picos.expressions.exp_mtxgeomean

Implements MatrixGeometricMean.

Classes

class picos.expressions.exp_mtxgeomean.MatrixGeometricMean(X, Y, power=0.5)[source]

Bases: Expression

Matrix geometric mean of an affine expression.

Definition

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

X^{1/2} (X^{-1/2}Y^{-1}X^{-1/2})^p X^{1/2}.

for a given scalar p\in[-1, 2], where p=1/2 by default.

Warning

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

__init__(X, Y, power=0.5)[source]

Construct an MatrixGeometricMean.

Parameters
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 power

The power p.

property tr

Trace of the matrix geometric mean.

class picos.expressions.exp_mtxgeomean.TrMatrixGeometricMean(X, Y, power=0.5)[source]

Bases: MatrixGeometricMean

Trace matrix geometric mean 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} (X^{-1/2}Y^{-1}X^{-1/2})^p X^{1/2}).

for a given scalar p\in[-1, 2], where p=1/2 by default.

Warning

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

__ge__(other)[source]

Return a constraint that the expression is lower-bounded.

__init__(X, Y, power=0.5)[source]

Construct an MatrixGeometricMean.

Parameters
__le__(other)[source]

Return a constraint that the expression is upper-bounded.