def _get_var_offsets(self, objective, constraints):
"""Maps each variable to a horizontal offset.
Parameters
----------
objective : Expression
The canonicalized objective.
constraints : list
The canonicalized constraints.
Returns
-------
tuple
(map of variable to offset, length of variable vector)
"""
vars_ = lu.get_expr_vars(objective)
for constr in constraints:
vars_ += lu.get_expr_vars(constr.expr)
var_offsets = OrderedDict()
var_sizes = {}
# Ensure the variables are always in the same
# order for the same problem.
var_names = list(set(vars_))
var_names.sort(key=lambda (var_id, var_size): var_id)
# Map var ids to offsets.
vert_offset = 0
for var_id, var_size in var_names:
var_sizes[var_id] = var_size
var_offsets[var_id] = vert_offset
vert_offset += var_size[0]*var_size[1]
return (var_offsets, var_sizes, vert_offset)
def _get_var_offsets(self, objective, constraints):
"""Maps each variable to a horizontal offset.
Parameters
----------
objective : Expression
The canonicalized objective.
constraints : list
The canonicalized constraints.
Returns
-------
tuple
(map of variable to offset, length of variable vector)
"""
vars_ = lu.get_expr_vars(objective)
for constr in constraints:
vars_ += lu.get_expr_vars(constr.expr)
var_offsets = OrderedDict()
var_sizes = {}
# Ensure the variables are always in the same
# order for the same problem.
var_names = list(set(vars_))
var_names.sort(key=lambda (var_id, var_size): var_id)
# Map var ids to offsets.
vert_offset = 0
for var_id, var_size in var_names:
var_sizes[var_id] = var_size
var_offsets[var_id] = vert_offset
vert_offset += var_size[0] * var_size[1]
return (var_offsets, var_sizes, vert_offset)
def _get_var_offsets(self, objective, constraints, nonlinear=None):
"""Maps each variable to a horizontal offset.
Parameters
----------
objective : Expression
The canonicalized objective.
constraints : list
The canonicalized constraints.
nonlinear : list, optional
Non-linear constraints for CVXOPT.
Returns
-------
tuple
(map of variable to offset, length of variable vector)
"""
vars_ = lu.get_expr_vars(objective)
for constr in constraints:
vars_ += lu.get_expr_vars(constr.expr)
# If CVXOPT is the solver, some of the variables are
# in NonLinearConstraints.
if nonlinear is not None:
for constr in nonlinear:
for nonlin_var in constr.variables():
vars_ += lu.get_expr_vars(nonlin_var)
var_offsets = OrderedDict()
var_sizes = {}
# Ensure the variables are always in the same
# order for the same problem.
var_names = list(set(vars_))
var_names.sort(key=lambda (var_id, var_size): var_id)
# Map var ids to offsets.
vert_offset = 0
for var_id, var_size in var_names:
var_sizes[var_id] = var_size
var_offsets[var_id] = vert_offset
vert_offset += var_size[0]*var_size[1]
return (var_offsets, var_sizes, vert_offset)
def get_var_offsets(objective, constraints, nonlinear):
"""Maps each variable to a horizontal offset.
Parameters
----------
objective : LinOp
The canonicalized objective.
constraints : list
The canonicalized constraints.
nonlinear : list
Non-linear constraints for CVXOPT.
Returns
-------
tuple
(map of variable to offset, length of variable vector)
"""
vars_ = lu.get_expr_vars(objective)
for constr in constraints:
vars_ += lu.get_expr_vars(constr.expr)
# If CVXOPT is the solver, some of the variables are
# in NonLinearConstraints.
for constr in nonlinear:
for nonlin_var in constr.args:
vars_ += lu.get_expr_vars(nonlin_var)
var_offsets = OrderedDict()
# Ensure the variables are always in the same
# order for the same problem.
var_names = list(set(vars_))
var_names.sort(key=lambda id_and_shape: id_and_shape[0])
# Map var ids to offsets and shape.
var_shapes = {}
vert_offset = 0
for var_id, var_shape in var_names:
var_shapes[var_id] = var_shape
var_offsets[var_id] = vert_offset
vert_offset += np.prod(var_shape, dtype=int)
return (var_offsets, var_shapes, vert_offset)
def presolve(objective, constr_map):
"""Eliminates unnecessary constraints and short circuits the solver
if possible.
