private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 tests P00_GAUSS_HERMITE against the polynomials.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 May 2009
//
// Author:
//
// John Burkardt
//
{
int m;
Problem00.p00Data data = new();
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" P00_GAUSS_HERMITE applies a Gauss-Hermite rule to");
Console.WriteLine(" estimate the integral x^m exp(-x*x) over (-oo,+oo).");
const int problem = 6;
Console.WriteLine("");
Console.WriteLine(" M Order Estimate Exact Error");
for (m = 0; m <= 6; m++)
{
Problem06.p06_param(ref data.p6data, 'S', 'M', ref m);
double exact = Problem00.p00_exact(ref data, problem);
Console.WriteLine("");
int order;
for (order = 1; order <= 3 + m / 2; order++)
{
double estimate = Problem00.p00_gauss_hermite(ref data, problem, order);
double error = Math.Abs(exact - estimate);
Console.WriteLine(" " + m.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + order.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + estimate.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(14)
+ " " + error.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
}
private static void test02()
//****************************************************************************80
//
// Purpose:
//
// TEST02 tests P00_EXACT.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 May 2009
//
// Author:
//
// John Burkardt
//
{
int problem;
Problem00.p00Data data = new();
Console.WriteLine("");
Console.WriteLine("TEST02");
Console.WriteLine(" P00_EXACT returns the \"exact\" integral.");
int problem_num = Problem00.p00_problem_num();
int m = 4;
Problem06.p06_param(ref data.p6data, 'S', 'M', ref m);
Console.WriteLine("");
Console.WriteLine(" Problem EXACT");
Console.WriteLine("");
for (problem = 1; problem <= problem_num; problem++)
{
double exact = Problem00.p00_exact(ref data, problem);
Console.WriteLine(" " + problem.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + exact.ToString("0.################").PadLeft(24) + "");
}
}
public void Problem06_Return_Result_25164150()
{
double act = Problem06.SumSquareDifference();
Assert.True(act.Equals(25164150));
}
private static void test06()
//****************************************************************************80
//
// Purpose:
//
// TEST06 tests P00_MONTE_CARLO.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 17 May 2010
//
// Author:
//
// John Burkardt
//
{
int problem;
Problem00.p00Data data = new();
Console.WriteLine("");
Console.WriteLine("TEST06");
Console.WriteLine(" P00_MONTE_CARLO uses a weighted form of the Monte Carlo method");
Console.WriteLine(" to estimate a Hermite integral on (-oo,+oo).");
int problem_num = Problem00.p00_problem_num();
int m = 4;
Problem06.p06_param(ref data.p6data, 'S', 'M', ref m);
Console.WriteLine("");
Console.WriteLine(" Problem Order Estimate Exact Error");
for (problem = 1; problem <= problem_num; problem++)
{
double exact = Problem00.p00_exact(ref data, problem);
int order = 128;
Console.WriteLine("");
int order_log;
for (order_log = 0; order_log <= 6; order_log++)
{
double estimate = Problem00.p00_monte_carlo(ref data, problem, order);
double error = Math.Abs(exact - estimate);
Console.WriteLine(" " + problem.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + order.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + estimate.ToString("0.######").PadLeft(14)
+ " " + exact.ToString("0.######").PadLeft(14)
+ " " + error.ToString("0.######").PadLeft(14) + "");
order *= 4;
}
}
}
private static void test04()
//****************************************************************************80
//
// Purpose:
//
// TEST04 tests P00_TURING.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 May 2009
//
// Author:
//
// John Burkardt
//
{
int n = 0;
int test;
double tol = 0;
Problem00.p00Data data = new();
Console.WriteLine("");
Console.WriteLine("TEST04");
Console.WriteLine(" P00_TURING applies a Turing procedure");
Console.WriteLine(" to estimate an integral on (-oo,+oo).");
int problem_num = Problem00.p00_problem_num();
int m = 4;
Problem06.p06_param(ref data.p6data, 'S', 'M', ref m);
for (test = 1; test <= 2; test++)
{
tol = test switch
{
1 => 1.0E-4,
2 => 1.0E-07,
_ => tol
};
Console.WriteLine("");
Console.WriteLine(" Using a tolerance of TOL = " + tol + "");
Console.WriteLine("");
Console.WriteLine(" Problem Order Estimate Exact Error");
int problem;
for (problem = 1; problem <= problem_num; problem++)
{
double exact = Problem00.p00_exact(ref data, problem);
double h = 1.0;
Console.WriteLine("");
int order_log;
for (order_log = 0; order_log <= 6; order_log++)
{
double estimate = Problem00.p00_turing(ref data, problem, h, tol, ref n);
double error = Math.Abs(exact - estimate);
Console.WriteLine(" " + problem.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + h.ToString(CultureInfo.InvariantCulture).PadLeft(10)
+ " " + n.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + estimate.ToString("0.######").PadLeft(14)
+ " " + exact.ToString("0.######").PadLeft(14)
