private static void test03(int degree, int n, string header)
//****************************************************************************80
//
// Purpose:
//
// TEST03 gets a rule and creates GNUPLOT input files.
//
// Licensing:
//
// This code is distributed under the GNU GPL license.
//
// Modified:
//
// 11 July 2014
//
// Author:
//
// Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
// C++ version by John Burkardt.
//
// Reference:
//
// Hong Xiao, Zydrunas Gimbutas,
// A numerical algorithm for the construction of efficient quadrature
// rules in two and higher dimensions,
// Computers and Mathematics with Applications,
// Volume 59, 2010, pages 663-676.
//
// Parameters:
//
// Input, int DEGREE, the desired total polynomial degree exactness
// of the quadrature rule. 0 <= DEGREE <= 15.
//
// Input, int N, the number of nodes to be used by the rule.
//
// Input, string HEADER, an identifier for the filenames.
//
{
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" Get a quadrature rule for the tetrahedron.");
Console.WriteLine(" Set up GNUPLOT graphics input.");
Console.WriteLine(" Polynomial exactness degree DEGREE = " + degree + "");
//
// Retrieve a symmetric quadrature rule.
//
double[] x = new double[3 * n];
double[] w = new double[n];
QuadratureRule.tetrahedron_arbq(degree, n, ref x, ref w);
//
// Create files for input to GNUPLOT.
//
QuadratureRule.tetrahedron_arbq_gnuplot(n, x, header);
}
private static void test01(int degree, int n)
//****************************************************************************80
//
// Purpose:
//
// TEST01 calls TETRAHEDRON_ARBQ for a quadrature rule of given order.
//
// Licensing:
//
// This code is distributed under the GNU GPL license.
//
// Modified:
//
// 11 July 2014
//
// Author:
//
// Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
// C++ version by John Burkardt.
//
// Reference:
//
// Hong Xiao, Zydrunas Gimbutas,
// A numerical algorithm for the construction of efficient quadrature
// rules in two and higher dimensions,
// Computers and Mathematics with Applications,
// Volume 59, 2010, pages 663-676.
//
// Parameters:
//
// Input, int DEGREE, the desired total polynomial degree exactness
// of the quadrature rule. 1 <= DEGREE <= 15.
//
// Input, int N, the number of nodes.
//
{
int j;
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" Quadrature rule for a tetrahedron.");
Console.WriteLine(" Polynomial exactness degree DEGREE = " + degree + "");
double volume = Math.Sqrt(8.0) / 3.0;
//
// Retrieve and print a symmetric quadrature rule.
//
double[] x = new double[3 * n];
double[] w = new double[n];
QuadratureRule.tetrahedron_arbq(degree, n, ref x, ref w);
Console.WriteLine("");
Console.WriteLine(" Number of nodes N = " + n + "");
Console.WriteLine("");
Console.WriteLine(" J W X Y Z");
Console.WriteLine("");
for (j = 0; j < n; j++)
{
Console.WriteLine(j.ToString(CultureInfo.InvariantCulture).PadLeft(4) + " "
+ w[j].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ x[0 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ x[1 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ x[2 + j * 3].ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
double d = typeMethods.r8vec_sum(n, w);
Console.WriteLine(" Sum " + d + "");
Console.WriteLine(" Volume " + volume + "");
}
private static void test04(int degree, int n)
//****************************************************************************80
//
// Purpose:
//
// TEST04 gets a rule and tests its accuracy.
//
// Licensing:
//
// This code is distributed under the GNU GPL license.
//
// Modified:
//
// 11 July 2014
//
// Author:
//
// Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
// C++ version by John Burkardt.
//
// Reference:
//
// Hong Xiao, Zydrunas Gimbutas,
// A numerical algorithm for the construction of efficient quadrature
// rules in two and higher dimensions,
// Computers and Mathematics with Applications,
// Volume 59, 2010, pages 663-676.
//
// Parameters:
//
// Input, int DEGREE, the desired total polynomial degree exactness
// of the quadrature rule. 0 <= DEGREE <= 15.
//
// Input, int N, the number of nodes to be used by the rule.
//
{
int i;
int j;
double[] z = new double[3];
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" Get a quadrature rule for the tetrahedron.");
Console.WriteLine(" Test its accuracy.");
Console.WriteLine(" Polynomial exactness degree DEGREE = " + degree + "");
//
// Retrieve a quadrature rule.
//
double[] x = new double[3 * n];
double[] w = new double[n];
QuadratureRule.tetrahedron_arbq(degree, n, ref x, ref w);
int npols = (degree + 1) * (degree + 2) * (degree + 3) / 6;
double[] rints = new double[npols];
for (j = 0; j < npols; j++)
{
rints[j] = 0.0;
}
for (i = 0; i < n; i++)
{
z[0] = x[0 + i * 3];
z[1] = x[1 + i * 3];
z[2] = x[2 + i * 3];
double[] pols = Polynomial.ortho3eva(degree, z);
for (j = 0; j < npols; j++)
{
rints[j] += w[i] * pols[j];
}
}
double volume = Math.Sqrt(8.0) / 3.0;
double d = 0.0;
d = Math.Pow(rints[0] - Math.Sqrt(volume), 2);
for (i = 1; i < npols; i++)
{
d += Math.Pow(rints[i], 2);
}
d = Math.Sqrt(d) / npols;
Console.WriteLine("");
Console.WriteLine(" RMS error = " + d + "");
}
private static void test02(int degree, int n, string header)
//****************************************************************************80
//
// Purpose:
//
// TEST02 gets a rule and writes it to a file.
//
// Licensing:
//
// This code is distributed under the GNU GPL license.
//
// Modified:
//
// 11 July 2014
//
// Author:
//
// Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
// C++ version by John Burkardt.
//
// Reference:
//
// Hong Xiao, Zydrunas Gimbutas,
// A numerical algorithm for the construction of efficient quadrature
// rules in two and higher dimensions,
// Computers and Mathematics with Applications,
// Volume 59, 2010, pages 663-676.
//
// Parameters:
//
// Input, int DEGREE, the desired total polynomial degree exactness
// of the quadrature rule. 0 <= DEGREE <= 15.
//
// Input, int N, the number of nodes to be used by the rule.
//
// Input, string HEADER, an identifier for the filenames.
//
{
int i;
List <string> rule_unit = new();
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" Get a quadrature rule for the tetrahedron.");
Console.WriteLine(" Then write it to a file.");
Console.WriteLine(" Polynomial exactness degree DEGREE = " + degree + "");
//
// Retrieve a quadrature rule.
//
double[] x = new double[3 * n];
double[] w = new double[n];
QuadratureRule.tetrahedron_arbq(degree, n, ref x, ref w);
//
// Write the points and weights to a file.
//
string rule_filename = header + ".txt";
for (i = 0; i < n; i++)
{
rule_unit.Add(x[0 + i * 3] + " "
+ x[1 + i * 3] + " "
+ x[2 + i * 3] + " "
+ w[i] + "");
}
File.WriteAllLines(rule_filename, rule_unit);
Console.WriteLine("");
Console.WriteLine(" Quadrature rule written to file '" + rule_filename + "'");
}