public static double p20_exact(ref p20Data data)
//****************************************************************************80
//
// Purpose:
//
// P20_EXACT returns the exact integral for problem 20.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 December 2011
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, double P20_EXACT, the value of the integral.
//
{
double exact = (
Math.Log(1.5) / Math.Pow(2.0, p20Data.beta)
- 1.0 / Math.Pow(2.0, p20Data.beta + 1.0) *
Math.Log((16.0 + Math.Pow(0.25, p20Data.beta)) / (1.0 + Math.Pow(0.25, p20Data.beta)))
- Math.Atan(Math.Pow(2.0, p20Data.beta + 2.0)) - Math.Atan(Math.Pow(2.0, p20Data.beta))
) / (1.0 + Math.Pow(0.25, p20Data.beta));
return(exact);
}
public static double[] p20_fun(ref p20Data data, int n, double[] x)
//****************************************************************************80
//
// Purpose:
//
// P20_FUN evaluates the integrand for problem 20.
//
// Integral:
//
// Integral ( 0 <= x < +oo )
// 1 / ( 2^beta * ( ( x - 1 )^2 + (1/4)^beta ) * ( x - 2 ) ) dx
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 27 December 2011
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Robert Piessens, Elise de Doncker-Kapenga,
// Christian Ueberhuber, David Kahaner,
// QUADPACK: A Subroutine Package for Automatic Integration,
// Springer, 1983, page 84.
//
// Parameters:
//
// Input, int N, the number of evaluation points.
//
// Input, double X[N], the evaluation points.
//
// Output, double P20_FUN[N], the integrand values.
//
{
int i;
double[] fx = new double[n];
for (i = 0; i < n; i++)
{
if (Math.Pow(x[i] - 1.0, 2) + Math.Pow(0.25, p20Data.beta) == 0.0 || Math.Abs(x[i] - 2.0) <= double.Epsilon)
{
fx[i] = 0.0;
}
else
{
fx[i] = 1.0 /
(Math.Pow(2.0, p20Data.beta)
* (Math.Pow(x[i] - 1.0, 2) + Math.Pow(0.25, p20Data.beta))
* (x[i] - 2.0));
}
}
return(fx);
}