def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE)
self.assertEqual(x.canonicalize()[0].size, (2,1))
self.assertEqual(x.canonicalize()[1], [])
# Scalar variable
coeff = self.a.coefficients(self.intf)
self.assertEqual(coeff[self.a], 1)
# Vector variable.
coeffs = x.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [x])
vec = coeffs[x]
self.assertEqual(vec.size, (2,2))
self.assertEqual(list(vec), [1,0,0,1])
# Matrix variable.
coeffs = self.A.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [self.A])
mat = coeffs[self.A]
self.assertEqual(mat.size, (2,2))
self.assertEqual(list(mat), [1,0,0,1])
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2, 1))
self.assertEqual(y.size, (1, 1))
self.assertEqual(x.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(x.canonical_form[0].size, (2, 1))
self.assertEqual(x.canonical_form[1], [])
# Scalar variable
coeff = self.a.coefficients()
self.assertEqual(coeff[self.a.id], [1])
# Vector variable.
coeffs = x.coefficients()
self.assertItemsEqual(coeffs.keys(), [x.id])
vec = coeffs[x.id][0]
self.assertEqual(vec.shape, (2, 2))
self.assertEqual(vec[0, 0], 1)
# Matrix variable.
coeffs = self.A.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.A.id])
self.assertEqual(len(coeffs[self.A.id]), 2)
mat = coeffs[self.A.id][1]
self.assertEqual(mat.shape, (2, 4))
self.assertEqual(mat[0, 2], 1)
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(x.canonical_form[0].size, (2,1))
self.assertEqual(x.canonical_form[1], [])
# Scalar variable
coeff = self.a.coefficients()
self.assertEqual(coeff[self.a], [1])
# Vector variable.
coeffs = x.coefficients()
self.assertItemsEqual(coeffs.keys(), [x])
vec = coeffs[x][0]
self.assertEqual(vec.size, (2,2))
self.assertEqual(vec[0,0], 1)
# Matrix variable.
coeffs = self.A.coefficients()
self.assertItemsEqual(coeffs.keys(), [self.A])
self.assertEqual(len(coeffs[self.A]), 2)
mat = coeffs[self.A][1]
self.assertEqual(mat.size, (2,4))
self.assertEqual(mat[0,2], 1)
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(x.canonical_form[0].size, (2,1))
self.assertEqual(x.canonical_form[1], [])
def test_consistency(self):
"""Test that variables and constraints keep a consistent order.
"""
import itertools
num_solves = 4
vars_lists = []
ineqs_lists = []
for k in range(num_solves):
sum = 0
constraints = []
for i in range(100):
var = Variable(name=str(i))
sum += var
constraints.append(var >= i)
obj = Minimize(sum)
p = Problem(obj, constraints)
objective, constr_map, dims = p.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.INEQ])
var_info = p._get_var_offsets(objective, all_ineq)
sorted_vars, var_offsets, x_length = var_info
vars_lists.append([int(v.name()) for v in sorted_vars])
ineqs_lists.append(constr_map[s.INEQ])
# Verify order of variables is consistent.
for i in range(num_solves):
self.assertEqual(range(100), vars_lists[i])
for i in range(num_solves):
for idx, constr in enumerate(ineqs_lists[i]):
var = constr.variables()[0]
self.assertEqual(idx, int(var.name()))
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2, 1))
self.assertEqual(y.size, (1, 1))
self.assertEqual(x.curvature, s.AFFINE)
self.assertEqual(x.canonical_form[0].size, (2, 1))
self.assertEqual(x.canonical_form[1], [])
self.assertEqual(repr(self.x), "Variable(2, 1)")
self.assertEqual(repr(self.A), "Variable(2, 2)")
def test_consistency(self):
"""Test that variables and constraints keep a consistent order.
"""
import itertools
num_solves = 4
vars_lists = []
ineqs_lists = []
for k in range(num_solves):
sum = 0
constraints = []
for i in range(100):
var = Variable(name=str(i))
sum += var
constraints.append(var >= i)
obj = Minimize(sum)
p = Problem(obj, constraints)
objective, constr_map, dims = p.canonicalize()
all_ineq = itertools.chain(constr_map[s.EQ], constr_map[s.INEQ])
var_info = p._get_var_offsets(objective, all_ineq)
sorted_vars, var_offsets, x_length = var_info
vars_lists.append([int(v.name()) for v in sorted_vars])
ineqs_lists.append(constr_map[s.INEQ])
# Verify order of variables is consistent.
for i in range(num_solves):
self.assertEqual(range(100), vars_lists[i])
for i in range(num_solves):
for idx, constr in enumerate(ineqs_lists[i]):
var = constr.variables()[0]
self.assertEqual(idx, int(var.name()))
class TestExpressions(unittest.TestCase):
""" Unit tests for the expression/expression module. """
def setUp(self):
self.a = Variable(name='a')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2,2,name='A')
self.B = Variable(2,2,name='B')
self.C = Variable(3,2,name='C')
self.intf = intf.DEFAULT_INTERFACE
# Test the Variable class.
def test_variable(self):
x = Variable(2)
y = Variable(2)
assert y.name() != x.name()
x = Variable(2, name='x')
y = Variable()
self.assertEqual(x.name(), 'x')
self.assertEqual(x.size, (2,1))
self.assertEqual(y.size, (1,1))
self.assertEqual(x.curvature, u.Curvature.AFFINE)
self.assertEqual(x.canonicalize()[0].size, (2,1))
self.assertEqual(x.canonicalize()[1], [])
# Scalar variable
coeff = self.a.coefficients(self.intf)
self.assertEqual(coeff[self.a], 1)
# Vector variable.
coeffs = x.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [x])
vec = coeffs[x]
self.assertEqual(vec.size, (2,2))
self.assertEqual(list(vec), [1,0,0,1])
# Matrix variable.
coeffs = self.A.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [self.A])
mat = coeffs[self.A]
self.assertEqual(mat.size, (2,2))
self.assertEqual(list(mat), [1,0,0,1])
# Test the TransposeVariable class.
def test_transpose_variable(self):
var = self.a.T
self.assertEquals(var.name(), "a")
self.assertEquals(var.size, (1,1))
self.a.save_value(2)
self.assertEquals(var.value, 2)
var = self.x.T
self.assertEquals(var.name(), "x.T")
self.assertEquals(var.size, (1,2))
self.x.save_value( matrix([1,2]) )
self.assertEquals(var.value[0,0], 1)
self.assertEquals(var.value[0,1], 2)
var = self.C.T
self.assertEquals(var.name(), "C.T")
self.assertEquals(var.size, (2,3))
coeffs = var.coefficients(self.intf)
self.assertItemsEqual(coeffs.keys(), [var])
mat = coeffs[var]
self.assertEqual(mat.size, (2,2))
self.assertEqual(list(mat), [1,0,0,1])
index = var[1,0]
self.assertEquals(index.name(), "C[0,1]")
self.assertEquals(index.size, (1,1))
var = self.x.T.T
self.assertEquals(var.name(), "x")
self.assertEquals(var.size, (2,1))
# Test the Constant class.
def test_constants(self):
c = Constant(2)
self.assertEqual(c.name(), str(2))
c = Constant(2, name="c")
self.assertEqual(c.name(), "c")
self.assertEqual(c.value, 2)
self.assertEqual(c.size, (1,1))
self.assertEqual(c.curvature, u.Curvature.CONSTANT)
self.assertEqual(c.sign, u.Sign.POSITIVE)
self.assertEqual(Constant(-2).sign, u.Sign.NEGATIVE)
self.assertEqual(Constant(0).sign, u.Sign.ZERO)
self.assertEqual(c.canonicalize()[0].size, (1,1))
self.assertEqual(c.canonicalize()[1], [])
coeffs = c.coefficients(self.intf)
self.assertEqual(coeffs.keys(), [s.CONSTANT])
self.assertEqual(coeffs[s.CONSTANT], 2)
# Test the sign.
c = Constant([[2],[2]])
self.assertEqual(c.size, (1,2))
self.assertEqual(c.sign.neg_mat.value.shape, (1,2))
# Test the Parameter class.
def test_parameters(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.size, (1,1))
# Test the AddExpresion class.
def test_add_expression(self):
# Vectors
c = Constant([2,2])
exp = self.x + c
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (2,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), self.x.name() + " + " + c.name())
self.assertEqual(exp.size, (2,1))
z = Variable(2, name='z')
exp = exp + z + self.x
with self.assertRaises(Exception) as cm:
(self.x + self.y)
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Matrices
exp = self.A + self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.size, (2,2))
with self.assertRaises(Exception) as cm:
(self.A + self.C)
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Test the SubExpresion class.
def test_sub_expression(self):
# Vectors
c = Constant([2,2])
exp = self.x - c
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (2,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), self.x.name() + " - " + Constant([2,2]).name())
self.assertEqual(exp.size, (2,1))
z = Variable(2, name='z')
exp = exp - z - self.x
with self.assertRaises(Exception) as cm:
(self.x - self.y)
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Matrices
exp = self.A - self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.size, (2,2))
with self.assertRaises(Exception) as cm:
(self.A - self.C)
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
# Test the MulExpresion class.
def test_mul_expression(self):
# Vectors
c = Constant([[2],[2]])
exp = c*self.x
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual((c[0]*self.x).sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (1,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.size, (1,1))
with self.assertRaises(Exception) as cm:
([2,2,3]*self.x)
const_name = Constant([2,2,3]).name()
self.assertEqual(str(cm.exception),
"Incompatible dimensions.")
