public static void cube_unit_nd(int setting, Func <int, int, double[], double> func, ref double[] qa,
ref double[] qb, int n, int k)
//****************************************************************************80
//
// Purpose:
//
// CUBE_UNIT_ND approximates an integral inside the unit cube in ND.
//
// Integration region:
//
// -1 <= X(1:N) <= 1
//
// Discussion:
//
// A K**N point product formula is used.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 13 April 2008
//
// Author:
//
// John Burkardt
//
// Reference:
//
// James Lyness, BJJ McHugh,
// Integration Over Multidimensional Hypercubes,
// A Progressive Procedure,
// The Computer Journal,
// Volume 6, 1963, pages 264-270.
//
// Arthur Stroud,
// Approximate Calculation of Multiple Integrals,
// Prentice Hall, 1971,
// ISBN: 0130438936,
// LC: QA311.S85.
//
// Parameters:
//
// Input, Func < int, double[], double> func, the name of the
// user supplied function to be integrated.
//
// Output, double QA[K], QB[K], two sets of estimates for
// the integral. The QB entries are obtained from the
// QA entries by Richardson extrapolation, and QB(K) is
// the best estimate for the integral.
//
// Input, int N, the dimension of the cube.
//
// Input, int K, the highest order of integration, and the order
// of Richardson extrapolation. K can be no greater than 10.
//
{
double[] g = new double[10 * 10];
int i;
const int kmax = 10;
g[0 + 0 * 10] = 1.0E+00;
g[1 + 0 * 10] = -0.3333333333333E+00;
g[1 + 1 * 10] = 0.1333333333333E+01;
g[2 + 0 * 10] = 0.4166666666667E-01;
g[2 + 1 * 10] = -0.1066666666667E+01;
g[2 + 2 * 10] = 0.2025000000000E+01;
g[3 + 0 * 10] = -0.2777777777778E-02;
g[3 + 1 * 10] = 0.3555555555556E+00;
g[3 + 2 * 10] = -0.2603571428571E+01;
g[3 + 3 * 10] = 0.3250793650794E+01;
g[4 + 0 * 10] = 0.1157407407407E-03;
g[4 + 1 * 10] = -0.6772486772487E-01;
g[4 + 2 * 10] = 0.1464508928571E+01;
g[4 + 3 * 10] = -0.5779188712522E+01;
g[4 + 4 * 10] = 0.5382288910935E+01;
g[5 + 0 * 10] = -0.3306878306878E-05;
g[5 + 1 * 10] = 0.8465608465608E-02;
g[5 + 2 * 10] = -0.4881696428571E+00;
g[5 + 3 * 10] = 0.4623350970018E+01;
g[5 + 4 * 10] = -0.1223247479758E+02;
g[5 + 5 * 10] = 0.9088831168831E+01;
g[6 + 0 * 10] = 0.6889329805996E-07;
g[6 + 1 * 10] = -0.7524985302763E-03;
g[6 + 2 * 10] = 0.1098381696429E+00;
g[6 + 3 * 10] = -0.2241624712736E+01;
g[6 + 4 * 10] = 0.1274216124748E+02;
g[6 + 5 * 10] = -0.2516907092907E+02;
g[6 + 6 * 10] = 0.1555944865432E+02;
g[7 + 0 * 10] = -0.1093544413650E-08;
g[7 + 1 * 10] = 0.5016656868509E-04;
g[7 + 2 * 10] = -0.1797351866883E-01;
g[7 + 3 * 10] = 0.7472082375786E+00;
g[7 + 4 * 10] = -0.8168052081717E+01;
g[7 + 5 * 10] = 0.3236023405166E+02;
g[7 + 6 * 10] = -0.5082753227079E+02;
g[7 + 7 * 10] = 0.2690606541646E+02;
g[8 + 0 * 10] = 0.1366930517063E-10;
g[8 + 1 * 10] = -0.2606055516108E-05;
g[8 + 2 * 10] = 0.2246689833604E-02;
g[8 + 3 * 10] = -0.1839281815578E+00;
g[8 + 4 * 10] = 0.3646451822195E+01;
g[8 + 5 * 10] = -0.2588818724133E+02;
g[8 + 6 * 10] = 0.7782965878964E+02;
g[8 + 7 * 10] = -0.1012934227443E+03;
g[8 + 8 * 10] = 0.4688718347156E+02;
g[9 + 0 * 10] = -0.1380737896023E-12;
g[9 + 1 * 10] = 0.1085856465045E-06;
g[9 + 2 * 10] = -0.2222000934334E-03;
g[9 + 3 * 10] = 0.3503393934435E-01;
g[9 + 4 * 10] = -0.1215483940732E+01;
g[9 + 5 * 10] = 0.1456210532325E+02;
g[9 + 6 * 10] = -0.7477751530769E+02;
g[9 + 7 * 10] = 0.1800771959898E+03;
g[9 + 8 * 10] = -0.1998874663788E+03;
g[9 + 9 * 10] = 0.8220635246624E+02;
if (kmax < k)
{
Console.WriteLine("");
Console.WriteLine("CUBE_UNIT_ND - Fatal error!");
Console.WriteLine(" K must be no greater than KMAX = " + kmax + "");
Console.WriteLine(" but the input K is " + k + "");
return;
}
for (i = 0; i < k; i++)
{
qa[i] = QuadratureRule.qmdpt(setting, func, n, i + 1);
}
qb[0] = qa[0];
for (i = 1; i < k; i++)
{
qb[i] = 0.0;
int j;
for (j = 0; j <= i; j++)
{
qb[i] += g[i + j * 10] * qa[j];
}
}
}