public static Correlation.CorrelationResult sample_paths_cholesky(FullertonLib.BesselData globaldata, FullertonLib.r8BESKData kdata, int n, int n2, double rhomax, double rho0,
Func <FullertonLib.BesselData, FullertonLib.r8BESKData, int, double[], double, Correlation.CorrelationResult> correlation, ref typeMethods.r8vecNormalData data, ref int seed)
//****************************************************************************80
//
// Purpose:
//
// SAMPLE_PATHS_CHOLESKY: sample paths for stationary correlation functions.
//
// Discussion:
//
// This method uses the Cholesky factorization of the correlation matrix.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int N, the number of points on each path.
//
// Input, int N2, the number of paths.
//
// Input, double RHOMAX, the maximum value of RHO.
//
// Input, double RHO0, the correlation length.
//
// Input, double *CORRELATION ( int n, double rho_vec[], double rho0),
// the name of the function which evaluates the correlation.
//
// Input/output, int &SEED, a seed for the random number
// generator.
//
// Output, double X[N*N2], the sample paths.
//
{
int flag = 0;
int j;
//
// Choose N equally spaced sample points from 0 to RHOMAX.
//
const double rhomin = 0.0;
double[] rho_vec = typeMethods.r8vec_linspace_new(n, rhomin, rhomax);
//
// Evaluate the correlation function.
//
Correlation.CorrelationResult tr = correlation(globaldata, kdata, n, rho_vec, rho0);
double[] cor_vec = tr.result;
globaldata = tr.data;
//
// Construct the correlation matrix;
//
// From the vector
// [ C(0), C(1), C(2), ... C(N-1) ]
// construct the vector
// [ C(N-1), ..., C(2), C(1), C(0), C(1), C(2), ... C(N-1) ]
// Every row of the correlation matrix can be constructed by a subvector
// of this vector.
//
double[] cor = new double[n * n];
for (j = 0; j < n; j++)
{
int i;
for (i = 0; i < n; i++)
{
int k = typeMethods.i4_wrap(j - i, 0, n - 1);
cor[i + j * n] = cor_vec[k];
}
}
//
// Get the Cholesky factorization of COR:
//
// COR = L * L'.
//
double[] l = typeMethods.r8mat_cholesky_factor(n, cor, ref flag);
switch (flag)
{
//
// The matrix might not be nonnegative definite.
//
case 2:
Console.WriteLine("");
Console.WriteLine("SAMPLE_PATHS_CHOLESKY - Fatal error!");
Console.WriteLine(" The correlation matrix is not");
Console.WriteLine(" symmetric nonnegative definite.");
return(null);
}
//
// Compute a matrix of N by N2 normally distributed values.
//
double[] r = typeMethods.r8mat_normal_01_new(n, n2, ref data, ref seed);
//
// Compute the sample path.
//
double[] x = typeMethods.r8mat_mm_new(n, n, n2, l, r);
Correlation.CorrelationResult res = new() { result = x, data = globaldata };
return(res);
}
public static CorrelationResult correlation_matern(FullertonLib.BesselData globaldata, FullertonLib.r8BESKData data, int n, double[] rho, double rho0)
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_MATERN evaluates the Matern correlation function.
//
// Discussion:
//
// In order to call this routine under a dummy name, I had to drop NU from
// the parameter list.
//
// The Matern correlation is
//
// rho1 = 2 * sqrt ( nu ) * rho / rho0
//
// c(rho) = ( rho1 )^nu * BesselK ( nu, rho1 )
// / gamma ( nu ) / 2 ^ ( nu - 1 )
//
// The Matern covariance has the form:
//
// K(rho) = sigma^2 * c(rho)
//
// A Gaussian process with Matern covariance has sample paths that are
// differentiable (nu - 1) times.
//
// When nu = 0.5, the Matern covariance is the exponential covariance.
//
// As nu goes to +oo, the correlation converges to exp ( - (rho/rho0)^2 ).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 November 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int N, the number of arguments.
//
// Input, double RHO[N], the arguments.
// 0.0 <= RHO.
//
// Input, double RHO0, the correlation length.
// 0.0 < RHO0.
//
// Output, double C[N], the correlations.
//
{
int i;
const double nu = 2.5;
double[] c = new double[n];
for (i = 0; i < n; i++)
{
double rho1 = 2.0 * Math.Sqrt(nu) * Math.Abs(rho[i]) / rho0;
c[i] = rho1 switch
{
0.0 => 1.0,
_ => Math.Pow(rho1, nu) * FullertonLib.r8_besk(ref globaldata, ref data, nu, rho1) / r8_gamma(nu) /
Math.Pow(2.0, nu - 1.0)
};
}
return(new CorrelationResult {
result = c, data = globaldata, kdata = data
});
}
}