# Matrices
with self.assertRaises(Exception) as cm:
Constant([[2, 1],[2, 2]]) * self.C
self.assertEqual(str(cm.exception), "Incompatible dimensions.")
with self.assertRaises(Exception) as cm:
(self.A * self.B)
self.assertEqual(str(cm.exception), "Cannot multiply two non-constants.")
# Constant expressions
T = Constant([[1,2,3],[3,5,5]])
exp = (T + T) * self.B
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.size, (3,2))
# Expression that would break sign multiplication without promotion.
c = Constant([[2],[2],[-2]])
exp = [[1],[2]] + c*self.C
self.assertEqual(exp.sign.pos_mat.value.shape, (1,2))
# Test the NegExpression class.
def test_neg_expression(self):
# Vectors
exp = -self.x
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (2,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), "-%s" % self.x.name())
self.assertEqual(exp.size, self.x.size)
# Matrices
exp = -self.C
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.size, (3,2))
# Test promotion of scalar constants.
def test_scalar_const_promotion(self):
# Vectors
exp = self.x + 2
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEqual(exp.canonicalize()[0].size, (2,1))
self.assertEqual(exp.canonicalize()[1], [])
self.assertEqual(exp.name(), self.x.name() + " + " + Constant(2).name())
self.assertEqual(exp.size, (2,1))
self.assertEqual((4 - self.x).size, (2,1))
self.assertEqual((4 * self.x).size, (2,1))
self.assertEqual((4 <= self.x).size, (2,1))
self.assertEqual((4 == self.x).size, (2,1))
self.assertEqual((self.x >= 4).size, (2,1))
# Matrices
exp = (self.A + 2) + 4
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual((3 * self.A).size, (2,2))
self.assertEqual(exp.size, (2,2))
# Test indexing expression.
def test_index_expression(self):
# Tuple of integers as key.
exp = self.x[1,0]
self.assertEqual(exp.name(), "x[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
coeff = exp.coefficients(self.intf)
self.assertEqual(coeff[exp], 1)
self.assertEqual(exp.value, None)
with self.assertRaises(Exception) as cm:
(self.x[2,0])
self.assertEqual(str(cm.exception), "Invalid indices 2,0 for 'x'.")
# Slicing
exp = self.C[0:2,1]
self.assertEquals(exp.name(), "C[0:2,1]")
self.assertEquals(exp.size, (2,1))
exp = self.C[0:,0:2]
self.assertEquals(exp.name(), "C[0:,0:2]")
self.assertEquals(exp.size, (3,2))
exp = self.C[0::2,0::2]
self.assertEquals(exp.name(), "C[0::2,0::2]")
self.assertEquals(exp.size, (2,1))
exp = self.C[:3,:1:2]
self.assertEquals(exp.name(), "C[0:3,0]")
self.assertEquals(exp.size, (3,1))
c = Constant([[1,-2],[0,4]])
exp = c[1,1]
print exp
self.assertEqual(exp.curvature, u.Curvature.CONSTANT)
self.assertEqual(exp.sign, u.Sign.POSITIVE)
self.assertEqual(c[0,1].sign, u.Sign.ZERO)
self.assertEqual(c[1,0].sign, u.Sign.NEGATIVE)
self.assertEquals(exp.size, (1,1))
self.assertEqual(exp.value, 4)
c = Constant([[1,-2,3],[0,4,5],[7,8,9]])
exp = c[0:3,0:4:2]
self.assertEqual(exp.curvature, u.Curvature.CONSTANT)
self.assertEquals(exp.size, (3,2))
self.assertEqual(exp[0,1].value, 7)
# Arithmetic expression indexing
exp = (self.x + self.z)[1,0]
self.assertEqual(exp.name(), "x[1,0] + z[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEqual(exp.sign, u.Sign.UNKNOWN)
self.assertEquals(exp.size, (1,1))
exp = (self.x + self.a)[1,0]
self.assertEqual(exp.name(), "x[1,0] + a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
exp = (self.x - self.z)[1,0]
self.assertEqual(exp.name(), "x[1,0] - z[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
exp = (self.x - self.a)[1,0]
self.assertEqual(exp.name(), "x[1,0] - a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
exp = (-self.x)[1,0]
self.assertEqual(exp.name(), "-x[1,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
c = Constant([[1,2],[3,4]])
exp = (c*self.x)[1,0]
self.assertEqual(exp.name(), "[[2], [4]] * x[0:,0]")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
c = Constant([[1,2],[3,4]])
exp = (c*self.a)[1,0]
self.assertEqual(exp.name(), "2 * a")
self.assertEqual(exp.curvature, u.Curvature.AFFINE)
self.assertEquals(exp.size, (1,1))
class TestProblem(BaseTest):
""" Unit tests for the expression/expression module. """
def setUp(self):
self.a = Variable(name='a')
self.b = Variable(name='b')
self.c = Variable(name='c')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2, 2, name='A')
self.B = Variable(2, 2, name='B')
self.C = Variable(3, 2, name='C')
def test_to_str(self):
"""Test string representations.
"""
obj = Minimize(self.a)
prob = Problem(obj)
self.assertEqual(repr(prob), "Problem(%s, %s)" % (repr(obj), repr([])))
constraints = [self.x * 2 == self.x, self.x == 0]
prob = Problem(obj, constraints)
self.assertEqual(repr(prob),
"Problem(%s, %s)" % (repr(obj), repr(constraints)))
# Test str.
result = "minimize %(name)s\nsubject to %(name)s == 0\n 0 <= %(name)s" % {
"name": self.a.name()
}
prob = Problem(Minimize(self.a), [self.a == 0, self.a >= 0])
self.assertEqual(str(prob), result)
def test_variables(self):
"""Test the variables method.
"""
p = Problem(Minimize(self.a), [self.a <= self.x, self.b <= self.A + 2])
vars_ = p.variables()
ref = [self.a, self.x, self.b, self.A]
if PY2:
self.assertItemsEqual(vars_, ref)
else:
self.assertCountEqual(vars_, ref)
def test_parameters(self):
"""Test the parameters method.
"""
p1 = Parameter()
p2 = Parameter(3, sign="negative")
p3 = Parameter(4, 4, sign="positive")
p = Problem(Minimize(p1), [self.a + p1 <= p2, self.b <= p3 + p3 + 2])
params = p.parameters()
ref = [p1, p2, p3]
if PY2:
self.assertItemsEqual(params, ref)
else:
self.assertCountEqual(params, ref)
def test_get_problem_data(self):
"""Test get_problem_data method.
"""
with self.assertRaises(Exception) as cm:
Problem(Maximize(exp(self.a))).get_problem_data(s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
data = Problem(Maximize(exp(self.a) + 2)).get_problem_data(s.SCS)
dims = data["dims"]
self.assertEqual(dims['ep'], 1)
self.assertEqual(data["c"].shape, (2, ))
self.assertEqual(data["A"].shape, (3, 2))
data = Problem(Minimize(norm(self.x) + 3)).get_problem_data(s.ECOS)
dims = data["dims"]
self.assertEqual(dims["q"], [3])
self.assertEqual(data["c"].shape, (3, ))
self.assertEqual(data["A"].shape, (0, 3))
self.assertEqual(data["G"].shape, (3, 3))
data = Problem(Minimize(norm(self.x) + 3)).get_problem_data(s.CVXOPT)
dims = data["dims"]
self.assertEqual(dims["q"], [3])
self.assertEqual(data["c"].size, (3, 1))
self.assertEqual(data["A"].size, (0, 3))
self.assertEqual(data["G"].size, (3, 3))
def test_unpack_results(self):
"""Test unpack results method.
"""
with self.assertRaises(Exception) as cm:
Problem(Minimize(exp(self.a))).unpack_results("blah", None)
self.assertEqual(str(cm.exception), "Unknown solver.")
prob = Problem(Minimize(exp(self.a)), [self.a == 0])
args = prob.get_problem_data(s.SCS)
data = {"c": args["c"], "A": args["A"], "b": args["b"]}
results_dict = scs.solve(data, args["dims"])
prob = Problem(Minimize(exp(self.a)), [self.a == 0])
prob.unpack_results(s.SCS, results_dict)
self.assertAlmostEqual(self.a.value, 0, places=4)
self.assertAlmostEqual(prob.value, 1, places=3)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
args = prob.get_problem_data(s.ECOS)
results_dict = ecos.solve(args["c"], args["G"], args["h"],
args["dims"], args["A"], args["b"])
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
prob.unpack_results(s.ECOS, results_dict)
self.assertItemsAlmostEqual(self.x.value, [0, 0])
self.assertAlmostEqual(prob.value, 0)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
args = prob.get_problem_data(s.CVXOPT)
results_dict = cvxopt.solvers.conelp(args["c"], args["G"], args["h"],
args["dims"], args["A"],
args["b"])
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
prob.unpack_results(s.CVXOPT, results_dict)
self.assertItemsAlmostEqual(self.x.value, [0, 0])
self.assertAlmostEqual(prob.value, 0)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
# Test silencing and enabling solver messages.
def test_verbose(self):
import sys
# From http://stackoverflow.com/questions/5136611/capture-stdout-from-a-script-in-python
# setup the environment
outputs = {True: [], False: []}
backup = sys.stdout
# ####
for verbose in [True, False]:
for solver in installed_solvers():
# Don't test GLPK because there's a race
# condition in setting CVXOPT solver options.
if solver in ["GLPK", "GLPK_MI"]:
