private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests COMB by generating all 3-subsets of a 5 set.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 01 April 2016
//
// Author:
//
// John Burkardt
//
{
const int k = 3;
int l;
const int n = 5;
int lmax = FullertonLib.i4_binom(n, k);
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Generate all K-subsets of an N set.");
Console.WriteLine(" K = " + k + "");
Console.WriteLine(" N = " + n + "");
Console.WriteLine(" LMAX =" + lmax + "");
if (!typeMethods.i4_choose_check(n, k))
{
Console.WriteLine("");
Console.WriteLine("TEST01 - Warning!");
Console.WriteLine(" The binomial coefficient cannot be");
Console.WriteLine(" computed in integer arithmetic for");
Console.WriteLine(" this choice of parameters.");
return;
}
Console.WriteLine("");
for (l = 1; l <= lmax; l++)
{
int[] c = Comb.comb(n, k, l);
string cout = " " + l.ToString().PadLeft(4) + ": ";
int i;
for (i = 0; i < k; i++)
{
cout += " " + c[i].ToString().PadLeft(4);
}
Console.WriteLine(cout);
}
}
public static CorrelationResult correlation_besselj(FullertonLib.BesselData globaldata, FullertonLib.r8BESJ0Data data, int n, double[] rho, double rho0)
//****************************************************************************80
//
// Purpose:
//
// CORRELATION_BESSELJ evaluates the Bessel J 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++)
{
double rhohat = Math.Abs(rho[i]) / rho0;
c[i] = FullertonLib.r8_besj0(ref globaldata, ref data, rhohat);
}
CorrelationResult result = new() { result = c, data = globaldata, j0data = data };
return(result);
}
private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 tests COMB by generating 10 random 10-subsets of a 100 set.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 01 April 2016
//
// Author:
//
// John Burkardt
//
{
int j;
const int k = 10;
const int n = 100;
int lmax = FullertonLib.i4_binom(n, k);
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" Generate 10 random K-subsets of an N set.");
Console.WriteLine(" K = " + k + "");
Console.WriteLine(" N = " + n + "");
Console.WriteLine(" LMAX =" + lmax + "");
Console.WriteLine("");
Console.WriteLine(" Note that this function is already");
Console.WriteLine(" failing because LMAX is negative.");
Console.WriteLine(" The combinatorial coefficient C(100,10)");
Console.WriteLine(" is too large to store in an integer.");
Console.WriteLine("");
Console.WriteLine(" Although the program continues to give");
Console.WriteLine(" results, they cannot be relied on.");
if (!typeMethods.i4_choose_check(n, k))
{
Console.WriteLine("");
Console.WriteLine("TEST05 - Warning!");
Console.WriteLine(" The binomial coefficient cannot be");
Console.WriteLine(" computed in integer arithmetic for");
Console.WriteLine(" this choice of parameters.");
return;
}
Console.WriteLine("");
int seed = 123456789;
for (j = 1; j <= 10; j++)
{
int l = UniformRNG.i4_uniform_ab(1, lmax, ref seed);
int[] c = Comb.comb(n, k, l);
string cout = " " + l.ToString().PadLeft(4) + ": ";
int i;
for (i = 0; i < k; i++)
{
cout += " " + c[i].ToString().PadLeft(4);
}
Console.WriteLine(cout);
}
}
private static void test04()
//****************************************************************************80
//
// Purpose:
//
// TEST04 tests COMB by generating 10 random 3-subsets of a 100 set.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 01 April 2016
//
// Author:
//
// John Burkardt
//
{
int j;
const int k = 3;
const int n = 100;
int lmax = FullertonLib.i4_binom(n, k);
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" Generate 10 random K-subsets of an N set.");
Console.WriteLine(" K = " + k + "");
Console.WriteLine(" N = " + n + "");
Console.WriteLine(" LMAX =" + lmax + "");
if (!typeMethods.i4_choose_check(n, k))
{
Console.WriteLine("");
Console.WriteLine("TEST04 - Warning!");
Console.WriteLine(" The binomial coefficient cannot be");
Console.WriteLine(" computed in integer arithmetic for");
Console.WriteLine(" this choice of parameters.");
return;
}
Console.WriteLine("");
int seed = 123456789;
for (j = 1; j <= 10; j++)
{
int l = UniformRNG.i4_uniform_ab(1, lmax, ref seed);
int[] c = Comb.comb(n, k, l);
string cout = " " + l.ToString().PadLeft(4) + ": ";
int i;
for (i = 0; i < k; i++)
{
cout += " " + c[i].ToString().PadLeft(4);
}
Console.WriteLine(cout);
}
}
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
});
}
}
