private static void Main(string[] args)
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for INT_EXACTNESS_GEN_LAGUERRE.
//
// Discussion:
//
// This program investigates a generalized Gauss-Laguerre quadrature rule
// by using it to integrate monomials over [0,+oo), and comparing the
// approximate result to the known exact value.
//
// The user specifies:
// * the "root" name of the R, W and X files that specify the rule;
// * DEGREE_MAX, the maximum monomial degree to be checked.
// * ALPHA, the power of X in the weighting function.
// * OPTION, whether the rule is for x^alpha*exp(-x)*f(x) or f(x).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 05 August 2009
//
// Author:
//
// John Burkardt
//
{
double alpha;
int degree;
int degree_max;
int i;
int option;
string quad_filename;
Console.WriteLine("");
Console.WriteLine("INT_EXACTNESS_GEN_LAGUERRE");
Console.WriteLine("");
Console.WriteLine(" Investigate the polynomial exactness of a generalized Gauss-Laguerre");
Console.WriteLine(" quadrature rule by integrating exponentially weighted");
Console.WriteLine(" monomials up to a given degree over the [0,+oo) interval.");
Console.WriteLine("");
Console.WriteLine(" The rule may be defined on another interval, [A,+oo)");
Console.WriteLine(" in which case it is adjusted to the [0,+oo) interval.");
//
// Get the quadrature file rootname.
//
try
{
quad_filename = args[0];
}
catch
{
Console.WriteLine("");
Console.WriteLine(" Enter the quadrature file rootname:");
quad_filename = Console.ReadLine();
}
Console.WriteLine("");
Console.WriteLine(" The quadrature file rootname is \"" + quad_filename + "\".");
//
// Create the names of:
// the quadrature X file;
// the quadrature W file;
// the quadrature R file;
//
string quad_w_filename = quad_filename + "_w.txt";
string quad_x_filename = quad_filename + "_x.txt";
string quad_r_filename = quad_filename + "_r.txt";
//
// Get the maximum degree:
//
try
{
degree_max = Convert.ToInt32(args[1]);
}
catch
{
Console.WriteLine("");
Console.WriteLine(" Enter DEGREE_MAX, the maximum monomial degree to check.");
degree_max = Convert.ToInt32(Console.ReadLine());
}
Console.WriteLine("");
Console.WriteLine(" The requested maximum monomial degree is = " + degree_max + "");
//
// Get the exponent ALPHA:
//
try
{
alpha = Convert.ToDouble(args[2]);
}
catch
{
Console.WriteLine("");
Console.WriteLine(" ALPHA is the power of X in the weighting function.");
Console.WriteLine("");
Console.WriteLine(" ALPHA is a real number greater than -1.0;");
Console.WriteLine("");
Console.WriteLine(" Enter ALPHA.");
alpha = Convert.ToDouble(Console.ReadLine());
}
Console.WriteLine("");
Console.WriteLine(" The requested value of ALPHA = " + alpha + "");
//
// The fourth command line argument is OPTION.
// 0 for the standard rule for integrating x^alpha*exp(-x)*f(x),
// 1 for a rule for integrating f(x).
//
try
{
option = Convert.ToInt32(args[3]);
}
catch
{
Console.WriteLine("");
Console.WriteLine("OPTION chooses the standard or modified rule.");
Console.WriteLine("0: standard rule for integrating x^allpha*exp(-x)*f(x)");
Console.WriteLine("1: modified rule for integrating f(x)");
option = Convert.ToInt32(Console.ReadLine());
}
//
// Summarize the input.
//
Console.WriteLine("");
Console.WriteLine("INT_EXACTNESS_GEN_LAGUERRE: 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 degree to check = " + degree_max + "");
Console.WriteLine(" Weighting exponent ALPHA = " + alpha + "");
switch (option)
{
case 0:
Console.WriteLine(" OPTION = 0, integrate x^alpha*exp(-x)*f(x)");
break;
default:
Console.WriteLine(" OPTION = 1, integrate f(x)");
break;
}
//
// Read the X file.
//
TableHeader h = typeMethods.r8mat_header_read(quad_x_filename);
int dim_num = h.m;
int order = h.n;
if (dim_num != 1)
{
Console.WriteLine("");
Console.WriteLine("INT_EXACTNESS_GEN_LAGUERRE - Fatal error!");
Console.WriteLine(" The spatial dimension of X should be 1.");
Console.WriteLine(" The implicit input dimension was DIM_NUM = " + dim_num + "");
return;
}
Console.WriteLine("");
Console.WriteLine(" Spatial dimension = " + dim_num + "");
Console.WriteLine(" Number of points = " + order + "");
double[] x = typeMethods.r8mat_data_read(quad_x_filename, dim_num, order);
//
// Read the W file.
