Source code for cvxpy.reductions.reduction

Copyright 2013 Steven Diamond

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import abc

[docs]class Reduction(object): """Abstract base class for reductions. A reduction is an actor that transforms a problem into an equivalent problem. By equivalent we mean that there exists a mapping between solutions of either problem: if we reduce a problem :math:`A` to another problem :math:`B` and then proceed to find a solution to :math:`B`, we can convert it to a solution of :math:`A` with at most a moderate amount of effort. A reduction that is instantiated with a non-None problem offers two key methods: `reduce` and `retrieve`. The `reduce()` method converts the problem the reduction was instantiated with to an equivalent problem. The `retrieve()` method takes as an argument a Solution for the equivalent problem and returns a Solution for the problem owned by the reduction. Every reduction offers three low-level methods: accepts, apply, and invert. The accepts method of a particular reduction specifies the types of problems that it is applicable to; the apply method takes a problem and reduces it to an equivalent form, and the invert method maps solutions from reduced-to problems to their problems of provenance. Attributes: ---------- problem : Problem A problem owned by this reduction; possibly None. """ __metaclass__ = abc.ABCMeta
[docs] def __init__(self, problem=None): """Construct a reduction for reducing `problem`. If `problem` is not None, then a subsequent invocation of `reduce()` will reduce `problem` and return an equivalent one. """ self.problem = problem
[docs] def accepts(self, problem): """States whether the reduction accepts a problem. Parameters ---------- problem : Problem The problem to check. Returns ------- bool True if the reduction can be applied, False otherwise. """ return NotImplemented
[docs] def reduce(self): """Reduces the owned problem to an equivalent problem. Returns ------- Problem or dict An equivalent problem, encoded either as a Problem or a dict. Raises ------ ValueError If this Reduction was constructed without a Problem. """ if hasattr(self, '_emitted_problem'): return self._emitted_problem if self.problem is None: raise ValueError( "The reduction was constructed without a Problem.") problem, retrieval_data = self.apply(self.problem) self._emitted_problem = problem self._retrieval_data = retrieval_data return problem
[docs] def retrieve(self, solution): """Retrieves a solution to the owned problem. Parameters ---------- solution : Solution A solution to the problem emitted by `reduce()`. Returns ------- Solution A solution to the owned problem. Raises ------ ValueError If `self.problem` is None, or if `reduce()` was not previously called. """ if not hasattr(self, '_retrieval_data'): raise ValueError("`reduce()` must be called before `retrieve()`.") return self.invert(solution, self._retrieval_data)
[docs] @abc.abstractmethod def apply(self, problem): """Applies the reduction to a problem and returns an equivalent problem. Parameters ---------- problem : Problem The problem to which the reduction will be applied. Returns ------- Problem or dict An equivalent problem, encoded either as a Problem or a dict. InverseData, list or dict Data needed by the reduction in order to invert this particular application. """ return NotImplemented
[docs] @abc.abstractmethod def invert(self, solution, inverse_data): """Returns a solution to the original problem given the inverse_data. Parameters ---------- solution : Solution A solution to a problem that generated the inverse_data. inverse_data The data encoding the original problem. Returns ------- Solution A solution to the original problem. """ return NotImplemented