private static void correlation_test06()
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_TEST06 plots sample paths with SAMPLE_PATHS2_CHOLESKY/EIGEN/FFT.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 12 November 2012
//
// Author:
//
// John Burkardt
//
{
Console.WriteLine("");
Console.WriteLine("CORRELATION_TEST06");
Console.WriteLine(" For non-stationary correlation functions:");
Console.WriteLine("");
Console.WriteLine(" SAMPLE_PATHS2_CHOLESKY generates sample paths from the");
Console.WriteLine(" correlation matrix, factored using the Cholesky factor.");
Console.WriteLine(" It requires that the correlation matrix is nonnegative definite.");
Console.WriteLine("");
Console.WriteLine(" SAMPLE_PATHS2_EIGEN generates sample paths from the");
Console.WriteLine(" correlation matrix, factored using the eigen factorization.");
Console.WriteLine(" If the correlation matrix is not nonnegative definite,");
Console.WriteLine(" we simply suppress negative eigenvalues.");
Console.WriteLine("");
Console.WriteLine(" SAMPLE_PATHS2_FFT generates sample paths from the");
Console.WriteLine(" correlation matrix, factored using the FFT factorization");
Console.WriteLine(" of the correlation matrix after embedding in a circulant.");
Console.WriteLine("");
/*
* brownian
*/
const int n = 101;
const int n2 = 3;
const double rhomin = 0.0;
const double rhomax = 10.0;
const double rho0 = 1.0;
int seed = 123456789;
typeMethods.r8vecNormalData data = new();
double[] x = SamplePaths.sample_paths2_cholesky(n, n2, rhomin, rhomax, rho0, Correlation.correlation_brownian, ref data, ref seed);
double[] rho = typeMethods.r8vec_linspace_new(n, rhomin, rhomax);
Paths.paths_plot(n, n2, rho, x, "brownian", "Brownian correlation");
}
private static void correlation_test02()
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_TEST02 plots sample paths with SAMPLE_PATHS_CHOLESKY.
//
// Discussion:
//
// Most paths will be blue, but make the LAST one red so that there will
// always be one distinguished path that is easy to follow.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2012
//
// Author:
//
// John Burkardt
//
{
const double rho0 = 1.0;
const double rhomax = 10.0;
const double rhomin = 0.0;
Console.WriteLine("");
Console.WriteLine("CORRELATION_TEST02");
Console.WriteLine(" SAMPLE_PATHS_CHOLESKY generates sample paths from the");
Console.WriteLine(" correlation matrix, factored using the Cholesky factor.");
Console.WriteLine(" It requires that the correlation matrix is nonnegative definite.");
Console.WriteLine("");
Console.WriteLine(" SAMPLE_PATHS_EIGEN generates sample paths from the");
Console.WriteLine(" correlation matrix, factored using the eigen factorization.");
Console.WriteLine(" If the correlation matrix is not nonnegative definite,");
Console.WriteLine(" we simply suppress negative eigenvalues.");
Console.WriteLine("");
FullertonLib.BesselData globaldata = new();
const int n = 101;
const int n2 = 3;
double[] rho = typeMethods.r8vec_linspace_new(n, rhomin, rhomax);
//
// besselj
// Use EIGEN, because CHOLESKY fails.
//
int seed = 123456789;
typeMethods.r8vecNormalData data = new();
FullertonLib.r8BESJ0Data jdata = new();
Correlation.CorrelationResult tr = SamplePaths.sample_paths_eigen(globaldata, jdata, n, n2, rhomax, rho0, Correlation.correlation_besselj, ref data, ref seed);
globaldata = tr.data;
double[] x = tr.result;
jdata = tr.j0data;
Paths.paths_plot(n, n2, rho, x, "besselj", "Bessel J correlation");
//
// besselk
//
seed = 123456789;
FullertonLib.r8BESK1Data k1data = new();
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_besselk, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "besselk", "Bessel K correlation");
//
// circular
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_circular, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "circular", "Circular correlation");
//
// constant
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_constant, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "constant", "Constant correlation");
//
// cubic
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_cubic, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "cubic", "Cubic correlation");
//
// damped_cosine
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_damped_cosine, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "damped_cosine", "Damped cosine correlation");
//
// damped_sine
// Use EIGEN, because CHOLESKY fails.
//
seed = 123456789;
tr = SamplePaths.sample_paths_eigen(globaldata, jdata, n, n2, rhomax, rho0, Correlation.correlation_damped_sine, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
jdata = tr.j0data;
Paths.paths_plot(n, n2, rho, x, "damped_sine", "Damped sine correlation");
//
// exponential
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_exponential, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "exponential", "Exponential correlation");
//
// gaussian
// Use EIGEN, because CHOLESKY fails.
//
seed = 123456789;
tr = SamplePaths.sample_paths_eigen(globaldata, jdata, n, n2, rhomax, rho0, Correlation.correlation_gaussian, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
jdata = tr.j0data;
Paths.paths_plot(n, n2, rho, x, "gaussian", "Gaussian correlation");
//
// hole
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_hole, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "hole", "Hole correlation");
//
// linear
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_linear, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "linear", "Linear correlation");
//
// matern ( nu = 2.5 )
//
seed = 123456789;
FullertonLib.r8BESKData kdata = new();
tr = SamplePaths.sample_paths_cholesky(globaldata, kdata, n, n2, rhomax, rho0, Correlation.correlation_matern, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
kdata = tr.kdata;
Paths.paths_plot(n, n2, rho, x, "matern", "Matern correlation (nu=2.5)");
//
// pentaspherical
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_pentaspherical, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "pentaspherical", "Pentaspherical correlation");
//
// power ( e = 2.0 )
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_power, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "power", "Power correlation (e=2.0)");
//
// rational_quadratic
// Use EIGEN, because CHOLESKY fails.
//
seed = 123456789;
tr = SamplePaths.sample_paths_eigen(globaldata, jdata, n, n2, rhomax, rho0, Correlation.correlation_rational_quadratic, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
jdata = tr.j0data;
Paths.paths_plot(n, n2, rho, x, "rational_quadratic", "Rational quadratic correlation");
//
// spherical
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_spherical, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "spherical", "Spherical correlation");
//
// white_noise
//
seed = 123456789;
tr = SamplePaths.sample_paths_cholesky(globaldata, k1data, n, n2, rhomax, rho0, Correlation.correlation_white_noise, ref data, ref seed);
globaldata = tr.data;
x = tr.result;
k1data = tr.k1data;
Paths.paths_plot(n, n2, rho, x, "white_noise", "White noise correlation");
}