Parameters
----------
objective : LinOp
The canonicalized objective.
constr_map : dict
A map of constraint type to a list of constraints.
Returns
-------
bool
Is the problem infeasible?
"""
# Remove redundant constraints.
for key, constraints in constr_map.items():
ids = set()
uniq_constr = []
for c in constraints:
if c.constr_id not in ids:
uniq_constr.append(c)
ids.add(c.constr_id)
constr_map[key] = uniq_constr
# If there are no constraints, the problem is unbounded
# if any of the coefficients are non-zero.
# If all the coefficients are zero then return the constant term
# and set all variables to 0.
if not any(constr_map.values()):
str(objective) # TODO
# Remove constraints with no variables or parameters.
for key in [s.EQ, s.LEQ]:
new_constraints = []
for constr in constr_map[key]:
vars_ = lu.get_expr_vars(constr.expr)
if len(vars_) == 0 and not lu.get_expr_params(constr.expr):
V, I, J, coeff = canonInterface.get_problem_matrix(
[constr])
is_pos, is_neg = intf.sign(coeff)
# For equality constraint, coeff must be zero.
# For inequality (i.e. <= 0) constraint,
# coeff must be negative.
if key == s.EQ and not (is_pos and is_neg) or \
key == s.LEQ and not is_neg:
return s.INFEASIBLE
else:
new_constraints.append(constr)
constr_map[key] = new_constraints
return None
def test_get_vars(self):
"""Test getting vars from an expression.
"""
shape = (5, 4)
x = create_var(shape)
y = create_var(shape)
A = create_const(np.ones(shape), shape)
# Expanding dict.
add_expr = sum_expr([x, y, A])
vars_ = get_expr_vars(add_expr)
ref = [(x.data, shape), (y.data, shape)]
self.assertCountEqual(vars_, ref)
def test_leq_constr(self):
"""Test creating a less than or equal constraint.
"""
shape = (5, 5)
x = create_var(shape)
y = create_var(shape)
lh_expr = sum_expr([x, y])
value = np.ones(shape)
rh_expr = create_const(value, shape)
constr = create_leq(lh_expr, rh_expr)
self.assertEqual(constr.shape, shape)
vars_ = get_expr_vars(constr.expr)
ref = [(x.data, shape), (y.data, shape)]
self.assertCountEqual(vars_, ref)
def presolve(objective, constr_map, check_params=False):
"""Eliminates unnecessary constraints and short circuits the solver
if possible.
Parameters
----------
objective : LinOp
The canonicalized objective.
constr_map : dict
A map of constraint type to a list of constraints.
check_params : bool, optional
Should constraints with parameters be evaluated?
Returns
-------
bool
Is the problem infeasible?
"""
# Remove redundant constraints.
for key, constraints in constr_map.items():
uniq_constr = unique(constraints,
key=lambda c: c.constr_id)
constr_map[key] = list(uniq_constr)
# If there are no constraints, the problem is unbounded
# if any of the coefficients are non-zero.
# If all the coefficients are zero then return the constant term
# and set all variables to 0.
if not any(constr_map.values()):
str(objective) # TODO
# Remove constraints with no variables or parameters.
for key in [s.EQ, s.LEQ]:
new_constraints = []
for constr in constr_map[key]:
vars_ = lu.get_expr_vars(constr.expr)
if len(vars_) == 0 and not lu.get_expr_params(constr.expr):
coeff = op2mat.get_constant_coeff(constr.expr)
sign = intf.sign(coeff)
# For equality constraint, coeff must be zero.
# For inequality (i.e. <= 0) constraint,
# coeff must be negative.
if key is s.EQ and not sign.is_zero() or \
key is s.LEQ and not sign.is_negative():
return s.INFEASIBLE
else:
new_constraints.append(constr)
constr_map[key] = new_constraints
return None
def presolve(objective, constr_map, check_params=False):
"""Eliminates unnecessary constraints and short circuits the solver
if possible.
Parameters
----------
objective : LinOp
The canonicalized objective.
constr_map : dict
A map of constraint type to a list of constraints.
check_params : bool, optional
Should constraints with parameters be evaluated?
Returns
-------
bool
Is the problem infeasible?
