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); }