picos.expressions.exp_oprelentr¶

Implements OperatorRelativeEntropy.

Classes

class picos.expressions.exp_oprelentr.OperatorRelativeEntropy(X, Y)[source]¶

Bases: Expression

Operator relative entropy of an affine expression.

Definition

For $n \times n$ -dimensional symmetric or Hermitian matrices $X$ and $Y$ , this is defined as

$X^{1/2} \log(X^{1/2}Y^{-1}X^{1/2}) X^{1/2}.$

Warning

When you pose an upper bound on this expression, then PICOS enforces $X \succeq 0$ and $Y \succeq 0$ through an auxiliary constraint during solution search.

__init__(X, Y)[source]¶

Construct an OperatorRelativeEntropy.

Parameters

X (AffineExpression) – The affine expression $X$ .
Y (AffineExpression) – The affine expression $Y$ . This should have the same dimensions as $X$ .

property X¶: The expression $X$ .

property Y¶: The additional expression $Y$ .

property iscomplex¶: Whether X and Y are complex expressions or not.

property n¶: Lengths of X and Y.

property tr¶: Trace of the operator relative entropy.

class picos.expressions.exp_oprelentr.TrOperatorRelativeEntropy(X, Y)[source]¶

Bases: OperatorRelativeEntropy

Trace operator relative entropy of an affine expression.

Definition

For $n \times n$ -dimensional symmetric or Hermitian matrices $X$ and $Y$ , this is defined as

$\operatorname{Tr}(X^{1/2} \log(X^{1/2}Y^{-1}X^{1/2}) X^{1/2}).$

Warning

When you pose an upper bound on this expression, then PICOS enforces $X \succeq 0$ and $Y \succeq 0$ through an auxiliary constraint during solution search.

__init__(X, Y)[source]¶

Construct an OperatorRelativeEntropy.

Parameters

X (AffineExpression) – The affine expression $X$ .
Y (AffineExpression) – The affine expression $Y$ . This should have the same dimensions as $X$ .

__le__(other)[source]¶: Return a constraint that the expression is upper-bounded.

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