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);
}
