private static void squaresym_monomial_integral_test() //****************************************************************************80 // // Purpose: // // SQUARESYM_MONOMIAL_INTEGRAL_TEST tests SQUARESYM_MONOMIAL_INTEGRAL. // // Licensing: // // This code is distributed under the GNU LGPL license. // // Modified: // // 21 February 2018 // // Author: // // John Burkardt // { const int m = 2; const int n = 4192; int test; const int test_num = 20; Console.WriteLine(""); Console.WriteLine("SQUARESYM_MONOMIAL_INTEGRAL_TEST"); Console.WriteLine(" SQUARESYM_MONOMIAL_INTEGRAL returns the exact integral"); Console.WriteLine(" of a monomial over the interior of the symmetric unit square in 2D."); Console.WriteLine(" Compare exact and estimated values."); // // Get sample points. // int seed = 123456789; double[] x = Integrals.squaresym_sample(n, ref seed); Console.WriteLine(""); Console.WriteLine(" Number of sample points is " + n + ""); // // Randomly choose 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, 7, ref seed); double[] value = Monomial.monomial_value(m, n, e, x); double result = Integrals.squaresym_area() * typeMethods.r8vec_sum(n, value) / n; double exact = Integrals.squaresym_monomial_integral(e); double error = Math.Abs(result - exact); Console.WriteLine(" " + e[0].ToString().PadLeft(2) + " " + e[1].ToString().PadLeft(2) + " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14) + " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(14) + ""); } }
public static double square_minimal_rule_error_max(int degree) //****************************************************************************80 // // Purpose: // // SQUARE_MINIMAL_RULE_ERROR_MAX returns the maximum error. // // Discussion: // // The rule of given DEGREE should theoretically have zero error // for all monomials of degrees 0 <= D <= DEGREE. This function // checks every such monomial and reports the maximum error. // // Licensing: // // This code is distributed under the GNU GPL license. // // Modified: // // 22 February 2018 // // Author: // // John Burkardt. // // Reference: // // Mattia Festa, Alvise Sommariva, // Computing almost minimal formulas on the square, // Journal of Computational and Applied Mathematics, // Volume 17, Number 236, November 2012, pages 4296-4302. // // Parameters: // // Input, int DEGREE, the desired total polynomial degree exactness // of the quadrature rule. // // Output, double SQUARE_MINIMAL_RULE_ERROR_MAX, the maximum error observed // when using the rule to compute the integrals of all monomials of degree // between 0 and DEGREE. // { int d; int[] e = new int[2]; int order = square_minimal_rule_order(degree); double[] xyw = square_minimal_rule(degree); double error_max = 0.0; for (d = 0; d <= degree; d++) { int i; for (i = 0; i <= d; i++) { int j = d - i; e[0] = i; e[1] = j; double exact = Integrals.squaresym_monomial_integral(e); double s = 0.0; int k; for (k = 0; k < order; k++) { s += xyw[2 + k * 3] * Math.Pow(xyw[0 + k * 3], i) * Math.Pow(xyw[1 + k * 3], j); } double err = Math.Abs(exact - s); if (error_max < err) { error_max = err; } } } return(error_max); }