private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 uses CIRCLE01_SAMPLE with an increasing number of points.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 12 January 2014
//
// Author:
//
// John Burkardt
//
{
const int m = 2;
const int n = 4192;
int test;
const int test_num = 20;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Use CIRCLE01_SAMPLE to compare exact and");
Console.WriteLine(" estimated integrals along the circumference");
Console.WriteLine(" of the unit circle in 2D.");
//
// Get sample points.
//
int seed = 123456789;
double[] x = Integrals.circle01_sample(n, ref seed);
Console.WriteLine("");
Console.WriteLine(" Number of sample points used is " + n + "");
//
// Randomly choose X, Y exponents.
//
Console.WriteLine("");
Console.WriteLine(" If any exponent is odd, the integral is zero.");
Console.WriteLine(" We restrict this test to randomly chosen even exponents.");
Console.WriteLine("");
Console.WriteLine(" Ex Ey MC-Estimate Exact Error");
Console.WriteLine("");
for (test = 1; test <= test_num; test++)
{
int[] e = UniformRNG.i4vec_uniform_ab_new(m, 0, 5, ref seed);
int i;
for (i = 0; i < m; i++)
{
e[i] *= 2;
}
double[] value = Monomial.monomial_value(m, n, e, x);
double result = Integrals.circle01_length() * typeMethods.r8vec_sum(n, value)
/ n;
double exact = Integrals.circle01_monomial_integral(e);
double error = Math.Abs(result - exact);
Console.WriteLine(" " + e[0].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + e[1].ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(10) + "");
}
}
