private static void triangle_unit_monomial_test(int degree_max)
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE_UNIT_MONOMIAL_TEST tests TRIANGLE_UNIT_MONOMIAL.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 16 April 2009
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int DEGREE_MAX, the maximum total degree of the
// monomials to check.
//
{
int alpha;
int[] expon = new int[2];
Console.WriteLine("");
Console.WriteLine("TRIANGLE_UNIT_MONOMIAL_TEST");
Console.WriteLine(" For the unit triangle,");
Console.WriteLine(" TRIANGLE_UNIT_MONOMIAL returns the exact value of the");
Console.WriteLine(" integral of X^ALPHA Y^BETA");
Console.WriteLine("");
Console.WriteLine(" Volume = " + QuadratureRule.triangle_unit_volume() + "");
Console.WriteLine("");
Console.WriteLine(" ALPHA BETA INTEGRAL");
Console.WriteLine("");
for (alpha = 0; alpha <= degree_max; alpha++)
{
expon[0] = alpha;
int beta;
for (beta = 0; beta <= degree_max - alpha; beta++)
{
expon[1] = beta;
double value = QuadratureRule.triangle_unit_monomial(expon);
Console.WriteLine(" " + expon[0].ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + expon[1].ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + value.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
}
private static void triangle_unit_quad_test(int degree_max)
//****************************************************************************80
//
// Purpose:
//
// TRIANGLE_UNIT_QUAD_TEST tests the rules for the unit triangle.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2008
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int DEGREE_MAX, the maximum total degree of the
// monomials to check.
//
{
const int DIM_NUM = 2;
int[] expon = new int[DIM_NUM];
int h = 0;
int t = 0;
Console.WriteLine("");
Console.WriteLine("TRIANGLE_UNIT_QUAD_TEST");
Console.WriteLine(" For the unit triangle,");
Console.WriteLine(" we approximate monomial integrals with:");
Console.WriteLine(" TRIANGLE_UNIT_O01,");
Console.WriteLine(" TRIANGLE_UNIT_O03,");
Console.WriteLine(" TRIANGLE_UNIT_O03b,");
Console.WriteLine(" TRIANGLE_UNIT_O06,");
Console.WriteLine(" TRIANGLE_UNIT_O06b,");
Console.WriteLine(" TRIANGLE_UNIT_O07,");
Console.WriteLine(" TRIANGLE_UNIT_O12,");
bool more = false;
SubCompData data = new();
for (;;)
{
SubComp.subcomp_next(ref data, degree_max, DIM_NUM, ref expon, ref more, ref h, ref t);
Console.WriteLine("");
string cout = " Monomial exponents: ";
int dim;
for (dim = 0; dim < DIM_NUM; dim++)
{
cout += " " + expon[dim].ToString(CultureInfo.InvariantCulture).PadLeft(2);
}
Console.WriteLine(cout);
Console.WriteLine("");
int order = 1;
double[] w = new double[order];
double[] xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o01(ref w, ref xy);
double[] v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
double quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 3;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o03(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 3;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o03b(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 6;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o06(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 6;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o06b(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 7;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o07(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
order = 12;
w = new double[order];
xy = new double[DIM_NUM * order];
QuadratureRule.triangle_unit_o12(ref w, ref xy);
v = Monomial.monomial_value(DIM_NUM, order, expon, xy);
quad = QuadratureRule.triangle_unit_volume() * typeMethods.r8vec_dot_product(order, w, v);
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(6)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
Console.WriteLine("");
quad = QuadratureRule.triangle_unit_monomial(expon);
Console.WriteLine(" " + " Exact"
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
if (!more)
{
break;
}
}
}
