private static void test10()
//*****************************************************************************/
//
// Purpose:
//
// TEST10 tests GM_GENERAL_RULE_SET.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 March 2017
//
// Author:
//
// John Burkardt
//
{
int[] e = new int[3];
int[] e_test =
{
0, 0, 0,
1, 0, 0,
0, 1, 0,
0, 0, 1,
2, 0, 0,
1, 1, 0,
1, 0, 1,
0, 2, 0,
0, 1, 1,
0, 0, 2
};
int i;
int j;
const int m = 3;
int rule;
double[] t =
{
1.0, 0.0, 0.0,
2.0, 0.0, 0.0,
1.0, 2.0, 0.0,
1.0, 0.0, 3.0
};
string cout;
Console.WriteLine("");
Console.WriteLine("TEST10");
Console.WriteLine(" GM_GENERAL_RULE_SET determines the weights and abscissas");
Console.WriteLine(" of a Grundmann-Moeller quadrature rule for");
Console.WriteLine(" the M dimensional general simplex,");
Console.WriteLine(" using a rule of index RULE,");
Console.WriteLine(" which will have degree of exactness 2*RULE+1.");
Console.WriteLine("");
Console.WriteLine(" In this test, look at all the monomials up to");
Console.WriteLine(" some maximum degree, choose a few low order rules");
Console.WriteLine(" and determine the quadrature error for each.");
Console.WriteLine("");
Console.WriteLine(" Simplex vertices:");
Console.WriteLine("");
for (j = 0; j < 4; j++)
{
cout = "";
for (i = 0; i < 3; i++)
{
cout += " " + t[i + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
}
double volume = Simplex.simplex_general_volume(m, t);
Console.WriteLine("");
Console.WriteLine(" Simplex volume = " + volume + "");
Console.WriteLine("");
Console.WriteLine(" Here we use M = " + m + "");
Console.WriteLine("");
Console.WriteLine(" N 1 X Y " +
" Z X^2 XY XZ" +
" Y^2 YZ Z^2");
Console.WriteLine("");
for (rule = 0; rule <= 5; rule++)
{
int n = GrundmannMoellerRule.gm_rule_size(rule, m);
double[] w = new double[n];
double[] x = new double[m * n];
GrundmannMoellerRule.gm_general_rule_set(rule, m, n, t, ref w, ref x);
cout = " " + n.ToString().PadLeft(8);
int k;
for (k = 0; k < 10; k++)
{
for (i = 0; i < m; i++)
{
e[i] = e_test[i + k * m];
}
double[] value = Monomial.monomial_value(m, n, e, x);
double result = typeMethods.r8vec_dot_product(n, w, value);
cout += " " + result.ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
}
}
private static void test08()
//****************************************************************************80
//
// Purpose:
//
// TEST08 tests GM_GENERAL_RULE_SET.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 March 2017
//
// Author:
//
// John Burkardt
//
{
int i;
int j;
double[] t =
{
1.0, 0.0, 0.0,
2.0, 0.0, 0.0,
1.0, 2.0, 0.0,
1.0, 0.0, 3.0
};
string cout;
Console.WriteLine("");
Console.WriteLine("TEST08");
Console.WriteLine(" GM_GENERAL_RULE_SET determines the weights and abscissas");
Console.WriteLine(" of a Grundmann-Moeller quadrature rule for");
Console.WriteLine(" the M dimensional general simplex,");
Console.WriteLine(" using a rule of index RULE,");
Console.WriteLine(" which will have degree of exactness 2*RULE+1.");
const int m = 3;
const int rule = 2;
Console.WriteLine("");
Console.WriteLine(" Here we use M = " + m + "");
Console.WriteLine(" RULE = " + rule + "");
Console.WriteLine(" DEGREE = " + 2 * rule + 1 + "");
Console.WriteLine("");
Console.WriteLine(" Simplex vertices:");
Console.WriteLine("");
for (j = 0; j < 4; j++)
{
cout = "";
for (i = 0; i < 3; i++)
{
cout += " " + t[i + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14);
}
Console.WriteLine(cout);
}
int n = GrundmannMoellerRule.gm_rule_size(rule, m);
double[] w = new double[n];
double[] x = new double[m * n];
GrundmannMoellerRule.gm_general_rule_set(rule, m, n, t, ref w, ref x);
Console.WriteLine("");
Console.WriteLine(" POINT W X Y Z");
Console.WriteLine("");
for (j = 0; j < n; j++)
{
cout = " " + j.ToString().PadLeft(8)
+ " " + w[j].ToString(CultureInfo.InvariantCulture).PadLeft(12);
for (i = 0; i < m; i++)
{
cout += " " + x[i + j * m].ToString(CultureInfo.InvariantCulture).PadLeft(12);
}
Console.WriteLine(cout);
}
}