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sparse_grid_hw_prb.cpp
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# include <cstdlib>
# include <iostream>
# include <iomanip>
# include <cmath>
# include <ctime>
# include <cstring>
using namespace std;
# include "sparse_grid_hw.hpp"
int main ( );
void ccl_test ( );
void ccl_sparse_test ( );
void ccs_test ( );
void ccs_sparse_test ( );
void cce_test ( );
void cce_sparse_test ( );
void get_seq_test ( );
void gqn_test ( );
void gqn_sparse_test ( );
void gqn2_sparse_test ( );
void gqu_test ( );
void gqu_sparse_test ( );
void kpn_test ( );
void kpn_sparse_test ( );
void kpu_test ( );
void kpu_sparse_test ( );
void nwspgr_size_test ( );
void nwspgr_time_test ( );
void nwspgr_test ( );
void order_report ( );
void symmetric_sparse_size_test ( );
void tensor_product_test ( );
void tensor_product_cell_test ( );
//****************************************************************************80
int main ( )
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for SPARSE_GRID_HW_PRB.
//
// Discussion:
//
// SPARSE_GRID_HW_PRB tests the SPARSE_GRID_HW library.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 February 2014
//
// Author:
//
// John Burkardt
//
{
timestamp ( );
cout << "\n";
cout << "SPARSE_GRID_HW_PRB\n";
cout << " C++ version\n";
cout << " Test the SPARSE_GRID_HW library.\n";
ccl_test ( );
ccl_sparse_test ( );
ccs_test ( );
ccs_sparse_test ( );
cce_test ( );
cce_sparse_test ( );
get_seq_test ( );
gqn_test ( );
gqn_sparse_test ( );
gqn2_sparse_test ( );
gqu_test ( );
gqu_sparse_test ( );
kpn_test ( );
kpn_sparse_test ( );
kpu_test ( );
kpu_sparse_test ( );
nwspgr_size_test ( );
nwspgr_time_test ( );
nwspgr_test ( );
order_report ( );
symmetric_sparse_size_test ( );
tensor_product_test ( );
tensor_product_cell_test ( );
//
// Terminate.
//
cout << "\n";
cout << "SPARSE_GRID_HW_PRB\n";
cout << " Normal end of execution.\n";
cout << "\n";
timestamp ( );
return 0;
}
//****************************************************************************80
void ccl_test ( )
//****************************************************************************80
//
// Purpose:
//
// CCL_TEST uses CCL_ORDER + CC for 1D quadrature over [0,1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 February 2014
//
// Author:
//
// John Burkardt
//
{
int d;
double e;
double exact;
double *fx;
int l;
int n;
double q;
double *w;
double *x;
cout << "\n";
cout << "CCL_TEST:\n";
cout << " CCL_ORDER + CC\n";
cout << " Clenshaw Curtis Linear (CCL) quadrature over [0,1]:\n";
cout << "\n";
cout << " Level Nodes Estimate Error\n";
cout << "\n";
d = 1;
exact = fu_integral ( d );
for ( l = 1; l <= 5; l++ )
{
n = ccl_order ( l );
x = new double[n];
w = new double[n];
cc ( n, x, w );
fx = fu_value ( d, n, x );
q = r8vec_dot_product ( n, w, fx );
e = r8_abs ( q - exact ) / exact;
cout << " " << setw(2) << l
<< " " << setw(6) << n
<< " " << setw(14) << q
<< " " << setw(14) << e << "\n";
delete [] fx;
delete [] w;
delete [] x;
}
return;
}
//****************************************************************************80
void ccl_sparse_test ( )
//****************************************************************************80
//
// Purpose:
//
// CCL_SPARSE_TEST uses CCL_ORDER + CC for a sparse grid.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 February 2014
//
// Author:
//
// John Burkardt
//
// Local parameters:
//
// Local, int D, the spatial dimension.
//
// Local, int MAXK, the maximum level to check.
