private static void test_boundary()
//****************************************************************************80
//
// Purpose:
//
// TEST_BOUNDARY tests wrightomega() near boundaries.
//
// Discussion:
//
// This is a test driver to evaluate the Wright Omega function along the
// boundaries of the different regions of the approximations.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 17 May 2016
//
// Author:
//
// Piers Lawrence, Robert Corless, David Jeffrey
//
// Reference:
//
// Piers Lawrence, Robert Corless, David Jeffrey,
// Algorithm 917: Complex Double-Precision Evaluation of the Wright Omega
// Function,
// ACM Transactions on Mathematical Software,
// Volume 38, Number 3, Article 20, April 2012, 17 pages.
//
{
Complex cond = new();
Complex e = new();
const double exp_num = 160.0;
const string filename = "results.txt";
List <string> fp = new();
int i;
const int n = 100;
Complex r = new();
Complex w = new();
double[] x = new double[2];
double[] y = new double[2];
Complex z;
Console.WriteLine("");
Console.WriteLine("TEST_BOUNDARY:");
Console.WriteLine(" Test wrightomega_ext() near approximation region boundaries.");
Console.WriteLine(" Store results in a file for comparison with benchmark data.");
//
// We want trailing zeros, to make comparison with benchmark easier.
//
//
// Region 1;
// x=(-2.0,1.0] ,y=2*pi
//
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
x[1] = 1.0;
y[0] = NextAfterNS.NextAfter.nextafter(2.0 * Math.PI, -1.0);
double td = (x[1] - x[0]) / n;
for (i = 0; i < n; i++)
{
z = new Complex(x[0] + td * i, y[0]);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 2;
// x=1.0 ,y=(1.0,2*pi)
//
x[0] = 1.0;
y[0] = NextAfterNS.NextAfter.nextafter(1.0, 2.0);
y[1] = NextAfterNS.NextAfter.nextafter(2.0 * Math.PI, 1.0);
td = -(y[1] - y[0]) / n;
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[1] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 3;
// x=(-2.0,1.0] ,y=1.0
//
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
x[1] = 1.0;
td = -(x[1] - x[0]) / n;
y[0] = NextAfterNS.NextAfter.nextafter(1.0, 2.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[1] + td * i, y[0]);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 4;
// x=-2.0 ,y=(1.0,2*pi)
//
y[0] = NextAfterNS.NextAfter.nextafter(1.0, 2.0);
y[1] = NextAfterNS.NextAfter.nextafter(2.0 * Math.PI, -1.0);
td = (y[1] - y[0]) / n;
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[0] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 5;
// x=(-2.0,1.0] ,y=-2*pi
//
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
x[1] = 1.0;
y[0] = NextAfterNS.NextAfter.nextafter(-2.0 * Math.PI, 1.0);
td = (x[1] - x[0]) / n;
for (i = 0; i < n; i++)
{
z = new Complex(x[0] + td * i, y[0]);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 6;
// x=1.0, y=(-2*pi,-1.0)
//
y[0] = NextAfterNS.NextAfter.nextafter(-2.0 * Math.PI, 1.0);
y[1] = NextAfterNS.NextAfter.nextafter(-1.0, -2.0);
td = (y[1] - y[0]) / n;
x[0] = 1.0;
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[0] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 7;
// x=(-2.0,1.0] ,y=-1.0
//
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
x[1] = 1.0;
td = (x[0] - x[1]) / n;
y[0] = NextAfterNS.NextAfter.nextafter(-1.0, -2.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[1] + td * i, y[0]);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 8;
// x=-2.0 ,y=(-2*pi,-1.0)
//
y[0] = NextAfterNS.NextAfter.nextafter(-2.0 * Math.PI, 1.0);
y[1] = NextAfterNS.NextAfter.nextafter(-1.0, -2.0);
td = (y[0] - y[1]) / n;
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[1] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 9;
// x=-2.0 y=[-1.0,1.0]
//
y[0] = -1.0;
y[1] = 1.0;
td = (y[1] - y[0]) / n;
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[0] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 10;
// x=(-2.0,1.0] y=1.0
//
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
x[1] = 1.0;
td = (x[1] - x[0]) / n;
y[0] = 1.0;
for (i = 0; i < n; i++)
{
z = new Complex(x[0] + td * i, y[0]);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 11
// x=1.0 y=[1.0,pi]
//
y[0] = 1.0;
y[1] = Math.PI;
td = (y[1] - y[0]) / n;
x[0] = NextAfterNS.NextAfter.nextafter(1.0, 2.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[0] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 12
// (x-0.1e1)*(x-0.1e1)+y*y=pi*pi)
// (on inside)
//
td = Math.PI / n;
