 0.0655893176896967, 0.6813809432255310, 0.2530297390847723, 0.0655893176896965, 0.3570399048945097, 0.6401266872236777, 0.0028334078818126, 0.6401266872236777, 0.3570399048945097, 0.0028334078818124, 0.2870606892116554, 0.6768867950216703, 0.0360525157666745, 0.6768867950216702, 0.2870606892116554, 0.0360525157666742, 0.1361313516311361, 0.8497124512417364, 0.0141561971271276, 0.8497124512417363, 0.1361313516311361, 0.0141561971271272, 0.1322241256617750, 0.8040030646660921, 0.0637728096721329, 0.8040030646660922, 0.1322241256617751, 0.0637728096721326, 0.1079242198395523, 0.8585223406145746, 0.0335534395458731, 0.8585223406145744, 0.1079242198395524, 0.0335534395458729, 0.1528869021413866, 0.7475340532550706, 0.0995790446035428, 0.7475340532550706, 0.1528869021413866, 0.0995790446035426, 0.1881017719296066, 0.7472490760453540, 0.0646491520250393, 0.7472490760453540, 0.1881017719296067, 0.0646491520250392, 0.2549824291508879, 0.7301188439783041, 0.0148987268708080, 0.7301188439783041, 0.2549824291508879, 0.0148987268708078, 0.2230780804812777, 0.7740674722407084, 0.0028544472780139, 0.7740674722407084, 0.2230780804812778, 0.0028544472780137, 0.3995665255269703, 0.3995665255269703, 0.2008669489460594, 0.1640507360210325, 0.8331184921577857, 0.0028307718211819, 0.8331184921577858, 0.1640507360210327, 0.0028307718211816, 0.2881511174189886, 0.7090129357844225, 0.0028359467965890, 0.7090129357844225, 0.2881511174189885, 0.0028359467965888, 0.3409577888740615, 0.5534095248477606, 0.1056326862781778, 0.5534095248477606, 0.3409577888740616, 0.1056326862781778, 0.2682934480692839, 0.5262976561479694, 0.2054088957827467, 0.5262976561479694, 0.2682934480692839, 0.2054088957827466, 0.3194090035283247, 0.6131123654037490, 0.0674786310679263, 0.6131123654037490, 0.3194090035283247, 0.0674786310679262, 0.1922954651859523, 0.7927714274510961, 0.0149331073629516, 0.7927714274510962, 0.1922954651859524, 0.0149331073629514, 0.1604140534029236, 0.8042006531916337, 0.0353852934054428, 0.8042006531916338, 0.1604140534029238, 0.0353852934054425, 0.2212534989804217, 0.7424945051857205, 0.0362519958338579, 0.7424945051857206, 0.2212534989804218, 0.0362519958338575, 0.2711942240688135, 0.6222060789581492, 0.1065996969730373, 0.6222060789581491, 0.2711942240688137, 0.1065996969730372, 0.3923234112997704, 0.5411068810465550, 0.0665697076536745, 0.5411068810465550, 0.3923234112997703, 0.0665697076536745, 0.4667610577855150, 0.4667610577855150, 0.0664778844289700, 0.1030954855760305, 0.7938090288479388, 0.1030954855760309 }; static double b_save[] = { 0.0018100550930818, 0.0018100550930815, 0.9963798898138368, 0.3146077513838779, 0.3146077513838779, 0.3707844972322444, 0.2563350843211284, 0.3718324578394359, 0.3718324578394359, 0.0267728022087155, 0.9338478958692606, 0.0393793019220242, 0.0267728022087155, 0.0393793019220238, 0.9338478958692606, 0.0214673861123130, 0.0708749727266859, 0.9076576411610012, 0.0214673861123130, 0.9076576411610013, 0.0708749727266862, 0.0119851112427548, 0.0227676589099523, 0.9652472298472929, 0.0119851112427548, 0.9652472298472929, 0.0227676589099527, 0.0964112026242690, 0.2127026585190980, 0.6908861388566332, 0.0964112026242690, 0.6908861388566333, 0.2127026585190982, 0.1279782228464328, 0.1970799949415202, 0.6749417822120471, 0.1279782228464328, 0.6749417822120471, 0.1970799949415204, 0.0363020796483313, 0.4818489601758345, 0.4818489601758346, 0.0423991066111562, 0.0639130414360007, 0.8936878519528434, 0.0423991066111562, 0.8936878519528434, 0.0639130414360010, 0.0116869974011747, 0.0916254632757577, 0.8966875393230677, 0.0116869974011747, 0.8966875393230677, 0.0916254632757580, 0.0632415329385832, 0.0889175403557380, 0.8478409267056790, 0.0632415329385832, 0.8478409267056790, 0.0889175403557383, 0.0148409448407795, 0.4592305589036991, 0.5259284962555217, 0.0148409448407795, 0.5259284962555215, 0.4592305589036992, 0.0018400396156131, 0.0338843822348439, 0.9642755781495430, 0.0018400396156131, 0.9642755781495433, 0.0338843822348442, 0.2580571137398717, 0.3200752104066155, 0.4218676758535131, 0.2580571137398717, 0.4218676758535130, 0.3200752104066156, 0.1422819983084210, 0.1422819983084208, 0.7154360033831585, 0.0362192254340186, 0.4220684925318890, 0.5417122820340926, 0.0362192254340186, 0.5417122820340925, 0.4220684925318892, 0.0105439660443664, 0.0478764410729283, 0.9415795928827053, 0.0105439660443664, 0.9415795928827053, 0.0478764410729287, 0.1746336148663418, 0.1746336148663417, 0.6507327702673166, 0.1496038431697201, 0.4251980784151401, 0.4251980784151402, 0.1510268874995656, 0.3617990227060763, 0.4871740897943584, 0.1510268874995656, 0.4871740897943583, 0.3617990227060764, 0.2099773723379179, 0.2099773723379178, 0.5800452553241644, 0.0024820609017324, 0.0684569430922209, 0.9290609960060469, 0.0024820609017324, 0.9290609960060469, 0.0684569430922213, 0.1549577670219629, 0.2362884725964561, 0.6087537603815814, 0.1549577670219629, 0.6087537603815814, 0.2362884725964562, 0.1519615536650989, 0.2978954189850497, 0.5501430273498518, 0.1519615536650989, 0.5501430273498517, 0.2978954189850498, 0.0023775457303722, 0.1125572515239218, 0.8850652027457062, 0.0023775457303722, 0.8850652027457062, 0.1125572515239221, 0.0030492380858382, 0.0120658629713075, 0.9848848989428544, 0.0030492380858382, 0.9848848989428544, 0.0120658629713080, 0.0150754657505243, 0.3906530970863170, 0.5942714371631590, 0.0150754657505243, 0.5942714371631588, 0.3906530970863172, 0.0028845541075685, 0.4274107273739702, 0.5697047185184615, 0.0028845541075685, 0.5697047185184614, 0.4274107273739705, 0.2627399736253429, 0.2627399736253428, 0.4745200527493146, 0.1047651377258457, 0.4118455220977198, 0.4833893401764348, 0.1047651377258457, 0.4833893401764347, 0.4118455220977200, 0.0027927215377714, 0.4986036392311144, 0.4986036392311146, 0.0148317675755722, 0.3222211945168437, 0.6629470379075844, 0.0148317675755722, 0.6629470379075841, 0.3222211945168439, 0.0367451935646272, 0.3545249016308813, 0.6087299048044917, 0.0367451935646272, 0.6087299048044916, 0.3545249016308816, 0.2028329770562543, 0.3320276172987798, 0.4651394056449663, 0.2028329770562543, 0.4651394056449661, 0.3320276172987799, 0.0655893176896967, 0.2530297390847723, 0.6813809432255312, 0.0655893176896967, 0.6813809432255311, 0.2530297390847726, 0.0028334078818125, 0.3570399048945098, 0.6401266872236778, 0.0028334078818125, 0.6401266872236778, 0.3570399048945100, 0.0360525157666744, 0.2870606892116554, 0.6768867950216704, 0.0360525157666744, 0.6768867950216704, 0.2870606892116557, 0.0141561971271275, 0.1361313516311361, 0.8497124512417367, 0.0141561971271275, 0.8497124512417367, 0.1361313516311364, 0.0637728096721328, 0.1322241256617750, 0.8040030646660923, 0.0637728096721328, 0.8040030646660923, 0.1322241256617753, 0.0335534395458731, 0.1079242198395524, 0.8585223406145748, 0.0335534395458731, 0.8585223406145748, 0.1079242198395527, 0.0995790446035428, 0.1528869021413866, 0.7475340532550708, 0.0995790446035428, 0.7475340532550708, 0.1528869021413868, 0.0646491520250394, 0.1881017719296067, 0.7472490760453542, 0.0646491520250394, 0.7472490760453542, 0.1881017719296069, 0.0148987268708080, 0.2549824291508879, 0.7301188439783043, 0.0148987268708080, 0.7301188439783043, 0.2549824291508882, 0.0028544472780139, 0.2230780804812777, 0.7740674722407086, 0.0028544472780139, 0.7740674722407086, 0.2230780804812780, 0.2008669489460595, 0.3995665255269704, 0.3995665255269705, 0.0028307718211818, 0.1640507360210326, 0.8331184921577858, 0.0028307718211818, 0.8331184921577858, 0.1640507360210328, 0.0028359467965890, 0.2881511174189886, 0.7090129357844227, 0.0028359467965890, 0.7090129357844227, 0.2881511174189888, 0.1056326862781779, 0.3409577888740616, 0.5534095248477607, 0.1056326862781779, 0.5534095248477606, 0.3409577888740618, 0.2054088957827467, 0.2682934480692840, 0.5262976561479695, 0.2054088957827467, 0.5262976561479695, 0.2682934480692841, 0.0674786310679263, 0.3194090035283247, 0.6131123654037492, 0.0674786310679263, 0.6131123654037491, 0.3194090035283249, 0.0149331073629516, 0.1922954651859523, 0.7927714274510964, 0.0149331073629516, 0.7927714274510963, 0.1922954651859526, 0.0353852934054427, 0.1604140534029236, 0.8042006531916338, 0.0353852934054427, 0.8042006531916338, 0.1604140534029239, 0.0362519958338577, 0.2212534989804218, 0.7424945051857206, 0.0362519958338577, 0.7424945051857206, 0.2212534989804221, 0.1065996969730374, 0.2711942240688135, 0.6222060789581494, 0.1065996969730374, 0.6222060789581492, 0.2711942240688138, 0.0665697076536746, 0.3923234112997704, 0.5411068810465552, 0.0665697076536746, 0.5411068810465551, 0.3923234112997706, 0.0664778844289701, 0.4667610577855150, 0.4667610577855152, 0.1030954855760308, 0.1030954855760305, 0.7938090288479389 }; static double c_save[] = { 0.9963798898138366, 0.0018100550930820, 0.0018100550930812, 0.3707844972322443, 0.3146077513838778, 0.3146077513838778, 0.3718324578394358, 0.2563350843211282, 0.3718324578394358, 0.0393793019220238, 0.0267728022087154, 0.9338478958692605, 0.9338478958692605, 0.0267728022087156, 0.0393793019220237, 0.9076576411610010, 0.0214673861123131, 0.0708749727266856, 0.0708749727266860, 0.0214673861123128, 0.9076576411610010, 0.9652472298472928, 0.0119851112427549, 0.0227676589099521, 0.0227676589099524, 0.0119851112427546, 0.9652472298472928, 0.6908861388566330, 0.0964112026242691, 0.2127026585190978, 0.2127026585190979, 0.0964112026242688, 0.6908861388566330, 0.6749417822120470, 0.1279782228464328, 0.1970799949415201, 0.1970799949415202, 0.1279782228464326, 0.6749417822120470, 0.4818489601758343, 0.0363020796483312, 0.4818489601758342, 0.8936878519528431, 0.0423991066111563, 0.0639130414360004, 0.0639130414360007, 0.0423991066111559, 0.8936878519528431, 0.8966875393230676, 0.0116869974011747, 0.0916254632757575, 0.0916254632757577, 0.0116869974011745, 0.8966875393230674, 0.8478409267056789, 0.0632415329385832, 0.0889175403557377, 0.0889175403557380, 0.0632415329385829, 0.8478409267056788, 0.5259284962555214, 0.0148409448407794, 0.4592305589036988, 0.4592305589036991, 0.0148409448407795, 0.5259284962555213, 0.9642755781495431, 0.0018400396156131, 0.0338843822348437, 0.0338843822348438, 0.0018400396156127, 0.9642755781495430, 0.4218676758535130, 0.2580571137398716, 0.3200752104066153, 0.3200752104066154, 0.2580571137398716, 0.4218676758535129, 0.7154360033831584, 0.1422819983084209, 0.1422819983084206, 0.5417122820340924, 0.0362192254340185, 0.4220684925318888, 0.4220684925318889, 0.0362192254340186, 0.5417122820340923, 0.9415795928827051, 0.0105439660443666, 0.0478764410729281, 0.0478764410729285, 0.0105439660443661, 0.9415795928827052, 0.6507327702673167, 0.1746336148663418, 0.1746336148663415, 0.4251980784151400, 0.1496038431697200, 0.4251980784151398, 0.4871740897943582, 0.1510268874995655, 0.3617990227060761, 0.3617990227060762, 0.1510268874995654, 0.4871740897943581, 0.5800452553241644, 0.2099773723379179, 0.2099773723379177, 0.9290609960060467, 0.0024820609017325, 0.0684569430922207, 0.0684569430922210, 0.0024820609017321, 0.9290609960060465, 0.6087537603815811, 0.1549577670219628, 0.2362884725964558, 0.2362884725964560, 0.1549577670219626, 0.6087537603815811, 0.5501430273498515, 0.1519615536650988, 0.2978954189850495, 0.2978954189850496, 0.1519615536650988, 0.5501430273498515, 0.8850652027457060, 0.0023775457303721, 0.1125572515239215, 0.1125572515239217, 0.0023775457303720, 0.8850652027457059, 0.9848848989428542, 0.0030492380858382, 0.0120658629713072, 0.0120658629713077, 0.0030492380858379, 0.9848848989428541, 0.5942714371631588, 0.0150754657505242, 0.3906530970863167, 0.3906530970863169, 0.0150754657505242, 0.5942714371631587, 0.5697047185184613, 0.0028845541075685, 0.4274107273739701, 0.4274107273739701, 0.0028845541075684, 0.5697047185184612, 0.4745200527493144, 0.2627399736253428, 0.2627399736253426, 0.4833893401764346, 0.1047651377258456, 0.4118455220977196, 0.4118455220977197, 0.1047651377258456, 0.4833893401764344, 0.4986036392311142, 0.0027927215377713, 0.4986036392311141, 0.6629470379075842, 0.0148317675755721, 0.3222211945168434, 0.3222211945168437, 0.0148317675755720, 0.6629470379075840, 0.6087299048044915, 0.0367451935646272, 0.3545249016308811, 0.3545249016308814, 0.0367451935646270, 0.6087299048044914, 0.4651394056449660, 0.2028329770562542, 0.3320276172987795, 0.3320276172987797, 0.2028329770562542, 0.4651394056449660, 0.6813809432255311, 0.0655893176896966, 0.2530297390847721, 0.2530297390847723, 0.0655893176896966, 0.6813809432255310, 0.6401266872236778, 0.0028334078818125, 0.3570399048945095, 0.3570399048945098, 0.0028334078818125, 0.6401266872236776, 0.6768867950216702, 0.0360525157666743, 0.2870606892116552, 0.2870606892116555, 0.0360525157666742, 0.6768867950216702, 0.8497124512417364, 0.0141561971271275, 0.1361313516311358, 0.1361313516311362, 0.0141561971271272, 0.8497124512417363, 0.8040030646660922, 0.0637728096721329, 0.1322241256617749, 0.1322241256617750, 0.0637728096721326, 0.8040030646660921, 0.8585223406145746, 0.0335534395458731, 0.1079242198395520, 0.1079242198395524, 0.0335534395458729, 0.8585223406145744, 0.7475340532550706, 0.0995790446035428, 0.1528869021413863, 0.1528869021413866, 0.0995790446035426, 0.7475340532550705, 0.7472490760453540, 0.0646491520250394, 0.1881017719296064, 0.1881017719296067, 0.0646491520250391, 0.7472490760453538, 0.7301188439783041, 0.0148987268708080, 0.2549824291508876, 0.2549824291508879, 0.0148987268708077, 0.7301188439783040, 0.7740674722407084, 0.0028544472780139, 0.2230780804812775, 0.2230780804812778, 0.0028544472780136, 0.7740674722407084, 0.3995665255269703, 0.2008669489460594, 0.3995665255269701, 0.8331184921577857, 0.0028307718211818, 0.1640507360210324, 0.1640507360210325, 0.0028307718211816, 0.8331184921577856, 0.7090129357844225, 0.0028359467965889, 0.2881511174189882, 0.2881511174189886, 0.0028359467965887, 0.7090129357844224, 0.5534095248477605, 0.1056326862781777, 0.3409577888740615, 0.3409577888740615, 0.1056326862781778, 0.5534095248477604, 0.5262976561479693, 0.2054088957827466, 0.2682934480692838, 0.2682934480692838, 0.2054088957827466, 0.5262976561479693, 0.6131123654037490, 0.0674786310679262, 0.3194090035283245, 0.3194090035283246, 0.0674786310679262, 0.6131123654037488, 0.7927714274510961, 0.0149331073629516, 0.1922954651859521, 0.1922954651859523, 0.0149331073629514, 0.7927714274510961, 0.8042006531916337, 0.0353852934054427, 0.1604140534029234, 0.1604140534029235, 0.0353852934054425, 0.8042006531916336, 0.7424945051857205, 0.0362519958338578, 0.2212534989804216, 0.2212534989804217, 0.0362519958338576, 0.7424945051857204, 0.6222060789581491, 0.1065996969730373, 0.2711942240688133, 0.2711942240688135, 0.1065996969730372, 0.6222060789581491, 0.5411068810465549, 0.0665697076536745, 0.3923234112997702, 0.3923234112997703, 0.0665697076536745, 0.5411068810465549, 0.4667610577855149, 0.0664778844289700, 0.4667610577855147, 0.7938090288479388, 0.1030954855760307, 0.1030954855760302 }; static double w_save[] = { 0.0000522093231255, 0.0000522093231255, 0.0000522093231255, 0.0064432696708827, 0.0064432696708827, 0.0064432696708827, 0.0056462037725046, 0.0056462037725046, 0.0056462037725046, 0.0009466339964529, 0.0009466339964529, 0.0009466339964529, 0.0009466339964529, 0.0009466339964529, 0.0009466339964529, 0.0010778383293871, 0.0010778383293871, 0.0010778383293871, 0.0010778383293871, 0.0010778383293871, 0.0010778383293871, 0.0005535514063046, 0.0005535514063046, 0.0005535514063046, 0.0005535514063046, 0.0005535514063046, 0.0005535514063046, 0.0037447209152800, 0.0037447209152800, 0.0037447209152800, 0.0037447209152800, 0.0037447209152800, 0.0037447209152800, 0.0040737392096224, 0.0040737392096224, 0.0040737392096224, 0.0040737392096224, 0.0040737392096224, 0.0040737392096224, 0.0029751068247424, 0.0029751068247424, 0.0029751068247424, 0.0017887545706646, 0.0017887545706646, 0.0017887545706646, 0.0017887545706646, 0.0017887545706646, 0.0017887545706646, 0.0010314247381435, 0.0010314247381435, 0.0010314247381435, 0.0010314247381435, 0.0010314247381435, 0.0010314247381435, 0.0025322072683271, 0.0025322072683271, 0.0025322072683271, 0.0025322072683271, 0.0025322072683271, 0.0025322072683271, 0.0022524785579246, 0.0022524785579246, 0.0022524785579246, 0.0022524785579246, 0.0022524785579246, 0.0022524785579246, 0.0002818375084659, 0.0002818375084659, 0.0002818375084659, 0.0002818375084659, 0.0002818375084659, 0.0002818375084659, 0.0061093730696482, 0.0061093730696482, 0.0061093730696482, 0.0061093730696482, 0.0061093730696482, 0.0061093730696482, 0.0042449557771112, 0.0042449557771112, 0.0042449557771112, 0.0033089712153024, 0.0033089712153024, 0.0033089712153024, 0.0033089712153024, 0.0033089712153024, 0.0033089712153024, 0.0007503403741006, 0.0007503403741006, 0.0007503403741006, 0.0007503403741006, 0.0007503403741006, 0.0007503403741006, 0.0050362517089764, 0.0050362517089764, 0.0050362517089764, 0.0060101004771622, 0.0060101004771622, 0.0060101004771622, 0.0062236592332096, 0.0062236592332096, 0.0062236592332096, 0.0062236592332096, 0.0062236592332096, 0.0062236592332096, 0.0060772289969774, 0.0060772289969774, 0.0060772289969774, 0.0004904208710143, 0.0004904208710143, 0.0004904208710143, 0.0004904208710143, 0.0004904208710143, 0.0004904208710143, 0.0058906442657042, 0.0058906442657042, 0.0058906442657042, 0.0058906442657042, 0.0058906442657042, 0.0058906442657042, 0.0062381201191140, 0.0062381201191140, 0.0062381201191140, 0.0062381201191140, 0.0062381201191140, 0.0062381201191140, 0.0005889181881281, 0.0005889181881281, 0.0005889181881281, 0.0005889181881281, 0.0005889181881281, 0.0005889181881281, 0.0002390515618048, 0.0002390515618048, 0.0002390515618048, 0.0002390515618048, 0.0002390515618048, 0.0002390515618048, 0.0023381337598691, 0.0023381337598691, 0.0023381337598691, 0.0023381337598691, 0.0023381337598691, 0.0023381337598691, 0.0010454329707756, 0.0010454329707756, 0.0010454329707756, 0.0010454329707756, 0.0010454329707756, 0.0010454329707756, 0.0067671402084225, 0.0067671402084225, 0.0067671402084225, 0.0059901891203096, 0.0059901891203096, 0.0059901891203096, 0.0059901891203096, 0.0059901891203096, 0.0059901891203096, 0.0010236399703004, 0.0010236399703004, 0.0010236399703004, 0.0022882495872613, 0.0022882495872613, 0.0022882495872613, 0.0022882495872613, 0.0022882495872613, 0.0022882495872613, 0.0036104870565558, 0.0036104870565558, 0.0036104870565558, 0.0036104870565558, 0.0036104870565558, 0.0036104870565558, 0.0070586578085502, 0.0070586578085502, 0.0070586578085502, 0.0070586578085502, 0.0070586578085502, 0.0070586578085502, 0.0043785525737028, 0.0043785525737028, 0.0043785525737028, 0.0043785525737028, 0.0043785525737028, 0.0043785525737028, 0.0010171383589503, 0.0010171383589503, 0.0010171383589503, 0.0010171383589503, 0.0010171383589503, 0.0010171383589503, 0.0034554845247205, 0.0034554845247205, 0.0034554845247205, 0.0034554845247205, 0.0034554845247205, 0.0034554845247205, 0.0016626192415772, 0.0016626192415772, 0.0016626192415772, 0.0016626192415772, 0.0016626192415772, 0.0016626192415772, 0.0033511706532687, 0.0033511706532687, 0.0033511706532687, 0.0033511706532687, 0.0033511706532687, 0.0033511706532687, 0.0023865646505329, 0.0023865646505329, 0.0023865646505329, 0.0023865646505329, 0.0023865646505329, 0.0023865646505329, 0.0041753789931688, 0.0041753789931688, 0.0041753789931688, 0.0041753789931688, 0.0041753789931688, 0.0041753789931688, 0.0038711214885426, 0.0038711214885426, 0.0038711214885426, 0.0038711214885426, 0.0038711214885426, 0.0038711214885426, 0.0021923391960439, 0.0021923391960439, 0.0021923391960439, 0.0021923391960439, 0.0021923391960439, 0.0021923391960439, 0.0009127323365215, 0.0009127323365215, 0.0009127323365215, 0.0009127323365215, 0.0009127323365215, 0.0009127323365215, 0.0072301097329517, 0.0072301097329517, 0.0072301097329517, 0.0008028346526154, 0.0008028346526154, 0.0008028346526154, 0.0008028346526154, 0.0008028346526154, 0.0008028346526154, 0.0009793596015786, 0.0009793596015786, 0.0009793596015786, 0.0009793596015786, 0.0009793596015786, 0.0009793596015786, 0.0059550867608881, 0.0059550867608881, 0.0059550867608881, 0.0059550867608881, 0.0059550867608881, 0.0059550867608881, 0.0067525153387175, 0.0067525153387175, 0.0067525153387175, 0.0067525153387175, 0.0067525153387175, 0.0067525153387175, 0.0049326746082459, 0.0049326746082459, 0.0049326746082459, 0.0049326746082459, 0.0049326746082459, 0.0049326746082459, 0.0019995171236440, 0.0019995171236440, 0.0019995171236440, 0.0019995171236440, 0.0019995171236440, 0.0019995171236440, 0.0028581698928275, 0.0028581698928275, 0.0028581698928275, 0.0028581698928275, 0.0028581698928275, 0.0028581698928275, 0.0032573829494494, 0.0032573829494494, 0.0032573829494494, 0.0032573829494494, 0.0032573829494494, 0.0032573829494494, 0.0058722816583725, 0.0058722816583725, 0.0058722816583725, 0.0058722816583725, 0.0058722816583725, 0.0058722816583725, 0.0050950784475005, 0.0050950784475005, 0.0050950784475005, 0.0050950784475005, 0.0050950784475005, 0.0050950784475005, 0.0051338703252384, 0.0051338703252384, 0.0051338703252384, 0.0039695690393596, 0.0039695690393596, 0.0039695690393596 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule42 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule42() returns the rule of precision 42. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4023719251097932, 0.4023719251097932, 0.1952561497804134, 0.0013653925759540, 0.9972692148480916, 0.0013653925759544, 0.3305538536843531, 0.6678757207141839, 0.0015704256014629, 0.6678757207141840, 0.3305538536843532, 0.0015704256014628, 0.4975317296252054, 0.4975317296252054, 0.0049365407495892, 0.9699539651466832, 0.0204313657326067, 0.0096146691207099, 0.0204313657326067, 0.9699539651466832, 0.0096146691207102, 0.0571983061939757, 0.9208981351903950, 0.0219035586156294, 0.9208981351903950, 0.0571983061939758, 0.0219035586156291, 0.4799002957544191, 0.4799002957544192, 0.0401994084911617, 0.0664663290557836, 0.8670673418884325, 0.0664663290557839, 0.4532709716379456, 0.5452354770717635, 0.0014935512902909, 0.5452354770717635, 0.4532709716379456, 0.0014935512902909, 0.1407324739067203, 0.8038260264189151, 0.0554414996743646, 0.8038260264189151, 0.1407324739067203, 0.0554414996743643, 0.1837886303019410, 0.6975178002766640, 0.1186935694213951, 0.6975178002766639, 0.1837886303019411, 0.1186935694213948, 0.0432363893877460, 0.9135272212245076, 0.0432363893877464, 0.0321121524868778, 0.9664947902959359, 0.0013930572171864, 0.9664947902959361, 0.0321121524868780, 0.0013930572171859, 0.4903050142016467, 0.4903050142016467, 0.0193899715967066, 0.0429640722006761, 0.9467364526174824, 0.0102994751818416, 0.9467364526174824, 0.0429640722006762, 0.0102994751818411, 0.0105248427300749, 0.9868904472776370, 0.0025847099922883, 0.9868904472776370, 0.0105248427300750, 0.0025847099922879, 0.0753790285629703, 0.8851466587208721, 0.0394743127161577, 0.8851466587208721, 0.0753790285629704, 0.0394743127161574, 0.4363333620899560, 0.5513727993854914, 0.0122938385245525, 0.5513727993854914, 0.4363333620899560, 0.0122938385245524, 0.2704907465149770, 0.7269194442371774, 0.0025898092478457, 0.7269194442371772, 0.2704907465149770, 0.0025898092478455, 0.3508136433810974, 0.6116299677466058, 0.0375563888722968, 0.6116299677466057, 0.3508136433810974, 0.0375563888722968, 0.3727655119742921, 0.6101399413050006, 0.0170945467207073, 0.6101399413050006, 0.3727655119742921, 0.0170945467207072, 0.2171073522633415, 0.6971343314423426, 0.0857583162943159, 0.6971343314423426, 0.2171073522633415, 0.0857583162943157, 0.1927563650090058, 0.7492579900268798, 0.0579856449641145, 0.7492579900268798, 0.1927563650090059, 0.0579856449641142, 0.4206850306864163, 0.5454667964305935, 0.0338481728829903, 0.5454667964305935, 0.4206850306864162, 0.0338481728829902, 0.0269988226283730, 0.9460023547432537, 0.0269988226283734, 0.2124851854370911, 0.7849881231777003, 0.0025266913852087, 0.7849881231777003, 0.2124851854370911, 0.0025266913852085, 0.3192572087291873, 0.6700862491552849, 0.0106565421155276, 0.6700862491552850, 0.3192572087291874, 0.0106565421155275, 0.1385048069103228, 0.7229903861793542, 0.1385048069103231, 0.4670132073557640, 0.4670132073557640, 0.0659735852884720, 0.2516382355125726, 0.7349320912451689, 0.0134296732422586, 0.7349320912451689, 0.2516382355125727, 0.0134296732422583, 0.1522119814568094, 0.7594462402499256, 0.0883417782932651, 0.7594462402499256, 0.1522119814568094, 0.0883417782932648, 0.1111420947940333, 0.8559357869948059, 0.0329221182111609, 0.8559357869948060, 0.1111420947940334, 0.0329221182111606, 0.3581500588512503, 0.4470491803714221, 0.1948007607773276, 0.4470491803714221, 0.3581500588512503, 0.1948007607773276, 0.1637998569561501, 0.8047391270819582, 0.0314610159618919, 0.8047391270819582, 0.1637998569561501, 0.0314610159618916, 0.1021127733366743, 0.8305189164987998, 0.0673683101645260, 0.8305189164987997, 0.1021127733366744, 0.0673683101645256, 0.2335557030193516, 0.5798790527806756, 0.1865652441999727, 0.5798790527806756, 0.2335557030193516, 0.1865652441999726, 0.3214164628317113, 0.6147000537558933, 0.0638834834123954, 0.6147000537558933, 0.3214164628317114, 0.0638834834123952, 0.2233361848957126, 0.7440925933093376, 0.0325712217949499, 0.7440925933093376, 0.2233361848957126, 0.0325712217949497, 0.1905881189463203, 0.7961383982975219, 0.0132734827561579, 0.7961383982975220, 0.1905881189463203, 0.0132734827561576, 0.2273558402454795, 0.6364103842453923, 0.1362337755091281, 0.6364103842453924, 0.2273558402454797, 0.1362337755091279, 0.1065804258588588, 0.7868391482822822, 0.1065804258588591, 0.1567679227871600, 0.8406166996789507, 0.0026153775338892, 0.8406166996789507, 0.1567679227871602, 0.0026153775338890, 0.1340333349867785, 0.8524854538080647, 0.0134812112051569, 0.8524854538080647, 0.1340333349867785, 0.0134812112051566, 0.2957211757454536, 0.5123947199023402, 0.1918841043522062, 0.5123947199023402, 0.2957211757454536, 0.1918841043522061, 0.1067192718130004, 0.8907334465548298, 0.0025472816321699, 0.8907334465548298, 0.1067192718130003, 0.0025472816321696, 0.4125664194839165, 0.4863962861603238, 0.1010372943557596, 0.4863962861603238, 0.4125664194839165, 0.1010372943557596, 0.3078519829928861, 0.4423972758418252, 0.2497507411652887, 0.4423972758418251, 0.3078519829928861, 0.2497507411652886, 0.0870205486996966, 0.8992668260117453, 0.0137126252885581, 0.8992668260117453, 0.0870205486996967, 0.0137126252885578, 0.3894283316812197, 0.6072270728853777, 0.0033445954334026, 0.6072270728853777, 0.3894283316812197, 0.0033445954334026, 0.3117353910725873, 0.3765292178548252, 0.3117353910725873, 0.2612939703141770, 0.6830313992552178, 0.0556746304306052, 0.6830313992552177, 0.2612939703141770, 0.0556746304306051, 0.0649755331098119, 0.9322207082966478, 0.0028037585935404, 0.9322207082966478, 0.0649755331098119, 0.0028037585935401, 0.2719500060981310, 0.6316994938246291, 0.0963505000772399, 0.6316994938246292, 0.2719500060981311, 0.0963505000772396, 0.2930903642725462, 0.6777105291270178, 0.0291991066004360, 0.6777105291270178, 0.2930903642725463, 0.0291991066004358, 0.3946648265878192, 0.5417606227500117, 0.0635745506621692, 0.5417606227500116, 0.3946648265878193, 0.0635745506621691, 0.3568522181929828, 0.4992192017414733, 0.1439285800655438, 0.4992192017414734, 0.3568522181929829, 0.1439285800655437, 0.2448605758688817, 0.5102788482622364, 0.2448605758688818, 0.3413613516388763, 0.5594299486078240, 0.0992086997532998, 0.5594299486078240, 0.3413613516388763, 0.0992086997532997, 0.2895129410795146, 0.5700981374990226, 0.1403889214214628, 0.5700981374990226, 0.2895129410795146, 0.1403889214214627, 0.1748351458111906, 0.6503297083776184, 0.1748351458111909, 0.4275693341501904, 0.4275693341501904, 0.1448613316996191, 0.3742701566784477, 0.3742701566784477, 0.2514596866431046 }; static double b_save[] = { 0.1952561497804135, 0.4023719251097934, 0.4023719251097935, 0.0013653925759543, 0.0013653925759540, 0.9972692148480918, 0.0015704256014629, 0.3305538536843532, 0.6678757207141842, 0.0015704256014629, 0.6678757207141840, 0.3305538536843535, 0.0049365407495893, 0.4975317296252054, 0.4975317296252056, 0.0096146691207101, 0.9699539651466834, 0.0204313657326070, 0.0096146691207101, 0.0204313657326066, 0.9699539651466834, 0.0219035586156294, 0.0571983061939757, 0.9208981351903952, 0.0219035586156294, 0.9208981351903952, 0.0571983061939760, 0.0401994084911617, 0.4799002957544192, 0.4799002957544193, 0.0664663290557839, 0.0664663290557836, 0.8670673418884327, 0.0014935512902910, 0.4532709716379457, 0.5452354770717637, 0.0014935512902910, 0.5452354770717636, 0.4532709716379458, 0.0554414996743645, 0.1407324739067203, 0.8038260264189153, 0.0554414996743645, 0.8038260264189153, 0.1407324739067206, 0.1186935694213950, 0.1837886303019410, 0.6975178002766641, 0.1186935694213950, 0.6975178002766641, 0.1837886303019413, 0.0432363893877463, 0.0432363893877460, 0.9135272212245078, 0.0013930572171862, 0.0321121524868778, 0.9664947902959360, 0.0013930572171862, 0.9664947902959360, 0.0321121524868782, 0.0193899715967067, 0.4903050142016467, 0.4903050142016469, 0.0102994751818414, 0.0429640722006761, 0.9467364526174826, 0.0102994751818414, 0.9467364526174826, 0.0429640722006765, 0.0025847099922882, 0.0105248427300749, 0.9868904472776371, 0.0025847099922882, 0.9868904472776371, 0.0105248427300752, 0.0394743127161577, 0.0753790285629703, 0.8851466587208722, 0.0394743127161577, 0.8851466587208722, 0.0753790285629706, 0.0122938385245525, 0.4363333620899560, 0.5513727993854917, 0.0122938385245525, 0.5513727993854916, 0.4363333620899563, 0.0025898092478457, 0.2704907465149770, 0.7269194442371776, 0.0025898092478457, 0.7269194442371776, 0.2704907465149773, 0.0375563888722969, 0.3508136433810974, 0.6116299677466061, 0.0375563888722969, 0.6116299677466058, 0.3508136433810976, 0.0170945467207073, 0.3727655119742921, 0.6101399413050007, 0.0170945467207073, 0.6101399413050007, 0.3727655119742924, 0.0857583162943159, 0.2171073522633416, 0.6971343314423428, 0.0857583162943159, 0.6971343314423428, 0.2171073522633418, 0.0579856449641144, 0.1927563650090059, 0.7492579900268799, 0.0579856449641144, 0.7492579900268799, 0.1927563650090061, 0.0338481728829903, 0.4206850306864163, 0.5454667964305936, 0.0338481728829903, 0.5454667964305936, 0.4206850306864165, 0.0269988226283733, 0.0269988226283730, 0.9460023547432538, 0.0025266913852086, 0.2124851854370911, 0.7849881231777005, 0.0025266913852086, 0.7849881231777005, 0.2124851854370913, 0.0106565421155276, 0.3192572087291874, 0.6700862491552853, 0.0106565421155276, 0.6700862491552851, 0.3192572087291877, 0.1385048069103230, 0.1385048069103228, 0.7229903861793542, 0.0659735852884721, 0.4670132073557641, 0.4670132073557642, 0.0134296732422585, 0.2516382355125726, 0.7349320912451690, 0.0134296732422585, 0.7349320912451689, 0.2516382355125729, 0.0883417782932651, 0.1522119814568094, 0.7594462402499257, 0.0883417782932651, 0.7594462402499258, 0.1522119814568096, 0.0329221182111608, 0.1111420947940333, 0.8559357869948060, 0.0329221182111608, 0.8559357869948060, 0.1111420947940336, 0.1948007607773277, 0.3581500588512503, 0.4470491803714222, 0.1948007607773277, 0.4470491803714221, 0.3581500588512505, 0.0314610159618918, 0.1637998569561501, 0.8047391270819583, 0.0314610159618918, 0.8047391270819583, 0.1637998569561504, 0.0673683101645259, 0.1021127733366743, 0.8305189164987999, 0.0673683101645259, 0.8305189164987999, 0.1021127733366746, 0.1865652441999728, 0.2335557030193517, 0.5798790527806759, 0.1865652441999728, 0.5798790527806759, 0.2335557030193518, 0.0638834834123953, 0.3214164628317114, 0.6147000537558934, 0.0638834834123953, 0.6147000537558934, 0.3214164628317117, 0.0325712217949499, 0.2233361848957126, 0.7440925933093379, 0.0325712217949499, 0.7440925933093377, 0.2233361848957128, 0.0132734827561578, 0.1905881189463202, 0.7961383982975221, 0.0132734827561578, 0.7961383982975221, 0.1905881189463206, 0.1362337755091281, 0.2273558402454796, 0.6364103842453925, 0.1362337755091281, 0.6364103842453924, 0.2273558402454798, 0.1065804258588591, 0.1065804258588588, 0.7868391482822823, 0.0026153775338892, 0.1567679227871601, 0.8406166996789509, 0.0026153775338892, 0.8406166996789507, 0.1567679227871604, 0.0134812112051568, 0.1340333349867785, 0.8524854538080648, 0.0134812112051568, 0.8524854538080648, 0.1340333349867788, 0.1918841043522063, 0.2957211757454537, 0.5123947199023403, 0.1918841043522063, 0.5123947199023402, 0.2957211757454539, 0.0025472816321698, 0.1067192718130003, 0.8907334465548301, 0.0025472816321698, 0.8907334465548301, 0.1067192718130007, 0.1010372943557597, 0.4125664194839166, 0.4863962861603239, 0.1010372943557597, 0.4863962861603238, 0.4125664194839167, 0.2497507411652888, 0.3078519829928861, 0.4423972758418253, 0.2497507411652888, 0.4423972758418253, 0.3078519829928862, 0.0137126252885580, 0.0870205486996967, 0.8992668260117456, 0.0137126252885580, 0.8992668260117456, 0.0870205486996970, 0.0033445954334026, 0.3894283316812198, 0.6072270728853779, 0.0033445954334026, 0.6072270728853778, 0.3894283316812200, 0.3117353910725875, 0.3117353910725874, 0.3765292178548253, 0.0556746304306052, 0.2612939703141770, 0.6830313992552181, 0.0556746304306052, 0.6830313992552179, 0.2612939703141772, 0.0028037585935403, 0.0649755331098119, 0.9322207082966479, 0.0028037585935403, 0.9322207082966479, 0.0649755331098122, 0.0963505000772398, 0.2719500060981311, 0.6316994938246292, 0.0963505000772398, 0.6316994938246292, 0.2719500060981313, 0.0291991066004360, 0.2930903642725463, 0.6777105291270180, 0.0291991066004360, 0.6777105291270179, 0.2930903642725465, 0.0635745506621692, 0.3946648265878193, 0.5417606227500118, 0.0635745506621692, 0.5417606227500117, 0.3946648265878194, 0.1439285800655438, 0.3568522181929829, 0.4992192017414736, 0.1439285800655438, 0.4992192017414734, 0.3568522181929830, 0.2448605758688819, 0.2448605758688818, 0.5102788482622366, 0.0992086997532998, 0.3413613516388764, 0.5594299486078241, 0.0992086997532998, 0.5594299486078240, 0.3413613516388765, 0.1403889214214629, 0.2895129410795146, 0.5700981374990227, 0.1403889214214629, 0.5700981374990226, 0.2895129410795148, 0.1748351458111909, 0.1748351458111907, 0.6503297083776187, 0.1448613316996193, 0.4275693341501904, 0.4275693341501906, 0.2514596866431047, 0.3742701566784478, 0.3742701566784478 }; static double c_save[] = { 0.4023719251097932, 0.1952561497804133, 0.4023719251097931, 0.9972692148480916, 0.0013653925759544, 0.0013653925759537, 0.6678757207141840, 0.0015704256014629, 0.3305538536843530, 0.3305538536843531, 0.0015704256014627, 0.6678757207141837, 0.4975317296252054, 0.0049365407495893, 0.4975317296252051, 0.0204313657326067, 0.0096146691207099, 0.9699539651466832, 0.9699539651466833, 0.0096146691207102, 0.0204313657326064, 0.9208981351903950, 0.0219035586156293, 0.0571983061939754, 0.0571983061939757, 0.0219035586156290, 0.9208981351903949, 0.4799002957544191, 0.0401994084911617, 0.4799002957544190, 0.8670673418884325, 0.0664663290557839, 0.0664663290557834, 0.5452354770717635, 0.0014935512902909, 0.4532709716379454, 0.4532709716379456, 0.0014935512902908, 0.5452354770717632, 0.8038260264189151, 0.0554414996743646, 0.1407324739067201, 0.1407324739067204, 0.0554414996743643, 0.8038260264189151, 0.6975178002766640, 0.1186935694213950, 0.1837886303019408, 0.1837886303019411, 0.1186935694213948, 0.6975178002766640, 0.9135272212245077, 0.0432363893877464, 0.0432363893877458, 0.9664947902959360, 0.0013930572171863, 0.0321121524868776, 0.0321121524868777, 0.0013930572171860, 0.9664947902959359, 0.4903050142016466, 0.0193899715967066, 0.4903050142016465, 0.9467364526174825, 0.0102994751818415, 0.0429640722006758, 0.0429640722006762, 0.0102994751818412, 0.9467364526174823, 0.9868904472776369, 0.0025847099922882, 0.0105248427300747, 0.0105248427300748, 0.0025847099922879, 0.9868904472776370, 0.8851466587208721, 0.0394743127161577, 0.0753790285629702, 0.0753790285629703, 0.0394743127161575, 0.8851466587208719, 0.5513727993854914, 0.0122938385245525, 0.4363333620899558, 0.4363333620899560, 0.0122938385245525, 0.5513727993854913, 0.7269194442371774, 0.0025898092478457, 0.2704907465149767, 0.2704907465149771, 0.0025898092478455, 0.7269194442371772, 0.6116299677466058, 0.0375563888722968, 0.3508136433810972, 0.3508136433810974, 0.0375563888722968, 0.6116299677466057, 0.6101399413050006, 0.0170945467207073, 0.3727655119742920, 0.3727655119742921, 0.0170945467207072, 0.6101399413050004, 0.6971343314423426, 0.0857583162943158, 0.2171073522633413, 0.2171073522633415, 0.0857583162943156, 0.6971343314423424, 0.7492579900268798, 0.0579856449641144, 0.1927563650090056, 0.1927563650090058, 0.0579856449641142, 0.7492579900268797, 0.5454667964305934, 0.0338481728829902, 0.4206850306864162, 0.4206850306864162, 0.0338481728829901, 0.5454667964305933, 0.9460023547432537, 0.0269988226283734, 0.0269988226283727, 0.7849881231777003, 0.0025266913852086, 0.2124851854370908, 0.2124851854370911, 0.0025266913852084, 0.7849881231777003, 0.6700862491552849, 0.0106565421155277, 0.3192572087291872, 0.3192572087291873, 0.0106565421155275, 0.6700862491552848, 0.7229903861793543, 0.1385048069103230, 0.1385048069103226, 0.4670132073557639, 0.0659735852884719, 0.4670132073557638, 0.7349320912451689, 0.0134296732422585, 0.2516382355125725, 0.2516382355125726, 0.0134296732422584, 0.7349320912451688, 0.7594462402499256, 0.0883417782932650, 0.1522119814568091, 0.1522119814568094, 0.0883417782932648, 0.7594462402499256, 0.8559357869948060, 0.0329221182111608, 0.1111420947940330, 0.1111420947940332, 0.0329221182111606, 0.8559357869948059, 0.4470491803714220, 0.1948007607773276, 0.3581500588512502, 0.3581500588512502, 0.1948007607773276, 0.4470491803714220, 0.8047391270819582, 0.0314610159618918, 0.1637998569561498, 0.1637998569561500, 0.0314610159618917, 0.8047391270819580, 0.8305189164987998, 0.0673683101645259, 0.1021127733366741, 0.1021127733366744, 0.0673683101645256, 0.8305189164987997, 0.5798790527806756, 0.1865652441999727, 