private static void test06()
//****************************************************************************80
//
// Purpose:
//
// TEST06 tests FILON_FUN_COS.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 20 May 2014
//
// Author:
//
// John Burkardt
//
{
int j;
//
// Example suggested by James Roedder.
//
Console.WriteLine("");
Console.WriteLine("TEST06");
Console.WriteLine(" Integrate F(X)=log(1+X)*Math.Sin(T*X):");
Console.WriteLine(" Supply integrand as a function.");
Console.WriteLine(" T = 10, and N increases");
Console.WriteLine("");
Console.WriteLine(" N Approximate Exact Error");
Console.WriteLine("");
double a = 0.0;
double b = 2.0 * Math.PI;
for (j = 1; j <= 6; j++)
{
int n = (int)Math.Pow(2, j) * 10 + 1;
double t = 10.0;
double result = Filon.filon_fun_sin(n, log_integrand, a, b, t);
double exact = -0.19762680771872;
double error = result - exact;
Console.WriteLine(n.ToString(CultureInfo.InvariantCulture).PadLeft(6) + " "
+ result.ToString(CultureInfo.InvariantCulture).PadLeft(24) + " "
+ exact.ToString(CultureInfo.InvariantCulture).PadLeft(24) + " "
+ error.ToString(CultureInfo.InvariantCulture).PadLeft(24) + "");
}
}
private static void test01()
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests FILON_TAB_COS.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 20 May 2014
//
// Author:
//
// John Burkardt
//
{
double exact = 0;
double[] ftab = new double[1];
int i;
int k;
double t = 0;
const double a = 0.0;
const double b = 2.0 * Math.PI;
int n = 11;
//
// Set the X values.
//
double[] x = new double[n];
for (i = 0; i < n; i++)
{
x[i] = ((n - i - 1) * a
+ i * b)
/ (n - 1);
}
Console.WriteLine("");
Console.WriteLine("TEST01");
Console.WriteLine(" FILON_TAB_COS estimates the integral of.");
Console.WriteLine(" F(X) * COS ( T * X )");
Console.WriteLine(" Use integrands F(X)=1, X, X^2.");
Console.WriteLine("");
Console.WriteLine(" A = " + a + "");
Console.WriteLine(" B = " + b + "");
Console.WriteLine(" N = " + n + "");
Console.WriteLine("");
Console.WriteLine(" T Approximate Exact");
for (k = 1; k <= 3; k++)
{
t = k switch
{
1 => 1.0,
2 => 2.0,
3 => 10.0,
_ => t
};
Console.WriteLine("");
for (i = 1; i <= 3; i++)
{
ftab = i switch
{
1 => zero_integrand(n, x),
2 => one_integrand(n, x),
3 => two_integrand(n, x),
_ => ftab
};
double result = Filon.filon_tab_cos(n, ftab, a, b, t);
exact = i switch
{
1 => (Math.Sin(t * b) - Math.Sin(t * a)) / t,
2 => (Math.Cos(t * b) + t * b * Math.Sin(t * b) - (Math.Cos(t * a) + t * a * Math.Sin(t * a))) / t /
t,
3 => (2.0 * t * b * Math.Cos(t * b) + (t * t * b * b - 2.0) * Math.Sin(t * b) -
(2.0 * t * a * Math.Cos(t * a) + (t * t * a * a - 2.0) * Math.Sin(t * a))) / t / t / t,
_ => exact
};
Console.WriteLine(t.ToString(CultureInfo.InvariantCulture).PadLeft(24) + " "
+ result.ToString(CultureInfo.InvariantCulture).PadLeft(24) + " "
+ exact.ToString(CultureInfo.InvariantCulture).PadLeft(24) + "");
}
}
}
private static void test05()
//****************************************************************************80
//
// Purpose:
//
// TEST05 tests FILON_TAB_COS.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 20 May 2014
//
// Author:
//
// John Burkardt
//
{
int j;
//
// Example suggested by James Roedder.
//
Console.WriteLine("");
Console.WriteLine("TEST05");
Console.WriteLine(" Integrate F(X)=log(1+X)*Math.Sin(T*X):");
Console.WriteLine(" Supply integrand as a table.");
Console.WriteLine(" T = 10, and N increases");
Console.WriteLine("");
Console.WriteLine(" N Approximate Exact Error");
Console.WriteLine("");
const double a = 0.0;
const double b = 2.0 * Math.PI;
for (j = 1; j <= 6; j++)
{
int n = (int)Math.Pow(2, j) * 10 + 1;
//
// Set the X values.
//
double[] x = new double[n];
int i;
for (i = 0; i < n; i++)
{
x[i] = ((n - i - 1) * a
+ i * b)
/ (n - 1);
}
double[] ftab = log_integrand(n, x);
double t = 10.0;
double result = Filon.filon_tab_sin(n, ftab, a, b, t);
double exact = -0.19762680771872;
double error = result - exact;
Console.WriteLine(n.ToString(CultureInfo.InvariantCulture).PadLeft(6) + " "
+ result.ToString(CultureInfo.InvariantCulture).PadLeft(24) + " "
+ exact.ToString(CultureInfo.InvariantCulture).PadLeft(24) + " "
+ error.ToString(CultureInfo.InvariantCulture).PadLeft(24) + "");
}
}
