Source code for cvxpy.reductions.dgp2dcp.dgp2dcp

"""
Copyright 2018 Akshay Agrawal

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""
import numpy as np

from cvxpy import settings
from cvxpy.reductions.canonicalization import Canonicalization
from cvxpy.reductions.dgp2dcp.canonicalizers import DgpCanonMethods


class Dgp2Dcp(Canonicalization):
    """Reduce DGP problems to DCP problems.

    This reduction takes as input a DGP problem and returns an equivalent DCP
    problem. Because every (generalized) geometric program is a DGP problem,
    this reduction can be used to convert geometric programs into convex form.

    Example
    -------

    >>> import cvxpy as cp
    >>>
    >>> x1 = cp.Variable(pos=True)
    >>> x2 = cp.Variable(pos=True)
    >>> x3 = cp.Variable(pos=True)
    >>>
    >>> monomial = 3.0 * x_1**0.4 * x_2 ** 0.2 * x_3 ** -1.4
    >>> posynomial = monomial + 2.0 * x_1 * x_2
    >>> dgp_problem = cp.Problem(cp.Minimize(posynomial), [monomial == 4.0])
    >>>
    >>> dcp2cone = cvxpy.reductions.Dcp2Cone()
    >>> assert not dcp2cone.accepts(dgp_problem)
    >>>
    >>> gp2dcp = cvxpy.reductions.Dgp2Dcp(dgp_problem)
    >>> dcp_problem = gp2dcp.reduce()
    >>>
    >>> assert dcp2cone.accepts(dcp_problem)
    >>> dcp_problem.solve()
    >>>
    >>> dgp_problem.unpack(gp2dcp.retrieve(dcp_problem.solution))
    >>> print(dgp_problem.value)
    >>> print(dgp_problem.variables())
    """
    def __init__(self, problem=None) -> None:
        # Canonicalization of DGP is stateful; canon_methods created
        # in `apply`.
        super(Dgp2Dcp, self).__init__(canon_methods=None, problem=problem)

    def accepts(self, problem):
        """A problem is accepted if it is DGP.
        """
        return problem.is_dgp() and all(
            p.value is not None for p in problem.parameters())

    def apply(self, problem):
        """Converts a DGP problem to a DCP problem.
        """
        if not self.accepts(problem):
            raise ValueError("The supplied problem is not DGP.")

        self.canon_methods = DgpCanonMethods()
        equiv_problem, inverse_data = super(Dgp2Dcp, self).apply(problem)
        inverse_data._problem = problem
        return equiv_problem, inverse_data

    def canonicalize_expr(self, expr, args):
        if type(expr) in self.canon_methods:
            return self.canon_methods[type(expr)](expr, args)
        else:
            return expr.copy(args), []

    def invert(self, solution, inverse_data):
        solution = super(Dgp2Dcp, self).invert(solution, inverse_data)
        if solution.status == settings.SOLVER_ERROR:
            return solution
        for vid, value in solution.primal_vars.items():
            solution.primal_vars[vid] = np.exp(value)
        # f(x) = e^{F(u)}.
        solution.opt_val = np.exp(solution.opt_val)
        return solution