"""
Copyright 2013 Steven Diamond
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 scipy.sparse as sp
import cvxpy.settings as s
from cvxpy.constraints import (
PSD,
SOC,
Equality,
ExpCone,
Inequality,
NonNeg,
NonPos,
PowCone3D,
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, cvx_attr2constr
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,
nonpos2nonneg,
)
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.
nonneg : int
The dimension of the non-negative 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.
"""
EQ_DIM = s.EQ_DIM
LEQ_DIM = s.LEQ_DIM
EXP_DIM = s.EXP_DIM
SOC_DIM = s.SOC_DIM
PSD_DIM = s.PSD_DIM
P3D_DIM = 'p3'
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]]
p3d = []
if constr_map[PowCone3D]:
p3d = np.concatenate([c.alpha.value for c in constr_map[PowCone3D]]).tolist()
self.p3d = p3d
def __repr__(self) -> str:
return "(zero: {0}, nonneg: {1}, exp: {2}, soc: {3}, psd: {4}, p3d: {5})".format(
self.zero, self.nonneg, self.exp, self.soc, self.psd, self.p3d)
def __str__(self) -> str:
"""String representation.
"""
return ("%i equalities, %i inequalities, %i exponential cones, \n"
"SOC constraints: %s, PSD constraints: %s,\n"
" 3d power cones %s.") % (self.zero,
self.nonneg,
self.exp,
self.soc,
self.psd,
self.p3d)
def __getitem__(self, key):
if key == self.EQ_DIM:
return self.zero
elif key == self.LEQ_DIM:
return self.nonneg
elif key == self.EXP_DIM:
return self.exp
elif key == self.SOC_DIM:
return self.soc
elif key == self.PSD_DIM:
return self.psd
elif key == self.P3D_DIM:
return self.p3d
else:
raise KeyError(key)
# TODO(akshayka): unit tests
[docs]class ParamConeProg(ParamProb):
"""Represents a parameterized cone program
minimize c'x + d + [(1/2)x'Px]
subject to cone_constr1(A_1*x + b_1, ...)
...
cone_constrK(A_i*x + b_i, ...)
The constant offsets d and b are the last column of c and A.
"""
def __init__(self, c, x, A,
variables,
var_id_to_col,
constraints,
parameters,
param_id_to_col,
P=None,
formatted: bool = False) -> None:
# The problem data tensors; c is for the constraint, and A for
# the problem data matrix
self.c = c
self.A = A
self.P = P
# The variable
self.x = x
# 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.constr_map = group_constraints(constraints)
self.cone_dims = ConeDims(self.constr_map)
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, quad_obj: 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.
quad_obj: (optional) if True, include quadratic objective term.
"""
self.reduced_A.cache(keep_zeros)
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)
c, d = canonInterface.get_matrix_from_tensor(
self.c, param_vec, self.x.size, with_offset=True)
c = c.toarray().flatten()
A, b = self.reduced_A.get_matrix_from_tensor(param_vec, with_offset=True)
if quad_obj:
self.reduced_P.cache(keep_zeros)
P, _ = self.reduced_P.get_matrix_from_tensor(param_vec, with_offset=False)
return P, c, d, A, np.atleast_1d(b)
else:
return c, d, A, np.atleast_1d(b)
[docs] def apply_param_jac(self, delc, delA, delb, active_params=None):
"""Multiplies by Jacobian of parameter mapping.
Assumes delA is sparse.
Returns:
A dictionary param.id -> dparam
"""
if self.P is not None:
raise ValueError("Can't apply Jacobian with a quadratic objective.")
if active_params is None:
active_params = {p.id for p in self.parameters}
del_param_vec = delc @ self.c[:-1]
flatdelA = delA.reshape((np.prod(delA.shape), 1), order='F')
delAb = sp.vstack([flatdelA, sp.csc_matrix(delb[:, None])])
one_gig_of_doubles = 125000000
if delAb.shape[0] < one_gig_of_doubles:
# fast path: if delAb is small enough, just materialize it
# in memory because sparse-matrix @ dense vector is much faster
# than sparse @ sparse
del_param_vec += np.squeeze(self.A.T.dot(delAb.toarray()))
else:
# slow path.
# TODO: make this faster by intelligently operating on the
# sparse matrix data / making use of reduced_A
del_param_vec += np.squeeze((delAb.T @ self.A).A)
del_param_vec = np.squeeze(del_param_vec)
param_id_to_delta_param = {}
for param_id, col in self.param_id_to_col.items():
if param_id in active_params:
param = self.id_to_param[param_id]
delta = del_param_vec[col:col + param.size]
param_id_to_delta_param[param_id] = np.reshape(
delta, param.shape, order='F')
return param_id_to_delta_param
[docs] def split_solution(self, sltn, active_vars=None):
"""Splits the solution into individual variables.
