private static void test14()
//****************************************************************************80
//
// Purpose:
//
// TEST14 demonstrates R_JACOBI.
//
// Discussion:
//
// R_JACOBI returns recursion coefficients ALPHA and BETA for rules
// using a Jacobi type weight w(x) = (1-x)^A * (1+x)^B.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 17 July 2013
//
// Author:
//
// John Burkardt
//
// Reference
//
// Walter Gautschi,
// Orthogonal Polynomials: Computation and Approximation,
// Oxford, 2004,
// ISBN: 0-19-850672-4,
// LC: QA404.5 G3555.
//
{
int i;
Console.WriteLine("");
Console.WriteLine("TEST14");
Console.WriteLine(" R_JACOBI computes recursion coefficients ALPHA and BETA");
Console.WriteLine(" Gauss quadrature rule, given the ALPHA and BETA");
Console.WriteLine(" recursion coefficients.");
//
// Legendre rule.
//
int n = 10;
double a = 0.0;
double b = 0.0;
double[] alpha = new double[n];
double[] beta = new double[n];
Jacobi.r_jacobi(n, a, b, ref alpha, ref beta);
Console.WriteLine("");
Console.WriteLine(" Legendre weight");
Console.WriteLine(" A = " + a + ", B = " + b + "");
Console.WriteLine(" Alpha Beta");
Console.WriteLine("");
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + alpha[i].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + beta[i].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
//
// Chebyshev Type 1 rule.
//
n = 10;
a = -0.5;
b = -0.5;
alpha = new double[n];
beta = new double[n];
Jacobi.r_jacobi(n, a, b, ref alpha, ref beta);
Console.WriteLine("");
Console.WriteLine(" Chebyshev Type 1 weight");
Console.WriteLine(" A = " + a + ", B = " + b + "");
Console.WriteLine(" Alpha Beta");
Console.WriteLine("");
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + alpha[i].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + beta[i].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
//
// Chebyshev Type 2 rule.
//
n = 10;
a = +0.5;
b = +0.5;
alpha = new double[n];
beta = new double[n];
Jacobi.r_jacobi(n, a, b, ref alpha, ref beta);
Console.WriteLine("");
Console.WriteLine(" Chebyshev Type 2 weight");
Console.WriteLine(" A = " + a + ", B = " + b + "");
Console.WriteLine(" Alpha Beta");
Console.WriteLine("");
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + alpha[i].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + beta[i].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
//
// General Jacobi rule.
//
n = 10;
a = +0.5;
b = +1.5;
alpha = new double[n];
beta = new double[n];
Jacobi.r_jacobi(n, a, b, ref alpha, ref beta);
Console.WriteLine("");
Console.WriteLine(" General Jacobi weight");
Console.WriteLine(" A = " + a + ", B = " + b + "");
Console.WriteLine(" Alpha Beta");
Console.WriteLine("");
for (i = 0; i < n; i++)
{
Console.WriteLine(" " + alpha[i].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + beta[i].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}