picos.expressions.variables

Implements all mathematical variable types and their base class.

Classes

class picos.expressions.variables.BaseVariable(name, vectorization, lower=None, upper=None)[source]

Bases: Mutable

Primary base class for all variable types.

Variables need to inherit this class with priority (first class listed) and ComplexAffineExpression or AffineExpression without priority.

__init__(name, vectorization, lower=None, upper=None)[source]

Perform basic initialization for BaseVariable instances.

Parameters

  • name (str) – Name of the variable. A leading “__” denotes a private variable and is replaced by a sequence containing the variable’s unique ID.

  • vectorization (BaseVectorization) – Vectorization format used to store the value.

  • lower – Constant lower bound on the variable. May contain float("-inf") to denote unbounded elements.

  • upper – Constant upper bound on the variable. May contain float("inf") to denote unbounded elements.

copy(new_name=None)[source]

Return an independent copy of the variable.

classmethod make_var_type(*args, **kwargs)[source]

Create a detailed variable type from subtype parameters.

See also var_type.

property bound_constraint[source]

The variable bounds as a PICOS constraint, or None.

property bound_dicts[source]

Variable bounds as a pair of mappings from index to scalar bound.

The indices and bound values are with respect to the internal representation of the variable, whose value can be accessed with internal_value.

Upper and lower bounds set to float("inf") and float("-inf") on variable creation, respectively, are not included.

property long_string[source]

Long string representation for printing a Problem.

property num_bounds

Number of scalar bounds associated with the variable.

property var_subtype

The subtype part of the detailed variable type.

See also var_type.

property var_type

The detailed variable type.

This intentionally does not override Expression.type so that the variable still behaves as the affine expression that it represents when prediction constraint outcomes.

class picos.expressions.variables.BinaryVariable(name, shape=(1, 1))[source]

Bases: BaseVariable, AffineExpression

A \{0,1\}-valued variable.

__init__(name, shape=(1, 1))[source]

Create a BinaryVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of a vector or matrix variable.

class picos.expressions.variables.ComplexVariable(name, shape=(1, 1))[source]

Bases: BaseVariable, ComplexAffineExpression

A complex-valued variable.

Passed to solvers as a real variable vector with 2mn entries.

__init__(name, shape=(1, 1))[source]

Create a ComplexVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of a vector or matrix variable.

class picos.expressions.variables.HermitianVariable(name, shape)[source]

Bases: BaseVariable, ComplexAffineExpression

A hermitian matrix variable.

Stored internally and passed to solvers as the horizontal concatenation of a real symmetric vectorization with \frac{n(n+1)}{2} entries and a real skew-symmetric vectorization with \frac{n(n-1)}{2} entries, resulting in a real vector with only n^2 entries total.

__init__(name, shape)[source]

Create a HermitianVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of the matrix.

class picos.expressions.variables.IntegerVariable(name, shape=(1, 1), lower=None, upper=None)[source]

Bases: BaseVariable, AffineExpression

An integer-valued variable.

__init__(name, shape=(1, 1), lower=None, upper=None)[source]

Create an IntegerVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of a vector or matrix variable.

  • lower – Constant lower bound on the variable. May contain float("-inf") to denote unbounded elements.

  • upper – Constant upper bound on the variable. May contain float("inf") to denote unbounded elements.

class picos.expressions.variables.LowerTriangularVariable(name, shape=(1, 1), lower=None, upper=None)[source]

Bases: BaseVariable, AffineExpression

A lower triangular matrix variable.

Stored internally and passed to solvers as a lower triangular vectorization with only \frac{n(n+1)}{2} entries.

__init__(name, shape=(1, 1), lower=None, upper=None)[source]

Create a LowerTriangularVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of the matrix.

  • lower – Constant lower bound on the variable. May contain float("-inf") to denote unbounded elements.

  • upper – Constant upper bound on the variable. May contain float("inf") to denote unbounded elements.

class picos.expressions.variables.RealVariable(name, shape=(1, 1), lower=None, upper=None)[source]

Bases: BaseVariable, AffineExpression

A real-valued variable.

__init__(name, shape=(1, 1), lower=None, upper=None)[source]

Create a RealVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of a vector or matrix variable.

  • lower – Constant lower bound on the variable. May contain float("-inf") to denote unbounded elements.

  • upper – Constant upper bound on the variable. May contain float("inf") to denote unbounded elements.

class picos.expressions.variables.SkewSymmetricVariable(name, shape=(1, 1), lower=None, upper=None)[source]

Bases: BaseVariable, AffineExpression

A skew-symmetric matrix variable.

Stored internally and passed to solvers as a skew-symmetric vectorization with only \frac{n(n-1)}{2} entries.

__init__(name, shape=(1, 1), lower=None, upper=None)[source]

Create a SkewSymmetricVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of the matrix.

  • lower – Constant lower bound on the variable. May contain float("-inf") to denote unbounded elements.

  • upper – Constant upper bound on the variable. May contain float("inf") to denote unbounded elements.

class picos.expressions.variables.SymmetricVariable(name, shape=(1, 1), lower=None, upper=None)[source]

Bases: BaseVariable, AffineExpression

A symmetric matrix variable.

Stored internally and passed to solvers as a symmetric vectorization with only \frac{n(n+1)}{2} entries.

__init__(name, shape=(1, 1), lower=None, upper=None)[source]

Create a SymmetricVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of the matrix.

  • lower – Constant lower bound on the variable. May contain float("-inf") to denote unbounded elements.

  • upper – Constant upper bound on the variable. May contain float("inf") to denote unbounded elements.

class picos.expressions.variables.UpperTriangularVariable(name, shape=(1, 1), lower=None, upper=None)[source]

Bases: BaseVariable, AffineExpression

An upper triangular matrix variable.

Stored internally and passed to solvers as an upper triangular vectorization with only \frac{n(n+1)}{2} entries.

__init__(name, shape=(1, 1), lower=None, upper=None)[source]

Create a UpperTriangularVariable.

Parameters

  • name (str) – The variable’s name, used for both string description and identification.

  • shape (int or tuple or list) – The shape of the matrix.

  • lower – Constant lower bound on the variable. May contain float("-inf") to denote unbounded elements.

  • upper – Constant upper bound on the variable. May contain float("inf") to denote unbounded elements.

class picos.expressions.variables.VariableType(theClass, subtype)[source]

Bases: DetailedType

The detailed type of a variable for predicting reformulation outcomes.

Objects

picos.expressions.variables.CONTINUOUS_VARTYPES

Built-in immutable sequence.

If no argument is given, the constructor returns an empty tuple. If iterable is specified the tuple is initialized from iterable’s items.

If the argument is a tuple, the return value is the same object.

Default value
(<class 'picos.expressions.variables.RealVariable'>,
 <class 'picos.expressions.variables.ComplexVariable'>,
 <class 'picos.expressions.variables.SymmetricVariable'>,
 <class 'picos.expressions.variables.SkewSymmetricVariable'>,
 <class...