private static void test01(int nt)
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests CIRCLE_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 06 April 2014
//
// Author:
//
// John Burkardt
//
{
int[] e = new int[2];
int e1;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" CIRCLE_RULE can compute a rule Q(f) for the unit circle");
Console.WriteLine(" using NT equally spaced angles.");
Console.WriteLine(" Estimate integrals I(f) where f = x^e(1) * y^e(2)");
Console.WriteLine(" using " + nt + " points.");
//
// Compute the quadrature rule.
//
double[] w = new double[nt];
double[] t = new double[nt];
QuadratureRule.circle_rule(nt, ref w, ref t);
//
// Apply it to integrands.
//
Console.WriteLine("");
Console.WriteLine(" E(1) E(2) I(f) Q(f)");
Console.WriteLine("");
//
// Specify a monomial.
//
for (e1 = 0; e1 <= 6; e1 += 2)
{
e[0] = e1;
int e2;
for (e2 = e1; e2 <= 6; e2 += 2)
{
e[1] = e2;
double q = 0.0;
int i;
for (i = 0; i < nt; i++)
{
double x = Math.Cos(t[i]);
double y = Math.Sin(t[i]);
q += w[i] * Math.Pow(x, e[0]) * Math.Pow(y, e[1]);
}
q = 2.0 * Math.PI * q;
double exact = Integrals.circle01_monomial_integral(e);
Console.WriteLine(" " + e[0].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + e[1].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + q.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
}