"""
if active_vars is None:
active_vars = [v.id for v in self.variables]
# var id to solution.
sltn_dict = {}
for var_id, col in self.var_id_to_col.items():
if var_id in active_vars:
var = self.id_to_var[var_id]
value = sltn[col:var.size+col]
if var.attributes_were_lowered():
orig_var = var.variable_of_provenance()
value = cvx_attr2constr.recover_value_for_variable(
orig_var, value, project=False)
sltn_dict[orig_var.id] = np.reshape(
value, orig_var.shape, order='F')
else:
sltn_dict[var_id] = np.reshape(
value, var.shape, order='F')
return sltn_dict
[docs] def split_adjoint(self, del_vars=None):
"""Adjoint of split_solution.
"""
var_vec = np.zeros(self.x.size)
for var_id, delta in del_vars.items():
var = self.id_to_var[var_id]
col = self.var_id_to_col[var_id]
if var.attributes_were_lowered():
orig_var = var.variable_of_provenance()
if cvx_attr2constr.attributes_present(
[orig_var], cvx_attr2constr.SYMMETRIC_ATTRIBUTES):
delta = delta + delta.T - np.diag(np.diag(delta))
delta = cvx_attr2constr.lower_value(orig_var, delta)
var_vec[col:col + var.size] = delta.flatten(order='F')
return var_vec
[docs]class ConeMatrixStuffing(MatrixStuffing):
"""Construct matrices for linear cone problems.
Linear cone problems are assumed to have a linear objective and cone
constraints which may have zero or more arguments, all of which must be
affine.
"""
CONSTRAINTS = 'ordered_constraints'
def __init__(self, quad_obj: bool = False, canon_backend: str | None = None):
# Assume a quadratic objective?
self.quad_obj = quad_obj
self.canon_backend = canon_backend
[docs] def accepts(self, problem):
valid_obj_curv = (self.quad_obj and problem.objective.expr.is_quadratic()) or \
problem.objective.expr.is_affine()
return (type(problem.objective) == Minimize
and valid_obj_curv
and not cvx_attr2constr.convex_attributes(problem.variables())
and are_args_affine(problem.constraints)
and problem.is_dpp())
[docs] def stuffed_objective(self, problem, extractor):
# concatenate all variables in one vector
boolean, integer = extract_mip_idx(problem.variables())
x = Variable(extractor.x_length, boolean=boolean, integer=integer)
if self.quad_obj:
# extract to 0.5 * x.T * P * x + q.T * x + r
expr = problem.objective.expr.copy()
params_to_P, params_to_c = extractor.quad_form(expr)
# Handle 0.5 factor.
params_to_P = 2*params_to_P
else:
# Extract to c.T * x + r; c is represented by a ma
params_to_c = extractor.affine(problem.objective.expr)
params_to_P = None
return params_to_P, params_to_c, x
[docs] def apply(self, problem):
inverse_data = InverseData(problem)
# Form the constraints
extractor = CoeffExtractor(inverse_data, self.canon_backend)
params_to_P, params_to_c, 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)
elif isinstance(con, SOC) and con.axis == 1:
con = SOC(con.args[0], con.args[1].T, axis=0,
constr_id=con.constr_id)
elif isinstance(con, PowCone3D) and con.args[0].ndim > 1:
x, y, z = con.args
alpha = con.alpha
con = PowCone3D(x.flatten(), y.flatten(), z.flatten(), alpha.flatten(),
constr_id=con.constr_id)
elif isinstance(con, ExpCone) and con.args[0].ndim > 1:
x, y, z = con.args
con = ExpCone(x.flatten(), y.flatten(), z.flatten(),
constr_id=con.constr_id)
cons.append(con)
# Reorder constraints to Zero, NonNeg, SOC, PSD, EXP, PowCone3D
constr_map = group_constraints(cons)
ordered_cons = constr_map[Zero] + constr_map[NonNeg] + \
constr_map[SOC] + constr_map[PSD] + constr_map[ExpCone] + constr_map[PowCone3D]
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_problem_data = extractor.affine(expr_list)
inverse_data.minimize = type(problem.objective) == Minimize
new_prob = ParamConeProg(params_to_c,
flattened_variable,
params_to_problem_data,
problem.variables(),
inverse_data.var_offsets,
ordered_cons,
problem.parameters(),
inverse_data.param_id_map,
P=params_to_P)
return new_prob, inverse_data
[docs] def invert(self, solution, inverse_data):
"""Retrieves a solution to the original problem"""
var_map = inverse_data.var_offsets
con_map = inverse_data.cons_id_map
# 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:
for old_con, new_con in con_map.items():
con_obj = inverse_data.id2cons[old_con]
shape = con_obj.shape
# TODO rationalize Exponential.
if shape == () or isinstance(con_obj, (ExpCone, SOC)):
dual_vars[old_con] = solution.dual_vars[new_con]
else:
dual_vars[old_con] = np.reshape(
solution.dual_vars[new_con],
shape,
order='F'
)
return Solution(solution.status, opt_val, primal_vars, dual_vars,
solution.attr)