private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 compares exact and estimated integrals in 3D.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 16 January 2014
//
// Author:
//
// John Burkardt
//
{
const int m = 3;
const int n = 4192;
int test;
const int test_num = 20;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Estimate monomial integrals using Monte Carlo");
Console.WriteLine(" over the interior of the unit simplex in M dimensions.");
//
// Get sample points.
//
int seed = 123456789;
double[] x = Integrals.simplex01_sample(m, n, ref seed);
Console.WriteLine("");
Console.WriteLine(" Number of sample points used is " + n + "");
//
// Randomly choose exponents.
//
Console.WriteLine("");
Console.WriteLine(" We randomly choose the exponents.");
Console.WriteLine("");
Console.WriteLine(" Ex Ey Ez MC-Estimate Exact Error");
Console.WriteLine("");
for (test = 1; test <= test_num; test++)
{
int[] e = UniformRNG.i4vec_uniform_ab_new(m, 0, 4, ref seed);
double[] value = Monomial.monomial_value(m, n, e, x);
double result = Integrals.simplex01_volume(m) * typeMethods.r8vec_sum(n, value)
/ n;
double exact = Integrals.simplex01_monomial_integral(m, e);
double error = Math.Abs(result - exact);
Console.WriteLine(" " + e[0].ToString().PadLeft(2)
+ " " + e[1].ToString().PadLeft(2)
+ " " + e[2].ToString().PadLeft(2)
+ " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
