private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 compares exact and estimated monomial integrals.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 14 April 2014
//
// Author:
//
// John Burkardt
//
{
const int e_max = 6;
int e3;
int[] expon = new int[3];
const int m = 3;
const int n = 500000;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Compare exact and estimated integrals ");
Console.WriteLine(" over the unit pyramid in 3D.");
//
// Get sample points.
//
int seed = 123456789;
double[] x = Integrals.pyramid01_sample(n, ref seed);
Console.WriteLine("");
Console.WriteLine(" Number of sample points used is " + n + "");
Console.WriteLine("");
Console.WriteLine(" E1 E2 E3 MC-Estimate Exact Error");
Console.WriteLine("");
//
// Check all monomials, with only even dependence on X or Y,
// up to total degree E_MAX.
//
for (e3 = 0; e3 <= e_max; e3++)
{
expon[2] = e3;
int e2;
for (e2 = 0; e2 <= e_max - e3; e2 += 2)
{
expon[1] = e2;
int e1;
for (e1 = 0; e1 <= e_max - e3 - e2; e1 += 2)
{
expon[0] = e1;
double[] value = Monomial.monomial_value(m, n, expon, x);
double q = Integrals.pyramid01_volume() * typeMethods.r8vec_sum(n, value) / n;
double exact = Integrals.pyramid01_monomial_integral(expon);
double error = Math.Abs(q - exact);
Console.WriteLine(" " + expon[0].ToString().PadLeft(2)
+ " " + expon[1].ToString().PadLeft(2)
+ " " + expon[2].ToString().PadLeft(2)
+ " " + q.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(12) + "");
}
}
}
}
