Macro information::joint_entropy

macro_rules! joint_entropy {
    ($prob:expr) => { ... };
}

Joint Entropy

Generalization of Entropy to multiple dimensions

https://en.wikipedia.org/wiki/Joint_entropy

Joint entropy is calculated for multiple variables as:

H(Xi ... Xn) = - Σi ... Σn P( xi, ..., xn ) * ln[ P(xi, ..., xn) ]

Usage

use ndarray::{Array1, Array2, Array3, Array4};
use ndarray_rand::{RandomExt, rand_distr::Uniform};
use information::joint_entropy;

// 1D Entropy
let c_x = Array1::random(10, Uniform::new(0.1, 0.8));
let p_x = &c_x / c_x.sum();
let h = joint_entropy!(&p_x);
assert!(h >= 0.0);

// 2D Entropy
let c_xy = Array2::random((2, 10), Uniform::new(0.1, 0.8));
let p_xy = &c_xy / c_xy.sum();
let h = joint_entropy!(&p_xy);
assert!(h >= 0.0);

// 3D Entropy
let c_xy = Array3::random((2, 2, 10), Uniform::new(0.1, 0.8));
let p_xy = &c_xy / c_xy.sum();
let h = joint_entropy!(&p_xy);
assert!(h >= 0.0);

// 4D Entropy
let c_xy = Array4::random((2, 2, 2, 10), Uniform::new(0.1, 0.8));
let p_xy = &c_xy / c_xy.sum();
let h = joint_entropy!(&p_xy);
assert!(h >= 0.0);