"""
Copyright 2016 Jaehyun Park, 2017 Robin Verschueren
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.
"""
from __future__ import annotations
import numpy as np
import cvxpy.settings as s
from cvxpy.constraints import (
PSD,
SOC,
Equality,
ExpCone,
Inequality,
NonNeg,
NonPos,
Zero,
)
from cvxpy.cvxcore.python import canonInterface
from cvxpy.expressions.variable import Variable
from cvxpy.problems.objective import Minimize
from cvxpy.problems.param_prob import ParamProb
from cvxpy.reductions import InverseData, Solution
from cvxpy.reductions.cvx_attr2constr import convex_attributes
from cvxpy.reductions.dcp2cone.cone_matrix_stuffing import nonpos2nonneg
from cvxpy.reductions.matrix_stuffing import MatrixStuffing, extract_mip_idx
from cvxpy.reductions.utilities import (
ReducedMat,
are_args_affine,
group_constraints,
lower_equality,
lower_ineq_to_nonneg,
)
from cvxpy.utilities.coeff_extractor import CoeffExtractor
[docs]class ConeDims:
"""Summary of cone dimensions present in constraints.
Constraints must be formatted as dictionary that maps from
constraint type to a list of constraints of that type.
Attributes
----------
zero : int
The dimension of the zero cone.
nonpos : int
The dimension of the non-positive cone.
exp : int
The number of 3-dimensional exponential cones
soc : list of int
A list of the second-order cone dimensions.
psd : list of int
A list of the positive semidefinite cone dimensions, where the
dimension of the PSD cone of k by k matrices is k.
"""
def __init__(self, constr_map) -> None:
self.zero = int(sum(c.size for c in constr_map[Zero]))
self.nonneg = int(sum(c.size for c in constr_map[NonNeg]))
self.exp = int(sum(c.num_cones() for c in constr_map[ExpCone]))
self.soc = [int(dim) for c in constr_map[SOC] for dim in c.cone_sizes()]
self.psd = [int(c.shape[0]) for c in constr_map[PSD]]
def __repr__(self) -> str:
return "(zero: {0}, nonpos: {1}, exp: {2}, soc: {3}, psd: {4})".format(
self.zero, self.nonneg, self.exp, self.soc, self.psd)
def __str__(self) -> str:
"""String representation.
"""
return ("%i equalities, %i inequalities, %i exponential cones, \n"
"SOC constraints: %s, PSD constraints: %s.") % (self.zero,
self.nonneg,
self.exp,
self.soc,
self.psd)
def __getitem__(self, key):
if key == s.EQ_DIM:
return self.zero
elif key == s.LEQ_DIM:
return self.nonneg
elif key == s.EXP_DIM:
return self.exp
elif key == s.SOC_DIM:
return self.soc
elif key == s.PSD_DIM:
return self.psd
else:
raise KeyError(key)
[docs]class ParamQuadProg(ParamProb):
"""Represents a parameterized quadratic program.
minimize x'Px + q^Tx + d
subject to (in)equality_constr1(A_1*x + b_1, ...)
...
(in)equality_constrK(A_i*x + b_i, ...)
The constant offsets d and b are the last column of c and A.
"""
def __init__(self, P, q, x, A,
variables,
var_id_to_col,
constraints,
parameters,
param_id_to_col,
formatted: bool = False) -> None:
self.P = P
self.q = q
self.x = x
self.A = A
# Form a reduced representation of A and P, for faster application
# of parameters.
self.reduced_A = ReducedMat(self.A, self.x.size)
self.reduced_P = ReducedMat(self.P, self.x.size, quad_form=True)
self.constraints = constraints
self.constr_size = sum([c.size for c in constraints])
self.parameters = parameters
self.param_id_to_col = param_id_to_col
self.id_to_param = {p.id: p for p in self.parameters}
self.param_id_to_size = {p.id: p.size for p in self.parameters}
self.total_param_size = sum([p.size for p in self.parameters])
# TODO technically part of inverse data.
self.variables = variables
self.var_id_to_col = var_id_to_col
self.id_to_var = {v.id: v for v in self.variables}
# whether this param cone prog has been formatted for a solver
self.formatted = formatted
[docs] def is_mixed_integer(self) -> bool:
"""Is the problem mixed-integer?"""
return self.x.attributes['boolean'] or \
self.x.attributes['integer']
[docs] def apply_parameters(self, id_to_param_value=None, zero_offset: bool = False,
keep_zeros: bool = False):
"""Returns A, b after applying parameters (and reshaping).
