/// <summary>
/// Lanczos window.
/// Periodic version, useful e.g. for FFT purposes.
/// </summary>
public static double[] LanczosPeriodic(int width)
{
double phaseStep = 2.0 / width;
var w = new double[width];
for (int i = 0; i < w.Length; i++)
{
w[i] = Trig.Sinc(i * phaseStep - 1.0);
}
return(w);
}
Exponential()
{
double exp = Math.Exp(real);
if (IsReal)
{
return(new Complex(exp, 0d));
}
return(new Complex(
exp * Trig.Cosine(imag),
exp * Trig.Sine(imag)
));
}
HyperbolicCotangent()
{
if (IsReal)
{
return(new Complex(Trig.HyperbolicCotangent(real), 0d));
}
double sini = Trig.Sine(imag);
double sinhr = Trig.HyperbolicSine(real);
double denom = sini * sini + sinhr * sinhr;
return(new Complex(
sinhr * Trig.HyperbolicCosine(real) / denom,
sini * Trig.Cosine(imag) / denom
));
}
HyperbolicTangent()
{
if (IsReal)
{
return(new Complex(Trig.HyperbolicTangent(real), 0d));
}
double cosi = Trig.Cosine(imag);
double sinhr = Trig.HyperbolicSine(real);
double denom = cosi * cosi + sinhr * sinhr;
return(new Complex(
Trig.HyperbolicCosine(real) * sinhr / denom,
cosi * Trig.Sine(imag) / denom
));
}
Cosecant()
{
if (IsReal)
{
return(new Complex(Trig.Cosecant(real), 0d));
}
double sinr = Trig.Sine(real);
double sinhi = Trig.HyperbolicSine(imag);
double denom = sinr * sinr + sinhi * sinhi;
return(new Complex(
sinr * Trig.HyperbolicCosine(imag) / denom,
-Trig.Cosine(real) * sinhi / denom
));
}
Tangent()
{
if (IsReal)
{
return(new Complex(Trig.Tangent(real), 0d));
}
double cosr = Trig.Cosine(real);
double sinhi = Trig.HyperbolicSine(imag);
double denom = cosr * cosr + sinhi * sinhi;
return(new Complex(
Trig.Sine(real) * cosr / denom,
sinhi * Trig.HyperbolicCosine(imag) / denom
));
}
public static Complex Tanh(Complex value)
{
return(Trig.Tanh(value));
}
public static Complex Cosh(Complex value)
{
return(Trig.Cosh(value));
}
public static Complex Sinh(Complex value)
{
return(Trig.Sinh(value));
}
public static Complex Atan(Complex value)
{
return(Trig.Atan(value));
}
public static Complex Acos(Complex value)
{
return(Trig.Acos(value));
}
/// <summary>Trigonometric Hyperbolic Cosine (cosh, Cosinus hyperbolicus) of this <c>Complex</c>.</summary>
public Complex HyperbolicCosine()
{
if (IsReal)
{
return(new Complex(Trig.HyperbolicCosine(real), 0d));
}
return(new Complex(Trig.HyperbolicCosine(real) * Trig.Cosine(imag), Trig.HyperbolicSine(real) * Trig.Sine(imag)));
}