picos.expressions.exp_entropy¶
Implements Entropy
and NegativeEntropy
.
Classes
- class picos.expressions.exp_entropy.Entropy(x, y=None)[source]¶
Bases:
Expression
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.
If no additional expression
is given, this is the entropy
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 x¶
The expression
.
- class picos.expressions.exp_entropy.NegativeEntropy(x, y=None)[source]¶
Bases:
Expression
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.
If no additional expression
is given, this is the negative entropy
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 x¶
The expression
.