continue
# if solver == "GLPK":
# # GLPK's stdout is separate from python,
# # so we have to do this.
# # Note: This probably breaks (badly) on Windows.
# import os
# import tempfile
# stdout_fd = 1
# tmp_handle = tempfile.TemporaryFile(bufsize = 0)
# os.dup2(tmp_handle.fileno(), stdout_fd)
# else:
sys.stdout = StringIO() # capture output
p = Problem(Minimize(self.a + self.x[0]),
[self.a >= 2, self.x >= 2])
if SOLVERS[solver].MIP_CAPABLE:
p.constraints.append(Bool() == 0)
p.solve(verbose=verbose, solver=solver)
if SOLVERS[solver].EXP_CAPABLE:
p = Problem(Minimize(self.a), [log(self.a) >= 2])
p.solve(verbose=verbose, solver=solver)
# if solver == "GLPK":
# # GLPK's stdout is separate from python,
# # so we have to do this.
# tmp_handle.seek(0)
# out = tmp_handle.read()
# tmp_handle.close()
# else:
out = sys.stdout.getvalue() # release output
outputs[verbose].append((out, solver))
# ####
sys.stdout.close() # close the stream
sys.stdout = backup # restore original stdout
for output, solver in outputs[True]:
print(solver)
assert len(output) > 0
for output, solver in outputs[False]:
print(solver)
assert len(output) == 0
# Test registering other solve methods.
def test_register_solve(self):
Problem.register_solve("test", lambda self: 1)
p = Problem(Minimize(1))
result = p.solve(method="test")
self.assertEqual(result, 1)
def test(self, a, b=2):
return (a, b)
Problem.register_solve("test", test)
p = Problem(Minimize(0))
result = p.solve(1, b=3, method="test")
self.assertEqual(result, (1, 3))
result = p.solve(1, method="test")
self.assertEqual(result, (1, 2))
result = p.solve(1, method="test", b=4)
self.assertEqual(result, (1, 4))
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, constraints = p.canonicalize()
sym_data = SymData(objective, constraints, SOLVERS[s.ECOS])
# Sort by offset.
vars_ = sorted(sym_data.var_offsets.items(),
key=lambda key_val: key_val[1])
vars_ = [var_id for (var_id, offset) in vars_]
vars_lists.append(vars_)
ineqs_lists.append(sym_data.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)
# Test removing duplicate constraint objects.
def test_duplicate_constraints(self):
eq = (self.x == 2)
le = (self.x <= 2)
obj = 0
def test(self):
objective, constraints = self.canonicalize()
sym_data = SymData(objective, constraints, SOLVERS[s.ECOS])
return (len(sym_data.constr_map[s.EQ]),
len(sym_data.constr_map[s.LEQ]))
Problem.register_solve("test", test)
p = Problem(Minimize(obj), [eq, eq, le, le])
result = p.solve(method="test")
self.assertEqual(result, (1, 1))
# Internal constraints.
X = Semidef(2)
obj = sum_entries(X + X)
p = Problem(Minimize(obj))
result = p.solve(method="test")
self.assertEqual(result, (0, 1))
# Duplicates from non-linear constraints.
exp = norm(self.x, 2)
prob = Problem(Minimize(0), [exp <= 1, exp <= 2])
result = prob.solve(method="test")
self.assertEqual(result, (0, 4))
# Test the is_dcp method.
def test_is_dcp(self):
p = Problem(Minimize(normInf(self.a)))
self.assertEqual(p.is_dcp(), True)
p = Problem(Maximize(normInf(self.a)))
self.assertEqual(p.is_dcp(), False)
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception),
"Problem does not follow DCP rules.")
p.solve(ignore_dcp=True)
# Test problems involving variables with the same name.
def test_variable_name_conflict(self):
var = Variable(name='a')
p = Problem(Maximize(self.a + var), [var == 2 + self.a, var <= 3])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 1)
self.assertAlmostEqual(var.value, 3)
# Test scalar LP problems.
def test_scalar_lp(self):
p = Problem(Minimize(3 * self.a), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 6)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Maximize(3 * self.a - self.b),
[self.a <= 2, self.b == self.a, self.b <= 5])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 2)
self.assertAlmostEqual(self.b.value, 2)
# With a constant in the objective.
p = Problem(Minimize(3 * self.a - self.b + 100), [
self.a >= 2, self.b + 5 * self.c - 2 == self.a,
self.b <= 5 + self.c
])
result = p.solve()
self.assertAlmostEqual(result, 101 + 1.0 / 6)
self.assertAlmostEqual(self.a.value, 2)
self.assertAlmostEqual(self.b.value, 5 - 1.0 / 6)
self.assertAlmostEqual(self.c.value, -1.0 / 6)
# Test status and value.
exp = Maximize(self.a)
p = Problem(exp, [self.a <= 2])
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.OPTIMAL)
assert self.a.value is not None
assert p.constraints[0].dual_value is not None
# Unbounded problems.
p = Problem(Maximize(self.a), [self.a >= 2])
p.solve(solver=s.ECOS)
self.assertEqual(p.status, s.UNBOUNDED)
assert numpy.isinf(p.value)
assert p.value > 0
assert self.a.value is None
assert p.constraints[0].dual_value is None
p = Problem(Minimize(-self.a), [self.a >= 2])
result = p.solve(solver=s.CVXOPT)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.UNBOUNDED)
assert numpy.isinf(p.value)
assert p.value < 0
# Infeasible problems.
p = Problem(Maximize(self.a), [self.a >= 2, self.a <= 1])
self.a.save_value(2)
p.constraints[0].save_value(2)
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.INFEASIBLE)
assert numpy.isinf(p.value)
assert p.value < 0
assert self.a.value is None
assert p.constraints[0].dual_value is None
p = Problem(Minimize(-self.a), [self.a >= 2, self.a <= 1])
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.INFEASIBLE)
assert numpy.isinf(p.value)
assert p.value > 0
# Test vector LP problems.
def test_vector_lp(self):
c = matrix([1, 2])
p = Problem(Minimize(c.T * self.x), [self.x >= c])
result = p.solve()
self.assertAlmostEqual(result, 5)
self.assertItemsAlmostEqual(self.x.value, [1, 2])
A = matrix([[3, 5], [1, 2]])
I = Constant([[1, 0], [0, 1]])
p = Problem(Minimize(c.T * self.x + self.a), [
A * self.x >= [-1, 1], 4 * I * self.z == self.x, self.z >= [2, 2],
self.a >= 2
])
result = p.solve()
self.assertAlmostEqual(result, 26, places=3)
obj = c.T * self.x.value + self.a.value
self.assertAlmostEqual(obj[0, 0], result)
self.assertItemsAlmostEqual(self.x.value, [8, 8], places=3)
self.assertItemsAlmostEqual(self.z.value, [2, 2], places=3)
def test_ecos_noineq(self):
"""Test ECOS with no inequality constraints.
"""
T = matrix(1, (2, 2))
p = Problem(Minimize(1), [self.A == T])
result = p.solve(solver=s.ECOS)
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, T)
# Test matrix LP problems.
def test_matrix_lp(self):
T = matrix(1, (2, 2))
p = Problem(Minimize(1), [self.A == T])
result = p.solve()
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, T)
T = matrix(2, (2, 3))
c = matrix([3, 4])
p = Problem(Minimize(1),
[self.A >= T * self.C, self.A == self.B, self.C == T.T])
result = p.solve()
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, self.B.value)
self.assertItemsAlmostEqual(self.C.value, T)
assert (self.A.value >= T * self.C.value).all()
# Test variables are dense.
self.assertEqual(type(self.A.value),
intf.DEFAULT_INTERFACE.TARGET_MATRIX)
# Test variable promotion.
def test_variable_promotion(self):
p = Problem(Minimize(self.a), [self.x <= self.a, self.x == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Minimize(self.a),
[self.A <= self.a, self.A == [[1, 2], [3, 4]]])
result = p.solve()
self.assertAlmostEqual(result, 4)
self.assertAlmostEqual(self.a.value, 4)
# Promotion must happen before the multiplication.
p = Problem(Minimize([[1], [1]] * (self.x + self.a + 1)),
[self.a + self.x >= [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 5)
# Test parameter promotion.
def test_parameter_promotion(self):
a = Parameter()
exp = [[1, 2], [3, 4]] * a
a.value = 2
assert not (exp.value - 2 * numpy.array([[1, 2], [3, 4]]).T).any()
def test_parameter_problems(self):
"""Test problems with parameters.
