private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests TETRAHEDRON_NCC_RULE_NUM, TETRAHEDRON_NCC_DEGREE, TETRAHEDRON_NCC_ORDER_NUM.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 31 January 2007
//
// Author:
//
// John Burkardt
//
{
int rule;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" TETRAHEDRON_NCC_RULE_NUM returns the number of rules;");
Console.WriteLine(" TETRAHEDRON_NCC_DEGREE returns the degree of a rule;");
Console.WriteLine(" TETRAHEDRON_NCC_ORDER_NUM returns the order of a rule.");
int rule_num = NewtonCotesClosed.tetrahedron_ncc_rule_num();
Console.WriteLine("");
Console.WriteLine(" Number of available rules = " + rule_num + "");
Console.WriteLine("");
Console.WriteLine(" Rule Degree Order");
Console.WriteLine("");
for (rule = 1; rule <= rule_num; rule++)
{
int order_num = NewtonCotesClosed.tetrahedron_ncc_order_num(rule);
int degree = NewtonCotesClosed.tetrahedron_ncc_degree(rule);
Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + degree.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + order_num.ToString(CultureInfo.InvariantCulture).PadLeft(8) + "");
}
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 tests TETRAHEDRON_NCC_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 31 January 2007
//
// Author:
//
// John Burkardt
//
{
const int dim_num = 3;
int rule;
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" TETRAHEDRON_NCC_RULE returns the points and weights");
Console.WriteLine(" of an NCC rule for the tetrahedron.");
Console.WriteLine("");
Console.WriteLine(" In this test, we simply check that the weights");
Console.WriteLine(" sum to 1.");
int rule_num = NewtonCotesClosed.tetrahedron_ncc_rule_num();
Console.WriteLine("");
Console.WriteLine(" Number of available rules = " + rule_num + "");
Console.WriteLine("");
Console.WriteLine(" Rule Sum of weights");
Console.WriteLine("");
for (rule = 1; rule <= rule_num; rule++)
{
int order_num = NewtonCotesClosed.tetrahedron_ncc_order_num(rule);
double[] xyztab = new double[dim_num * order_num];
double[] wtab = new double[order_num];
NewtonCotesClosed.tetrahedron_ncc_rule(rule, order_num, ref xyztab, ref wtab);
double wtab_sum = 0.0;
int order;
for (order = 0; order < order_num; order++)
{
wtab_sum += wtab[order];
}
Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + wtab_sum.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
private static void test04()
//****************************************************************************80
//
// Purpose:
//
// TEST04 tests TETRAHEDRON_NCC_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 31 January 2007
//
// Author:
//
// John Burkardt
//
{
int a;
const int dim_num = 3;
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" TETRAHEDRON_NCC_RULE returns the points and weights of");
Console.WriteLine(" an NCC rule for the unit tetrahedron.");
Console.WriteLine("");
Console.WriteLine(" This routine uses those rules to estimate the");
Console.WriteLine(" integral of monomomials in the unit tetrahedron.");
int rule_num = NewtonCotesClosed.tetrahedron_ncc_rule_num();
const double volume = 1.0 / 6.0;
for (a = 0; a <= 6; a++)
{
int b;
for (b = 0; b <= 6 - a; b++)
{
int c;
for (c = 0; c <= 6 - a - b; c++)
{
//
// Multiplying X**A * Y**B * Z**C by COEF will give us an integrand
// whose integral is exactly 1. This makes the error calculations easy.
//
double coef = 1.0;
// for ( i = 1; i <= a; i++ )
// {
// coef = coef * i / i;
// }
int i;
for (i = a + 1; i <= a + b; i++)
{
coef = coef * i / (i - a);
}
for (i = a + b + 1; i <= a + b + c; i++)
{
coef = coef * i / (i - a - b);
}
for (i = a + b + c + 1; i <= a + b + c + 3; i++)
{
coef *= i;
}
Console.WriteLine("");
Console.WriteLine(" Integrate " + coef
+ " * X^" + a
+ " * Y^" + b
+ " * Z^" + c + "");
Console.WriteLine("");
Console.WriteLine(" Rule QUAD ERROR");
Console.WriteLine("");
int rule;
for (rule = 1; rule <= rule_num; rule++)
{
int order_num = NewtonCotesClosed.tetrahedron_ncc_order_num(rule);
double[] xyztab = new double[dim_num * order_num];
double[] wtab = new double[order_num];
NewtonCotesClosed.tetrahedron_ncc_rule(rule, order_num, ref xyztab, ref wtab);
double quad = 0.0;
int order;
for (order = 0; order < order_num; order++)
{
double x = xyztab[0 + order * dim_num];
double y = xyztab[1 + order * dim_num];
double z = xyztab[2 + order * dim_num];
//
// Some tedious calculations to avoid 0**0 complaints.
//
double value = coef;
if (a != 0)
{
value *= Math.Pow(x, a);
}
if (b != 0)
{
value *= Math.Pow(y, b);
}
if (c != 0)
{
value *= Math.Pow(z, c);
}
quad += wtab[order] * value;
}
quad = volume * quad;
double exact = 1.0;
double err = Math.Abs(exact - quad);
Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + quad.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + err.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
}
}
}
private static void test03()
//****************************************************************************80
//
// Purpose:
//
// TEST03 tests TETRAHEDRON_NCC_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 January 2007
//
// Author:
//
// John Burkardt
//
{
int rule;
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" TETRAHEDRON_NCC_RULE returns the points and weights");
Console.WriteLine(" of an NCC rule for the tetrahedron.");
Console.WriteLine("");
Console.WriteLine(" In this test, we simply check that, for each");
Console.WriteLine(" quadrature point, the barycentric coordinates");
Console.WriteLine(" add up to 1.");
int rule_num = NewtonCotesClosed.tetrahedron_ncc_rule_num();
Console.WriteLine("");
Console.WriteLine(" Rule Suborder Sum of coordinates");
Console.WriteLine("");
for (rule = 1; rule <= rule_num; rule++)
{
int suborder_num = NewtonCotesClosed.tetrahedron_ncc_suborder_num(rule);
double[] suborder_xyz = new double[4 * suborder_num];
double[] suborder_w = new double[suborder_num];
NewtonCotesClosed.tetrahedron_ncc_subrule(rule, suborder_num, ref suborder_xyz, ref suborder_w);
Console.WriteLine("");
Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + suborder_num.ToString(CultureInfo.InvariantCulture).PadLeft(8) + "");
int suborder;
for (suborder = 0; suborder < suborder_num; suborder++)
{
double xyz_sum = suborder_xyz[0 + suborder * 4]
+ suborder_xyz[1 + suborder * 4]
+ suborder_xyz[2 + suborder * 4]
+ suborder_xyz[3 + suborder * 4];
Console.WriteLine(" "
+ " " + xyz_sum.ToString("0.################").PadLeft(25) + "");
}
}
}