private static void cpv_test01()
//****************************************************************************80
//
// Purpose:
//
// CPV_TEST01 seeks the CPV of Integral ( -1 <= t <= 1 ) exp(t) / t dt
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 01 April 2015
//
// Author:
//
// John Burkardt
//
{
int n;
Console.WriteLine("");
Console.WriteLine("CPV_TEST01:");
Console.WriteLine(" CPV of Integral ( -1 <= t <= 1 ) exp(t) / t dt");
Console.WriteLine("");
Console.WriteLine(" N Estimate Error");
Console.WriteLine("");
double exact = 2.11450175075;
double a = -1.0;
double b = +1.0;
for (n = 2; n <= 8; n += 2)
{
double value = CauchyPrincipalValue.cpv(f01, a, b, n);
Console.WriteLine(" " + n.ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + value.ToString(CultureInfo.InvariantCulture).PadLeft(24)
+ " " + Math.Abs(value - exact).ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
private static void cpv_test02()
//****************************************************************************80
//
// Purpose:
//
// CPV_TEST02 is another test.
//
// Discussion:
//
// We seek
// CPV ( Integral ( 1-delta <= t <= 1+delta ) 1/(1-t)^3 dt )
// which we must rewrite as
// CPV ( Integral ( 1-delta <= t <= 1+delta ) 1/(1+t+t^2) 1/(1-t) dt )
// so that our "integrand" is 1/(1+t+t^2).
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 01 April 2015
//
// Author:
//
// John Burkardt
//
{
int k;
Console.WriteLine("");
Console.WriteLine("CPV_TEST02:");
Console.WriteLine(" Compute CPV ( Integral ( 1-delta <= t <= 1+delta ) 1/(1-t)^3 dt )");
Console.WriteLine(" Try this for delta = 1, 1/2, 1/4.");
Console.WriteLine("");
Console.WriteLine(" N Estimate Exact Error");
double delta = 1.0;
for (k = 1; k <= 3; k++)
{
Console.WriteLine("");
double r1 = Math.Pow(delta + 1.5, 2) + 0.75;
double r2 = Math.Pow(-delta + 1.5, 2) + 0.75;
double r3 = Math.Atan(Math.Sqrt(0.75) / (delta + 1.5));
double r4 = Math.Atan(Math.Sqrt(0.75) / (-delta + 1.5));
double exact = -Math.Log(r1 / r2) / 6.0 + (r3 - r4) / Math.Sqrt(3.0);
int n;
for (n = 2; n <= 8; n += 2)
{
double a = 1.0 - delta;
double b = 1.0 + delta;
double value = CauchyPrincipalValue.cpv(f02, a, b, n);
Console.WriteLine(" " + n.ToString(CultureInfo.InvariantCulture).PadLeft(2)
+ " " + value.ToString(CultureInfo.InvariantCulture).PadLeft(24)
+ " " + exact.ToString(CultureInfo.InvariantCulture).PadLeft(24)
+ " " + Math.Abs(value - exact).ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
delta /= 2.0;
}
}