komm.entropy

Computes the entropy of a random variable with a given pmf. Let $X$ be a random variable with pmf $p_X$ and alphabet $\mathcal{X}$. Its entropy is given by $$ \mathrm{H}(X) = \sum_{x \in \mathcal{X}} p_X(x) \log \frac{1}{p_X(x)}. $$ By default, the base of the logarithm is $2$, in which case the entropy is measured in bits. For more details, see CT06, Ch. 2.

Parameters:

• pmf (Array1D[float]) –

  The probability mass function $p_X$ of the random variable. It must be a valid pmf, that is, all of its values must be non-negative and sum up to $1$.

• base (Optional[float | str]) –

  The base of the logarithm to be used. It must be a positive float or the string 'e'. The default value is 2.0.

Returns:

• entropy (float) –

  The entropy $\mathrm{H}(X)$ of the random variable.

Examples:

>>> komm.entropy([1/4, 1/4, 1/4, 1/4])
np.float64(2.0)

>>> komm.entropy(pmf=[1/3, 1/3, 1/3], base=3.0)
np.float64(1.0)

>>> komm.entropy([0.5, 0.5], base='e')
np.float64(0.6931471805599453)