picos.expressions.uncertain.uexp_affine¶

Implements UncertainAffineExpression.

Outline¶

Classes¶

UncertainAffineExpression

A multidimensional uncertain affine expression.

Classes¶

UncertainAffineExpression¶

class picos.expressions.uncertain.uexp_affine.UncertainAffineExpression(string, shape=(1, 1), coefficients={})[source]¶

Bases: picos.expressions.uncertain.uexpression.UncertainExpression, picos.expressions.exp_biaffine.BiaffineExpression

A multidimensional uncertain affine expression.

This expression has the form

$A(x,\theta) = B(x,\theta) + P(x) + Q(\theta) + C$

where $B$ , $P$ , $Q$ , $C$ and $x$ are defined as for the BiaffineExpression base class and $\theta$ is an uncertain perturbation parameter confined to (distributed according to) a perturbation set (distribution) $\Theta$ .

If no coefficient matrices defining $B$ and $P$ are provided, then this expression represents uncertain data confined to an uncertainty set $\{Q(\theta) + C \mid \theta \in \Theta\}$ (distributed according to $Q(\Theta) + C$ ) where $C$ can be understood as a nominal data value while $Q(\theta)$ quantifies the uncertainty on the data.

__init__(string, shape=(1, 1), coefficients={})[source]¶

Construct an UncertainAffineExpression.

Extends exp_biaffine.BiaffineExpression.__init__.

This constructor is meant for internal use. As a user, you will want to first define a universe (e.g. ConicPerturbationSet) for a perturbation parameter and use that parameter as a building block to create more complex uncertain expressions.