public static Correlation.CorrelationResult sample_paths_eigen(FullertonLib.BesselData globaldata, FullertonLib.r8BESJ0Data jdata, int n, int n2, double rhomax, double rho0,
Func <FullertonLib.BesselData, FullertonLib.r8BESJ0Data, int, double[], double, Correlation.CorrelationResult> correlation, ref typeMethods.r8vecNormalData data, ref int seed)
//****************************************************************************80
//
// Purpose:
//
// SAMPLE_PATHS_EIGEN: sample paths for stationary correlation functions.
//
// Discussion:
//
// This method uses the eigen-decomposition of the correlation matrix.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 12 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 i;
int j;
int k;
//
// 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, jdata, n, rho_vec, rho0);
double[] cor_vec = tr.result;
globaldata = tr.data;
jdata = tr.j0data;
//
// 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++)
{
for (i = 0; i < n; i++)
{
k = typeMethods.i4_wrap(Math.Abs(i - j), 0, n - 1);
cor[i + j * n] = cor_vec[k];
}
}
//
// Get the eigendecomposition of COR:
//
// COR = V * D * V'.
//
// Because COR is symmetric, V is orthogonal.
//
double[] d = new double[n];
double[] w = new double[n];
double[] v = new double[n * n];
TRED2.tred2(n, cor, ref d, ref w, ref v);
TQL2.tql2(n, ref d, ref w, v);
//
// We assume COR is non-negative definite, and hence that there
// are no negative eigenvalues.
//
double dmin = typeMethods.r8vec_min(n, d);
if (dmin < -Math.Sqrt(typeMethods.r8_epsilon()))
{
Console.WriteLine("");
Console.WriteLine("SAMPLE_PATHS_EIGEN - Warning!");
Console.WriteLine(" Negative eigenvalues observed as low as " + dmin + "");
}
for (i = 0; i < n; i++)
{
d[i] = Math.Max(d[i], 0.0);
}
//
// Compute the eigenvalues of the factor C.
//
for (i = 0; i < n; i++)
{
d[i] = Math.Sqrt(d[i]);
}
//
// Compute C, such that C' * C = COR.
//
double[] c = new double[n * n];
for (j = 0; j < n; j++)
{
for (i = 0; i < n; i++)
{
c[i + j * n] = 0.0;
for (k = 0; k < n; k++)
{
c[i + j * n] += d[k] * v[i + k * n] * v[j + k * n];
}
}
}
//
// Compute N by N2 independent random normal values.
//
double[] r = typeMethods.r8mat_normal_01_new(n, n2, ref data, ref seed);
//
// Multiply to get the variables X which have correlation COR.
//
double[] x = typeMethods.r8mat_mm_new(n, n, n2, c, r);
Correlation.CorrelationResult result = new() { result = x, data = globaldata };
return(result);
}
public static double[] sample_paths2_eigen(int n, int n2, double rhomin, double rhomax,
double rho0, Func <int, int, double[], double[], double, double[]> correlation2, ref typeMethods.r8vecNormalData data, ref int seed)
//****************************************************************************80
//
// Purpose:
//
// SAMPLE_PATHS2_EIGEN: sample paths for stationary correlation functions.
//
// Discussion:
//
// This method uses the eigen-decomposition of the correlation matrix.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 12 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 RHOMIN, RHOMAX, the range of RHO.
//
// Input, double RHO0, the correlation length.
//
// Input, double *CORRELATION2 ( int m, int n, double s[], double t[],
// 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 i;
int j;
//
// Choose N equally spaced sample points from RHOMIN to RHOMAX.
//
double[] s = typeMethods.r8vec_linspace_new(n, rhomin, rhomax);
//
// Evaluate the correlation function.
//
double[] cor = correlation2(n, n, s, s, rho0);
//
// Get the eigendecomposition of COR:
//
// COR = V * D * V'.
//
// Because COR is symmetric, V is orthogonal.
//
double[] d = new double[n];
double[] w = new double[n];
double[] v = new double[n * n];
TRED2.tred2(n, cor, ref d, ref w, ref v);
TQL2.tql2(n, ref d, ref w, v);
//
// We assume COR is non-negative definite, and hence that there
// are no negative eigenvalues.
//
double dmin = typeMethods.r8vec_min(n, d);
if (dmin < -Math.Sqrt(typeMethods.r8_epsilon()))
{
Console.WriteLine("");
Console.WriteLine("SAMPLE_PATHS2_EIGEN - Warning!");
Console.WriteLine(" Negative eigenvalues observed as low as " + dmin + "");
}
for (i = 0; i < n; i++)
{
d[i] = Math.Max(d[i], 0.0);
}
//
// Compute the eigenvalues of the factor C.
//
for (i = 0; i < n; i++)
{
d[i] = Math.Sqrt(d[i]);
}
//
// Compute C, such that C' * C = COR.
//
double[] c = new double[n * n];
for (j = 0; j < n; j++)
{
for (i = 0; i < n; i++)
{
c[i + j * n] = 0.0;
int k;
for (k = 0; k < n; k++)
{
c[i + j * n] += d[k] * v[i + k * n] * v[j + k * n];
}
}
}
//
// Compute N by N2 independent random normal values.
//
double[] r = typeMethods.r8mat_normal_01_new(n, n2, ref data, ref seed);
//
// Multiply to get the variables X which have correlation COR.
//
double[] x = typeMethods.r8mat_mm_new(n, n, n2, c, r);
return(x);
}