0.2335557030193514, 0.2335557030193516, 0.1865652441999726, 0.5798790527806756, 0.6147000537558933, 0.0638834834123953, 0.3214164628317112, 0.3214164628317113, 0.0638834834123952, 0.6147000537558932, 0.7440925933093376, 0.0325712217949498, 0.2233361848957123, 0.2233361848957125, 0.0325712217949498, 0.7440925933093375, 0.7961383982975219, 0.0132734827561579, 0.1905881189463200, 0.1905881189463202, 0.0132734827561576, 0.7961383982975219, 0.6364103842453924, 0.1362337755091281, 0.2273558402454794, 0.2273558402454795, 0.1362337755091280, 0.6364103842453923, 0.7868391482822822, 0.1065804258588590, 0.1065804258588586, 0.8406166996789508, 0.0026153775338892, 0.1567679227871598, 0.1567679227871601, 0.0026153775338892, 0.8406166996789505, 0.8524854538080647, 0.0134812112051568, 0.1340333349867783, 0.1340333349867785, 0.0134812112051567, 0.8524854538080646, 0.5123947199023401, 0.1918841043522061, 0.2957211757454535, 0.2957211757454535, 0.1918841043522062, 0.5123947199023400, 0.8907334465548298, 0.0025472816321699, 0.1067192718130000, 0.1067192718130004, 0.0025472816321696, 0.8907334465548297, 0.4863962861603238, 0.1010372943557597, 0.4125664194839165, 0.4125664194839166, 0.1010372943557597, 0.4863962861603237, 0.4423972758418251, 0.2497507411652887, 0.3078519829928861, 0.3078519829928861, 0.2497507411652886, 0.4423972758418251, 0.8992668260117453, 0.0137126252885580, 0.0870205486996963, 0.0870205486996966, 0.0137126252885578, 0.8992668260117452, 0.6072270728853777, 0.0033445954334025, 0.3894283316812195, 0.3894283316812197, 0.0033445954334025, 0.6072270728853775, 0.3765292178548252, 0.3117353910725874, 0.3117353910725874, 0.6830313992552178, 0.0556746304306052, 0.2612939703141767, 0.2612939703141771, 0.0556746304306051, 0.6830313992552177, 0.9322207082966478, 0.0028037585935403, 0.0649755331098116, 0.0649755331098119, 0.0028037585935402, 0.9322207082966477, 0.6316994938246291, 0.0963505000772398, 0.2719500060981309, 0.2719500060981310, 0.0963505000772397, 0.6316994938246290, 0.6777105291270178, 0.0291991066004360, 0.2930903642725460, 0.2930903642725462, 0.0291991066004359, 0.6777105291270177, 0.5417606227500116, 0.0635745506621690, 0.3946648265878190, 0.3946648265878193, 0.0635745506621691, 0.5417606227500115, 0.4992192017414734, 0.1439285800655438, 0.3568522181929827, 0.3568522181929827, 0.1439285800655437, 0.4992192017414732, 0.5102788482622364, 0.2448605758688819, 0.2448605758688817, 0.5594299486078239, 0.0992086997532996, 0.3413613516388762, 0.3413613516388762, 0.0992086997532997, 0.5594299486078238, 0.5700981374990226, 0.1403889214214628, 0.2895129410795144, 0.2895129410795145, 0.1403889214214628, 0.5700981374990224, 0.6503297083776185, 0.1748351458111909, 0.1748351458111904, 0.4275693341501904, 0.1448613316996192, 0.4275693341501903, 0.3742701566784477, 0.2514596866431046, 0.3742701566784476 }; static double w_save[] = { 0.0035464400159772, 0.0035464400159772, 0.0035464400159772, 0.0000347195354366, 0.0000347195354366, 0.0000347195354366, 0.0005327316943405, 0.0005327316943405, 0.0005327316943405, 0.0005327316943405, 0.0005327316943405, 0.0005327316943405, 0.0010141696428327, 0.0010141696428327, 0.0010141696428327, 0.0004390770271698, 0.0004390770271698, 0.0004390770271698, 0.0004390770271698, 0.0004390770271698, 0.0004390770271698, 0.0010370250465354, 0.0010370250465354, 0.0010370250465354, 0.0010370250465354, 0.0010370250465354, 0.0010370250465354, 0.0028441859570122, 0.0028441859570122, 0.0028441859570122, 0.0018709815380229, 0.0018709815380229, 0.0018709815380229, 0.0005595519502280, 0.0005595519502280, 0.0005595519502280, 0.0005595519502280, 0.0005595519502280, 0.0005595519502280, 0.0025379205064648, 0.0025379205064648, 0.0025379205064648, 0.0025379205064648, 0.0025379205064648, 0.0025379205064648, 0.0040581577981140, 0.0040581577981140, 0.0040581577981140, 0.0040581577981140, 0.0040581577981140, 0.0040581577981140, 0.0013326250004080, 0.0013326250004080, 0.0013326250004080, 0.0002266425752075, 0.0002266425752075, 0.0002266425752075, 0.0002266425752075, 0.0002266425752075, 0.0002266425752075, 0.0021926816815859, 0.0021926816815859, 0.0021926816815859, 0.0006818533431415, 0.0006818533431415, 0.0006818533431415, 0.0006818533431415, 0.0006818533431415, 0.0006818533431415, 0.0001870930686156, 0.0001870930686156, 0.0001870930686156, 0.0001870930686156, 0.0001870930686156, 0.0001870930686156, 0.0016866296698237, 0.0016866296698237, 0.0016866296698237, 0.0016866296698237, 0.0016866296698237, 0.0016866296698237, 0.0019025497964579, 0.0019025497964579, 0.0019025497964579, 0.0019025497964579, 0.0019025497964579, 0.0019025497964579, 0.0007733670252998, 0.0007733670252998, 0.0007733670252998, 0.0007733670252998, 0.0007733670252998, 0.0007733670252998, 0.0031723878909002, 0.0031723878909002, 0.0031723878909002, 0.0031723878909002, 0.0031723878909002, 0.0031723878909002, 0.0021685247098617, 0.0021685247098617, 0.0021685247098617, 0.0021685247098617, 0.0021685247098617, 0.0021685247098617, 0.0040741174736407, 0.0040741174736407, 0.0040741174736407, 0.0040741174736407, 0.0040741174736407, 0.0040741174736407, 0.0033720890143962, 0.0033720890143962, 0.0033720890143962, 0.0033720890143962, 0.0033720890143962, 0.0033720890143962, 0.0033374654153493, 0.0033374654153493, 0.0033374654153493, 0.0033374654153493, 0.0033374654153493, 0.0033374654153493, 0.0009524059556547, 0.0009524059556547, 0.0009524059556547, 0.0007443004607122, 0.0007443004607122, 0.0007443004607122, 0.0007443004607122, 0.0007443004607122, 0.0007443004607122, 0.0017490056575093, 0.0017490056575093, 0.0017490056575093, 0.0017490056575093, 0.0017490056575093, 0.0017490056575093, 0.0043598500418925, 0.0043598500418925, 0.0043598500418925, 0.0045325322550328, 0.0045325322550328, 0.0045325322550328, 0.0019031683954380, 0.0019031683954380, 0.0019031683954380, 0.0019031683954380, 0.0019031683954380, 0.0019031683954380, 0.0039581444907566, 0.0039581444907566, 0.0039581444907566, 0.0039581444907566, 0.0039581444907566, 0.0039581444907566, 0.0021633300119175, 0.0021633300119175, 0.0021633300119175, 0.0021633300119175, 0.0021633300119175, 0.0021633300119175, 0.0062667413965418, 0.0062667413965418, 0.0062667413965418, 0.0062667413965418, 0.0062667413965418, 0.0062667413965418, 0.0024314709447528, 0.0024314709447528, 0.0024314709447528, 0.0024314709447528, 0.0024314709447528, 0.0024314709447528, 0.0028265780976025, 0.0028265780976025, 0.0028265780976025, 0.0028265780976025, 0.0028265780976025, 0.0028265780976025, 0.0064753562254833, 0.0064753562254833, 0.0064753562254833, 0.0064753562254833, 0.0064753562254833, 0.0064753562254833, 0.0042484824512542, 0.0042484824512542, 0.0042484824512542, 0.0042484824512542, 0.0042484824512542, 0.0042484824512542, 0.0029100859090623, 0.0029100859090623, 0.0029100859090623, 0.0029100859090623, 0.0029100859090623, 0.0029100859090623, 0.0017543943309314, 0.0017543943309314, 0.0017543943309314, 0.0017543943309314, 0.0017543943309314, 0.0017543943309314, 0.0053278143635326, 0.0053278143635326, 0.0053278143635326, 0.0053278143635326, 0.0053278143635326, 0.0053278143635326, 0.0036960706615539, 0.0036960706615539, 0.0036960706615539, 0.0007117355150534, 0.0007117355150534, 0.0007117355150534, 0.0007117355150534, 0.0007117355150534, 0.0007117355150534, 0.0015685196181434, 0.0015685196181434, 0.0015685196181434, 0.0015685196181434, 0.0015685196181434, 0.0015685196181434, 0.0069096837033853, 0.0069096837033853, 0.0069096837033853, 0.0069096837033853, 0.0069096837033853, 0.0069096837033853, 0.0006077668893384, 0.0006077668893384, 0.0006077668893384, 0.0006077668893384, 0.0006077668893384, 0.0006077668893384, 0.0058599060505518, 0.0058599060505518, 0.0058599060505518, 0.0058599060505518, 0.0058599060505518, 0.0058599060505518, 0.0077651860406297, 0.0077651860406297, 0.0077651860406297, 0.0077651860406297, 0.0077651860406297, 0.0077651860406297, 0.0013100408329861, 0.0013100408329861, 0.0013100408329861, 0.0013100408329861, 0.0013100408329861, 0.0013100408329861, 0.0010570972491723, 0.0010570972491723, 0.0010570972491723, 0.0010570972491723, 0.0010570972491723, 0.0010570972491723, 0.0080973376090284, 0.0080973376090284, 0.0080973376090284, 0.0040411976507506, 0.0040411976507506, 0.0040411976507506, 0.0040411976507506, 0.0040411976507506, 0.0040411976507506, 0.0005242478913459, 0.0005242478913459, 0.0005242478913459, 0.0005242478913459, 0.0005242478913459, 0.0005242478913459, 0.0052048680063201, 0.0052048680063201, 0.0052048680063201, 0.0052048680063201, 0.0052048680063201, 0.0052048680063201, 0.0030333113262699, 0.0030333113262699, 0.0030333113262699, 0.0030333113262699, 0.0030333113262699, 0.0030333113262699, 0.0048685523603979, 0.0048685523603979, 0.0048685523603979, 0.0048685523603979, 0.0048685523603979, 0.0048685523603979, 0.0066028726180890, 0.0066028726180890, 0.0066028726180890, 0.0066028726180890, 0.0066028726180890, 0.0066028726180890, 0.0072906010527868, 0.0072906010527868, 0.0072906010527868, 0.0056531366883124, 0.0056531366883124, 0.0056531366883124, 0.0056531366883124, 0.0056531366883124, 0.0056531366883124, 0.0061919290123439, 0.0061919290123439, 0.0061919290123439, 0.0061919290123439, 0.0061919290123439, 0.0061919290123439, 0.0060555267820254, 0.0060555267820254, 0.0060555267820254, 0.0067589446392298, 0.0067589446392298, 0.0067589446392298, 0.0079220445765913, 0.0079220445765913, 0.0079220445765913 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule43 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule43() returns the rule of precision 43. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4117801708599338, 0.4117801708599338, 0.1764396582801323, 0.4755758670991315, 0.4755758670991315, 0.0488482658017370, 0.2297394365272492, 0.6248067680849181, 0.1454537953878327, 0.6248067680849182, 0.2297394365272493, 0.1454537953878325, 0.4991798367344780, 0.4991798367344780, 0.0016403265310439, 0.2962479881688698, 0.4075040236622601, 0.2962479881688698, 0.3605580760887838, 0.6070264490694377, 0.0324154748417785, 0.6070264490694376, 0.3605580760887839, 0.0324154748417784, 0.0959172276669437, 0.8916698641086179, 0.0124129082244385, 0.8916698641086179, 0.0959172276669437, 0.0124129082244381, 0.1898015101110885, 0.6723403719974184, 0.1378581178914931, 0.6723403719974185, 0.1898015101110885, 0.1378581178914929, 0.4010584512926051, 0.4636054175537986, 0.1353361311535962, 0.4636054175537986, 0.4010584512926052, 0.1353361311535961, 0.2775825322761021, 0.5788906758314212, 0.1435267918924767, 0.5788906758314212, 0.2775825322761021, 0.1435267918924765, 0.3531888048870007, 0.3531888048870007, 0.2936223902259985, 0.3061183766903350, 0.6584300317131508, 0.0354515915965141, 0.6584300317131508, 0.3061183766903349, 0.0354515915965140, 0.4951059808027699, 0.4951059808027699, 0.0097880383944601, 0.4182891701734248, 0.5462922966952530, 0.0354185331313221, 0.5462922966952531, 0.4182891701734248, 0.0354185331313221, 0.0329098159605346, 0.9341803680789306, 0.0329098159605350, 0.0965099243357524, 0.8476962075384494, 0.0557938681257983, 0.8476962075384494, 0.0965099243357524, 0.0557938681257979, 0.1328397411105292, 0.8031840240996622, 0.0639762347898087, 0.8031840240996622, 0.1328397411105293, 0.0639762347898084, 0.0969643297980663, 0.8727730904601626, 0.0302625797417711, 0.8727730904601626, 0.0969643297980663, 0.0302625797417709, 0.4865637511306883, 0.4865637511306884, 0.0268724977386232, 0.4287537536910129, 0.5566086299500186, 0.0146376163589685, 0.5566086299500185, 0.4287537536910130, 0.0146376163589684, 0.0627150483897617, 0.8745699032204765, 0.0627150483897621, 0.1368534453260830, 0.8495413037445184, 0.0136052509293986, 0.8495413037445184, 0.1368534453260831, 0.0136052509293983, 0.3635619090992528, 0.6339620502785548, 0.0024760406221923, 0.6339620502785549, 0.3635619090992528, 0.0024760406221921, 0.1447435597702214, 0.7105128804595570, 0.1447435597702216, 0.3361435723276197, 0.5209304542944508, 0.1429259733779294, 0.5209304542944510, 0.3361435723276198, 0.1429259733779293, 0.0133646206082616, 0.9732707587834765, 0.0133646206082620, 0.0940988534499003, 0.9034803688043024, 0.0024207777457974, 0.9034803688043024, 0.0940988534499004, 0.0024207777457970, 0.2427105866699005, 0.5621390733405861, 0.1951503399895134, 0.5621390733405861, 0.2427105866699005, 0.1951503399895132, 0.4252384428310576, 0.5107064553472853, 0.0640551018216570, 0.5107064553472853, 0.4252384428310577, 0.0640551018216569, 0.3642781269741873, 0.6225342617933295, 0.0131876112324832, 0.6225342617933295, 0.3642781269741873, 0.0131876112324831, 0.1776637264896365, 0.7604631914033508, 0.0618730821070127, 0.7604631914033508, 0.1776637264896365, 0.0618730821070125, 0.0588456479492051, 0.9385418797080261, 0.0026124723427690, 0.9385418797080262, 0.0588456479492050, 0.0026124723427685, 0.2500996019098293, 0.7157099945300758, 0.0341904035600950, 0.7157099945300757, 0.2500996019098293, 0.0341904035600948, 0.0319725865365346, 0.9653765821329179, 0.0026508313305476, 0.9653765821329179, 0.0319725865365347, 0.0026508313305472, 0.2417239613576790, 0.7556844695525968, 0.0025915690897241, 0.7556844695525969, 0.2417239613576790, 0.0025915690897238, 0.1844047074392018, 0.8013219460698174, 0.0142733464909807, 0.8013219460698174, 0.1844047074392019, 0.0142733464909806, 0.0612563890152720, 0.9248872032992935, 0.0138564076854347, 0.9248872032992935, 0.0612563890152721, 0.0138564076854343, 0.0132571416922719, 0.9842490320417303, 0.0024938262659979, 0.9842490320417302, 0.0132571416922719, 0.0024938262659976, 0.0025649413700201, 0.9948701172599593, 0.0025649413700206, 0.1877722427785784, 0.6244555144428430, 0.1877722427785786, 0.1379731400814552, 0.7615859288601728, 0.1004409310583720, 0.7615859288601727, 0.1379731400814552, 0.1004409310583717, 0.0332056799273113, 0.9530968777199650, 0.0136974423527239, 0.9530968777199650, 0.0332056799273114, 0.0136974423527234, 0.3825643087869355, 0.3825643087869355, 0.2348713824261289, 0.1944661967811065, 0.7713906073293495, 0.0341431958895441, 0.7713906073293495, 0.1944661967811065, 0.0341431958895439, 0.2394826350852045, 0.7467127396201542, 0.0138046252946413, 0.7467127396201542, 0.2394826350852046, 0.0138046252946411, 0.3645542277763408, 0.4489485579241042, 0.1864972142995550, 0.4489485579241042, 0.3645542277763408, 0.1864972142995550, 0.1373564023661998, 0.8601018382691165, 0.0025417593646838, 0.8601018382691165, 0.1373564023661998, 0.0025417593646835, 0.2322320373188904, 0.7047330289764286, 0.0630349337046811, 0.7047330289764286, 0.2322320373188905, 0.0630349337046808, 0.2926613950722469, 0.6434616923483870, 0.0638769125793660, 0.6434616923483871, 0.2926613950722470, 0.0638769125793659, 0.3176481163981567, 0.4403990384263681, 0.2419528451754751, 0.4403990384263682, 0.3176481163981567, 0.2419528451754750, 0.3003015966157783, 0.6850991321252453, 0.0145992712589764, 0.6850991321252453, 0.3003015966157784, 0.0145992712589763, 0.3005613537168110, 0.6966205316862629, 0.0028181145969260, 0.6966205316862629, 0.3005613537168111, 0.0028181145969259, 0.0605239793987312, 0.9053415210418889, 0.0341344995593799, 0.9053415210418890, 0.0605239793987313, 0.0341344995593795, 0.3007859192338894, 0.5058586034896924, 0.1933554772764183, 0.5058586034896924, 0.3007859192338894, 0.1933554772764182, 0.1895507039776852, 0.7130863262721638, 0.0973629697501509, 0.7130863262721640, 0.1895507039776853, 0.0973629697501507, 0.4301399033621489, 0.5670717942327397, 0.0027883024051114, 0.5670717942327397, 0.4301399033621489, 0.0027883024051113, 0.1870185722176647, 0.8102254653358516, 0.0027559624464837, 0.8102254653358516, 0.1870185722176648, 0.0027559624464835, 0.3791895225090074, 0.5229833703321247, 0.0978271071588677, 0.5229833703321248, 0.3791895225090075, 0.0978271071588676, 0.3129669769821593, 0.5874593373809698, 0.0995736856368709, 0.5874593373809698, 0.3129669769821594, 0.0995736856368708, 0.1418044870172890, 0.8240811613164462, 0.0341143516662649, 0.8240811613164462, 0.1418044870172891, 0.0341143516662646, 0.4528922608459510, 0.4528922608459510, 0.0942154783080979, 0.2481814600155885, 0.6513210967114831, 0.1004974432729285, 0.6513210967114831, 0.2481814600155886, 0.1004974432729282, 0.3587978354079987, 0.5795283608954496, 0.0616738036965517, 0.5795283608954497, 0.3587978354079988, 0.0616738036965515, 0.0928670462140479, 0.8142659075719040, 0.0928670462140481, 0.2524849326490907, 0.4950301347018184, 0.2524849326490909 }; static double b_save[] = { 0.1764396582801324, 0.4117801708599339, 0.4117801708599340, 0.0488482658017371, 0.4755758670991315, 0.4755758670991317, 0.1454537953878326, 0.2297394365272493, 0.6248067680849183, 0.1454537953878326, 0.6248067680849183, 0.2297394365272494, 0.0016403265310440, 0.4991798367344781, 0.4991798367344782, 0.2962479881688700, 0.2962479881688700, 0.4075040236622604, 0.0324154748417785, 0.3605580760887839, 0.6070264490694378, 0.0324154748417785, 0.6070264490694377, 0.3605580760887841, 0.0124129082244384, 0.0959172276669437, 0.8916698641086181, 0.0124129082244384, 0.8916698641086181, 0.0959172276669440, 0.1378581178914931, 0.1898015101110885, 0.6723403719974186, 0.1378581178914931, 0.6723403719974186, 0.1898015101110887, 0.1353361311535962, 0.4010584512926053, 0.4636054175537988, 0.1353361311535962, 0.4636054175537987, 0.4010584512926054, 0.1435267918924767, 0.2775825322761022, 0.5788906758314213, 0.1435267918924767, 0.5788906758314213, 0.2775825322761024, 0.2936223902259986, 0.3531888048870008, 0.3531888048870009, 0.0354515915965142, 0.3061183766903350, 0.6584300317131511, 0.0354515915965142, 0.6584300317131511, 0.3061183766903353, 0.0097880383944602, 0.4951059808027700, 0.4951059808027701, 0.0354185331313222, 0.4182891701734248, 0.5462922966952534, 0.0354185331313222, 0.5462922966952531, 0.4182891701734250, 0.0329098159605348, 0.0329098159605345, 0.9341803680789307, 0.0557938681257981, 0.0965099243357524, 0.8476962075384495, 0.0557938681257981, 0.8476962075384497, 0.0965099243357527, 0.0639762347898086, 0.1328397411105292, 0.8031840240996623, 0.0639762347898086, 0.8031840240996623, 0.1328397411105295, 0.0302625797417711, 0.0969643297980663, 0.8727730904601628, 0.0302625797417711, 0.8727730904601628, 0.0969643297980667, 0.0268724977386233, 0.4865637511306884, 0.4865637511306886, 0.0146376163589685, 0.4287537536910130, 0.5566086299500187, 0.0146376163589685, 0.5566086299500186, 0.4287537536910132, 0.0627150483897619, 0.0627150483897616, 0.8745699032204766, 0.0136052509293985, 0.1368534453260830, 0.8495413037445185, 0.0136052509293985, 0.8495413037445186, 0.1368534453260834, 0.0024760406221923, 0.3635619090992529, 0.6339620502785551, 0.0024760406221923, 0.6339620502785550, 0.3635619090992531, 0.1447435597702217, 0.1447435597702214, 0.7105128804595572, 0.1429259733779294, 0.3361435723276198, 0.5209304542944510, 0.1429259733779294, 0.5209304542944510, 0.3361435723276199, 0.0133646206082619, 0.0133646206082616, 0.9732707587834766, 0.0024207777457973, 0.0940988534499003, 0.9034803688043025, 0.0024207777457973, 0.9034803688043025, 0.0940988534499007, 0.1951503399895134, 0.2427105866699006, 0.5621390733405862, 0.1951503399895134, 0.5621390733405862, 0.2427105866699007, 0.0640551018216570, 0.4252384428310577, 0.5107064553472855, 0.0640551018216570, 0.5107064553472854, 0.4252384428310579, 0.0131876112324832, 0.3642781269741873, 0.6225342617933296, 0.0131876112324832, 0.6225342617933296, 0.3642781269741875, 0.0618730821070127, 0.1776637264896365, 0.7604631914033511, 0.0618730821070127, 0.7604631914033509, 0.1776637264896368, 0.0026124723427688, 0.0588456479492050, 0.9385418797080262, 0.0026124723427688, 0.9385418797080264, 0.0588456479492054, 0.0341904035600950, 0.2500996019098293, 0.7157099945300760, 0.0341904035600950, 0.7157099945300759, 0.2500996019098295, 0.0026508313305474, 0.0319725865365346, 0.9653765821329181, 0.0026508313305474, 0.9653765821329181, 0.0319725865365349, 0.0025915690897240, 0.2417239613576791, 0.7556844695525970, 0.0025915690897240, 0.7556844695525970, 0.2417239613576793, 0.0142733464909807, 0.1844047074392018, 0.8013219460698178, 0.0142733464909807, 0.8013219460698175, 0.1844047074392021, 0.0138564076854345, 0.0612563890152719, 0.9248872032992936, 0.0138564076854345, 0.9248872032992936, 0.0612563890152723, 0.0024938262659979, 0.0132571416922719, 0.9842490320417305, 0.0024938262659979, 0.9842490320417305, 0.0132571416922722, 0.0025649413700205, 0.0025649413700201, 0.9948701172599594, 0.1877722427785786, 0.1877722427785785, 0.6244555144428431, 0.1004409310583719, 0.1379731400814553, 0.7615859288601730, 0.1004409310583719, 0.7615859288601730, 0.1379731400814555, 0.0136974423527237, 0.0332056799273113, 0.9530968777199650, 0.0136974423527237, 0.9530968777199653, 0.0332056799273116, 0.2348713824261290, 0.3825643087869356, 0.3825643087869356, 0.0341431958895440, 0.1944661967811065, 0.7713906073293497, 0.0341431958895440, 0.7713906073293496, 0.1944661967811067, 0.0138046252946413, 0.2394826350852046, 0.7467127396201543, 0.0138046252946413, 0.7467127396201543, 0.2394826350852048, 0.1864972142995551, 0.3645542277763408, 0.4489485579241043, 0.1864972142995551, 0.4489485579241042, 0.3645542277763409, 0.0025417593646838, 0.1373564023661998, 0.8601018382691167, 0.0025417593646838, 0.8601018382691167, 0.1373564023662001, 0.0630349337046810, 0.2322320373188904, 0.7047330289764286, 0.0630349337046810, 0.7047330289764286, 0.2322320373188907, 0.0638769125793660, 0.2926613950722469, 0.6434616923483873, 0.0638769125793660, 0.6434616923483871, 0.2926613950722471, 0.2419528451754752, 0.3176481163981568, 0.4403990384263682, 0.2419528451754752, 0.4403990384263682, 0.3176481163981569, 0.0145992712589763, 0.3003015966157783, 0.6850991321252455, 0.0145992712589763, 0.6850991321252453, 0.3003015966157786, 0.0028181145969261, 0.3005613537168110, 0.6966205316862633, 0.0028181145969261, 0.6966205316862629, 0.3005613537168113, 0.0341344995593797, 0.0605239793987312, 0.9053415210418891, 0.0341344995593797, 0.9053415210418891, 0.0605239793987315, 0.1933554772764183, 0.3007859192338894, 0.5058586034896925, 0.1933554772764183, 0.5058586034896925, 0.3007859192338895, 0.0973629697501509, 0.1895507039776853, 0.7130863262721642, 0.0973629697501509, 0.7130863262721641, 0.1895507039776855, 0.0027883024051114, 0.4301399033621490, 0.5670717942327399, 0.0027883024051114, 0.5670717942327398, 0.4301399033621491, 0.0027559624464837, 0.1870185722176647, 0.8102254653358518, 0.0027559624464837, 0.8102254653358517, 0.1870185722176650, 0.0978271071588678, 0.3791895225090076, 0.5229833703321249, 0.0978271071588678, 0.5229833703321249, 0.3791895225090077, 0.0995736856368710, 0.3129669769821593, 0.5874593373809700, 0.0995736856368710, 0.5874593373809698, 0.3129669769821595, 0.0341143516662649, 0.1418044870172890, 0.8240811613164464, 0.0341143516662649, 0.8240811613164463, 0.1418044870172893, 0.0942154783080980, 0.4528922608459511, 0.4528922608459512, 0.1004974432729284, 0.2481814600155886, 0.6513210967114832, 0.1004974432729284, 0.6513210967114832, 0.2481814600155887, 0.0616738036965517, 0.3587978354079987, 0.5795283608954498, 0.0616738036965517, 0.5795283608954497, 0.3587978354079990, 0.0928670462140481, 0.0928670462140479, 0.8142659075719042, 0.2524849326490909, 0.2524849326490908, 0.4950301347018185 }; static double c_save[] = { 0.4117801708599338, 0.1764396582801323, 0.4117801708599337, 0.4755758670991314, 0.0488482658017370, 0.4755758670991312, 0.6248067680849181, 0.1454537953878327, 0.2297394365272490, 0.2297394365272492, 0.1454537953878324, 0.6248067680849181, 0.4991798367344780, 0.0016403265310440, 0.4991798367344778, 0.4075040236622602, 0.2962479881688699, 0.2962479881688699, 0.6070264490694376, 0.0324154748417784, 0.3605580760887837, 0.3605580760887839, 0.0324154748417784, 0.6070264490694375, 0.8916698641086179, 0.0124129082244384, 0.0959172276669434, 0.0959172276669437, 0.0124129082244381, 0.8916698641086179, 0.6723403719974185, 0.1378581178914932, 0.1898015101110884, 0.1898015101110885, 0.1378581178914929, 0.6723403719974185, 0.4636054175537986, 0.1353361311535962, 0.4010584512926051, 0.4010584512926051, 0.1353361311535961, 0.4636054175537985, 0.5788906758314213, 0.1435267918924766, 0.2775825322761020, 0.2775825322761022, 0.1435267918924766, 0.5788906758314212, 0.3531888048870007, 0.2936223902259986, 0.3531888048870007, 0.6584300317131508, 0.0354515915965142, 0.3061183766903348, 0.3061183766903350, 0.0354515915965140, 0.6584300317131507, 0.4951059808027699, 0.0097880383944601, 0.4951059808027697, 0.5462922966952530, 0.0354185331313221, 0.4182891701734245, 0.4182891701734247, 0.0354185331313220, 0.5462922966952530, 0.9341803680789306, 0.0329098159605349, 0.0329098159605343, 0.8476962075384495, 0.0557938681257982, 0.0965099243357521, 0.0965099243357524, 0.0557938681257980, 0.8476962075384494, 0.8031840240996622, 0.0639762347898086, 0.1328397411105290, 0.1328397411105292, 0.0639762347898084, 0.8031840240996621, 0.8727730904601625, 0.0302625797417711, 0.0969643297980661, 0.0969643297980663, 0.0302625797417709, 0.8727730904601624, 0.4865637511306883, 0.0268724977386232, 0.4865637511306882, 0.5566086299500186, 0.0146376163589684, 0.4287537536910128, 0.4287537536910130, 0.0146376163589684, 0.5566086299500184, 0.8745699032204765, 0.0627150483897619, 0.0627150483897614, 0.8495413037445185, 0.0136052509293985, 0.1368534453260828, 0.1368534453260831, 0.0136052509293983, 0.8495413037445183, 0.6339620502785549, 0.0024760406221923, 0.3635619090992527, 0.3635619090992528, 0.0024760406221922, 0.6339620502785547, 0.7105128804595570, 0.1447435597702217, 0.1447435597702212, 0.5209304542944508, 0.1429259733779293, 0.3361435723276197, 0.3361435723276196, 0.1429259733779292, 0.5209304542944507, 0.9732707587834766, 0.0133646206082620, 0.0133646206082614, 0.9034803688043024, 0.0024207777457973, 0.0940988534499001, 0.0940988534499004, 0.0024207777457971, 0.9034803688043024, 0.5621390733405861, 0.1951503399895133, 0.2427105866699004, 0.2427105866699005, 0.1951503399895133, 0.5621390733405861, 0.5107064553472853, 0.0640551018216570, 0.4252384428310575, 0.4252384428310577, 0.0640551018216570, 0.5107064553472852, 0.6225342617933295, 0.0131876112324832, 0.3642781269741872, 0.3642781269741873, 0.0131876112324831, 0.6225342617933294, 0.7604631914033508, 0.0618730821070127, 0.1776637264896362, 0.1776637264896365, 0.0618730821070125, 0.7604631914033507, 0.9385418797080261, 0.0026124723427689, 0.0588456479492049, 0.0588456479492050, 0.0026124723427686, 0.9385418797080262, 0.7157099945300758, 0.0341904035600950, 0.2500996019098289, 0.2500996019098294, 0.0341904035600947, 0.7157099945300756, 0.9653765821329180, 0.0026508313305475, 0.0319725865365343, 0.0319725865365347, 0.0026508313305472, 0.9653765821329180, 0.7556844695525969, 0.0025915690897241, 0.2417239613576789, 0.2417239613576791, 0.0025915690897239, 0.7556844695525968, 0.8013219460698174, 0.0142733464909807, 0.1844047074392015, 0.1844047074392018, 0.0142733464909806, 0.8013219460698173, 0.9248872032992935, 0.0138564076854345, 0.0612563890152718, 0.0612563890152719, 0.0138564076854343, 0.9248872032992934, 0.9842490320417303, 0.0024938262659978, 0.0132571416922715, 0.0132571416922719, 0.0024938262659976, 0.9842490320417302, 0.9948701172599593, 0.0025649413700205, 0.0025649413700199, 0.6244555144428430, 0.1877722427785785, 0.1877722427785783, 0.7615859288601728, 0.1004409310583719, 0.1379731400814550, 0.1379731400814553, 0.1004409310583718, 0.7615859288601728, 0.9530968777199651, 0.0136974423527237, 0.0332056799273112, 0.0332056799273113, 0.0136974423527233, 0.9530968777199650, 0.3825643087869355, 0.2348713824261289, 0.3825643087869354, 0.7713906073293495, 0.0341431958895440, 0.1944661967811062, 0.1944661967811065, 0.0341431958895438, 0.7713906073293494, 0.7467127396201543, 0.0138046252946413, 0.2394826350852044, 0.2394826350852046, 0.0138046252946411, 0.7467127396201541, 0.4489485579241042, 0.1864972142995550, 0.3645542277763407, 0.3645542277763407, 0.1864972142995550, 0.4489485579241040, 0.8601018382691163, 0.0025417593646838, 0.1373564023661995, 0.1373564023661998, 0.0025417593646836, 0.8601018382691163, 0.7047330289764286, 0.0630349337046809, 0.2322320373188903, 0.2322320373188904, 0.0630349337046808, 0.7047330289764285, 0.6434616923483871, 0.0638769125793661, 0.2926613950722466, 0.2926613950722469, 0.0638769125793659, 0.6434616923483869, 0.4403990384263681, 0.2419528451754751, 0.3176481163981567, 0.3176481163981567, 0.2419528451754751, 0.4403990384263681, 0.6850991321252454, 0.0145992712589764, 0.3003015966157780, 0.3003015966157783, 0.0145992712589763, 0.6850991321252452, 0.6966205316862629, 0.0028181145969260, 0.3005613537168107, 0.3005613537168110, 0.0028181145969260, 0.6966205316862628, 0.9053415210418890, 0.0341344995593799, 0.0605239793987310, 0.0605239793987312, 0.0341344995593795, 0.9053415210418889, 0.5058586034896924, 0.1933554772764182, 0.3007859192338892, 0.3007859192338893, 0.1933554772764182, 0.5058586034896922, 0.7130863262721640, 0.0973629697501509, 0.1895507039776850, 0.1895507039776852, 0.0973629697501507, 0.7130863262721638, 0.5670717942327397, 0.0027883024051114, 0.4301399033621487, 0.4301399033621489, 0.0027883024051113, 0.5670717942327396, 0.8102254653358516, 0.0027559624464837, 0.1870185722176645, 0.1870185722176647, 0.0027559624464836, 0.8102254653358514, 0.5229833703321248, 0.0978271071588677, 0.3791895225090074, 0.3791895225090074, 0.0978271071588676, 0.5229833703321246, 0.5874593373809698, 0.0995736856368709, 0.3129669769821590, 0.3129669769821593, 0.0995736856368709, 0.5874593373809696, 0.8240811613164462, 0.0341143516662649, 0.1418044870172886, 0.1418044870172890, 0.0341143516662646, 0.8240811613164462, 0.4528922608459510, 0.0942154783080978, 0.4528922608459508, 0.6513210967114831, 0.1004974432729284, 0.2481814600155884, 0.2481814600155885, 0.1004974432729283, 0.6513210967114831, 0.5795283608954496, 0.0616738036965517, 0.3587978354079986, 0.3587978354079986, 0.0616738036965515, 0.5795283608954496, 0.8142659075719041, 0.0928670462140481, 0.0928670462140476, 0.4950301347018183, 0.2524849326490907, 0.2524849326490906 }; static double w_save[] = { 0.0030799655691816, 0.0030799655691816, 0.0030799655691816, 0.0024873482202465, 0.0024873482202465, 0.0024873482202465, 0.0039126383408176, 0.0039126383408176, 0.0039126383408176, 0.0039126383408176, 0.0039126383408176, 0.0039126383408176, 0.0006086157221808, 0.0006086157221808, 0.0006086157221808, 0.0058780823337592, 0.0058780823337592, 0.0058780823337592, 0.0026575597720771, 0.0026575597720771, 0.0026575597720771, 0.0026575597720771, 0.0026575597720771, 0.0026575597720771, 0.0010403858576164, 0.0010403858576164, 0.0010403858576164, 0.0010403858576164, 0.0010403858576164, 0.0010403858576164, 0.0038688222455242, 0.0038688222455242, 0.0038688222455242, 0.0038688222455242, 0.0038688222455242, 0.0038688222455242, 0.0054360079215851, 0.0054360079215851, 0.0054360079215851, 0.0054360079215851, 0.0054360079215851, 0.0054360079215851, 0.0051330210770134, 0.0051330210770134, 0.0051330210770134, 0.0051330210770134, 0.0051330210770134, 0.0051330210770134, 0.0068684889665150, 0.0068684889665150, 0.0068684889665150, 0.0027248852604065, 0.0027248852604065, 0.0027248852604065, 0.0027248852604065, 0.0027248852604065, 0.0027248852604065, 0.0016143072439158, 0.0016143072439158, 0.0016143072439158, 0.0030819278277026, 0.0030819278277026, 0.0030819278277026, 0.0030819278277026, 0.0030819278277026, 0.0030819278277026, 0.0010836224292710, 0.0010836224292710, 0.0010836224292710, 0.0021960146608965, 0.0021960146608965, 0.0021960146608965, 0.0021960146608965, 0.0021960146608965, 0.0021960146608965, 0.0027071716291895, 0.0027071716291895, 0.0027071716291895, 0.0027071716291895, 0.0027071716291895, 0.0027071716291895, 0.0017732505663030, 0.0017732505663030, 0.0017732505663030, 0.0017732505663030, 0.0017732505663030, 0.0017732505663030, 0.0027166050682952, 0.0027166050682952, 0.0027166050682952, 0.0021194095320856, 0.0021194095320856, 0.0021194095320856, 0.0021194095320856, 0.0021194095320856, 0.0021194095320856, 0.0020243293045497, 0.0020243293045497, 0.0020243293045497, 0.0013822658273997, 0.0013822658273997, 0.0013822658273997, 0.0013822658273997, 0.0013822658273997, 0.0013822658273997, 0.0008287796022760, 0.0008287796022760, 0.0008287796022760, 0.0008287796022760, 0.0008287796022760, 0.0008287796022760, 0.0042454319210643, 0.0042454319210643, 0.0042454319210643, 0.0057609299703683, 0.0057609299703683, 0.0057609299703683, 0.0057609299703683, 0.0057609299703683, 0.0057609299703683, 0.0004721021055792, 0.0004721021055792, 0.0004721021055792, 0.0004866406535789, 0.0004866406535789, 0.0004866406535789, 0.0004866406535789, 0.0004866406535789, 0.0004866406535789, 0.0060611706044967, 0.0060611706044967, 0.0060611706044967, 0.0060611706044967, 0.0060611706044967, 0.0060611706044967, 0.0039591603530013, 0.0039591603530013, 0.0039591603530013, 0.0039591603530013, 0.0039591603530013, 0.0039591603530013, 0.0019515305614847, 0.0019515305614847, 0.0019515305614847, 0.0019515305614847, 0.0019515305614847, 0.0019515305614847, 0.0031758640195785, 0.0031758640195785, 0.0031758640195785, 0.0031758640195785, 0.0031758640195785, 0.0031758640195785, 0.0004177689784025, 0.0004177689784025, 0.0004177689784025, 0.0004177689784025, 0.0004177689784025, 0.0004177689784025, 0.0028037985130037, 0.0028037985130037, 0.0028037985130037, 0.0028037985130037, 0.0028037985130037, 0.0028037985130037, 0.0003074323001241, 0.0003074323001241, 0.0003074323001241, 0.0003074323001241, 0.0003074323001241, 0.0003074323001241, 0.0007580478745157, 0.0007580478745157, 0.0007580478745157, 0.0007580478745157, 0.0007580478745157, 0.0007580478745157, 0.0016285601871914, 0.0016285601871914, 0.0016285601871914, 0.0016285601871914, 0.0016285601871914, 0.0016285601871914, 0.0010015815151317, 0.0010015815151317, 0.0010015815151317, 0.0010015815151317, 0.0010015815151317, 0.0010015815151317, 0.0001897035092211, 0.0001897035092211, 0.0001897035092211, 0.0001897035092211, 0.0001897035092211, 0.0001897035092211, 0.0000857325766799, 0.0000857325766799, 0.0000857325766799, 0.0053352753423962, 0.0053352753423962, 0.0053352753423962, 0.0039225937188264, 0.0039225937188264, 0.0039225937188264, 0.0039225937188264, 0.0039225937188264, 0.0039225937188264, 0.0007352644490711, 0.0007352644490711, 0.0007352644490711, 0.0007352644490711, 0.0007352644490711, 0.0007352644490711, 0.0069496808690566, 0.0069496808690566, 0.0069496808690566, 0.0026277500982666, 0.0026277500982666, 0.0026277500982666, 0.0026277500982666, 0.0026277500982666, 0.0026277500982666, 0.0018416339190279, 0.0018416339190279, 0.0018416339190279, 0.0018416339190279, 0.0018416339190279, 0.0018416339190279, 0.0059250327726738, 0.0059250327726738, 0.0059250327726738, 0.0059250327726738, 0.0059250327726738, 0.0059250327726738, 0.0006123388408143, 0.0006123388408143, 0.0006123388408143, 0.0006123388408143, 0.0006123388408143, 0.0006123388408143, 0.0038249634484789, 0.0038249634484789, 0.0038249634484789, 0.0038249634484789, 0.0038249634484789, 0.0038249634484789, 0.0041283032222063, 0.0041283032222063, 0.0041283032222063, 0.0041283032222063, 0.0041283032222063, 0.0041283032222063, 0.0066920320417412, 0.0066920320417412, 0.0066920320417412, 0.0066920320417412, 0.0066920320417412, 0.0066920320417412, 0.0020472829473930, 0.0020472829473930, 0.0020472829473930, 0.0020472829473930, 0.0020472829473930, 0.0020472829473930, 0.0008780156791651, 0.0008780156791651, 0.0008780156791651, 0.0008780156791651, 0.0008780156791651, 0.0008780156791651, 0.0015777851185459, 0.0015777851185459, 0.0015777851185459, 0.0015777851185459, 0.0015777851185459, 0.0015777851185459, 0.0063074359109884, 0.0063074359109884, 0.0063074359109884, 0.0063074359109884, 0.0063074359109884, 0.0063074359109884, 0.0042726398210532, 0.0042726398210532, 0.0042726398210532, 0.0042726398210532, 0.0042726398210532, 0.0042726398210532, 0.0009698373462393, 0.0009698373462393, 0.0009698373462393, 0.0009698373462393, 0.0009698373462393, 0.0009698373462393, 0.0007380182704579, 0.0007380182704579, 0.0007380182704579, 0.0007380182704579, 0.0007380182704579, 0.0007380182704579, 0.0052618813601275, 0.0052618813601275, 0.0052618813601275, 0.0052618813601275, 0.0052618813601275, 0.0052618813601275, 0.0053002719749983, 0.0053002719749983, 0.0053002719749983, 0.0053002719749983, 0.0053002719749983, 0.0053002719749983, 0.0024558010102792, 0.0024558010102792, 0.0024558010102792, 0.0024558010102792, 0.0024558010102792, 0.0024558010102792, 0.0053328054204010, 0.0053328054204010, 0.0053328054204010, 0.0050556103951577, 0.0050556103951577, 0.0050556103951577, 0.0050556103951577, 0.0050556103951577, 0.0050556103951577, 0.0044341909691302, 0.0044341909691302, 0.0044341909691302, 0.0044341909691302, 0.0044341909691302, 0.0044341909691302, 0.0032907061458540, 0.0032907061458540, 0.0032907061458540, 0.0073142091431203, 0.0073142091431203, 0.0073142091431203 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule44 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule44() returns the rule of precision 44. