public static void scqf(int nt, double[] t, int[] mlt, double[] wts, int nwts, int[] ndx,
ref double[] swts, ref double[] st, int kind, double alpha, double beta, double a,
double b)
//****************************************************************************80
//
// Purpose:
//
// SCQF scales a quadrature formula to a nonstandard interval.
//
// Discussion:
//
// The arrays WTS and SWTS may coincide.
//
// The arrays T and ST may coincide.
//
// 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.
//
// 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 original knots.
//
// Input, int MLT[NT], the multiplicity of the knots.
//
// Input, double WTS[NWTS], the weights.
//
// Input, int NWTS, the number of weights.
//
// Input, int NDX[NT], used to index the array WTS.
// For more details see the comments in CAWIQ.
//
// Output, double SWTS[NWTS], the scaled weights.
//
// Output, double ST[NT], the scaled 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.
//
{
double al = 0;
double be = 0;
double shft = 0;
double slp = 0;
double temp = typeMethods.r8_epsilon();
PARCHK.parchk(kind, 1, alpha, beta);
switch (kind)
{
case 1:
{
al = 0.0;
be = 0.0;
if (Math.Abs(b - a) <= temp)
{
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" |B - A| too small.");
return;
}
shft = (a + b) / 2.0;
slp = (b - a) / 2.0;
break;
}
case 2:
{
al = -0.5;
be = -0.5;
if (Math.Abs(b - a) <= temp)
{
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" |B - A| too small.");
return;
}
shft = (a + b) / 2.0;
slp = (b - a) / 2.0;
break;
}
case 3:
{
al = alpha;
be = alpha;
if (Math.Abs(b - a) <= temp)
{
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" |B - A| too small.");
return;
}
shft = (a + b) / 2.0;
slp = (b - a) / 2.0;
break;
}
case 4:
{
al = alpha;
be = beta;
if (Math.Abs(b - a) <= temp)
{
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" |B - A| too small.");
return;
}
shft = (a + b) / 2.0;
slp = (b - a) / 2.0;
break;
}
case 5 when b <= 0.0:
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" B <= 0");
return;
case 5:
shft = a;
slp = 1.0 / b;
al = alpha;
be = 0.0;
break;
case 6 when b <= 0.0:
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" B <= 0.");
return;
case 6:
shft = a;
slp = 1.0 / Math.Sqrt(b);
al = alpha;
be = 0.0;
break;
case 7:
{
al = alpha;
be = 0.0;
if (Math.Abs(b - a) <= temp)
{
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" |B - A| too small.");
return;
}
shft = (a + b) / 2.0;
slp = (b - a) / 2.0;
break;
}
case 8 when a + b <= 0.0:
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" A + B <= 0.");
return;
case 8:
shft = a;
slp = a + b;
al = alpha;
be = beta;
break;
case 9:
{
al = 0.5;
be = 0.5;
if (Math.Abs(b - a) <= temp)
{
Console.WriteLine("");
Console.WriteLine("SCQF - Fatal error!");
Console.WriteLine(" |B - A| too small.");
return;
}
shft = (a + b) / 2.0;
slp = (b - a) / 2.0;
break;
}
}
double p = Math.Pow(slp, al + be + 1.0);
for (int k = 0; k < nt; k++)
{
st[k] = shft + slp * t[k];
int l = Math.Abs(ndx[k]);
if (l == 0)
{
continue;
}
double tmp = p;
for (int i = l - 1; i <= l - 1 + mlt[k] - 1; i++)
{
swts[i] = wts[i] * tmp;
tmp *= slp;
}
}
}
public static void cdgqf(int nt, int kind, double alpha, double beta, ref double[] t,
ref double[] wts)
//****************************************************************************80
//
// Purpose:
//
// CDGQF computes a Gauss quadrature formula with default A, B and simple knots.
//
// Discussion:
//
// This routine computes all the knots and weights of a Gauss quadrature
// formula with a classical weight function with default values for A and B,
// and only simple knots.
//
// There are no moments checks and no printing is done.
//
// Use routine EIQFS to evaluate a quadrature computed by CGQFS.
//
// 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,inf) (x-a)^alpha*exp(-b*(x-a))
// 6, Generalized Hermite, (-inf,inf) |x-a|^alpha*exp(-b*(x-a)^2)
// 7, Exponential, (a,b) |x-(a+b)/2.0|^alpha
// 8, Rational, (a,inf) (x-a)^alpha*(x+b)^beta
//
// Input, double ALPHA, the value of Alpha, if needed.