"""
p1 = Parameter()
p2 = Parameter(3, sign="negative")
p3 = Parameter(4, 4, sign="positive")
p = Problem(Maximize(p1 * self.a),
[self.a + p1 <= p2, self.b <= p3 + p3 + 2])
p1.value = 2
p2.value = -numpy.ones((3, 1))
p3.value = numpy.ones((4, 4))
result = p.solve()
self.assertAlmostEqual(result, -6)
# Test problems with normInf
def test_normInf(self):
# Constant argument.
p = Problem(Minimize(normInf(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(normInf(self.a)), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Minimize(3 * normInf(self.a + 2 * self.b) + self.c),
[self.a >= 2, self.b <= -1, self.c == 3])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertAlmostEqual(self.a.value + 2 * self.b.value, 0)
self.assertAlmostEqual(self.c.value, 3)
# Maximize
p = Problem(Maximize(-normInf(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(normInf(self.x - self.z) + 5),
[self.x >= [2, 3], self.z <= [-1, -4]])
result = p.solve()
self.assertAlmostEqual(float(result), 12)
self.assertAlmostEqual(
float(list(self.x.value)[1] - list(self.z.value)[1]), 7)
# Test problems with norm1
def test_norm1(self):
# Constant argument.
p = Problem(Minimize(norm1(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(norm1(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, -2)
# Maximize
p = Problem(Maximize(-norm1(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(norm1(self.x - self.z) + 5),
[self.x >= [2, 3], self.z <= [-1, -4]])
result = p.solve()
self.assertAlmostEqual(float(result), 15)
self.assertAlmostEqual(
float(list(self.x.value)[1] - list(self.z.value)[1]), 7)
# Test problems with norm2
def test_norm2(self):
# Constant argument.
p = Problem(Minimize(norm2(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(norm2(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, -2)
# Maximize
p = Problem(Maximize(-norm2(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(norm2(self.x - self.z) + 5),
[self.x >= [2, 3], self.z <= [-1, -4]])
result = p.solve()
self.assertAlmostEqual(result, 12.61577)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
self.assertItemsAlmostEqual(self.z.value, [-1, -4])
# Row arguments.
p = Problem(Minimize(norm2((self.x - self.z).T) + 5),
[self.x >= [2, 3], self.z <= [-1, -4]])
result = p.solve()
self.assertAlmostEqual(result, 12.61577)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
self.assertItemsAlmostEqual(self.z.value, [-1, -4])
# Test problems with abs
def test_abs(self):
p = Problem(Minimize(sum_entries(abs(self.A))), [-2 >= self.A])
result = p.solve()
self.assertAlmostEqual(result, 8)
self.assertItemsAlmostEqual(self.A.value, [-2, -2, -2, -2])
# Test problems with quad_form.
def test_quad_form(self):
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(self.x, self.A))).solve()
self.assertEqual(
str(cm.exception),
"At least one argument to quad_form must be constant.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(1, self.A))).solve()
self.assertEqual(str(cm.exception),
"Invalid dimensions for arguments.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(self.x, [[-1, 0], [0, 9]]))).solve()
self.assertEqual(str(cm.exception),
"P has both positive and negative eigenvalues.")
P = [[4, 0], [0, 9]]
p = Problem(Minimize(quad_form(self.x, P)), [self.x >= 1])
result = p.solve()
self.assertAlmostEqual(result, 13, places=3)
c = [1, 2]
p = Problem(Minimize(quad_form(c, self.A)), [self.A >= 1])
result = p.solve()
self.assertAlmostEqual(result, 9)
c = [1, 2]
P = [[4, 0], [0, 9]]
p = Problem(Minimize(quad_form(c, P)))
result = p.solve()
self.assertAlmostEqual(result, 40)
# Test combining atoms
def test_mixed_atoms(self):
p = Problem(
Minimize(
norm2(5 + norm1(self.z) + norm1(self.x) +
normInf(self.x - self.z))), [
self.x >= [2, 3], self.z <= [-1, -4],
norm2(self.x + self.z) <= 2
])
result = p.solve()
self.assertAlmostEqual(result, 22)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
self.assertItemsAlmostEqual(self.z.value, [-1, -4])
# Test multiplying by constant atoms.
def test_mult_constant_atoms(self):
p = Problem(Minimize(norm2([3, 4]) * self.a), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertAlmostEqual(self.a.value, 2)
# Test recovery of dual variables.
def test_dual_variables(self):
p = Problem(Minimize(norm1(self.x + self.z)), [
self.x >= [2, 3], [[1, 2], [3, 4]] * self.z == [-1, -4],
norm2(self.x + self.z) <= 100
])
result = p.solve()
self.assertAlmostEqual(result, 4)
self.assertItemsAlmostEqual(self.x.value, [4, 3])
self.assertItemsAlmostEqual(self.z.value, [-4, 1])
# Dual values
self.assertItemsAlmostEqual(p.constraints[0].dual_value, [0, 1])
self.assertItemsAlmostEqual(p.constraints[1].dual_value, [-1, 0.5])
self.assertAlmostEqual(p.constraints[2].dual_value, 0)
T = matrix(2, (2, 3))
c = matrix([3, 4])
p = Problem(Minimize(1),
[self.A >= T * self.C, self.A == self.B, self.C == T.T])
result = p.solve()
# Dual values
self.assertItemsAlmostEqual(p.constraints[0].dual_value, 4 * [0])
self.assertItemsAlmostEqual(p.constraints[1].dual_value, 4 * [0])
self.assertItemsAlmostEqual(p.constraints[2].dual_value, 6 * [0])
# Test problems with indexing.
def test_indexing(self):
# Vector variables
p = Problem(Maximize(self.x[0, 0]),
[self.x[0, 0] <= 2, self.x[1, 0] == 3])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
n = 10
A = matrix(range(n * n), (n, n))
x = Variable(n, n)
p = Problem(Minimize(sum_entries(x)), [x == A])
result = p.solve()
answer = n * n * (n * n + 1) / 2 - n * n
self.assertAlmostEqual(result, answer)
# Matrix variables
p = Problem(
Maximize(sum(self.A[i, i] + self.A[i, 1 - i] for i in range(2))),
[self.A <= [[1, -2], [-3, 4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
self.assertItemsAlmostEqual(self.A.value, [1, -2, -3, 4])
# Indexing arithmetic expressions.
exp = [[1, 2], [3, 4]] * self.z + self.x
p = Problem(Minimize(exp[1, 0]), [self.x == self.z, self.z == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.x.value, self.z.value)
# Test problems with slicing.
def test_slicing(self):
p = Problem(Maximize(sum_entries(self.C)),
[self.C[1:3, :] <= 2, self.C[0, :] == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2 * [1, 2, 2])
p = Problem(Maximize(sum_entries(self.C[0:3:2, 1])),
[self.C[1:3, :] <= 2, self.C[0, :] == 1])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.C.value[0:3:2, 1], [1, 2])
p = Problem(Maximize(sum_entries((self.C[0:2, :] + self.A)[:, 0:2])),
[
self.C[1:3, :] <= 2, self.C[0, :] == 1,
(self.A + self.B)[:, 0] == 3,
(self.A + self.B)[:, 1] == 2, self.B == 1
])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.C.value[0:2, :], [1, 2, 1, 2])
self.assertItemsAlmostEqual(self.A.value, [2, 2, 1, 1])
p = Problem(Maximize([[3], [4]] * (self.C[0:2, :] + self.A)[:, 0]), [
self.C[1:3, :] <= 2, self.C[0, :] == 1, [[1], [2]] *
(self.A + self.B)[:, 0] == 3,
(self.A + self.B)[:, 1] == 2, self.B == 1, 3 * self.A[:, 0] <= 3
])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.C.value[0:2, 0], [1, 2])
self.assertItemsAlmostEqual(self.A.value, [1, -.5, 1, 1])
p = Problem(Minimize(norm2((self.C[0:2, :] + self.A)[:, 0])),
[
self.C[1:3, :] <= 2, self.C[0, :] == 1,
(self.A + self.B)[:, 0] == 3,
(self.A + self.B)[:, 1] == 2, self.B == 1
])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.C.value[0:2, 0], [1, -2])
self.assertItemsAlmostEqual(self.A.value, [2, 2, 1, 1])
# Transpose of slice.
p = Problem(Maximize(sum_entries(self.C)),
[self.C[1:3, :].T <= 2, self.C[0, :].T == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2 * [1, 2, 2])
# Test the vstack atom.
def test_vstack(self):
c = matrix(1, (1, 5))
p = Problem(Minimize(c * vstack(self.x, self.y)),
[self.x == [1, 2], self.y == [3, 4, 5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1, 4))
p = Problem(Minimize(c * vstack(self.x, self.x)), [self.x == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2, 2))
p = Problem(Minimize(sum_entries(vstack(self.A, self.C))),
[self.A >= 2 * c, self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
c = matrix(1, (1, 2))
p = Problem(Minimize(sum_entries(vstack(c * self.A, c * self.B))),
[self.A >= 2, self.B == -2])
result = p.solve()
self.assertAlmostEqual(result, 0)
c = matrix([1, -1])
p = Problem(Minimize(c.T * vstack(square(self.a), sqrt(self.b))),
[self.a == 2, self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception),
"Problem does not follow DCP rules.")
# Test the hstack atom.
def test_hstack(self):
c = matrix(1, (1, 5))
p = Problem(Minimize(c * hstack(self.x.T, self.y.T).T),
[self.x == [1, 2], self.y == [3, 4, 5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1, 4))
p = Problem(Minimize(c * hstack(self.x.T, self.x.T).T),
[self.x == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2, 2))
p = Problem(Minimize(sum_entries(hstack(self.A.T, self.C.T))),
[self.A >= 2 * c, self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
D = Variable(3, 3)
expr = hstack(self.C, D)
p = Problem(Minimize(expr[0, 1] + sum_entries(hstack(expr, expr))),
[self.C >= 0, D >= 0, D[0, 0] == 2, self.C[0, 1] == 3])
result = p.solve()
self.assertAlmostEqual(result, 13)
c = matrix([1, -1])
p = Problem(Minimize(c.T * hstack(square(self.a).T,
sqrt(self.b).T).T),
[self.a == 2, self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception),
"Problem does not follow DCP rules.")
def test_bad_objective(self):
"""Test using a cvxpy expression as an objective.
