# picos.expressions.exp_entropy¶

Implements Entropy and NegativeEntropy.

Classes

class picos.expressions.exp_entropy.Entropy(x, y=None)[source]

Entropy or negative relative entropy of an affine expression.

Negative relative entropy is also known as the perspective of the logarithm.

Definition

Let be an -dimensional real affine expression.

1. If no additional expression is given, this is the entropy 2. If an additional affine expression of same shape as is given, this is the negative relative entropy (or logarithmic perspective) Warning

When you pose a lower bound on this expression, then PICOS enforces through an auxiliary constraint during solution search. When an additional expression is given, PICOS enforces as well.

__init__(x, y=None)[source]

Construct an Entropy.

Parameters
• x (AffineExpression) – The affine expression .

• y (AffineExpression) – An additional affine expression . If necessary, PICOS will attempt to reshape or broadcast it to the shape of .

property n

Length of x.

property x

The expression .

property y

The additional expression , or None.

class picos.expressions.exp_entropy.NegativeEntropy(x, y=None)[source]

Negative or relative entropy of an affine expression.

Relative entropy is also known as the Kullback-Leibler divergence.

Definition

Let be an -dimensional real affine expression.

1. If no additional expression is given, this is the negative entropy 2. If an additional affine expression of same shape as is given, this is the relative entropy (or Kullback-Leibler divergence) Warning

When you pose an upper bound on this expression, then PICOS enforces through an auxiliary constraint during solution search. When an additional expression is given, PICOS enforces as well.

__init__(x, y=None)[source]

Construct a NegativeEntropy.

Parameters
• x (AffineExpression) – The affine expression .

• y (AffineExpression) – An additional affine expression . If necessary, PICOS will attempt to reshape or broadcast it to the shape of .

property n

Length of x.

property x

The expression .

property y

The additional expression , or None.