//
// Input, double BETA, the value of Beta, if needed.
//
// Output, double T[NT], the knots.
//
// Output, double WTS[NT], the weights.
//
{
PARCHK.parchk(kind, 2 * nt, alpha, beta);
//
// Get the Jacobi matrix and zero-th moment.
//
double[] aj = new double[nt];
double[] bj = new double[nt];
double zemu = Matrix.class_matrix(kind, nt, alpha, beta, ref aj, ref bj);
//
// Compute the knots and weights.
//
SGQF.sgqf(nt, aj, ref bj, zemu, ref t, ref wts);
}
public static double[] wm(int m, int kind, double alpha, double beta)
//****************************************************************************80
//
// Purpose:
//
// WM evaluates the first M moments of classical weight functions.
//
// Discussion:
//
// W(K) = Integral ( A <= X <= B ) X**(K-1) * W(X) dx
//
// 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.
//
// 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 M, the number of moments to evaluate.
//
// 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.
//
// Output, double WM[M], the first M moments.
//
{
double als;
int k;
double rk;
PARCHK.parchk(kind, m, alpha, beta);
double[] w = new double[m];
for (k = 2; k <= m; k += 2)
{
w[k - 1] = 0.0;
}
switch (kind)
{
case 1:
{
for (k = 1; k <= m; k += 2)
{
rk = k;
w[k - 1] = 2.0 / rk;
}
break;
}
case 2:
{
w[0] = Math.PI;
for (k = 3; k <= m; k += 2)
{
rk = k;
w[k - 1] = w[k - 3] * (rk - 2.0) / (rk - 1.0);
}
break;
}
case 3:
{
w[0] = Math.Sqrt(Math.PI) * typeMethods.r8_gamma(alpha + 1.0)
/ typeMethods.r8_gamma(alpha + 3.0 / 2.0);
for (k = 3; k <= m; k += 2)
{
rk = k;
w[k - 1] = w[k - 3] * (rk - 2.0) / (2.0 * alpha + rk);
}
break;
}
case 4:
{
als = alpha + beta + 1.0;
w[0] = Math.Pow(2.0, als) * typeMethods.r8_gamma(alpha + 1.0)
/ typeMethods.r8_gamma(als + 1.0) * typeMethods.r8_gamma(beta + 1.0);
for (k = 2; k <= m; k++)
{
double sum = 0.0;
double trm = 1.0;
rk = k;
int i;
for (i = 0; i <= (k - 2) / 2; i++)
{
double tmpa = trm;
int ja;
for (ja = 1; ja <= 2 * i; ja++)
{
tmpa = tmpa * (alpha + ja) / (als + ja);
}
int jb;
for (jb = 1; jb <= k - 2 * i - 1; jb++)
{
tmpa = tmpa * (beta + jb) / (als + 2 * i + jb);
}
tmpa = tmpa / (2 * i + 1.0) *
(2 * i * (beta + alpha) + beta - (rk - 1.0) * alpha)
/ (beta + rk - 2 * i - 1.0);
sum += tmpa;
trm = trm * (rk - 2 * i - 1.0)
/ (2 * i + 1.0) * (rk - 2 * i - 2.0) / (2 * i + 2.0);
}
if (k % 2 != 0)
{
double tmpb = 1.0;
for (i = 1; i <= k - 1; i++)
{
tmpb = tmpb * (alpha + i) / (als + i);
}
sum += tmpb;
}
w[k - 1] = sum * w[0];
}
break;
}
case 5:
{
w[0] = typeMethods.r8_gamma(alpha + 1.0);
for (k = 2; k <= m; k++)
{
rk = k;
w[k - 1] = (alpha + rk - 1.0) * w[k - 2];
}
break;
}
case 6:
{
w[0] = typeMethods.r8_gamma((alpha + 1.0) / 2.0);
for (k = 3; k <= m; k += 2)
{
rk = k;
w[k - 1] = w[k - 3] * (alpha + rk - 2.0) / 2.0;
}
break;
}
case 7:
{
als = alpha;
for (k = 1; k <= m; k += 2)
{
rk = k;
w[k - 1] = 2.0 / (rk + als);
}
break;
}
case 8:
{
w[0] = typeMethods.r8_gamma(alpha + 1.0)
* typeMethods.r8_gamma(-alpha - beta - 1.0)
/ typeMethods.r8_gamma(-beta);
for (k = 2; k <= m; k++)
{
rk = k;
w[k - 1] = -w[k - 2] * (alpha + rk - 1.0) / (alpha + beta + rk);
}
break;
}
case 9:
{
w[0] = Math.PI / 2.0;
for (k = 3; k <= m; k += 2)
{
rk = k;
w[k - 1] = w[k - 3] * (rk - 2.0) / (rk + 1.0);
}
break;
}
}
return(w);
}
public static double class_matrix(int kind, int m, double alpha, double beta, ref double[] aj,
ref double[] bj)
//****************************************************************************80
//
// Purpose:
//
// CLASS_MATRIX computes the Jacobi matrix for a quadrature rule.