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.0017123075799637, 0.9965753848400722, 0.0017123075799641, 0.0197551676157197, 0.9694881128275959, 0.0107567195566844, 0.9694881128275961, 0.0197551676157198, 0.0107567195566840, 0.0995165813818446, 0.8997028327182934, 0.0007805858998620, 0.8997028327182934, 0.0995165813818448, 0.0007805858998617, 0.1534945447552139, 0.8445671223319955, 0.0019383329127907, 0.8445671223319955, 0.1534945447552140, 0.0019383329127904, 0.4606074520039989, 0.5376064055154758, 0.0017861424805254, 0.5376064055154757, 0.4606074520039989, 0.0017861424805253, 0.0296420604264444, 0.9686037144025027, 0.0017542251710529, 0.9686037144025029, 0.0296420604264444, 0.0017542251710524, 0.3338406248248118, 0.6656420809155281, 0.0005172942596601, 0.6656420809155281, 0.3338406248248119, 0.0005172942596599, 0.0291673514653005, 0.9416652970693987, 0.0291673514653009, 0.0495499879123024, 0.9009000241753948, 0.0495499879123029, 0.1194266872274120, 0.8730274418468819, 0.0075458709257062, 0.8730274418468820, 0.1194266872274120, 0.0075458709257059, 0.1733118066994289, 0.8151956468477657, 0.0114925464528055, 0.8151956468477658, 0.1733118066994291, 0.0114925464528051, 0.0593978633857566, 0.9163391688931388, 0.0242629677211046, 0.9163391688931388, 0.0593978633857567, 0.0242629677211044, 0.2594461646278431, 0.7307561420696972, 0.0097976933024596, 0.7307561420696972, 0.2594461646278433, 0.0097976933024595, 0.2696648795311178, 0.7284359696406738, 0.0018991508282084, 0.7284359696406739, 0.2696648795311180, 0.0018991508282082, 0.3234284104109564, 0.6688969097328992, 0.0076746798561443, 0.6688969097328992, 0.3234284104109564, 0.0076746798561442, 0.2093976094351925, 0.7878951862570389, 0.0027072043077686, 0.7878951862570389, 0.2093976094351925, 0.0027072043077684, 0.0107937373867395, 0.9864998660560905, 0.0027063965571701, 0.9864998660560905, 0.0107937373867397, 0.0027063965571697, 0.0416577600266789, 0.9478795059436815, 0.0104627340296397, 0.9478795059436816, 0.0416577600266790, 0.0104627340296393, 0.1393007744184822, 0.8391863652965978, 0.0215128602849200, 0.8391863652965978, 0.1393007744184823, 0.0215128602849197, 0.4877239805831534, 0.4877239805831534, 0.0245520388336932, 0.0971407574555291, 0.8800347069095190, 0.0228245356349520, 0.8800347069095190, 0.0971407574555291, 0.0228245356349517, 0.1511248097389706, 0.7487866599562394, 0.1000885303047901, 0.7487866599562394, 0.1511248097389706, 0.1000885303047898, 0.4960618044654749, 0.4960618044654750, 0.0078763910690500, 0.3939323955351545, 0.6029080349282100, 0.0031595695366355, 0.6029080349282100, 0.3939323955351544, 0.0031595695366353, 0.1276374594173248, 0.8287949653018399, 0.0435675752808352, 0.8287949653018402, 0.1276374594173247, 0.0435675752808349, 0.2153427859170523, 0.7218418378371082, 0.0628153762458395, 0.7218418378371081, 0.2153427859170524, 0.0628153762458394, 0.1805238872560285, 0.7847849261270403, 0.0346911866169312, 0.7847849261270403, 0.1805238872560286, 0.0346911866169310, 0.3706974787497283, 0.6133503854822405, 0.0159521357680312, 0.6133503854822404, 0.3706974787497284, 0.0159521357680310, 0.2389043466345939, 0.7245299623844421, 0.0365656909809640, 0.7245299623844421, 0.2389043466345939, 0.0365656909809638, 0.0765961156051737, 0.8468077687896521, 0.0765961156051742, 0.4035445047649169, 0.4735882468281119, 0.1228672484069711, 0.4735882468281119, 0.4035445047649169, 0.1228672484069711, 0.2510886184010617, 0.6268501895654275, 0.1220611920335108, 0.6268501895654275, 0.2510886184010617, 0.1220611920335106, 0.3100924603530019, 0.6020796526141913, 0.0878278870328068, 0.6020796526141913, 0.3100924603530019, 0.0878278870328066, 0.4171889370681111, 0.5171299598756924, 0.0656811030561965, 0.5171299598756924, 0.4171889370681111, 0.0656811030561964, 0.4759518460527712, 0.4759518460527714, 0.0480963078944574, 0.0842771975158688, 0.8700026552993007, 0.0457201471848306, 0.8700026552993007, 0.0842771975158688, 0.0457201471848303, 0.2875172818904952, 0.6596793072144378, 0.0528034108950670, 0.6596793072144378, 0.2875172818904952, 0.0528034108950669, 0.1090955419572377, 0.7818089160855244, 0.1090955419572380, 0.3421421849069924, 0.6245951075427290, 0.0332627075502785, 0.6245951075427290, 0.3421421849069924, 0.0332627075502785, 0.2312470036938409, 0.5375059926123180, 0.2312470036938411, 0.1959081982236505, 0.6081836035526987, 0.1959081982236506, 0.2907813356274843, 0.6861277132074860, 0.0230909511650299, 0.6861277132074859, 0.2907813356274844, 0.0230909511650297, 0.0777385297161003, 0.9138493473952539, 0.0084121228886461, 0.9138493473952539, 0.0777385297161003, 0.0084121228886456, 0.0583538087981567, 0.9397903465114041, 0.0018558446904393, 0.9397903465114043, 0.0583538087981568, 0.0018558446904388, 0.3537362173911874, 0.4944025611096592, 0.1518612214991533, 0.4944025611096592, 0.3537362173911875, 0.1518612214991532, 0.1941036834219221, 0.6592024700825740, 0.1466938464955038, 0.6592024700825740, 0.1941036834219222, 0.1466938464955036, 0.1152446802620743, 0.8116970473144409, 0.0730582724234849, 0.8116970473144409, 0.1152446802620743, 0.0730582724234846, 0.2526489188568274, 0.6640305665631259, 0.0833205145800467, 0.6640305665631260, 0.2526489188568274, 0.0833205145800466, 0.3706381279110351, 0.5316917725696112, 0.0976700995193537, 0.5316917725696112, 0.3706381279110351, 0.0976700995193536, 0.1975107662353285, 0.7003617605288512, 0.1021274732358203, 0.7003617605288514, 0.1975107662353285, 0.1021274732358200, 0.2191021787766396, 0.7639576985765668, 0.0169401226467936, 0.7639576985765668, 0.2191021787766396, 0.0169401226467933, 0.1647494714555341, 0.7706431138900716, 0.0646074146543943, 0.7706431138900717, 0.1647494714555343, 0.0646074146543940, 0.3487568874306149, 0.4569496207074597, 0.1942934918619253, 0.4569496207074596, 0.3487568874306151, 0.1942934918619253, 0.3558533300586623, 0.5853570821660166, 0.0587895877753212, 0.5853570821660165, 0.3558533300586624, 0.0587895877753211, 0.3487165289854694, 0.4076984951293575, 0.2435849758851730, 0.4076984951293575, 0.3487165289854693, 0.2435849758851730, 0.4223218082071514, 0.4223218082071514, 0.1553563835856973, 0.4548817499595059, 0.4548817499595060, 0.0902365000809880, 0.2907043355496960, 0.5231696984941406, 0.1861259659561632, 0.5231696984941406, 0.2907043355496960, 0.1861259659561631, 0.1439001195404208, 0.7121997609191582, 0.1439001195404210, 0.2898629348171137, 0.4717800456303300, 0.2383570195525562, 0.4717800456303302, 0.2898629348171137, 0.2383570195525561, 0.4023404478547354, 0.4023404478547353, 0.1953191042905292, 0.3093835754454580, 0.5593868077625690, 0.1312296167919730, 0.5593868077625690, 0.3093835754454579, 0.1312296167919728, 0.2469795390992444, 0.5845614823482763, 0.1684589785524792, 0.5845614823482763, 0.2469795390992445, 0.1684589785524790, 0.4353451951214652, 0.5515293353673113, 0.0131254695112235, 0.5515293353673113, 0.4353451951214652, 0.0131254695112233, 0.2942957656908339, 0.4114084686183320, 0.2942957656908339, 0.3516157887957689, 0.3516157887957689, 0.2967684224084619, 0.4137012893148831, 0.5518852701665368, 0.0344134405185802, 0.5518852701665367, 0.4137012893148831, 0.0344134405185801 }; static double b_save[] = { 0.0017123075799640, 0.0017123075799637, 0.9965753848400725, 0.0107567195566843, 0.0197551676157197, 0.9694881128275962, 0.0107567195566843, 0.9694881128275962, 0.0197551676157201, 0.0007805858998619, 0.0995165813818446, 0.8997028327182935, 0.0007805858998619, 0.8997028327182935, 0.0995165813818450, 0.0019383329127906, 0.1534945447552139, 0.8445671223319957, 0.0019383329127906, 0.8445671223319957, 0.1534945447552142, 0.0017861424805254, 0.4606074520039989, 0.5376064055154759, 0.0017861424805254, 0.5376064055154758, 0.4606074520039992, 0.0017542251710528, 0.0296420604264444, 0.9686037144025029, 0.0017542251710528, 0.9686037144025031, 0.0296420604264447, 0.0005172942596601, 0.3338406248248119, 0.6656420809155283, 0.0005172942596601, 0.6656420809155282, 0.3338406248248121, 0.0291673514653008, 0.0291673514653005, 0.9416652970693989, 0.0495499879123027, 0.0495499879123024, 0.9009000241753949, 0.0075458709257061, 0.1194266872274120, 0.8730274418468821, 0.0075458709257061, 0.8730274418468821, 0.1194266872274123, 0.0114925464528053, 0.1733118066994289, 0.8151956468477658, 0.0114925464528053, 0.8151956468477658, 0.1733118066994292, 0.0242629677211045, 0.0593978633857566, 0.9163391688931390, 0.0242629677211045, 0.9163391688931390, 0.0593978633857569, 0.0097976933024596, 0.2594461646278432, 0.7307561420696975, 0.0097976933024596, 0.7307561420696972, 0.2594461646278435, 0.0018991508282083, 0.2696648795311178, 0.7284359696406740, 0.0018991508282083, 0.7284359696406739, 0.2696648795311181, 0.0076746798561443, 0.3234284104109565, 0.6688969097328994, 0.0076746798561443, 0.6688969097328994, 0.3234284104109568, 0.0027072043077686, 0.2093976094351925, 0.7878951862570391, 0.0027072043077686, 0.7878951862570391, 0.2093976094351928, 0.0027063965571699, 0.0107937373867395, 0.9864998660560906, 0.0027063965571699, 0.9864998660560906, 0.0107937373867399, 0.0104627340296395, 0.0416577600266789, 0.9478795059436816, 0.0104627340296395, 0.9478795059436816, 0.0416577600266793, 0.0215128602849199, 0.1393007744184823, 0.8391863652965980, 0.0215128602849199, 0.8391863652965980, 0.1393007744184826, 0.0245520388336933, 0.4877239805831535, 0.4877239805831536, 0.0228245356349520, 0.0971407574555291, 0.8800347069095191, 0.0228245356349520, 0.8800347069095191, 0.0971407574555294, 0.1000885303047900, 0.1511248097389706, 0.7487866599562395, 0.1000885303047900, 0.7487866599562395, 0.1511248097389709, 0.0078763910690501, 0.4960618044654750, 0.4960618044654752, 0.0031595695366355, 0.3939323955351545, 0.6029080349282102, 0.0031595695366355, 0.6029080349282102, 0.3939323955351547, 0.0435675752808352, 0.1276374594173248, 0.8287949653018403, 0.0435675752808352, 0.8287949653018403, 0.1276374594173251, 0.0628153762458396, 0.2153427859170523, 0.7218418378371083, 0.0628153762458396, 0.7218418378371083, 0.2153427859170526, 0.0346911866169312, 0.1805238872560285, 0.7847849261270404, 0.0346911866169312, 0.7847849261270404, 0.1805238872560288, 0.0159521357680312, 0.3706974787497284, 0.6133503854822406, 0.0159521357680312, 0.6133503854822405, 0.3706974787497286, 0.0365656909809640, 0.2389043466345939, 0.7245299623844423, 0.0365656909809640, 0.7245299623844423, 0.2389043466345942, 0.0765961156051741, 0.0765961156051737, 0.8468077687896522, 0.1228672484069712, 0.4035445047649170, 0.4735882468281121, 0.1228672484069712, 0.4735882468281120, 0.4035445047649171, 0.1220611920335108, 0.2510886184010618, 0.6268501895654277, 0.1220611920335108, 0.6268501895654277, 0.2510886184010619, 0.0878278870328068, 0.3100924603530020, 0.6020796526141915, 0.0878278870328068, 0.6020796526141915, 0.3100924603530022, 0.0656811030561965, 0.4171889370681111, 0.5171299598756927, 0.0656811030561965, 0.5171299598756924, 0.4171889370681113, 0.0480963078944575, 0.4759518460527713, 0.4759518460527715, 0.0457201471848306, 0.0842771975158688, 0.8700026552993009, 0.0457201471848306, 0.8700026552993009, 0.0842771975158691, 0.0528034108950670, 0.2875172818904953, 0.6596793072144379, 0.0528034108950670, 0.6596793072144379, 0.2875172818904955, 0.1090955419572379, 0.1090955419572376, 0.7818089160855246, 0.0332627075502786, 0.3421421849069925, 0.6245951075427292, 0.0332627075502786, 0.6245951075427292, 0.3421421849069927, 0.2312470036938411, 0.2312470036938410, 0.5375059926123180, 0.1959081982236507, 0.1959081982236506, 0.6081836035526990, 0.0230909511650298, 0.2907813356274843, 0.6861277132074860, 0.0230909511650298, 0.6861277132074860, 0.2907813356274845, 0.0084121228886458, 0.0777385297161002, 0.9138493473952539, 0.0084121228886458, 0.9138493473952539, 0.0777385297161006, 0.0018558446904391, 0.0583538087981567, 0.9397903465114043, 0.0018558446904391, 0.9397903465114043, 0.0583538087981571, 0.1518612214991534, 0.3537362173911875, 0.4944025611096594, 0.1518612214991534, 0.4944025611096593, 0.3537362173911877, 0.1466938464955038, 0.1941036834219222, 0.6592024700825742, 0.1466938464955038, 0.6592024700825742, 0.1941036834219224, 0.0730582724234848, 0.1152446802620743, 0.8116970473144410, 0.0730582724234848, 0.8116970473144410, 0.1152446802620745, 0.0833205145800467, 0.2526489188568274, 0.6640305665631261, 0.0833205145800467, 0.6640305665631261, 0.2526489188568276, 0.0976700995193538, 0.3706381279110351, 0.5316917725696113, 0.0976700995193538, 0.5316917725696113, 0.3706381279110353, 0.1021274732358202, 0.1975107662353285, 0.7003617605288514, 0.1021274732358202, 0.7003617605288514, 0.1975107662353287, 0.0169401226467935, 0.2191021787766396, 0.7639576985765670, 0.0169401226467935, 0.7639576985765670, 0.2191021787766399, 0.0646074146543942, 0.1647494714555342, 0.7706431138900717, 0.0646074146543942, 0.7706431138900717, 0.1647494714555344, 0.1942934918619254, 0.3487568874306151, 0.4569496207074598, 0.1942934918619254, 0.4569496207074597, 0.3487568874306152, 0.0587895877753212, 0.3558533300586624, 0.5853570821660167, 0.0587895877753212, 0.5853570821660166, 0.3558533300586625, 0.2435849758851731, 0.3487165289854695, 0.4076984951293576, 0.2435849758851731, 0.4076984951293576, 0.3487165289854696, 0.1553563835856973, 0.4223218082071514, 0.4223218082071515, 0.0902365000809881, 0.4548817499595060, 0.4548817499595061, 0.1861259659561633, 0.2907043355496962, 0.5231696984941409, 0.1861259659561633, 0.5231696984941409, 0.2907043355496963, 0.1439001195404211, 0.1439001195404208, 0.7121997609191584, 0.2383570195525562, 0.2898629348171138, 0.4717800456303302, 0.2383570195525562, 0.4717800456303302, 0.2898629348171138, 0.1953191042905293, 0.4023404478547354, 0.4023404478547355, 0.1312296167919730, 0.3093835754454580, 0.5593868077625692, 0.1312296167919730, 0.5593868077625692, 0.3093835754454582, 0.1684589785524792, 0.2469795390992445, 0.5845614823482764, 0.1684589785524792, 0.5845614823482764, 0.2469795390992447, 0.0131254695112235, 0.4353451951214652, 0.5515293353673115, 0.0131254695112235, 0.5515293353673113, 0.4353451951214655, 0.2942957656908340, 0.2942957656908340, 0.4114084686183322, 0.2967684224084621, 0.3516157887957691, 0.3516157887957691, 0.0344134405185802, 0.4137012893148831, 0.5518852701665369, 0.0344134405185802, 0.5518852701665368, 0.4137012893148834 }; static double c_save[] = { 0.9965753848400724, 0.0017123075799641, 0.0017123075799634, 0.9694881128275959, 0.0107567195566844, 0.0197551676157194, 0.0197551676157196, 0.0107567195566841, 0.9694881128275959, 0.8997028327182934, 0.0007805858998619, 0.0995165813818445, 0.0995165813818446, 0.0007805858998616, 0.8997028327182933, 0.8445671223319956, 0.0019383329127906, 0.1534945447552136, 0.1534945447552139, 0.0019383329127903, 0.8445671223319955, 0.5376064055154757, 0.0017861424805253, 0.4606074520039987, 0.4606074520039989, 0.0017861424805253, 0.5376064055154756, 0.9686037144025029, 0.0017542251710529, 0.0296420604264441, 0.0296420604264443, 0.0017542251710524, 0.9686037144025029, 0.6656420809155281, 0.0005172942596600, 0.3338406248248116, 0.3338406248248118, 0.0005172942596600, 0.6656420809155280, 0.9416652970693987, 0.0291673514653008, 0.0291673514653003, 0.9009000241753948, 0.0495499879123028, 0.0495499879123021, 0.8730274418468819, 0.0075458709257062, 0.1194266872274118, 0.1194266872274119, 0.0075458709257060, 0.8730274418468817, 0.8151956468477658, 0.0114925464528054, 0.1733118066994287, 0.1733118066994289, 0.0114925464528052, 0.8151956468477657, 0.9163391688931388, 0.0242629677211045, 0.0593978633857564, 0.0593978633857566, 0.0242629677211043, 0.9163391688931387, 0.7307561420696972, 0.0097976933024596, 0.2594461646278429, 0.2594461646278431, 0.0097976933024596, 0.7307561420696971, 0.7284359696406738, 0.0018991508282084, 0.2696648795311175, 0.2696648795311177, 0.0018991508282081, 0.7284359696406737, 0.6688969097328993, 0.0076746798561443, 0.3234284104109563, 0.3234284104109565, 0.0076746798561442, 0.6688969097328989, 0.7878951862570389, 0.0027072043077686, 0.2093976094351923, 0.2093976094351925, 0.0027072043077684, 0.7878951862570389, 0.9864998660560906, 0.0027063965571700, 0.0107937373867393, 0.0107937373867396, 0.0027063965571696, 0.9864998660560905, 0.9478795059436815, 0.0104627340296396, 0.0416577600266786, 0.0416577600266789, 0.0104627340296394, 0.9478795059436814, 0.8391863652965978, 0.0215128602849199, 0.1393007744184821, 0.1393007744184823, 0.0215128602849198, 0.8391863652965976, 0.4877239805831534, 0.0245520388336932, 0.4877239805831531, 0.8800347069095189, 0.0228245356349519, 0.0971407574555289, 0.0971407574555290, 0.0228245356349518, 0.8800347069095188, 0.7487866599562394, 0.1000885303047900, 0.1511248097389705, 0.1511248097389706, 0.1000885303047899, 0.7487866599562393, 0.4960618044654749, 0.0078763910690500, 0.4960618044654748, 0.6029080349282100, 0.0031595695366355, 0.3939323955351542, 0.3939323955351545, 0.0031595695366354, 0.6029080349282099, 0.8287949653018400, 0.0435675752808353, 0.1276374594173245, 0.1276374594173247, 0.0435675752808350, 0.8287949653018400, 0.7218418378371082, 0.0628153762458395, 0.2153427859170521, 0.2153427859170524, 0.0628153762458393, 0.7218418378371080, 0.7847849261270403, 0.0346911866169312, 0.1805238872560283, 0.1805238872560285, 0.0346911866169309, 0.7847849261270403, 0.6133503854822404, 0.0159521357680311, 0.3706974787497281, 0.3706974787497284, 0.0159521357680311, 0.6133503854822404, 0.7245299623844421, 0.0365656909809640, 0.2389043466345937, 0.2389043466345939, 0.0365656909809637, 0.7245299623844421, 0.8468077687896521, 0.0765961156051742, 0.0765961156051735, 0.4735882468281119, 0.1228672484069712, 0.4035445047649167, 0.4035445047649169, 0.1228672484069712, 0.4735882468281118, 0.6268501895654275, 0.1220611920335107, 0.2510886184010614, 0.2510886184010617, 0.1220611920335106, 0.6268501895654275, 0.6020796526141913, 0.0878278870328068, 0.3100924603530018, 0.3100924603530019, 0.0878278870328065, 0.6020796526141912, 0.5171299598756924, 0.0656811030561965, 0.4171889370681109, 0.4171889370681111, 0.0656811030561965, 0.5171299598756923, 0.4759518460527713, 0.0480963078944573, 0.4759518460527711, 0.8700026552993007, 0.0457201471848306, 0.0842771975158686, 0.0842771975158688, 0.0457201471848304, 0.8700026552993005, 0.6596793072144378, 0.0528034108950669, 0.2875172818904951, 0.2875172818904952, 0.0528034108950669, 0.6596793072144376, 0.7818089160855244, 0.1090955419572380, 0.1090955419572374, 0.6245951075427290, 0.0332627075502785, 0.3421421849069923, 0.3421421849069924, 0.0332627075502784, 0.6245951075427288, 0.5375059926123179, 0.2312470036938410, 0.2312470036938409, 0.6081836035526988, 0.1959081982236507, 0.1959081982236505, 0.6861277132074860, 0.0230909511650297, 0.2907813356274841, 0.2907813356274843, 0.0230909511650296, 0.6861277132074858, 0.9138493473952539, 0.0084121228886459, 0.0777385297161001, 0.0777385297161002, 0.0084121228886457, 0.9138493473952537, 0.9397903465114041, 0.0018558446904391, 0.0583538087981564, 0.0583538087981567, 0.0018558446904390, 0.9397903465114040, 0.4944025611096592, 0.1518612214991533, 0.3537362173911873, 0.3537362173911874, 0.1518612214991532, 0.4944025611096591, 0.6592024700825742, 0.1466938464955038, 0.1941036834219220, 0.1941036834219222, 0.1466938464955035, 0.6592024700825739, 0.8116970473144409, 0.0730582724234848, 0.1152446802620740, 0.1152446802620743, 0.0730582724234846, 0.8116970473144408, 0.6640305665631259, 0.0833205145800467, 0.2526489188568272, 0.2526489188568273, 0.0833205145800465, 0.6640305665631258, 0.5316917725696111, 0.0976700995193537, 0.3706381279110349, 0.3706381279110350, 0.0976700995193536, 0.5316917725696111, 0.7003617605288512, 0.1021274732358203, 0.1975107662353283, 0.1975107662353284, 0.1021274732358201, 0.7003617605288512, 0.7639576985765669, 0.0169401226467936, 0.2191021787766394, 0.2191021787766397, 0.0169401226467933, 0.7639576985765668, 0.7706431138900716, 0.0646074146543943, 0.1647494714555340, 0.1647494714555341, 0.0646074146543941, 0.7706431138900716, 0.4569496207074596, 0.1942934918619252, 0.3487568874306149, 0.3487568874306150, 0.1942934918619252, 0.4569496207074596, 0.5853570821660165, 0.0587895877753211, 0.3558533300586620, 0.3558533300586623, 0.0587895877753211, 0.5853570821660163, 0.4076984951293574, 0.2435849758851730, 0.3487165289854693, 0.3487165289854693, 0.2435849758851731, 0.4076984951293575, 0.4223218082071513, 0.1553563835856972, 0.4223218082071513, 0.4548817499595059, 0.0902365000809880, 0.4548817499595058, 0.5231696984941406, 0.1861259659561632, 0.2907043355496960, 0.2907043355496961, 0.1861259659561630, 0.5231696984941407, 0.7121997609191582, 0.1439001195404210, 0.1439001195404206, 0.4717800456303301, 0.2383570195525562, 0.2898629348171136, 0.2898629348171136, 0.2383570195525561, 0.4717800456303301, 0.4023404478547353, 0.1953191042905292, 0.4023404478547353, 0.5593868077625691, 0.1312296167919730, 0.3093835754454578, 0.3093835754454580, 0.1312296167919729, 0.5593868077625690, 0.5845614823482763, 0.1684589785524792, 0.2469795390992443, 0.2469795390992445, 0.1684589785524792, 0.5845614823482763, 0.5515293353673113, 0.0131254695112235, 0.4353451951214650, 0.4353451951214652, 0.0131254695112234, 0.5515293353673112, 0.4114084686183320, 0.2942957656908339, 0.2942957656908339, 0.3516157887957689, 0.2967684224084620, 0.3516157887957690, 0.5518852701665368, 0.0344134405185801, 0.4137012893148829, 0.4137012893148831, 0.0344134405185802, 0.5518852701665365 }; static double w_save[] = { 0.0000443040909141, 0.0000443040909141, 0.0000443040909141, 0.0004119756464370, 0.0004119756464370, 0.0004119756464370, 0.0004119756464370, 0.0004119756464370, 0.0004119756464370, 0.0002732408460037, 0.0002732408460037, 0.0002732408460037, 0.0002732408460037, 0.0002732408460037, 0.0002732408460037, 0.0005393284439299, 0.0005393284439299, 0.0005393284439299, 0.0005393284439299, 0.0005393284439299, 0.0005393284439299, 0.0006709789705820, 0.0006709789705820, 0.0006709789705820, 0.0006709789705820, 0.0006709789705820, 0.0006709789705820, 0.0002259315361139, 0.0002259315361139, 0.0002259315361139, 0.0002259315361139, 0.0002259315361139, 0.0002259315361139, 0.0003220663094183, 0.0003220663094183, 0.0003220663094183, 0.0003220663094183, 0.0003220663094183, 0.0003220663094183, 0.0011229773828237, 0.0011229773828237, 0.0011229773828237, 0.0017451515655329, 0.0017451515655329, 0.0017451515655329, 0.0009677673027951, 0.0009677673027951, 0.0009677673027951, 0.0009677673027951, 0.0009677673027951, 0.0009677673027951, 0.0013466648921818, 0.0013466648921818, 0.0013466648921818, 0.0013466648921818, 0.0013466648921818, 0.0013466648921818, 0.0013375082839812, 0.0013375082839812, 0.0013375082839812, 0.0013375082839812, 0.0013375082839812, 0.0013375082839812, 0.0012094280366882, 0.0012094280366882, 0.0012094280366882, 0.0012094280366882, 0.0012094280366882, 0.0012094280366882, 0.0005973761417619, 0.0005973761417619, 0.0005973761417619, 0.0005973761417619, 0.0005973761417619, 0.0005973761417619, 0.0014682010637336, 0.0014682010637336, 0.0014682010637336, 0.0014682010637336, 0.0014682010637336, 0.0014682010637336, 0.0008010544852012, 0.0008010544852012, 0.0008010544852012, 0.0008010544852012, 0.0008010544852012, 0.0008010544852012, 0.0001855670423377, 0.0001855670423377, 0.0001855670423377, 0.0001855670423377, 0.0001855670423377, 0.0001855670423377, 0.0007214220264261, 0.0007214220264261, 0.0007214220264261, 0.0007214220264261, 0.0007214220264261, 0.0007214220264261, 0.0015321667240474, 0.0015321667240474, 0.0015321667240474, 0.0015321667240474, 0.0015321667240474, 0.0015321667240474, 0.0027296527164899, 0.0027296527164899, 0.0027296527164899, 0.0015090266204283, 0.0015090266204283, 0.0015090266204283, 0.0015090266204283, 0.0015090266204283, 0.0015090266204283, 0.0034017224729490, 0.0034017224729490, 0.0034017224729490, 0.0034017224729490, 0.0034017224729490, 0.0034017224729490, 0.0012045060134119, 0.0012045060134119, 0.0012045060134119, 0.0010359881638064, 0.0010359881638064, 0.0010359881638064, 0.0010359881638064, 0.0010359881638064, 0.0010359881638064, 0.0023774876927799, 0.0023774876927799, 0.0023774876927799, 0.0023774876927799, 0.0023774876927799, 0.0023774876927799, 0.0033953912341847, 0.0033953912341847, 0.0033953912341847, 0.0033953912341847, 0.0033953912341847, 0.0033953912341847, 0.0027040883824818, 0.0027040883824818, 0.0027040883824818, 0.0027040883824818, 0.0027040883824818, 0.0027040883824818, 0.0020170033902913, 0.0020170033902913, 0.0020170033902913, 0.0020170033902913, 0.0020170033902913, 0.0020170033902913, 0.0027918811324258, 0.0027918811324258, 0.0027918811324258, 0.0027918811324258, 0.0027918811324258, 0.0027918811324258, 0.0023657933107792, 0.0023657933107792, 0.0023657933107792, 0.0043004588657305, 0.0043004588657305, 0.0043004588657305, 0.0043004588657305, 0.0043004588657305, 0.0043004588657305, 0.0049838565291938, 0.0049838565291938, 0.0049838565291938, 0.0049838565291938, 0.0049838565291938, 0.0049838565291938, 0.0046532962756670, 0.0046532962756670, 0.0046532962756670, 0.0046532962756670, 0.0046532962756670, 0.0046532962756670, 0.0041278760422565, 0.0041278760422565, 0.0041278760422565, 0.0041278760422565, 0.0041278760422565, 0.0041278760422565, 0.0035111942683412, 0.0035111942683412, 0.0035111942683412, 0.0020578217623525, 0.0020578217623525, 0.0020578217623525, 0.0020578217623525, 0.0020578217623525, 0.0020578217623525, 0.0038938204584288, 0.0038938204584288, 0.0038938204584288, 0.0038938204584288, 0.0038938204584288, 0.0038938204584288, 0.0029434680471958, 0.0029434680471958, 0.0029434680471958, 0.0027707613965555, 0.0027707613965555, 0.0027707613965555, 0.0027707613965555, 0.0027707613965555, 0.0027707613965555, 0.0067232428984731, 0.0067232428984731, 0.0067232428984731, 0.0049798588125189, 0.0049798588125189, 0.0049798588125189, 0.0024801439985068, 0.0024801439985068, 0.0024801439985068, 0.0024801439985068, 0.0024801439985068, 0.0024801439985068, 0.0008629021808335, 0.0008629021808335, 0.0008629021808335, 0.0008629021808335, 0.0008629021808335, 0.0008629021808335, 0.0003209331775743, 0.0003209331775743, 0.0003209331775743, 0.0003209331775743, 0.0003209331775743, 0.0003209331775743, 0.0049810086106174, 0.0049810086106174, 0.0049810086106174, 0.0049810086106174, 0.0049810086106174, 0.0049810086106174, 0.0050195779180815, 0.0050195779180815, 0.0050195779180815, 0.0050195779180815, 0.0050195779180815, 0.0050195779180815, 0.0027692328182935, 0.0027692328182935, 0.0027692328182935, 0.0027692328182935, 0.0027692328182935, 0.0027692328182935, 0.0037015806596788, 0.0037015806596788, 0.0037015806596788, 0.0037015806596788, 0.0037015806596788, 0.0037015806596788, 0.0050750374591620, 0.0050750374591620, 0.0050750374591620, 0.0050750374591620, 0.0050750374591620, 0.0050750374591620, 0.0042676766915482, 0.0042676766915482, 0.0042676766915482, 0.0042676766915482, 0.0042676766915482, 0.0042676766915482, 0.0017292273039881, 0.0017292273039881, 0.0017292273039881, 0.0017292273039881, 0.0017292273039881, 0.0017292273039881, 0.0032247399122439, 0.0032247399122439, 0.0032247399122439, 0.0032247399122439, 0.0032247399122439, 0.0032247399122439, 0.0052879477129619, 0.0052879477129619, 0.0052879477129619, 0.0052879477129619, 0.0052879477129619, 0.0052879477129619, 0.0040195842863651, 0.0040195842863651, 0.0040195842863651, 0.0040195842863651, 0.0040195842863651, 0.0040195842863651, 0.0060608332073000, 0.0060608332073000, 0.0060608332073000, 0.0060608332073000, 0.0060608332073000, 0.0060608332073000, 0.0049208372452468, 0.0049208372452468, 0.0049208372452468, 0.0050214750285976, 0.0050214750285976, 0.0050214750285976, 0.0057991370585633, 0.0057991370585633, 0.0057991370585633, 0.0057991370585633, 0.0057991370585633, 0.0057991370585633, 0.0044465932407613, 0.0044465932407613, 0.0044465932407613, 0.0063931475211100, 0.0063931475211100, 0.0063931475211100, 0.0063931475211100, 0.0063931475211100, 0.0063931475211100, 0.0046466127645844, 0.0046466127645844, 0.0046466127645844, 0.0056546750089884, 0.0056546750089884, 0.0056546750089884, 0.0056546750089884, 0.0056546750089884, 0.0056546750089884, 0.0053110494169000, 0.0053110494169000, 0.0053110494169000, 0.0053110494169000, 0.0053110494169000, 0.0053110494169000, 0.0019732304214759, 0.0019732304214759, 0.0019732304214759, 0.0019732304214759, 0.0019732304214759, 0.0019732304214759, 0.0064254720501743, 0.0064254720501743, 0.0064254720501743, 0.0062655878836268, 0.0062655878836268, 0.0062655878836268, 0.0035554794715669, 0.0035554794715669, 0.0035554794715669, 0.0035554794715669, 0.0035554794715669, 0.0035554794715669 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule45 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule45() returns the rule of precision 45. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.0126048038307362, 0.9801027666184203, 0.0072924295508435, 0.9801027666184204, 0.0126048038307363, 0.0072924295508431, 0.0046054766314413, 0.9940445261864481, 0.0013499971821107, 0.9940445261864482, 0.0046054766314413, 0.0013499971821102, 0.0679464966039112, 0.9251943274580282, 0.0068591759380607, 0.9251943274580283, 0.0679464966039112, 0.0068591759380603, 0.0693380043634408, 0.9294322276406242, 0.0012297679959350, 0.9294322276406243, 0.0693380043634408, 0.0012297679959347, 0.4682708598709480, 0.5229490399283573, 0.0087801002006947, 0.5229490399283572, 0.4682708598709480, 0.0087801002006947, 0.2504951703352215, 0.7478218033035982, 0.0016830263611803, 0.7478218033035983, 0.2504951703352215, 0.0016830263611800, 0.0179231013398374, 0.9803189260766274, 0.0017579725835354, 0.9803189260766274, 0.0179231013398374, 0.0017579725835349, 0.3594568419950528, 0.6390675443517843, 0.0014756136531630, 0.6390675443517843, 0.3594568419950528, 0.0014756136531628, 0.2211539847849475, 0.6251828877524599, 0.1536631274625926, 0.6251828877524600, 0.2211539847849475, 0.1536631274625923, 0.2389731948786961, 0.5334015889840547, 0.2276252161372492, 0.5334015889840547, 0.2389731948786961, 0.2276252161372491, 0.1298066533002767, 0.7403866933994464, 0.1298066533002770, 0.2265228859811758, 0.6592740762673123, 0.1142030377515119, 0.6592740762673124, 0.2265228859811758, 0.1142030377515117, 0.2395905240377902, 0.6800344164936584, 0.0803750594685514, 0.6800344164936585, 0.2395905240377902, 0.0803750594685512, 0.1782914029925923, 0.7910902333249177, 0.0306183636824901, 0.7910902333249177, 0.1782914029925923, 0.0306183636824899, 0.2063496656308830, 0.5873006687382336, 0.2063496656308832, 0.1750845888069398, 0.6498308223861201, 0.1750845888069402, 0.2825866891204175, 0.6904712080981594, 0.0269421027814231, 0.6904712080981593, 0.2825866891204175, 0.0269421027814229, 0.1372571102587296, 0.8299456761943377, 0.0327972135469328, 0.8299456761943378, 0.1372571102587296, 0.0327972135469324, 0.4995045768679594, 0.4995045768679594, 0.0009908462640811, 0.1002544152365696, 0.8670184720297813, 0.0327271127336490, 0.8670184720297813, 0.1002544152365697, 0.0327271127336487, 0.0517074765599653, 0.9331324221261621, 0.0151601013138727, 0.9331324221261622, 0.0517074765599654, 0.0151601013138723, 0.2606148551376569, 0.5685004919093655, 0.1708846529529776, 0.5685004919093656, 0.2606148551376569, 0.1708846529529774, 0.2272143249599573, 0.7441223888358753, 0.0286632862041673, 0.7441223888358756, 0.2272143249599574, 0.0286632862041670, 0.3110404872350509, 0.6762638411989882, 0.0126956715659609, 0.6762638411989881, 0.3110404872350510, 0.0126956715659608, 0.0552204190605028, 0.8895591618789941, 0.0552204190605031, 0.1856238762990532, 0.7264745884520657, 0.0879015352488812, 0.7264745884520657, 0.1856238762990533, 0.0879015352488808, 0.0658626437608178, 0.9034170100624399, 0.0307203461767425, 0.9034170100624398, 0.0658626437608178, 0.0307203461767422, 0.3015904700953623, 0.6955949792647613, 0.0028145506398765, 0.6955949792647613, 0.3015904700953622, 0.0028145506398762, 0.2925426576542363, 0.6276179259734721, 0.0798394163722916, 0.6276179259734721, 0.2925426576542364, 0.0798394163722914, 0.0273024847528849, 0.9593763173443479, 0.0133211979027673, 0.9593763173443479, 0.0273024847528850, 0.0133211979027669, 0.2991527658365939, 0.4016944683268121, 0.2991527658365939, 0.3715719205775442, 0.6188258934043402, 0.0096021860181155, 0.6188258934043402, 0.3715719205775442, 0.0096021860181154, 0.2010073039936871, 0.7964902586210802, 0.0025024373852327, 0.7964902586210802, 0.2010073039936872, 0.0025024373852325, 0.2931831293722664, 0.5050860425617371, 0.2017308280659965, 0.5050860425617371, 0.2931831293722664, 0.2017308280659964, 0.2333318911036226, 0.7139904265957288, 0.0526776823006487, 0.7139904265957289, 0.2333318911036226, 0.0526776823006484, 0.1792991418970043, 0.7649317119922271, 0.0557691461107687, 0.7649317119922271, 0.1792991418970044, 0.0557691461107684, 0.3669822772564582, 0.3669822772564582, 0.2660354454870835, 0.2934353311290930, 0.6583279675616898, 0.0482367013092171, 0.6583279675616899, 0.2934353311290930, 0.0482367013092171, 0.3298405962756192, 0.4364618201712586, 0.2336975835531220, 0.4364618201712586, 0.3298405962756192, 0.2336975835531221, 0.1381756936115276, 0.7691621557796962, 0.0926621506087763, 0.7691621557796963, 0.1381756936115277, 0.0926621506087759, 0.3585128657761011, 0.4680323661208265, 0.1734547681030723, 0.4680323661208265, 0.3585128657761011, 0.1734547681030723, 0.4203377834665488, 0.5618113228868684, 0.0178508936465827, 0.5618113228868684, 0.4203377834665488, 0.0178508936465827, 0.2790511330034806, 0.6010021745006722, 0.1199466924958471, 0.6010021745006722, 0.2790511330034807, 0.1199466924958470, 0.0934626722493711, 0.8925527104988681, 0.0139846172517610, 0.8925527104988681, 0.0934626722493711, 0.0139846172517607, 0.3874089876890199, 0.4932332479959026, 0.1193577643150775, 0.4932332479959027, 0.3874089876890199, 0.1193577643150774, 0.4071846956615202, 0.5192306493531181, 0.0735846549853617, 0.5192306493531181, 0.4071846956615202, 0.0735846549853617, 0.1876405833897097, 0.7996426687617495, 0.0127167478485408, 0.7996426687617495, 0.1876405833897097, 0.0127167478485406, 0.2649216423903805, 0.4701567152192389, 0.2649216423903806, 0.1522255260382763, 0.8453340935540358, 0.0024403804076879, 0.8453340935540359, 0.1522255260382763, 0.0024403804076877, 0.1741420017865634, 0.6959673722361421, 0.1298906259772944, 0.6959673722361421, 0.1741420017865634, 0.1298906259772943, 0.3984690684139450, 0.3984690684139450, 0.2030618631721098, 0.3214081551755261, 0.5347112144371693, 0.1438806303873045, 0.5347112144371693, 0.3214081551755262, 0.1438806303873043, 0.0888043361734265, 0.8523358545382167, 0.0588598092883569, 0.8523358545382167, 0.0888043361734265, 0.0588598092883565, 0.1304289155517122, 0.8092737430634784, 0.0602973413848094, 0.8092737430634784, 0.1304289155517123, 0.0602973413848091, 0.4526201907514942, 0.4526201907514942, 0.0947596184970115, 0.1368379127222100, 0.8499366346784312, 0.0132254525993589, 0.8499366346784312, 0.1368379127222101, 0.0132254525993586, 0.3528533591796706, 0.5898753813183408, 0.0572712595019886, 0.5898753813183407, 0.3528533591796706, 0.0572712595019886, 0.2463869002171422, 0.7426794521965718, 0.0109336475862860, 0.7426794521965718, 0.2463869002171423, 0.0109336475862858, 0.4268610495333074, 0.4268610495333074, 0.1462779009333850, 0.3333333333333333, 0.3435200440594713, 0.5605547908509811, 0.0959251650895475, 0.5605547908509811, 0.3435200440594713, 0.0959251650895474, 0.4162089636364642, 0.5441206066477789, 0.0396704297157567, 0.5441206066477789, 0.4162089636364643, 0.0396704297157567, 0.0945724371334944, 0.8108551257330109, 0.0945724371334948, 0.4729894708688973, 0.4729894708688974, 0.0540210582622052, 0.0390118106999858, 0.9581931415494848, 0.0027950477505296, 0.9581931415494848, 0.0390118106999859, 0.0027950477505291, 0.1071807141346061, 0.8901526742127170, 0.0026666116526771, 0.8901526742127172, 0.1071807141346060, 0.0026666116526766, 0.4264238197063261, 0.5710366502174161, 0.0025395300762577, 0.5710366502174161, 0.4264238197063261, 0.0025395300762577, 0.0340851411567991, 0.9318297176864013, 0.0340851411567996, 0.3519601313638296, 0.6193084930778816, 0.0287313755582888, 0.6193084930778816, 0.3519601313638297, 0.0287313755582886, 0.4869989968257815, 0.4869989968257815, 0.0260020063484370 }; static double b_save[] = { 0.0072924295508434, 0.0126048038307362, 0.9801027666184206, 0.0072924295508434, 0.9801027666184206, 0.0126048038307365, 0.0013499971821105, 0.0046054766314413, 0.9940445261864482, 0.0013499971821105, 0.9940445261864485, 0.0046054766314416, 0.0068591759380605, 0.0679464966039111, 0.9251943274580284, 0.0068591759380605, 0.9251943274580284, 0.0679464966039115, 0.0012297679959349, 0.0693380043634408, 0.9294322276406244, 0.0012297679959349, 0.9294322276406244, 0.0693380043634411, 0.0087801002006948, 0.4682708598709480, 0.5229490399283575, 0.0087801002006948, 0.5229490399283574, 0.4682708598709482, 0.0016830263611803, 0.2504951703352215, 0.7478218033035984, 0.0016830263611803, 0.7478218033035984, 0.2504951703352218, 0.0017579725835351, 0.0179231013398374, 0.9803189260766274, 0.0017579725835351, 0.9803189260766277, 0.0179231013398377, 0.0014756136531629, 0.3594568419950528, 0.6390675443517844, 0.0014756136531629, 0.6390675443517843, 0.3594568419950530, 0.1536631274625925, 0.2211539847849475, 0.6251828877524600, 0.1536631274625925, 0.6251828877524601, 0.2211539847849477, 0.2276252161372493, 0.2389731948786962, 0.5334015889840548, 0.2276252161372493, 0.5334015889840548, 0.2389731948786963, 0.1298066533002769, 0.1298066533002767, 0.7403866933994465, 0.1142030377515119, 0.2265228859811758, 0.6592740762673125, 0.1142030377515119, 0.6592740762673125, 0.2265228859811760, 0.0803750594685514, 0.2395905240377902, 0.6800344164936586, 0.0803750594685514, 0.6800344164936585, 0.2395905240377905, 0.0306183636824900, 0.1782914029925923, 0.7910902333249178, 0.0306183636824900, 0.7910902333249178, 0.1782914029925926, 0.2063496656308833, 0.2063496656308831, 0.5873006687382338, 0.1750845888069401, 0.1750845888069399, 0.6498308223861201, 0.0269421027814231, 0.2825866891204175, 0.6904712080981597, 0.0269421027814231, 0.6904712080981594, 0.2825866891204177, 0.0327972135469327, 0.1372571102587296, 0.8299456761943379, 0.0327972135469327, 0.8299456761943380, 0.1372571102587299, 0.0009908462640811, 0.4995045768679595, 0.4995045768679597, 0.0327271127336490, 0.1002544152365696, 0.8670184720297816, 0.0327271127336490, 0.8670184720297816, 0.1002544152365700, 0.0151601013138726, 0.0517074765599653, 0.9331324221261622, 0.0151601013138726, 0.9331324221261622, 0.0517074765599656, 0.1708846529529776, 0.2606148551376569, 0.5685004919093657, 0.1708846529529776, 0.5685004919093657, 0.2606148551376571, 0.0286632862041672, 0.2272143249599573, 0.7441223888358756, 0.0286632862041672, 0.7441223888358756, 0.2272143249599576, 0.0126956715659609, 0.3110404872350509, 0.6762638411989884, 0.0126956715659609, 0.6762638411989882, 0.3110404872350512, 0.0552204190605031, 0.0552204190605028, 0.8895591618789943, 0.0879015352488811, 0.1856238762990532, 0.7264745884520658, 0.0879015352488811, 0.7264745884520658, 0.1856238762990535, 0.0307203461767424, 0.0658626437608177, 0.9034170100624400, 0.0307203461767424, 0.9034170100624400, 0.0658626437608181, 0.0028145506398764, 0.3015904700953623, 0.6955949792647615, 0.0028145506398764, 0.6955949792647615, 0.3015904700953626, 