Source code for cvxpy.reductions.complex2real.complex2real

Copyright 2017 Robin Verschueren

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from cvxpy import problems
from cvxpy import settings as s
from cvxpy.atoms.affine.upper_tri import vec_to_upper_tri
from cvxpy.constraints import (
from cvxpy.constraints.constraint import Constraint
from cvxpy.expressions import cvxtypes
from cvxpy.lin_ops import lin_utils as lu
from cvxpy.reductions import InverseData, Solution
from cvxpy.reductions.complex2real.canonicalizers import CANON_METHODS as elim_cplx_methods
from cvxpy.reductions.reduction import Reduction

def accepts(problem) -> bool:
    leaves = problem.variables() + problem.parameters() + problem.constants()
    return any(leaf.is_complex() for leaf in leaves)

[docs]class Complex2Real(Reduction): """Lifts complex numbers to a real representation.""" UNIMPLEMENTED_COMPLEX_DUALS = (SOC, OpRelEntrConeQuad)
[docs] def accepts(self, problem) -> None: accepts(problem)
[docs] def apply(self, problem): inverse_data = InverseData(problem) real2imag = { lu.get_id() for var in problem.variables() if var.is_complex()} constr_dict = { lu.get_id() for cons in problem.constraints if cons.is_complex()} real2imag.update(constr_dict) inverse_data.real2imag = real2imag leaf_map = {} real_obj, imag_obj = self.canonicalize_tree( problem.objective, inverse_data.real2imag, leaf_map) assert imag_obj is None constrs = [] for constraint in problem.constraints: # real2imag maps variable id to a potential new variable # created for the imaginary part. real_constrs, imag_constrs = self.canonicalize_tree( constraint, inverse_data.real2imag, leaf_map) if isinstance(real_constrs, list): constrs.extend(real_constrs) elif isinstance(real_constrs, Constraint): constrs.append(real_constrs) if isinstance(imag_constrs, list): constrs.extend(imag_constrs) elif isinstance(imag_constrs, Constraint): constrs.append(imag_constrs) new_problem = problems.problem.Problem(real_obj, constrs) return new_problem, inverse_data
[docs] def invert(self, solution, inverse_data): pvars = {} dvars = {} if solution.status in s.SOLUTION_PRESENT: # # Primal variables # for vid, var in inverse_data.id2var.items(): if var.is_real(): # Purely real variables pvars[vid] = solution.primal_vars[vid] elif var.is_imag(): # Purely imaginary variables imag_id = inverse_data.real2imag[vid] pvars[vid] = 1j*solution.primal_vars[imag_id] elif var.is_complex() and var.is_hermitian(): # Hermitian variables pvars[vid] = solution.primal_vars[vid] imag_id = inverse_data.real2imag[vid] if imag_id in solution.primal_vars: imag_val = solution.primal_vars[imag_id] imag_val = vec_to_upper_tri(imag_val, True).value imag_val -= imag_val.T pvars[vid] = pvars[vid] + 1j*imag_val elif var.is_complex(): # General complex variables pvars[vid] = solution.primal_vars[vid] imag_id = inverse_data.real2imag[vid] if imag_id in solution.primal_vars: imag_val = solution.primal_vars[imag_id] pvars[vid] = pvars[vid] + 1j*imag_val if solution.dual_vars: # # Dual variables # for cid, cons in inverse_data.id2cons.items(): if cons.is_real(): dvars[cid] = solution.dual_vars[cid] elif cons.is_imag(): imag_id = inverse_data.real2imag[cid] dvars[cid] = 1j*solution.dual_vars[imag_id] # All cases that follow are for complex-valued constraints: # 1. check equality constraints. # 2. check PSD constraints. # 3. check if a constraint is known to lack a complex dual implementation # 4. raise an error elif isinstance(cons, (Equality, Zero)): imag_id = inverse_data.real2imag[cid] if imag_id in solution.dual_vars: dvars[cid] = solution.dual_vars[cid] + \ 1j*solution.dual_vars[imag_id] else: dvars[cid] = solution.dual_vars[cid] elif isinstance(cons, PSD): # Suppose we have a constraint con_x = X >> 0 where X is Hermitian. # # Define the matrix # Y := [re(X) , im(X)] # [-im(X), re(X)] # and the constraint con_y = Y >> 0. # # The real part the dual variable for con_x is the upper-left # block of the dual variable for con_y. # # The imaginary part of the dual variable for con_x is the # upper-right block of the dual variable for con_y. n = cons.args[0].shape[0] dual = solution.dual_vars[cid] dvars[cid] = dual[:n, :n] + 1j*dual[n:, :n] elif isinstance(cons, self.UNIMPLEMENTED_COMPLEX_DUALS): # TODO: implement dual variable recovery pass else: raise Exception("Unknown constraint type.") return Solution(solution.status, solution.opt_val, pvars, dvars, solution.attr)
def canonicalize_tree(self, expr, real2imag, leaf_map): # TODO don't copy affine expressions? if type(expr) == cvxtypes.partial_problem(): raise NotImplementedError() else: real_args = [] imag_args = [] for arg in expr.args: real_arg, imag_arg = self.canonicalize_tree(arg, real2imag, leaf_map) real_args.append(real_arg) imag_args.append(imag_arg) real_out, imag_out = self.canonicalize_expr(expr, real_args, imag_args, real2imag, leaf_map) return real_out, imag_out def canonicalize_expr(self, expr, real_args, imag_args, real2imag, leaf_map): if type(expr) in elim_cplx_methods: # Only canonicalize a variable/constant/parameter once. if len(expr.args) == 0 and expr in leaf_map: return leaf_map[expr] result = elim_cplx_methods[type(expr)](expr, real_args, imag_args, real2imag) if len(expr.args) == 0: leaf_map[expr] = result return result else: assert all(v is None for v in imag_args) real_out = expr.copy(real_args) return real_out, None