private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 tests DIFFER_INVERSE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 November 2013
//
// Author:
//
// John Burkardt
//
{
int n;
const int N_MAX = 8;
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" DIFFER_INVERSE returns the inverse of a DIFFER matrix;");
Console.WriteLine("");
Console.WriteLine(" N Inverse error");
int seed = 123456789;
for (n = 2; n <= N_MAX; n++)
{
Console.WriteLine("");
int test;
for (test = 1; test <= 5; test++)
{
double[] x = UniformRNG.r8vec_uniform_01_new(n, ref seed);
double[] a = Differ.differ_matrix(n, x);
double[] b = Differ.differ_inverse(n, x);
double err = Helpers.inverse_error(n, a, b);
Console.WriteLine(" " + n.ToString().PadLeft(2)
+ " " + err.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests DIFFER_MATRIX.
//
// Discussion:
//
// DIFFER_MATRIX computes a modified Vandermonde matrix A1.
//
// The solution of a system A1 * X1 = B is related to the solution
// of the system A2 * X2 = B, where A2 is the standard Vandermonde
// matrix, simply by X2(I) = X1(I) * A(I,1).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 November 2013
//
// Author:
//
// John Burkardt
//
{
int i;
int info = 0;
const int n = 4;
double[] stencil =
{
2.5, 3.3, -1.3, 0.5
}
;
double[] x =
{
1.0, 2.0, 3.0, 4.0
}
;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Demonstrate that the DIFFER matrix is 'really'");
Console.WriteLine(" a Vandermonde matrix.");
double[] a = Differ.differ_matrix(n, stencil);
typeMethods.r8mat_print(n, n, a, " Stencil matrix:");
double[] b = typeMethods.r8mat_mv_new(n, n, a, x);
//
// Set up and solve the DIFFER system.
//
a = Differ.differ_matrix(n, stencil);
double[] x1 = typeMethods.r8mat_fs_new(n, a, b);
typeMethods.r8vec_print(n, x1, " Solution of DIFFER system:");
//
// R8VM_SL solves the related Vandermonde system.
// A simple transformation gives us the solution to the DIFFER system.
//
const int job = 0;
double[] x2 = typeMethods.r8vm_sl_new(n, stencil, b, job, ref info);
if (info != 0)
{
Console.WriteLine("");
Console.WriteLine("TEST01 - Warning!");
Console.WriteLine(" VANDERMONDE system is singular.");
return;
}
typeMethods.r8vec_print(n, x2, " Solution of VANDERMONDE system:");
for (i = 0; i < n; i++)
{
x2[i] /= stencil[i];
}
typeMethods.r8vec_print(n, x2, " Transformed solution of VANDERMONDE system:");
}
private static void test03()
//****************************************************************************80
//
// Purpose:
//
// TEST03 tests DIFFER_MATRIX.
//
// Discussion:
//
// Reproduce a specific example.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 28 October 2013
//
// Author:
//
// John Burkardt
//
{
int i;
const int n = 4;
double[] stencil =
{
-3.0, -2.0, -1.0, 1.0
}
;
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" Reproduce a specific example.");
//
// Compute the coefficients for a specific stencil.
//
double[] b = new double[n];
for (i = 0; i < n; i++)
{
b[i] = 0.0;
}
const int order = 1;
b[order - 1] = 1.0;
double[] a = Differ.differ_matrix(n, stencil);
double[] c = typeMethods.r8mat_fs_new(n, a, b);
typeMethods.r8vec_print(n, c, " Solution of DIFFER system:");
//
// Use the coefficients C to estimate the first derivative of EXP(X)
// at X0, using a spacing of DX = 0.1.
//
const double x0 = 1.3;
const double dx = 0.1;
double df = 0.0;
for (i = 0; i < n; i++)
{
df += c[i] * (Math.Exp(x0 + stencil[i] * dx) - Math.Exp(x0));
}
double dfdx = df / dx;
Console.WriteLine("");
Console.WriteLine(" DFDX = " + dfdx + "");
Console.WriteLine(" d Math.Exp(x) /dx = " + Math.Exp(x0) + "");
}