picos.expressions.expression¶
Backend for expression type implementations.
Outline¶
Classes¶
Abstract base class for mathematical expressions, including variables. 

The detailed type of an expression for predicting constraint outcomes. 
Functions¶
Cast 

Validate that the constraint outcome matches the predicted outcome. 
Exceptions¶
The operation cannot be performed due to a variable without a value. 

Denotes that comparing two expressions will not form a constraint. 
Classes¶
Expression¶

class
picos.expressions.expression.
Expression
(typeStr, symbStr)[source]¶ Bases:
abc.ABC
Abstract base class for mathematical expressions, including variables.
For variables, this is the secondary base class, with
BaseVariable
being the primary one.
__init__
(typeStr, symbStr)[source]¶ Perform basic initialization for
Expression
instances.

is_valued
()[source]¶ Whether the expression is valued.
Deprecated since version 2.0: Use
valued
instead.

classmethod
make_type
(*args, **kwargs)[source]¶ Create a detailed expression type from subtype parameters.

replace_variables
(new_variables)[source]¶ Return a copy of the expression concerning different variables.
New variables must have the same shape and vectorization format as the variables that they replace. This means in particular that
RealVariable
,IntegerVariable
andBinaryVariable
of same shape are interchangeable.If the variables to be replaced do not appear in the expression, then the expression is not copied but returned as is.

set_value
(value)[source]¶ Set the value of an expression, usually a variable.
Deprecated since version 2.0: Use
value
instead.

property
concave
¶ Whether the expression is concave.

property
convex
¶ Whether the expression is convex.

property
refined
¶ A refined version of the expression.
The refined expression can be an instance of a different
Expression
subclass than the original expression, if that type is better suited for the mathematical object in question.The refined expression is automatically used instead of the original one whenever a constraint is created, and in some other places.
The idea behind refined expressions is that operations that produce new expressions can be executed quickly without checking for exceptionnel cases. For instance, the sum of two
ComplexAffineExpression
instances could have the complex part eliminated so that storing the result as anAffineExpression
would be prefered, but checking for this case on every addition would be too slow. Refinement is used sparingly to detect such cases at times where it makes the most sense.

property
shape
¶ Return the algebraic shape of the expression.

property
string
¶ Symbolic string representation of the expression.
Use this over Python’s
str
if you want to output the symbolic representation even when the expression is valued.

property
subtype
¶ The subtype part of the expression’s detailed type.
Returns a hashable object that, together with the Python class part of the expression’s type, is sufficient to predict the constraint outcome (constraint class and subtype) of any comparison operation with any other expression.
By convention the object returned is a
namedtuple
instance.

property
type
¶ The expression’s detailed type for constraint prediction.
The returned value is suffcient to predict the detailed type of any constraint that can be created by comparing with another expression.
Since constraints are created from
refined
expressions only, the Python class part of the detailed type may differ from the type of the expression whosetype
is queried.

property
value
¶ Value of the expression.
It is defined (not
None
) if the expression is constant or if all variables involved in the expression are valued. Variables can be valued directly by writing to theirvalue
attribute, or they can be valued by PICOS when an optimization solution is found.Some expressions can also be valued directly if PICOS can find a minimal norm variable assignment that makes the expression have the desired value. In particular, this works with affine expressions whose linear part has an under or welldetermined coefficient matrix.
 Example
>>> from picos import RealVariable >>> x = RealVariable("x", (1,3)) >>> y = RealVariable("y", (1,3)) >>> e = x  2*y + 3 >>> print("e:", e) e: x  2·y + [3] >>> e.value = [4, 5, 6] >>> print("e: ", e, "\nx: ", x, "\ny: ", y, sep = "") e: [ 4.00e+00 5.00e+00 6.00e+00] x: [ 2.00e01 4.00e01 6.00e01] y: [4.00e01 8.00e01 1.20e+00]
Unlike
value_as_matrix
, scalars are returned as scalar types.

property
value_as_matrix
¶ Value of the expression, as a CVXOPT matrix type.
Refer to
value
for when it is defined (notNone
).Unlike
value
, scalars are returned in the form of 1x1 matrices.

property
valued
¶ Whether the expression is valued.
Note
Querying this attribute is not faster than immediately querying
value
and checking whether it isNone
. Use it only if you do not need to know the value, but only whether it is available. Example
>>> from picos import RealVariable >>> x = RealVariable("x", 3) >>> x.valued False >>> x.value >>> print((x1)) ∑(x) >>> x.value = [1, 2, 3] >>> (x1).valued True >>> print((x1)) 6.0

property
variables
¶ Return the set of variables that are involved in the expression.

ExpressionType¶

class
picos.expressions.expression.
ExpressionType
(theClass, subtype)[source]¶ Bases:
picos.containers.DetailedType
The detailed type of an expression for predicting constraint outcomes.
This is suffcient to predict the detailed type of any constraint that can be created by comparing with another expression.
The prediction is done by using the relevant operator on instances of this class, as opposed to the expressions themselves. Note that operators used to create new expressions as opposed to constraints are not handled.
Functions¶
refine_operands¶

picos.expressions.expression.
refine_operands
(stop_at_affine=False)[source]¶ Cast
refined
on both operands.If the left hand side operand (i.e.
self
) is refined to an instance of a different type, then, instead of the decorated method, the method with the same name on the refined type is invoked with the (refined) right hand side operand as its argument.This decorator is supposed to be used on all constraint creating binary operator methods so that degenerated instances (e.g. a complex affine expression with an imaginary part of zero) can occur but are not used in constraints. This speeds up many computations involving expressions as these degenerate cases do not need to be detected. Note that
Expression.type
also refers to the refined version of an expression. Parameters
stop_at_affine (bool) – Do not refine any affine expressions, in particular do not refine complex affine expressions to real ones.
Exceptions¶
NotValued¶

exception
picos.expressions.expression.
NotValued
[source]¶ Bases:
RuntimeError
The operation cannot be performed due to a variable without a value.
Note that the
value
andvalue_as_matrix
attributes do not raise this exception, but returnNone
.
__init__
()¶ Initialize self. See help(type(self)) for accurate signature.

__new__
()¶ Create and return a new object. See help(type) for accurate signature.

PredictedFailure¶

exception
picos.expressions.expression.
PredictedFailure
[source]¶ Bases:
TypeError
Denotes that comparing two expressions will not form a constraint.

__init__
()¶ Initialize self. See help(type(self)) for accurate signature.

__new__
()¶ Create and return a new object. See help(type) for accurate signature.