//
{
int d;
double error_mc;
double error_sg;
double estimate;
double *fx;
int k;
int maxk;
int n;
int n2;
int r;
double *s;
int s_num;
int seed;
double trueval;
double *w;
double *x;
d = 10;
maxk = 7;
trueval = fu_integral ( d );
cout << "\n";
cout << "CCL_SPARSE_TEST:\n";
cout << " CCL_ORDER + CC\n";
cout << " Sparse Clenshaw Curtis Linear quadrature over [0,1].\n";
cout << "\n";
cout << " D Level Nodes SG error MC error\n";
cout << "\n";
for ( k = 2; k <= maxk; k++ )
{
//
// Compute sparse grid estimate.
//
n = nwspgr_size ( ccl_order, d, k );
x = new double[d*n];
w = new double[n];
nwspgr ( cc, ccl_order, d, k, n, n2, x, w );
fx = fu_value ( d, n2, x );
estimate = r8vec_dot_product ( n2, w, fx );
error_sg = r8_abs ( ( estimate - trueval ) / trueval );
delete [] fx;
delete [] w;
delete [] x;
//
// Compute 1000 Monte Carlo estimates with same number of points, and average.
//
s_num = 1000;
s = new double[s_num];
seed = 123456789;
for ( r = 0; r < 1000; r++ )
{
x = r8mat_uniform_01_new ( d, n2, seed );
fx = fu_value ( d, n2, x );
s[r] = r8vec_sum ( n2, fx ) / ( double ) ( n2 );
delete [] fx;
delete [] x;
}
error_mc = 0.0;
for ( r = 0; r < s_num; r++ )
{
error_mc = error_mc + pow ( s[r] - trueval, 2 );
}
error_mc = sqrt ( error_mc / ( double ) ( s_num ) ) / trueval;
cout << " " << setw(2) << d
<< " " << setw(5) << k
<< " " << setw(6) << n2
<< " " << setw(10) << error_sg
<< " " << setw(10) << error_mc << "\n";
delete [] s;
}
return;
}
//****************************************************************************80
void ccs_test ( )
//****************************************************************************80
//
// Purpose:
//
// CCS_TEST uses CCS_ORDER + CC for 1D quadrature over [0,1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 February 2014
//
// Author:
//
// John Burkardt
//
{
int d;
double e;
double exact;
double *fx;
int l;
int n;
double q;
double *w;
double *x;
cout << "\n";
cout << "CCS_TEST:\n";
cout << " CCS_ORDER + CC\n";
cout << " Clenshaw Curtis Slow quadrature over [0,1]:\n";
cout << "\n";
cout << " Level Nodes Estimate Error\n";
cout << "\n";
d = 1;
exact = fu_integral ( d );
for ( l = 1; l <= 5; l++ )
{
n = ccs_order ( l );
x = new double[n];
w = new double[n];
cc ( n, x, w );
fx = fu_value ( d, n, x );
q = r8vec_dot_product ( n, w, fx );
e = r8_abs ( q - exact ) / exact;
cout << " " << setw(2) << l
<< " " << setw(6) << n
<< " " << setw(14) << q
<< " " << setw(14) << e << "\n";
delete [] fx;
delete [] w;
delete [] x;
}
return;
}
//****************************************************************************80
void ccs_sparse_test ( )
//****************************************************************************80
//
// Purpose:
//
// CCS_SPARSE_TEST uses CCS_ORDER + CC for a sparse grid.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 February 2014
//
// Author:
//
// John Burkardt
//
// Local parameters:
//
// Local, int D, the spatial dimension.
//
// Local, int MAXK, the maximum level to check.
