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) + "");
}
}
private static void square_minimal_rule_print_test(int degree)
//****************************************************************************80
//
// Purpose:
//
// SQUARE_MINIMAL_RULE_PRINT_TEST tests SQUARE_MINIMAL_RULE_PRINT.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 22 February 2018
//
// Author:
//
// John Burkardt
//
{
int j;
Console.WriteLine("");
Console.WriteLine("SQUARE_MINIMAL_RULE_PRINT_TEST");
Console.WriteLine(" SQUARE_MINIMAL_RULE_PRINT prints a quadrature rule");
Console.WriteLine(" for the symmetric unit square.");
Console.WriteLine(" Minimal quadrature rule for a square.");
Console.WriteLine(" Polynomial exactness degree DEGREE = " + degree + "");
//
// Retrieve and print a symmetric quadrature rule.
//
double[] xyw = MinimalRule.square_minimal_rule(degree);
int order = MinimalRule.square_minimal_rule_order(degree);
Console.WriteLine("");
Console.WriteLine(" Number of nodes N = " + order + "");
Console.WriteLine("");
Console.WriteLine(" J X Y W");
Console.WriteLine("");
for (j = 0; j < order; j++)
{
Console.WriteLine(" " + j.ToString().PadLeft(4)
+ " " + xyw[0 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + xyw[1 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + xyw[2 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
double d = 0.0;
for (j = 0; j < order; j++)
{
d += xyw[2 + j * 3];
}
Console.WriteLine("");
Console.WriteLine(" Sum " + d.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
double area = Integrals.squaresym_area();
Console.WriteLine(" Area " + area.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
