klDiv

constexpr double klDiv(const std::vector<Complex> &X, const std::vector<Complex> &Y) noexcept: Calculates the Kullback–Leibler (KL) divergence [1] of two complex sequences.

Parameters

const std::vector<Complex> &X

A complex sequence.

const std::vector<Complex> &Y

A complex sequence.

Returns

double

A real number.

In information theory, the KL divergence of two discrete probability distributions is defined as:

\[\DeclareMathOperator\KL{KL} D_{\KL}(P || Q) = -\sum_{x \in \mathcal{X}}P(x)\log(\frac{P(x)}{Q(x)})\]

Both sequences are normalized beforehand.

Example

std::vector<Complex> X = {1, 2, 3, 4, 5};
std::vector<Complex> Y = {1, 2, 3, 4, 5};

std::cout << klDiv(X, Y) << "\n";

Output:

References