+ " " + error.ToString("0.######").PadLeft(14) + "");
h /= 2.0;
}
}
}
}
private static void test03()
//****************************************************************************80
//
// Purpose:
//
// TEST03 tests P00_GAUSS_HERMITE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 May 2009
//
// Author:
//
// John Burkardt
//
{
int problem;
Problem00.p00Data data = new();
Console.WriteLine("");
Console.WriteLine("TEST03");
Console.WriteLine(" P00_GAUSS_HERMITE applies a Gauss-Hermite rule");
Console.WriteLine(" to estimate an integral on (-oo,+oo).");
int problem_num = Problem00.p00_problem_num();
int m = 4;
Problem06.p06_param(ref data.p6data, 'S', 'M', ref m);
Console.WriteLine("");
Console.WriteLine(" Problem Order Estimate Exact Error");
for (problem = 1; problem <= problem_num; problem++)
{
double exact = Problem00.p00_exact(ref data, problem);
int order = 1;
Console.WriteLine("");
int order_log;
for (order_log = 0; order_log <= 6; order_log++)
{
double estimate = Problem00.p00_gauss_hermite(ref data, problem, order);
double error = Math.Abs(exact - estimate);
Console.WriteLine(" " + problem.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + order.ToString(CultureInfo.InvariantCulture).PadLeft(8)
+ " " + estimate.ToString("0.######").PadLeft(14)
+ " " + exact.ToString("0.######").PadLeft(14)
+ " " + error.ToString("0.######").PadLeft(14) + "");
order *= 2;
}
}
}
public static void p00_fun(ref p00Data data, int problem, int option, int n, double[] x, ref double[] f)
//****************************************************************************80
//
// Purpose:
//
// P00_FUN evaluates the integrand for any problem.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 31 July 2010
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROBLEM, the index of the problem.
//
// Input, int OPTION:
// 0, integrand is f(x).
// 1, integrand is exp(-x*x) * f(x);
// 2, integrand is exp(-x*x/2) * f(x);
//
// Input, int N, the number of points.
//
// Input, double X[N], the evaluation points.
//
// Output, double F[N], the function values.
//
{
switch (problem)
{
case 1:
Problem01.p01_fun(option, n, x, ref f);
break;
case 2:
Problem02.p02_fun(option, n, x, ref f);
break;
case 3:
Problem03.p03_fun(option, n, x, ref f);
break;
case 4:
Problem04.p04_fun(option, n, x, ref f);
break;
case 5:
Problem05.p05_fun(option, n, x, ref f);
break;
case 6:
Problem06.p06_fun(ref data.p6data, option, n, x, ref f);
break;
case 7:
Problem07.p07_fun(option, n, x, ref f);
break;
case 8:
Problem08.p08_fun(option, n, x, ref f);
break;
default:
Console.WriteLine("");
Console.WriteLine("P00_FUN - Fatal error!");
Console.WriteLine(" Illegal problem number = " + problem + "");
break;
}
}
public static string p00_title(int problem)
//****************************************************************************80
//
// Purpose:
//
// P00_TITLE returns the title for any problem.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 February 2010
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROBLEM, the index of the problem.
//
// Output, string P00_TITLE, the title of the problem.
//
{
string title;
switch (problem)
{
case 1:
title = Problem01.p01_title();
break;
case 2:
title = Problem02.p02_title();
break;
case 3:
title = Problem03.p03_title();
break;
case 4:
title = Problem04.p04_title();
break;
case 5:
title = Problem05.p05_title();
break;
case 6:
title = Problem06.p06_title();
break;
case 7:
title = Problem07.p07_title();
break;
case 8:
title = Problem08.p08_title();
break;
default:
Console.WriteLine("");
Console.WriteLine("P00_TITLE - Fatal error!");
Console.WriteLine(" Illegal problem number = " + problem + "");
return("");
}
return(title);
}
public static double p00_exact(ref p00Data data, int problem)
//****************************************************************************80
//
// Purpose:
//
// P00_EXACT returns the exact integral for any problem.
//
// Discussion:
//
// This routine provides a "generic" interface to the exact integral
// routines for the various problems, and allows a problem to be called
// by index (PROBLEM) rather than by name.
//
// In most cases, the "exact" value of the integral is not given;
// instead a "respectable" approximation is available.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 31 Julyl 2010
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROBLEM, the index of the problem.
//
// Output, double P00_EXACT, the exact value of the integral.
//
{
double exact;
switch (problem)
{
case 1:
exact = Problem01.p01_exact();
break;
case 2:
exact = Problem02.p02_exact();
break;
case 3:
exact = Problem03.p03_exact();
break;
case 4:
exact = Problem04.p04_exact();
break;
case 5:
exact = Problem05.p05_exact();
break;
case 6:
exact = Problem06.p06_exact(ref data.p6data);
break;
case 7:
exact = Problem07.p07_exact();
break;
case 8:
exact = Problem08.p08_exact();
break;
default:
Console.WriteLine("");
Console.WriteLine("P00_EXACT - Fatal error!");
Console.WriteLine(" Illegal problem number = " + problem + "");
return(1);
}
return(exact);
}