0.0798394163722916, 0.2925426576542363, 0.6276179259734722, 0.0798394163722916, 0.6276179259734722, 0.2925426576542366, 0.0133211979027671, 0.0273024847528849, 0.9593763173443480, 0.0133211979027671, 0.9593763173443480, 0.0273024847528853, 0.2991527658365941, 0.2991527658365941, 0.4016944683268122, 0.0096021860181156, 0.3715719205775442, 0.6188258934043405, 0.0096021860181156, 0.6188258934043404, 0.3715719205775445, 0.0025024373852327, 0.2010073039936871, 0.7964902586210805, 0.0025024373852327, 0.7964902586210802, 0.2010073039936874, 0.2017308280659965, 0.2931831293722665, 0.5050860425617372, 0.2017308280659965, 0.5050860425617372, 0.2931831293722666, 0.0526776823006486, 0.2333318911036226, 0.7139904265957290, 0.0526776823006486, 0.7139904265957289, 0.2333318911036229, 0.0557691461107686, 0.1792991418970043, 0.7649317119922272, 0.0557691461107686, 0.7649317119922272, 0.1792991418970046, 0.2660354454870836, 0.3669822772564583, 0.3669822772564584, 0.0482367013092172, 0.2934353311290930, 0.6583279675616901, 0.0482367013092172, 0.6583279675616900, 0.2934353311290932, 0.2336975835531222, 0.3298405962756193, 0.4364618201712588, 0.2336975835531222, 0.4364618201712587, 0.3298405962756194, 0.0926621506087761, 0.1381756936115276, 0.7691621557796964, 0.0926621506087761, 0.7691621557796964, 0.1381756936115279, 0.1734547681030724, 0.3585128657761012, 0.4680323661208267, 0.1734547681030724, 0.4680323661208267, 0.3585128657761013, 0.0178508936465828, 0.4203377834665488, 0.5618113228868687, 0.0178508936465828, 0.5618113228868685, 0.4203377834665490, 0.1199466924958472, 0.2790511330034807, 0.6010021745006724, 0.1199466924958472, 0.6010021745006723, 0.2790511330034809, 0.0139846172517609, 0.0934626722493711, 0.8925527104988682, 0.0139846172517609, 0.8925527104988682, 0.0934626722493714, 0.1193577643150775, 0.3874089876890200, 0.4932332479959028, 0.1193577643150775, 0.4932332479959027, 0.3874089876890201, 0.0735846549853618, 0.4071846956615202, 0.5192306493531184, 0.0735846549853618, 0.5192306493531181, 0.4071846956615204, 0.0127167478485408, 0.1876405833897097, 0.7996426687617497, 0.0127167478485408, 0.7996426687617497, 0.1876405833897100, 0.2649216423903806, 0.2649216423903806, 0.4701567152192390, 0.0024403804076879, 0.1522255260382763, 0.8453340935540361, 0.0024403804076879, 0.8453340935540361, 0.1522255260382766, 0.1298906259772945, 0.1741420017865634, 0.6959673722361424, 0.1298906259772945, 0.6959673722361424, 0.1741420017865636, 0.2030618631721099, 0.3984690684139451, 0.3984690684139452, 0.1438806303873045, 0.3214081551755262, 0.5347112144371695, 0.1438806303873045, 0.5347112144371694, 0.3214081551755264, 0.0588598092883568, 0.0888043361734265, 0.8523358545382169, 0.0588598092883568, 0.8523358545382169, 0.0888043361734268, 0.0602973413848094, 0.1304289155517122, 0.8092737430634785, 0.0602973413848094, 0.8092737430634785, 0.1304289155517125, 0.0947596184970116, 0.4526201907514942, 0.4526201907514944, 0.0132254525993588, 0.1368379127222100, 0.8499366346784313, 0.0132254525993588, 0.8499366346784313, 0.1368379127222104, 0.0572712595019887, 0.3528533591796706, 0.5898753813183411, 0.0572712595019887, 0.5898753813183409, 0.3528533591796708, 0.0109336475862860, 0.2463869002171422, 0.7426794521965722, 0.0109336475862860, 0.7426794521965718, 0.2463869002171425, 0.1462779009333851, 0.4268610495333075, 0.4268610495333077, 0.3333333333333334, 0.0959251650895476, 0.3435200440594713, 0.5605547908509814, 0.0959251650895476, 0.5605547908509813, 0.3435200440594715, 0.0396704297157568, 0.4162089636364643, 0.5441206066477793, 0.0396704297157568, 0.5441206066477792, 0.4162089636364644, 0.0945724371334947, 0.0945724371334944, 0.8108551257330111, 0.0540210582622053, 0.4729894708688974, 0.4729894708688976, 0.0027950477505294, 0.0390118106999857, 0.9581931415494850, 0.0027950477505294, 0.9581931415494850, 0.0390118106999862, 0.0026666116526769, 0.1071807141346060, 0.8901526742127170, 0.0026666116526769, 0.8901526742127174, 0.1071807141346064, 0.0025395300762578, 0.4264238197063261, 0.5710366502174163, 0.0025395300762578, 0.5710366502174162, 0.4264238197063264, 0.0340851411567994, 0.0340851411567991, 0.9318297176864015, 0.0287313755582888, 0.3519601313638296, 0.6193084930778818, 0.0287313755582888, 0.6193084930778817, 0.3519601313638299, 0.0260020063484371, 0.4869989968257816, 0.4869989968257817 }; static double c_save[] = { 0.9801027666184204, 0.0072924295508435, 0.0126048038307359, 0.0126048038307362, 0.0072924295508432, 0.9801027666184203, 0.9940445261864482, 0.0013499971821106, 0.0046054766314411, 0.0046054766314413, 0.0013499971821102, 0.9940445261864481, 0.9251943274580283, 0.0068591759380607, 0.0679464966039108, 0.0679464966039111, 0.0068591759380604, 0.9251943274580282, 0.9294322276406243, 0.0012297679959350, 0.0693380043634406, 0.0693380043634408, 0.0012297679959348, 0.9294322276406242, 0.5229490399283573, 0.0087801002006947, 0.4682708598709479, 0.4682708598709481, 0.0087801002006946, 0.5229490399283572, 0.7478218033035983, 0.0016830263611803, 0.2504951703352213, 0.2504951703352215, 0.0016830263611801, 0.7478218033035982, 0.9803189260766274, 0.0017579725835352, 0.0179231013398372, 0.0179231013398374, 0.0017579725835349, 0.9803189260766273, 0.6390675443517843, 0.0014756136531629, 0.3594568419950526, 0.3594568419950528, 0.0014756136531630, 0.6390675443517841, 0.6251828877524599, 0.1536631274625926, 0.2211539847849474, 0.2211539847849475, 0.1536631274625924, 0.6251828877524599, 0.5334015889840545, 0.2276252161372492, 0.2389731948786961, 0.2389731948786961, 0.2276252161372491, 0.5334015889840545, 0.7403866933994465, 0.1298066533002769, 0.1298066533002765, 0.6592740762673124, 0.1142030377515119, 0.2265228859811755, 0.2265228859811758, 0.1142030377515116, 0.6592740762673124, 0.6800344164936584, 0.0803750594685514, 0.2395905240377899, 0.2395905240377901, 0.0803750594685513, 0.6800344164936583, 0.7910902333249177, 0.0306183636824900, 0.1782914029925921, 0.1782914029925923, 0.0306183636824898, 0.7910902333249177, 0.5873006687382337, 0.2063496656308832, 0.2063496656308830, 0.6498308223861200, 0.1750845888069400, 0.1750845888069398, 0.6904712080981594, 0.0269421027814231, 0.2825866891204173, 0.2825866891204176, 0.0269421027814231, 0.6904712080981593, 0.8299456761943378, 0.0327972135469327, 0.1372571102587293, 0.1372571102587296, 0.0327972135469324, 0.8299456761943377, 0.4995045768679595, 0.0009908462640812, 0.4995045768679592, 0.8670184720297814, 0.0327271127336490, 0.1002544152365694, 0.1002544152365697, 0.0327271127336487, 0.8670184720297813, 0.9331324221261621, 0.0151601013138726, 0.0517074765599651, 0.0517074765599652, 0.0151601013138724, 0.9331324221261621, 0.5685004919093655, 0.1708846529529776, 0.2606148551376568, 0.2606148551376569, 0.1708846529529774, 0.5685004919093655, 0.7441223888358754, 0.0286632862041673, 0.2272143249599571, 0.2272143249599572, 0.0286632862041670, 0.7441223888358753, 0.6762638411989881, 0.0126956715659609, 0.3110404872350506, 0.3110404872350510, 0.0126956715659609, 0.6762638411989881, 0.8895591618789941, 0.0552204190605031, 0.0552204190605027, 0.7264745884520657, 0.0879015352488811, 0.1856238762990530, 0.1856238762990532, 0.0879015352488809, 0.7264745884520658, 0.9034170100624398, 0.0307203461767424, 0.0658626437608175, 0.0658626437608178, 0.0307203461767421, 0.9034170100624398, 0.6955949792647614, 0.0028145506398763, 0.3015904700953620, 0.3015904700953623, 0.0028145506398762, 0.6955949792647612, 0.6276179259734721, 0.0798394163722916, 0.2925426576542361, 0.2925426576542363, 0.0798394163722914, 0.6276179259734720, 0.9593763173443480, 0.0133211979027672, 0.0273024847528847, 0.0273024847528849, 0.0133211979027669, 0.9593763173443478, 0.4016944683268120, 0.2991527658365938, 0.2991527658365939, 0.6188258934043401, 0.0096021860181155, 0.3715719205775441, 0.3715719205775442, 0.0096021860181154, 0.6188258934043400, 0.7964902586210802, 0.0025024373852326, 0.2010073039936868, 0.2010073039936870, 0.0025024373852326, 0.7964902586210801, 0.5050860425617371, 0.2017308280659965, 0.2931831293722663, 0.2931831293722664, 0.2017308280659964, 0.5050860425617369, 0.7139904265957288, 0.0526776823006486, 0.2333318911036223, 0.2333318911036225, 0.0526776823006485, 0.7139904265957286, 0.7649317119922271, 0.0557691461107686, 0.1792991418970041, 0.1792991418970043, 0.0557691461107684, 0.7649317119922271, 0.3669822772564583, 0.2660354454870835, 0.3669822772564582, 0.6583279675616899, 0.0482367013092172, 0.2934353311290928, 0.2934353311290929, 0.0482367013092170, 0.6583279675616898, 0.4364618201712586, 0.2336975835531220, 0.3298405962756191, 0.3298405962756191, 0.2336975835531220, 0.4364618201712585, 0.7691621557796963, 0.0926621506087762, 0.1381756936115274, 0.1381756936115276, 0.0926621506087759, 0.7691621557796962, 0.4680323661208265, 0.1734547681030723, 0.3585128657761010, 0.3585128657761011, 0.1734547681030721, 0.4680323661208264, 0.5618113228868685, 0.0178508936465828, 0.4203377834665486, 0.4203377834665488, 0.0178508936465828, 0.5618113228868683, 0.6010021745006722, 0.1199466924958471, 0.2790511330034805, 0.2790511330034807, 0.1199466924958471, 0.6010021745006722, 0.8925527104988680, 0.0139846172517608, 0.0934626722493708, 0.0934626722493710, 0.0139846172517607, 0.8925527104988679, 0.4932332479959026, 0.1193577643150775, 0.3874089876890197, 0.3874089876890198, 0.1193577643150774, 0.4932332479959025, 0.5192306493531180, 0.0735846549853617, 0.4071846956615199, 0.4071846956615201, 0.0735846549853617, 0.5192306493531180, 0.7996426687617495, 0.0127167478485408, 0.1876405833897095, 0.1876405833897097, 0.0127167478485406, 0.7996426687617494, 0.4701567152192389, 0.2649216423903806, 0.2649216423903804, 0.8453340935540358, 0.0024403804076879, 0.1522255260382760, 0.1522255260382763, 0.0024403804076876, 0.8453340935540357, 0.6959673722361421, 0.1298906259772944, 0.1741420017865631, 0.1741420017865634, 0.1298906259772943, 0.6959673722361421, 0.3984690684139450, 0.2030618631721098, 0.3984690684139450, 0.5347112144371693, 0.1438806303873045, 0.3214081551755260, 0.3214081551755262, 0.1438806303873045, 0.5347112144371693, 0.8523358545382167, 0.0588598092883569, 0.0888043361734262, 0.0888043361734265, 0.0588598092883565, 0.8523358545382168, 0.8092737430634784, 0.0602973413848094, 0.1304289155517121, 0.1304289155517122, 0.0602973413848092, 0.8092737430634783, 0.4526201907514942, 0.0947596184970116, 0.4526201907514941, 0.8499366346784312, 0.0132254525993588, 0.1368379127222098, 0.1368379127222100, 0.0132254525993586, 0.8499366346784311, 0.5898753813183408, 0.0572712595019885, 0.3528533591796703, 0.3528533591796706, 0.0572712595019885, 0.5898753813183406, 0.7426794521965718, 0.0109336475862860, 0.2463869002171418, 0.2463869002171422, 0.0109336475862859, 0.7426794521965717, 0.4268610495333075, 0.1462779009333851, 0.4268610495333073, 0.3333333333333333, 0.5605547908509813, 0.0959251650895475, 0.3435200440594711, 0.3435200440594713, 0.0959251650895475, 0.5605547908509811, 0.5441206066477791, 0.0396704297157568, 0.4162089636364640, 0.4162089636364643, 0.0396704297157565, 0.5441206066477789, 0.8108551257330110, 0.0945724371334948, 0.0945724371334941, 0.4729894708688974, 0.0540210582622052, 0.4729894708688971, 0.9581931415494849, 0.0027950477505295, 0.0390118106999854, 0.0390118106999858, 0.0027950477505291, 0.9581931415494848, 0.8901526742127170, 0.0026666116526769, 0.1071807141346058, 0.1071807141346060, 0.0026666116526767, 0.8901526742127169, 0.5710366502174161, 0.0025395300762577, 0.4264238197063259, 0.4264238197063261, 0.0025395300762576, 0.5710366502174160, 0.9318297176864014, 0.0340851411567995, 0.0340851411567989, 0.6193084930778816, 0.0287313755582888, 0.3519601313638294, 0.3519601313638296, 0.0287313755582886, 0.6193084930778815, 0.4869989968257814, 0.0260020063484369, 0.4869989968257813 }; static double w_save[] = { 0.0001943064247755, 0.0001943064247755, 0.0001943064247755, 0.0001943064247755, 0.0001943064247755, 0.0001943064247755, 0.0000593664802978, 0.0000593664802978, 0.0000593664802978, 0.0000593664802978, 0.0000593664802978, 0.0000593664802978, 0.0004806887075027, 0.0004806887075027, 0.0004806887075027, 0.0004806887075027, 0.0004806887075027, 0.0004806887075027, 0.0002301249335002, 0.0002301249335002, 0.0002301249335002, 0.0002301249335002, 0.0002301249335002, 0.0002301249335002, 0.0012944627170681, 0.0012944627170681, 0.0012944627170681, 0.0012944627170681, 0.0012944627170681, 0.0012944627170681, 0.0004605208982907, 0.0004605208982907, 0.0004605208982907, 0.0004605208982907, 0.0004605208982907, 0.0004605208982907, 0.0001550690080029, 0.0001550690080029, 0.0001550690080029, 0.0001550690080029, 0.0001550690080029, 0.0001550690080029, 0.0005264320168997, 0.0005264320168997, 0.0005264320168997, 0.0005264320168997, 0.0005264320168997, 0.0005264320168997, 0.0040776028008772, 0.0040776028008772, 0.0040776028008772, 0.0040776028008772, 0.0040776028008772, 0.0040776028008772, 0.0027273371555633, 0.0027273371555633, 0.0027273371555633, 0.0027273371555633, 0.0027273371555633, 0.0027273371555633, 0.0032024171503526, 0.0032024171503526, 0.0032024171503526, 0.0038178383600418, 0.0038178383600418, 0.0038178383600418, 0.0038178383600418, 0.0038178383600418, 0.0038178383600418, 0.0032435899284887, 0.0032435899284887, 0.0032435899284887, 0.0032435899284887, 0.0032435899284887, 0.0032435899284887, 0.0018849657183849, 0.0018849657183849, 0.0018849657183849, 0.0018849657183849, 0.0018849657183849, 0.0018849657183849, 0.0046373488411220, 0.0046373488411220, 0.0046373488411220, 0.0040870604654873, 0.0040870604654873, 0.0040870604654873, 0.0021807223876070, 0.0021807223876070, 0.0021807223876070, 0.0021807223876070, 0.0021807223876070, 0.0021807223876070, 0.0018345812391610, 0.0018345812391610, 0.0018345812391610, 0.0018345812391610, 0.0018345812391610, 0.0018345812391610, 0.0004831135230320, 0.0004831135230320, 0.0004831135230320, 0.0016273397954327, 0.0016273397954327, 0.0016273397954327, 0.0016273397954327, 0.0016273397954327, 0.0016273397954327, 0.0008285328211727, 0.0008285328211727, 0.0008285328211727, 0.0008285328211727, 0.0008285328211727, 0.0008285328211727, 0.0051074900867677, 0.0051074900867677, 0.0051074900867677, 0.0051074900867677, 0.0051074900867677, 0.0051074900867677, 0.0022391133588916, 0.0022391133588916, 0.0022391133588916, 0.0022391133588916, 0.0022391133588916, 0.0022391133588916, 0.0016401723644210, 0.0016401723644210, 0.0016401723644210, 0.0016401723644210, 0.0016401723644210, 0.0016401723644210, 0.0016926101405552, 0.0016926101405552, 0.0016926101405552, 0.0036716713931777, 0.0036716713931777, 0.0036716713931777, 0.0036716713931777, 0.0036716713931777, 0.0036716713931777, 0.0014130049415994, 0.0014130049415994, 0.0014130049415994, 0.0014130049415994, 0.0014130049415994, 0.0014130049415994, 0.0007644420008621, 0.0007644420008621, 0.0007644420008621, 0.0007644420008621, 0.0007644420008621, 0.0007644420008621, 0.0039540316260532, 0.0039540316260532, 0.0039540316260532, 0.0039540316260532, 0.0039540316260532, 0.0039540316260532, 0.0006448335449571, 0.0006448335449571, 0.0006448335449571, 0.0006448335449571, 0.0006448335449571, 0.0006448335449571, 0.0068337553756981, 0.0068337553756981, 0.0068337553756981, 0.0015547569025381, 0.0015547569025381, 0.0015547569025381, 0.0015547569025381, 0.0015547569025381, 0.0015547569025381, 0.0006264797924812, 0.0006264797924812, 0.0006264797924812, 0.0006264797924812, 0.0006264797924812, 0.0006264797924812, 0.0059918057501739, 0.0059918057501739, 0.0059918057501739, 0.0059918057501739, 0.0059918057501739, 0.0059918057501739, 0.0030584178145640, 0.0030584178145640, 0.0030584178145640, 0.0030584178145640, 0.0030584178145640, 0.0030584178145640, 0.0029964079041531, 0.0029964079041531, 0.0029964079041531, 0.0029964079041531, 0.0029964079041531, 0.0029964079041531, 0.0068925047985870, 0.0068925047985870, 0.0068925047985870, 0.0032333735833172, 0.0032333735833172, 0.0032333735833172, 0.0032333735833172, 0.0032333735833172, 0.0032333735833172, 0.0066463643649800, 0.0066463643649800, 0.0066463643649800, 0.0066463643649800, 0.0066463643649800, 0.0066463643649800, 0.0031949049329089, 0.0031949049329089, 0.0031949049329089, 0.0031949049329089, 0.0031949049329089, 0.0031949049329089, 0.0061619916829777, 0.0061619916829777, 0.0061619916829777, 0.0061619916829777, 0.0061619916829777, 0.0061619916829777, 0.0021838177312897, 0.0021838177312897, 0.0021838177312897, 0.0021838177312897, 0.0021838177312897, 0.0021838177312897, 0.0048382287535973, 0.0048382287535973, 0.0048382287535973, 0.0048382287535973, 0.0048382287535973, 0.0048382287535973, 0.0011709435195081, 0.0011709435195081, 0.0011709435195081, 0.0011709435195081, 0.0011709435195081, 0.0011709435195081, 0.0054074968564398, 0.0054074968564398, 0.0054074968564398, 0.0054074968564398, 0.0054074968564398, 0.0054074968564398, 0.0045333891237490, 0.0045333891237490, 0.0045333891237490, 0.0045333891237490, 0.0045333891237490, 0.0045333891237490, 0.0015268444445366, 0.0015268444445366, 0.0015268444445366, 0.0015268444445366, 0.0015268444445366, 0.0015268444445366, 0.0063146569930329, 0.0063146569930329, 0.0063146569930329, 0.0005985557587521, 0.0005985557587521, 0.0005985557587521, 0.0005985557587521, 0.0005985557587521, 0.0005985557587521, 0.0042213374314073, 0.0042213374314073, 0.0042213374314073, 0.0042213374314073, 0.0042213374314073, 0.0042213374314073, 0.0065583075001979, 0.0065583075001979, 0.0065583075001979, 0.0055145622313395, 0.0055145622313395, 0.0055145622313395, 0.0055145622313395, 0.0055145622313395, 0.0055145622313395, 0.0023371778099107, 0.0023371778099107, 0.0023371778099107, 0.0023371778099107, 0.0023371778099107, 0.0023371778099107, 0.0027879889526797, 0.0027879889526797, 0.0027879889526797, 0.0027879889526797, 0.0027879889526797, 0.0027879889526797, 0.0050168594859682, 0.0050168594859682, 0.0050168594859682, 0.0014305749953706, 0.0014305749953706, 0.0014305749953706, 0.0014305749953706, 0.0014305749953706, 0.0014305749953706, 0.0039720422418774, 0.0039720422418774, 0.0039720422418774, 0.0039720422418774, 0.0039720422418774, 0.0039720422418774, 0.0016230214293911, 0.0016230214293911, 0.0016230214293911, 0.0016230214293911, 0.0016230214293911, 0.0016230214293911, 0.0058825091261753, 0.0058825091261753, 0.0058825091261753, 0.0069414696543850, 0.0048308548778951, 0.0048308548778951, 0.0048308548778951, 0.0048308548778951, 0.0048308548778951, 0.0048308548778951, 0.0035396788161465, 0.0035396788161465, 0.0035396788161465, 0.0035396788161465, 0.0035396788161465, 0.0035396788161465, 0.0031371434621643, 0.0031371434621643, 0.0031371434621643, 0.0040930651478197, 0.0040930651478197, 0.0040930651478197, 0.0003670659894181, 0.0003670659894181, 0.0003670659894181, 0.0003670659894181, 0.0003670659894181, 0.0003670659894181, 0.0005709699094042, 0.0005709699094042, 0.0005709699094042, 0.0005709699094042, 0.0005709699094042, 0.0005709699094042, 0.0008761135391688, 0.0008761135391688, 0.0008761135391688, 0.0008761135391688, 0.0008761135391688, 0.0008761135391688, 0.0012513146853205, 0.0012513146853205, 0.0012513146853205, 0.0030871109749242, 0.0030871109749242, 0.0030871109749242, 0.0030871109749242, 0.0030871109749242, 0.0030871109749242, 0.0030558057702988, 0.0030558057702988, 0.0030558057702988 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule46 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule46() returns the rule of precision 46. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.4791627094810211, 0.4791627094810211, 0.0416745810379577, 0.3979697646407098, 0.4479070861932129, 0.1541231491660771, 0.4479070861932128, 0.3979697646407099, 0.1541231491660771, 0.4143076079881758, 0.4725556860878008, 0.1131367059240233, 0.4725556860878007, 0.4143076079881759, 0.1131367059240234, 0.3297282498766237, 0.5972534223436730, 0.0730183277797033, 0.5972534223436731, 0.3297282498766237, 0.0730183277797032, 0.2257592423300578, 0.6644373808625786, 0.1098033768073635, 0.6644373808625786, 0.2257592423300578, 0.1098033768073634, 0.0486830795833199, 0.9026338408333598, 0.0486830795833202, 0.4868494344525785, 0.4868494344525786, 0.0263011310948430, 0.3286993475605237, 0.5684647770684034, 0.1028358753710730, 0.5684647770684034, 0.3286993475605237, 0.1028358753710729, 0.0570245183292809, 0.9325204663263090, 0.0104550153444102, 0.9325204663263090, 0.0570245183292810, 0.0104550153444098, 0.2181534906276071, 0.6343242478263365, 0.1475222615460565, 0.6343242478263365, 0.2181534906276072, 0.1475222615460563, 0.2023063458834636, 0.7455675573091064, 0.0521260968074301, 0.7455675573091063, 0.2023063458834636, 0.0521260968074299, 0.2132832098088080, 0.7066325944250231, 0.0800841957661689, 0.7066325944250231, 0.2132832098088080, 0.0800841957661687, 0.0082133588712220, 0.9896258607741097, 0.0021607803546684, 0.9896258607741097, 0.0082133588712220, 0.0021607803546680, 0.4615153616123003, 0.5271208360379724, 0.0113638023497272, 0.5271208360379723, 0.4615153616123003, 0.0113638023497272, 0.3546224673127057, 0.5155990090696432, 0.1297785236176510, 0.5155990090696433, 0.3546224673127058, 0.1297785236176509, 0.3109206435860316, 0.6401420778067229, 0.0489372786072454, 0.6401420778067229, 0.3109206435860316, 0.0489372786072453, 0.3049557841332307, 0.5366266568593034, 0.1584175590074660, 0.5366266568593034, 0.3049557841332306, 0.1584175590074658, 0.2507944375639041, 0.5737054769976868, 0.1755000854384091, 0.5737054769976868, 0.2507944375639042, 0.1755000854384089, 0.1962948092294495, 0.6074103815411007, 0.1962948092294496, 0.1657987165670959, 0.6684025668658078, 0.1657987165670963, 0.4338692218644805, 0.5130043968250232, 0.0531263813104962, 0.5130043968250232, 0.4338692218644806, 0.0531263813104962, 0.0770376986253196, 0.8720533240163508, 0.0509089773583296, 0.8720533240163508, 0.0770376986253197, 0.0509089773583293, 0.2768361860195224, 0.7120424143833398, 0.0111213995971378, 0.7120424143833398, 0.2768361860195226, 0.0111213995971376, 0.1736371621034214, 0.8145830842158606, 0.0117797536807180, 0.8145830842158606, 0.1736371621034215, 0.0117797536807177, 0.3354336886613770, 0.6527581850349298, 0.0118081263036934, 0.6527581850349297, 0.3354336886613770, 0.0118081263036932, 0.3750642184523966, 0.5736918975567098, 0.0512438839908936, 0.5736918975567098, 0.3750642184523967, 0.0512438839908935, 0.3467112861299004, 0.4707474573939668, 0.1825412564761328, 0.4707474573939667, 0.3467112861299005, 0.1825412564761327, 0.2559685112606641, 0.6901296172890430, 0.0539018714502929, 0.6901296172890431, 0.2559685112606642, 0.0539018714502927, 0.2920069207885316, 0.6806497657499146, 0.0273433134615538, 0.6806497657499146, 0.2920069207885317, 0.0273433134615535, 0.2364172395795756, 0.7338403785411441, 0.0297423818792803, 0.7338403785411441, 0.2364172395795756, 0.0297423818792801, 0.4661508981294354, 0.5316578071895072, 0.0021912946810573, 0.5316578071895072, 0.4661508981294354, 0.0021912946810573, 0.2234826291455856, 0.7639437050178102, 0.0125736658366042, 0.7639437050178102, 0.2234826291455856, 0.0125736658366041, 0.3973680138780006, 0.5911123169924868, 0.0115196691295125, 0.5911123169924869, 0.3973680138780006, 0.0115196691295124, 0.2856792432449899, 0.5036527190882436, 0.2106680376667663, 0.5036527190882436, 0.2856792432449899, 0.2106680376667662, 0.2290071177870446, 0.5419857644259105, 0.2290071177870448, 0.2998981018797286, 0.4002037962405427, 0.2998981018797286, 0.4009919122964068, 0.5968372374211253, 0.0021708502824680, 0.5968372374211253, 0.4009919122964067, 0.0021708502824680, 0.1562735104040767, 0.7879600672161253, 0.0557664223797980, 0.7879600672161253, 0.1562735104040768, 0.0557664223797977, 0.0477858936846818, 0.9501161980450165, 0.0020979082703018, 0.9501161980450166, 0.0477858936846819, 0.0020979082703013, 0.1822491599313741, 0.7886726424890335, 0.0290781975795925, 0.7886726424890333, 0.1822491599313742, 0.0290781975795923, 0.3660812614114254, 0.3660812614114254, 0.2678374771771491, 0.0893475681919859, 0.8990694649639888, 0.0115829668440254, 0.8990694649639889, 0.0893475681919860, 0.0115829668440250, 0.1652198812399128, 0.7473177571098144, 0.0874623616502729, 0.7473177571098144, 0.1652198812399128, 0.0874623616502726, 0.0805280047391684, 0.9173934916626123, 0.0020785035982195, 0.9173934916626122, 0.0805280047391685, 0.0020785035982190, 0.3305415015675990, 0.4329807146876172, 0.2364777837447837, 0.4329807146876172, 0.3305415015675991, 0.2364777837447836, 0.1750740132522936, 0.7021169686939935, 0.1228090180537130, 0.7021169686939934, 0.1750740132522937, 0.1228090180537126, 0.1133949730294224, 0.8315999985260938, 0.0550050284444840, 0.8315999985260938, 0.1133949730294224, 0.0550050284444836, 0.0945442284064488, 0.8766622383664391, 0.0287935332271122, 0.8766622383664391, 0.0945442284064488, 0.0287935332271118, 0.0589589423608463, 0.9147477258472858, 0.0262933317918678, 0.9147477258472859, 0.0589589423608463, 0.0262933317918676, 0.3554461171023697, 0.6162465555124068, 0.0283073273852236, 0.6162465555124067, 0.3554461171023696, 0.0283073273852235, 0.4206278444454289, 0.5512452167474322, 0.0281269388071388, 0.5512452167474322, 0.4206278444454289, 0.0281269388071388, 0.0307693439520818, 0.9384613120958362, 0.0307693439520821, 0.2763424771664457, 0.7215566217404850, 0.0021009010930694, 0.7215566217404851, 0.2763424771664458, 0.0021009010930691, 0.1358344051381373, 0.8336434944596028, 0.0305221004022600, 0.8336434944596030, 0.1358344051381374, 0.0305221004022596, 0.1214324449203873, 0.7904245130980823, 0.0881430419815304, 0.7904245130980824, 0.1214324449203874, 0.0881430419815301, 0.0824986937635583, 0.8350026124728831, 0.0824986937635587, 0.1292544813329482, 0.8581647113948480, 0.0125808072722039, 0.8581647113948480, 0.1292544813329483, 0.0125808072722036, 0.2729393183303263, 0.6431846260118416, 0.0838760556578322, 0.6431846260118415, 0.2729393183303264, 0.0838760556578320, 0.4608230043475881, 0.4608230043475881, 0.0783539913048237, 0.2762244316742870, 0.5989839678810083, 0.1247916004447048, 0.5989839678810083, 0.2762244316742870, 0.1247916004447046, 0.1665310619918011, 0.8312386887187595, 0.0022302492894395, 0.8312386887187594, 0.1665310619918010, 0.0022302492894393, 0.3373238618789556, 0.6603914710100434, 0.0022846671110011, 0.6603914710100434, 0.3373238618789556, 0.0022846671110009, 0.2666157086976967, 0.4667685826046064, 0.2666157086976969, 0.1284394349475123, 0.7431211301049753, 0.1284394349475125, 0.3899848376803788, 0.5268218597395553, 0.0831933025800658, 0.5268218597395553, 0.3899848376803788, 0.0831933025800657, 0.3333333333333333, 0.2190574020296069, 0.7785355668785605, 0.0024070310918327, 0.7785355668785605, 0.2190574020296069, 0.0024070310918324, 0.1203413424430903, 0.8772415939384313, 0.0024170636184784, 0.8772415939384313, 0.1203413424430904, 0.0024170636184781, 0.3975115754020483, 0.3975115754020484, 0.2049768491959033, 0.0321434597854268, 0.9549696683961201, 0.0128868718184532, 0.9549696683961202, 0.0321434597854269, 0.0128868718184528, 0.0128796984358850, 0.9742406031282296, 0.0128796984358854, 0.0239783625881974, 0.9734342386997918, 0.0025873987120110, 0.9734342386997918, 0.0239783625881975, 0.0025873987120104, 0.0004929222424058, 0.9990141555151880, 0.0004929222424063 }; static double b_save[] = { 0.0416745810379578, 0.4791627094810212, 0.4791627094810214, 0.1541231491660773, 0.3979697646407100, 0.4479070861932131, 0.1541231491660773, 0.4479070861932130, 0.3979697646407100, 0.1131367059240234, 0.4143076079881759, 0.4725556860878009, 0.1131367059240234, 0.4725556860878009, 0.4143076079881760, 0.0730183277797033, 0.3297282498766238, 0.5972534223436732, 0.0730183277797033, 0.5972534223436731, 0.3297282498766239, 0.1098033768073636, 0.2257592423300578, 0.6644373808625790, 0.1098033768073636, 0.6644373808625788, 0.2257592423300580, 0.0486830795833202, 0.0486830795833199, 0.9026338408333601, 0.0263011310948430, 0.4868494344525785, 0.4868494344525787, 0.1028358753710730, 0.3286993475605237, 0.5684647770684035, 0.1028358753710730, 0.5684647770684035, 0.3286993475605239, 0.0104550153444101, 0.0570245183292809, 0.9325204663263091, 0.0104550153444101, 0.9325204663263091, 0.0570245183292812, 0.1475222615460564, 0.2181534906276071, 0.6343242478263366, 0.1475222615460564, 0.6343242478263366, 0.2181534906276073, 0.0521260968074301, 0.2023063458834636, 0.7455675573091065, 0.0521260968074301, 0.7455675573091065, 0.2023063458834639, 0.0800841957661689, 0.2132832098088080, 0.7066325944250232, 0.0800841957661689, 0.7066325944250232, 0.2132832098088083, 0.0021607803546683, 0.0082133588712219, 0.9896258607741099, 0.0021607803546683, 0.9896258607741099, 0.0082133588712223, 0.0113638023497273, 0.4615153616123004, 0.5271208360379727, 0.0113638023497273, 0.5271208360379724, 0.4615153616123006, 0.1297785236176510, 0.3546224673127058, 0.5155990090696434, 0.1297785236176510, 0.5155990090696433, 0.3546224673127060, 0.0489372786072454, 0.3109206435860317, 0.6401420778067232, 0.0489372786072454, 0.6401420778067232, 0.3109206435860319, 0.1584175590074660, 0.3049557841332307, 0.5366266568593036, 0.1584175590074660, 0.5366266568593036, 0.3049557841332309, 0.1755000854384091, 0.2507944375639042, 0.5737054769976869, 0.1755000854384091, 0.5737054769976868, 0.2507944375639043, 0.1962948092294497, 0.1962948092294495, 0.6074103815411009, 0.1657987165670962, 0.1657987165670960, 0.6684025668658079, 0.0531263813104963, 0.4338692218644806, 0.5130043968250234, 0.0531263813104963, 0.5130043968250232, 0.4338692218644807, 0.0509089773583296, 0.0770376986253196, 0.8720533240163509, 0.0509089773583296, 0.8720533240163509, 0.0770376986253199, 0.0111213995971377, 0.2768361860195225, 0.7120424143833399, 0.0111213995971377, 0.7120424143833398, 0.2768361860195228, 0.0117797536807180, 0.1736371621034214, 0.8145830842158608, 0.0117797536807180, 0.8145830842158608, 0.1736371621034218, 0.0118081263036934, 0.3354336886613770, 0.6527581850349299, 0.0118081263036934, 0.6527581850349298, 0.3354336886613772, 0.0512438839908936, 0.3750642184523967, 0.5736918975567099, 0.0512438839908936, 0.5736918975567098, 0.3750642184523969, 0.1825412564761328, 0.3467112861299005, 0.4707474573939669, 0.1825412564761328, 0.4707474573939668, 0.3467112861299007, 0.0539018714502929, 0.2559685112606642, 0.6901296172890432, 0.0539018714502929, 0.6901296172890431, 0.2559685112606644, 0.0273433134615537, 0.2920069207885316, 0.6806497657499148, 0.0273433134615537, 0.6806497657499148, 0.2920069207885319, 0.0297423818792803, 0.2364172395795756, 0.7338403785411444, 0.0297423818792803, 0.7338403785411444, 0.2364172395795759, 0.0021912946810574, 0.4661508981294356, 0.5316578071895074, 0.0021912946810574, 0.5316578071895073, 0.4661508981294357, 0.0125736658366043, 0.2234826291455856, 0.7639437050178104, 0.0125736658366043, 0.7639437050178103, 0.2234826291455859, 0.0115196691295125, 0.3973680138780006, 0.5911123169924871, 0.0115196691295125, 0.5911123169924870, 0.3973680138780009, 0.2106680376667663, 0.2856792432449901, 0.5036527190882438, 0.2106680376667663, 0.5036527190882438, 0.2856792432449901, 0.2290071177870448, 0.2290071177870447, 0.5419857644259106, 0.2998981018797288, 0.2998981018797287, 0.4002037962405428, 0.0021708502824680, 0.4009919122964068, 0.5968372374211254, 0.0021708502824680, 0.5968372374211253, 0.4009919122964070, 0.0557664223797979, 0.1562735104040768, 0.7879600672161254, 0.0557664223797979, 0.7879600672161254, 0.1562735104040771, 0.0020979082703016, 0.0477858936846818, 0.9501161980450167, 0.0020979082703016, 0.9501161980450167, 0.0477858936846822, 0.0290781975795925, 0.1822491599313741, 0.7886726424890337, 0.0290781975795925, 0.7886726424890335, 0.1822491599313744, 0.2678374771771493, 0.3660812614114254, 0.3660812614114256, 0.0115829668440253, 0.0893475681919859, 0.8990694649639890, 0.0115829668440253, 0.8990694649639890, 0.0893475681919862, 0.0874623616502728, 0.1652198812399128, 0.7473177571098146, 0.0874623616502728, 0.7473177571098146, 0.1652198812399130, 0.0020785035982193, 0.0805280047391684, 0.9173934916626123, 0.0020785035982193, 0.9173934916626123, 0.0805280047391688, 0.2364777837447838, 0.3305415015675991, 0.4329807146876173, 0.2364777837447838, 0.4329807146876173, 0.3305415015675992, 0.1228090180537129, 0.1750740132522937, 0.7021169686939935, 0.1228090180537129, 0.7021169686939936, 0.1750740132522939, 0.0550050284444838, 0.1133949730294223, 0.8315999985260939, 0.0550050284444838, 0.8315999985260939, 0.1133949730294226, 0.0287935332271121, 0.0945442284064488, 0.8766622383664393, 0.0287935332271121, 0.8766622383664393, 0.0945442284064491, 0.0262933317918678, 0.0589589423608463, 0.9147477258472861, 0.0262933317918678, 0.9147477258472861, 0.0589589423608466, 0.0283073273852236, 0.3554461171023697, 0.6162465555124070, 0.0283073273852236, 0.6162465555124069, 0.3554461171023699, 0.0281269388071389, 0.4206278444454289, 0.5512452167474324, 0.0281269388071389, 0.5512452167474323, 0.4206278444454292, 0.0307693439520821, 0.0307693439520817, 0.9384613120958364, 0.0021009010930693, 0.2763424771664457, 0.7215566217404851, 0.0021009010930693, 0.7215566217404851, 0.2763424771664461, 0.0305221004022599, 0.1358344051381373, 0.8336434944596030, 0.0305221004022599, 0.8336434944596030, 0.1358344051381376, 0.0881430419815303, 0.1214324449203873, 0.7904245130980825, 0.0881430419815303, 0.7904245130980825, 0.1214324449203876, 0.0824986937635586, 0.0824986937635583, 0.8350026124728833, 0.0125808072722039, 0.1292544813329482, 0.8581647113948481, 0.0125808072722039, 0.8581647113948480, 0.1292544813329486, 0.0838760556578322, 0.2729393183303264, 0.6431846260118417, 0.0838760556578322, 0.6431846260118417, 0.2729393183303265, 0.0783539913048238, 0.4608230043475882, 0.4608230043475884, 0.1247916004447048, 0.2762244316742871, 0.5989839678810084, 0.1247916004447048, 0.5989839678810084, 0.2762244316742872, 0.0022302492894395, 0.1665310619918011, 0.8312386887187597, 0.0022302492894395, 0.8312386887187597, 0.1665310619918013, 0.0022846671110010, 0.3373238618789556, 0.6603914710100435, 0.0022846671110010, 0.6603914710100435, 0.3373238618789559, 0.2666157086976969, 0.2666157086976969, 0.4667685826046065, 0.1284394349475125, 0.1284394349475123, 0.7431211301049754, 0.0831933025800659, 0.3899848376803789, 0.5268218597395556, 0.0831933025800659, 0.5268218597395554, 0.3899848376803791, 0.3333333333333334, 0.0024070310918326, 0.2190574020296069, 0.7785355668785606, 0.0024070310918326, 0.7785355668785606, 0.2190574020296072, 0.0024170636184783, 0.1203413424430903, 0.8772415939384315, 0.0024170636184783, 0.8772415939384315, 0.1203413424430907, 0.2049768491959034, 0.3975115754020485, 0.3975115754020485, 0.0128868718184530, 0.0321434597854268, 0.9549696683961202, 0.0128868718184530, 0.9549696683961204, 0.0321434597854271, 0.0128796984358853, 0.0128796984358850, 0.9742406031282298, 0.0025873987120107, 0.0239783625881974, 0.9734342386997918, 0.0025873987120107, 0.9734342386997921, 0.0239783625881978, 0.0004929222424061, 0.0004929222424058, 0.9990141555151881 }; static double c_save[] = { 0.4791627094810211, 0.0416745810379577, 0.4791627094810209, 0.4479070861932128, 0.1541231491660772, 0.3979697646407097, 0.3979697646407099, 0.1541231491660771, 0.4479070861932128, 0.4725556860878008, 0.1131367059240233, 0.4143076079881757, 0.4143076079881758, 0.1131367059240233, 0.4725556860878006, 0.5972534223436731, 0.0730183277797032, 0.3297282498766235, 0.3297282498766236, 0.0730183277797033, 0.5972534223436730, 0.6644373808625788, 0.1098033768073635, 0.2257592423300575, 0.2257592423300578, 0.1098033768073634, 0.6644373808625785, 0.9026338408333600, 0.0486830795833202, 0.0486830795833197, 0.4868494344525785, 0.0263011310948429, 0.4868494344525783, 0.5684647770684034, 0.1028358753710729, 0.3286993475605235, 0.3286993475605237, 0.1028358753710729, 0.5684647770684033, 0.9325204663263090, 0.0104550153444101, 0.0570245183292806, 0.0570245183292809, 0.0104550153444098, 0.9325204663263090, 0.6343242478263366, 0.1475222615460564, 0.2181534906276069, 0.2181534906276071, 0.1475222615460562, 0.6343242478263365, 0.7455675573091064, 0.0521260968074300, 0.2023063458834634, 0.2023063458834636, 0.0521260968074299, 0.7455675573091063, 0.7066325944250231, 0.0800841957661688, 0.2132832098088079, 0.2132832098088080, 0.0800841957661688, 0.7066325944250230, 0.9896258607741097, 0.0021607803546683, 0.0082133588712218, 0.0082133588712219, 0.0021607803546680, 0.9896258607741096, 0.5271208360379724, 0.0113638023497272, 0.4615153616123001, 0.4615153616123004, 0.0113638023497272, 0.5271208360379722, 0.5155990090696433, 0.1297785236176510, 0.3546224673127056, 0.3546224673127056, 0.1297785236176509, 0.5155990090696431, 0.6401420778067229, 0.0489372786072454, 0.3109206435860313, 0.3109206435860317, 0.0489372786072452, 0.6401420778067228, 0.5366266568593034, 0.1584175590074658, 0.3049557841332305, 0.3049557841332306, 0.1584175590074658, 0.5366266568593033, 0.5737054769976867, 0.1755000854384089, 0.2507944375639041, 0.2507944375639041, 0.1755000854384090, 0.5737054769976868, 0.6074103815411007, 0.1962948092294498, 0.1962948092294494, 0.6684025668658078, 0.1657987165670962, 0.1657987165670959, 0.5130043968250232, 0.0531263813104962, 0.4338692218644803, 0.4338692218644805, 0.0531263813104962, 0.5130043968250230, 0.8720533240163508, 0.0509089773583296, 0.0770376986253195, 0.0770376986253196, 0.0509089773583294, 0.8720533240163507, 0.7120424143833398, 0.0111213995971377, 0.2768361860195223, 0.2768361860195224, 0.0111213995971376, 0.7120424143833397, 0.8145830842158607, 0.0117797536807180, 0.1736371621034212, 0.1736371621034214, 0.0117797536807177, 0.8145830842158606, 0.6527581850349298, 0.0118081263036933, 0.3354336886613768, 0.3354336886613770, 0.0118081263036932, 0.6527581850349296, 0.5736918975567097, 0.0512438839908935, 0.3750642184523966, 0.3750642184523966, 0.0512438839908935, 0.5736918975567096, 0.4707474573939667, 0.1825412564761327, 0.3467112861299004, 0.3467112861299004, 0.1825412564761327, 0.4707474573939667, 0.6901296172890430, 0.0539018714502928, 0.2559685112606639, 0.2559685112606641, 0.0539018714502927, 0.6901296172890430, 0.6806497657499146, 0.0273433134615537, 0.2920069207885315, 0.2920069207885316, 0.0273433134615536, 