//
// Discussion:
//
// This routine computes the diagonal AJ and sub-diagonal BJ
// elements of the order M tridiagonal symmetric Jacobi matrix
// associated with the polynomials orthogonal with respect to
// the weight function specified by KIND.
//
// For weight functions 1-7, M elements are defined in BJ even
// though only M-1 are needed. For weight function 8, BJ(M) is
// set to zero.
//
// The zero-th moment of the weight function is returned in ZEMU.
//
// 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 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,inf) (x-a)^alpha*exp(-b*(x-a))
// 6, Generalized Hermite, (-inf,inf) |x-a|^alpha*exp(-b*(x-a)^2)
// 7, Exponential, (a,b) |x-(a+b)/2.0|^alpha
// 8, Rational, (a,inf) (x-a)^alpha*(x+b)^beta
//
// Input, int M, the order of the Jacobi matrix.
//
// Input, double ALPHA, the value of Alpha, if needed.
//
// Input, double BETA, the value of Beta, if needed.
//
// Output, double AJ[M], BJ[M], the diagonal and subdiagonal
// of the Jacobi matrix.
//
// Output, double CLASS_MATRIX, the zero-th moment.
//
{
double ab;
double abi;
double abj;
int i;
double zemu = 0;
double temp = typeMethods.r8_epsilon();
PARCHK.parchk(kind, 2 * m - 1, alpha, beta);
const double temp2 = 0.5;
if (500.0 * temp < Math.Abs(Math.Pow(Helpers.Gamma(temp2), 2) - Math.PI))
{
Console.WriteLine("");
Console.WriteLine("CLASS_MATRIX - Fatal error!");
Console.WriteLine(" Gamma function does not match machine parameters.");
return(1);
}
switch (kind)
{
case 1:
{
ab = 0.0;
zemu = 2.0 / (ab + 1.0);
for (i = 0; i < m; i++)
{
aj[i] = 0.0;
}
for (i = 1; i <= m; i++)
{
abi = i + ab * (i % 2);
abj = 2 * i + ab;
bj[i - 1] = Math.Sqrt(abi * abi / (abj * abj - 1.0));
}
break;
}
case 2:
{
zemu = Math.PI;
for (i = 0; i < m; i++)
{
aj[i] = 0.0;
}
bj[0] = Math.Sqrt(0.5);
for (i = 1; i < m; i++)
{
bj[i] = 0.5;
}
break;
}
case 3:
{
ab = alpha * 2.0;
zemu = Math.Pow(2.0, ab + 1.0) * Math.Pow(Helpers.Gamma(alpha + 1.0), 2)
/ Helpers.Gamma(ab + 2.0);
for (i = 0; i < m; i++)
{
aj[i] = 0.0;
}
bj[0] = Math.Sqrt(1.0 / (2.0 * alpha + 3.0));
for (i = 2; i <= m; i++)
{
bj[i - 1] = Math.Sqrt(i * (i + ab) / (4.0 * Math.Pow(i + alpha, 2) - 1.0));
}
break;
}
case 4:
{
ab = alpha + beta;
abi = 2.0 + ab;
zemu = Math.Pow(2.0, ab + 1.0) * Helpers.Gamma(alpha + 1.0)
* Helpers.Gamma(beta + 1.0) / Helpers.Gamma(abi);
aj[0] = (beta - alpha) / abi;
bj[0] = Math.Sqrt(4.0 * (1.0 + alpha) * (1.0 + beta)
/ ((abi + 1.0) * abi * abi));
double a2b2 = beta * beta - alpha * alpha;
for (i = 2; i <= m; i++)
{
abi = 2.0 * i + ab;
aj[i - 1] = a2b2 / ((abi - 2.0) * abi);
abi *= abi;
bj[i - 1] = Math.Sqrt(4.0 * i * (i + alpha) * (i + beta) * (i + ab)
/ ((abi - 1.0) * abi));
}
break;
}
case 5:
{
zemu = Helpers.Gamma(alpha + 1.0);