"""
with self.assertRaises(Exception) as cm:
Problem(self.x + 2)
self.assertEqual(str(cm.exception),
"Problem objective must be Minimize or Maximize.")
# Test variable transpose.
def test_transpose(self):
p = Problem(Minimize(sum_entries(self.x)),
[self.x.T >= matrix([1, 2]).T])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.x.value, [1, 2])
p = Problem(Minimize(sum_entries(self.C)),
[matrix([1, 1]).T * self.C.T >= matrix([0, 1, 2]).T])
result = p.solve()
value = self.C.value
constraints = [
1 * self.C[i, 0] + 1 * self.C[i, 1] >= i for i in range(3)
]
p = Problem(Minimize(sum_entries(self.C)), constraints)
result2 = p.solve()
self.assertAlmostEqual(result, result2)
self.assertItemsAlmostEqual(self.C.value, value)
p = Problem(Minimize(self.A[0, 1] - self.A.T[1, 0]),
[self.A == [[1, 2], [3, 4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
exp = (-self.x).T
p = Problem(Minimize(sum_entries(self.x)), [(-self.x).T <= 1])
result = p.solve()
self.assertAlmostEqual(result, -2)
c = matrix([1, -1])
p = Problem(Minimize(max_elemwise(c.T, 2, 2 + c.T)[1]))
result = p.solve()
self.assertAlmostEqual(result, 2)
c = matrix([[1, -1, 2], [1, -1, 2]])
p = Problem(Minimize(sum_entries(max_elemwise(c, 2, 2 + c).T[:, 0])))
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix([[1, -1, 2], [1, -1, 2]])
p = Problem(Minimize(sum_entries(square(c.T).T[:, 0])))
result = p.solve()
self.assertAlmostEqual(result, 6)
# Slice of transpose.
p = Problem(Maximize(sum_entries(self.C)),
[self.C.T[:, 1:3] <= 2, self.C.T[:, 0] == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2 * [1, 2, 2])
# Test multiplication on the left by a non-constant.
def test_multiplication_on_left(self):
c = matrix([1, 2])
p = Problem(Minimize(c.T * self.A * c), [self.A >= 2])
result = p.solve()
self.assertAlmostEqual(result, 18)
p = Problem(Minimize(self.a * 2), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 4)
p = Problem(Minimize(self.x.T * c), [self.x >= 2])
result = p.solve()
self.assertAlmostEqual(result, 6)
p = Problem(Minimize((self.x.T + self.z.T) * c),
[self.x >= 2, self.z >= 1])
result = p.solve()
self.assertAlmostEqual(result, 9)
# Test redundant constraints in cvxopt.
def test_redundant_constraints(self):
obj = Minimize(sum_entries(self.x))
constraints = [self.x == 2, self.x == 2, self.x.T == 2, self.x[0] == 2]
p = Problem(obj, constraints)
result = p.solve(solver=s.CVXOPT)
self.assertAlmostEqual(result, 4)
obj = Minimize(sum_entries(square(self.x)))
constraints = [self.x == self.x]
p = Problem(obj, constraints)
result = p.solve(solver=s.CVXOPT)
self.assertAlmostEqual(result, 0)
# Test that symmetry is enforced.
def test_sdp_symmetry(self):
# TODO should these raise exceptions?
# with self.assertRaises(Exception) as cm:
# lambda_max([[1,2],[3,4]])
# self.assertEqual(str(cm.exception), "lambda_max called on non-symmetric matrix.")
# with self.assertRaises(Exception) as cm:
# lambda_min([[1,2],[3,4]])
# self.assertEqual(str(cm.exception), "lambda_min called on non-symmetric matrix.")
p = Problem(Minimize(lambda_max(self.A)), [self.A >= 2])
result = p.solve()
self.assertItemsAlmostEqual(self.A.value, self.A.value.T)
p = Problem(Minimize(lambda_max(self.A)), [self.A == [[1, 2], [3, 4]]])
result = p.solve()
self.assertEqual(p.status, s.INFEASIBLE)
# Test SDP
def test_sdp(self):
# Ensure sdp constraints enforce transpose.
obj = Maximize(self.A[1, 0] - self.A[0, 1])
p = Problem(obj, [
lambda_max(self.A) <= 100, self.A[0, 0] == 2, self.A[1, 1] == 2,
self.A[1, 0] == 2
])
result = p.solve()
self.assertAlmostEqual(result, 0)
# Test getting values for expressions.
def test_expression_values(self):
diff_exp = self.x - self.z
inf_exp = normInf(diff_exp)
sum_entries_exp = 5 + norm1(self.z) + norm1(self.x) + inf_exp
constr_exp = norm2(self.x + self.z)
obj = norm2(sum_entries_exp)
p = Problem(Minimize(obj),
[self.x >= [2, 3], self.z <= [-1, -4], constr_exp <= 2])
result = p.solve()
self.assertAlmostEqual(result, 22)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
self.assertItemsAlmostEqual(self.z.value, [-1, -4])
# Expression values.
self.assertItemsAlmostEqual(diff_exp.value,
self.x.value - self.z.value)
self.assertAlmostEqual(inf_exp.value,
LA.norm(self.x.value - self.z.value, numpy.inf))
self.assertAlmostEqual(sum_entries_exp.value,
5 + LA.norm(self.z.value, 1) + LA.norm(self.x.value, 1) + \
LA.norm(self.x.value - self.z.value, numpy.inf))
self.assertAlmostEqual(constr_exp.value,
LA.norm(self.x.value + self.z.value, 2))
self.assertAlmostEqual(obj.value, result)
def test_mult_by_zero(self):
"""Test multiplication by zero.
"""
exp = 0 * self.a
self.assertEqual(exp.value, 0)
obj = Minimize(exp)
p = Problem(obj)
result = p.solve()
self.assertAlmostEqual(result, 0)
assert self.a.value is not None
def test_div(self):
"""Tests a problem with division.
"""
obj = Minimize(normInf(self.A / 5))
p = Problem(obj, [self.A >= 5])
result = p.solve()
self.assertAlmostEqual(result, 1)
def test_mul_elemwise(self):
"""Tests problems with mul_elemwise.
"""
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.A)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.A == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
# Test with a sparse matrix.
import cvxopt
interface = intf.get_matrix_interface(cvxopt.spmatrix)
c = interface.const_to_matrix([1, 2])
expr = mul_elemwise(c, self.x)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.x == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, 10])
# Test promotion.
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.a)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.a == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
def test_invalid_solvers(self):
"""Tests that errors occur when you use an invalid solver.
"""
with self.assertRaises(Exception) as cm:
Problem(Minimize(-log(self.a))).solve(solver=s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(lambda_max(self.a))).solve(solver=s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(self.a)).solve(solver=s.SCS)
self.assertEqual(str(cm.exception),
"The solver SCS cannot solve the problem.")
def test_reshape(self):
"""Tests problems with reshape.
"""
# Test on scalars.
self.assertEqual(reshape(1, 1, 1).value, 1)
# Test vector to matrix.
x = Variable(4)
mat = matrix([[1, -1], [2, -2]])
vec = matrix([1, 2, 3, 4])
vec_mat = matrix([[1, 2], [3, 4]])
expr = reshape(x, 2, 2)
obj = Minimize(sum_entries(mat * expr))
prob = Problem(obj, [x == vec])
result = prob.solve()
self.assertAlmostEqual(result, sum(mat * vec_mat))
# Test on matrix to vector.
c = [1, 2, 3, 4]
expr = reshape(self.A, 4, 1)
obj = Minimize(expr.T * c)
constraints = [self.A == [[-1, -2], [3, 4]]]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 20)
self.assertItemsAlmostEqual(expr.value, [-1, -2, 3, 4])
self.assertItemsAlmostEqual(reshape(expr, 2, 2).value, [-1, -2, 3, 4])
# Test matrix to matrix.
expr = reshape(self.C, 2, 3)
mat = numpy.matrix([[1, -1], [2, -2]])
C_mat = numpy.matrix([[1, 4], [2, 5], [3, 6]])
obj = Minimize(sum_entries(mat * expr))
prob = Problem(obj, [self.C == C_mat])
result = prob.solve()
reshaped = numpy.reshape(C_mat, (2, 3), 'F')
self.assertAlmostEqual(result, (mat.dot(reshaped)).sum())
self.assertItemsAlmostEqual(expr.value, C_mat)
# Test promoted expressions.
c = matrix([[1, -1], [2, -2]])
expr = reshape(c * self.a, 1, 4)
obj = Minimize(expr * [1, 2, 3, 4])
prob = Problem(obj, [self.a == 2])
result = prob.solve()
self.assertAlmostEqual(result, -6)
self.assertItemsAlmostEqual(expr.value, 2 * c)
expr = reshape(c * self.a, 4, 1)
obj = Minimize(expr.T * [1, 2, 3, 4])
prob = Problem(obj, [self.a == 2])
result = prob.solve()
self.assertAlmostEqual(result, -6)
self.assertItemsAlmostEqual(expr.value, 2 * c)
def test_vec(self):
"""Tests problems with vec.
