Implements 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.


Denote the Euclidean or Frobenius norm of the expression.


Return self>=value.

__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.


Return self<=value.