0.6806497657499146, 0.7338403785411441, 0.0297423818792803, 0.2364172395795753, 0.2364172395795756, 0.0297423818792800, 0.7338403785411441, 0.5316578071895072, 0.0021912946810573, 0.4661508981294352, 0.4661508981294354, 0.0021912946810573, 0.5316578071895071, 0.7639437050178102, 0.0125736658366042, 0.2234826291455854, 0.2234826291455856, 0.0125736658366041, 0.7639437050178101, 0.5911123169924869, 0.0115196691295126, 0.3973680138780004, 0.3973680138780006, 0.0115196691295124, 0.5911123169924868, 0.5036527190882437, 0.2106680376667663, 0.2856792432449899, 0.2856792432449901, 0.2106680376667662, 0.5036527190882436, 0.5419857644259105, 0.2290071177870448, 0.2290071177870446, 0.4002037962405426, 0.2998981018797286, 0.2998981018797285, 0.5968372374211253, 0.0021708502824679, 0.4009919122964066, 0.4009919122964067, 0.0021708502824680, 0.5968372374211250, 0.7879600672161253, 0.0557664223797979, 0.1562735104040766, 0.1562735104040767, 0.0557664223797977, 0.7879600672161251, 0.9501161980450165, 0.0020979082703017, 0.0477858936846814, 0.0477858936846818, 0.0020979082703013, 0.9501161980450166, 0.7886726424890335, 0.0290781975795925, 0.1822491599313738, 0.1822491599313741, 0.0290781975795923, 0.7886726424890333, 0.3660812614114253, 0.2678374771771492, 0.3660812614114253, 0.8990694649639888, 0.0115829668440253, 0.0893475681919856, 0.0893475681919859, 0.0115829668440250, 0.8990694649639888, 0.7473177571098144, 0.0874623616502728, 0.1652198812399125, 0.1652198812399128, 0.0874623616502725, 0.7473177571098144, 0.9173934916626123, 0.0020785035982193, 0.0805280047391682, 0.0805280047391685, 0.0020785035982192, 0.9173934916626122, 0.4329807146876172, 0.2364777837447836, 0.3305415015675990, 0.3305415015675990, 0.2364777837447836, 0.4329807146876172, 0.7021169686939934, 0.1228090180537128, 0.1750740132522935, 0.1750740132522937, 0.1228090180537127, 0.7021169686939934, 0.8315999985260938, 0.0550050284444839, 0.1133949730294221, 0.1133949730294224, 0.0550050284444837, 0.8315999985260938, 0.8766622383664391, 0.0287935332271121, 0.0945442284064485, 0.0945442284064488, 0.0287935332271119, 0.8766622383664391, 0.9147477258472859, 0.0262933317918679, 0.0589589423608460, 0.0589589423608463, 0.0262933317918675, 0.9147477258472857, 0.6162465555124067, 0.0283073273852235, 0.3554461171023694, 0.3554461171023697, 0.0283073273852236, 0.6162465555124066, 0.5512452167474322, 0.0281269388071388, 0.4206278444454288, 0.4206278444454289, 0.0281269388071387, 0.5512452167474320, 0.9384613120958362, 0.0307693439520821, 0.0307693439520814, 0.7215566217404850, 0.0021009010930693, 0.2763424771664456, 0.2763424771664457, 0.0021009010930692, 0.7215566217404850, 0.8336434944596028, 0.0305221004022599, 0.1358344051381370, 0.1358344051381372, 0.0305221004022597, 0.8336434944596028, 0.7904245130980824, 0.0881430419815304, 0.1214324449203871, 0.1214324449203873, 0.0881430419815301, 0.7904245130980823, 0.8350026124728831, 0.0824986937635586, 0.0824986937635580, 0.8581647113948480, 0.0125808072722038, 0.1292544813329480, 0.1292544813329482, 0.0125808072722037, 0.8581647113948477, 0.6431846260118415, 0.0838760556578321, 0.2729393183303261, 0.2729393183303264, 0.0838760556578320, 0.6431846260118415, 0.4608230043475882, 0.0783539913048238, 0.4608230043475879, 0.5989839678810082, 0.1247916004447047, 0.2762244316742869, 0.2762244316742870, 0.1247916004447046, 0.5989839678810082, 0.8312386887187595, 0.0022302492894394, 0.1665310619918008, 0.1665310619918011, 0.0022302492894393, 0.8312386887187594, 0.6603914710100434, 0.0022846671110010, 0.3373238618789555, 0.3373238618789556, 0.0022846671110009, 0.6603914710100431, 0.4667685826046063, 0.2666157086976967, 0.2666157086976967, 0.7431211301049753, 0.1284394349475124, 0.1284394349475121, 0.5268218597395554, 0.0831933025800658, 0.3899848376803786, 0.3899848376803788, 0.0831933025800659, 0.5268218597395552, 0.3333333333333333, 0.7785355668785605, 0.0024070310918325, 0.2190574020296067, 0.2190574020296069, 0.0024070310918324, 0.7785355668785604, 0.8772415939384313, 0.0024170636184784, 0.1203413424430901, 0.1203413424430904, 0.0024170636184782, 0.8772415939384312, 0.3975115754020483, 0.2049768491959031, 0.3975115754020483, 0.9549696683961202, 0.0128868718184531, 0.0321434597854267, 0.0321434597854268, 0.0128868718184527, 0.9549696683961202, 0.9742406031282297, 0.0128796984358854, 0.0128796984358848, 0.9734342386997918, 0.0025873987120108, 0.0239783625881972, 0.0239783625881974, 0.0025873987120104, 0.9734342386997918, 0.9990141555151881, 0.0004929222424062, 0.0004929222424056 }; static double w_save[] = { 0.0015063623878996, 0.0015063623878996, 0.0015063623878996, 0.0044537081869330, 0.0044537081869330, 0.0044537081869330, 0.0044537081869330, 0.0044537081869330, 0.0044537081869330, 0.0043200095246416, 0.0043200095246416, 0.0043200095246416, 0.0043200095246416, 0.0043200095246416, 0.0043200095246416, 0.0030868796559389, 0.0030868796559389, 0.0030868796559389, 0.0030868796559389, 0.0030868796559389, 0.0030868796559389, 0.0034302258154803, 0.0034302258154803, 0.0034302258154803, 0.0034302258154803, 0.0034302258154803, 0.0034302258154803, 0.0012474691816453, 0.0012474691816453, 0.0012474691816453, 0.0021895163833001, 0.0021895163833001, 0.0021895163833001, 0.0037827619823913, 0.0037827619823913, 0.0037827619823913, 0.0037827619823913, 0.0037827619823913, 0.0037827619823913, 0.0006704306400626, 0.0006704306400626, 0.0006704306400626, 0.0006704306400626, 0.0006704306400626, 0.0006704306400626, 0.0041741147673405, 0.0041741147673405, 0.0041741147673405, 0.0041741147673405, 0.0041741147673405, 0.0041741147673405, 0.0025583666569760, 0.0025583666569760, 0.0025583666569760, 0.0025583666569760, 0.0025583666569760, 0.0025583666569760, 0.0031839869521233, 0.0031839869521233, 0.0031839869521233, 0.0031839869521233, 0.0031839869521233, 0.0031839869521233, 0.0001317170927954, 0.0001317170927954, 0.0001317170927954, 0.0001317170927954, 0.0001317170927954, 0.0001317170927954, 0.0016456723831060, 0.0016456723831060, 0.0016456723831060, 0.0016456723831060, 0.0016456723831060, 0.0016456723831060, 0.0045954830932586, 0.0045954830932586, 0.0045954830932586, 0.0045954830932586, 0.0045954830932586, 0.0045954830932586, 0.0028688601568156, 0.0028688601568156, 0.0028688601568156, 0.0028688601568156, 0.0028688601568156, 0.0028688601568156, 0.0047267340609202, 0.0047267340609202, 0.0047267340609202, 0.0047267340609202, 0.0047267340609202, 0.0047267340609202, 0.0048087317688295, 0.0048087317688295, 0.0048087317688295, 0.0048087317688295, 0.0048087317688295, 0.0048087317688295, 0.0045326165183418, 0.0045326165183418, 0.0045326165183418, 0.0041121335512161, 0.0041121335512161, 0.0041121335512161, 0.0031927670836935, 0.0031927670836935, 0.0031927670836935, 0.0031927670836935, 0.0031927670836935, 0.0031927670836935, 0.0017487650502894, 0.0017487650502894, 0.0017487650502894, 0.0017487650502894, 0.0017487650502894, 0.0017487650502894, 0.0014306703323830, 0.0014306703323830, 0.0014306703323830, 0.0014306703323830, 0.0014306703323830, 0.0014306703323830, 0.0012681752789353, 0.0012681752789353, 0.0012681752789353, 0.0012681752789353, 0.0012681752789353, 0.0012681752789353, 0.0015790337439117, 0.0015790337439117, 0.0015790337439117, 0.0015790337439117, 0.0015790337439117, 0.0015790337439117, 0.0032154452084321, 0.0032154452084321, 0.0032154452084321, 0.0032154452084321, 0.0032154452084321, 0.0032154452084321, 0.0053977058220170, 0.0053977058220170, 0.0053977058220170, 0.0053977058220170, 0.0053977058220170, 0.0053977058220170, 0.0030627052030109, 0.0030627052030109, 0.0030627052030109, 0.0030627052030109, 0.0030627052030109, 0.0030627052030109, 0.0023192184096375, 0.0023192184096375, 0.0023192184096375, 0.0023192184096375, 0.0023192184096375, 0.0023192184096375, 0.0022961002901773, 0.0022961002901773, 0.0022961002901773, 0.0022961002901773, 0.0022961002901773, 0.0022961002901773, 0.0007338103320712, 0.0007338103320712, 0.0007338103320712, 0.0007338103320712, 0.0007338103320712, 0.0007338103320712, 0.0014437602767408, 0.0014437602767408, 0.0014437602767408, 0.0014437602767408, 0.0014437602767408, 0.0014437602767408, 0.0016586663239643, 0.0016586663239643, 0.0016586663239643, 0.0016586663239643, 0.0016586663239643, 0.0016586663239643, 0.0055707293081133, 0.0055707293081133, 0.0055707293081133, 0.0055707293081133, 0.0055707293081133, 0.0055707293081133, 0.0053362839978633, 0.0053362839978633, 0.0053362839978633, 0.0064756219278226, 0.0064756219278226, 0.0064756219278226, 0.0007214374344646, 0.0007214374344646, 0.0007214374344646, 0.0007214374344646, 0.0007214374344646, 0.0007214374344646, 0.0026221278244148, 0.0026221278244148, 0.0026221278244148, 0.0026221278244148, 0.0026221278244148, 0.0026221278244148, 0.0003035796033724, 0.0003035796033724, 0.0003035796033724, 0.0003035796033724, 0.0003035796033724, 0.0003035796033724, 0.0021000870011484, 0.0021000870011484, 0.0021000870011484, 0.0021000870011484, 0.0021000870011484, 0.0021000870011484, 0.0065283169454314, 0.0065283169454314, 0.0065283169454314, 0.0009662986187413, 0.0009662986187413, 0.0009662986187413, 0.0009662986187413, 0.0009662986187413, 0.0009662986187413, 0.0032046723702290, 0.0032046723702290, 0.0032046723702290, 0.0032046723702290, 0.0032046723702290, 0.0032046723702290, 0.0003922950453873, 0.0003922950453873, 0.0003922950453873, 0.0003922950453873, 0.0003922950453873, 0.0003922950453873, 0.0062575812080365, 0.0062575812080365, 0.0062575812080365, 0.0062575812080365, 0.0062575812080365, 0.0062575812080365, 0.0037812405140909, 0.0037812405140909, 0.0037812405140909, 0.0037812405140909, 0.0037812405140909, 0.0037812405140909, 0.0023063619647722, 0.0023063619647722, 0.0023063619647722, 0.0023063619647722, 0.0023063619647722, 0.0023063619647722, 0.0015964303372989, 0.0015964303372989, 0.0015964303372989, 0.0015964303372989, 0.0015964303372989, 0.0015964303372989, 0.0012488360135939, 0.0012488360135939, 0.0012488360135939, 0.0012488360135939, 0.0012488360135939, 0.0012488360135939, 0.0025556284082945, 0.0025556284082945, 0.0025556284082945, 0.0025556284082945, 0.0025556284082945, 0.0025556284082945, 0.0026782849316906, 0.0026782849316906, 0.0026782849316906, 0.0026782849316906, 0.0026782849316906, 0.0026782849316906, 0.0009717097001371, 0.0009717097001371, 0.0009717097001371, 0.0006413900158338, 0.0006413900158338, 0.0006413900158338, 0.0006413900158338, 0.0006413900158338, 0.0006413900158338, 0.0019107173540585, 0.0019107173540585, 0.0019107173540585, 0.0019107173540585, 0.0019107173540585, 0.0019107173540585, 0.0030285648566490, 0.0030285648566490, 0.0030285648566490, 0.0030285648566490, 0.0030285648566490, 0.0030285648566490, 0.0024386979014754, 0.0024386979014754, 0.0024386979014754, 0.0011940194745138, 0.0011940194745138, 0.0011940194745138, 0.0011940194745138, 0.0011940194745138, 0.0011940194745138, 0.0039897861442201, 0.0039897861442201, 0.0039897861442201, 0.0039897861442201, 0.0039897861442201, 0.0039897861442201, 0.0041882040717764, 0.0041882040717764, 0.0041882040717764, 0.0047741598764475, 0.0047741598764475, 0.0047741598764475, 0.0047741598764475, 0.0047741598764475, 0.0047741598764475, 0.0005681012975307, 0.0005681012975307, 0.0005681012975307, 0.0005681012975307, 0.0005681012975307, 0.0005681012975307, 0.0007292897898915, 0.0007292897898915, 0.0007292897898915, 0.0007292897898915, 0.0007292897898915, 0.0007292897898915, 0.0059862742964751, 0.0059862742964751, 0.0059862742964751, 0.0037734801565331, 0.0037734801565331, 0.0037734801565331, 0.0043995561699861, 0.0043995561699861, 0.0043995561699861, 0.0043995561699861, 0.0043995561699861, 0.0043995561699861, 0.0066350471232072, 0.0006789589985773, 0.0006789589985773, 0.0006789589985773, 0.0006789589985773, 0.0006789589985773, 0.0006789589985773, 0.0005314441134062, 0.0005314441134062, 0.0005314441134062, 0.0005314441134062, 0.0005314441134062, 0.0005314441134062, 0.0064816472544865, 0.0064816472544865, 0.0064816472544865, 0.0006475246634133, 0.0006475246634133, 0.0006475246634133, 0.0006475246634133, 0.0006475246634133, 0.0006475246634133, 0.0004493467102800, 0.0004493467102800, 0.0004493467102800, 0.0002613279460023, 0.0002613279460023, 0.0002613279460023, 0.0002613279460023, 0.0002613279460023, 0.0002613279460023, 0.0000140952201360, 0.0000140952201360, 0.0000140952201360 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule47 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule47() returns the rule of precision 47. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3491775041543910, 0.3491775041543910, 0.3016449916912180, 0.0132182347742615, 0.9798556571067439, 0.0069261081189949, 0.9798556571067438, 0.0132182347742616, 0.0069261081189944, 0.1820741432615592, 0.7362900096274552, 0.0816358471109855, 0.7362900096274553, 0.1820741432615592, 0.0816358471109853, 0.1505809273177014, 0.7632227066935655, 0.0861963659887331, 0.7632227066935656, 0.1505809273177015, 0.0861963659887328, 0.3028965441179143, 0.3942069117641712, 0.3028965441179143, 0.0764329826567075, 0.8732738368131011, 0.0502931805301914, 0.8732738368131011, 0.0764329826567076, 0.0502931805301912, 0.0138326160976293, 0.9851184849524532, 0.0010488989499177, 0.9851184849524532, 0.0138326160976294, 0.0010488989499173, 0.0267452272430761, 0.9632342751915716, 0.0100204975653523, 0.9632342751915717, 0.0267452272430762, 0.0100204975653520, 0.0505319024623014, 0.8989361950753969, 0.0505319024623018, 0.3711902367525145, 0.4251355102023056, 0.2036742530451798, 0.4251355102023055, 0.3711902367525146, 0.2036742530451798, 0.3688949727921184, 0.4717783433339480, 0.1593266838739336, 0.4717783433339479, 0.3688949727921184, 0.1593266838739335, 0.4215093928787094, 0.4215093928787095, 0.1569812142425811, 0.1070745798931199, 0.8395567175421841, 0.0533687025646961, 0.8395567175421841, 0.1070745798931200, 0.0533687025646957, 0.1152179121673602, 0.7994860233403234, 0.0852960644923165, 0.7994860233403234, 0.1152179121673603, 0.0852960644923162, 0.4746270243429588, 0.4746270243429588, 0.0507459513140823, 0.4179628539698995, 0.5305548481010338, 0.0514822979290668, 0.5305548481010337, 0.4179628539698995, 0.0514822979290667, 0.0795728420692438, 0.8408543158615120, 0.0795728420692443, 0.0462992599159319, 0.9261471086445946, 0.0275536314394737, 0.9261471086445946, 0.0462992599159320, 0.0275536314394733, 0.3250299373159994, 0.5562680355150597, 0.1187020271689408, 0.5562680355150598, 0.3250299373159994, 0.1187020271689407, 0.2230214568534538, 0.6919169659768531, 0.0850615771696930, 0.6919169659768531, 0.2230214568534538, 0.0850615771696929, 0.3822400802517831, 0.4996324113070245, 0.1181275084411924, 0.4996324113070245, 0.3822400802517831, 0.1181275084411923, 0.3186810168040575, 0.4286106325432008, 0.2527083506527416, 0.4286106325432009, 0.3186810168040575, 0.2527083506527416, 0.3161024291972920, 0.4781516295945364, 0.2057459412081715, 0.4781516295945364, 0.3161024291972920, 0.2057459412081715, 0.0236802291430403, 0.9526395417139191, 0.0236802291430406, 0.2017143602625017, 0.7696399026320835, 0.0286457371054150, 0.7696399026320834, 0.2017143602625018, 0.0286457371054148, 0.3040953744572968, 0.6672038004510813, 0.0287008250916218, 0.6672038004510813, 0.3040953744572970, 0.0287008250916217, 0.2509406000944529, 0.7199771640567535, 0.0290822358487937, 0.7199771640567536, 0.2509406000944530, 0.0290822358487933, 0.2701136854877469, 0.6081440785715926, 0.1217422359406605, 0.6081440785715926, 0.2701136854877470, 0.1217422359406603, 0.4230078867718429, 0.5490451947911587, 0.0279469184369985, 0.5490451947911587, 0.4230078867718429, 0.0279469184369984, 0.2188381084082620, 0.6590218248333656, 0.1221400667583725, 0.6590218248333655, 0.2188381084082620, 0.1221400667583722, 0.2630564357703722, 0.4738871284592553, 0.2630564357703724, 0.3155582824301563, 0.5240287324788191, 0.1604129850910246, 0.5240287324788190, 0.3155582824301562, 0.1604129850910245, 0.3599942050767867, 0.5879673898202077, 0.0520384051030056, 0.5879673898202077, 0.3599942050767868, 0.0520384051030055, 0.0761492805627097, 0.8958426221108554, 0.0280080973264349, 0.8958426221108555, 0.0761492805627098, 0.0280080973264346, 0.3616871250428565, 0.6099486756638904, 0.0283641992932530, 0.6099486756638904, 0.3616871250428564, 0.0283641992932528, 0.4420693972638305, 0.4420693972638306, 0.1158612054723388, 0.4861601074836898, 0.4861601074836898, 0.0276797850326204, 0.3969570429794791, 0.5212280019989164, 0.0818149550216045, 0.5212280019989164, 0.3969570429794791, 0.0818149550216044, 0.2635821046503857, 0.5242839990330530, 0.2121338963165611, 0.5242839990330530, 0.2635821046503858, 0.2121338963165610, 0.1925350542122712, 0.7550197415648126, 0.0524452042229163, 0.7550197415648127, 0.1925350542122711, 0.0524452042229161, 0.1550537980019329, 0.8157685255653345, 0.0291776764327327, 0.8157685255653344, 0.1550537980019330, 0.0291776764327324, 0.0808139183670610, 0.9075107861434476, 0.0116752954894916, 0.9075107861434475, 0.0808139183670610, 0.0116752954894912, 0.1621461225224503, 0.6757077549550992, 0.1621461225224506, 0.0494903005695828, 0.9391567442455215, 0.0113529551848958, 0.9391567442455215, 0.0494903005695828, 0.0113529551848954, 0.3736911818051820, 0.3736911818051820, 0.2526176363896359, 0.3013661191750608, 0.6458926721701388, 0.0527412086548005, 0.6458926721701387, 0.3013661191750608, 0.0527412086548003, 0.2125512689048137, 0.5748974621903724, 0.2125512689048139, 0.1455590941243064, 0.8005045213785598, 0.0539363844971339, 0.8005045213785598, 0.1455590941243065, 0.0539363844971336, 0.0339239311459584, 0.9640491722702409, 0.0020268965838009, 0.9640491722702410, 0.0339239311459585, 0.0020268965838004, 0.4598321741495011, 0.4598321741495011, 0.0803356517009977, 0.4609203982983521, 0.5277054877228970, 0.0113741139787508, 0.5277054877228969, 0.4609203982983522, 0.0113741139787508, 0.2096506369927426, 0.6256296272091983, 0.1647197357980590, 0.6256296272091983, 0.2096506369927426, 0.1647197357980589, 0.3356188307276363, 0.5818958864945520, 0.0824852827778115, 0.5818958864945520, 0.3356188307276363, 0.0824852827778114, 0.1191983560948026, 0.8689356180957589, 0.0118660258094385, 0.8689356180957590, 0.1191983560948028, 0.0118660258094381, 0.1127517427175889, 0.8582596771591932, 0.0289885801232180, 0.8582596771591932, 0.1127517427175889, 0.0289885801232177, 0.2446044849937105, 0.7017862630356211, 0.0536092519706684, 0.7017862630356212, 0.2446044849937105, 0.0536092519706682, 0.2613278952130154, 0.5737048122005965, 0.1649672925863881, 0.5737048122005964, 0.2613278952130155, 0.1649672925863880, 0.2767102223588470, 0.6391563190057649, 0.0841334586353880, 0.6391563190057650, 0.2767102223588471, 0.0841334586353878, 0.3310576983055140, 0.6572241609092210, 0.0117181407852651, 0.6572241609092210, 0.3310576983055140, 0.0117181407852649, 0.1711659603535230, 0.7090088803710917, 0.1198251592753853, 0.7090088803710918, 0.1711659603535231, 0.1198251592753851, 0.2148380935404156, 0.7733534324086832, 0.0118084740509012, 0.7733534324086832, 0.2148380935404157, 0.0118084740509010, 0.1640325957882373, 0.8240691684958087, 0.0118982357159542, 0.8240691684958087, 0.1640325957882374, 0.0118982357159538, 0.2705995205192744, 0.7175528792727295, 0.0118476002079961, 0.7175528792727296, 0.2705995205192745, 0.0118476002079958, 0.3948815299054212, 0.5935890233675787, 0.0115294467270000, 0.5935890233675788, 0.3948815299054213, 0.0115294467269999, 0.4989185291486734, 0.4989185291486734, 0.0021629417026531, 0.0976801440609630, 0.9000701501104615, 0.0022497058285756, 0.9000701501104615, 0.0976801440609631, 0.0022497058285752, 0.4316631884764961, 0.5661587284043652, 0.0021780831191386, 0.5661587284043652, 0.4316631884764962, 0.0021780831191386, 0.1403238605725803, 0.8574167083299471, 0.0022594310974726, 0.8574167083299471, 0.1403238605725803, 0.0022594310974724, 0.1249745067489113, 0.7500509865021772, 0.1249745067489116, 0.2437969001075017, 0.7539541488475877, 0.0022489510449106, 0.7539541488475877, 0.2437969001075018, 0.0022489510449104, 0.0619939934379152, 0.9357952236180167, 0.0022107829440681, 0.9357952236180167, 0.0619939934379153, 0.0022107829440677, 0.3029504928419904, 0.6947995757284657, 0.0022499314295440, 0.6947995757284656, 0.3029504928419905, 0.0022499314295438, 0.1892661005029103, 0.8084698602350489, 0.0022640392620409, 0.8084698602350490, 0.1892661005029104, 0.0022640392620406, 0.3659190279368091, 0.6318674601421832, 0.0022135119210076, 0.6318674601421833, 0.3659190279368091, 0.0022135119210075, 0.0026050966947360, 0.9947898066105276, 0.0026050966947365 }; static double b_save[] = { 0.3016449916912181, 0.3491775041543910, 0.3491775041543911, 0.0069261081189947, 0.0132182347742614, 0.9798556571067439, 0.0069261081189947, 0.9798556571067439, 0.0132182347742619, 0.0816358471109855, 0.1820741432615593, 0.7362900096274555, 0.0816358471109855, 0.7362900096274555, 0.1820741432615595, 0.0861963659887331, 0.1505809273177014, 0.7632227066935657, 0.0861963659887331, 0.7632227066935657, 0.1505809273177016, 0.3028965441179145, 0.3028965441179144, 0.3942069117641713, 0.0502931805301914, 0.0764329826567075, 0.8732738368131013, 0.0502931805301914, 0.8732738368131013, 0.0764329826567078, 0.0010488989499175, 0.0138326160976293, 0.9851184849524532, 0.0010488989499175, 0.9851184849524532, 0.0138326160976297, 0.0100204975653523, 0.0267452272430761, 0.9632342751915718, 0.0100204975653523, 0.9632342751915718, 0.0267452272430765, 0.0505319024623017, 0.0505319024623013, 0.8989361950753971, 0.2036742530451799, 0.3711902367525146, 0.4251355102023057, 0.2036742530451799, 0.4251355102023057, 0.3711902367525147, 0.1593266838739337, 0.3688949727921184, 0.4717783433339481, 0.1593266838739337, 0.4717783433339481, 0.3688949727921186, 0.1569812142425812, 0.4215093928787095, 0.4215093928787095, 0.0533687025646960, 0.1070745798931199, 0.8395567175421843, 0.0533687025646960, 0.8395567175421843, 0.1070745798931203, 0.0852960644923164, 0.1152179121673602, 0.7994860233403235, 0.0852960644923164, 0.7994860233403235, 0.1152179121673605, 0.0507459513140824, 0.4746270243429588, 0.4746270243429590, 0.0514822979290668, 0.4179628539698995, 0.5305548481010339, 0.0514822979290668, 0.5305548481010338, 0.4179628539698997, 0.0795728420692441, 0.0795728420692439, 0.8408543158615122, 0.0275536314394735, 0.0462992599159318, 0.9261471086445947, 0.0275536314394735, 0.9261471086445947, 0.0462992599159322, 0.1187020271689408, 0.3250299373159995, 0.5562680355150599, 0.1187020271689408, 0.5562680355150599, 0.3250299373159996, 0.0850615771696930, 0.2230214568534538, 0.6919169659768534, 0.0850615771696930, 0.6919169659768533, 0.2230214568534540, 0.1181275084411924, 0.3822400802517831, 0.4996324113070247, 0.1181275084411924, 0.4996324113070246, 0.3822400802517833, 0.2527083506527417, 0.3186810168040576, 0.4286106325432010, 0.2527083506527417, 0.4286106325432010, 0.3186810168040576, 0.2057459412081716, 0.3161024291972920, 0.4781516295945366, 0.2057459412081716, 0.4781516295945365, 0.3161024291972921, 0.0236802291430406, 0.0236802291430402, 0.9526395417139194, 0.0286457371054149, 0.2017143602625017, 0.7696399026320836, 0.0286457371054149, 0.7696399026320834, 0.2017143602625020, 0.0287008250916218, 0.3040953744572970, 0.6672038004510815, 0.0287008250916218, 0.6672038004510813, 0.3040953744572972, 0.0290822358487935, 0.2509406000944530, 0.7199771640567536, 0.0290822358487935, 0.7199771640567536, 0.2509406000944532, 0.1217422359406605, 0.2701136854877469, 0.6081440785715928, 0.1217422359406605, 0.6081440785715927, 0.2701136854877472, 0.0279469184369985, 0.4230078867718430, 0.5490451947911588, 0.0279469184369985, 0.5490451947911587, 0.4230078867718431, 0.1221400667583725, 0.2188381084082620, 0.6590218248333657, 0.1221400667583725, 0.6590218248333657, 0.2188381084082622, 0.2630564357703725, 0.2630564357703724, 0.4738871284592555, 0.1604129850910247, 0.3155582824301563, 0.5240287324788192, 0.1604129850910247, 0.5240287324788192, 0.3155582824301565, 0.0520384051030056, 0.3599942050767868, 0.5879673898202079, 0.0520384051030056, 0.5879673898202077, 0.3599942050767870, 0.0280080973264348, 0.0761492805627097, 0.8958426221108556, 0.0280080973264348, 0.8958426221108556, 0.0761492805627100, 0.0283641992932530, 0.3616871250428565, 0.6099486756638907, 0.0283641992932530, 0.6099486756638907, 0.3616871250428568, 0.1158612054723389, 0.4420693972638307, 0.4420693972638308, 0.0276797850326205, 0.4861601074836898, 0.4861601074836900, 0.0818149550216045, 0.3969570429794792, 0.5212280019989165, 0.0818149550216045, 0.5212280019989165, 0.3969570429794793, 0.2121338963165612, 0.2635821046503858, 0.5242839990330532, 0.2121338963165612, 0.5242839990330532, 0.2635821046503860, 0.0524452042229163, 0.1925350542122712, 0.7550197415648128, 0.0524452042229163, 0.7550197415648128, 0.1925350542122714, 0.0291776764327326, 0.1550537980019329, 0.8157685255653346, 0.0291776764327326, 0.8157685255653346, 0.1550537980019333, 0.0116752954894915, 0.0808139183670610, 0.9075107861434477, 0.0116752954894915, 0.9075107861434477, 0.0808139183670613, 0.1621461225224505, 0.1621461225224504, 0.6757077549550993, 0.0113529551848956, 0.0494903005695827, 0.9391567442455218, 0.0113529551848956, 0.9391567442455218, 0.0494903005695831, 0.2526176363896360, 0.3736911818051821, 0.3736911818051821, 0.0527412086548005, 0.3013661191750608, 0.6458926721701389, 0.0527412086548005, 0.6458926721701388, 0.3013661191750611, 0.2125512689048139, 0.2125512689048138, 0.5748974621903725, 0.0539363844971338, 0.1455590941243064, 0.8005045213785600, 0.0539363844971338, 0.8005045213785600, 0.1455590941243067, 0.0020268965838007, 0.0339239311459583, 0.9640491722702410, 0.0020268965838007, 0.9640491722702410, 0.0339239311459588, 0.0803356517009978, 0.4598321741495012, 0.4598321741495013, 0.0113741139787509, 0.4609203982983522, 0.5277054877228973, 0.0113741139787509, 0.5277054877228970, 0.4609203982983524, 0.1647197357980591, 0.2096506369927426, 0.6256296272091985, 0.1647197357980591, 0.6256296272091985, 0.2096506369927428, 0.0824852827778116, 0.3356188307276364, 0.5818958864945523, 0.0824852827778116, 0.5818958864945523, 0.3356188307276366, 0.0118660258094384, 0.1191983560948026, 0.8689356180957590, 0.0118660258094384, 0.8689356180957590, 0.1191983560948030, 0.0289885801232180, 0.1127517427175889, 0.8582596771591934, 0.0289885801232180, 0.8582596771591934, 0.1127517427175892, 0.0536092519706684, 0.2446044849937105, 0.7017862630356213, 0.0536092519706684, 0.7017862630356212, 0.2446044849937108, 0.1649672925863881, 0.2613278952130155, 0.5737048122005965, 0.1649672925863881, 0.5737048122005965, 0.2613278952130156, 0.0841334586353880, 0.2767102223588471, 0.6391563190057651, 0.0841334586353880, 0.6391563190057651, 0.2767102223588473, 0.0117181407852650, 0.3310576983055140, 0.6572241609092212, 0.0117181407852650, 0.6572241609092211, 0.3310576983055142, 0.1198251592753853, 0.1711659603535231, 0.7090088803710918, 0.1198251592753853, 0.7090088803710918, 0.1711659603535233, 0.0118084740509012, 0.2148380935404156, 0.7733534324086834, 0.0118084740509012, 0.7733534324086833, 0.2148380935404159, 0.0118982357159540, 0.1640325957882373, 0.8240691684958088, 0.0118982357159540, 0.8240691684958088, 0.1640325957882376, 0.0118476002079960, 0.2705995205192745, 0.7175528792727297, 0.0118476002079960, 0.7175528792727297, 0.2705995205192748, 0.0115294467270000, 0.3948815299054213, 0.5935890233675789, 0.0115294467270000, 0.5935890233675788, 0.3948815299054215, 0.0021629417026532, 0.4989185291486735, 0.4989185291486736, 0.0022497058285755, 0.0976801440609630, 0.9000701501104617, 0.0022497058285755, 0.9000701501104617, 0.0976801440609633, 0.0021780831191386, 0.4316631884764962, 0.5661587284043654, 0.0021780831191386, 0.5661587284043653, 0.4316631884764964, 0.0022594310974726, 0.1403238605725803, 0.8574167083299473, 0.0022594310974726, 0.8574167083299473, 0.1403238605725806, 0.1249745067489116, 0.1249745067489113, 0.7500509865021772, 0.0022489510449106, 0.2437969001075017, 0.7539541488475879, 0.0022489510449106, 0.7539541488475878, 0.2437969001075020, 0.0022107829440680, 0.0619939934379152, 0.9357952236180170, 0.0022107829440680, 0.9357952236180170, 0.0619939934379155, 0.0022499314295439, 0.3029504928419904, 0.6947995757284657, 0.0022499314295439, 0.6947995757284657, 0.3029504928419907, 0.0022640392620408, 0.1892661005029103, 0.8084698602350490, 0.0022640392620408, 0.8084698602350490, 0.1892661005029106, 0.0022135119210076, 0.3659190279368091, 0.6318674601421835, 0.0022135119210076, 0.6318674601421833, 0.3659190279368094, 0.0026050966947363, 0.0026050966947360, 0.9947898066105276 }; static double c_save[] = { 0.3491775041543909, 0.3016449916912180, 0.3491775041543909, 0.9798556571067439, 0.0069261081189946, 0.0132182347742612, 0.0132182347742615, 0.0069261081189945, 0.9798556571067437, 0.7362900096274552, 0.0816358471109856, 0.1820741432615590, 0.1820741432615592, 0.0816358471109854, 0.7362900096274553, 0.7632227066935656, 0.0861963659887331, 0.1505809273177011, 0.1505809273177013, 0.0861963659887328, 0.7632227066935655, 0.3942069117641712, 0.3028965441179144, 0.3028965441179144, 0.8732738368131011, 0.0502931805301914, 0.0764329826567073, 0.0764329826567075, 0.0502931805301911, 0.8732738368131009, 0.9851184849524532, 0.0010488989499175, 0.0138326160976291, 0.0138326160976293, 0.0010488989499173, 0.9851184849524531, 0.9632342751915716, 0.0100204975653523, 0.0267452272430758, 0.0267452272430761, 0.0100204975653521, 0.9632342751915716, 0.8989361950753969, 0.0505319024623018, 0.0505319024623011, 0.4251355102023056, 0.2036742530451798, 0.3711902367525145, 0.3711902367525145, 0.2036742530451797, 0.4251355102023054, 0.4717783433339480, 0.1593266838739336, 0.3688949727921183, 0.3688949727921184, 0.1593266838739335, 0.4717783433339479, 0.4215093928787094, 0.1569812142425810, 0.4215093928787093, 0.8395567175421841, 0.0533687025646960, 0.1070745798931196, 0.1070745798931199, 0.0533687025646957, 0.8395567175421840, 0.7994860233403234, 0.0852960644923164, 0.1152179121673601, 0.1152179121673602, 0.0852960644923163, 0.7994860233403233, 0.4746270243429588, 0.0507459513140824, 0.4746270243429587, 0.5305548481010337, 0.0514822979290667, 0.4179628539698993, 0.4179628539698995, 0.0514822979290667, 0.5305548481010335, 0.8408543158615120, 0.0795728420692441, 0.0795728420692435, 0.9261471086445946, 0.0275536314394736, 0.0462992599159315, 0.0462992599159319, 0.0275536314394733, 0.9261471086445946, 0.5562680355150597, 0.1187020271689408, 0.3250299373159993, 0.3250299373159994, 0.1187020271689406, 0.5562680355150597, 0.6919169659768531, 0.0850615771696930, 0.2230214568534536, 0.2230214568534538, 0.0850615771696929, 0.6919169659768531, 0.4996324113070245, 0.1181275084411924, 0.3822400802517830, 0.3822400802517831, 0.1181275084411922, 0.4996324113070245, 0.4286106325432009, 0.2527083506527416, 0.3186810168040574, 0.3186810168040575, 0.2527083506527415, 0.4286106325432008, 0.4781516295945364, 0.2057459412081716, 0.3161024291972919, 0.3161024291972919, 0.2057459412081715, 0.4781516295945364, 0.9526395417139192, 0.0236802291430407, 0.0236802291430399, 0.7696399026320834, 0.0286457371054148, 0.2017143602625014, 0.2017143602625017, 0.0286457371054148, 0.7696399026320832, 0.6672038004510813, 0.0287008250916218, 0.3040953744572966, 0.3040953744572968, 0.0287008250916218, 0.6672038004510812, 0.7199771640567535, 0.0290822358487935, 0.2509406000944527, 0.2509406000944528, 0.0290822358487934, 0.7199771640567535, 0.6081440785715926, 0.1217422359406605, 0.2701136854877467, 0.2701136854877469, 0.1217422359406602, 0.6081440785715925, 0.5490451947911585, 0.0279469184369984, 0.4230078867718428, 0.4230078867718428, 0.0279469184369984, 0.5490451947911585, 0.6590218248333655, 0.1221400667583724, 0.2188381084082618, 0.2188381084082621, 0.1221400667583723, 0.6590218248333655, 0.4738871284592553, 0.2630564357703724, 0.2630564357703721, 0.5240287324788191, 0.1604129850910246, 0.3155582824301562, 0.3155582824301563, 0.1604129850910246, 0.5240287324788190, 0.5879673898202077, 0.0520384051030055, 0.3599942050767865, 0.3599942050767868, 0.0520384051030055, 0.5879673898202076, 0.8958426221108555, 0.0280080973264349, 0.0761492805627094, 0.0761492805627097, 0.0280080973264346, 0.8958426221108554, 0.6099486756638904, 0.0283641992932530, 0.3616871250428563, 0.3616871250428565, 0.0283641992932530, 0.6099486756638903, 0.4420693972638305, 0.1158612054723388, 0.4420693972638304, 0.4861601074836898, 0.0276797850326204, 0.4861601074836896, 0.5212280019989164, 0.0818149550216044, 0.3969570429794790, 0.3969570429794791, 0.0818149550216044, 0.5212280019989163, 0.5242839990330531, 0.2121338963165612, 0.2635821046503857, 0.2635821046503858, 0.2121338963165610, 0.5242839990330529, 0.7550197415648126, 0.0524452042229163, 0.1925350542122709, 0.1925350542122711, 0.0524452042229161, 0.7550197415648124, 0.8157685255653345, 0.0291776764327325, 0.1550537980019326, 0.1550537980019330, 0.0291776764327324, 0.8157685255653343, 0.9075107861434475, 0.0116752954894914, 0.0808139183670606, 0.0808139183670610, 0.0116752954894913, 0.9075107861434475, 0.6757077549550992, 0.1621461225224504, 0.1621461225224502, 0.9391567442455215, 0.0113529551848957, 0.0494903005695825, 0.0494903005695828, 0.0113529551848954, 0.9391567442455216, 0.3736911818051820, 0.2526176363896359, 0.3736911818051819, 0.6458926721701387, 0.0527412086548004, 0.3013661191750606, 0.3013661191750608, 0.0527412086548004, 0.6458926721701386, 0.5748974621903724, 0.2125512689048138, 0.2125512689048136, 0.8005045213785599, 0.0539363844971338, 0.1455590941243061, 0.1455590941243064, 0.0539363844971336, 0.8005045213785598, 0.9640491722702410, 0.0020268965838008, 0.0339239311459582, 0.0339239311459583, 0.0020268965838005, 0.9640491722702408, 0.4598321741495012, 0.0803356517009977, 0.4598321741495010, 0.5277054877228970, 0.0113741139787508, 0.4609203982983520, 0.4609203982983522, 0.0113741139787508, 0.5277054877228968, 0.6256296272091982, 0.1647197357980590, 0.2096506369927426, 0.2096506369927426, 0.1647197357980589, 0.6256296272091983, 0.5818958864945520, 0.0824852827778115, 0.3356188307276362, 0.3356188307276363, 0.0824852827778114, 0.5818958864945520, 0.8689356180957589, 0.0118660258094384, 0.1191983560948024, 0.1191983560948026, 0.0118660258094382, 0.8689356180957588, 0.8582596771591932, 0.0289885801232179, 0.1127517427175887, 0.1127517427175889, 0.0289885801232178, 0.8582596771591930, 0.7017862630356212, 0.0536092519706684, 0.2446044849937103, 0.2446044849937104, 0.0536092519706682, 0.7017862630356210, 0.5737048122005965, 0.1649672925863880, 0.2613278952130154, 0.2613278952130155, 0.1649672925863880, 0.5737048122005964, 0.6391563190057650, 0.0841334586353881, 0.2767102223588469, 0.2767102223588470, 0.0841334586353878, 0.6391563190057650, 0.6572241609092210, 0.0117181407852650, 0.3310576983055137, 0.3310576983055140, 0.0117181407852649, 0.6572241609092209, 0.7090088803710918, 0.1198251592753853, 0.1711659603535228, 0.1711659603535229, 0.1198251592753851, 0.7090088803710917, 0.7733534324086833, 0.0118084740509012, 0.2148380935404154, 0.2148380935404157, 0.0118084740509010, 0.7733534324086830, 0.8240691684958087, 0.0118982357159540, 0.1640325957882370, 0.1640325957882373, 0.0118982357159538, 0.8240691684958086, 0.7175528792727296, 0.0118476002079960, 0.2705995205192742, 0.2705995205192744, 0.0118476002079958, 0.7175528792727295, 0.5935890233675787, 0.0115294467270000, 0.3948815299054211, 0.3948815299054212, 0.0115294467269998, 0.5935890233675787, 0.4989185291486735, 0.0021629417026531, 0.4989185291486732, 0.9000701501104614, 0.0022497058285755, 0.0976801440609628, 0.0976801440609630, 0.0022497058285752, 0.9000701501104615, 0.5661587284043652, 0.0021780831191386, 0.4316631884764959, 0.4316631884764962, 0.0021780831191386, 0.5661587284043650, 0.8574167083299471, 0.0022594310974726, 0.1403238605725801, 0.1403238605725803, 0.0022594310974724, 0.8574167083299470, 0.7500509865021772, 0.1249745067489115, 0.1249745067489112, 0.7539541488475877, 0.0022489510449106, 0.2437969001075014, 0.2437969001075017, 0.0022489510449104, 0.7539541488475876, 0.9357952236180168, 0.0022107829440681, 0.0619939934379149, 0.0619939934379153, 0.0022107829440677, 0.9357952236180168, 0.6947995757284657, 0.0022499314295438, 0.3029504928419903, 0.3029504928419904, 0.0022499314295438, 0.6947995757284655, 0.8084698602350490, 0.0022640392620409, 0.1892661005029100, 0.1892661005029102, 0.0022640392620407, 0.8084698602350489, 0.6318674601421833, 0.0022135119210077, 0.3659190279368089, 0.3659190279368091, 0.0022135119210075, 0.6318674601421832, 0.9947898066105277, 0.0026050966947364, 0.0026050966947359 }; static double w_save[] = { 0.0043146569583335, 0.0043146569583335, 0.0043146569583335, 0.0002127820065249, 0.0002127820065249, 0.0002127820065249, 0.0002127820065249, 0.0002127820065249, 0.0002127820065249, 0.0022514827449286, 0.0022514827449286, 0.0022514827449286, 0.0022514827449286, 0.0022514827449286, 0.0022514827449286, 0.0022650701154880, 0.0022650701154880, 0.0022650701154880, 0.0022650701154880, 0.0022650701154880, 0.0022650701154880, 0.0046991712312519, 0.0046991712312519, 0.0046991712312519, 0.0014027295746802, 0.0014027295746802, 0.0014027295746802, 0.0014027295746802, 0.0014027295746802, 0.0014027295746802, 0.0000978099168127, 0.0000978099168127, 0.0000978099168127, 0.0000978099168127, 0.0000978099168127, 0.0000978099168127, 0.0004038629868035, 0.0004038629868035, 0.0004038629868035, 0.0004038629868035, 0.0004038629868035, 0.0004038629868035, 0.0012364924097053, 0.0012364924097053, 0.0012364924097053, 0.0051536553206131, 0.0051536553206131, 0.0051536553206131, 0.0051536553206131, 0.0051536553206131, 0.0051536553206131, 0.0045094710563839, 0.0045094710563839, 0.0045094710563839, 0.0045094710563839, 0.0045094710563839, 0.0045094710563839, 0.0045159973781931, 0.0045159973781931, 0.0045159973781931, 0.0019145889672060, 0.0019145889672060, 0.0019145889672060, 0.0019145889672060, 0.0019145889672060, 0.0019145889672060, 0.0026062651829993, 0.0026062651829993, 0.0026062651829993, 0.0026062651829993, 0.0026062651829993, 0.0026062651829993, 0.0029444810662743, 0.0029444810662743, 0.0029444810662743, 0.0030761572742866, 0.0030761572742866, 