private static void test06()
//****************************************************************************80
//
// Purpose:
//
// TEST06 tests the stereographic mapping.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 15 December 2013
//
// Author:
//
// John Burkardt
//
{
int m;
Console.WriteLine("");
Console.WriteLine("TEST06");
Console.WriteLine(" Test the stereographic mapping:");
Console.WriteLine(" HYPERSPHERE_STEREOGRAPH maps hypersphere points to the plane.");
Console.WriteLine(" HYPERSPHERE_STEREOGRAPH_INVERSE inverts the mapping.");
Console.WriteLine("");
Console.WriteLine(" Pick a random X1 on the hypersphere.");
Console.WriteLine(" Map it to a point X2 on the plane.");
Console.WriteLine(" Map it back to a point X3 on the hypersphere.");
Console.WriteLine(" Consider norm of difference.");
Console.WriteLine("");
Console.WriteLine(" M || X1 - X3 ||");
int seed = 123456789;
typeMethods.r8vecNormalData data = new();
const int n = 1;
for (m = 2; m <= 5; m++)
{
Console.WriteLine("");
int test;
for (test = 1; test <= 5; test++)
{
double[] x1 = Hypersphere.hypersphere_01_surface_uniform(m, n, ref data, ref seed);
double[] x2 = Hypersphere.hypersphere_stereograph(m, n, x1);
double[] x3 = Hypersphere.hypersphere_stereograph_inverse(m, n, x2);
double err = typeMethods.r8mat_norm_fro_affine(m, n, x1, x3);
Console.WriteLine(" " + m.ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + err.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 tests HYPERSPHERE_01_SURFACE_UNIFORM.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 15 December 2013
//
// Author:
//
// John Burkardt
//
{
int m;
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" HYPERSPHERE_01_SURFACE_UNIFORM samples uniformly from the");
Console.WriteLine(" surface of the unit hypersphere");
int seed = 123456789;
typeMethods.r8vecNormalData data = new();
const int n = 1;
for (m = 1; m <= 5; m++)
{
int test;
for (test = 1; test <= 3; test++)
{
double[] x = Hypersphere.hypersphere_01_surface_uniform(m, n, ref data, ref seed);
typeMethods.r8vec_transpose_print(m, x, " Random hypersphere point:");
}
}
}