"""
c = [1, 2, 3, 4]
expr = vec(self.A)
obj = Minimize(expr.T * c)
constraints = [self.A == [[-1, -2], [3, 4]]]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 20)
self.assertItemsAlmostEqual(expr.value, [-1, -2, 3, 4])
def test_diag_prob(self):
"""Test a problem with diag.
"""
C = Variable(3, 3)
obj = Maximize(C[0, 2])
constraints = [
diag(C) == 1, C[0, 1] == 0.6, C[1, 2] == -0.3, C == Semidef(3)
]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 0.583151)
def test_presolve_constant_constraints(self):
"""Test that the presolver removes constraints with no variables.
"""
x = Variable()
obj = Maximize(sqrt(x))
prob = Problem(obj)
data = prob.get_problem_data(s.ECOS)
A = data["A"]
G = data["G"]
for row in range(A.shape[0]):
assert A[row, :].nnz > 0
for row in range(G.shape[0]):
assert G[row, :].nnz > 0
def test_presolve_parameters(self):
"""Test presolve with parameters.
"""
# Test with parameters.
gamma = Parameter(sign="positive")
x = Variable()
obj = Minimize(x)
prob = Problem(obj, [gamma == 1, x >= 0])
gamma.value = 0
prob.solve(solver=s.SCS)
self.assertEqual(prob.status, s.INFEASIBLE)
gamma.value = 1
prob.solve(solver=s.CVXOPT)
self.assertEqual(prob.status, s.OPTIMAL)
def test_parameter_expressions(self):
"""Test that expressions with parameters are updated properly.
"""
x = Variable()
y = Variable()
x0 = Parameter()
xSquared = x0 * x0 + 2 * x0 * (x - x0)
# initial guess for x
x0.value = 2
# make the constraint x**2 - y == 0
g = xSquared - y
# set up the problem
obj = abs(x - 1)
prob = Problem(Minimize(obj), [g == 0])
prob.solve()
x0.value = 1
prob.solve()
self.assertAlmostEqual(g.value, 0)
# Test multiplication.
prob = Problem(Minimize(x0 * x), [x == 1])
x0.value = 2
prob.solve()
x0.value = 1
prob.solve()
self.assertAlmostEqual(prob.value, 1)
def test_geo_mean(self):
import numpy as np
x = Variable(2)
cost = geo_mean(x)
prob = Problem(Maximize(cost), [x <= 1])
prob.solve()
self.assertAlmostEqual(prob.value, 1)
prob = Problem(Maximize(cost), [sum(x) <= 1])
prob.solve()
self.assertItemsAlmostEqual(x.value, [.5, .5])
x = Variable(3, 3)
self.assertRaises(ValueError, geo_mean, x)
x = Variable(3, 1)
g = geo_mean(x)
self.assertSequenceEqual(g.w, [Fraction(1, 3)] * 3)
x = Variable(1, 5)
g = geo_mean(x)
self.assertSequenceEqual(g.w, [Fraction(1, 5)] * 5)
# check that we get the right answer for
# max geo_mean(x) s.t. sum(x) <= 1
p = np.array([.07, .12, .23, .19, .39])
def short_geo_mean(x, p):
p = np.array(p) / sum(p)
x = np.array(x)
return np.prod(x**p)
x = Variable(5)
prob = Problem(Maximize(geo_mean(x, p)), [sum(x) <= 1])
prob.solve()
x = np.array(x.value).flatten()
x_true = p / sum(p)
self.assertTrue(np.allclose(prob.value, geo_mean(list(x), p).value))
self.assertTrue(np.allclose(prob.value, short_geo_mean(x, p)))
self.assertTrue(np.allclose(x, x_true, 1e-3))
# check that we get the right answer for
# max geo_mean(x) s.t. norm(x) <= 1
x = Variable(5)
prob = Problem(Maximize(geo_mean(x, p)), [norm(x) <= 1])
prob.solve()
x = np.array(x.value).flatten()
x_true = np.sqrt(p / sum(p))
self.assertTrue(np.allclose(prob.value, geo_mean(list(x), p).value))
self.assertTrue(np.allclose(prob.value, short_geo_mean(x, p)))
self.assertTrue(np.allclose(x, x_true, 1e-3))
def test_pnorm(self):
import numpy as np
x = Variable(3, name='x')
a = np.array([1.0, 2, 3])
for p in (1, 1.6, 1.2, 2, 1.99, 3, 3.7, np.inf):
prob = Problem(Minimize(pnorm(x, p=p)), [x.T * a >= 1])
prob.solve()
# formula is true for any a >= 0 with p > 1
if p == np.inf:
x_true = np.ones_like(a) / sum(a)
elif p == 1:
# only works for the particular a = [1,2,3]
x_true = np.array([0, 0, 1.0 / 3])
else:
x_true = a**(1.0 / (p - 1)) / a.dot(a**(1.0 / (p - 1)))
x_alg = np.array(x.value).flatten()
self.assertTrue(np.allclose(x_alg, x_true, 1e-3))
self.assertTrue(np.allclose(prob.value, np.linalg.norm(x_alg, p)))
self.assertTrue(
np.allclose(np.linalg.norm(x_alg, p),
pnorm(x_alg, p).value))
def test_power(self):
x = Variable()
prob = Problem(
Minimize(power(x, 1.7) + power(x, -2.3) - power(x, .45)))
prob.solve()
x = x.value
self.assertTrue(__builtins__['abs'](1.7 * x**.7 - 2.3 * x**-3.3 -
.45 * x**-.55) <= 1e-3)
class TestProblem(BaseTest):
""" Unit tests for the expression/expression module. """
def setUp(self):
self.a = Variable(name='a')
self.b = Variable(name='b')
self.c = Variable(name='c')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2,2,name='A')
self.B = Variable(2,2,name='B')
self.C = Variable(3,2,name='C')
def test_to_str(self):
"""Test string representations.
"""
obj = Minimize(self.a)
prob = Problem(obj)
self.assertEqual(repr(prob), "Problem(%s, %s)" % (repr(obj), repr([])))
constraints = [self.x*2 == self.x, self.x == 0]
prob = Problem(obj, constraints)
self.assertEqual(repr(prob), "Problem(%s, %s)" % (repr(obj), repr(constraints)))
# Test str.
result = "minimize %(name)s\nsubject to %(name)s == 0\n 0 <= %(name)s" % {"name": self.a.name()}
prob = Problem(Minimize(self.a), [self.a == 0, self.a >= 0])
self.assertEqual(str(prob), result)
def test_variables(self):
"""Test the variables method.
"""
p = Problem(Minimize(self.a), [self.a <= self.x, self.b <= self.A + 2])
vars_ = p.variables()
self.assertItemsEqual(vars_, [self.a, self.x, self.b, self.A])
def test_parameters(self):
"""Test the parameters method.
"""
p1 = Parameter()
p2 = Parameter(3, sign="negative")
p3 = Parameter(4, 4, sign="positive")
p = Problem(Minimize(p1), [self.a + p1 <= p2, self.b <= p3 + p3 + 2])
params = p.parameters()
self.assertItemsEqual(params, [p1, p2, p3])
def test_get_problem_data(self):
"""Test get_problem_data method.
"""
with self.assertRaises(Exception) as cm:
Problem(Maximize(exp(self.a))).get_problem_data(s.ECOS)
self.assertEqual(str(cm.exception), "The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Maximize(exp(self.a))).get_problem_data(s.CVXOPT)
self.assertEqual(str(cm.exception), "Cannot return problem data for the solver CVXOPT.")
args = Problem(Maximize(exp(self.a) + 2)).get_problem_data(s.SCS)
data, dims = args
self.assertEqual(dims['ep'], 1)
self.assertEqual(data["c"].shape, (2,))
self.assertEqual(data["A"].shape, (3, 2))
args = Problem(Minimize(norm(self.x) + 3)).get_problem_data(s.ECOS)
c, G, h, dims, A, b = args
self.assertEqual(dims["q"], [3])
self.assertEqual(c.shape, (3,))
self.assertEqual(A.shape, (0, 3))
self.assertEqual(G.shape, (3, 3))
args = Problem(Minimize(norm(self.x) + 3)).get_problem_data(s.CVXOPT)
c, G, h, dims, A, b = args
self.assertEqual(dims["q"], [3])
self.assertEqual(c.size, (3, 1))
self.assertEqual(A.size, (0, 3))
self.assertEqual(G.size, (3, 3))
# Test silencing and enabling solver messages.
def test_verbose(self):
# From http://stackoverflow.com/questions/5136611/capture-stdout-from-a-script-in-python
# setup the environment
outputs = {True: [], False: []}
backup = sys.stdout
# ####
for verbose in [True, False]:
for solver in [s.ECOS, s.CVXOPT, s.SCS]:
sys.stdout = StringIO() # capture output
p = Problem(Minimize(self.a + self.x[0]), [self.a >= 2, self.x >= 2])
p.solve(verbose=verbose, solver=solver)
if solver != s.ECOS:
p = Problem(Minimize(self.a), [log(self.a) >= 2])
p.solve(verbose=verbose, solver=solver)
out = sys.stdout.getvalue() # release output
outputs[verbose].append(out.upper())
# ####
sys.stdout.close() # close the stream
sys.stdout = backup # restore original stdout
for output in outputs[True]:
assert len(output) > 0
for output in outputs[False]:
assert len(output) == 0
# Test registering other solve methods.
def test_register_solve(self):
Problem.register_solve("test",lambda self: 1)
p = Problem(Minimize(1))
result = p.solve(method="test")
self.assertEqual(result, 1)
def test(self, a, b=2):
return (a,b)
Problem.register_solve("test", test)
p = Problem(Minimize(0))
result = p.solve(1,b=3,method="test")
self.assertEqual(result, (1,3))
result = p.solve(1,method="test")
self.assertEqual(result, (1,2))
result = p.solve(1,method="test",b=4)
self.assertEqual(result, (1,4))
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)
# Test removing duplicate constraint objects.
def test_duplicate_constraints(self):
eq = (self.x == 2)
le = (self.x <= 2)
obj = 0
def test(self):
objective, constr_map = self.canonicalize()
self._presolve(objective, constr_map)
print len(constr_map[s.SOC])
dims = self._format_for_solver(constr_map, s.ECOS)
return (len(constr_map[s.EQ]),len(constr_map[s.LEQ]))
Problem.register_solve("test", test)
p = Problem(Minimize(obj),[eq,eq,le,le])
result = p.solve(method="test")
self.assertEqual(result, (1, 1))
