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) + ""); } }