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Function std.numeric.kullbackLeiblerDivergence
Computes the Kullback-Leibler divergence between input ranges
abai * log(ai / bi). The base
of logarithm is 2. The ranges are assumed to contain elements in [0, 1]. Usually the ranges are normalized probability distributions,
but this is not required or checked by kullbackLeiblerDivergencebi is zero and the
corresponding element ai nonzero, returns infinity. (Otherwise,
if ai == 0 && bi == 0, the term ai * log(ai / bi) is
considered zero.) If the inputs are normalized, the result is
positive.
Prototype
CommonType!(ElementType!Range1,ElementType!Range2) kullbackLeiblerDivergence(Range1, Range2)( Range1 a, Range2 b ) if (isInputRange!Range1 && isInputRange!Range2);
Example
double[] p = [ 0.0, 0, 0, 1 ]; assert(kullbackLeiblerDivergence(p, p) == 0); double[] p1 = [ 0.25, 0.25, 0.25, 0.25 ]; assert(kullbackLeiblerDivergence(p1, p1) == 0); assert(kullbackLeiblerDivergence(p, p1) == 2); assert(kullbackLeiblerDivergence(p1, p) == double.infinity); double[] p2 = [ 0.2, 0.2, 0.2, 0.4 ]; assert(approxEqual(kullbackLeiblerDivergence(p1, p2), 0.0719281)); assert(approxEqual(kullbackLeiblerDivergence(p2, p1), 0.0780719));
Authors
Andrei Alexandrescu, Don Clugston, Robert Jacques