private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 writes a rule created by LYNESS_RULE to a file.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 September 2010
//
// Author:
//
// John Burkardt
//
{
double[] r =
{
0.0, 0.0,
1.0, 0.0,
0.0, 1.0
};
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" LYNESS_RULE returns the points and weights");
Console.WriteLine(" of a Lyness rule for the triangle.");
Console.WriteLine("");
Console.WriteLine(" In this test, we simply print a rule.");
const int rule = 18;
int order = LynessRule.lyness_order(rule);
int precision = LynessRule.lyness_precision(rule);
Console.WriteLine("");
Console.WriteLine(" Rule = " + rule + "");
Console.WriteLine(" Order = " + order + "");
Console.WriteLine(" Precision = " + precision + "");
double[] w = new double[order];
double[] x = new double[2 * order];
LynessRule.lyness_rule(rule, order, ref w, ref x);
typeMethods.r8mat_write("lyness_18_r.txt", 2, 3, r);
Console.WriteLine("");
Console.WriteLine(" Wrote the region file \"lyness_18_r.txt\".");
typeMethods.r8mat_write("lyness_18_w.txt", 1, order, w);
Console.WriteLine(" Wrote the weight file \"lyness_18_w.txt\".");
typeMethods.r8mat_write("lyness_18_x.txt", 2, order, x);
Console.WriteLine(" Wrote the point file \"lyness_18_x.txt\".");
}
private static void test03()
//****************************************************************************80
//
// Purpose:
//
// TEST03 performs the barycentric coordinate sum test on Lyness rules.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 September 2010
//
// Author:
//
// John Burkardt
//
{
int rule;
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" LYNESS_RULE returns the points and weights");
Console.WriteLine(" of a Lyness rule for the triangle.");
Console.WriteLine("");
Console.WriteLine(" In this test, we simply check that, for each");
Console.WriteLine(" quadrature point, the barycentric coordinates");
Console.WriteLine(" sum to 1.");
int rule_num = LynessRule.lyness_rule_num();
Console.WriteLine("");
Console.WriteLine(" Rule Suborder Sum of coordinates");
for (rule = 0; rule < rule_num; rule++)
{
int suborder_num = LynessRule.lyness_suborder_num(rule);
double[] sub_w = new double[suborder_num];
double[] sub_xyz = new double[3 * suborder_num];
LynessRule.lyness_subrule(rule, suborder_num, ref sub_xyz, ref sub_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 = typeMethods.r8vec_sum(3, sub_xyz, +3 * suborder);
Console.WriteLine(" " + xyz_sum + "");
}
}
}
private static void test04()
//****************************************************************************80
//
// Purpose:
//
// TEST04 prints a rule generated by LYNESS_RULE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 September 2010
//
// Author:
//
// John Burkardt
//
{
int j;
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" LYNESS_RULE returns the points and weights");
Console.WriteLine(" of a Lyness rule for the triangle.");
Console.WriteLine("");
Console.WriteLine(" In this test, we simply print a rule.");
int rule = 18;
int order = LynessRule.lyness_order(rule);
int precision = LynessRule.lyness_precision(rule);
Console.WriteLine("");
Console.WriteLine(" Rule = " + rule + "");
Console.WriteLine(" Order = " + order + "");
Console.WriteLine(" Precision = " + precision + "");
double[] w = new double[order];
double[] x = new double[2 * order];
LynessRule.lyness_rule(rule, order, ref w, ref x);
Console.WriteLine("");
Console.WriteLine(" I W X Y");
Console.WriteLine("");
for (j = 0; j < order; j++)
{
Console.WriteLine(" " + j.ToString(CultureInfo.InvariantCulture).PadLeft(4)
+ " " + w[j].ToString("0.################").PadLeft(24)
+ " " + x[0 + j * 2].ToString("0.################").PadLeft(24)
+ " " + x[1 + j * 2].ToString("0.################").PadLeft(24) + "");
}
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 performs the weight sum test on Lyness rules.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 September 2010
//
// Author:
//
// John Burkardt
//
{
int rule;
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" LYNESS_RULE returns the points and weights");
Console.WriteLine(" of a Lyness 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 = LynessRule.lyness_rule_num();
Console.WriteLine("");
Console.WriteLine(" Number of available rules = " + rule_num + "");
Console.WriteLine("");
Console.WriteLine(" Rule Sum of weights");
Console.WriteLine("");
for (rule = 0; rule <= rule_num; rule++)
{
int order = LynessRule.lyness_order(rule);
double[] x = new double[2 * order];
double[] w = new double[order];
LynessRule.lyness_rule(rule, order, ref w, ref x);
double w_sum = typeMethods.r8vec_sum(order, w);
Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + w_sum.ToString(CultureInfo.InvariantCulture).PadLeft(25) + "");
}
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests LYNESS_RULE_NUM, LYNESS_DEGREE, LYNESS_ORDER_NUM.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 29 September 2010
//
// Author:
//
// John Burkardt
//
{
int rule;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" LYNESS_RULE_NUM returns the number of rules;");
Console.WriteLine(" LYNESS_DEGREE returns the degree of a rule;");
Console.WriteLine(" LYNESS_ORDER_NUM returns the order of a rule.");
int rule_num = LynessRule.lyness_rule_num();
Console.WriteLine("");
Console.WriteLine(" Number of available rules = " + rule_num + "");
Console.WriteLine("");
Console.WriteLine(" Rule Order Precision");
Console.WriteLine("");
for (rule = 0; rule <= rule_num; rule++)
{
int order = LynessRule.lyness_order(rule);
int precision = LynessRule.lyness_precision(rule);
Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + order.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + precision.ToString(CultureInfo.InvariantCulture).PadLeft(8) + "");
}
}
private static void test06()
//****************************************************************************80
//
// Purpose:
//
// TEST06 tests the Lyness rules for exact integration of monomials.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 30 September 2010
//
// Author:
//
// John Burkardt
//
{
int degree;
const int degree_max = 10;
double value = 0;
Console.WriteLine("");
Console.WriteLine("TEST06");
Console.WriteLine(" LYNESS_RULE returns the points and weights of");
Console.WriteLine(" a Lyness 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 = LynessRule.lyness_rule_num();
double area = 0.5;
for (degree = 0; degree <= degree_max; degree++)
{
int a;
for (a = 0; a <= degree; a++)
{
int b = degree - a;
//
// 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 = 0; rule <= rule_num; rule++)
{
int order = LynessRule.lyness_order(rule);
double[] w = new double[order];
double[] x = new double[2 * order];
LynessRule.lyness_rule(rule, order, ref w, ref x);
double quad = 0.0;
int j;
for (j = 0; j < order; j++)
{
switch (a)
{
case 0 when b == 0:
value = coef;
break;
case 0 when b != 0:
value = coef * Math.Pow(x[1 + j * 2], b);
break;
default:
{
if (a != 0 && b == 0)
{
value = coef * Math.Pow(x[0 + j * 2], a);
}
else if (a != 0 && b != 0)
{
value = coef * Math.Pow(x[0 + j * 2], a) * Math.Pow(x[1 + j * 2], b);
}
break;
}
}
quad += w[j] * value;
}
quad = area * quad;
double exact = 1.0;
double err = Math.Abs(exact - quad);
Console.WriteLine(" " + rule.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + quad.ToString("0.######").PadLeft(14)
+ " " + err.ToString("0.##").PadLeft(10) + "");
}
}
}
}
