private static void test01(int prob, double p, int m, int nd)
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests SHEPARD_INTERP on an irregular grid.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 October 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROB, the problem number.
//
// Input, double P, the power used in the distance weighting.
//
// Input, int M, the spatial dimension.
//
// Input, int ND, the number of data points.
//
{
Console.WriteLine("");
Console.WriteLine("TEST01:");
Console.WriteLine(" Interpolate data from TEST_INTERP_ND problem #" + prob + "");
Console.WriteLine(" using Shepard interpolation with P = " + p + "");
Console.WriteLine(" spatial dimension M = " + m + "");
Console.WriteLine(" and an irregular grid of ND = " + nd + " data points.");
//
// Set problem parameters:
//
int seed = 123456789;
double[] c = UniformRNG.r8vec_uniform_01_new(m, ref seed);
double[] w = UniformRNG.r8vec_uniform_01_new(m, ref seed);
double[] xd = UniformRNG.r8mat_uniform_01_new(m, nd, ref seed);
double[] zd = Data_nD.p00_f(prob, m, c, w, nd, xd);
//
// #1: Does interpolant match function at interpolation points?
//
int ni = nd;
double[] xi = typeMethods.r8mat_copy_new(m, ni, xd);
double[] zi = Shepard.shepard_interp_nd(m, nd, xd, zd, p, ni, xi);
double int_error = typeMethods.r8vec_norm_affine(ni, zi, zd) / ni;
Console.WriteLine("");
Console.WriteLine(" L2 interpolation error averaged per interpolant node = " + int_error + "");
//
// #2: Approximation test. Estimate the integral (f-interp(f))^2.
//
ni = 1000;
ni = 50;
xi = UniformRNG.r8mat_uniform_01_new(m, ni, ref seed);
zi = Shepard.shepard_interp_nd(m, nd, xd, zd, p, ni, xi);
double[] ze = Data_nD.p00_f(prob, m, c, w, ni, xi);
double app_error = typeMethods.r8vec_norm_affine(ni, zi, ze) / ni;
Console.WriteLine(" L2 approximation error averaged per 1000 samples = " + app_error + "");
}
private static void test02(int prob, double p, int m, int n1d)
//****************************************************************************80
//
// Purpose:
//
// TEST02 tests SHEPARD_INTERP_ND on a regular N1D^M grid.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 October 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROB, the problem number.
//
// Input, double P, the power used in the distance weighting.
//
// Input, int M, the spatial dimension.
//
// Input, int N1D, the number of points in 1D.
//
{
int i;
//
// Set problem parameters:
//
int seed = 123456789;
double[] c = UniformRNG.r8vec_uniform_01_new(m, ref seed);
double[] w = UniformRNG.r8vec_uniform_01_new(m, ref seed);
int nd = (int)Math.Pow(n1d, m);
Console.WriteLine("");
Console.WriteLine("TEST02:");
Console.WriteLine(" Interpolate data from TEST_INTERP_ND problem #" + prob + "");
Console.WriteLine(" using Shepard interpolation with P = " + p + "");
Console.WriteLine(" spatial dimension M = " + m + "");
Console.WriteLine(" and a regular grid of N1D^M = " + nd + " data points.");
const double a = 0.0;
const double b = 1.0;
double[] x1d = typeMethods.r8vec_linspace_new(n1d, a, b);
double[] xd = new double[m * nd];
for (i = 0; i < m; i++)
{
typeMethods.r8vecDPData data = new();
typeMethods.r8vec_direct_product(ref data, i, n1d, x1d, m, nd, ref xd);
}
double[] zd = Data_nD.p00_f(prob, m, c, w, nd, xd);
//
// #1: Does interpolant match function at interpolation points?
//
int ni = nd;
double[] xi = typeMethods.r8mat_copy_new(m, nd, xd);
double[] zi = Shepard.shepard_interp_nd(m, nd, xd, zd, p, ni, xi);
double int_error = typeMethods.r8vec_norm_affine(ni, zi, zd) / ni;
Console.WriteLine("");
Console.WriteLine(" L2 interpolation error averaged per interpolant node = " + int_error + "");
//
// #2: Approximation test. Estimate the integral (f-interp(f))^2.
//
ni = 1000;
xi = UniformRNG.r8mat_uniform_01_new(m, ni, ref seed);
zi = Shepard.shepard_interp_nd(m, nd, xd, zd, p, ni, xi);
double[] ze = Data_nD.p00_f(prob, m, c, w, ni, xi);
double app_error = typeMethods.r8vec_norm_affine(ni, zi, ze) / ni;
Console.WriteLine(" L2 approximation error averaged per 1000 samples = " + app_error + "");
}