Args:
id_to_param_value: (optional) dict mapping parameter ids to values
zero_offset: (optional) if True, zero out the constant offset in the
parameter vector
keep_zeros: (optional) if True, store explicit zeros in A where
parameters are affected
"""
def param_value(idx):
return (np.array(self.id_to_param[idx].value) if id_to_param_value
is None else id_to_param_value[idx])
param_vec = canonInterface.get_parameter_vector(
self.total_param_size,
self.param_id_to_col,
self.param_id_to_size,
param_value,
zero_offset=zero_offset)
self.reduced_P.cache(keep_zeros)
P, _ = self.reduced_P.get_matrix_from_tensor(param_vec, with_offset=False)
q, d = canonInterface.get_matrix_from_tensor(
self.q, param_vec, self.x.size, with_offset=True)
q = q.toarray().flatten()
self.reduced_A.cache(keep_zeros)
A, b = self.reduced_A.get_matrix_from_tensor(param_vec, with_offset=True)
return P, q, d, A, np.atleast_1d(b)
[docs] def apply_param_jac(self, delP, delq, delA, delb, active_params=None):
"""Multiplies by Jacobian of parameter mapping.
Assumes delA is sparse.
Returns:
A dictionary param.id -> dparam
"""
raise NotImplementedError
[docs] def split_solution(self, sltn, active_vars=None):
"""Splits the solution into individual variables.
"""
raise NotImplementedError
[docs] def split_adjoint(self, del_vars=None):
"""Adjoint of split_solution.
"""
raise NotImplementedError
[docs]class QpMatrixStuffing(MatrixStuffing):
"""Fills in numeric values for this problem instance.
Outputs a DCP-compliant minimization problem with an objective
of the form
QuadForm(x, p) + q.T * x
and Zero/NonNeg constraints, both of which exclusively carry
affine arguments.
"""
def __init__(self, canon_backend: str | None = None):
self.canon_backend = canon_backend
[docs] @staticmethod
def accepts(problem):
return (type(problem.objective) == Minimize
and problem.objective.is_quadratic()
and problem.is_dcp()
and not convex_attributes(problem.variables())
and all(type(c) in [Zero, NonNeg, Equality, Inequality]
for c in problem.constraints)
and are_args_affine(problem.constraints)
and problem.is_dpp())
[docs] def stuffed_objective(self, problem, extractor):
# extract to 0.5 * x.T * P * x + q.T * x + r
expr = problem.objective.expr.copy()
params_to_P, params_to_q = extractor.quad_form(expr)
# Handle 0.5 factor.
params_to_P = 2*params_to_P
# concatenate all variables in one vector
boolean, integer = extract_mip_idx(problem.variables())
x = Variable(extractor.x_length, boolean=boolean, integer=integer)
return params_to_P, params_to_q, x
[docs] def apply(self, problem):
"""See docstring for MatrixStuffing.apply"""
inverse_data = InverseData(problem)
# Form the constraints
extractor = CoeffExtractor(inverse_data, self.canon_backend)
params_to_P, params_to_q, flattened_variable = self.stuffed_objective(
problem, extractor)
# Lower equality and inequality to Zero and NonNeg.
cons = []
for con in problem.constraints:
if isinstance(con, Equality):
con = lower_equality(con)
elif isinstance(con, Inequality):
con = lower_ineq_to_nonneg(con)
elif isinstance(con, NonPos):
con = nonpos2nonneg(con)
cons.append(con)
# Reorder constraints to Zero, NonNeg.
constr_map = group_constraints(cons)
ordered_cons = constr_map[Zero] + constr_map[NonNeg]
inverse_data.cons_id_map = {con.id: con.id for con in ordered_cons}
inverse_data.constraints = ordered_cons
# Batch expressions together, then split apart.
expr_list = [arg for c in ordered_cons for arg in c.args]
params_to_Ab = extractor.affine(expr_list)
inverse_data.minimize = type(problem.objective) == Minimize
new_prob = ParamQuadProg(params_to_P,
params_to_q,
flattened_variable,
params_to_Ab,
problem.variables(),
inverse_data.var_offsets,
ordered_cons,
problem.parameters(),
inverse_data.param_id_map)
return new_prob, inverse_data
[docs] def invert(self, solution, inverse_data):
"""Retrieves the solution to the original problem."""
var_map = inverse_data.var_offsets
# Flip sign of opt val if maximize.
opt_val = solution.opt_val
if solution.status not in s.ERROR and not inverse_data.minimize:
opt_val = -solution.opt_val
primal_vars, dual_vars = {}, {}
if solution.status not in s.SOLUTION_PRESENT:
return Solution(solution.status, opt_val, primal_vars, dual_vars,
solution.attr)
# Split vectorized variable into components.
x_opt = list(solution.primal_vars.values())[0]
for var_id, offset in var_map.items():
shape = inverse_data.var_shapes[var_id]
size = np.prod(shape, dtype=int)
primal_vars[var_id] = np.reshape(x_opt[offset:offset+size], shape,
order='F')
# Remap dual variables if dual exists (problem is convex).
if solution.dual_vars is not None:
# Giant dual variable.
dual_var = list(solution.dual_vars.values())[0]
offset = 0
for constr in inverse_data.constraints:
# QP constraints can only have one argument.
dual_vars[constr.id] = np.reshape(
dual_var[offset:offset+constr.args[0].size],
constr.args[0].shape,
order='F'
)
offset += constr.size
return Solution(solution.status, opt_val, primal_vars, dual_vars,
solution.attr)