for (i = 1; i <= m; i++)
{
aj[i - 1] = 2.0 * i - 1.0 + alpha;
bj[i - 1] = Math.Sqrt(i * (i + alpha));
}
break;
}
case 6:
{
zemu = Helpers.Gamma((alpha + 1.0) / 2.0);
for (i = 0; i < m; i++)
{
aj[i] = 0.0;
}
for (i = 1; i <= m; i++)
{
bj[i - 1] = Math.Sqrt((i + alpha * (i % 2)) / 2.0);
}
break;
}
case 7:
{
ab = alpha;
zemu = 2.0 / (ab + 1.0);
for (i = 0; i < m; i++)
{
aj[i] = 0.0;
}
for (i = 1; i <= m; i++)
{
abi = i + ab * (i % 2);
abj = 2 * i + ab;
bj[i - 1] = Math.Sqrt(abi * abi / (abj * abj - 1.0));
}
break;
}
case 8:
{
ab = alpha + beta;
zemu = Helpers.Gamma(alpha + 1.0) * Helpers.Gamma(-(ab + 1.0))
/ Helpers.Gamma(-beta);
double apone = alpha + 1.0;
double aba = ab * apone;
aj[0] = -apone / (ab + 2.0);
bj[0] = -aj[0] * (beta + 1.0) / (ab + 2.0) / (ab + 3.0);
double abti;
for (i = 2; i <= m; i++)
{
abti = ab + 2.0 * i;
aj[i - 1] = aba + 2.0 * (ab + i) * (i - 1);
aj[i - 1] = -aj[i - 1] / abti / (abti - 2.0);
}
for (i = 2; i <= m - 1; i++)
{
abti = ab + 2.0 * i;
bj[i - 1] = i * (alpha + i) / (abti - 1.0) * (beta + i)
/ (abti * abti) * (ab + i) / (abti + 1.0);
}
bj[m - 1] = 0.0;
for (i = 0; i < m; i++)
{
bj[i] = Math.Sqrt(bj[i]);
}
break;
}
case 9:
{
zemu = Math.PI / 2.0;
for (i = 0; i < m; i++)
{
aj[i] = 0.0;
}
for (i = 0; i < m; i++)
{
bj[i] = 0.5;
}
break;
}
}
return(zemu);
}
public static void chkqf(double[] t, double[] wts, int[] mlt, int nt, int nwts, int[] ndx,
int key, int mop, int mex, int kind, double alpha, double beta, int lo,
double a, double b)
//****************************************************************************80
//
// Purpose:
//
// CHKQF computes and prints the moments of a quadrature formula.
//
// Discussion:
//
// The quadrature formula is based on a clasical weight function with
// any valid A, B.
//
// No check can be made for non-classical weight functions.
//
// 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.
//
// 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, double T[NT], the knots.
//
// Input, double WTS[NWTS], the weights.
//
// Input, int MLT[NT], the multiplicity of the knots.
//
// Input, int NT, the number of knots.
//
// Input, int NWTS, the number of weights.
//
// Input, int NDX[NT], used to index the 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 MOP, the expected order of precision of the
// quadrature formula.
//
// Input, int MEX, the number of moments required to be
// tested. Set MEX = 1 and LO < 0 for no moments check.
//
// 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, selects the action to carry out.
// > 0, print weights and moment tests.
// = 0, print nothing. compute moment test.
// < 0, print weights only. don't compute moment tests.
//
// Input, double A, B, the interval endpoints.
