public static double p06_exact(ref p06Data data)
//****************************************************************************80
//
// Purpose:
//
// P06_EXACT returns the exact integral for problem 6.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 May 2009
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, double P06_EXACT, the value of the integral.
//
{
double exact;
int m = 0;
const double r8_pi = 3.141592653589793;
p06_param(ref data, 'G', 'M', ref m);
switch (m)
{
case <= -1:
exact = -typeMethods.r8_huge();
break;
default:
{
exact = (m % 2) switch
{
1 => 0.0,
_ => typeMethods.i4_factorial2(m - 1) * Math.Sqrt(r8_pi) / Math.Pow(2.0, (double)m / 2)
};
break;
}
}
return(exact);
}
public static void p06_fun(ref p06Data data, int option, int n, double[] x, ref double[] f)
//****************************************************************************80
//
// Purpose:
//
// P06_FUN evaluates the integrand for problem 6.
//
// Discussion:
//
// The exact value is (m-1)!! * sqrt ( pi ) / sqrt ( 2**m ).
//
// Integral ( -oo < x < +oo ) x^m exp (-x*x) dx
//
// The parameter M is set by calling P06_PARAM.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 May 2009
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// 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.
//
{
int i;
int m = 0;
p06_param(ref data, 'G', 'M', ref m);
for (i = 0; i < n; i++)
{
f[i] = Math.Pow(x[i], m);
}
switch (option)
{
case 0:
{
for (i = 0; i < n; i++)
{
f[i] *= Math.Exp(-x[i] * x[i]);
}
break;
}
case 1:
break;
case 2:
{
for (i = 0; i < n; i++)
{
f[i] *= Math.Exp(-x[i] * x[i] / 2.0);
}
break;
}
}
}
public static void p06_param(ref p06Data data, char action, char name, ref int value)
//****************************************************************************80
//
// Purpose:
//
// P06_PARAM gets or sets parameters for problem 6.
//
// Discussion:
//
// The parameter is named "M", and it represents the value of the exponent
// in the integrand function:
//
// Integral ( -oo < x < +oo ) x^m exp (-x*x) dx
//
// M must be greater than -1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 May 2009
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, char ACTION, the action.
// 'S' to set the value,
// 'G' to get the value.
//
// Input, char NAME, the parameter name.
// 'M', the exponent.
//
// Input/output, int *VALUE, the parameter value.
// If ACTION = 'S', then VALUE is an input quantity, and M is set to VALUE.
// If ACTION = 'G', then VALUE is an output quantity, and VALUE is set to M.
//
{
switch (action)
{
case 'S':
case 's':
{
switch (value)
{
case <= -1:
Console.WriteLine("");
Console.WriteLine("P06_PARAM - Fatal error!");
Console.WriteLine(" Parameter M must be greater than -1.");
return;
}
data.m = value;
break;
}
case 'G':
case 'g':
value = data.m;
break;
default:
Console.WriteLine("");
Console.WriteLine("P06_PARAM - Fatal error!");
Console.WriteLine(" Unrecognized value of ACTION = \"" + action + "\".");
break;
}
}