# Internal constraints.
X = Semidef(2)
obj = sum_entries(X + X)
p = Problem(Minimize(obj))
result = p.solve(method="test")
self.assertEqual(result, (1, 1))
# Duplicates from non-linear constraints.
exp = norm(self.x, 2)
prob = Problem(Minimize(0), [exp <= 1, exp <= 2])
result = prob.solve(method="test")
self.assertEqual(result, (0, 4))
# Test the is_dcp method.
def test_is_dcp(self):
p = Problem(Minimize(normInf(self.a)))
self.assertEqual(p.is_dcp(), True)
p = Problem(Maximize(normInf(self.a)))
self.assertEqual(p.is_dcp(), False)
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception), "Problem does not follow DCP rules.")
p.solve(ignore_dcp=True)
# Test problems involving variables with the same name.
def test_variable_name_conflict(self):
var = Variable(name='a')
p = Problem(Maximize(self.a + var), [var == 2 + self.a, var <= 3])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 1)
self.assertAlmostEqual(var.value, 3)
# Test scalar LP problems.
def test_scalar_lp(self):
p = Problem(Minimize(3*self.a), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 6)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Maximize(3*self.a - self.b),
[self.a <= 2, self.b == self.a, self.b <= 5])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 2)
self.assertAlmostEqual(self.b.value, 2)
# With a constant in the objective.
p = Problem(Minimize(3*self.a - self.b + 100),
[self.a >= 2,
self.b + 5*self.c - 2 == self.a,
self.b <= 5 + self.c])
result = p.solve()
self.assertAlmostEqual(result, 101 + 1.0/6)
self.assertAlmostEqual(self.a.value, 2)
self.assertAlmostEqual(self.b.value, 5-1.0/6)
self.assertAlmostEqual(self.c.value, -1.0/6)
# Test status and value.
exp = Maximize(self.a)
p = Problem(exp, [self.a <= 2])
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.OPTIMAL)
assert self.a.value is not None
assert p.constraints[0].dual_value is not None
# Unbounded problems.
p = Problem(Maximize(self.a), [self.a >= 2])
p.solve(solver=s.ECOS)
self.assertEqual(p.status, s.UNBOUNDED)
assert numpy.isinf(p.value)
assert p.value > 0
assert self.a.value is None
assert p.constraints[0].dual_value is None
p = Problem(Minimize(-self.a), [self.a >= 2])
result = p.solve(solver=s.CVXOPT)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.UNBOUNDED)
assert numpy.isinf(p.value)
assert p.value < 0
# Infeasible problems.
p = Problem(Maximize(self.a), [self.a >= 2, self.a <= 1])
self.a.save_value(2)
p.constraints[0].save_value(2)
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.INFEASIBLE)
assert numpy.isinf(p.value)
assert p.value < 0
assert self.a.value is None
assert p.constraints[0].dual_value is None
p = Problem(Minimize(-self.a), [self.a >= 2, self.a <= 1])
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.INFEASIBLE)
assert numpy.isinf(p.value)
assert p.value > 0
# Test vector LP problems.
def test_vector_lp(self):
c = matrix([1,2])
p = Problem(Minimize(c.T*self.x), [self.x >= c])
result = p.solve()
self.assertAlmostEqual(result, 5)
self.assertItemsAlmostEqual(self.x.value, [1,2])
A = matrix([[3,5],[1,2]])
I = Constant([[1,0],[0,1]])
p = Problem(Minimize(c.T*self.x + self.a),
[A*self.x >= [-1,1],
4*I*self.z == self.x,
self.z >= [2,2],
self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 26, places=3)
obj = c.T*self.x.value + self.a.value
self.assertAlmostEqual(obj[0], result)
self.assertItemsAlmostEqual(self.x.value, [8,8], places=3)
self.assertItemsAlmostEqual(self.z.value, [2,2], places=3)
def test_ecos_noineq(self):
"""Test ECOS with no inequality constraints.
"""
T = matrix(1, (2, 2))
p = Problem(Minimize(1), [self.A == T])
result = p.solve(solver=s.ECOS)
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, T)
# Test matrix LP problems.
def test_matrix_lp(self):
T = matrix(1, (2, 2))
p = Problem(Minimize(1), [self.A == T])
result = p.solve()
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, T)
T = matrix(2,(2,3))
c = matrix([3,4])
p = Problem(Minimize(1), [self.A >= T*self.C,
self.A == self.B, self.C == T.T])
result = p.solve()
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, self.B.value)
self.assertItemsAlmostEqual(self.C.value, T)
assert (self.A.value >= T*self.C.value).all()
# Test variables are dense.
self.assertEqual(type(self.A.value), p._DENSE_INTF.TARGET_MATRIX)
# Test variable promotion.
def test_variable_promotion(self):
p = Problem(Minimize(self.a), [self.x <= self.a, self.x == [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Minimize(self.a),
[self.A <= self.a,
self.A == [[1,2],[3,4]]
])
result = p.solve()
self.assertAlmostEqual(result, 4)
self.assertAlmostEqual(self.a.value, 4)
# Promotion must happen before the multiplication.
p = Problem(Minimize([[1],[1]]*(self.x + self.a + 1)),
[self.a + self.x >= [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 5)
# Test parameter promotion.
def test_parameter_promotion(self):
a = Parameter()
exp = [[1,2],[3,4]]*a
a.value = 2
assert not (exp.value - 2*numpy.array([[1,2],[3,4]]).T).any()
def test_parameter_problems(self):
"""Test problems with parameters.
"""
p1 = Parameter()
p2 = Parameter(3, sign="negative")
p3 = Parameter(4, 4, sign="positive")
p = Problem(Maximize(p1*self.a), [self.a + p1 <= p2, self.b <= p3 + p3 + 2])
p1.value = 2
p2.value = -numpy.ones((3,1))
p3.value = numpy.ones((4, 4))
result = p.solve()
self.assertAlmostEqual(result, -6)
# Test problems with normInf
def test_normInf(self):
# Constant argument.
p = Problem(Minimize(normInf(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(normInf(self.a)), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Minimize(3*normInf(self.a + 2*self.b) + self.c),
[self.a >= 2, self.b <= -1, self.c == 3])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertAlmostEqual(self.a.value + 2*self.b.value, 0)
self.assertAlmostEqual(self.c.value, 3)
# Maximize
p = Problem(Maximize(-normInf(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(normInf(self.x - self.z) + 5),
[self.x >= [2,3], self.z <= [-1,-4]])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertAlmostEqual(list(self.x.value)[1] - list(self.z.value)[1], 7)
# Test problems with norm1
def test_norm1(self):
# Constant argument.
p = Problem(Minimize(norm1(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(norm1(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, -2)
# Maximize
p = Problem(Maximize(-norm1(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(norm1(self.x - self.z) + 5),
[self.x >= [2,3], self.z <= [-1,-4]])
result = p.solve()
self.assertAlmostEqual(result, 15)
self.assertAlmostEqual(list(self.x.value)[1] - list(self.z.value)[1], 7)
# Test problems with norm2
def test_norm2(self):
# Constant argument.
p = Problem(Minimize(norm2(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(norm2(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, -2)
# Maximize
p = Problem(Maximize(-norm2(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(norm2(self.x - self.z) + 5),
[self.x >= [2,3], self.z <= [-1,-4]])
result = p.solve()
self.assertAlmostEqual(result, 12.61577)
self.assertItemsAlmostEqual(self.x.value, [2,3])
self.assertItemsAlmostEqual(self.z.value, [-1,-4])
# Row arguments.
p = Problem(Minimize(norm2((self.x - self.z).T) + 5),
[self.x >= [2,3], self.z <= [-1,-4]])
result = p.solve()
self.assertAlmostEqual(result, 12.61577)
self.assertItemsAlmostEqual(self.x.value, [2,3])
self.assertItemsAlmostEqual(self.z.value, [-1,-4])
# Test problems with abs
def test_abs(self):
p = Problem(Minimize(sum_entries(abs(self.A))), [-2 >= self.A])
result = p.solve()
self.assertAlmostEqual(result, 8)
self.assertItemsAlmostEqual(self.A.value, [-2,-2,-2,-2])
# Test problems with quad_form.
def test_quad_form(self):
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(self.x, self.A))).solve()
self.assertEqual(str(cm.exception), "At least one argument to quad_form must be constant.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(1, self.A))).solve()
self.assertEqual(str(cm.exception), "Invalid dimensions for arguments.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(self.x, [[-1, 0], [0, 9]]))).solve()
self.assertEqual(str(cm.exception), "P has both positive and negative eigenvalues.")
