private static void test09()
//*****************************************************************************/
//
// Purpose:
//
// TEST09 tests GM_UNIT_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
};
const int m = 3;
int rule;
Console.WriteLine("");
Console.WriteLine("TEST09");
Console.WriteLine(" GM_UNIT_RULE_SET determines the weights and abscissas");
Console.WriteLine(" of a Grundmann-Moeller quadrature rule for");
Console.WriteLine(" the M dimensional unit 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.");
double volume = Simplex.simplex_unit_volume(m);
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_unit_rule_set(rule, m, n, ref w, ref x);
string cout = " " + n.ToString().PadLeft(8);
int k;
for (k = 0; k < 10; k++)
{
int i;
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 test07()
//****************************************************************************80
//
// Purpose:
//
// TEST07 tests GM_UNIT_RULE_SET.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 10 July 2007
//
// Author:
//
// John Burkardt
//
{
int degree;
const int degree_max = 4;
int h = 0;
const int m = 5;
const int rule_max = 3;
int t = 0;
Console.WriteLine("");
Console.WriteLine("TEST07");
Console.WriteLine(" GM_UNIT_RULE_SET determines the weights and abscissas");
Console.WriteLine(" of a Grundmann-Moeller quadrature rule for");
Console.WriteLine(" the M dimensional unit 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(" Here we use M = " + m + "");
Console.WriteLine("");
Console.WriteLine(" Rule Order Quad_Error");
Console.WriteLine("");
int[] expon = new int[m];
for (degree = 0; degree <= degree_max; degree++)
{
bool more = false;
for (;;)
{
Comp.comp_next(degree, m, ref expon, ref more, ref h, ref t);
Console.WriteLine("");
Console.WriteLine(" F(X) = X1^" + expon[0]
+ " * X2^" + expon[1]
+ " * X3^" + expon[2]
+ " * X4^" + expon[3]
+ " * X5^" + expon[4] + "");
Console.WriteLine("");
int rule;
for (rule = 0; rule <= rule_max; rule++)
{
int n = GrundmannMoellerRule.gm_rule_size(rule, m);
double[] w = new double[n];
double[] x = new double[m * n];
GrundmannMoellerRule.gm_unit_rule_set(rule, m, n, ref w, ref x);
double quad_error = Simplex.simplex_unit_monomial_quadrature(m, expon,
n, x, w);
Console.WriteLine(" " + rule.ToString().PadLeft(8)
+ " " + n.ToString().PadLeft(8)
+ " " + quad_error.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
if (!more)
{
break;
}
}
}
}
private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 tests GM_UNIT_RULE_SET.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 10 July 2007
//
// Author:
//
// John Burkardt
//
{
const int TEST_NUM = 4;
int[] m_test = { 2, 3, 5, 10 };
int test;
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" GM_UNIT_RULE_SET determines the weights and abscissas");
Console.WriteLine(" of a Grundmann-Moeller quadrature rule for");
Console.WriteLine(" the M dimensional unit 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, we compute various rules, and simply");
Console.WriteLine(" report the number of points, and the sum of weights.");
Console.WriteLine("");
Console.WriteLine(" M RULE N WEIGHT SUM");
for (test = 0; test < TEST_NUM; test++)
{
int m = m_test[test];
Console.WriteLine("");
int rule;
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_unit_rule_set(rule, m, n, ref w, ref x);
double w_sum = 0.0;
int point;
for (point = 0; point < n; point++)
{
w_sum += w[point];
}
Console.WriteLine(" " + m.ToString().PadLeft(8)
+ " " + rule.ToString().PadLeft(8)
+ " " + n.ToString().PadLeft(8)
+ " " + w_sum.ToString("0.################").PadLeft(24) + "");
}
}
}
private static void test06()
//****************************************************************************80
//
// Purpose:
//
// TEST06 tests GM_UNIT_RULE_SET.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 10 July 2007
//
// Author:
//
// John Burkardt
//
{
int point;
List <string> w_unit = new();
List <string> x_unit = new();
Console.WriteLine("");
Console.WriteLine("TEST06");
Console.WriteLine(" GM_UNIT_RULE_SET determines the weights and abscissas");
Console.WriteLine(" of a Grundmann-Moeller quadrature rule for");
Console.WriteLine(" the M dimensional unit 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, we write a rule to a file.");
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 + "");
int n = GrundmannMoellerRule.gm_rule_size(rule, m);
double[] w = new double[n];
double[] x = new double[m * n];
GrundmannMoellerRule.gm_unit_rule_set(rule, m, n, ref w, ref x);
string w_file = "gm" + rule + "_" + m + "d_w.txt";
for (point = 0; point < n; point++)
{
w_unit.Add(w[point].ToString("0.################").PadLeft(20) + "");
}
File.WriteAllLines(w_file, w_unit);
string x_file = "gm" + rule + "_" + m + "d_x.txt";
for (point = 0; point < n; point++)
{
string tmp = "";
int dim;
for (dim = 0; dim < m; dim++)
{
tmp += x[dim + point * m].ToString("0.################").PadLeft(20);
}
x_unit.Add(tmp);
}
File.WriteAllLines(x_file, x_unit);
Console.WriteLine("");
Console.WriteLine(" Wrote rule " + rule
+ " to \"" + w_file
+ "\" and \"" + x_file + "");
}
private static void test04()
//****************************************************************************80
//
// Purpose:
//
// TEST04 tests GM_UNIT_RULE_SET.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 10 July 2007
//
// Author:
//
// John Burkardt
//
{
int point;
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" GM_UNIT_RULE_SET determines the weights and abscissas");
Console.WriteLine(" of a Grundmann-Moeller quadrature rule for");
Console.WriteLine(" the M dimensional unit 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 + "");
int n = GrundmannMoellerRule.gm_rule_size(rule, m);
double[] w = new double[n];
double[] x = new double[m * n];
GrundmannMoellerRule.gm_unit_rule_set(rule, m, n, ref w, ref x);
Console.WriteLine("");
Console.WriteLine(" POINT W X Y Z");
Console.WriteLine("");
for (point = 0; point < n; point++)
{
string cout = " " + (point + 1).ToString().PadLeft(8)
+ " " + w[point].ToString(CultureInfo.InvariantCulture).PadLeft(12);
int dim;
for (dim = 0; dim < m; dim++)
{
cout += " " + x[dim + point * m].ToString(CultureInfo.InvariantCulture).PadLeft(12);
}
Console.WriteLine(cout);
}
}