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#pragma once
#include <complex>
#include <random>
template <class T = double> class complex_normal_distribution {
private:
std::normal_distribution<T> d;
double δx;
double δy;
std::complex<T> μ;
std::complex<T> eθ;
public:
complex_normal_distribution(std::complex<T> μ, T σ, std::complex<T> κ) : μ(μ), d(0, σ / sqrt(2)) {
δx = sqrt(1 + std::abs(κ));
δy = sqrt(1 - std::abs(κ));
eθ = std::polar(1.0, std::arg(κ));
}
template <class Generator> std::complex<T> operator()(Generator& g) {
// First generate an axis-aligned complex number centered at the origin.
std::complex<T> z(d(g) * δx, d(g) * δy);
// Shift and rotate the number.
return μ + eθ * z;
}
};
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