public static double[] ciqf(int nt, double[] t, int[] mlt, int nwts, ref int[] ndx, int key,
int kind, double alpha, double beta, double a, double b, int lo)
//****************************************************************************80
//
// Purpose:
//
// CIQF computes weights for a classical weight function and any interval.
//
// Discussion:
//
// This routine compute somes or all the weights of a quadrature formula
// for a classical weight function with any valid A, B and a given set of
// knots and multiplicities.
//
// The weights may be packed into the output array WTS according to a
// user-defined pattern or sequentially.
//
// The routine will also optionally print knots and weights and a check
// of the moments.
//
// 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 MLT[NT], the multiplicity of the knots.
//
// Input, int NWTS, the number of weights.
//
// Input/output, int NDX[NT], used to index the output
// array WTS. If KEY = 1, then NDX need not be preset. For more
// details see the comments in CAWIQ.
//
// Input, int KEY, indicates the structure of the WTS
// array. It will normally be set to 1. This will cause the weights to be
// packed sequentially in array WTS. For more details see the comments
// in CAWIQ.
//
// 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, selects the actions to perform.
// > 0, compute and print weights. Print moments check.
// = 0, compute weights.
// < 0, compute and print weights.
//
// Output, double CIQF[NWTS], the weights.
//
{
int j;
int m = 1;
int l = Math.Abs(key);
for (j = 0; j < nt; j++)
{
if (l == 1 || Math.Abs(ndx[j]) != 0)
{
m += mlt[j];
}
}
if (nwts + 1 < m)
{
Console.WriteLine("");
Console.WriteLine("CIQF - Fatal error!");
Console.WriteLine(" NWTS + 1 < M.");
return(null);
}
int mex = 2 + m;
//
// Scale the knots to default A, B.
//
double[] st = SCT.sct(nt, t, kind, a, b);
//
// Compute the weights.
//
const int lu = 0;
double[] wts = CIQFS.ciqfs(nt, st, mlt, nwts, ref ndx, key, kind, alpha, beta, lu);
//
// Don't scale user's knots - only scale weights.
//
SCQF.scqf(nt, st, mlt, wts, nwts, ndx, ref wts, ref st, kind, alpha, beta, a, b);
if (lo == 0)
{
return(wts);
}
int mop = m - 1;
CHKQF.chkqf(t, wts, mlt, nt, nwts, ndx, key, mop, mex, kind,
alpha, beta, lo, a, b);
return(wts);
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests CIQFS.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 05 January 2010
//
// Author:
//
// Original FORTRAN77 version by Sylvan Elhay, Jaroslav Kautsky.
// C++ version by John Burkardt.
//
{
int i;
Console.WriteLine(" ----------------------------------------");
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Test CIQFS.");
//
// Number of knots.
//
int nt = 5;
//
// Set the knots in the default interval [-1,+1].
//
double[] t = new double[nt];
for (i = 1; i <= nt; i++)
{
t[i - 1] = Math.Cos((2 * i - 1) * Math.PI / (2 * nt));
}
//
// Set the knot multiplicities.
//
int[] mlt = new int[nt];
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];
}
//
// 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;
//
// Request Legendre weight function.
//
const int kind = 1;
//
// ALPHA, BETA not used in Legendre weight function but set anyway.
//
const double alpha = 0.0;
const double beta = 0.0;
//
// LU controls printing.
// A positive value requests that we compute and print weights, and
// conduct a moments check.
//
const int lu = 6;
//
// This call returns the WTS array.
//
CIQFS.ciqfs(nt, t, mlt, nwts, ref ndx, key, kind, alpha, beta, lu);
}
public static double[] cliqfs(int nt, double[] t, int kind, double alpha, double beta,
int lo)
//****************************************************************************80
//
// Purpose:
//
// CLIQFS computes the weights of a quadrature formula in the default interval.
//
// Discussion:
//
// This routine computes the weights of an interpolatory quadrature formula
// with a classical weight function, in the default interval A, B,
// using only simple knots.
//
// It can optionally print knots and weights and a check of the moments.
//
// To evaluate a quadrature computed by CLIQFS, call 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, int LO, chooses the printing option.
// > 0, compute weights, print them, print the moment check results.
// 0, compute weights.
// < 0, compute weights and print them.
//
// Output, double CLIQFS[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 = CIQFS.ciqfs(nt, t, mlt, nt, ref ndx, key, kind, alpha, beta, lo);
return(wts);
}
public static double ceiqfs(int nt, double[] t, int[] mlt, int kind, double alpha,
double beta, Func <double, int, double> f)
//****************************************************************************80
//
// Purpose:
//
// CEIQFS computes and applies a quadrature formula based on user knots.
//
// Discussion:
//
// The knots may have multiplicity. The quadrature interval is over
// the standard interval A, B for the classical weight function selected
// by the user.
//
// 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 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 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 CEIQFS, 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];
}
int[] ndx = new int[nt];
const int key = 1;
double[] wts = CIQFS.ciqfs(nt, t, mlt, n, ref ndx, key, kind, alpha, beta, lu);
double qfsum = EIQF.eiqf(nt, t, mlt, wts, n, ndx, key, f);
return(qfsum);
}