x[0] = Math.PI / 2.0;
for (i = 0; i < n; i++)
{
double a = NextAfterNS.NextAfter.nextafter(Math.PI, -1.0) * Math.Cos(x[0] - td * i)
+ NextAfterNS.NextAfter.nextafter(1.0, -1.0);
double b = NextAfterNS.NextAfter.nextafter(Math.PI, -1.0) * Math.Sin(x[0] - td * i);
z = new Complex(a, b);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 13
// x=1.0 y=[-pi,-1.0]
//
y[0] = -Math.PI;
y[1] = -1.0;
td = (y[1] - y[0]) / n;
x[0] = NextAfterNS.NextAfter.nextafter(1.0, 2.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[0] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 14
// x=(-2.0,1.0] y=-1.0
//
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
x[1] = 1.0;
td = (x[1] - x[0]) / n;
y[0] = -1.0;
for (i = 0; i < n; i++)
{
z = new Complex(x[0] + td * i, y[0]);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 15
// x=(-inf,-2) y=pi^+
//
for (i = 0; i < n; i++)
{
x[0] = NextAfterNS.NextAfter.nextafter(-1.0 - Math.Exp((n - 1 - i) / exp_num),
typeMethods.r8_huge());
y[0] = NextAfterNS.NextAfter.nextafter(Math.PI - 0.75 * (x[0] + 1.0), typeMethods.r8_huge());
z = new Complex(x[0], y[0]);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 16
//
y[0] = 0.75 + Math.PI;
y[1] = 2.0 * Math.PI;
td = (y[1] - y[0]) / n;
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, -3.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[0] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 17
// x=(-2.0,1.0] ,y=2*pi
//
x[0] = NextAfterNS.NextAfter.nextafter(-2.0, 1.0);
x[1] = 1.0;
y[0] = 2.0 * Math.PI;
td = (x[1] - x[0]) / n;
for (i = 0; i < n; i++)
{
z = new Complex(x[0] + td * i, y[0]);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
/*
* Region 18
* x=1.0 ,y=(pi,2*pi)
*/
y[0] = NextAfterNS.NextAfter.nextafter(Math.PI, 6.0);
y[1] = NextAfterNS.NextAfter.nextafter(2.0 * Math.PI, 1.0);
td = -(y[1] - y[0]) / n;
x[0] = NextAfterNS.NextAfter.nextafter(1.0, 2.0);
for (i = 0; i < n; i++)
{
z = new Complex(x[0], y[1] + td * i);
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref cond);
fp.Add(z.Real + " "
+ z.Imaginary + " "
+ w.Real + " "
+ w.Imaginary + "");
}
//
// Region 19
// (x-0.1e1)*(x-0.1e1)+y*y=pi*pi)
// (on outside)
//
td = Math.PI / (n - 1);
y[0] = Math.PI / 2.0;
for (i = 0; i < n; i++)
{
y[1] = Math.PI * Math.Sin(y[0] - td * i);
x[0] = Math.Sqrt(Math.PI * Math.PI - y[1] * y[1]) + 1.0;
z = y[1] switch
{
private static void driver(Complex z)
//****************************************************************************80
//
// Purpose:
//
// DRIVER calls the simple and extended Wright Omega evaluators.
//
// Modified:
//
// 14 May 2016
//
// Author:
//
// Piers Lawrence, Robert Corless, David Jeffrey
//
// Reference:
//
// Piers Lawrence, Robert Corless, David Jeffrey,
// Algorithm 917: Complex Double-Precision Evaluation of the Wright Omega
// Function,
// ACM Transactions on Mathematical Software,
// Volume 38, Number 3, Article 20, April 2012, 17 pages.
//
// Parameters:
//
// Input, Complex Z, the argument of the Wright Omega function.
//
{
Complex condest = new();
Complex e = new();
Complex r = new();
Console.WriteLine("");
Console.WriteLine("DRIVER:");
Console.WriteLine(" Demonstrate simple and extended Wright Omega evaluators.");
//
// Simple evaluator.
//
Complex w = WrightOmega.wrightomega(z);
Console.WriteLine("");
Console.WriteLine(" Calling:");
Console.WriteLine(" w = wrightomega(z);");
Console.WriteLine(" returns:");
Console.WriteLine(" w = omega(" + z.Real
+ ", " + z.Imaginary
+ ") = ( " + w.Real
+ ", " + w.Imaginary + ")");
//
// Extended evaluator.
//
WrightOmega.wrightomega_ext(z, ref w, ref e, ref r, ref condest);
Console.WriteLine("");
Console.WriteLine(" Calling:");
Console.WriteLine(" wrightomega_ext ( z, w, e, r, condest );");
Console.WriteLine(" returns:");
Console.WriteLine(" w = omega(" + z.Real
+ ", " + z.Imaginary
+ ") = ( " + w.Real
+ ", " + w.Imaginary + ")");
Console.WriteLine(" e = last update step = ( " + e.Real
+ ", " + e.Imaginary + ")");
Console.WriteLine(" r = penultimate residual = ( " + r.Real
+ ", " + r.Imaginary + ")");
Console.WriteLine(" condest = condition number estimate = ( " + condest.Real
+ ", " + condest.Imaginary + ")");
//
// Calculate and print ultimate residual.
//
Complex r_ult = (2.0 * w * w - 8.0 * w - 1.0)
/ Complex.Pow(1.0 + w, 6.0) * r * r * r * r;
Console.WriteLine("");
Console.WriteLine(" ultimate residual = ( " + r_ult.Real
+ ", " + r_ult.Imaginary + ")");
}