0.0030761572742866, 0.0030761572742866, 0.0030761572742866, 0.0030761572742866, 0.0020830024863947, 0.0020830024863947, 0.0020830024863947, 0.0010328123125119, 0.0010328123125119, 0.0010328123125119, 0.0010328123125119, 0.0010328123125119, 0.0010328123125119, 0.0043543612304128, 0.0043543612304128, 0.0043543612304128, 0.0043543612304128, 0.0043543612304128, 0.0043543612304128, 0.0033920879178230, 0.0033920879178230, 0.0033920879178230, 0.0033920879178230, 0.0033920879178230, 0.0033920879178230, 0.0045331567046035, 0.0045331567046035, 0.0045331567046035, 0.0045331567046035, 0.0045331567046035, 0.0045331567046035, 0.0053697193075647, 0.0053697193075647, 0.0053697193075647, 0.0053697193075647, 0.0053697193075647, 0.0053697193075647, 0.0050112518902677, 0.0050112518902677, 0.0050112518902677, 0.0050112518902677, 0.0050112518902677, 0.0050112518902677, 0.0006630078632668, 0.0006630078632668, 0.0006630078632668, 0.0019533942747889, 0.0019533942747889, 0.0019533942747889, 0.0019533942747889, 0.0019533942747889, 0.0019533942747889, 0.0022701532915994, 0.0022701532915994, 0.0022701532915994, 0.0022701532915994, 0.0022701532915994, 0.0022701532915994, 0.0021386729830485, 0.0021386729830485, 0.0021386729830485, 0.0021386729830485, 0.0021386729830485, 0.0021386729830485, 0.0042781341832724, 0.0042781341832724, 0.0042781341832724, 0.0042781341832724, 0.0042781341832724, 0.0042781341832724, 0.0025070193444428, 0.0025070193444428, 0.0025070193444428, 0.0025070193444428, 0.0025070193444428, 0.0025070193444428, 0.0039737311003985, 0.0039737311003985, 0.0039737311003985, 0.0039737311003985, 0.0039737311003985, 0.0039737311003985, 0.0055982544326031, 0.0055982544326031, 0.0055982544326031, 0.0047404136863378, 0.0047404136863378, 0.0047404136863378, 0.0047404136863378, 0.0047404136863378, 0.0047404136863378, 0.0031609021577845, 0.0031609021577845, 0.0031609021577845, 0.0031609021577845, 0.0031609021577845, 0.0031609021577845, 0.0013064930317837, 0.0013064930317837, 0.0013064930317837, 0.0013064930317837, 0.0013064930317837, 0.0013064930317837, 0.0024224165705941, 0.0024224165705941, 0.0024224165705941, 0.0024224165705941, 0.0024224165705941, 0.0024224165705941, 0.0045518145135699, 0.0045518145135699, 0.0045518145135699, 0.0025072813505809, 0.0025072813505809, 0.0025072813505809, 0.0041337585903884, 0.0041337585903884, 0.0041337585903884, 0.0041337585903884, 0.0041337585903884, 0.0041337585903884, 0.0051051331812112, 0.0051051331812112, 0.0051051331812112, 0.0051051331812112, 0.0051051331812112, 0.0051051331812112, 0.0026976233339834, 0.0026976233339834, 0.0026976233339834, 0.0026976233339834, 0.0026976233339834, 0.0026976233339834, 0.0018809643979073, 0.0018809643979073, 0.0018809643979073, 0.0018809643979073, 0.0018809643979073, 0.0018809643979073, 0.0009142190102743, 0.0009142190102743, 0.0009142190102743, 0.0009142190102743, 0.0009142190102743, 0.0009142190102743, 0.0040644299258672, 0.0040644299258672, 0.0040644299258672, 0.0007010656028691, 0.0007010656028691, 0.0007010656028691, 0.0007010656028691, 0.0007010656028691, 0.0007010656028691, 0.0055051135413514, 0.0055051135413514, 0.0055051135413514, 0.0031901056487151, 0.0031901056487151, 0.0031901056487151, 0.0031901056487151, 0.0031901056487151, 0.0031901056487151, 0.0049446615998697, 0.0049446615998697, 0.0049446615998697, 0.0024338258411055, 0.0024338258411055, 0.0024338258411055, 0.0024338258411055, 0.0024338258411055, 0.0024338258411055, 0.0002508474514575, 0.0002508474514575, 0.0002508474514575, 0.0002508474514575, 0.0002508474514575, 0.0002508474514575, 0.0040657898075942, 0.0040657898075942, 0.0040657898075942, 0.0017108131277605, 0.0017108131277605, 0.0017108131277605, 0.0017108131277605, 0.0017108131277605, 0.0017108131277605, 0.0045280121334294, 0.0045280121334294, 0.0045280121334294, 0.0045280121334294, 0.0045280121334294, 0.0045280121334294, 0.0040081392301490, 0.0040081392301490, 0.0040081392301490, 0.0040081392301490, 0.0040081392301490, 0.0040081392301490, 0.0011195403999073, 0.0011195403999073, 0.0011195403999073, 0.0011195403999073, 0.0011195403999073, 0.0011195403999073, 0.0016556490812277, 0.0016556490812277, 0.0016556490812277, 0.0016556490812277, 0.0016556490812277, 0.0016556490812277, 0.0030745572112736, 0.0030745572112736, 0.0030745572112736, 0.0030745572112736, 0.0030745572112736, 0.0030745572112736, 0.0048300704241971, 0.0048300704241971, 0.0048300704241971, 0.0048300704241971, 0.0048300704241971, 0.0048300704241971, 0.0038986974038214, 0.0038986974038214, 0.0038986974038214, 0.0038986974038214, 0.0038986974038214, 0.0038986974038214, 0.0016458519911547, 0.0016458519911547, 0.0016458519911547, 0.0016458519911547, 0.0016458519911547, 0.0016458519911547, 0.0037119048709275, 0.0037119048709275, 0.0037119048709275, 0.0037119048709275, 0.0037119048709275, 0.0037119048709275, 0.0014185756078616, 0.0014185756078616, 0.0014185756078616, 0.0014185756078616, 0.0014185756078616, 0.0014185756078616, 0.0012890581955709, 0.0012890581955709, 0.0012890581955709, 0.0012890581955709, 0.0012890581955709, 0.0012890581955709, 0.0015614900549058, 0.0015614900549058, 0.0015614900549058, 0.0015614900549058, 0.0015614900549058, 0.0015614900549058, 0.0016952718909460, 0.0016952718909460, 0.0016952718909460, 0.0016952718909460, 0.0016952718909460, 0.0016952718909460, 0.0007488308612040, 0.0007488308612040, 0.0007488308612040, 0.0004528022725679, 0.0004528022725679, 0.0004528022725679, 0.0004528022725679, 0.0004528022725679, 0.0004528022725679, 0.0007453398310664, 0.0007453398310664, 0.0007453398310664, 0.0007453398310664, 0.0007453398310664, 0.0007453398310664, 0.0005323481472587, 0.0005323481472587, 0.0005323481472587, 0.0005323481472587, 0.0005323481472587, 0.0005323481472587, 0.0036321398556638, 0.0036321398556638, 0.0036321398556638, 0.0006576196836264, 0.0006576196836264, 0.0006576196836264, 0.0006576196836264, 0.0006576196836264, 0.0006576196836264, 0.0003620690511307, 0.0003620690511307, 0.0003620690511307, 0.0003620690511307, 0.0003620690511307, 0.0003620690511307, 0.0007060119456705, 0.0007060119456705, 0.0007060119456705, 0.0007060119456705, 0.0007060119456705, 0.0007060119456705, 0.0006018771022200, 0.0006018771022200, 0.0006018771022200, 0.0006018771022200, 0.0006018771022200, 0.0006018771022200, 0.0007326393465497, 0.0007326393465497, 0.0007326393465497, 0.0007326393465497, 0.0007326393465497, 0.0007326393465497, 0.0000892536614181, 0.0000892536614181, 0.0000892536614181 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule48 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule48() returns the rule of precision 48. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.3477244587108094, 0.3477244587108095, 0.3045510825783810, 0.3695672915901662, 0.4147320642402169, 0.2157006441696168, 0.4147320642402170, 0.3695672915901662, 0.2157006441696168, 0.3084818979933622, 0.5832166020846338, 0.1083014999220039, 0.5832166020846338, 0.3084818979933622, 0.1083014999220039, 0.3196427292245513, 0.6456613180043123, 0.0346959527711365, 0.6456613180043123, 0.3196427292245514, 0.0346959527711363, 0.3734312712553221, 0.3734312712553221, 0.2531374574893558, 0.9962559654771519, 0.0023979705918987, 0.0013460639309493, 0.0023979705918986, 0.9962559654771519, 0.0013460639309497, 0.3280848178088313, 0.6527443981108471, 0.0191707840803216, 0.6527443981108471, 0.3280848178088314, 0.0191707840803215, 0.3198129082727195, 0.4038255264164708, 0.2763615653108096, 0.4038255264164707, 0.3198129082727195, 0.2763615653108096, 0.1589266013618200, 0.8394322302943624, 0.0016411683438175, 0.8394322302943625, 0.1589266013618200, 0.0016411683438173, 0.1962759771972356, 0.7504008293814409, 0.0533231934213236, 0.7504008293814409, 0.1962759771972357, 0.0533231934213233, 0.4893390535628532, 0.4893390535628532, 0.0213218928742936, 0.2933421845901817, 0.6237289790086799, 0.0829288364011385, 0.6237289790086799, 0.2933421845901818, 0.0829288364011382, 0.0484109248251399, 0.9031781503497199, 0.0484109248251403, 0.0801595487479756, 0.8396809025040485, 0.0801595487479760, 0.1247273258813976, 0.8519536569694208, 0.0233190171491816, 0.8519536569694209, 0.1247273258813976, 0.0233190171491812, 0.3115932459432796, 0.5496936600973348, 0.1387130939593856, 0.5496936600973348, 0.3115932459432795, 0.1387130939593854, 0.4790902659592135, 0.4790902659592136, 0.0418194680815729, 0.4666424153484346, 0.4666424153484346, 0.0667151693031307, 0.1105414410318808, 0.8789179195599967, 0.0105406394081227, 0.8789179195599968, 0.1105414410318809, 0.0105406394081222, 0.2974171962759172, 0.6922355531565748, 0.0103472505675080, 0.6922355531565748, 0.2974171962759173, 0.0103472505675078, 0.2940680586522785, 0.6521500596889448, 0.0537818816587767, 0.6521500596889448, 0.2940680586522786, 0.0537818816587766, 0.1114012176063108, 0.8188384243732427, 0.0697603580204465, 0.8188384243732427, 0.1114012176063108, 0.0697603580204462, 0.4437434538636293, 0.5407542433571197, 0.0155023027792509, 0.5407542433571196, 0.4437434538636293, 0.0155023027792509, 0.3676357119294025, 0.5927417808117805, 0.0396225072588170, 0.5927417808117805, 0.3676357119294025, 0.0396225072588168, 0.0483834188936243, 0.9398058801827116, 0.0118107009236643, 0.9398058801827116, 0.0483834188936244, 0.0118107009236638, 0.4261985460348483, 0.5385135616187795, 0.0352878923463722, 0.5385135616187795, 0.4261985460348482, 0.0352878923463721, 0.3464037075083426, 0.5888811994896823, 0.0647150930019751, 0.5888811994896823, 0.3464037075083425, 0.0647150930019750, 0.0761686440792015, 0.9134087843531564, 0.0104225715676421, 0.9134087843531565, 0.0761686440792015, 0.0104225715676419, 0.3198558059892070, 0.4530392764801240, 0.2271049175306689, 0.4530392764801241, 0.3198558059892070, 0.2271049175306689, 0.1149767499763278, 0.8418683619431016, 0.0431548880805707, 0.8418683619431017, 0.1149767499763279, 0.0431548880805703, 0.1553411874863350, 0.7956838642952746, 0.0489749482183905, 0.7956838642952746, 0.1553411874863350, 0.0489749482183902, 0.1536641394780652, 0.8368813116799081, 0.0094545488420268, 0.8368813116799082, 0.1536641394780653, 0.0094545488420265, 0.0798538207718234, 0.9182518733490639, 0.0018943058791128, 0.9182518733490640, 0.0798538207718235, 0.0018943058791124, 0.0117045744671133, 0.9765908510657730, 0.0117045744671137, 0.1978601121285484, 0.7901115654677587, 0.0120283224036928, 0.7901115654677586, 0.1978601121285484, 0.0120283224036928, 0.3169153803807818, 0.6811801518412819, 0.0019044677779363, 0.6811801518412819, 0.3169153803807819, 0.0019044677779362, 0.1645639771634135, 0.8092307990442300, 0.0262052237923566, 0.8092307990442301, 0.1645639771634135, 0.0262052237923562, 0.3611298359799379, 0.5443992424960357, 0.0944709215240264, 0.5443992424960357, 0.3611298359799380, 0.0944709215240263, 0.4198259774542294, 0.4838506735119869, 0.0963233490337836, 0.4838506735119869, 0.4198259774542294, 0.0963233490337836, 0.2431752245746631, 0.7033344581619095, 0.0534903172634275, 0.7033344581619095, 0.2431752245746631, 0.0534903172634272, 0.1459832231136435, 0.7744922982855192, 0.0795244786008372, 0.7744922982855195, 0.1459832231136434, 0.0795244786008370, 0.0272392832679803, 0.9617299619505478, 0.0110307547814721, 0.9617299619505478, 0.0272392832679803, 0.0110307547814717, 0.2453137089647784, 0.7425000580712428, 0.0121862329639789, 0.7425000580712428, 0.2453137089647784, 0.0121862329639786, 0.2678465137111688, 0.4643069725776622, 0.2678465137111689, 0.1165542190734529, 0.8813325626640695, 0.0021132182624777, 0.8813325626640695, 0.1165542190734529, 0.0021132182624774, 0.0535856828700446, 0.9191953264718842, 0.0272189906580713, 0.9191953264718841, 0.0535856828700446, 0.0272189906580709, 0.0851355181500169, 0.8886082228375111, 0.0262562590124721, 0.8886082228375112, 0.0851355181500170, 0.0262562590124718, 0.4084926257856331, 0.5290322767639966, 0.0624750974503704, 0.5290322767639964, 0.4084926257856331, 0.0624750974503703, 0.3822510450948138, 0.4439727450289927, 0.1737762098761934, 0.4439727450289928, 0.3822510450948139, 0.1737762098761934, 0.0259740322065890, 0.9719768417503413, 0.0020491260430698, 0.9719768417503415, 0.0259740322065892, 0.0020491260430693, 0.3856891887600643, 0.5954207695783936, 0.0188900416615421, 0.5954207695783936, 0.3856891887600644, 0.0188900416615419, 0.1907464794314031, 0.7266345676228985, 0.0826189529456984, 0.7266345676228985, 0.1907464794314032, 0.0826189529456982, 0.0493146516048518, 0.9484053916083951, 0.0022799567867532, 0.9484053916083951, 0.0493146516048519, 0.0022799567867528, 0.4264825454980466, 0.5687452023816508, 0.0047722521203026, 0.5687452023816508, 0.4264825454980467, 0.0047722521203026, 0.1513647526705651, 0.7324328909178469, 0.1162023564115880, 0.7324328909178468, 0.1513647526705652, 0.1162023564115878, 0.2410855603909864, 0.6733891753666466, 0.0855252642423671, 0.6733891753666466, 0.2410855603909864, 0.0855252642423669, 0.2120362112054797, 0.7581870004717137, 0.0297767883228067, 0.7581870004717137, 0.2120362112054797, 0.0297767883228064, 0.0773420280842538, 0.8724044348798747, 0.0502535370358714, 0.8724044348798747, 0.0773420280842540, 0.0502535370358712, 0.2659270236545313, 0.5177727692431142, 0.2163002071023543, 0.5177727692431143, 0.2659270236545314, 0.2163002071023542, 0.2131382724801908, 0.5737234550396183, 0.2131382724801909, 0.0102781124040352, 0.9874036799114877, 0.0023182076844773, 0.9874036799114878, 0.0102781124040354, 0.0023182076844769, 0.4336266613666109, 0.4336266613666109, 0.1327466772667780, 0.3637486804898151, 0.6298211317204232, 0.0064301877897617, 0.6298211317204232, 0.3637486804898151, 0.0064301877897616, 0.3698202051067137, 0.4970686798278148, 0.1331111150654714, 0.4970686798278148, 0.3698202051067137, 0.1331111150654714, 0.1599009144405388, 0.6801981711189222, 0.1599009144405390, 0.0280636634926782, 0.9438726730146434, 0.0280636634926786, 0.2622368556255414, 0.5695106590028955, 0.1682524853715630, 0.5695106590028955, 0.2622368556255415, 0.1682524853715628, 0.2058652741989988, 0.7917570821001609, 0.0023776437008403, 0.7917570821001609, 0.2058652741989988, 0.0023776437008400, 0.3210612992391711, 0.4996635238460939, 0.1792751769147349, 0.4996635238460939, 0.3210612992391711, 0.1792751769147348, 0.2670089253528111, 0.7045277230351698, 0.0284633516120191, 0.7045277230351698, 0.2670089253528112, 0.0284633516120189, 0.2586045410103510, 0.7391689918977531, 0.0022264670918959, 0.7391689918977531, 0.2586045410103511, 0.0022264670918957, 0.1996247626773604, 0.6800108677503900, 0.1203643695722495, 0.6800108677503900, 0.1996247626773605, 0.1203643695722494, 0.2088908643844065, 0.6267746739288779, 0.1643344616867157, 0.6267746739288779, 0.2088908643844065, 0.1643344616867155, 0.1080471292423059, 0.7839057415153878, 0.1080471292423062, 0.2533336006018089, 0.6227789405605143, 0.1238874588376767, 0.6227789405605143, 0.2533336006018089, 0.1238874588376766, 0.4971756372384661, 0.4971756372384660, 0.0056487255230678, 0.4637961227465663, 0.5360438668640494, 0.0001600103893842, 0.5360438668640494, 0.4637961227465663, 0.0001600103893842, 0.3837177990505464, 0.6161736917477099, 0.0001085092017437, 0.6161736917477099, 0.3837177990505465, 0.0001085092017435 }; static double b_save[] = { 0.3045510825783811, 0.3477244587108095, 0.3477244587108096, 0.2157006441696169, 0.3695672915901663, 0.4147320642402171, 0.2157006441696169, 0.4147320642402170, 0.3695672915901664, 0.1083014999220040, 0.3084818979933623, 0.5832166020846340, 0.1083014999220040, 0.5832166020846339, 0.3084818979933624, 0.0346959527711364, 0.3196427292245514, 0.6456613180043125, 0.0346959527711364, 0.6456613180043123, 0.3196427292245516, 0.2531374574893559, 0.3734312712553222, 0.3734312712553222, 0.0013460639309495, 0.9962559654771520, 0.0023979705918990, 0.0013460639309495, 0.0023979705918986, 0.9962559654771520, 0.0191707840803216, 0.3280848178088313, 0.6527443981108473, 0.0191707840803216, 0.6527443981108472, 0.3280848178088315, 0.2763615653108097, 0.3198129082727196, 0.4038255264164710, 0.2763615653108097, 0.4038255264164710, 0.3198129082727196, 0.0016411683438175, 0.1589266013618200, 0.8394322302943628, 0.0016411683438175, 0.8394322302943628, 0.1589266013618204, 0.0533231934213235, 0.1962759771972356, 0.7504008293814409, 0.0533231934213235, 0.7504008293814409, 0.1962759771972359, 0.0213218928742936, 0.4893390535628533, 0.4893390535628534, 0.0829288364011384, 0.2933421845901818, 0.6237289790086800, 0.0829288364011384, 0.6237289790086800, 0.2933421845901819, 0.0484109248251402, 0.0484109248251399, 0.9031781503497200, 0.0801595487479759, 0.0801595487479756, 0.8396809025040486, 0.0233190171491815, 0.1247273258813976, 0.8519536569694212, 0.0233190171491815, 0.8519536569694212, 0.1247273258813979, 0.1387130939593856, 0.3115932459432796, 0.5496936600973350, 0.1387130939593856, 0.5496936600973350, 0.3115932459432798, 0.0418194680815730, 0.4790902659592136, 0.4790902659592137, 0.0667151693031307, 0.4666424153484347, 0.4666424153484348, 0.0105406394081225, 0.1105414410318807, 0.8789179195599968, 0.0105406394081225, 0.8789179195599968, 0.1105414410318811, 0.0103472505675079, 0.2974171962759173, 0.6922355531565749, 0.0103472505675079, 0.6922355531565749, 0.2974171962759176, 0.0537818816587767, 0.2940680586522786, 0.6521500596889449, 0.0537818816587767, 0.6521500596889449, 0.2940680586522788, 0.0697603580204464, 0.1114012176063108, 0.8188384243732429, 0.0697603580204464, 0.8188384243732429, 0.1114012176063111, 0.0155023027792511, 0.4437434538636293, 0.5407542433571200, 0.0155023027792511, 0.5407542433571197, 0.4437434538636296, 0.0396225072588169, 0.3676357119294025, 0.5927417808117806, 0.0396225072588169, 0.5927417808117806, 0.3676357119294028, 0.0118107009236641, 0.0483834188936242, 0.9398058801827117, 0.0118107009236641, 0.9398058801827117, 0.0483834188936246, 0.0352878923463722, 0.4261985460348483, 0.5385135616187797, 0.0352878923463722, 0.5385135616187796, 0.4261985460348485, 0.0647150930019751, 0.3464037075083426, 0.5888811994896825, 0.0647150930019751, 0.5888811994896824, 0.3464037075083428, 0.0104225715676421, 0.0761686440792014, 0.9134087843531568, 0.0104225715676421, 0.9134087843531568, 0.0761686440792017, 0.2271049175306690, 0.3198558059892071, 0.4530392764801242, 0.2271049175306690, 0.4530392764801242, 0.3198558059892072, 0.0431548880805706, 0.1149767499763278, 0.8418683619431018, 0.0431548880805706, 0.8418683619431018, 0.1149767499763281, 0.0489749482183904, 0.1553411874863350, 0.7956838642952748, 0.0489749482183904, 0.7956838642952748, 0.1553411874863353, 0.0094545488420267, 0.1536641394780652, 0.8368813116799082, 0.0094545488420267, 0.8368813116799082, 0.1536641394780656, 0.0018943058791126, 0.0798538207718234, 0.9182518733490641, 0.0018943058791126, 0.9182518733490641, 0.0798538207718237, 0.0117045744671136, 0.0117045744671133, 0.9765908510657733, 0.0120283224036929, 0.1978601121285484, 0.7901115654677591, 0.0120283224036929, 0.7901115654677587, 0.1978601121285486, 0.0019044677779363, 0.3169153803807819, 0.6811801518412820, 0.0019044677779363, 0.6811801518412820, 0.3169153803807821, 0.0262052237923565, 0.1645639771634134, 0.8092307990442302, 0.0262052237923565, 0.8092307990442302, 0.1645639771634138, 0.0944709215240264, 0.3611298359799380, 0.5443992424960359, 0.0944709215240264, 0.5443992424960358, 0.3611298359799381, 0.0963233490337837, 0.4198259774542294, 0.4838506735119871, 0.0963233490337837, 0.4838506735119870, 0.4198259774542296, 0.0534903172634274, 0.2431752245746631, 0.7033344581619096, 0.0534903172634274, 0.7033344581619096, 0.2431752245746634, 0.0795244786008372, 0.1459832231136435, 0.7744922982855196, 0.0795244786008372, 0.7744922982855196, 0.1459832231136438, 0.0110307547814719, 0.0272392832679802, 0.9617299619505479, 0.0110307547814719, 0.9617299619505479, 0.0272392832679806, 0.0121862329639789, 0.2453137089647784, 0.7425000580712430, 0.0121862329639789, 0.7425000580712430, 0.2453137089647787, 0.2678465137111690, 0.2678465137111689, 0.4643069725776624, 0.0021132182624776, 0.1165542190734529, 0.8813325626640697, 0.0021132182624776, 0.8813325626640697, 0.1165542190734533, 0.0272189906580712, 0.0535856828700446, 0.9191953264718844, 0.0272189906580712, 0.9191953264718844, 0.0535856828700449, 0.0262562590124721, 0.0851355181500168, 0.8886082228375113, 0.0262562590124721, 0.8886082228375112, 0.0851355181500172, 0.0624750974503704, 0.4084926257856331, 0.5290322767639968, 0.0624750974503704, 0.5290322767639967, 0.4084926257856333, 0.1737762098761935, 0.3822510450948139, 0.4439727450289929, 0.1737762098761935, 0.4439727450289928, 0.3822510450948140, 0.0020491260430696, 0.0259740322065890, 0.9719768417503415, 0.0020491260430696, 0.9719768417503415, 0.0259740322065894, 0.0188900416615420, 0.3856891887600644, 0.5954207695783937, 0.0188900416615420, 0.5954207695783937, 0.3856891887600646, 0.0826189529456984, 0.1907464794314031, 0.7266345676228987, 0.0826189529456984, 0.7266345676228986, 0.1907464794314034, 0.0022799567867531, 0.0493146516048518, 0.9484053916083952, 0.0022799567867531, 0.9484053916083952, 0.0493146516048521, 0.0047722521203026, 0.4264825454980467, 0.5687452023816510, 0.0047722521203026, 0.5687452023816508, 0.4264825454980468, 0.1162023564115881, 0.1513647526705651, 0.7324328909178470, 0.1162023564115881, 0.7324328909178470, 0.1513647526705654, 0.0855252642423671, 0.2410855603909865, 0.6733891753666467, 0.0855252642423671, 0.6733891753666467, 0.2410855603909867, 0.0297767883228067, 0.2120362112054797, 0.7581870004717138, 0.0297767883228067, 0.7581870004717138, 0.2120362112054800, 0.0502535370358714, 0.0773420280842539, 0.8724044348798750, 0.0502535370358714, 0.8724044348798748, 0.0773420280842542, 0.2163002071023544, 0.2659270236545314, 0.5177727692431144, 0.2163002071023544, 0.5177727692431144, 0.2659270236545315, 0.2131382724801910, 0.2131382724801908, 0.5737234550396184, 0.0023182076844771, 0.0102781124040352, 0.9874036799114877, 0.0023182076844771, 0.9874036799114877, 0.0102781124040356, 0.1327466772667781, 0.4336266613666110, 0.4336266613666112, 0.0064301877897617, 0.3637486804898151, 0.6298211317204234, 0.0064301877897617, 0.6298211317204232, 0.3637486804898154, 0.1331111150654715, 0.3698202051067138, 0.4970686798278151, 0.1331111150654715, 0.4970686798278149, 0.3698202051067139, 0.1599009144405390, 0.1599009144405389, 0.6801981711189224, 0.0280636634926785, 0.0280636634926781, 0.9438726730146435, 0.1682524853715630, 0.2622368556255416, 0.5695106590028957, 0.1682524853715630, 0.5695106590028957, 0.2622368556255417, 0.0023776437008402, 0.2058652741989988, 0.7917570821001612, 0.0023776437008402, 0.7917570821001612, 0.2058652741989991, 0.1792751769147349, 0.3210612992391713, 0.4996635238460941, 0.1792751769147349, 0.4996635238460940, 0.3210612992391713, 0.0284633516120191, 0.2670089253528111, 0.7045277230351701, 0.0284633516120191, 0.7045277230351698, 0.2670089253528115, 0.0022264670918959, 0.2586045410103511, 0.7391689918977533, 0.0022264670918959, 0.7391689918977531, 0.2586045410103514, 0.1203643695722496, 0.1996247626773605, 0.6800108677503902, 0.1203643695722496, 0.6800108677503902, 0.1996247626773607, 0.1643344616867156, 0.2088908643844065, 0.6267746739288781, 0.1643344616867156, 0.6267746739288781, 0.2088908643844067, 0.1080471292423062, 0.1080471292423059, 0.7839057415153881, 0.1238874588376767, 0.2533336006018089, 0.6227789405605146, 0.1238874588376767, 0.6227789405605145, 0.2533336006018092, 0.0056487255230679, 0.4971756372384661, 0.4971756372384663, 0.0001600103893843, 0.4637961227465663, 0.5360438668640496, 0.0001600103893843, 0.5360438668640495, 0.4637961227465666, 0.0001085092017437, 0.3837177990505464, 0.6161736917477101, 0.0001085092017437, 0.6161736917477100, 0.3837177990505467 }; static double c_save[] = { 0.3477244587108094, 0.3045510825783810, 0.3477244587108094, 0.4147320642402169, 0.2157006441696168, 0.3695672915901662, 0.3695672915901661, 0.2157006441696168, 0.4147320642402169, 0.5832166020846338, 0.1083014999220039, 0.3084818979933620, 0.3084818979933622, 0.1083014999220039, 0.5832166020846337, 0.6456613180043121, 0.0346959527711364, 0.3196427292245511, 0.3196427292245513, 0.0346959527711364, 0.6456613180043120, 0.3734312712553221, 0.2531374574893557, 0.3734312712553220, 0.0023979705918986, 0.0013460639309494, 0.9962559654771518, 0.9962559654771519, 0.0013460639309495, 0.0023979705918983, 0.6527443981108471, 0.0191707840803216, 0.3280848178088310, 0.3280848178088314, 0.0191707840803215, 0.6527443981108469, 0.4038255264164708, 0.2763615653108097, 0.3198129082727195, 0.3198129082727195, 0.2763615653108096, 0.4038255264164708, 0.8394322302943625, 0.0016411683438176, 0.1589266013618197, 0.1589266013618200, 0.0016411683438172, 0.8394322302943623, 0.7504008293814409, 0.0533231934213235, 0.1962759771972354, 0.1962759771972356, 0.0533231934213233, 0.7504008293814408, 0.4893390535628532, 0.0213218928742935, 0.4893390535628531, 0.6237289790086799, 0.0829288364011384, 0.2933421845901816, 0.2933421845901818, 0.0829288364011382, 0.6237289790086799, 0.9031781503497199, 0.0484109248251402, 0.0484109248251396, 0.8396809025040486, 0.0801595487479759, 0.0801595487479754, 0.8519536569694209, 0.0233190171491816, 0.1247273258813973, 0.1247273258813976, 0.0233190171491812, 0.8519536569694208, 0.5496936600973349, 0.1387130939593856, 0.3115932459432794, 0.3115932459432796, 0.1387130939593855, 0.5496936600973348, 0.4790902659592134, 0.0418194680815729, 0.4790902659592134, 0.4666424153484346, 0.0667151693031307, 0.4666424153484345, 0.8789179195599967, 0.0105406394081226, 0.1105414410318806, 0.1105414410318807, 0.0105406394081223, 0.8789179195599967, 0.6922355531565748, 0.0103472505675079, 0.2974171962759171, 0.2974171962759173, 0.0103472505675077, 0.6922355531565747, 0.6521500596889447, 0.0537818816587766, 0.2940680586522784, 0.2940680586522785, 0.0537818816587765, 0.6521500596889447, 0.8188384243732427, 0.0697603580204465, 0.1114012176063106, 0.1114012176063108, 0.0697603580204462, 0.8188384243732426, 0.5407542433571196, 0.0155023027792509, 0.4437434538636291, 0.4437434538636293, 0.0155023027792509, 0.5407542433571195, 0.5927417808117805, 0.0396225072588169, 0.3676357119294024, 0.3676357119294025, 0.0396225072588169, 0.5927417808117805, 0.9398058801827116, 0.0118107009236642, 0.0483834188936240, 0.0483834188936243, 0.0118107009236640, 0.9398058801827115, 0.5385135616187795, 0.0352878923463722, 0.4261985460348481, 0.4261985460348482, 0.0352878923463721, 0.5385135616187795, 0.5888811994896823, 0.0647150930019751, 0.3464037075083424, 0.3464037075083425, 0.0647150930019750, 0.5888811994896822, 0.9134087843531564, 0.0104225715676421, 0.0761686440792011, 0.0761686440792014, 0.0104225715676417, 0.9134087843531563, 0.4530392764801241, 0.2271049175306689, 0.3198558059892068, 0.3198558059892069, 0.2271049175306689, 0.4530392764801240, 0.8418683619431017, 0.0431548880805706, 0.1149767499763276, 0.1149767499763278, 0.0431548880805703, 0.8418683619431016, 0.7956838642952746, 0.0489749482183904, 0.1553411874863346, 0.1553411874863350, 0.0489749482183902, 0.7956838642952745, 0.8368813116799081, 0.0094545488420267, 0.1536641394780650, 0.1536641394780651, 0.0094545488420265, 0.8368813116799080, 0.9182518733490640, 0.0018943058791127, 0.0798538207718231, 0.0798538207718234, 0.0018943058791124, 0.9182518733490638, 0.9765908510657731, 0.0117045744671137, 0.0117045744671130, 0.7901115654677587, 0.0120283224036929, 0.1978601121285481, 0.1978601121285485, 0.0120283224036929, 0.7901115654677586, 0.6811801518412819, 0.0019044677779362, 0.3169153803807817, 0.3169153803807818, 0.0019044677779362, 0.6811801518412817, 0.8092307990442300, 0.0262052237923565, 0.1645639771634132, 0.1645639771634134, 0.0262052237923562, 0.8092307990442301, 0.5443992424960357, 0.0944709215240264, 0.3611298359799378, 0.3611298359799379, 0.0944709215240263, 0.5443992424960356, 0.4838506735119868, 0.0963233490337837, 0.4198259774542293, 0.4198259774542293, 0.0963233490337836, 0.4838506735119868, 0.7033344581619094, 0.0534903172634274, 0.2431752245746629, 0.2431752245746631, 0.0534903172634272, 0.7033344581619095, 0.7744922982855194, 0.0795244786008373, 0.1459832231136432, 0.1459832231136434, 0.0795244786008370, 0.7744922982855192, 0.9617299619505477, 0.0110307547814719, 0.0272392832679800, 0.0272392832679802, 0.0110307547814718, 0.9617299619505477, 0.7425000580712428, 0.0121862329639788, 0.2453137089647782, 0.2453137089647784, 0.0121862329639787, 0.7425000580712426, 0.4643069725776623, 0.2678465137111689, 0.2678465137111686, 0.8813325626640696, 0.0021132182624776, 0.1165542190734526, 0.1165542190734529, 0.0021132182624773, 0.8813325626640693, 0.9191953264718842, 0.0272189906580712, 0.0535856828700443, 0.0535856828700447, 0.0272189906580710, 0.9191953264718841, 0.8886082228375111, 0.0262562590124721, 0.0851355181500165, 0.0851355181500168, 0.0262562590124719, 0.8886082228375111, 0.5290322767639966, 0.0624750974503704, 0.4084926257856328, 0.4084926257856331, 0.0624750974503702, 0.5290322767639963, 0.4439727450289928, 0.1737762098761934, 0.3822510450948137, 0.3822510450948138, 0.1737762098761933, 0.4439727450289926, 0.9719768417503414, 0.0020491260430697, 0.0259740322065888, 0.0259740322065889, 0.0020491260430694, 0.9719768417503413, 0.5954207695783936, 0.0188900416615420, 0.3856891887600642, 0.3856891887600644, 0.0188900416615418, 0.5954207695783935, 0.7266345676228985, 0.0826189529456984, 0.1907464794314029, 0.1907464794314031, 0.0826189529456983, 0.7266345676228985, 0.9484053916083951, 0.0022799567867531, 0.0493146516048515, 0.0493146516048518, 0.0022799567867529, 0.9484053916083951, 0.5687452023816508, 0.0047722521203025, 0.4264825454980463, 0.4264825454980465, 0.0047722521203025, 0.5687452023816506, 0.7324328909178469, 0.1162023564115880, 0.1513647526705649, 0.1513647526705652, 0.1162023564115878, 0.7324328909178468, 0.6733891753666464, 0.0855252642423670, 0.2410855603909863, 0.2410855603909864, 0.0855252642423668, 0.6733891753666466, 0.7581870004717137, 0.0297767883228066, 0.2120362112054796, 0.2120362112054796, 0.0297767883228065, 0.7581870004717136, 0.8724044348798747, 0.0502535370358714, 0.0773420280842536, 0.0773420280842539, 0.0502535370358711, 0.8724044348798746, 0.5177727692431143, 0.2163002071023544, 0.2659270236545312, 0.2659270236545312, 0.2163002071023542, 0.5177727692431142, 0.5737234550396182, 0.2131382724801908, 0.2131382724801907, 0.9874036799114877, 0.0023182076844771, 0.0102781124040351, 0.0102781124040351, 0.0023182076844769, 0.9874036799114876, 0.4336266613666110, 0.1327466772667781, 0.4336266613666108, 0.6298211317204231, 0.0064301877897617, 0.3637486804898149, 0.3637486804898151, 0.0064301877897617, 0.6298211317204230, 0.4970686798278149, 0.1331111150654715, 0.3698202051067135, 0.3698202051067138, 0.1331111150654714, 0.4970686798278148, 0.6801981711189222, 0.1599009144405389, 0.1599009144405386, 0.9438726730146434, 0.0280636634926785, 0.0280636634926780, 0.5695106590028955, 0.1682524853715628, 0.2622368556255413, 0.2622368556255415, 0.1682524853715629, 0.5695106590028955, 0.7917570821001610, 0.0023776437008402, 0.2058652741989986, 0.2058652741989989, 0.0023776437008400, 0.7917570821001608, 0.4996635238460940, 0.1792751769147348, 0.3210612992391709, 0.3210612992391711, 0.1792751769147348, 0.4996635238460939, 0.7045277230351698, 0.0284633516120191, 0.2670089253528108, 0.2670089253528111, 0.0284633516120191, 0.7045277230351696, 0.7391689918977531, 0.0022264670918958, 0.2586045410103508, 0.2586045410103510, 0.0022264670918958, 0.7391689918977530, 0.6800108677503900, 0.1203643695722495, 0.1996247626773603, 0.1996247626773605, 0.1203643695722493, 0.6800108677503900, 0.6267746739288779, 0.1643344616867157, 0.2088908643844062, 0.2088908643844065, 0.1643344616867154, 0.6267746739288779, 0.7839057415153878, 0.1080471292423063, 0.1080471292423058, 0.6227789405605143, 0.1238874588376768, 0.2533336006018087, 0.2533336006018090, 0.1238874588376765, 0.6227789405605142, 0.4971756372384660, 0.0056487255230678, 0.4971756372384659, 0.5360438668640494, 0.0001600103893843, 0.4637961227465662, 0.4637961227465663, 0.0001600103893842, 0.5360438668640493, 0.6161736917477099, 0.0001085092017437, 0.3837177990505463, 0.3837177990505465, 0.0001085092017435, 0.6161736917477098 }; static double w_save[] = { 0.0043651387537827, 0.0043651387537827, 0.0043651387537827, 0.0037199314122967, 0.0037199314122967, 0.0037199314122967, 0.0037199314122967, 0.0037199314122967, 0.0037199314122967, 0.0030326109445702, 0.0030326109445702, 0.0030326109445702, 0.0030326109445702, 0.0030326109445702, 0.0030326109445702, 0.0018470108648335, 0.0018470108648335, 0.0018470108648335, 0.0018470108648335, 0.0018470108648335, 0.0018470108648335, 0.0039691750453026, 0.0039691750453026, 0.0039691750453026, 0.0000237729080849, 0.0000237729080849, 0.0000237729080849, 0.0000237729080849, 0.0000237729080849, 0.0000237729080849, 0.0015449674526410, 0.0015449674526410, 0.0015449674526410, 0.0015449674526410, 0.0015449674526410, 0.0015449674526410, 0.0050318869826994, 0.0050318869826994, 0.0050318869826994, 0.0050318869826994, 0.0050318869826994, 0.0050318869826994, 0.0003887357668010, 0.0003887357668010, 0.0003887357668010, 0.0003887357668010, 0.0003887357668010, 0.0003887357668010, 0.0022929693353195, 0.0022929693353195, 0.0022929693353195, 0.0022929693353195, 0.0022929693353195, 0.0022929693353195, 0.0018221145367845, 0.0018221145367845, 0.0018221145367845, 0.0032590081957709, 0.0032590081957709, 0.0032590081957709, 0.0032590081957709, 0.0032590081957709, 0.0032590081957709, 0.0012114472500650, 0.0012114472500650, 0.0012114472500650, 0.0019309544896271, 0.0019309544896271, 0.0019309544896271, 0.0012994343934015, 0.0012994343934015, 0.0012994343934015, 0.0012994343934015, 0.0012994343934015, 0.0012994343934015, 0.0040442317991415, 0.0040442317991415, 0.0040442317991415, 0.0040442317991415, 0.0040442317991415, 0.0040442317991415, 0.0026400243756411, 0.0026400243756411, 0.0026400243756411, 0.0032841920864061, 0.0032841920864061, 0.0032841920864061, 0.0008644791070945, 0.0008644791070945, 0.0008644791070945, 0.0008644791070945, 0.0008644791070945, 0.0008644791070945, 0.0012659714364757, 0.0012659714364757, 0.0012659714364757, 0.0012659714364757, 0.0012659714364757, 0.0012659714364757, 0.0027425885952415, 0.0027425885952415, 0.0027425885952415, 0.0027425885952415, 0.0027425885952415, 0.0027425885952415, 0.0021154075536657, 0.0021154075536657, 0.0021154075536657, 0.0021154075536657, 0.0021154075536657, 0.0021154075536657, 0.0016231545272857, 0.0016231545272857, 0.0016231545272857, 0.0016231545272857, 0.0016231545272857, 0.0016231545272857, 0.0025412737334053, 0.0025412737334053, 0.0025412737334053, 0.0025412737334053, 0.0025412737334053, 0.0025412737334053, 0.0006226354721122, 0.0006226354721122, 0.0006226354721122, 0.0006226354721122, 0.0006226354721122, 0.0006226354721122, 0.0026418403799763, 0.0026418403799763, 0.0026418403799763, 0.0026418403799763, 0.0026418403799763, 0.0026418403799763, 0.0032653171027574, 0.0032653171027574, 0.0032653171027574, 0.0032653171027574, 0.0032653171027574, 0.0032653171027574, 0.0007655145859224, 0.0007655145859224, 0.0007655145859224, 0.0007655145859224, 0.0007655145859224, 0.0007655145859224, 0.0051641360944715, 0.0051641360944715, 0.0051641360944715, 0.0051641360944715, 0.0051641360944715, 0.0051641360944715, 0.0018554389812758, 0.0018554389812758, 0.0018554389812758, 0.0018554389812758, 0.0018554389812758, 0.0018554389812758, 0.0022798100113623, 0.0022798100113623, 0.0022798100113623, 0.0022798100113623, 0.0022798100113623, 0.0022798100113623, 0.0010267946171961, 0.0010267946171961, 0.0010267946171961, 0.0010267946171961, 0.0010267946171961, 0.0010267946171961, 0.0003328431211266, 0.0003328431211266, 0.0003328431211266, 0.0003328431211266, 0.0003328431211266, 0.0003328431211266, 0.0003229449584348, 0.0003229449584348, 0.0003229449584348, 0.0012157493114517, 0.0012157493114517, 0.0012157493114517, 0.0012157493114517, 0.0012157493114517, 0.0012157493114517, 0.0005893115728957, 0.0005893115728957, 0.0005893115728957, 0.0005893115728957, 0.0005893115728957, 0.0005893115728957, 0.0017342658044949, 0.0017342658044949, 0.0017342658044949, 0.0017342658044949, 0.0017342658044949, 0.0017342658044949, 0.0040498750757605, 0.0040498750757605, 0.0040498750757605, 0.0040498750757605, 0.0040498750757605, 0.0040498750757605, 0.0042742322977128, 0.0042742322977128, 0.0042742322977128, 0.0042742322977128, 0.0042742322977128, 0.0042742322977128, 0.0028335085475802, 0.0028335085475802, 0.0028335085475802, 0.0028335085475802, 0.0028335085475802, 0.0028335085475802, 0.0027438125458837, 0.0027438125458837, 0.0027438125458837, 0.0027438125458837, 0.0027438125458837, 0.0027438125458837, 0.0004730214563551, 0.0004730214563551, 0.0004730214563551, 0.0004730214563551, 0.0004730214563551, 0.0004730214563551, 0.0013733177441610, 0.0013733177441610, 0.0013733177441610, 0.0013733177441610, 0.0013733177441610, 0.0013733177441610, 0.0054310463039951, 0.0054310463039951, 0.0054310463039951, 0.0004233009914606, 0.0004233009914606, 0.0004233009914606, 0.0004233009914606, 0.0004233009914606, 0.0004233009914606, 0.0010664611871638, 0.0010664611871638, 0.0010664611871638, 0.0010664611871638, 0.0010664611871638, 0.0010664611871638, 0.0013824010733117, 0.0013824010733117, 0.0013824010733117, 0.0013824010733117, 0.0013824010733117, 0.0013824010733117, 0.0036585117930270, 0.0036585117930270, 0.0036585117930270, 0.0036585117930270, 0.0036585117930270, 0.0036585117930270, 0.0052100048548666, 0.0052100048548666, 0.0052100048548666, 0.0052100048548666, 0.0052100048548666, 0.0052100048548666, 0.0002073105605908, 0.0002073105605908, 0.0002073105605908, 0.0002073105605908, 0.0002073105605908, 0.0002073105605908, 0.0019583162868632, 0.0019583162868632, 0.0019583162868632, 0.0019583162868632, 0.0019583162868632, 0.0019583162868632, 0.0032089225299188, 0.0032089225299188, 0.0032089225299188, 0.0032089225299188, 0.0032089225299188, 0.0032089225299188, 0.0003144151546132, 0.0003144151546132, 0.0003144151546132, 0.0003144151546132, 0.0003144151546132, 0.0003144151546132, 0.0010785145551204, 0.0010785145551204, 0.0010785145551204, 0.0010785145551204, 0.0010785145551204, 0.0010785145551204, 0.0036004269766152, 0.0036004269766152, 0.0036004269766152, 0.0036004269766152, 0.0036004269766152, 0.0036004269766152, 0.0036611914178426, 0.0036611914178426, 0.0036611914178426, 0.0036611914178426, 0.0036611914178426, 0.0036611914178426, 0.0021617123138751, 0.0021617123138751, 0.0021617123138751, 0.0021617123138751, 0.0021617123138751, 0.0021617123138751, 0.0018010562763862, 0.0018010562763862, 0.0018010562763862, 0.0018010562763862, 0.0018010562763862, 0.0018010562763862, 0.0054475592942759, 0.0054475592942759, 0.0054475592942759, 0.0054475592942759, 0.0054475592942759, 0.0054475592942759, 0.0051525605444838, 0.0051525605444838, 0.0051525605444838, 0.0001397852015244, 0.0001397852015244, 0.0001397852015244, 0.0001397852015244, 0.0001397852015244, 0.0001397852015244, 0.0049930051499418, 0.0049930051499418, 0.0049930051499418, 0.0011962011851953, 0.0011962011851953, 0.0011962011851953, 0.0011962011851953, 0.0011962011851953, 0.0011962011851953, 0.0049525658235836, 0.0049525658235836, 0.0049525658235836, 0.0049525658235836, 0.0049525658235836, 0.0049525658235836, 0.0042434984918542, 0.0042434984918542, 0.0042434984918542, 0.0008876005610246, 0.0008876005610246, 0.0008876005610246, 0.0050552058738964, 0.0050552058738964, 0.0050552058738964, 0.0050552058738964, 0.0050552058738964, 0.0050552058738964, 0.0006055910618992, 0.0006055910618992, 0.0006055910618992, 0.0006055910618992, 0.0006055910618992, 0.0006055910618992, 0.0053577902109237, 0.0053577902109237, 0.0053577902109237, 0.0053577902109237, 0.0053577902109237, 0.0053577902109237, 0.0023655352245003, 0.0023655352245003, 0.0023655352245003, 0.0023655352245003, 0.0023655352245003, 0.0023655352245003, 0.0006361760556450, 0.0006361760556450, 0.0006361760556450, 0.0006361760556450, 0.0006361760556450, 0.0006361760556450, 0.0041167794317584, 0.0041167794317584, 0.0041167794317584, 0.0041167794317584, 0.0041167794317584, 0.0041167794317584, 0.0047435661701725, 0.0047435661701725, 0.0047435661701725, 0.0047435661701725, 0.0047435661701725, 0.0047435661701725, 0.0031739283489719, 0.0031739283489719, 0.0031739283489719, 0.0046022674251482, 0.0046022674251482, 0.0046022674251482, 0.0046022674251482, 0.0046022674251482, 0.0046022674251482, 0.0012950799113896, 0.0012950799113896, 0.0012950799113896, 0.0002350089224806, 0.0002350089224806, 0.0002350089224806, 0.0002350089224806, 0.0002350089224806, 0.0002350089224806, 0.0002398736789311, 0.0002398736789311, 0.0002398736789311, 0.0002398736789311, 0.0002398736789311, 0.0002398736789311 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule49 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule49() returns the rule of precision 49. