private static void test02(int m)
//****************************************************************************80
//
// Purpose:
//
// TEST02 seeks Fekete points in [-1,+1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 13 April 2014
//
// Author:
//
// John Burkardt
//
// Reference:
//
// L Bos, N Levenberg,
// On the calculation of approximate Fekete points: the univariate case,
// Electronic Transactions on Numerical Analysis,
// Volume 30, pages 377-397, 2008.
//
// Parameters:
//
// Input, int M, the dimension of the polynomial space.
//
{
const int N = 5001;
int nf = 0;
const double a = -1.0;
const double b = +1.0;
double[] x = typeMethods.r8vec_linspace_new(N, a, b);
Console.WriteLine("");
Console.WriteLine("TEST02:");
Console.WriteLine(" Seek Fekete points in [" + a + "," + b + "]");
Console.WriteLine(" using " + N + " equally spaced sample points");
Console.WriteLine(" for polynomials of degree M = " + m + "");
Console.WriteLine(" with the Chebyshev basis.");
double[] wf = new double[m];
double[] xf = new double[m];
LineFekete.line_fekete_chebyshev(m, a, b, N, x, ref nf, ref xf, ref wf);
Console.WriteLine("");
Console.WriteLine(" NF = " + nf + "");
typeMethods.r8vec_print(nf, xf, " Estimated Fekete points XF:");
double wf_sum = typeMethods.r8vec_sum(nf, wf);
Console.WriteLine("");
Console.WriteLine(" Sum(WF) = " + wf_sum + "");
}
private static void test03(int m)
//****************************************************************************80
//
// Purpose:
//
// TEST03 seeks Fekete points in [-1,+1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 13 April 2014
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int M, the dimension of the polynomial space.
//
{
const int N = 5001;
int nf = 0;
const double a = -1.0;
const double b = +1.0;
double[] x = typeMethods.r8vec_linspace_new(N, a, b);
Console.WriteLine("");
Console.WriteLine("TEST03:");
Console.WriteLine(" Seek Fekete points in [" + a + "," + b + "]");
Console.WriteLine(" using " + N + " equally spaced sample points");
Console.WriteLine(" for polynomials of degree M = " + m + "");
Console.WriteLine(" with the Legendre basis and uniform weight.");
double[] wf = new double[m];
double[] xf = new double[m];
LineFekete.line_fekete_legendre(m, a, b, N, x, ref nf, ref xf, ref wf);
Console.WriteLine("");
Console.WriteLine(" NF = " + nf + "");
typeMethods.r8vec_print(nf, xf, " Estimated Fekete points XF:");
double wf_sum = typeMethods.r8vec_sum(nf, wf);
Console.WriteLine("");
Console.WriteLine(" Sum(WF) = " + wf_sum + "");
}
private static void test01(int m)
//****************************************************************************80
//
// Purpose:
//
// TEST01 seeks Fekete points in [-1,+1].
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 13 April 2014
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Alvise Sommariva, Marco Vianello,
// Computing approximate Fekete points by QR factorizations of Vandermonde
// matrices,
// Computers and Mathematics with Applications,
// Volume 57, 2009, pages 1324-1336.
//
// Parameters:
//
// Input, int M, the dimension of the polynomial space.
//
{
const int N = 5001;
int nf = 0;
const double a = -1.0;
const double b = +1.0;
double[] x = typeMethods.r8vec_linspace_new(N, a, b);
Console.WriteLine("");
Console.WriteLine("TEST01:");
Console.WriteLine(" Seek Fekete points in [" + a + "," + b + "]");
Console.WriteLine(" using " + N + " equally spaced sample points");
Console.WriteLine(" for polynomials of degree M = " + m + "");
Console.WriteLine(" using the monomial basis and uniform weight.");
double[] wf = new double[m];
double[] xf = new double[m];
LineFekete.line_fekete_monomial(m, a, b, N, x, ref nf, ref xf, ref wf);
Console.WriteLine("");
Console.WriteLine(" NF = " + nf + "");
typeMethods.r8vec_print(nf, xf, " Estimated Fekete points XF:");
double wf_sum = typeMethods.r8vec_sum(nf, wf);
Console.WriteLine("");
Console.WriteLine(" Sum(WF) = " + wf_sum + "");
}
