public static CorrelationResult correlation_spherical(FullertonLib.BesselData globaldata, FullertonLib.r8BESK1Data data, int n, double[] rho, double rho0)
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_SPHERICAL evaluates the spherical correlation function.
//
// Discussion:
//
// This correlation is based on the volume of overlap of two spheres
// of radius RHO0 and separation RHO.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2012
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Petter Abrahamsen,
// A Review of Gaussian Random Fields and Correlation Functions,
// Norwegian Computing Center, 1997.
//
// Parameters:
//
// Input, int N, the number of arguments.
//
// Input, double RHO[N], the arguments.
//
// Input, double RHO0, the correlation length.
//
// Output, double C[N], the correlations.
//
{
int i;
double[] c = new double[n];
for (i = 0; i < n; i++)
{
double rhohat = Math.Min(Math.Abs(rho[i]) / rho0, 1.0);
c[i] = 1.0 - 1.5 * rhohat + 0.5 * Math.Pow(rhohat, 3);
}
return(new CorrelationResult {
result = c, data = globaldata, k1data = data
});
}
public static CorrelationResult correlation_exponential(FullertonLib.BesselData globaldata, FullertonLib.r8BESK1Data data, int n, double[] rho, double rho0)
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_EXPONENTIAL evaluates the exponential correlation function.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2012
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Petter Abrahamsen,
// A Review of Gaussian Random Fields and Correlation Functions,
// Norwegian Computing Center, 1997.
//
// Parameters:
//
// Input, int N, the number of arguments.
//
// Input, double RHO[N], the arguments.
//
// Input, double RHO0, the correlation length.
//
// Output, double C[N], the correlations.
//
{
int i;
double[] c = new double[n];
for (i = 0; i < n; i++)
{
c[i] = Math.Exp(-Math.Abs(rho[i]) / rho0);
}
return(new CorrelationResult {
result = c, data = globaldata, k1data = data
});
}
public static CorrelationResult correlation_besselk(FullertonLib.BesselData globaldata, FullertonLib.r8BESK1Data data, int n, double[] rho, double rho0)
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_BESSELK evaluates the Bessel K correlation function.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2012
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Petter Abrahamsen,
// A Review of Gaussian Random Fields and Correlation Functions,
// Norwegian Computing Center, 1997.
//
// Parameters:
//
// Input, int N, the number of arguments.
//
// Input, double RHO[N], the arguments.
//
// Input, double RHO0, the correlation length.
//
// Output, double C[N], the correlations.
//
{
int i;
double[] c = new double[n];
for (i = 0; i < n; i++)
{
switch (rho[i])
{
case 0.0:
c[i] = 1.0;
break;
default:
double rhohat = Math.Abs(rho[i]) / rho0;
c[i] = rhohat * FullertonLib.r8_besk1(ref globaldata, ref data, rhohat);
break;
}
}
CorrelationResult res = new() { result = c, data = globaldata, k1data = data };
return(res);
}
}
public static CorrelationResult correlation_power(FullertonLib.BesselData globaldata, FullertonLib.r8BESK1Data data, int n, double[] rho, double rho0)
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_POWER evaluates the power correlation function.
//
// Discussion:
//
// In order to be able to call this routine under a dummy name, I had
// to drop E from the argument list.
//
// The power correlation is
//
// C(rho) = ( 1 - |rho| )^e if 0 <= |rho| <= 1
// = 0 otherwise
//
// The constraint on the exponent is 2 <= e.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 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.
//
// Input, double E, the exponent.
// E has a default value of 2.0;
// 2.0 <= E.
//
// Output, double C[N], the correlations.
//
{
int i;
const double e = 2.0;
double[] c = new double[n];
for (i = 0; i < n; i++)
{
double rhohat = Math.Abs(rho[i]) / rho0;
c[i] = rhohat switch
{
public static CorrelationResult correlation_hole(FullertonLib.BesselData globaldata, FullertonLib.r8BESK1Data data, int n, double[] rho, double rho0)
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_HOLE evaluates the hole correlation function.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 11 November 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int N, the number of arguments.
//
// Input, double RHO[N], the arguments.
//
// Input, double RHO0, the correlation length.
//
// Output, double C[N], the correlations.
//
{
int i;
double[] c = new double[n];
for (i = 0; i < n; i++)
{
c[i] = (1.0 - Math.Abs(rho[i]) / rho0)
* Math.Exp(-Math.Abs(rho[i]) / rho0);
}
return(new CorrelationResult {
result = c, data = globaldata, k1data = data
});
}
public static Correlation.CorrelationResult sample_paths_cholesky(FullertonLib.BesselData globaldata, FullertonLib.r8BESK1Data kdata, int n, int n2, double rhomax, double rho0,
Func <FullertonLib.BesselData, FullertonLib.r8BESK1Data, 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);
}