//
h = typeMethods.r8mat_header_read(quad_w_filename);
int dim_num2 = h.m;
int point_num = h.n;
if (dim_num2 != 1)
{
Console.WriteLine("");
Console.WriteLine("INT_EXACTNESS_GEN_LAGUERRE - Fatal error!");
Console.WriteLine(" The quadrature weight file should have exactly");
Console.WriteLine(" one value on each line.");
return;
}
if (point_num != order)
{
Console.WriteLine("");
Console.WriteLine("INT_EXACTNESS_GEN_LAGUERRE - 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, dim_num, order);
//
// Read the R file.
//
h = typeMethods.r8mat_header_read(quad_r_filename);
dim_num2 = h.m;
int point_num2 = h.n;
if (dim_num2 != dim_num)
{
Console.WriteLine("");
Console.WriteLine("INT_EXACTNESS_GEN_LAGUERRE - Fatal error!");
Console.WriteLine(" The quadrature region file should have the");
Console.WriteLine(" same number of values on each line as the");
Console.WriteLine(" abscissa file does.");
return;
}
if (point_num2 != 2)
{
Console.WriteLine("");
Console.WriteLine("INT_EXACTNESS_GEN_LAGUERDRE - Fatal error!");
Console.WriteLine(" The quadrature region file should have two lines.");
return;
}
double[] r = typeMethods.r8mat_data_read(quad_r_filename, dim_num, point_num2);
//
// Print the input quadrature rule.
//
double a = r[0];
Console.WriteLine("");
Console.WriteLine(" The quadrature rule to be tested is");
Console.WriteLine(" a generalized Gauss-Laguerre rule");
Console.WriteLine(" ORDER = " + order + "");
Console.WriteLine(" with A = " + a + "");
Console.WriteLine(" and ALPHA = " + alpha + "");
Console.WriteLine("");
switch (option)
{
case 0:
Console.WriteLine(" Standard rule:");
Console.WriteLine(" Integral ( A <= x < +oo ) x^alpha exp(-x) f(x) dx");
Console.WriteLine(" is to be approximated by");
Console.WriteLine(" sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).");
break;
default:
Console.WriteLine(" Modified rule:");
Console.WriteLine(" Integral ( A <= x < +oo ) f(x) dx");
Console.WriteLine(" is to be approximated by");
Console.WriteLine(" sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).");
break;
}
Console.WriteLine("");
Console.WriteLine(" Weights W:");
Console.WriteLine("");
for (i = 0; i < order; i++)
{
Console.WriteLine(" w[" + i.ToString().PadLeft(2)
+ "] = " + w[i].ToString("0.################").PadLeft(24) + "");
}
Console.WriteLine("");
Console.WriteLine(" Abscissas X:");
Console.WriteLine("");
for (i = 0; i < order; i++)
{
Console.WriteLine(" x[" + i.ToString().PadLeft(2)
+ "] = " + x[i].ToString("0.################").PadLeft(24) + "");
}
Console.WriteLine("");
Console.WriteLine(" Region R:");
Console.WriteLine("");
for (i = 0; i < 2; i++)
{
Console.WriteLine(" r[" + i.ToString().PadLeft(2)
+ "] = " + r[i].ToString("0.################").PadLeft(24) + "");
}
//
// Supposing the input rule is defined on [A,+oo),
// rescale the weights, and translate the abscissas,
// so our rule is defined on [0,+oo).
//
double volume = Math.Exp(-a);
for (i = 0; i < order; i++)
{
w[i] /= volume;
}
for (i = 0; i < order; i++)
{
x[i] -= a;
}
//
// Explore the monomials.
//
Console.WriteLine("");
Console.WriteLine(" A generalized Gauss-Laguerre rule would be able to exactly");
Console.WriteLine(" integrate monomials up to and including degree = " +
(2 * order - 1) + "");
Console.WriteLine("");
Console.WriteLine(" Error Degree");
Console.WriteLine("");
for (degree = 0; degree <= degree_max; degree++)
{
double quad_error = QuadratureRule.monomial_quadrature_gen_laguerre(degree, alpha, order,
option, w, x);
Console.WriteLine(" " + quad_error.ToString("0.################").PadLeft(24)
+ " " + degree.ToString().PadLeft(2) + "");
}
Console.WriteLine("");
Console.WriteLine("INT_EXACTNESS_GEN_LAGUERRE:");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}