private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 demonstrates REFERENCE_TO_PHYSICAL_T3.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 January 2007
//
// Author:
//
// John Burkardt
//
{
const int NODE_NUM = 3;
int node;
double[] node_xy =
{
0.0, 0.0,
1.0, 0.0,
0.0, 1.0
};
double[] node_xy2 =
{
1.0, 2.0,
1.0, 1.0,
3.0, 2.0
};
int order;
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" REFERENCE_TO_PHYSICAL_T3 transforms a rule");
Console.WriteLine(" on the unit (reference) triangle to a rule on ");
Console.WriteLine(" an arbitrary (physical) triangle.");
const int rule = 3;
int order_num = NewtonCotesClosed.triangle_ncc_order_num(rule);
double[] xy = new double[2 * order_num];
double[] xy2 = new double[2 * order_num];
double[] w = new double[order_num];
NewtonCotesClosed.triangle_ncc_rule(rule, order_num, ref xy, ref w);
//
// Here is the reference triangle, and its rule.
//
Console.WriteLine("");
Console.WriteLine(" The reference triangle:");
Console.WriteLine("");
for (node = 0; node < NODE_NUM; node++)
{
Console.WriteLine(" " + node + 1
+ " " + node_xy[0 + node * 2]
+ " " + node_xy[1 + node * 2] + "");
}
double area = Integrals.triangle_area(node_xy);
Console.WriteLine("");
Console.WriteLine(" Rule " + rule + " for reference triangle");
Console.WriteLine(" with area = " + area + "");
Console.WriteLine("");
Console.WriteLine(" X Y W");
Console.WriteLine("");
for (order = 0; order < order_num; order++)
{
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + xy[0 + order * 2].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + xy[1 + order * 2].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + w[order].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
//
// Transform the rule.
//
Reference.reference_to_physical_t3(node_xy2, order_num, xy, ref xy2);
//
// Here is the physical triangle, and its transformed rule.
//
Console.WriteLine("");
Console.WriteLine(" The physical triangle:");
Console.WriteLine("");
for (node = 0; node < NODE_NUM; node++)
{
Console.WriteLine(" " + (node + 1).ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + node_xy2[0 + node * 2].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + node_xy2[1 + node * 2].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
double area2 = Integrals.triangle_area(node_xy2);
Console.WriteLine("");
Console.WriteLine(" Rule " + rule + " for physical triangle");
Console.WriteLine(" with area = " + area2 + "");
Console.WriteLine("");
Console.WriteLine(" X Y W");
Console.WriteLine("");
for (order = 0; order < order_num; order++)
{
Console.WriteLine(" " + order.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + xy2[0 + order * 2].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + xy2[1 + order * 2].ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + w[order].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 tests TRIANGLE_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("TEST02");
Console.WriteLine(" TRIANGLE_NCC_RULE returns the points and weights");
Console.WriteLine(" of an NCC rule for the triangle.");
Console.WriteLine("");
Console.WriteLine(" In this test, we simply check that the weights");
Console.WriteLine(" sum to 1.");
int rule_num = NewtonCotesClosed.triangle_ncc_rule_num();
Console.WriteLine("");
Console.WriteLine(" Number of available rules = " + rule_num + "");
Console.WriteLine("");
Console.WriteLine(" Rule Order Sum of weights");
Console.WriteLine("");
for (rule = 1; rule <= rule_num; rule++)
{
int order_num = NewtonCotesClosed.triangle_ncc_order_num(rule);
double[] xytab = new double[2 * order_num];
double[] wtab = new double[order_num];
NewtonCotesClosed.triangle_ncc_rule(rule, order_num, ref xytab, 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)
+ " " + order_num.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + wtab_sum.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
private static void test04()
//****************************************************************************80
//
// Purpose:
//
// TEST04 tests TRIANGLE_NCC_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 January 2007
//
// Author:
//
// John Burkardt
//
{
int a;
const double area = 0.5;
double value = 0;
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" TRIANGLE_NCC_RULE returns the points and weights of");
Console.WriteLine(" an NCC rule for the unit triangle.");
Console.WriteLine("");
Console.WriteLine(" This routine uses those rules to estimate the");
Console.WriteLine(" integral of monomomials in the unit triangle.");
int rule_num = NewtonCotesClosed.triangle_ncc_rule_num();
for (a = 0; a <= 10; a++)
{
int b;
for (b = 0; b <= 10 - a; b++)
{
//
// Multiplying X^A * Y^B by COEF will give us an integrand
// whose integral is exactly 1. This makes the error calculations easy.
//
double coef = (a + b + 2) * (double)(a + b + 1);
int i;
for (i = 1; i <= b; i++)
{
coef = coef * (a + i) / i;
}
Console.WriteLine("");
Console.WriteLine(" Integrate " + coef
+ " * X^" + a
+ " * Y^" + b + "");
Console.WriteLine("");
Console.WriteLine(" Rule QUAD ERROR");
Console.WriteLine("");
int rule;
for (rule = 1; rule <= rule_num; rule++)
{
int order_num = NewtonCotesClosed.triangle_ncc_order_num(rule);
double[] xytab = new double[2 * order_num];
double[] wtab = new double[order_num];
NewtonCotesClosed.triangle_ncc_rule(rule, order_num, ref xytab, ref wtab);
double quad = 0.0;
int order;
for (order = 0; order < order_num; order++)
{
double x = xytab[0 + order * 2];
double y = xytab[1 + order * 2];
switch (a)
{
case 0 when b == 0:
value = coef;
break;
case 0 when b != 0:
value = coef * Math.Pow(y, b);
break;
default:
{
if (a != 0 && b == 0)
{
value = coef * Math.Pow(x, a);
}
else if (a != 0 && b != 0)
{
value = coef * Math.Pow(x, a) * Math.Pow(y, b);
}
break;
}
}
quad += wtab[order] * value;
}
quad = area * 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) + "");
}
}
}
}