private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TRIANGLE_EXACTNESS.
//
// Discussion:
//
// This program investigates the polynomial exactness of a quadrature
// rule for the triangle.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 31 July 2009
//
// Author:
//
// John Burkardt
//
{
int degree;
int degree_max;
bool error = false;
int last = 0;
int point;
string quad_filename;
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS");
Console.WriteLine("");
Console.WriteLine(" Investigate the polynomial exactness of a quadrature");
Console.WriteLine(" rule for the triangle by integrating all monomials");
Console.WriteLine(" of a given degree.");
Console.WriteLine("");
Console.WriteLine(" The rule will be adjusted to the unit triangle.");
//
// Get the quadrature file root name:
//
try
{
quad_filename = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS:");
Console.WriteLine(" Enter the \"root\" name of the quadrature files.");
quad_filename = Console.ReadLine();
}
//
// Create the names of:
// the quadrature X file;
// the quadrature W file;
// the quadrature R file;
//
string quad_r_filename = quad_filename + "_r.txt";
string quad_w_filename = quad_filename + "_w.txt";
string quad_x_filename = quad_filename + "_x.txt";
//
// The second command line argument is the maximum degree.
//
try
{
degree_max = typeMethods.s_to_i4(args[1], ref last, ref error);
}
catch
{
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS:");
Console.WriteLine(" Please enter the maximum total degree to check.");
degree_max = Convert.ToInt32(Console.ReadLine());
}
//
// Summarize the input.
//
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS: User input:");
Console.WriteLine(" Quadrature rule X file = \"" + quad_x_filename
+ "\".");
Console.WriteLine(" Quadrature rule W file = \"" + quad_w_filename
+ "\".");
Console.WriteLine(" Quadrature rule R file = \"" + quad_r_filename
+ "\".");
Console.WriteLine(" Maximum total degree to check = " + degree_max + "");
//
// Read the X file.
//
TableHeader hdr = typeMethods.r8mat_header_read(quad_x_filename);
int dim_num = hdr.m;
int point_num = hdr.n;
Console.WriteLine("");
Console.WriteLine(" Spatial dimension = " + dim_num + "");
Console.WriteLine(" Number of points = " + point_num + "");
if (dim_num != 2)
{
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature abscissas must be two dimensional.");
return;
}
double[] x = typeMethods.r8mat_data_read(quad_x_filename, dim_num, point_num);
//
// Read the W file.
//
hdr = typeMethods.r8mat_header_read(quad_w_filename);
int dim_num2 = hdr.m;
int point_num2 = hdr.n;
if (dim_num2 != 1)
{
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature weight file should have exactly");
Console.WriteLine(" one value on each line.");
return;
}
if (point_num2 != point_num)
{
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature weight file should have exactly");
Console.WriteLine(" the same number of lines as the abscissa file.");
return;
}
double[] w = typeMethods.r8mat_data_read(quad_w_filename, 1, point_num);
//
// Read the R file.
//
hdr = typeMethods.r8mat_header_read(quad_r_filename);
int dim_num3 = hdr.m;
int point_num3 = hdr.n;
if (dim_num3 != dim_num)
{
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature region file should have the same");
Console.WriteLine(" number of values on each line as the abscissa file");
Console.WriteLine(" does.");
return;
}
if (point_num3 != 3)
{
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS - Fatal error!");
Console.WriteLine(" The quadrature region file should have 3 lines.");
return;
}
double[] r = typeMethods.r8mat_data_read(quad_r_filename, dim_num, 3);
//
// Rescale the weights.
//
double area = Integrals.triangle_area(r);
for (point = 0; point < point_num; point++)
{
w[point] = 0.5 * w[point] / area;
}
//
// Translate the abscissas.
//
double[] x_ref = new double[2 * point_num];
Triangulation.triangle_order3_physical_to_reference(r, point_num, x, ref x_ref);
//
// Explore the monomials.
//
int[] expon = new int[dim_num];
Console.WriteLine("");
Console.WriteLine(" Error Degree Exponents");
for (degree = 0; degree <= degree_max; degree++)
{
Console.WriteLine("");
bool more = false;
int h = 0;
int t = 0;
for (;;)
{
Comp.comp_next(degree, dim_num, ref expon, ref more, ref h, ref t);
double quad_error = Integrals.triangle01_monomial_quadrature(dim_num, expon, point_num,
x_ref, w);
string cout = " " + quad_error.ToString(CultureInfo.InvariantCulture).PadLeft(12)
+ " " + degree.ToString().PadLeft(2)
+ " ";
int dim;
for (dim = 0; dim < dim_num; dim++)
{
cout += expon[dim].ToString().PadLeft(3);
}
Console.WriteLine(cout);
if (!more)
{
break;
}
}
}
Console.WriteLine("");
Console.WriteLine("TRIANGLE_EXACTNESS:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}