private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 tests CIQFS.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 16 February 2010
//
// Author:
//
// Original FORTRAN77 version by Sylvan Elhay, Jaroslav Kautsky.
// C++ version by John Burkardt.
//
{
int kind;
Console.WriteLine(" ----------------------------------------");
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" Test CIQF, CIQFS, CGQF and CGQFS");
Console.WriteLine(" with all classical weight functions.");
//
// Try all weight functions.
//
for (kind = 1; kind <= 9; kind++)
{
//
// Number of knots.
//
const int nt = 5;
//
// Set parameters ALPHA and BETA.
//
const double alpha = 0.5;
double beta;
if (kind != 8)
{
beta = 2.0;
}
else
{
beta = -16.0;
}
//
// Set A and B.
//
const double a = -0.5;
const double b = 2.0;
//
// Have CGQF compute the knots and weights.
//
int lu = 6;
double[] t = new double[nt];
double[] wts = new double[nt];
Console.WriteLine("");
Console.WriteLine(" Knots and weights of Gauss quadrature formula");
Console.WriteLine(" computed by CGQF.");
CGQF.cgqf(nt, kind, alpha, beta, a, b, lu, ref t, ref wts);
//
// Now compute the weights for the same knots by CIQF.
//
// Set the knot multiplicities.
//
int[] mlt = new int[nt];
int i;
for (i = 0; i < nt; i++)
{
mlt[i] = 2;
}
//
// Set the size of the weights array.
//
int nwts = 0;
for (i = 0; i < nt; i++)
{
nwts += mlt[i];
}
//
// We need to deallocate and reallocate WTS because it is now of
// dimension NWTS rather than NT.
//
wts = new double[nwts];
//
// Because KEY = 1, NDX will be set up for us.
//
int[] ndx = new int[nt];
//
// KEY = 1 indicates that the WTS array should hold the weights
// in the usual order.
//
const int key = 1;
//
// LU controls printing.
// A positive value requests that we compute and print weights, and
// conduct a moments check.
//
lu = 6;
Console.WriteLine("");
Console.WriteLine(" Weights of Gauss quadrature formula computed from the");
Console.WriteLine(" knots by CIQF.");
wts = CIQF.ciqf(nt, t, mlt, nwts, ref ndx, key, kind, alpha, beta, a, b, lu);
}
}
public static double ceiqf(int nt, double[] t, int[] mlt, int kind, double alpha,
double beta, double a, double b, Func <double, int, double> f)
//****************************************************************************80
//
// Purpose:
//
// CEIQF constructs and applies a quadrature formula based on user knots.
//
// Discussion:
//
// The knots may have multiplicity. The quadrature interval is over
// any valid A, B. A classical weight function is selected by the user.
//
// 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, double T[NT], the knots.
//
// Input, int MLT[NT], the multiplicity of the 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 A, B, the interval endpoints.
//
// 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 highest value of I will be the maximum value in MLT minus
// one. The value X will always be a knot.
//
// Output, double CEIQF, the value of the quadrature formula
// applied to F.
//
{
int i;
const int lu = 0;
int n = 0;
for (i = 0; i < nt; i++)
{
n += mlt[i];
}
const int key = 1;
int[] ndx = new int[nt];
double[] wts = CIQF.ciqf(nt, t, mlt, n, ref ndx, key, kind, alpha, beta, a, b, lu);
double qfsum = EIQF.eiqf(nt, t, mlt, wts, n, ndx, key, f);
return(qfsum);
}
public static double[] cliqf(int nt, double[] t, int kind, double alpha, double beta,
double a, double b, int lo)
//****************************************************************************80
//
// Purpose:
//
// CLIQF computes a classical quadrature formula, with optional printing.
//
// Discussion:
//
// This routine computes all the weights of an interpolatory
// quadrature formula with
// 1. only simple knots and
// 2. a classical weight function with any valid A and B, and
// 3. optionally prints the knots and weights and a check of the moments.
//
// To evaluate this quadrature formula for a given function F,
// call routine EIQFS.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 07 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, double T[NT], the 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 A, B, the interval endpoints.
//
// Input, int LO, indicates what is to be done.
// > 0, compute and print weights and moments check.
// = 0, compute weights.
// < 0, compute and print weights.
//
// Output, double CLIQF[NT], the weights.
//
{
int i;
const int key = 1;
int[] mlt = new int[nt];
for (i = 0; i < nt; i++)
{
mlt[i] = 1;
}
int[] ndx = new int[nt];
double[] wts = CIQF.ciqf(nt, t, mlt, nt, ref ndx, key, kind, alpha, beta, a, b, lo);
return(wts);
}