//
{
int d;
double error_mc;
double error_sg;
double estimate;
double *fx;
int k;
int maxk;
int n;
int n2;
int r;
double *s;
int s_num;
int seed;
double trueval;
double *w;
double *x;
d = 10;
maxk = 7;
trueval = fu_integral ( d );
cout << "\n";
cout << "CCS_SPARSE_TEST:\n";
cout << " CCS_ORDER + CC\n";
cout << " Sparse Clenshaw Curtis Slow quadrature over [0,1].\n";
cout << "\n";
cout << " D Level Nodes SG error MC error\n";
cout << "\n";
for ( k = 2; k <= maxk; k++ )
{
//
// Compute sparse grid estimate.
//
n = nwspgr_size ( ccs_order, d, k );
x = new double[d*n];
w = new double[n];
nwspgr ( cc, ccs_order, d, k, n, n2, x, w );
fx = fu_value ( d, n2, x );
estimate = r8vec_dot_product ( n2, w, fx );
error_sg = r8_abs ( ( estimate - trueval ) / trueval );
delete [] fx;
delete [] w;
delete [] x;
//
// Compute 1000 Monte Carlo estimates with same number of points, and average.
//
s_num = 1000;
s = new double[s_num];
seed = 123456789;
for ( r = 0; r < 1000; r++ )
{
x = r8mat_uniform_01_new ( d, n2, seed );
fx = fu_value ( d, n2, x );
s[r] = r8vec_sum ( n2, fx ) / ( double ) ( n2 );
delete [] fx;
delete [] x;
}
error_mc = 0.0;
for ( r = 0; r < s_num; r++ )
{
error_mc = error_mc + pow ( s[r] - trueval, 2 );
}
error_mc = sqrt ( error_mc / ( double ) ( s_num ) ) / trueval;
cout << " " << setw(2) << d
<< " " << setw(5) << k
<< " " << setw(6) << n2
<< " " << setw(10) << error_sg
<< " " << setw(10) << error_mc << "\n";
delete [] s;
}
return;
}
//****************************************************************************80
void cce_test ( )
//****************************************************************************80
//
// Purpose:
//
// CCE_TEST uses CCE_ORDER + CC for 1D quadrature over [0,1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 February 2014
//
// Author:
//
// John Burkardt
//
{
int d;
double e;
double exact;
double *fx;
int l;
int n;
double q;
double *w;
double *x;
cout << "\n";
cout << "CCE_TEST:\n";
cout << " CCE_ORDER + CC\n";
cout << " Clenshaw Curtis Exponential quadrature over [0,1]:\n";
cout << "\n";
cout << " Level Nodes Estimate Error\n";
cout << "\n";
d = 1;
exact = fu_integral ( d );
for ( l = 1; l <= 5; l++ )
{
n = cce_order ( l );
x = new double[n];
w = new double[n];
cc ( n, x, w );
fx = fu_value ( d, n, x );
q = r8vec_dot_product ( n, w, fx );
e = r8_abs ( q - exact ) / exact;
cout << " " << setw(2) << l
<< " " << setw(6) << n
<< " " << setw(14) << q
<< " " << setw(14) << e << "\n";
delete [] fx;
delete [] w;
delete [] x;
}
return;
}
//****************************************************************************80
void cce_sparse_test ( )
//****************************************************************************80
//
// Purpose:
//
// CCE_SPARSE_TEST uses CCE_ORDER + CC for a sparse grid.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 February 2014
//
// Author:
//
// John Burkardt
//
// Local parameters:
//
// Local, int D, the spatial dimension.
//
// Local, int MAXK, the maximum level to check.
//
{
int d;
double error_mc;
double error_sg;
double estimate;
double *fx;
int k;
int maxk;
int n;
int n2;
int r;
double *s;
int s_num;
int seed;
double trueval;
double *w;
double *x;
d = 10;
maxk = 7;
trueval = fu_integral ( d );
cout << "\n";
cout << "CCE_SPARSE_TEST:\n";
cout << " CCE_ORDER + CC\n";
cout << " Sparse Clenshaw Curtis Exponential quadrature over [0,1].\n";
cout << "\n";
cout << " D Level Nodes SG error MC error\n";
cout << "\n";
for ( k = 2; k <= maxk; k++ )
{
//
// Compute sparse grid estimate.
