public static void p_integral_test()
//****************************************************************************80
//
// Purpose:
//
// P_INTEGRAL_TEST tests P_INTEGRAL.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 15 March 2016
//
// Author:
//
// John Burkardt
//
{
int n;
Console.WriteLine("");
Console.WriteLine("P_INTEGRAL_TEST:");
Console.WriteLine(" P_INTEGRAL returns the integral of P(n,x) over [-1,+1].");
Console.WriteLine("");
Console.WriteLine(" N Integral");
Console.WriteLine("");
for (n = 0; n <= 10; n++)
{
double value = Legendre.p_integral(n);
Console.WriteLine(" " + n.ToString(CultureInfo.InvariantCulture).PadLeft(4)
+ " " + value.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
public static void p_quadrature_rule_test()
//****************************************************************************80
//
// Purpose:
//
// P_QUADRATURE_RULE_TEST tests P_QUADRATURE_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 14 March 2012
//
// Author:
//
// John Burkardt
//
{
int e;
Console.WriteLine("");
Console.WriteLine("P_QUADRATURE_RULE_TEST:");
Console.WriteLine(" P_QUADRATURE_RULE computes the quadrature rule");
Console.WriteLine(" associated with P(n,x)");
const int n = 7;
double[] x = new double[n];
double[] w = new double[n];
LegendreQuadrature.p_quadrature_rule(n, ref x, ref w);
typeMethods.r8vec2_print(n, x, w, " X W");
Console.WriteLine("");
Console.WriteLine(" Use the quadrature rule to estimate:");
Console.WriteLine("");
Console.WriteLine(" Q = Integral ( -1 <= X <= +1.0 ) X^E dx");
Console.WriteLine("");
Console.WriteLine(" E Q_Estimate Q_Exact");
Console.WriteLine("");
double[] f = new double[n];
for (e = 0; e <= 2 * n - 1; e++)
{
int i;
switch (e)
{
case 0:
{
for (i = 0; i < n; i++)
{
f[i] = 1.0;
}
break;
}
default:
{
for (i = 0; i < n; i++)
{
f[i] = Math.Pow(x[i], e);
}
break;
}
}
double q = typeMethods.r8vec_dot_product(n, w, f);
double q_exact = Legendre.p_integral(e);
Console.WriteLine(" " + e.ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + q.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + q_exact.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}