"""
# Remove redundant constraints.
for key, constraints in constr_map.items():
uniq_constr = unique(constraints, key=lambda c: c.constr_id)
constr_map[key] = list(uniq_constr)
# If there are no constraints, the problem is unbounded
# if any of the coefficients are non-zero.
# If all the coefficients are zero then return the constant term
# and set all variables to 0.
if not any(constr_map.values()):
str(objective) # TODO
# Remove constraints with no variables or parameters.
for key in [s.EQ, s.LEQ]:
new_constraints = []
for constr in constr_map[key]:
vars_ = lu.get_expr_vars(constr.expr)
if len(vars_) == 0 and not lu.get_expr_params(constr.expr):
coeff = op2mat.get_constant_coeff(constr.expr)
sign = intf.sign(coeff)
# For equality constraint, coeff must be zero.
# For inequality (i.e. <= 0) constraint,
# coeff must be negative.
if key is s.EQ and not sign.is_zero() or \
key is s.LEQ and not sign.is_negative():
return s.INFEASIBLE
else:
new_constraints.append(constr)
constr_map[key] = new_constraints
return None
def test_eq_constr(self):
"""Test creating an equality constraint.
"""
shape = (5, 5)
x = create_var(shape)
y = create_var(shape)
lh_expr = sum_expr([x, y])
value = np.ones(shape)
rh_expr = create_const(value, shape)
constr = create_eq(lh_expr, rh_expr)
self.assertEqual(constr.shape, shape)
vars_ = get_expr_vars(constr.expr)
ref = [(x.data, shape), (y.data, shape)]
if PY2:
self.assertItemsEqual(vars_, ref)
else:
self.assertCountEqual(vars_, ref)
def format(self, eq_constr, leq_constr, dims, solver):
"""Formats SDP constraints as inequalities for the solver.
Parameters
----------
eq_constr : list
A list of the equality constraints in the canonical problem.
leq_constr : list
A list of the inequality constraints in the canonical problem.
dims : dict
A dict with the dimensions of the conic constraints.
solver : str
The solver being called.
"""
new_eq = self.__format[0]
# If an equality constraint was introduced, update eq_constr and dims.
if new_eq:
eq_constr += new_eq
dims[s.EQ_DIM] += self.size[0] * self.size[1]
# Record the noncvx_var id.
bool_id = lu.get_expr_vars(self.noncvx_var)[0][0]
dims[self.CONSTR_TYPE].append(bool_id)
def format(self, eq_constr, leq_constr, dims, solver):
"""Formats SDP constraints as inequalities for the solver.
Parameters
----------
eq_constr : list
A list of the equality constraints in the canonical problem.
leq_constr : list
A list of the inequality constraints in the canonical problem.
dims : dict
A dict with the dimensions of the conic constraints.
solver : str
The solver being called.
"""
new_eq = self.__format[0]
# If an equality constraint was introduced, update eq_constr and dims.
if new_eq:
eq_constr += new_eq
dims[s.EQ_DIM] += self.size[0]*self.size[1]
# Record the noncvx_var id.
bool_id = lu.get_expr_vars(self.noncvx_var)[0][0]
dims[self.CONSTR_TYPE].append(bool_id)
def test_consistency(self):
"""Test that variables and constraints keep a consistent order.
"""
import itertools
num_solves = 4
vars_lists = []
ineqs_lists = []
var_ids_order_created = []
for k in range(num_solves):
sum = 0
constraints = []
var_ids = []
for i in range(100):
var = Variable(name=str(i))
var_ids.append(var.id)
sum += var
constraints.append(var >= i)
var_ids_order_created.append(var_ids)
obj = Minimize(sum)
p = Problem(obj, constraints)
objective, constr_map = p.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.LEQ])
var_offsets, var_sizes, x_length = p._get_var_offsets(objective, all_ineq)
# Sort by offset.
vars_ = sorted(var_offsets.items(), key=lambda (var_id, offset): offset)
vars_ = [var_id for (var_id, offset) in vars_]
vars_lists.append(vars_)
ineqs_lists.append(constr_map[s.LEQ])
# Verify order of variables is consistent.
for i in range(num_solves):
self.assertEqual(var_ids_order_created[i],
vars_lists[i])
for i in range(num_solves):
for idx, constr in enumerate(ineqs_lists[i]):
var_id, _ = lu.get_expr_vars(constr.expr)[0]
self.assertEqual(var_ids_order_created[i][idx],
var_id)
def test_consistency(self):
"""Test that variables and constraints keep a consistent order.