//
{
double tmp = 0;
double[] w = new double[mex];
PARCHK.parchk(kind, mex, alpha, beta);
if (lo != 0)
{
const int izero = 0;
Console.WriteLine("");
Console.WriteLine(" Interpolatory quadrature formula");
Console.WriteLine("");
Console.WriteLine(" Type Interval Weight function Name");
Console.WriteLine("");
switch (kind)
{
case 1:
Console.WriteLine(" 1 (a,b) 1.0 Legendre");
break;
case 2:
Console.WriteLine(" 2 (a,b) ((b-x)*(x-a))^(-0.5) Chebyshev Type 1");
break;
case 3:
Console.WriteLine(" 3 (a,b) ((b-x)*(x-a))^alpha Gegenbauer");
break;
case 4:
Console.WriteLine(" 4 (a,b) (b-x)^alpha*(x-a)^beta Jacobi");
break;
case 5:
Console.WriteLine(" 5 (a,+oo) (x-a)^alpha*exp(-b*(x-a)) Gen Laguerre");
break;
case 6:
Console.WriteLine(" 6 (-oo,+oo) |x-a|^alpha*exp(-b*(x-a)^2) Gen Hermite");
break;
case 7:
Console.WriteLine(" 7 (a,b) |x-(a+b)/2.0|^alpha Exponential");
break;
case 8:
Console.WriteLine(" 8 (a,+oo) (x-a)^alpha*(x+b)^beta Rational");
break;
case 9:
Console.WriteLine(" 9 (a,b) (b-x)*(x-a)^(+0.5) Chebyshev Type 2");
break;
}
Console.WriteLine("");
Console.WriteLine(" Parameters A " + a + "");
Console.WriteLine(" B " + b + "");
switch (kind)
{
case >= 3 and <= 8:
Console.WriteLine(" alpha " + alpha + "");
break;
}
switch (kind)
{
case 4:
case 8:
Console.WriteLine(" beta " + beta + "");
break;
}
CHKQFS.chkqfs(t, wts, mlt, nt, nwts, ndx, key, ref w, mop, mex, izero,
alpha, beta, -Math.Abs(lo));
}
switch (lo)
{
case >= 0:
{
//
// Compute the moments in W.
//
w = SCMM.scmm(mex, kind, alpha, beta, a, b);
switch (kind)
{
case 1:
case 2:
case 3:
case 4:
case 7:
case 9:
tmp = (b + a) / 2.0;
break;
case 5:
case 6:
case 8:
tmp = a;
break;
}
double[] t2 = new double[nt];
int i;
for (i = 0; i < nt; i++)
{
t2[i] = t[i] - tmp;
}
const int neg = -1;
//
// Check moments.
//
CHKQFS.chkqfs(t2, wts, mlt, nt, nwts, ndx, key, ref w, mop, mex, neg, alpha, beta,
lo);
break;
}
}
}
public static double[] wtfn(double[] t, int nt, int kind, double alpha, double beta)
//****************************************************************************80
//
// Purpose:
//
// WTFN evaluates the classical weight functions at given points.
//
// 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.
//
// 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, double T[NT], the points where the weight function
// is to be evaluated.
//
// Input, int NT, the number of evaluation points.
//
// 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.
//
// Output, double WTFN[NT], the value of the weight function.
//
{
int i;
PARCHK.parchk(kind, 1, alpha, beta);
double[] w = new double[nt];
switch (kind)
{
case 1:
{
for (i = 0; i < nt; i++)
{
w[i] = 1.0;
}
break;
}
case 2:
{
for (i = 0; i < nt; i++)
{
w[i] = 1.0 / Math.Sqrt((1.0 - t[i]) * (1.0 + t[i]));
}
break;
}
case 3 when alpha == 0.0:
{
for (i = 0; i < nt; i++)
{
w[i] = 1.0;
}
break;
}
case 3:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Pow((1.0 - t[i]) * (1.0 + t[i]), alpha);
}
break;
}
case 4:
{
switch (alpha)
{
case 0.0:
{
for (i = 0; i < nt; i++)
{
w[i] = 1.0;
}
break;
}
default:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Pow(1.0 - t[i], alpha);
}
break;
}
}
if (beta != 0.0)
{
for (i = 0; i < nt; i++)
{
w[i] *= Math.Pow(1.0 + t[i], beta);
}
}
break;
}
case 5 when alpha == 0.0:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Exp(-t[i]);
}
break;
}
case 5:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Exp(-t[i]) * Math.Pow(t[i], alpha);
}
break;
}
case 6 when alpha == 0.0:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Exp(-t[i] * t[i]);
}
break;
}
case 6:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Exp(-t[i] * t[i]) * Math.Pow(Math.Abs(t[i]), alpha);
}
break;
}
case 7 when alpha != 0.0:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Pow(Math.Abs(t[i]), alpha);
}
break;
}
case 7:
{
for (i = 0; i < nt; i++)
{
w[i] = 1.0;
}
break;
}
case 8:
{
switch (alpha)
{
case 0.0:
{
for (i = 0; i < nt; i++)
{
w[i] = 1.0;
}
break;
}
default:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Pow(t[i], alpha);
}
break;
}
}
if (beta != 0.0)
{
for (i = 0; i < nt; i++)
{
w[i] *= Math.Pow(1.0 + t[i], beta);
}
}
break;
}
case 9:
{
for (i = 0; i < nt; i++)
{
w[i] = Math.Sqrt((1.0 - t[i]) * (1.0 + t[i]));
}
break;
}
}
return(w);
}