//
n = nwspgr_size ( cce_order, d, k );
x = new double[d*n];
w = new double[n];
nwspgr ( cc, cce_order, d, k, n, n2, x, w );
fx = fu_value ( d, n2, x );
estimate = r8vec_dot_product ( n2, w, fx );
error_sg = r8_abs ( ( estimate - trueval ) / trueval );
delete [] fx;
delete [] w;
delete [] x;
//
// Compute 1000 Monte Carlo estimates with same number of points, and average.
//
s_num = 1000;
s = new double[s_num];
seed = 123456789;
for ( r = 0; r < 1000; r++ )
{
x = r8mat_uniform_01_new ( d, n2, seed );
fx = fu_value ( d, n2, x );
s[r] = r8vec_sum ( n2, fx ) / ( double ) ( n2 );
delete [] fx;
delete [] x;
}
error_mc = 0.0;
for ( r = 0; r < s_num; r++ )
{
error_mc = error_mc + pow ( s[r] - trueval, 2 );
}
error_mc = sqrt ( error_mc / ( double ) ( s_num ) ) / trueval;
cout << " " << setw(2) << d
<< " " << setw(5) << k
<< " " << setw(6) << n2
<< " " << setw(10) << error_sg
<< " " << setw(10) << error_mc << "\n";
delete [] s;
}
return;
}
//****************************************************************************80
void get_seq_test ( )
//****************************************************************************80
//
// Purpose:
//
// GET_SEQ_TEST tests GET_SEQ.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 January 2013
//
// Author:
//
// John Burkardt
//
{
int d;
int *fs;
int norm;
int seq_num;
cout << "\n";
cout << "GET_SEQ_TEST\n";
cout << " GET_SEQ returns all D-dimensional vectors that sum to NORM.\n";
d = 3;
norm = 6;
cout << "\n";
cout << " D = " << d << "\n";
cout << " NORM = " << norm << "\n";
seq_num = num_seq ( norm - d, d );
fs = get_seq ( d, norm, seq_num );
i4mat_print ( seq_num, d, fs, " The compositions" );
delete [] fs;
return;
}
//****************************************************************************80
void gqn_test ( )
//****************************************************************************80
//
// Purpose:
//
// GQN_TEST uses the GQN function for 1D quadrature over (-oo,+oo).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 January 2013
//
// Author:
//
// John Burkardt
//
{
int d;
double e;
double exact;
double *fx;
int i;
int l;
int n;
double q;
double *w;
double *x;
cout << "\n";
cout << "\n";
cout << "GQN_TEST:\n";
cout << " Gauss-Hermite quadrature over (-oo,+oo):\n";
cout << "\n";
cout << " Level Nodes Estimate Error\n";
cout << "\n";
d = 1;
exact = fn_integral ( d );
for ( l = 1; l <= 5; l++ )
{
n = l;
x = new double[n];
w = new double[n];
gqn ( n, x, w );
fx = fn_value ( d, n, x );
q = r8vec_dot_product ( n, w, fx );
e = r8_abs ( q - exact ) / exact;
cout << " " << setw(2) << l
<< " " << setw(6) << n
<< " " << setw(14) << q
<< " " << setw(14) << e << "\n";
delete [] fx;
delete [] w;
delete [] x;
}
return;
}
//****************************************************************************80
void gqn_sparse_test ( )
//****************************************************************************80
//
// Purpose:
//
// GQN_SPARSE_TEST uses the GQN function to build a sparse grid.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 January 2013
//
// Author:
//
// John Burkardt
//
// Local parameters:
//
// Local, int D, the spatial dimension.
//
// Local, int MAXK, the maximum level to check.
