private static void test09()
//****************************************************************************80
//
// Purpose:
//
// TEST09 calls CGQFS to compute and print generalized Gauss-Hermite rules.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 09 January 2009
//
// Author:
//
// John Burkardt
//
{
Console.WriteLine("");
Console.WriteLine("TEST09");
Console.WriteLine(" Call CGQFS to compute generalized Hermite rules.");
const int nt = 15;
const int kind = 6;
const double alpha = 1.0;
const double beta = 0.0;
const int io = -6;
double[] t = new double[nt];
double[] wts = new double[nt];
Console.WriteLine("");
Console.WriteLine(" NT = " + nt + "");
Console.WriteLine(" ALPHA = " + alpha + "");
CGQFS.cgqfs(nt, kind, alpha, beta, io, ref t, ref wts);
}
public static double cegqfs(int nt, int kind, double alpha, double beta,
Func <double, int, double> f)
//****************************************************************************80
//
// Purpose:
//
// CEGQFS estimates an integral using a standard quadrature formula.
//
// Discussion:
//
// The user chooses one of the standard quadrature rules
// with the default values of A and B. This routine determines
// the corresponding weights and evaluates the quadrature formula
// on a given function.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 08 January 2010
//
// Author:
//
// Original FORTRAN77 version by Sylvan Elhay, Jaroslav Kautsky.
// C++ version by John Burkardt.
//
// Reference:
//
// Sylvan Elhay, Jaroslav Kautsky,
// Algorithm 655: IQPACK, FORTRAN Subroutines for the Weights of
// Interpolatory Quadrature,
// ACM Transactions on Mathematical Software,
// Volume 13, Number 4, December 1987, pages 399-415.
//
// Parameters:
//
// Input, int NT, the number of knots.
//
// Input, int KIND, the rule.
// 1, Legendre, (a,b) 1.0
// 2, Chebyshev Type 1, (a,b) ((b-x)*(x-a))^-0.5)
// 3, Gegenbauer, (a,b) ((b-x)*(x-a))^alpha
// 4, Jacobi, (a,b) (b-x)^alpha*(x-a)^beta
// 5, Generalized Laguerre, (a,+oo) (x-a)^alpha*exp(-b*(x-a))
// 6, Generalized Hermite, (-oo,+oo) |x-a|^alpha*exp(-b*(x-a)^2)
// 7, Exponential, (a,b) |x-(a+b)/2.0|^alpha
// 8, Rational, (a,+oo) (x-a)^alpha*(x+b)^beta
// 9, Chebyshev Type 2, (a,b) ((b-x)*(x-a))^(+0.5)
//
// Input, double ALPHA, the value of Alpha, if needed.
//
// Input, double BETA, the value of Beta, if needed.
//
// Input, double F ( double X, int I ), the name of a routine which
// evaluates the function and some of its derivatives. The routine
// must return in F the value of the I-th derivative of the function
// at X. The value I will always be 0. The value X will always be a knot.
//
// Output, double CEGQFS, the value of the quadrature formula
// applied to F.
//
{
const int lu = 0;
double[] t = new double[nt];
double[] wts = new double[nt];
CGQFS.cgqfs(nt, kind, alpha, beta, lu, ref t, ref wts);
//
// Evaluate the quadrature sum.
//
double qfsum = EIQFS.eiqfs(nt, t, wts, f);
return(qfsum);
}