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.1747098543071731, 0.7852819906358907, 0.0400081550569363, 0.7852819906358907, 0.1747098543071732, 0.0400081550569361, 0.3869650571638262, 0.6043725256047221, 0.0086624172314518, 0.6043725256047220, 0.3869650571638262, 0.0086624172314517, 0.1260609334354054, 0.8726379574162407, 0.0013011091483540, 0.8726379574162407, 0.1260609334354055, 0.0013011091483536, 0.1783730162296315, 0.6432539675407367, 0.1783730162296319, 0.2839249520005005, 0.4704465426211537, 0.2456285053783458, 0.4704465426211537, 0.2839249520005004, 0.2456285053783457, 0.3302482693344623, 0.4190100944919284, 0.2507416361736092, 0.4190100944919285, 0.3302482693344623, 0.2507416361736091, 0.0728406536060113, 0.8543186927879770, 0.0728406536060117, 0.2560459410681578, 0.7424443214379617, 0.0015097374938804, 0.7424443214379618, 0.2560459410681578, 0.0015097374938802, 0.2603953161344762, 0.6306213036525985, 0.1089833802129252, 0.6306213036525986, 0.2603953161344763, 0.1089833802129251, 0.4289883556394070, 0.4289883556394070, 0.1420232887211859, 0.1707126963793420, 0.7273185867118819, 0.1019687169087761, 0.7273185867118819, 0.1707126963793419, 0.1019687169087760, 0.3746440580951249, 0.6055836533300153, 0.0197722885748599, 0.6055836533300152, 0.3746440580951250, 0.0197722885748598, 0.4351684572939831, 0.5634773574179233, 0.0013541852880936, 0.5634773574179233, 0.4351684572939831, 0.0013541852880936, 0.1390923912291039, 0.7732647562548985, 0.0876428525159975, 0.7732647562548985, 0.1390923912291041, 0.0876428525159973, 0.2801506543012279, 0.6414337667335724, 0.0784155789651995, 0.6414337667335726, 0.2801506543012280, 0.0784155789651994, 0.3463311874275595, 0.5909210399343486, 0.0627477726380918, 0.5909210399343486, 0.3463311874275596, 0.0627477726380916, 0.3811688378455703, 0.3811688378455702, 0.2376623243088594, 0.1142447933587818, 0.8786494761873791, 0.0071057304538392, 0.8786494761873791, 0.1142447933587818, 0.0071057304538389, 0.2601477827144039, 0.6989617430573259, 0.0408904742282701, 0.6989617430573259, 0.2601477827144039, 0.0408904742282700, 0.3385954503697221, 0.6289096666027175, 0.0324948830275603, 0.6289096666027175, 0.3385954503697222, 0.0324948830275602, 0.4405249471606921, 0.5507460085493718, 0.0087290442899361, 0.5507460085493717, 0.4405249471606921, 0.0087290442899361, 0.0857234837407636, 0.9127017575952171, 0.0015747586640192, 0.9127017575952172, 0.0857234837407637, 0.0015747586640189, 0.2007383675971185, 0.5985232648057627, 0.2007383675971187, 0.2859840866397785, 0.5124837078245130, 0.2015322055357083, 0.5124837078245130, 0.2859840866397785, 0.2015322055357083, 0.3022430648527080, 0.6463387716329330, 0.0514181635143590, 0.6463387716329331, 0.3022430648527081, 0.0514181635143589, 0.1145574257288858, 0.8664138254475557, 0.0190287488235586, 0.8664138254475557, 0.1145574257288858, 0.0190287488235582, 0.2122964300195307, 0.7469155107726292, 0.0407880592078402, 0.7469155107726291, 0.2122964300195309, 0.0407880592078400, 0.0462782231758691, 0.9074435536482615, 0.0462782231758695, 0.2971430888632479, 0.4057138222735041, 0.2971430888632479, 0.1465284297099020, 0.8249569583935215, 0.0285146118965767, 0.8249569583935213, 0.1465284297099020, 0.0285146118965764, 0.3740816461088270, 0.4722096952795328, 0.1537086586116402, 0.4722096952795327, 0.3740816461088270, 0.1537086586116402, 0.0817068303997551, 0.8936878492161561, 0.0246053203840890, 0.8936878492161561, 0.0817068303997551, 0.0246053203840887, 0.0108421217690070, 0.9783157564619855, 0.0108421217690075, 0.2941474788808447, 0.6823170191891728, 0.0235355019299825, 0.6823170191891728, 0.2941474788808447, 0.0235355019299824, 0.1750703694826515, 0.6872129092572276, 0.1377167212601208, 0.6872129092572277, 0.1750703694826515, 0.1377167212601206, 0.1028533816631290, 0.7942932366737417, 0.1028533816631293, 0.0476205378057730, 0.9414041521049951, 0.0109753100892320, 0.9414041521049952, 0.0476205378057731, 0.0109753100892315, 0.3175724815133269, 0.5219618612839483, 0.1604656572027248, 0.5219618612839483, 0.3175724815133269, 0.1604656572027247, 0.2881380539950774, 0.5789126782672228, 0.1329492677376997, 0.5789126782672228, 0.2881380539950775, 0.1329492677376996, 0.2679708893032962, 0.7232741594653924, 0.0087549512313114, 0.7232741594653924, 0.2679708893032962, 0.0087549512313113, 0.4841735634166949, 0.4841735634166949, 0.0316528731666102, 0.2393790592030269, 0.7398771788136165, 0.0207437619833566, 0.7398771788136166, 0.2393790592030269, 0.0207437619833564, 0.1918532715697031, 0.7883864387462218, 0.0197602896840751, 0.7883864387462219, 0.1918532715697031, 0.0197602896840748, 0.3873242425341850, 0.5697364716889479, 0.0429392857768670, 0.5697364716889479, 0.3873242425341850, 0.0429392857768670, 0.3535324158284108, 0.5285751660132987, 0.1178924181582904, 0.5285751660132987, 0.3535324158284108, 0.1178924181582903, 0.0521774890148561, 0.9224477815225601, 0.0253747294625839, 0.9224477815225601, 0.0521774890148562, 0.0253747294625835, 0.3237021161513139, 0.5827685017638400, 0.0935293820848460, 0.5827685017638401, 0.3237021161513140, 0.0935293820848459, 0.3720593606748486, 0.6259535358370784, 0.0019871034880730, 0.6259535358370782, 0.3720593606748486, 0.0019871034880730, 0.4136925346071049, 0.4776172690993892, 0.1086901962935059, 0.4776172690993891, 0.4136925346071050, 0.1086901962935058, 0.2508654436414371, 0.5742322222075992, 0.1749023341509636, 0.5742322222075992, 0.2508654436414372, 0.1749023341509635, 0.2368477035387836, 0.6961863830895678, 0.0669659133716486, 0.6961863830895679, 0.2368477035387836, 0.0669659133716483, 0.1099576830426482, 0.8490631831866196, 0.0409791337707323, 0.8490631831866197, 0.1099576830426484, 0.0409791337707320, 0.4297319028951815, 0.5458016820289727, 0.0244664150758457, 0.5458016820289727, 0.4297319028951816, 0.0244664150758457, 0.1437680374333725, 0.7995438742256191, 0.0566880883410085, 0.7995438742256191, 0.1437680374333726, 0.0566880883410082, 0.0774106779986908, 0.9129368386397628, 0.0096524833615466, 0.9129368386397629, 0.0774106779986908, 0.0096524833615462, 0.1557060056653469, 0.8331944267073318, 0.0110995676273212, 0.8331944267073320, 0.1557060056653469, 0.0110995676273209, 0.3128533024496512, 0.6851726257624122, 0.0019740717879365, 0.6851726257624123, 0.3128533024496513, 0.0019740717879363, 0.0260902661381798, 0.9628508665812467, 0.0110588672805734, 0.9628508665812469, 0.0260902661381799, 0.0110588672805730, 0.1656728608179916, 0.8318645947596423, 0.0024625444223663, 0.8318645947596421, 0.1656728608179916, 0.0024625444223660, 0.4932611955660527, 0.4932611955660527, 0.0134776088678945, 0.0742257546763114, 0.8793792323410512, 0.0463950129826375, 0.8793792323410513, 0.0742257546763114, 0.0463950129826371, 0.0288339172370140, 0.9690874828381117, 0.0020785999248743, 0.9690874828381117, 0.0288339172370142, 0.0020785999248739, 0.1868226606723151, 0.7448240425293629, 0.0683532967983221, 0.7448240425293629, 0.1868226606723152, 0.0683532967983218, 0.3270839281856873, 0.6622397675113322, 0.0106763043029805, 0.6622397675113322, 0.3270839281856875, 0.0106763043029803, 0.1038911034338268, 0.8269396131025599, 0.0691692834636134, 0.8269396131025599, 0.1038911034338268, 0.0691692834636131, 0.2155342882429546, 0.6837969023224015, 0.1006688094346437, 0.6837969023224016, 0.2155342882429546, 0.1006688094346435, 0.4057324719755224, 0.4057324719755224, 0.1885350560489550, 0.3431516130273899, 0.4556304494441659, 0.2012179375284442, 0.4556304494441658, 0.3431516130273899, 0.2012179375284441, 0.2224087587233254, 0.6341379927840377, 0.1434532484926369, 0.6341379927840377, 0.2224087587233254, 0.1434532484926367, 0.0534809769143942, 0.9443938625479114, 0.0021251605376946, 0.9443938625479115, 0.0534809769143944, 0.0021251605376941, 0.1304216449251314, 0.7391567101497368, 0.1304216449251318, 0.4387889688450269, 0.5097885287055710, 0.0514225024494020, 0.5097885287055710, 0.4387889688450270, 0.0514225024494020, 0.4614348056302963, 0.4614348056302963, 0.0771303887394074, 0.0275739602431112, 0.9448520795137773, 0.0275739602431116, 0.2318424453754739, 0.5363151092490520, 0.2318424453754740, 0.3517217766277714, 0.3517217766277714, 0.2965564467444570, 0.0022124213099818, 0.9955751573800362, 0.0022124213099822, 0.3919321013755558, 0.5299152656988659, 0.0781526329255782, 0.5299152656988659, 0.3919321013755558, 0.0781526329255781, 0.2110821798970346, 0.7824208956570436, 0.0064969244459219, 0.7824208956570435, 0.2110821798970346, 0.0064969244459216, 0.0117098573109518, 0.9861998362698954, 0.0020903064191530, 0.9861998362698954, 0.0117098573109518, 0.0020903064191526, 0.4987895646915128, 0.4987895646915129, 0.0024208706169742, 0.2063833537599898, 0.7934767827218625, 0.0001398635181475, 0.7934767827218626, 0.2063833537599898, 0.0001398635181473 }; static double b_save[] = { 0.0400081550569363, 0.1747098543071731, 0.7852819906358908, 0.0400081550569363, 0.7852819906358907, 0.1747098543071734, 0.0086624172314518, 0.3869650571638262, 0.6043725256047222, 0.0086624172314518, 0.6043725256047221, 0.3869650571638265, 0.0013011091483539, 0.1260609334354054, 0.8726379574162408, 0.0013011091483539, 0.8726379574162408, 0.1260609334354057, 0.1783730162296318, 0.1783730162296316, 0.6432539675407367, 0.2456285053783459, 0.2839249520005006, 0.4704465426211538, 0.2456285053783459, 0.4704465426211538, 0.2839249520005007, 0.2507416361736093, 0.3302482693344624, 0.4190100944919286, 0.2507416361736093, 0.4190100944919286, 0.3302482693344625, 0.0728406536060116, 0.0728406536060113, 0.8543186927879771, 0.0015097374938804, 0.2560459410681578, 0.7424443214379620, 0.0015097374938804, 0.7424443214379620, 0.2560459410681581, 0.1089833802129252, 0.2603953161344763, 0.6306213036525987, 0.1089833802129252, 0.6306213036525986, 0.2603953161344765, 0.1420232887211860, 0.4289883556394071, 0.4289883556394072, 0.1019687169087761, 0.1707126963793421, 0.7273185867118821, 0.1019687169087761, 0.7273185867118821, 0.1707126963793423, 0.0197722885748599, 0.3746440580951250, 0.6055836533300155, 0.0197722885748599, 0.6055836533300152, 0.3746440580951251, 0.0013541852880937, 0.4351684572939832, 0.5634773574179235, 0.0013541852880937, 0.5634773574179233, 0.4351684572939833, 0.0876428525159975, 0.1390923912291039, 0.7732647562548988, 0.0876428525159975, 0.7732647562548988, 0.1390923912291042, 0.0784155789651995, 0.2801506543012280, 0.6414337667335728, 0.0784155789651995, 0.6414337667335727, 0.2801506543012282, 0.0627477726380917, 0.3463311874275596, 0.5909210399343489, 0.0627477726380917, 0.5909210399343489, 0.3463311874275598, 0.2376623243088594, 0.3811688378455704, 0.3811688378455704, 0.0071057304538391, 0.1142447933587818, 0.8786494761873792, 0.0071057304538391, 0.8786494761873792, 0.1142447933587821, 0.0408904742282701, 0.2601477827144039, 0.6989617430573262, 0.0408904742282701, 0.6989617430573262, 0.2601477827144042, 0.0324948830275604, 0.3385954503697222, 0.6289096666027179, 0.0324948830275604, 0.6289096666027175, 0.3385954503697224, 0.0087290442899362, 0.4405249471606921, 0.5507460085493719, 0.0087290442899362, 0.5507460085493718, 0.4405249471606923, 0.0015747586640192, 0.0857234837407636, 0.9127017575952174, 0.0015747586640192, 0.9127017575952174, 0.0857234837407640, 0.2007383675971187, 0.2007383675971186, 0.5985232648057629, 0.2015322055357084, 0.2859840866397786, 0.5124837078245132, 0.2015322055357084, 0.5124837078245132, 0.2859840866397787, 0.0514181635143590, 0.3022430648527080, 0.6463387716329332, 0.0514181635143590, 0.6463387716329331, 0.3022430648527083, 0.0190287488235584, 0.1145574257288858, 0.8664138254475557, 0.0190287488235584, 0.8664138254475560, 0.1145574257288862, 0.0407880592078402, 0.2122964300195307, 0.7469155107726293, 0.0407880592078402, 0.7469155107726292, 0.2122964300195310, 0.0462782231758694, 0.0462782231758691, 0.9074435536482617, 0.2971430888632481, 0.2971430888632480, 0.4057138222735042, 0.0285146118965766, 0.1465284297099020, 0.8249569583935216, 0.0285146118965766, 0.8249569583935216, 0.1465284297099023, 0.1537086586116403, 0.3740816461088270, 0.4722096952795329, 0.1537086586116403, 0.4722096952795328, 0.3740816461088272, 0.0246053203840889, 0.0817068303997551, 0.8936878492161562, 0.0246053203840889, 0.8936878492161562, 0.0817068303997554, 0.0108421217690073, 0.0108421217690070, 0.9783157564619858, 0.0235355019299826, 0.2941474788808447, 0.6823170191891730, 0.0235355019299826, 0.6823170191891729, 0.2941474788808450, 0.1377167212601208, 0.1750703694826516, 0.6872129092572279, 0.1377167212601208, 0.6872129092572279, 0.1750703694826518, 0.1028533816631293, 0.1028533816631290, 0.7942932366737419, 0.0109753100892318, 0.0476205378057730, 0.9414041521049953, 0.0109753100892318, 0.9414041521049953, 0.0476205378057733, 0.1604656572027248, 0.3175724815133270, 0.5219618612839485, 0.1604656572027248, 0.5219618612839484, 0.3175724815133271, 0.1329492677376998, 0.2881380539950775, 0.5789126782672230, 0.1329492677376998, 0.5789126782672228, 0.2881380539950777, 0.0087549512313114, 0.2679708893032962, 0.7232741594653926, 0.0087549512313114, 0.7232741594653926, 0.2679708893032964, 0.0316528731666103, 0.4841735634166949, 0.4841735634166951, 0.0207437619833566, 0.2393790592030269, 0.7398771788136167, 0.0207437619833566, 0.7398771788136167, 0.2393790592030272, 0.0197602896840750, 0.1918532715697031, 0.7883864387462221, 0.0197602896840750, 0.7883864387462221, 0.1918532715697034, 0.0429392857768671, 0.3873242425341851, 0.5697364716889481, 0.0429392857768671, 0.5697364716889480, 0.3873242425341852, 0.1178924181582904, 0.3535324158284109, 0.5285751660132989, 0.1178924181582904, 0.5285751660132989, 0.3535324158284111, 0.0253747294625837, 0.0521774890148561, 0.9224477815225602, 0.0253747294625837, 0.9224477815225602, 0.0521774890148565, 0.0935293820848460, 0.3237021161513140, 0.5827685017638402, 0.0935293820848460, 0.5827685017638401, 0.3237021161513142, 0.0019871034880731, 0.3720593606748486, 0.6259535358370786, 0.0019871034880731, 0.6259535358370784, 0.3720593606748488, 0.1086901962935059, 0.4136925346071050, 0.4776172690993893, 0.1086901962935059, 0.4776172690993892, 0.4136925346071051, 0.1749023341509636, 0.2508654436414372, 0.5742322222075994, 0.1749023341509636, 0.5742322222075994, 0.2508654436414374, 0.0669659133716485, 0.2368477035387836, 0.6961863830895680, 0.0669659133716485, 0.6961863830895680, 0.2368477035387838, 0.0409791337707322, 0.1099576830426482, 0.8490631831866197, 0.0409791337707322, 0.8490631831866197, 0.1099576830426485, 0.0244664150758458, 0.4297319028951816, 0.5458016820289728, 0.0244664150758458, 0.5458016820289727, 0.4297319028951818, 0.0566880883410084, 0.1437680374333725, 0.7995438742256192, 0.0566880883410084, 0.7995438742256192, 0.1437680374333728, 0.0096524833615464, 0.0774106779986908, 0.9129368386397629, 0.0096524833615464, 0.9129368386397629, 0.0774106779986911, 0.0110995676273212, 0.1557060056653469, 0.8331944267073321, 0.0110995676273212, 0.8331944267073321, 0.1557060056653472, 0.0019740717879365, 0.3128533024496513, 0.6851726257624124, 0.0019740717879365, 0.6851726257624124, 0.3128533024496515, 0.0110588672805733, 0.0260902661381798, 0.9628508665812471, 0.0110588672805733, 0.9628508665812471, 0.0260902661381801, 0.0024625444223662, 0.1656728608179916, 0.8318645947596424, 0.0024625444223662, 0.8318645947596424, 0.1656728608179919, 0.0134776088678946, 0.4932611955660528, 0.4932611955660529, 0.0463950129826374, 0.0742257546763114, 0.8793792323410514, 0.0463950129826374, 0.8793792323410514, 0.0742257546763117, 0.0020785999248742, 0.0288339172370141, 0.9690874828381119, 0.0020785999248742, 0.9690874828381119, 0.0288339172370144, 0.0683532967983220, 0.1868226606723151, 0.7448240425293630, 0.0683532967983220, 0.7448240425293630, 0.1868226606723153, 0.0106763043029805, 0.3270839281856874, 0.6622397675113323, 0.0106763043029805, 0.6622397675113322, 0.3270839281856877, 0.0691692834636133, 0.1038911034338268, 0.8269396131025600, 0.0691692834636133, 0.8269396131025600, 0.1038911034338271, 0.1006688094346437, 0.2155342882429546, 0.6837969023224019, 0.1006688094346437, 0.6837969023224019, 0.2155342882429548, 0.1885350560489551, 0.4057324719755226, 0.4057324719755226, 0.2012179375284443, 0.3431516130273900, 0.4556304494441660, 0.2012179375284443, 0.4556304494441659, 0.3431516130273902, 0.1434532484926369, 0.2224087587233255, 0.6341379927840379, 0.1434532484926369, 0.6341379927840379, 0.2224087587233256, 0.0021251605376943, 0.0534809769143942, 0.9443938625479115, 0.0021251605376943, 0.9443938625479115, 0.0534809769143946, 0.1304216449251317, 0.1304216449251314, 0.7391567101497369, 0.0514225024494020, 0.4387889688450270, 0.5097885287055712, 0.0514225024494020, 0.5097885287055710, 0.4387889688450272, 0.0771303887394075, 0.4614348056302963, 0.4614348056302964, 0.0275739602431115, 0.0275739602431112, 0.9448520795137775, 0.2318424453754741, 0.2318424453754740, 0.5363151092490521, 0.2965564467444571, 0.3517217766277715, 0.3517217766277716, 0.0022124213099821, 0.0022124213099817, 0.9955751573800363, 0.0781526329255783, 0.3919321013755560, 0.5299152656988662, 0.0781526329255783, 0.5299152656988660, 0.3919321013755561, 0.0064969244459218, 0.2110821798970346, 0.7824208956570438, 0.0064969244459218, 0.7824208956570438, 0.2110821798970349, 0.0020903064191529, 0.0117098573109518, 0.9861998362698955, 0.0020903064191529, 0.9861998362698955, 0.0117098573109521, 0.0024208706169743, 0.4987895646915129, 0.4987895646915131, 0.0001398635181475, 0.2063833537599899, 0.7934767827218628, 0.0001398635181475, 0.7934767827218628, 0.2063833537599901 }; static double c_save[] = { 0.7852819906358905, 0.0400081550569363, 0.1747098543071729, 0.1747098543071730, 0.0400081550569361, 0.7852819906358905, 0.6043725256047220, 0.0086624172314517, 0.3869650571638260, 0.3869650571638262, 0.0086624172314517, 0.6043725256047218, 0.8726379574162407, 0.0013011091483539, 0.1260609334354051, 0.1260609334354054, 0.0013011091483537, 0.8726379574162407, 0.6432539675407367, 0.1783730162296317, 0.1783730162296314, 0.4704465426211537, 0.2456285053783457, 0.2839249520005004, 0.2839249520005004, 0.2456285053783457, 0.4704465426211537, 0.4190100944919284, 0.2507416361736092, 0.3302482693344622, 0.3302482693344622, 0.2507416361736092, 0.4190100944919284, 0.8543186927879770, 0.0728406536060116, 0.0728406536060112, 0.7424443214379618, 0.0015097374938805, 0.2560459410681576, 0.2560459410681578, 0.0015097374938803, 0.7424443214379617, 0.6306213036525986, 0.1089833802129253, 0.2603953161344761, 0.2603953161344762, 0.1089833802129251, 0.6306213036525985, 0.4289883556394071, 0.1420232887211860, 0.4289883556394070, 0.7273185867118819, 0.1019687169087761, 0.1707126963793417, 0.1707126963793420, 0.1019687169087760, 0.7273185867118818, 0.6055836533300152, 0.0197722885748597, 0.3746440580951246, 0.3746440580951249, 0.0197722885748598, 0.6055836533300151, 0.5634773574179232, 0.0013541852880936, 0.4351684572939829, 0.4351684572939831, 0.0013541852880936, 0.5634773574179230, 0.7732647562548985, 0.0876428525159975, 0.1390923912291037, 0.1390923912291040, 0.0876428525159972, 0.7732647562548985, 0.6414337667335724, 0.0784155789651995, 0.2801506543012278, 0.2801506543012279, 0.0784155789651994, 0.6414337667335724, 0.5909210399343487, 0.0627477726380918, 0.3463311874275593, 0.3463311874275596, 0.0627477726380915, 0.5909210399343485, 0.3811688378455703, 0.2376623243088594, 0.3811688378455702, 0.8786494761873791, 0.0071057304538391, 0.1142447933587816, 0.1142447933587818, 0.0071057304538390, 0.8786494761873790, 0.6989617430573259, 0.0408904742282701, 0.2601477827144038, 0.2601477827144039, 0.0408904742282700, 0.6989617430573258, 0.6289096666027175, 0.0324948830275603, 0.3385954503697218, 0.3385954503697221, 0.0324948830275603, 0.6289096666027174, 0.5507460085493718, 0.0087290442899360, 0.4405249471606919, 0.4405249471606921, 0.0087290442899360, 0.5507460085493715, 0.9127017575952171, 0.0015747586640193, 0.0857234837407633, 0.0857234837407636, 0.0015747586640189, 0.9127017575952171, 0.5985232648057627, 0.2007383675971187, 0.2007383675971185, 0.5124837078245131, 0.2015322055357084, 0.2859840866397785, 0.2859840866397786, 0.2015322055357083, 0.5124837078245130, 0.6463387716329331, 0.0514181635143590, 0.3022430648527078, 0.3022430648527079, 0.0514181635143588, 0.6463387716329327, 0.8664138254475557, 0.0190287488235584, 0.1145574257288857, 0.1145574257288858, 0.0190287488235582, 0.8664138254475556, 0.7469155107726292, 0.0407880592078401, 0.2122964300195305, 0.2122964300195307, 0.0407880592078399, 0.7469155107726290, 0.9074435536482616, 0.0462782231758695, 0.0462782231758688, 0.4057138222735040, 0.2971430888632479, 0.2971430888632479, 0.8249569583935215, 0.0285146118965766, 0.1465284297099018, 0.1465284297099021, 0.0285146118965763, 0.8249569583935213, 0.4722096952795327, 0.1537086586116401, 0.3740816461088269, 0.3740816461088270, 0.1537086586116402, 0.4722096952795326, 0.8936878492161561, 0.0246053203840889, 0.0817068303997548, 0.0817068303997550, 0.0246053203840887, 0.8936878492161560, 0.9783157564619857, 0.0108421217690075, 0.0108421217690068, 0.6823170191891728, 0.0235355019299825, 0.2941474788808445, 0.2941474788808447, 0.0235355019299824, 0.6823170191891725, 0.6872129092572277, 0.1377167212601209, 0.1750703694826513, 0.1750703694826515, 0.1377167212601206, 0.6872129092572276, 0.7942932366737416, 0.1028533816631292, 0.1028533816631289, 0.9414041521049952, 0.0109753100892319, 0.0476205378057727, 0.0476205378057730, 0.0109753100892317, 0.9414041521049951, 0.5219618612839482, 0.1604656572027248, 0.3175724815133267, 0.3175724815133268, 0.1604656572027247, 0.5219618612839482, 0.5789126782672228, 0.1329492677376997, 0.2881380539950772, 0.2881380539950774, 0.1329492677376997, 0.5789126782672227, 0.7232741594653924, 0.0087549512313114, 0.2679708893032959, 0.2679708893032962, 0.0087549512313112, 0.7232741594653922, 0.4841735634166949, 0.0316528731666103, 0.4841735634166947, 0.7398771788136165, 0.0207437619833566, 0.2393790592030267, 0.2393790592030269, 0.0207437619833564, 0.7398771788136165, 0.7883864387462219, 0.0197602896840751, 0.1918532715697029, 0.1918532715697031, 0.0197602896840748, 0.7883864387462218, 0.5697364716889479, 0.0429392857768670, 0.3873242425341848, 0.3873242425341850, 0.0429392857768670, 0.5697364716889477, 0.5285751660132988, 0.1178924181582904, 0.3535324158284107, 0.3535324158284109, 0.1178924181582903, 0.5285751660132987, 0.9224477815225602, 0.0253747294625838, 0.0521774890148559, 0.0521774890148561, 0.0253747294625836, 0.9224477815225601, 0.5827685017638400, 0.0935293820848460, 0.3237021161513138, 0.3237021161513139, 0.0935293820848458, 0.5827685017638400, 0.6259535358370784, 0.0019871034880730, 0.3720593606748485, 0.3720593606748486, 0.0019871034880731, 0.6259535358370780, 0.4776172690993891, 0.1086901962935058, 0.4136925346071049, 0.4136925346071049, 0.1086901962935058, 0.4776172690993891, 0.5742322222075993, 0.1749023341509636, 0.2508654436414369, 0.2508654436414372, 0.1749023341509633, 0.5742322222075992, 0.6961863830895679, 0.0669659133716486, 0.2368477035387834, 0.2368477035387836, 0.0669659133716484, 0.6961863830895679, 0.8490631831866196, 0.0409791337707322, 0.1099576830426480, 0.1099576830426481, 0.0409791337707320, 0.8490631831866196, 0.5458016820289726, 0.0244664150758456, 0.4297319028951814, 0.4297319028951815, 0.0244664150758457, 0.5458016820289725, 0.7995438742256191, 0.0566880883410084, 0.1437680374333722, 0.1437680374333725, 0.0566880883410082, 0.7995438742256189, 0.9129368386397629, 0.0096524833615464, 0.0774106779986905, 0.0774106779986907, 0.0096524833615462, 0.9129368386397628, 0.8331944267073319, 0.0110995676273213, 0.1557060056653466, 0.1557060056653468, 0.0110995676273210, 0.8331944267073319, 0.6851726257624123, 0.0019740717879365, 0.3128533024496510, 0.3128533024496512, 0.0019740717879363, 0.6851726257624122, 0.9628508665812470, 0.0110588672805735, 0.0260902661381796, 0.0260902661381799, 0.0110588672805730, 0.9628508665812469, 0.8318645947596423, 0.0024625444223662, 0.1656728608179914, 0.1656728608179917, 0.0024625444223660, 0.8318645947596420, 0.4932611955660528, 0.0134776088678945, 0.4932611955660526, 0.8793792323410513, 0.0463950129826374, 0.0742257546763111, 0.0742257546763113, 0.0463950129826372, 0.8793792323410512, 0.9690874828381117, 0.0020785999248742, 0.0288339172370139, 0.0288339172370141, 0.0020785999248739, 0.9690874828381117, 0.7448240425293629, 0.0683532967983221, 0.1868226606723149, 0.1868226606723151, 0.0683532967983219, 0.7448240425293629, 0.6622397675113322, 0.0106763043029804, 0.3270839281856872, 0.3270839281856874, 0.0106763043029804, 0.6622397675113321, 0.8269396131025599, 0.0691692834636133, 0.1038911034338266, 0.1038911034338268, 0.0691692834636132, 0.8269396131025599, 0.6837969023224016, 0.1006688094346438, 0.2155342882429544, 0.2155342882429546, 0.1006688094346436, 0.6837969023224016, 0.4057324719755225, 0.1885350560489550, 0.4057324719755224, 0.4556304494441658, 0.2012179375284441, 0.3431516130273898, 0.3431516130273898, 0.2012179375284442, 0.4556304494441656, 0.6341379927840377, 0.1434532484926368, 0.2224087587233252, 0.2224087587233254, 0.1434532484926366, 0.6341379927840376, 0.9443938625479115, 0.0021251605376944, 0.0534809769143939, 0.0534809769143942, 0.0021251605376941, 0.9443938625479114, 0.7391567101497369, 0.1304216449251317, 0.1304216449251313, 0.5097885287055710, 0.0514225024494020, 0.4387889688450268, 0.4387889688450269, 0.0514225024494019, 0.5097885287055708, 0.4614348056302962, 0.0771303887394074, 0.4614348056302961, 0.9448520795137773, 0.0275739602431116, 0.0275739602431110, 0.5363151092490519, 0.2318424453754740, 0.2318424453754738, 0.3517217766277715, 0.2965564467444571, 0.3517217766277714, 0.9955751573800361, 0.0022124213099820, 0.0022124213099816, 0.5299152656988658, 0.0781526329255781, 0.3919321013755557, 0.3919321013755558, 0.0781526329255781, 0.5299152656988657, 0.7824208956570436, 0.0064969244459218, 0.2110821798970344, 0.2110821798970347, 0.0064969244459216, 0.7824208956570435, 0.9861998362698954, 0.0020903064191529, 0.0117098573109514, 0.0117098573109518, 0.0020903064191528, 0.9861998362698953, 0.4987895646915129, 0.0024208706169743, 0.4987895646915126, 0.7934767827218626, 0.0001398635181476, 0.2063833537599896, 0.2063833537599898, 0.0001398635181474, 0.7934767827218625 }; static double w_save[] = { 0.0015179493827508, 0.0015179493827508, 0.0015179493827508, 0.0015179493827508, 0.0015179493827508, 0.0015179493827508, 0.0009640363088870, 0.0009640363088870, 0.0009640363088870, 0.0009640363088870, 0.0009640363088870, 0.0009640363088870, 0.0002813503665322, 0.0002813503665322, 0.0002813503665322, 0.0002813503665322, 0.0002813503665322, 0.0002813503665322, 0.0032298776744525, 0.0032298776744525, 0.0032298776744525, 0.0046862213374651, 0.0046862213374651, 0.0046862213374651, 0.0046862213374651, 0.0046862213374651, 0.0046862213374651, 0.0045178989983832, 0.0045178989983832, 0.0045178989983832, 0.0045178989983832, 0.0045178989983832, 0.0045178989983832, 0.0015790917860184, 0.0015790917860184, 0.0015790917860184, 0.0004264134812992, 0.0004264134812992, 0.0004264134812992, 0.0004264134812992, 0.0004264134812992, 0.0004264134812992, 0.0032468366301052, 0.0032468366301052, 0.0032468366301052, 0.0032468366301052, 0.0032468366301052, 0.0032468366301052, 0.0039309054788202, 0.0039309054788202, 0.0039309054788202, 0.0027113498937414, 0.0027113498937414, 0.0027113498937414, 0.0027113498937414, 0.0027113498937414, 0.0027113498937414, 0.0016327582269425, 0.0016327582269425, 0.0016327582269425, 0.0016327582269425, 0.0016327582269425, 0.0016327582269425, 0.0004790301761790, 0.0004790301761790, 0.0004790301761790, 0.0004790301761790, 0.0004790301761790, 0.0004790301761790, 0.0026002718294388, 0.0026002718294388, 0.0026002718294388, 0.0026002718294388, 0.0026002718294388, 0.0026002718294388, 0.0030738076620057, 0.0030738076620057, 0.0030738076620057, 0.0030738076620057, 0.0030738076620057, 0.0030738076620057, 0.0029878198502273, 0.0029878198502273, 0.0029878198502273, 0.0029878198502273, 0.0029878198502273, 0.0029878198502273, 0.0049958592249662, 0.0049958592249662, 0.0049958592249662, 0.0006925913496786, 0.0006925913496786, 0.0006925913496786, 0.0006925913496786, 0.0006925913496786, 0.0006925913496786, 0.0022641894958966, 0.0022641894958966, 0.0022641894958966, 0.0022641894958966, 0.0022641894958966, 0.0022641894958966, 0.0021683619372714, 0.0021683619372714, 0.0021683619372714, 0.0021683619372714, 0.0021683619372714, 0.0021683619372714, 0.0012603344824756, 0.0012603344824756, 0.0012603344824756, 0.0012603344824756, 0.0012603344824756, 0.0012603344824756, 0.0003019280054420, 0.0003019280054420, 0.0003019280054420, 0.0003019280054420, 0.0003019280054420, 0.0003019280054420, 0.0040779189028797, 0.0040779189028797, 0.0040779189028797, 0.0045616230274563, 0.0045616230274563, 0.0045616230274563, 0.0045616230274563, 0.0045616230274563, 0.0045616230274563, 0.0026431427639031, 0.0026431427639031, 0.0026431427639031, 0.0026431427639031, 0.0026431427639031, 0.0026431427639031, 0.0011314599292834, 0.0011314599292834, 0.0011314599292834, 0.0011314599292834, 0.0011314599292834, 0.0011314599292834, 0.0021088731883819, 0.0021088731883819, 0.0021088731883819, 0.0021088731883819, 0.0021088731883819, 0.0021088731883819, 0.0011717865482745, 0.0011717865482745, 0.0011717865482745, 0.0050840537579920, 0.0050840537579920, 0.0050840537579920, 0.0015608187011213, 0.0015608187011213, 0.0015608187011213, 0.0015608187011213, 0.0015608187011213, 0.0015608187011213, 0.0046308511124104, 0.0046308511124104, 0.0046308511124104, 0.0046308511124104, 0.0046308511124104, 0.0046308511124104, 0.0011648378245234, 0.0011648378245234, 0.0011648378245234, 0.0011648378245234, 0.0011648378245234, 0.0011648378245234, 0.0002909934397913, 0.0002909934397913, 0.0002909934397913, 0.0019078475871128, 0.0019078475871128, 0.0019078475871128, 0.0019078475871128, 0.0019078475871128, 0.0019078475871128, 0.0036207359330354, 0.0036207359330354, 0.0036207359330354, 0.0036207359330354, 0.0036207359330354, 0.0036207359330354, 0.0024679826387392, 0.0024679826387392, 0.0024679826387392, 0.0006047059166113, 0.0006047059166113, 0.0006047059166113, 0.0006047059166113, 0.0006047059166113, 0.0006047059166113, 0.0044715780288226, 0.0044715780288226, 0.0044715780288226, 0.0044715780288226, 0.0044715780288226, 0.0044715780288226, 0.0043217865559446, 0.0043217865559446, 0.0043217865559446, 0.0043217865559446, 0.0043217865559446, 0.0043217865559446, 0.0011834459680029, 0.0011834459680029, 0.0011834459680029, 0.0011834459680029, 0.0011834459680029, 0.0011834459680029, 0.0024475548918752, 0.0024475548918752, 0.0024475548918752, 0.0017098461192591, 0.0017098461192591, 0.0017098461192591, 0.0017098461192591, 0.0017098461192591, 0.0017098461192591, 0.0015260667775320, 0.0015260667775320, 0.0015260667775320, 0.0015260667775320, 0.0015260667775320, 0.0015260667775320, 0.0027529020694636, 0.0027529020694636, 0.0027529020694636, 0.0027529020694636, 0.0027529020694636, 0.0027529020694636, 0.0043632272367912, 0.0043632272367912, 0.0043632272367912, 0.0043632272367912, 0.0043632272367912, 0.0043632272367912, 0.0009662853562326, 0.0009662853562326, 0.0009662853562326, 0.0009662853562326, 0.0009662853562326, 0.0009662853562326, 0.0037815526680686, 0.0037815526680686, 0.0037815526680686, 0.0037815526680686, 0.0037815526680686, 0.0037815526680686, 0.0006035693127469, 0.0006035693127469, 0.0006035693127469, 0.0006035693127469, 0.0006035693127469, 0.0006035693127469, 0.0042551639608390, 0.0042551639608390, 0.0042551639608390, 0.0042551639608390, 0.0042551639608390, 0.0042551639608390, 0.0048490533224092, 0.0048490533224092, 0.0048490533224092, 0.0048490533224092, 0.0048490533224092, 0.0048490533224092, 0.0030254918153352, 0.0030254918153352, 0.0030254918153352, 0.0030254918153352, 0.0030254918153352, 0.0030254918153352, 0.0018302659109492, 0.0018302659109492, 0.0018302659109492, 0.0018302659109492, 0.0018302659109492, 0.0018302659109492, 0.0023112911452725, 0.0023112911452725, 0.0023112911452725, 0.0023112911452725, 0.0023112911452725, 0.0023112911452725, 0.0022976181282931, 0.0022976181282931, 0.0022976181282931, 0.0022976181282931, 0.0022976181282931, 0.0022976181282931, 0.0007737426014553, 0.0007737426014553, 0.0007737426014553, 0.0007737426014553, 0.0007737426014553, 0.0007737426014553, 0.0011091107906633, 0.0011091107906633, 0.0011091107906633, 0.0011091107906633, 0.0011091107906633, 0.0011091107906633, 0.0005917280070787, 0.0005917280070787, 0.0005917280070787, 0.0005917280070787, 0.0005917280070787, 0.0005917280070787, 0.0004663290783398, 0.0004663290783398, 0.0004663290783398, 0.0004663290783398, 0.0004663290783398, 0.0004663290783398, 0.0005060545142142, 0.0005060545142142, 0.0005060545142142, 0.0005060545142142, 0.0005060545142142, 0.0005060545142142, 0.0016834711767858, 0.0016834711767858, 0.0016834711767858, 0.0015462052435902, 0.0015462052435902, 0.0015462052435902, 0.0015462052435902, 0.0015462052435902, 0.0015462052435902, 0.0002238167725271, 0.0002238167725271, 0.0002238167725271, 0.0002238167725271, 0.0002238167725271, 0.0002238167725271, 0.0029561851838940, 0.0029561851838940, 0.0029561851838940, 0.0029561851838940, 0.0029561851838940, 0.0029561851838940, 0.0014290418491702, 0.0014290418491702, 0.0014290418491702, 0.0014290418491702, 0.0014290418491702, 0.0014290418491702, 0.0021458693484176, 0.0021458693484176, 0.0021458693484176, 0.0021458693484176, 0.0021458693484176, 0.0021458693484176, 0.0035847674194570, 0.0035847674194570, 0.0035847674194570, 0.0035847674194570, 0.0035847674194570, 0.0035847674194570, 0.0053654225406028, 0.0053654225406028, 0.0053654225406028, 0.0054527357782272, 0.0054527357782272, 0.0054527357782272, 0.0054527357782272, 0.0054527357782272, 0.0054527357782272, 0.0043816657756572, 0.0043816657756572, 0.0043816657756572, 0.0043816657756572, 0.0043816657756572, 0.0043816657756572, 0.0003071745359645, 0.0003071745359645, 0.0003071745359645, 0.0003071745359645, 0.0003071745359645, 0.0003071745359645, 0.0034992680317617, 0.0034992680317617, 0.0034992680317617, 0.0032381770164589, 0.0032381770164589, 0.0032381770164589, 0.0032381770164589, 0.0032381770164589, 0.0032381770164589, 0.0039600197915087, 0.0039600197915087, 0.0039600197915087, 0.0008319508889038, 0.0008319508889038, 0.0008319508889038, 0.0053644090708949, 0.0053644090708949, 0.0053644090708949, 0.0061267736075541, 0.0061267736075541, 0.0061267736075541, 0.0000646114299085, 0.0000646114299085, 0.0000646114299085, 0.0041053828589275, 0.0041053828589275, 0.0041053828589275, 0.0041053828589275, 0.0041053828589275, 0.0041053828589275, 0.0010683587323421, 0.0010683587323421, 0.0010683587323421, 0.0010683587323421, 0.0010683587323421, 0.0010683587323421, 0.0001423198916150, 0.0001423198916150, 0.0001423198916150, 0.0001423198916150, 0.0001423198916150, 0.0001423198916150, 0.0007885551654533, 0.0007885551654533, 0.0007885551654533, 0.0001605584705522, 0.0001605584705522, 0.0001605584705522, 0.0001605584705522, 0.0001605584705522, 0.0001605584705522 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } void rule50 ( int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: rule50() returns the rule of precision 50. Licensing: This code is distributed under the MIT license. Modified: 11 June 2023 Author: John Burkardt Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: int n: the number of points. Output: double a[n], b[n], c[n]: the