//
{
int d;
double error_mc;
double error_sg;
double estimate;
double *fx;
int k;
int maxk;
int n;
int n2;
int r;
double *s;
int s_num;
int seed;
double trueval;
double *w;
double *x;
d = 10;
maxk = 7;
trueval = fn_integral ( d );
cout << "\n";
cout << "GQN_SPARSE_TEST:\n";
cout << " GQN sparse grid:\n";
cout << " Sparse Gaussian quadrature with Hermite weight over (-oo,+oo).\n";
cout << "\n";
cout << " D Level Nodes SG error MC error\n";
cout << "\n";
for ( k = 2; k <= maxk; k++ )
{
//
// Compute sparse grid estimate.
//
n = nwspgr_size ( gqn_order, d, k );
x = new double[d*n];
w = new double[n];
nwspgr ( gqn, gqn_order, d, k, n, n2, x, w );
fx = fn_value ( d, n2, x );
estimate = r8vec_dot_product ( n2, w, fx );
error_sg = r8_abs ( ( estimate - trueval ) / trueval );
delete [] fx;
delete [] w;
delete [] x;
//
// Compute 1000 Monte Carlo estimates with same number of points, and average.
//
s_num = 1000;
s = new double[s_num];
seed = 123456789;
for ( r = 0; r < 1000; r++ )
{
x = r8mat_normal_01_new ( d, n2, seed );
fx = fn_value ( d, n2, x );
s[r] = r8vec_sum ( n2, fx ) / ( double ) ( n2 );
delete [] fx;
delete [] x;
}
error_mc = 0.0;
for ( r = 0; r < s_num; r++ )
{
error_mc = error_mc + pow ( s[r] - trueval, 2 );
}
error_mc = sqrt ( error_mc / ( double ) ( s_num ) ) / trueval;
cout << " " << setw(2) << d
<< " " << setw(5) << k
<< " " << setw(6) << n2
<< " " << setw(10) << error_sg
<< " " << setw(10) << error_mc << "\n";
delete [] s;
}
return;
}
//****************************************************************************80
void gqn2_sparse_test ( )
//****************************************************************************80
//
// Purpose:
//
// GQN2_SPARSE_TEST uses the GQN and GQN2_ORDER functions.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 February 2014
//
// Author:
//
// John Burkardt
//
// Local parameters:
//
// Local, int D, the spatial dimension.
//
// Local, int MAXK, the maximum level to check.
//
{
int d;
int j;
int k;
int maxk;
int n;
int n2;
double *w;
double *x;
d = 2;
maxk = 4;
cout << "\n";
cout << "GQN2_SPARSE_TEST:\n";
cout << " GQN sparse grid:\n";
cout << " Gauss-Hermite sparse grids over (-oo,+oo).\n";
cout << " Use GQN2_ORDER, the growth rule N = 2 * L - 1.\n";
for ( k = 2; k <= maxk; k++ )
{
cout << "\n";
cout << " J W X Y\n";
cout << "\n";
n = nwspgr_size ( gqn2_order, d, k );
x = new double[d*n];
w = new double[n];
nwspgr ( gqn, gqn2_order, d, k, n, n2, x, w );
for ( j = 0; j < n2; j++ )
{
cout << " " << setw(4) << j
<< " " << setw(14) << w[j]
<< " " << setw(14) << x[0+j*d]
<< " " << setw(14) << x[1+j*d] << "\n";
}
delete [] w;
delete [] x;
}
return;
}
//****************************************************************************80
void gqu_test ( )
//****************************************************************************80
//
// Purpose:
//
// GQU_TEST uses the GQU function for 1D quadrature over [0,1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 January 2013
//
// Author:
//
// John Burkardt
//
{
int d;
double e;
double exact;
double *fx;
int i;
int l;
int n;
double q;
double *w;
double *x;
cout << "\n";
cout << "GQU_TEST:\n";
cout << " Gauss-Legendre quadrature over [0,1]:\n";
cout << "\n";
cout << " Level Nodes Estimate Error\n";
cout << "\n";
d = 1;
exact = fu_integral ( d );
for ( l = 1; l <= 5; l++ )