# include # include # include # include using namespace std; # include "hypersphere_integrals.hpp" int main ( ); void test01 ( ); void test02 ( ); //****************************************************************************80 int main ( ) //****************************************************************************80 // // Purpose: // // MAIN is the main program for HYPERSPHERE_INTEGRALS_TEST. // // Discussion: // // HYPERSPHERE_INTEGRALS_TEST tests the HYPERSPHERE_INTEGRALS library. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 07 January 2014 // // Author: // // John Burkardt // { timestamp ( ); cout << "\n"; cout << "HYPERSPHERE_INTEGRALS_TEST\n"; cout << " C++ version\n"; cout << " Test the HYPERSPHERE_INTEGRALS library.\n"; test01 ( ); test02 ( ); // // Terminate. // cout << "\n"; cout << "HYPERSPHERE_INTEGRALS_TEST\n"; cout << " Normal end of execution.\n"; cout << "\n"; timestamp ( ); return 0; } //****************************************************************************80 void test01 ( ) //****************************************************************************80 // // Purpose: // // TEST01 uses HYPERSPHERE01_SAMPLE to estimate monomial integrands in 3D. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 07 January 2014 // // Author: // // John Burkardt // { int *e; double error; double exact; int i; int m = 3; int n = 4192; double result; int seed; int test; int test_num = 20; double *value; double *x; cout << "\n"; cout << "TEST01\n"; cout << " Estimate monomial integrals using Monte Carlo\n"; cout << " over the surface of the unit hypersphere in 3D.\n"; // // Get sample points. // seed = 123456789; x = hypersphere01_sample ( m, n, seed ); cout << "\n"; cout << " Number of sample points used is " << n << "\n"; // // Randomly choose X,Y,Z exponents between 0 and 8. // cout << "\n"; cout << " If any exponent is odd, the integral is zero.\n"; cout << " We will restrict this test to randomly chosen even exponents.\n"; cout << "\n"; cout << " Ex Ey Ez MC-Estimate Exact Error\n"; cout << "\n"; for ( test = 1; test <= test_num; test++ ) { e = i4vec_uniform_ab_new ( m, 0, 4, seed ); for ( i = 0; i < m; i++ ) { e[i] = e[i] * 2; } value = monomial_value ( m, n, e, x ); result = hypersphere01_area ( m ) * r8vec_sum ( n, value ) / ( double ) ( n ); exact = hypersphere01_monomial_integral ( m, e ); error = fabs ( result - exact ); cout << " " << setw(2) << e[0] << " " << setw(2) << e[1] << " " << setw(2) << e[2] << " " << setw(14) << result << " " << setw(14) << exact << " " << setw(10) << error << "\n"; delete [] e; delete [] value; } delete ( x ); return; } //****************************************************************************80 void test02 ( ) //****************************************************************************80 // // Purpose: // // TEST02 uses HYPERSPHERE01_SAMPLE to estimate monomial integrands in 6D. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 07 January 2014 // // Author: // // John Burkardt // { int *e; double error; double exact; int i; int m = 6; int n = 4192; double result; int seed; int test; int test_num = 20; double *value; double *x; cout << "\n"; cout << "TEST02\n"; cout << " Estimate monomial integrals using Monte Carlo\n"; cout << " over the surface of the unit hypersphere in 6D.\n"; // // Get sample points. // seed = 123456789; x = hypersphere01_sample ( m, n, seed ); cout << "\n"; cout << " Number of sample points used is " << n << "\n"; // // Randomly choose X,Y,Z exponents between 0 and 6. // cout << "\n"; cout << " If any exponent is odd, the integral is zero.\n"; cout << " We will restrict this test to randomly chosen even exponents.\n"; cout << "\n"; cout << " E1 E2 E3 E4 E5 E6 MC-Estimate Exact Error\n"; cout << "\n"; for ( test = 1; test <= test_num; test++ ) { e = i4vec_uniform_ab_new ( m, 0, 3, seed ); for ( i = 0; i < m; i++ ) { e[i] = e[i] * 2; } value = monomial_value ( m, n, e, x ); result = hypersphere01_area ( m ) * r8vec_sum ( n, value ) / ( double ) ( n ); exact = hypersphere01_monomial_integral ( m, e ); error = fabs ( result - exact ); cout << " " << setw(2) << e[0] << " " << setw(2) << e[1] << " " << setw(2) << e[2] << " " << setw(2) << e[3] << " " << setw(2) << e[4] << " " << setw(2) << e[5] << " " << setw(14) << result << " " << setw(14) << exact << " " << setw(10) << error << "\n"; delete [] e; delete [] value; } delete ( x ); return; }