"""
import itertools
num_solves = 4
vars_lists = []
ineqs_lists = []
var_ids_order_created = []
for k in range(num_solves):
sum = 0
constraints = []
var_ids = []
for i in range(100):
var = Variable(name=str(i))
var_ids.append(var.id)
sum += var
constraints.append(var >= i)
var_ids_order_created.append(var_ids)
obj = Minimize(sum)
p = Problem(obj, constraints)
objective, constr_map = p.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.LEQ])
var_offsets, var_sizes, x_length = p._get_var_offsets(
objective, all_ineq)
# Sort by offset.
vars_ = sorted(var_offsets.items(),
key=lambda (var_id, offset): offset)
vars_ = [var_id for (var_id, offset) in vars_]
vars_lists.append(vars_)
ineqs_lists.append(constr_map[s.LEQ])
# Verify order of variables is consistent.
for i in range(num_solves):
self.assertEqual(var_ids_order_created[i], vars_lists[i])
for i in range(num_solves):
for idx, constr in enumerate(ineqs_lists[i]):
var_id, _ = lu.get_expr_vars(constr.expr)[0]
self.assertEqual(var_ids_order_created[i][idx], var_id)
from cvxpy.lin_ops.tree_mat import mul, tmul, prune_constants import cvxpy.problems.iterative as iterative from cvxpy.problems.solvers.utilities import SOLVERS from cvxpy.problems.problem_data.sym_data import SymData import numpy as np import numpy.linalg import scipy.sparse as sp import scipy.linalg as LA import unittest import faoInterface # Convolution x = Variable(3) f = np.matrix(np.array([1, 2, 3])).T g = np.array([0, 1, 0.5]) f_conv_g = np.array([0., 1., 2.5, 4., 1.5]) expr = conv(f, x).canonical_form[0] vars_ = lu.get_expr_vars(expr) dag = fao.tree_to_dag(expr, vars_) input_arr = g output_arr = np.zeros(5) faoInterface.eval_FAO_DAG(dag, input_arr, output_arr) # self.assertItemsAlmostEqual(output_arr, f_conv_g) input_arr = np.array(range(5)) output_arr = np.zeros(3) toep = LA.toeplitz(np.array([1, 0, 0]), np.array([1, 2, 3, 0, 0])) faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False) print output_arr print toep
def test_fao_mul(self):
"""Test the mul method.
"""
n = 2
ones = np.ones(n)
# Matrix-vector multiplication.
x = Variable(n)
A = np.matrix("1 2; 3 4").A
expr = (A * x).canonical_form[0]
input_arr = np.ones(n)
output_arr = np.zeros(n)
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
assert (output_arr == A.dot(ones)).all()
input_arr = np.ones(n)
output_arr = np.zeros(n)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
assert (output_arr == A.T.dot(ones)).all()
n = 2
m = 3
ones = np.ones((m, n))
# Matrix-matrix multiplication.
x = Variable(m, n)
A = np.matrix("1 2 3; 4 5 6").A
expr = (A * x).canonical_form[0]
input_arr = np.ones(m * n)
output_arr = np.zeros(n * n)
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
assert (output_arr == A.dot(ones).flatten(order='F')).all()
ones = np.ones((n, n))
input_arr = np.ones(n * n)
output_arr = np.zeros(m * n)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
assert (output_arr == A.T.dot(ones).flatten(order='F')).all()
# Addition
n = 2
x = Variable(n, n)
y = Variable(n, n)
expr = (y + x).canonical_form[0]
input_arr = np.array(range(2 * n * n))
output_arr = np.zeros(n * n)
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
assert (output_arr == np.array([0 + 4, 1 + 5, 2 + 6, 3 + 7])).all()
input_arr = np.array(range(n * n))
output_arr = np.zeros(2 * n * n)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
assert (output_arr == np.hstack([input_arr, input_arr])).all()
# Negation
x = Variable(3, 2)
expr = (-x).canonical_form[0]
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
input_arr = np.arange(6)
output_arr = np.zeros(3 * 2)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
assert (output_arr == -input_arr).all()
input_arr = np.arange(6)
output_arr = np.zeros(3 * 2)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
assert (output_arr == -input_arr).all()
# Convolution
x = Variable(3)
f = np.matrix(np.array([1, 2, 3])).T
