// Return Exp(-Abs(x)) * I(v, z) where x = z.Real
public static Complex ScaledCbesi(double v, Complex z)
{
if (double.IsNaN(v) || double.IsNaN(z.Real) || double.IsNaN(z.Imaginary))
{
return(new Complex(double.NaN, double.NaN));
}
int sign = 1;
if (v < 0)
{
v = -v;
sign = -1;
}
int n = 1;
int kode = 2;
int nz = 0;
int ierr = 0;
double[] cyir = new double[n];
double[] cyii = new double[n];
for (int i = 0; i < n; i++)
{
cyir[i] = double.NaN;
cyii[i] = double.NaN;
}
AmosHelper.zbesi(z.Real, z.Imaginary, v, kode, n, cyir, cyii, ref nz, ref ierr);
Complex cyi = new Complex(cyir[0], cyii[0]);
if (sign == -1)
{
if (!ReflectI(cyi, v))
{
double[] cykr = new double[n];
double[] cyki = new double[n];
AmosHelper.zbesk(z.Real, z.Imaginary, v, kode, n, cykr, cyki, ref nz, ref ierr);
Complex cyk = new Complex(cykr[0], cyki[0]);
//adjust scaling to match zbesi
cyk = Rotate(cyk, -z.Imaginary / Math.PI);
if (z.Real > 0)
{
cyk = new Complex(cyk.Real * Math.Exp(-2 * z.Real), cyk.Imaginary * Math.Exp(-2 * z.Real));
}
//v -> -v
cyi = RotateI(cyi, cyk, v);
}
}
return(cyi);
}
// Returns K(v, z)
public static Complex Cbesk(double v, Complex z)
{
if (double.IsNaN(v) || double.IsNaN(z.Real) || double.IsNaN(z.Imaginary))
{
return(new Complex(double.NaN, double.NaN));
}
if (v < 0)
{
//K_v == K_{-v} even for non-integer v
v = -v;
}
int n = 1;
int kode = 1;
int nz = 0;
int ierr = 0;
double[] cykr = new double[n];
double[] cyki = new double[n];
for (int i = 0; i < n; i++)
{
cykr[i] = double.NaN;
cyki[i] = double.NaN;
}
AmosHelper.zbesk(z.Real, z.Imaginary, v, kode, n, cykr, cyki, ref nz, ref ierr);
Complex cyk = new Complex(cykr[0], cyki[0]);
if (ierr == 1)
{
if (z.Real == 0.0 && z.Imaginary == 0.0)
{
cyk = new Complex(double.PositiveInfinity, 0);
}
}
else if (ierr == 2)
{
if (z.Real >= 0 && z.Imaginary == 0)
{
//overflow
cyk = new Complex(double.PositiveInfinity, 0);
}
}
return(cyk);
}
// Returns I(v, z)
public static Complex Cbesi(double v, Complex z)
{
if (double.IsNaN(v) || double.IsNaN(z.Real) || double.IsNaN(z.Imaginary))
{
return(new Complex(double.NaN, double.NaN));
}
int sign = 1;
if (v < 0)
{
v = -v;
sign = -1;
}
int n = 1;
int kode = 1;
int nz = 0;
int ierr = 0;
double[] cyir = new double[n];
double[] cyii = new double[n];
for (int i = 0; i < n; i++)
{
cyir[i] = double.NaN;
cyii[i] = double.NaN;
}
AmosHelper.zbesi(z.Real, z.Imaginary, v, kode, n, cyir, cyii, ref nz, ref ierr);
Complex cyi = new Complex(cyir[0], cyii[0]);
if (ierr == 2)
{
//overflow
if (z.Imaginary == 0 && (z.Real >= 0 || v == Math.Floor(v)))
{
if (z.Real < 0 && v / 2 != Math.Floor(v / 2))
{
cyi = new Complex(double.NegativeInfinity, 0);
}
else
{
cyi = new Complex(double.PositiveInfinity, 0);
}
}
else
{
cyi = ScaledCbesi(v * sign, z);
cyi = new Complex(cyi.Real * double.PositiveInfinity, cyi.Imaginary * double.PositiveInfinity);
}
}
if (sign == -1)
{
if (!ReflectI(cyi, v))
{
double[] cykr = new double[n];
double[] cyki = new double[n];
AmosHelper.zbesk(z.Real, z.Imaginary, v, kode, n, cykr, cyki, ref nz, ref ierr);
Complex cyk = new Complex(cykr[0], cyki[0]);
cyi = RotateI(cyi, cyk, v);
}
}
return(cyi);
}