barycentric coordinates of quadrature points. double w[n]: the quadrature weights. */ { static double a_save[] = { 0.2563558633847908, 0.4872882732304182, 0.2563558633847909, 0.4433230868583420, 0.5557544570355875, 0.0009224561060704, 0.5557544570355875, 0.4433230868583420, 0.0009224561060704, 0.0259368938757904, 0.9516251148618965, 0.0224379912623133, 0.9516251148618965, 0.0259368938757906, 0.0224379912623128, 0.2401441052632695, 0.5370651664429976, 0.2227907282937328, 0.5370651664429976, 0.2401441052632695, 0.2227907282937327, 0.1345526180266427, 0.8423271680031109, 0.0231202139702464, 0.8423271680031110, 0.1345526180266427, 0.0231202139702461, 0.0450355724673314, 0.9541076477376595, 0.0008567797950091, 0.9541076477376597, 0.0450355724673315, 0.0008567797950087, 0.4087145665677719, 0.5864767957713561, 0.0048086376608720, 0.5864767957713561, 0.4087145665677719, 0.0048086376608719, 0.1714634577399832, 0.8050435299005781, 0.0234930123594386, 0.8050435299005783, 0.1714634577399832, 0.0234930123594384, 0.0016305781421460, 0.9967388437157076, 0.0016305781421465, 0.2101059247050331, 0.6964974281656032, 0.0933966471293636, 0.6964974281656033, 0.2101059247050331, 0.0933966471293634, 0.1392968201185850, 0.8189065432302668, 0.0417966366511482, 0.8189065432302668, 0.1392968201185851, 0.0417966366511480, 0.0703820539127592, 0.8802606341943795, 0.0493573118928615, 0.8802606341943796, 0.0703820539127593, 0.0493573118928611, 0.4903268692484512, 0.4903268692484513, 0.0193462615030975, 0.3726064881564940, 0.4745794048313449, 0.1528141070121611, 0.4745794048313449, 0.3726064881564940, 0.1528141070121610, 0.1479157172776441, 0.7869688527917342, 0.0651154299306216, 0.7869688527917343, 0.1479157172776442, 0.0651154299306213, 0.2140246435816437, 0.7625132132423355, 0.0234621431760209, 0.7625132132423355, 0.2140246435816437, 0.0234621431760206, 0.3302674030581440, 0.6177003187074449, 0.0520322782344111, 0.6177003187074449, 0.3302674030581441, 0.0520322782344110, 0.3699848635444039, 0.6285206173500637, 0.0014945191055323, 0.6285206173500638, 0.3699848635444039, 0.0014945191055322, 0.0675115690433361, 0.9204446840218713, 0.0120437469347927, 0.9204446840218714, 0.0675115690433362, 0.0120437469347923, 0.4370988411800967, 0.5062163732764420, 0.0566847855434612, 0.5062163732764420, 0.4370988411800968, 0.0566847855434611, 0.4225871685075206, 0.4225871685075206, 0.1548256629849586, 0.4145122211577853, 0.4706276367973991, 0.1148601420448156, 0.4706276367973991, 0.4145122211577853, 0.1148601420448156, 0.3623805122689274, 0.6063546515443636, 0.0312648361867088, 0.6063546515443636, 0.3623805122689275, 0.0312648361867088, 0.3122512855112035, 0.5855020743432547, 0.1022466401455417, 0.5855020743432547, 0.3122512855112035, 0.1022466401455416, 0.4805756764340300, 0.4805756764340301, 0.0388486471319398, 0.3926893217036879, 0.5589613764232392, 0.0483493018730729, 0.5589613764232392, 0.3926893217036880, 0.0483493018730728, 0.0260638541622880, 0.9639565689080692, 0.0099795769296427, 0.9639565689080694, 0.0260638541622881, 0.0099795769296424, 0.3983909958449554, 0.5176960633851162, 0.0839129407699283, 0.5176960633851162, 0.3983909958449555, 0.0839129407699283, 0.0458803913209149, 0.9473914769778008, 0.0067281317012844, 0.9473914769778008, 0.0458803913209150, 0.0067281317012840, 0.2510983078651668, 0.5715936673024646, 0.1773080248323685, 0.5715936673024647, 0.2510983078651668, 0.1773080248323682, 0.1831369339346112, 0.7741789783303032, 0.0426840877350856, 0.7741789783303031, 0.1831369339346113, 0.0426840877350855, 0.3540463032783623, 0.5715609286815995, 0.0743927680400381, 0.5715609286815995, 0.3540463032783623, 0.0743927680400380, 0.2992109871101671, 0.4572200650927965, 0.2435689477970363, 0.4572200650927966, 0.2992109871101671, 0.2435689477970362, 0.2908392329854116, 0.6327691972686006, 0.0763915697459878, 0.6327691972686005, 0.2908392329854118, 0.0763915697459877, 0.1861461318533070, 0.6896292784778069, 0.1242245896688862, 0.6896292784778069, 0.1861461318533070, 0.1242245896688860, 0.1336271749712246, 0.8565938166582099, 0.0097790083705656, 0.8565938166582099, 0.1336271749712248, 0.0097790083705652, 0.0689763351482116, 0.9030804628036242, 0.0279432020481643, 0.9030804628036242, 0.0689763351482117, 0.0279432020481639, 0.2614910192698080, 0.7137007122193398, 0.0248082685108522, 0.7137007122193398, 0.2614910192698081, 0.0248082685108520, 0.0439794560591168, 0.9348945435129993, 0.0211260004278840, 0.9348945435129993, 0.0439794560591169, 0.0211260004278836, 0.2469572317073108, 0.6848928980386439, 0.0681498702540453, 0.6848928980386439, 0.2469572317073108, 0.0681498702540452, 0.1916073029798411, 0.7395973901197243, 0.0687953069004347, 0.7395973901197241, 0.1916073029798412, 0.0687953069004345, 0.3173959823085313, 0.5262505405714473, 0.1563534771200214, 0.5262505405714473, 0.3173959823085312, 0.1563534771200213, 0.3938393062998427, 0.5903719225644825, 0.0157887711356747, 0.5903719225644825, 0.3938393062998428, 0.0157887711356747, 0.3181446682127857, 0.6584089238199839, 0.0234464079672303, 0.6584089238199841, 0.3181446682127858, 0.0234464079672302, 0.2803644875579968, 0.5837056989706170, 0.1359298134713862, 0.5837056989706170, 0.2803644875579968, 0.1359298134713861, 0.2299757300841567, 0.7253286729028012, 0.0446955970130422, 0.7253286729028012, 0.2299757300841567, 0.0446955970130419, 0.3494881250371351, 0.4044556242737054, 0.2460562506891595, 0.4044556242737053, 0.3494881250371351, 0.2460562506891595, 0.0964083579062225, 0.8928281693560606, 0.0107634727377169, 0.8928281693560607, 0.0964083579062225, 0.0107634727377166, 0.1003380079665996, 0.8728642223074309, 0.0267977697259696, 0.8728642223074310, 0.1003380079665996, 0.0267977697259692, 0.2894378430839789, 0.5106605002764818, 0.1999016566395393, 0.5106605002764818, 0.2894378430839789, 0.1999016566395392, 0.4595867718244119, 0.4595867718244119, 0.0808264563511762, 0.1786164539550919, 0.8117237531973031, 0.0096597928476050, 0.8117237531973032, 0.1786164539550919, 0.0096597928476048, 0.1133332341350742, 0.7733335317298511, 0.1133332341350746, 0.2861539226312519, 0.6702297883431256, 0.0436162890256225, 0.6702297883431256, 0.2861539226312521, 0.0436162890256222, 0.2293288959608979, 0.7610373084893327, 0.0096337955497694, 0.7610373084893327, 0.2293288959608979, 0.0096337955497692, 0.3542128961664716, 0.5293301016817759, 0.1164570021517525, 0.5293301016817759, 0.3542128961664716, 0.1164570021517524, 0.3449444915449854, 0.6455786313059102, 0.0094768771491044, 0.6455786313059101, 0.3449444915449854, 0.0094768771491043, 0.4316732308235539, 0.5403601528804488, 0.0279666162959972, 0.5403601528804488, 0.4316732308235539, 0.0279666162959972, 0.2207972237518396, 0.6319369320513635, 0.1472658441967969, 0.6319369320513635, 0.2207972237518397, 0.1472658441967967, 0.0109390130646629, 0.9781219738706738, 0.0109390130646634, 0.1531728350976843, 0.8449565979912814, 0.0018705669110343, 0.8449565979912815, 0.1531728350976843, 0.0018705669110340, 0.0786463619513997, 0.8427072760972003, 0.0786463619514000, 0.0091986167658109, 0.9887342430556623, 0.0020671401785269, 0.9887342430556624, 0.0091986167658110, 0.0020671401785264, 0.0235452342574103, 0.9744483849005658, 0.0020063808420239, 0.9744483849005658, 0.0235452342574104, 0.0020063808420235, 0.3457284797184662, 0.4576795280020015, 0.1965919922795323, 0.4576795280020015, 0.3457284797184662, 0.1965919922795323, 0.2501693088121573, 0.6423518250856121, 0.1074788661022307, 0.6423518250856121, 0.2501693088121574, 0.1074788661022305, 0.2555498626016329, 0.7425883280451013, 0.0018618093532657, 0.7425883280451014, 0.2555498626016329, 0.0018618093532655, 0.1032934352626250, 0.8464992721458153, 0.0502072925915598, 0.8464992721458153, 0.1032934352626251, 0.0502072925915595, 0.1702588823641313, 0.6594822352717371, 0.1702588823641316, 0.1134827791905402, 0.8074184540525852, 0.0790987667568747, 0.8074184540525853, 0.1134827791905403, 0.0790987667568744, 0.2020015191395728, 0.7961696111804121, 0.0018288696800152, 0.7961696111804121, 0.2020015191395729, 0.0018288696800149, 0.1996334593368171, 0.6007330813263655, 0.1996334593368173, 0.1554072933416661, 0.7470942459833944, 0.0974984606749396, 0.7470942459833944, 0.1554072933416663, 0.0974984606749393, 0.2837331258499088, 0.7059958314121547, 0.0102710427379366, 0.7059958314121546, 0.2837331258499087, 0.0102710427379364, 0.4006689325488300, 0.4006689325488300, 0.1986621349023399, 0.1406138740563841, 0.7187722518872315, 0.1406138740563844, 0.1101376107119611, 0.8879173225135152, 0.0019450667745238, 0.8879173225135152, 0.1101376107119612, 0.0019450667745234, 0.3511903644454155, 0.3511903644454155, 0.2976192711091689, 0.0422503625151380, 0.9154992749697237, 0.0422503625151384, 0.3116269863962924, 0.6863602986744455, 0.0020127149292622, 0.6863602986744455, 0.3116269863962924, 0.0020127149292620, 0.4986838983120579, 0.4986838983120579, 0.0026322033758840, 0.4560656275499566, 0.5340545482354229, 0.0098798242146205, 0.5340545482354229, 0.4560656275499566, 0.0098798242146206, 0.2964798675129709, 0.4070402649740581, 0.2964798675129710, 0.0740590746798509, 0.9237147727731391, 0.0022261525470102, 0.9237147727731391, 0.0740590746798510, 0.0022261525470098 }; static double b_save[] = { 0.2563558633847910, 0.2563558633847909, 0.4872882732304183, 0.0009224561060705, 0.4433230868583421, 0.5557544570355878, 0.0009224561060705, 0.5557544570355876, 0.4433230868583423, 0.0224379912623131, 0.0259368938757903, 0.9516251148618966, 0.0224379912623131, 0.9516251148618966, 0.0259368938757907, 0.2227907282937329, 0.2401441052632695, 0.5370651664429978, 0.2227907282937329, 0.5370651664429978, 0.2401441052632697, 0.0231202139702463, 0.1345526180266427, 0.8423271680031111, 0.0231202139702463, 0.8423271680031111, 0.1345526180266430, 0.0008567797950090, 0.0450355724673314, 0.9541076477376597, 0.0008567797950090, 0.9541076477376597, 0.0450355724673318, 0.0048086376608720, 0.4087145665677719, 0.5864767957713563, 0.0048086376608720, 0.5864767957713561, 0.4087145665677722, 0.0234930123594386, 0.1714634577399832, 0.8050435299005784, 0.0234930123594386, 0.8050435299005784, 0.1714634577399836, 0.0016305781421463, 0.0016305781421460, 0.9967388437157076, 0.0933966471293636, 0.2101059247050332, 0.6964974281656034, 0.0933966471293636, 0.6964974281656034, 0.2101059247050334, 0.0417966366511482, 0.1392968201185851, 0.8189065432302669, 0.0417966366511482, 0.8189065432302669, 0.1392968201185854, 0.0493573118928613, 0.0703820539127592, 0.8802606341943795, 0.0493573118928613, 0.8802606341943796, 0.0703820539127595, 0.0193462615030976, 0.4903268692484513, 0.4903268692484514, 0.1528141070121611, 0.3726064881564941, 0.4745794048313450, 0.1528141070121611, 0.4745794048313449, 0.3726064881564942, 0.0651154299306216, 0.1479157172776441, 0.7869688527917345, 0.0651154299306216, 0.7869688527917345, 0.1479157172776444, 0.0234621431760208, 0.2140246435816437, 0.7625132132423356, 0.0234621431760208, 0.7625132132423356, 0.2140246435816440, 0.0520322782344111, 0.3302674030581440, 0.6177003187074451, 0.0520322782344111, 0.6177003187074450, 0.3302674030581442, 0.0014945191055323, 0.3699848635444040, 0.6285206173500639, 0.0014945191055323, 0.6285206173500638, 0.3699848635444041, 0.0120437469347925, 0.0675115690433361, 0.9204446840218714, 0.0120437469347925, 0.9204446840218714, 0.0675115690433364, 0.0566847855434612, 0.4370988411800968, 0.5062163732764422, 0.0566847855434612, 0.5062163732764421, 0.4370988411800970, 0.1548256629849588, 0.4225871685075207, 0.4225871685075208, 0.1148601420448157, 0.4145122211577854, 0.4706276367973992, 0.1148601420448157, 0.4706276367973991, 0.4145122211577855, 0.0312648361867089, 0.3623805122689275, 0.6063546515443639, 0.0312648361867089, 0.6063546515443637, 0.3623805122689277, 0.1022466401455418, 0.3122512855112036, 0.5855020743432550, 0.1022466401455418, 0.5855020743432549, 0.3122512855112037, 0.0388486471319399, 0.4805756764340301, 0.4805756764340303, 0.0483493018730729, 0.3926893217036880, 0.5589613764232394, 0.0483493018730729, 0.5589613764232393, 0.3926893217036881, 0.0099795769296427, 0.0260638541622880, 0.9639565689080695, 0.0099795769296427, 0.9639565689080695, 0.0260638541622883, 0.0839129407699284, 0.3983909958449555, 0.5176960633851163, 0.0839129407699284, 0.5176960633851163, 0.3983909958449556, 0.0067281317012843, 0.0458803913209149, 0.9473914769778009, 0.0067281317012843, 0.9473914769778009, 0.0458803913209153, 0.1773080248323685, 0.2510983078651669, 0.5715936673024649, 0.1773080248323685, 0.5715936673024649, 0.2510983078651671, 0.0426840877350856, 0.1831369339346113, 0.7741789783303034, 0.0426840877350856, 0.7741789783303031, 0.1831369339346115, 0.0743927680400382, 0.3540463032783624, 0.5715609286815998, 0.0743927680400382, 0.5715609286815997, 0.3540463032783625, 0.2435689477970363, 0.2992109871101672, 0.4572200650927967, 0.2435689477970363, 0.4572200650927967, 0.2992109871101673, 0.0763915697459878, 0.2908392329854117, 0.6327691972686007, 0.0763915697459878, 0.6327691972686006, 0.2908392329854119, 0.1242245896688861, 0.1861461318533070, 0.6896292784778070, 0.1242245896688861, 0.6896292784778070, 0.1861461318533073, 0.0097790083705655, 0.1336271749712246, 0.8565938166582100, 0.0097790083705655, 0.8565938166582099, 0.1336271749712250, 0.0279432020481641, 0.0689763351482116, 0.9030804628036244, 0.0279432020481641, 0.9030804628036244, 0.0689763351482120, 0.0248082685108521, 0.2614910192698081, 0.7137007122193399, 0.0248082685108521, 0.7137007122193399, 0.2614910192698083, 0.0211260004278839, 0.0439794560591167, 0.9348945435129995, 0.0211260004278839, 0.9348945435129995, 0.0439794560591171, 0.0681498702540453, 0.2469572317073107, 0.6848928980386442, 0.0681498702540453, 0.6848928980386441, 0.2469572317073110, 0.0687953069004347, 0.1916073029798411, 0.7395973901197244, 0.0687953069004347, 0.7395973901197243, 0.1916073029798415, 0.1563534771200215, 0.3173959823085313, 0.5262505405714475, 0.1563534771200215, 0.5262505405714474, 0.3173959823085315, 0.0157887711356748, 0.3938393062998428, 0.5903719225644827, 0.0157887711356748, 0.5903719225644826, 0.3938393062998430, 0.0234464079672303, 0.3181446682127858, 0.6584089238199842, 0.0234464079672303, 0.6584089238199841, 0.3181446682127860, 0.1359298134713862, 0.2803644875579969, 0.5837056989706172, 0.1359298134713862, 0.5837056989706172, 0.2803644875579970, 0.0446955970130421, 0.2299757300841567, 0.7253286729028013, 0.0446955970130421, 0.7253286729028013, 0.2299757300841569, 0.2460562506891596, 0.3494881250371351, 0.4044556242737055, 0.2460562506891596, 0.4044556242737055, 0.3494881250371352, 0.0107634727377169, 0.0964083579062225, 0.8928281693560609, 0.0107634727377169, 0.8928281693560609, 0.0964083579062228, 0.0267977697259695, 0.1003380079665996, 0.8728642223074310, 0.0267977697259695, 0.8728642223074310, 0.1003380079665999, 0.1999016566395393, 0.2894378430839790, 0.5106605002764819, 0.1999016566395393, 0.5106605002764819, 0.2894378430839791, 0.0808264563511763, 0.4595867718244119, 0.4595867718244120, 0.0096597928476050, 0.1786164539550919, 0.8117237531973033, 0.0096597928476050, 0.8117237531973033, 0.1786164539550922, 0.1133332341350745, 0.1133332341350743, 0.7733335317298513, 0.0436162890256224, 0.2861539226312520, 0.6702297883431257, 0.0436162890256224, 0.6702297883431256, 0.2861539226312523, 0.0096337955497694, 0.2293288959608979, 0.7610373084893329, 0.0096337955497694, 0.7610373084893329, 0.2293288959608982, 0.1164570021517526, 0.3542128961664717, 0.5293301016817761, 0.1164570021517526, 0.5293301016817760, 0.3542128961664718, 0.0094768771491045, 0.3449444915449854, 0.6455786313059104, 0.0094768771491045, 0.6455786313059102, 0.3449444915449857, 0.0279666162959973, 0.4316732308235540, 0.5403601528804491, 0.0279666162959973, 0.5403601528804489, 0.4316732308235541, 0.1472658441967969, 0.2207972237518397, 0.6319369320513636, 0.1472658441967969, 0.6319369320513636, 0.2207972237518398, 0.0109390130646632, 0.0109390130646629, 0.9781219738706741, 0.0018705669110342, 0.1531728350976843, 0.8449565979912816, 0.0018705669110342, 0.8449565979912816, 0.1531728350976846, 0.0786463619514000, 0.0786463619513997, 0.8427072760972005, 0.0020671401785267, 0.0091986167658108, 0.9887342430556626, 0.0020671401785267, 0.9887342430556626, 0.0091986167658113, 0.0020063808420238, 0.0235452342574103, 0.9744483849005661, 0.0020063808420238, 0.9744483849005661, 0.0235452342574107, 0.1965919922795324, 0.3457284797184662, 0.4576795280020016, 0.1965919922795324, 0.4576795280020016, 0.3457284797184664, 0.1074788661022307, 0.2501693088121573, 0.6423518250856122, 0.1074788661022307, 0.6423518250856121, 0.2501693088121575, 0.0018618093532657, 0.2555498626016329, 0.7425883280451016, 0.0018618093532657, 0.7425883280451016, 0.2555498626016332, 0.0502072925915597, 0.1032934352626250, 0.8464992721458154, 0.0502072925915597, 0.8464992721458154, 0.1032934352626254, 0.1702588823641316, 0.1702588823641314, 0.6594822352717372, 0.0790987667568746, 0.1134827791905402, 0.8074184540525853, 0.0790987667568746, 0.8074184540525853, 0.1134827791905405, 0.0018288696800151, 0.2020015191395728, 0.7961696111804121, 0.0018288696800151, 0.7961696111804121, 0.2020015191395731, 0.1996334593368174, 0.1996334593368172, 0.6007330813263656, 0.0974984606749395, 0.1554072933416662, 0.7470942459833945, 0.0974984606749395, 0.7470942459833945, 0.1554072933416664, 0.0102710427379366, 0.2837331258499088, 0.7059958314121549, 0.0102710427379366, 0.7059958314121548, 0.2837331258499091, 0.1986621349023400, 0.4006689325488301, 0.4006689325488302, 0.1406138740563844, 0.1406138740563842, 0.7187722518872316, 0.0019450667745237, 0.1101376107119611, 0.8879173225135153, 0.0019450667745237, 0.8879173225135153, 0.1101376107119614, 0.2976192711091690, 0.3511903644454157, 0.3511903644454157, 0.0422503625151383, 0.0422503625151379, 0.9154992749697239, 0.0020127149292621, 0.3116269863962924, 0.6863602986744456, 0.0020127149292621, 0.6863602986744456, 0.3116269863962926, 0.0026322033758842, 0.4986838983120580, 0.4986838983120582, 0.0098798242146206, 0.4560656275499567, 0.5340545482354231, 0.0098798242146206, 0.5340545482354230, 0.4560656275499568, 0.2964798675129711, 0.2964798675129710, 0.4070402649740582, 0.0022261525470101, 0.0740590746798509, 0.9237147727731391, 0.0022261525470101, 0.9237147727731391, 0.0740590746798513 }; static double c_save[] = { 0.4872882732304181, 0.2563558633847908, 0.2563558633847908, 0.5557544570355876, 0.0009224561060704, 0.4433230868583419, 0.4433230868583421, 0.0009224561060704, 0.5557544570355873, 0.9516251148618966, 0.0224379912623132, 0.0259368938757901, 0.0259368938757904, 0.0224379912623128, 0.9516251148618964, 0.5370651664429976, 0.2227907282937328, 0.2401441052632693, 0.2401441052632695, 0.2227907282937326, 0.5370651664429976, 0.8423271680031109, 0.0231202139702464, 0.1345526180266424, 0.1345526180266427, 0.0231202139702461, 0.8423271680031108, 0.9541076477376595, 0.0008567797950090, 0.0450355724673311, 0.0450355724673314, 0.0008567797950089, 0.9541076477376594, 0.5864767957713561, 0.0048086376608720, 0.4087145665677717, 0.4087145665677718, 0.0048086376608719, 0.5864767957713560, 0.8050435299005783, 0.0234930123594386, 0.1714634577399831, 0.1714634577399832, 0.0234930123594385, 0.8050435299005780, 0.9967388437157076, 0.0016305781421463, 0.0016305781421458, 0.6964974281656032, 0.0933966471293636, 0.2101059247050330, 0.2101059247050331, 0.0933966471293634, 0.6964974281656032, 0.8189065432302668, 0.0417966366511481, 0.1392968201185849, 0.1392968201185850, 0.0417966366511480, 0.8189065432302667, 0.8802606341943795, 0.0493573118928613, 0.0703820539127590, 0.0703820539127591, 0.0493573118928611, 0.8802606341943794, 0.4903268692484512, 0.0193462615030974, 0.4903268692484511, 0.4745794048313449, 0.1528141070121611, 0.3726064881564939, 0.3726064881564940, 0.1528141070121611, 0.4745794048313448, 0.7869688527917343, 0.0651154299306217, 0.1479157172776440, 0.1479157172776441, 0.0651154299306214, 0.7869688527917342, 0.7625132132423355, 0.0234621431760209, 0.2140246435816435, 0.2140246435816437, 0.0234621431760207, 0.7625132132423355, 0.6177003187074449, 0.0520322782344111, 0.3302674030581437, 0.3302674030581440, 0.0520322782344109, 0.6177003187074448, 0.6285206173500638, 0.0014945191055323, 0.3699848635444037, 0.3699848635444039, 0.0014945191055323, 0.6285206173500637, 0.9204446840218714, 0.0120437469347926, 0.0675115690433359, 0.0675115690433361, 0.0120437469347924, 0.9204446840218713, 0.5062163732764421, 0.0566847855434612, 0.4370988411800966, 0.4370988411800968, 0.0566847855434610, 0.5062163732764419, 0.4225871685075206, 0.1548256629849586, 0.4225871685075206, 0.4706276367973990, 0.1148601420448155, 0.4145122211577852, 0.4145122211577852, 0.1148601420448156, 0.4706276367973988, 0.6063546515443636, 0.0312648361867088, 0.3623805122689273, 0.3623805122689275, 0.0312648361867088, 0.6063546515443634, 0.5855020743432547, 0.1022466401455417, 0.3122512855112033, 0.3122512855112035, 0.1022466401455416, 0.5855020743432546, 0.4805756764340300, 0.0388486471319398, 0.4805756764340299, 0.5589613764232392, 0.0483493018730728, 0.3926893217036876, 0.3926893217036879, 0.0483493018730727, 0.5589613764232391, 0.9639565689080692, 0.0099795769296427, 0.0260638541622878, 0.0260638541622880, 0.0099795769296424, 0.9639565689080694, 0.5176960633851162, 0.0839129407699283, 0.3983909958449553, 0.3983909958449554, 0.0839129407699283, 0.5176960633851161, 0.9473914769778008, 0.0067281317012843, 0.0458803913209147, 0.0458803913209149, 0.0067281317012841, 0.9473914769778008, 0.5715936673024646, 0.1773080248323685, 0.2510983078651667, 0.2510983078651668, 0.1773080248323683, 0.5715936673024647, 0.7741789783303032, 0.0426840877350855, 0.1831369339346111, 0.1831369339346113, 0.0426840877350855, 0.7741789783303030, 0.5715609286815996, 0.0743927680400381, 0.3540463032783622, 0.3540463032783624, 0.0743927680400380, 0.5715609286815995, 0.4572200650927966, 0.2435689477970363, 0.2992109871101671, 0.2992109871101670, 0.2435689477970362, 0.4572200650927965, 0.6327691972686005, 0.0763915697459877, 0.2908392329854115, 0.2908392329854117, 0.0763915697459877, 0.6327691972686005, 0.6896292784778069, 0.1242245896688861, 0.1861461318533069, 0.1861461318533070, 0.1242245896688859, 0.6896292784778068, 0.8565938166582099, 0.0097790083705655, 0.1336271749712244, 0.1336271749712246, 0.0097790083705653, 0.8565938166582098, 0.9030804628036243, 0.0279432020481642, 0.0689763351482113, 0.0689763351482117, 0.0279432020481639, 0.9030804628036241, 0.7137007122193398, 0.0248082685108521, 0.2614910192698079, 0.2614910192698081, 0.0248082685108519, 0.7137007122193397, 0.9348945435129993, 0.0211260004278840, 0.0439794560591165, 0.0439794560591169, 0.0211260004278836, 0.9348945435129994, 0.6848928980386439, 0.0681498702540453, 0.2469572317073105, 0.2469572317073108, 0.0681498702540452, 0.6848928980386438, 0.7395973901197243, 0.0687953069004346, 0.1916073029798410, 0.1916073029798412, 0.0687953069004344, 0.7395973901197241, 0.5262505405714473, 0.1563534771200214, 0.3173959823085311, 0.3173959823085313, 0.1563534771200213, 0.5262505405714472, 0.5903719225644826, 0.0157887711356747, 0.3938393062998425, 0.3938393062998428, 0.0157887711356747, 0.5903719225644823, 0.6584089238199839, 0.0234464079672303, 0.3181446682127855, 0.3181446682127856, 0.0234464079672302, 0.6584089238199838, 0.5837056989706170, 0.1359298134713862, 0.2803644875579966, 0.2803644875579968, 0.1359298134713861, 0.5837056989706170, 0.7253286729028012, 0.0446955970130421, 0.2299757300841565, 0.2299757300841567, 0.0446955970130419, 0.7253286729028011, 0.4044556242737053, 0.2460562506891595, 0.3494881250371350, 0.3494881250371350, 0.2460562506891594, 0.4044556242737053, 0.8928281693560607, 0.0107634727377169, 0.0964083579062222, 0.0964083579062225, 0.0107634727377166, 0.8928281693560606, 0.8728642223074309, 0.0267977697259695, 0.1003380079665994, 0.1003380079665995, 0.0267977697259694, 0.8728642223074308, 0.5106605002764818, 0.1999016566395392, 0.2894378430839788, 0.2894378430839789, 0.1999016566395392, 0.5106605002764817, 0.4595867718244118, 0.0808264563511762, 0.4595867718244117, 0.8117237531973032, 0.0096597928476050, 0.1786164539550917, 0.1786164539550919, 0.0096597928476049, 0.8117237531973031, 0.7733335317298512, 0.1133332341350746, 0.1133332341350741, 0.6702297883431256, 0.0436162890256224, 0.2861539226312518, 0.2861539226312519, 0.0436162890256223, 0.6702297883431255, 0.7610373084893327, 0.0096337955497694, 0.2293288959608977, 0.2293288959608979, 0.0096337955497692, 0.7610373084893326, 0.5293301016817759, 0.1164570021517525, 0.3542128961664713, 0.3542128961664716, 0.1164570021517525, 0.5293301016817757, 0.6455786313059102, 0.0094768771491044, 0.3449444915449851, 0.3449444915449855, 0.0094768771491044, 0.6455786313059100, 0.5403601528804489, 0.0279666162959972, 0.4316732308235537, 0.4316732308235539, 0.0279666162959972, 0.5403601528804487, 0.6319369320513635, 0.1472658441967969, 0.2207972237518395, 0.2207972237518396, 0.1472658441967968, 0.6319369320513635, 0.9781219738706739, 0.0109390130646633, 0.0109390130646625, 0.8449565979912814, 0.0018705669110343, 0.1531728350976840, 0.1531728350976842, 0.0018705669110340, 0.8449565979912813, 0.8427072760972004, 0.0786463619514000, 0.0786463619513995, 0.9887342430556624, 0.0020671401785269, 0.0091986167658106, 0.0091986167658109, 0.0020671401785265, 0.9887342430556624, 0.9744483849005660, 0.0020063808420239, 0.0235452342574101, 0.0235452342574104, 0.0020063808420235, 0.9744483849005658, 0.4576795280020015, 0.1965919922795324, 0.3457284797184662, 0.3457284797184662, 0.1965919922795322, 0.4576795280020013, 0.6423518250856121, 0.1074788661022306, 0.2501693088121572, 0.2501693088121573, 0.1074788661022305, 0.6423518250856119, 0.7425883280451014, 0.0018618093532657, 0.2555498626016327, 0.2555498626016329, 0.0018618093532655, 0.7425883280451013, 0.8464992721458153, 0.0502072925915597, 0.1032934352626248, 0.1032934352626250, 0.0502072925915594, 0.8464992721458152, 0.6594822352717371, 0.1702588823641315, 0.1702588823641312, 0.8074184540525853, 0.0790987667568746, 0.1134827791905400, 0.1134827791905401, 0.0790987667568744, 0.8074184540525852, 0.7961696111804120, 0.0018288696800151, 0.2020015191395726, 0.2020015191395728, 0.0018288696800149, 0.7961696111804120, 0.6007330813263656, 0.1996334593368173, 0.1996334593368171, 0.7470942459833944, 0.0974984606749394, 0.1554072933416659, 0.1554072933416661, 0.0974984606749393, 0.7470942459833942, 0.7059958314121547, 0.0102710427379365, 0.2837331258499085, 0.2837331258499088, 0.0102710427379364, 0.7059958314121545, 0.4006689325488301, 0.1986621349023399, 0.4006689325488300, 0.7187722518872315, 0.1406138740563843, 0.1406138740563839, 0.8879173225135152, 0.0019450667745237, 0.1101376107119609, 0.1101376107119611, 0.0019450667745236, 0.8879173225135152, 0.3511903644454155, 0.2976192711091688, 0.3511903644454155, 0.9154992749697237, 0.0422503625151383, 0.0422503625151377, 0.6863602986744455, 0.0020127149292621, 0.3116269863962923, 0.3116269863962924, 0.0020127149292620, 0.6863602986744454, 0.4986838983120579, 0.0026322033758840, 0.4986838983120577, 0.5340545482354228, 0.0098798242146205, 0.4560656275499564, 0.4560656275499565, 0.0098798242146204, 0.5340545482354226, 0.4070402649740580, 0.2964798675129709, 0.2964798675129709, 0.9237147727731390, 0.0022261525470100, 0.0740590746798507, 0.0740590746798509, 0.0022261525470099, 0.9237147727731388 }; static double w_save[] = { 0.0033286951747132, 0.0033286951747132, 0.0033286951747132, 0.0003473281594925, 0.0003473281594925, 0.0003473281594925, 0.0003473281594925, 0.0003473281594925, 0.0003473281594925, 0.0003000501019099, 0.0003000501019099, 0.0003000501019099, 0.0003000501019099, 0.0003000501019099, 0.0003000501019099, 0.0027304020592298, 0.0027304020592298, 0.0027304020592298, 0.0027304020592298, 0.0027304020592298, 0.0027304020592298, 0.0011329714517846, 0.0011329714517846, 0.0011329714517846, 0.0011329714517846, 0.0011329714517846, 0.0011329714517846, 0.0001365218409967, 0.0001365218409967, 0.0001365218409967, 0.0001365218409967, 0.0001365218409967, 0.0001365218409967, 0.0007693760667843, 0.0007693760667843, 0.0007693760667843, 0.0007693760667843, 0.0007693760667843, 0.0007693760667843, 0.0012969731946121, 0.0012969731946121, 0.0012969731946121, 0.0012969731946121, 0.0012969731946121, 0.0012969731946121, 0.0000365932242464, 0.0000365932242464, 0.0000365932242464, 0.0028058551621104, 0.0028058551621104, 0.0028058551621104, 0.0028058551621104, 0.0028058551621104, 0.0028058551621104, 0.0017088242229934, 0.0017088242229934, 0.0017088242229934, 0.0017088242229934, 0.0017088242229934, 0.0017088242229934, 0.0014835269432187, 0.0014835269432187, 0.0014835269432187, 0.0014835269432187, 0.0014835269432187, 0.0014835269432187, 0.0016513963572791, 0.0016513963572791, 0.0016513963572791, 0.0042541944332406, 0.0042541944332406, 0.0042541944332406, 0.0042541944332406, 0.0042541944332406, 0.0042541944332406, 0.0021977995867184, 0.0021977995867184, 0.0021977995867184, 0.0021977995867184, 0.0021977995867184, 0.0021977995867184, 0.0015485819478916, 0.0015485819478916, 0.0015485819478916, 0.0015485819478916, 0.0015485819478916, 0.0015485819478916, 0.0026032805301536, 0.0026032805301536, 0.0026032805301536, 0.0026032805301536, 0.0026032805301536, 0.0026032805301536, 0.0004661702641033, 0.0004661702641033, 0.0004661702641033, 0.0004661702641033, 0.0004661702641033, 0.0004661702641033, 0.0006575771563735, 0.0006575771563735, 0.0006575771563735, 0.0006575771563735, 0.0006575771563735, 0.0006575771563735, 0.0027864654094994, 0.0027864654094994, 0.0027864654094994, 0.0027864654094994, 0.0027864654094994, 0.0027864654094994, 0.0042590966781915, 0.0042590966781915, 0.0042590966781915, 0.0041296569531417, 0.0041296569531417, 0.0041296569531417, 0.0041296569531417, 0.0041296569531417, 0.0041296569531417, 0.0021542829173275, 0.0021542829173275, 0.0021542829173275, 0.0021542829173275, 0.0021542829173275, 0.0021542829173275, 0.0034759522016711, 0.0034759522016711, 0.0034759522016711, 0.0034759522016711, 0.0034759522016711, 0.0034759522016711, 0.0024242799574099, 0.0024242799574099, 0.0024242799574099, 0.0027066142543971, 0.0027066142543971, 0.0027066142543971, 0.0027066142543971, 0.0027066142543971, 0.0027066142543971, 0.0003857792869821, 0.0003857792869821, 0.0003857792869821, 0.0003857792869821, 0.0003857792869821, 0.0003857792869821, 0.0034396664292256, 0.0034396664292256, 0.0034396664292256, 0.0034396664292256, 0.0034396664292256, 0.0034396664292256, 0.0004380269370904, 0.0004380269370904, 0.0004380269370904, 0.0004380269370904, 0.0004380269370904, 0.0004380269370904, 0.0044060145278103, 0.0044060145278103, 0.0044060145278103, 0.0044060145278103, 0.0044060145278103, 0.0044060145278103, 0.0020175008084554, 0.0020175008084554, 0.0020175008084554, 0.0020175008084554, 0.0020175008084554, 0.0020175008084554, 0.0032382786045497, 0.0032382786045497, 0.0032382786045497, 0.0032382786045497, 0.0032382786045497, 0.0032382786045497, 0.0046662107991940, 0.0046662107991940, 0.0046662107991940, 0.0046662107991940, 0.0046662107991940, 0.0046662107991940, 0.0031592258177549, 0.0031592258177549, 0.0031592258177549, 0.0031592258177549, 0.0031592258177549, 0.0031592258177549, 0.0034735845184462, 0.0034735845184462, 0.0034735845184462, 0.0034735845184462, 0.0034735845184462, 0.0034735845184462, 0.0008953928804098, 0.0008953928804098, 0.0008953928804098, 0.0008953928804098, 0.0008953928804098, 0.0008953928804098, 0.0010804784836254, 0.0010804784836254, 0.0010804784836254, 0.0010804784836254, 0.0010804784836254, 0.0010804784836254, 0.0018129744491099, 0.0018129744491099, 0.0018129744491099, 0.0018129744491099, 0.0018129744491099, 0.0018129744491099, 0.0007651571304863, 0.0007651571304863, 0.0007651571304863, 0.0007651571304863, 0.0007651571304863, 0.0007651571304863, 0.0028576817042790, 0.0028576817042790, 0.0028576817042790, 0.0028576817042790, 0.0028576817042790, 0.0028576817042790, 0.0026558120905517, 0.0026558120905517, 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0.0011989487838384, 0.0011989487838384, 0.0005855934410211, 0.0005855934410211, 0.0005855934410211, 0.0005855934410211, 0.0005855934410211, 0.0005855934410211, 0.0007493220541052, 0.0007493220541052, 0.0007493220541052, 0.0014007748847512, 0.0014007748847512, 0.0014007748847512, 0.0014007748847512, 0.0014007748847512, 0.0014007748847512, 0.0057736389035923, 0.0057736389035923, 0.0057736389035923, 0.0003705055488142, 0.0003705055488142, 0.0003705055488142, 0.0003705055488142, 0.0003705055488142, 0.0003705055488142 }; r8vec_copy ( n, a_save, a ); r8vec_copy ( n, b_save, b ); r8vec_copy ( n, c_save, c ); r8vec_copy ( n, w_save, w ); return; } /******************************************************************************/ void triangle_symq_rule ( int p, int n, double a[], double b[], double c[], double w[] ) /******************************************************************************/ /* Purpose: triangle_symq_rule() returns the requested quadrature rule. Licensing: This code is distributed under the GNU GPL license. Modified: 11 June 2023 Author: Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas. This version by John Burkardt. Reference: Hong Xiao, Zydrunas Gimbutas, A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions, Computers and Mathematics with Applications, Volume 59, 2010, pages 663-676. Input: integer p: the precision, 0 <= p <= 50. integer n: the order of the rule. Output: real a(n), b(n), c(n): the barycentric coordinates of quadrature points. real w(n): the weights of quadrature points. */ { /* Copy the arrays defining the compressed rule. */ if ( p == 0 ) { rule00 ( n, a, b, c, w ); } else if ( p == 1 ) { rule01 ( n, a, b, c, w ); } else if ( p == 2 ) { rule02 ( n, a, b, c, w ); } else if ( p == 3 ) { rule03 ( n, a, b, c, w ); } else if ( p == 4 ) { rule04 ( n, a, b, c, w ); } else if ( p == 5 ) { rule05 ( n, a, b, c, w ); } else if ( p == 6 ) { rule06 ( n, a, b, c, w ); } else if ( p == 7 ) { rule07 ( n, a, b, c, w ); } else if ( p == 8 ) { rule08 ( n, a, b, c, w ); } else if ( p == 9 ) { rule09 ( n, a, b, c, w ); } else if ( p == 10 ) { rule10 ( n, a, b, c, w ); } else if ( p == 11 ) { rule11 ( n, a, b, c, w ); } else if ( p == 12 ) { rule12 ( n, a, b, c, w ); } else if ( p == 13 ) { rule13 ( n, a, b, c, w ); } else if ( p == 14 ) { rule14 ( n, a, b, c, w ); } else if ( p == 15 ) { rule15 ( n, a, b, c, w ); } else if ( p == 16 ) { rule16 ( n, a, b, c, w ); } else if ( p == 17 ) { rule17 ( n, a, b, c, w ); } else if ( p == 18 ) { rule18 ( n, a, b, c, w ); } else if ( p == 19 ) { rule19 ( n, a, b, c, w ); } else if ( p == 20 ) { rule20 ( n, a, b, c, w ); } else if ( p == 21 ) { rule21 ( n, a, b, c, w ); } else if ( p == 22 ) { rule22 ( n, a, b, c, w ); } else if ( p == 23 ) { rule23 ( n, a, b, c, w ); } else if ( p == 24 ) { rule24 ( n, a, b, c, w ); } else if ( p == 25 ) { rule25 ( n, a, b, c, w ); } else if ( p == 26 ) { rule26 ( n, a, b, c, w ); } else if ( p == 27 ) { rule27 ( n, a, b, c, w ); } else if ( p == 28 ) { rule28 ( n, a, b, c, w ); } else if ( p == 29 ) { rule29 ( n, a, b, c, w ); } else if ( p == 30 ) { rule30 ( n, a, b, c, w ); } else if ( p == 31 ) { rule31 ( n, a, b, c, w ); } else if ( p == 32 ) { rule32 ( n, a, b, c, w ); } else if ( p == 33 ) { rule33 ( n, a, b, c, w ); } else if ( p == 34 ) { rule34 ( n, a, b, c, w ); } else if ( p == 35 ) { rule35 ( n, a, b, c, w ); } else if ( p == 36 ) { rule36 ( n, a, b, c, w ); } else if ( p == 37 ) { rule37 ( n, a, b, c, w ); } else if ( p == 38 ) { rule38 ( n, a, b, c, w ); } else if ( p == 39 ) { rule39 ( n, a, b, c, w ); } else if ( p == 40 ) { rule40 ( n, a, b, c, w ); } else if ( p == 41 ) { rule41 ( n, a, b, c, w ); } else if ( p == 42 ) { rule42 ( n, a, b, c, w ); } else if ( p == 43 ) { rule43 ( n, a, b, c, w ); } else if ( p == 44 ) { rule44 ( n, a, b, c, w ); } else if ( p == 45 ) { rule45 ( n, a, b, c, w ); } else if ( p == 46 ) { rule46 ( n, a, b, c, w ); } else if ( p == 47 ) { rule47 ( n, a, b, c, w ); } else if ( p == 48 ) { rule48 ( n, a, b, c, w ); } else if ( p == 49 ) { rule49 ( n, a, b, c, w ); } else if ( p == 50 ) { rule50 ( n, a, b, c, w ); } else { fprintf ( stderr, "\n" ); fprintf ( stderr, "QUAEQUAD0 - Fatal error!\n" ); fprintf ( stderr, " Illegal input value of p.\n" ); fprintf ( stderr, " 1 <= p <= 50 required.\n" ); exit ( 1 ); } return; } /******************************************************************************/ double triangle_unit_area ( ) /******************************************************************************/ /* Purpose: triangle_unit_area() returns the area of a unit triangle. Licensing: This code is distributed under the GNU GPL license. Modified: 24 May 2023 Author: John Burkardt. Output: double triangle_unit_area: the area of the triangle. */ { double value; value = 0.5; return value; } /******************************************************************************/ double triangle_unit_monomial_integral ( int expon[] ) /******************************************************************************/ /* Purpose: triangle_unit_monomial_integral() integrates a monomial over the unit triangle. Discussion: This routine evaluates a monomial of the form product ( 1 <= dim <= dim_num ) x(dim)^expon(dim) where the exponents are nonnegative integers. Note that if the combination 0^0 is encountered, it should be treated as 1. Integral ( over unit triangle ) x^m y^n dx dy = m! * n! / ( m + n + 2 )! Licensing: This code is distributed under the MIT license. Modified: 04 July 2007 Author: John Burkardt Input: int EXPON[3], the exponents. Output: double triangle_unit_monomial_integral, the value of the integral. */ { int i; int k; double value; /* The first computation ends with VALUE = 1.0; */ value = 1.0; k = 0; for ( i = 1; i <= expon[0]; i++ ) { k = k + 1; /* value = value * ( double ) ( i ) / ( double ) ( k );*/ } for ( i = 1; i <= expon[1]; i++ ) { k = k + 1; value = value * ( double ) ( i ) / ( double ) ( k ); } k = k + 1; value = value / ( double ) ( k ); k = k + 1; value = value / ( double ) ( k ); return value; }