g = np.array([0, 1, 0.5])
f_conv_g = np.array([0., 1., 2.5, 4., 1.5])
expr = conv(f, x).canonical_form[0]
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
input_arr = g
output_arr = np.zeros(5)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
self.assertItemsAlmostEqual(output_arr, f_conv_g)
input_arr = np.array(range(5))
output_arr = np.zeros(3)
toep = LA.toeplitz(np.array([1, 0, 0]), np.array([1, 2, 3, 0, 0]))
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
print output_arr
print toep
self.assertItemsAlmostEqual(output_arr, toep.dot(input_arr))
from cvxpy.problems.solvers.utilities import SOLVERS
from cvxpy.problems.problem_data.sym_data import SymData
import numpy as np
import numpy.linalg
import scipy.sparse as sp
import scipy.linalg as LA
import unittest
import faoInterface
# Convolution
x = Variable(3)
f = np.matrix(np.array([1, 2, 3])).T
g = np.array([0, 1, 0.5])
f_conv_g = np.array([ 0., 1., 2.5, 4., 1.5])
expr = conv(f, x).canonical_form[0]
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
input_arr = g
output_arr = np.zeros(5)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
# self.assertItemsAlmostEqual(output_arr, f_conv_g)
input_arr = np.array(range(5))
output_arr = np.zeros(3)
toep = LA.toeplitz(np.array([1,0,0]),
np.array([1, 2, 3, 0, 0]))
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
print output_arr
print toep
def test_fao_mul(self):
"""Test the mul method.
"""
n = 2
ones = np.ones(n)
# Matrix-vector multiplication.
x = Variable(n)
A = np.matrix("1 2; 3 4").A
expr = (A*x).canonical_form[0]
input_arr = np.ones(n)
output_arr = np.zeros(n)
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
assert (output_arr == A.dot(ones)).all()
input_arr = np.ones(n)
output_arr = np.zeros(n)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
assert (output_arr == A.T.dot(ones)).all()
n = 2
m = 3
ones = np.ones((m,n))
# Matrix-matrix multiplication.
x = Variable(m,n)
A = np.matrix("1 2 3; 4 5 6").A
expr = (A*x).canonical_form[0]
input_arr = np.ones(m*n)
output_arr = np.zeros(n*n)
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
assert (output_arr == A.dot(ones).flatten(order='F')).all()
ones = np.ones((n,n))
input_arr = np.ones(n*n)
output_arr = np.zeros(m*n)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
assert (output_arr == A.T.dot(ones).flatten(order='F')).all()
# Addition
n = 2
x = Variable(n, n)
y = Variable(n, n)
expr = (y + x).canonical_form[0]
input_arr = np.array(range(2*n*n))
output_arr = np.zeros(n*n)
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
assert (output_arr == np.array([0 + 4, 1 + 5, 2 + 6, 3 + 7])).all()
input_arr = np.array(range(n*n))
output_arr = np.zeros(2*n*n)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
assert (output_arr == np.hstack([input_arr, input_arr])).all()
# Negation
x = Variable(3,2)
expr = (-x).canonical_form[0]
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
input_arr = np.arange(6)
output_arr = np.zeros(3*2)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
assert (output_arr == -input_arr).all()
input_arr = np.arange(6)
output_arr = np.zeros(3*2)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
assert (output_arr == -input_arr).all()
# Convolution
x = Variable(3)
f = np.matrix(np.array([1, 2, 3])).T
g = np.array([0, 1, 0.5])
f_conv_g = np.array([ 0., 1., 2.5, 4., 1.5])
expr = conv(f, x).canonical_form[0]
vars_ = lu.get_expr_vars(expr)
dag = fao.tree_to_dag(expr, vars_)
input_arr = g
output_arr = np.zeros(5)
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr)
self.assertItemsAlmostEqual(output_arr, f_conv_g)
input_arr = np.array(range(5))
output_arr = np.zeros(3)
toep = LA.toeplitz(np.array([1,0,0]),
np.array([1, 2, 3, 0, 0]))
faoInterface.eval_FAO_DAG(dag, input_arr, output_arr, forward=False)
print output_arr
print toep
self.assertItemsAlmostEqual(output_arr, toep.dot(input_arr))