P = [[4, 0], [0, 9]]
p = Problem(Minimize(quad_form(self.x, P)), [self.x >= 1])
result = p.solve()
self.assertAlmostEqual(result, 13, places=3)
c = [1,2]
p = Problem(Minimize(quad_form(c, self.A)), [self.A >= 1])
result = p.solve()
self.assertAlmostEqual(result, 9)
c = [1,2]
P = [[4, 0], [0, 9]]
p = Problem(Minimize(quad_form(c, P)))
result = p.solve()
self.assertAlmostEqual(result, 40)
# Test combining atoms
def test_mixed_atoms(self):
p = Problem(Minimize(norm2(5 + norm1(self.z)
+ norm1(self.x) +
normInf(self.x - self.z) ) ),
[self.x >= [2,3], self.z <= [-1,-4], norm2(self.x + self.z) <= 2])
result = p.solve()
self.assertAlmostEqual(result, 22)
self.assertItemsAlmostEqual(self.x.value, [2,3])
self.assertItemsAlmostEqual(self.z.value, [-1,-4])
# Test multiplying by constant atoms.
def test_mult_constant_atoms(self):
p = Problem(Minimize(norm2([3,4])*self.a), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertAlmostEqual(self.a.value, 2)
# Test recovery of dual variables.
def test_dual_variables(self):
p = Problem(Minimize( norm1(self.x + self.z) ),
[self.x >= [2,3],
[[1,2],[3,4]]*self.z == [-1,-4],
norm2(self.x + self.z) <= 100])
result = p.solve()
self.assertAlmostEqual(result, 4)
self.assertItemsAlmostEqual(self.x.value, [4,3])
self.assertItemsAlmostEqual(self.z.value, [-4,1])
# Dual values
self.assertItemsAlmostEqual(p.constraints[0].dual_value, [0, 1])
self.assertItemsAlmostEqual(p.constraints[1].dual_value, [-1, 0.5])
self.assertAlmostEqual(p.constraints[2].dual_value, 0)
T = matrix(2, (2, 3))
c = matrix([3,4])
p = Problem(Minimize(1),
[self.A >= T*self.C,
self.A == self.B,
self.C == T.T])
result = p.solve()
# Dual values
self.assertItemsAlmostEqual(p.constraints[0].dual_value, 4*[0])
self.assertItemsAlmostEqual(p.constraints[1].dual_value, 4*[0])
self.assertItemsAlmostEqual(p.constraints[2].dual_value, 6*[0])
# Test problems with indexing.
def test_indexing(self):
# Vector variables
p = Problem(Maximize(self.x[0,0]), [self.x[0,0] <= 2, self.x[1,0] == 3])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertItemsAlmostEqual(self.x.value, [2,3])
n = 10
A = matrix(range(n*n), (n,n))
x = Variable(n,n)
p = Problem(Minimize(sum_entries(x)), [x == A])
result = p.solve()
answer = n*n*(n*n+1)/2 - n*n
self.assertAlmostEqual(result, answer)
# Matrix variables
p = Problem(Maximize( sum(self.A[i,i] + self.A[i,1-i] for i in range(2)) ),
[self.A <= [[1,-2],[-3,4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
self.assertItemsAlmostEqual(self.A.value, [1,-2,-3,4])
# Indexing arithmetic expressions.
exp = [[1,2],[3,4]]*self.z + self.x
p = Problem(Minimize(exp[1,0]), [self.x == self.z, self.z == [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.x.value, self.z.value)
# Test problems with slicing.
def test_slicing(self):
p = Problem(Maximize(sum_entries(self.C)), [self.C[1:3,:] <= 2, self.C[0,:] == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2*[1,2,2])
p = Problem(Maximize(sum_entries(self.C[0:3:2,1])),
[self.C[1:3,:] <= 2, self.C[0,:] == 1])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.C.value[0:3:2,1], [1,2])
p = Problem(Maximize(sum_entries( (self.C[0:2,:] + self.A)[:,0:2] )),
[self.C[1:3,:] <= 2, self.C[0,:] == 1,
(self.A + self.B)[:,0] == 3, (self.A + self.B)[:,1] == 2,
self.B == 1])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.C.value[0:2,:], [1,2,1,2])
self.assertItemsAlmostEqual(self.A.value, [2,2,1,1])
p = Problem(Maximize( [[3],[4]]*(self.C[0:2,:] + self.A)[:,0] ),
[self.C[1:3,:] <= 2, self.C[0,:] == 1,
[[1],[2]]*(self.A + self.B)[:,0] == 3, (self.A + self.B)[:,1] == 2,
self.B == 1, 3*self.A[:,0] <= 3])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.C.value[0:2,0], [1,2])
self.assertItemsAlmostEqual(self.A.value, [1,-.5,1,1])
p = Problem(Minimize(norm2((self.C[0:2,:] + self.A)[:,0] )),
[self.C[1:3,:] <= 2, self.C[0,:] == 1,
(self.A + self.B)[:,0] == 3, (self.A + self.B)[:,1] == 2,
self.B == 1])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.C.value[0:2,0], [1,-2])
self.assertItemsAlmostEqual(self.A.value, [2,2,1,1])
# Transpose of slice.
p = Problem(Maximize(sum_entries(self.C)), [self.C[1:3,:].T <= 2, self.C[0,:].T == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2*[1,2,2])
# Test the vstack atom.
def test_vstack(self):
c = matrix(1, (1,5))
p = Problem(Minimize(c * vstack(self.x, self.y)),
[self.x == [1,2],
self.y == [3,4,5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1,4))
p = Problem(Minimize(c * vstack(self.x, self.x)),
[self.x == [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2,2))
p = Problem( Minimize( sum_entries(vstack(self.A, self.C)) ),
[self.A >= 2*c,
self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
c = matrix(1, (1,2))
p = Problem( Minimize( sum_entries(vstack(c*self.A, c*self.B)) ),
[self.A >= 2,
self.B == -2])
result = p.solve()
self.assertAlmostEqual(result, 0)
c = matrix([1,-1])
p = Problem( Minimize( c.T * vstack(square(self.a), sqrt(self.b))),
[self.a == 2,
self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception), "Problem does not follow DCP rules.")
# Test the hstack atom.
def test_hstack(self):
c = matrix(1, (1,5))
p = Problem(Minimize(c * hstack(self.x.T, self.y.T).T),
[self.x == [1,2],
self.y == [3,4,5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1,4))
p = Problem(Minimize(c * hstack(self.x.T, self.x.T).T),
[self.x == [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2,2))
p = Problem( Minimize( sum_entries(hstack(self.A.T, self.C.T)) ),
[self.A >= 2*c,
self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
D = Variable(3, 3)
expr = hstack(self.C, D)
p = Problem( Minimize( expr[0,1] + sum_entries(hstack(expr, expr)) ),
[self.C >= 0,
D >= 0, D[0,0] == 2, self.C[0,1] == 3])
result = p.solve()
self.assertAlmostEqual(result, 13)
c = matrix([1,-1])
p = Problem( Minimize( c.T * hstack(square(self.a).T, sqrt(self.b).T).T),
[self.a == 2,
self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception), "Problem does not follow DCP rules.")
def test_bad_objective(self):
"""Test using a cvxpy expression as an objective.
"""
with self.assertRaises(Exception) as cm:
Problem(self.x+2)
self.assertEqual(str(cm.exception), "Problem objective must be Minimize or Maximize.")
# Test variable transpose.
def test_transpose(self):
p = Problem(Minimize(sum_entries(self.x)), [self.x.T >= matrix([1,2]).T])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.x.value, [1,2])
p = Problem(Minimize(sum_entries(self.C)), [matrix([1,1]).T*self.C.T >= matrix([0,1,2]).T])
result = p.solve()
value = self.C.value
constraints = [1*self.C[i,0] + 1*self.C[i,1] >= i for i in range(3)]
p = Problem(Minimize(sum_entries(self.C)), constraints)
result2 = p.solve()
self.assertAlmostEqual(result, result2)
self.assertItemsAlmostEqual(self.C.value, value)
p = Problem(Minimize(self.A[0,1] - self.A.T[1,0]),
[self.A == [[1,2],[3,4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
exp = (-self.x).T
p = Problem(Minimize(sum_entries(self.x)), [(-self.x).T <= 1])
result = p.solve()
self.assertAlmostEqual(result, -2)
c = matrix([1,-1])
p = Problem(Minimize(max_elemwise(c.T, 2, 2 + c.T)[1]))
result = p.solve()
self.assertAlmostEqual(result, 2)
c = matrix([[1,-1,2],[1,-1,2]])
p = Problem(Minimize(sum_entries(max_elemwise(c, 2, 2 + c).T[:,0])))
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix([[1,-1,2],[1,-1,2]])
p = Problem(Minimize(sum_entries(square(c.T).T[:,0])))
result = p.solve()
self.assertAlmostEqual(result, 6)
# Slice of transpose.
p = Problem(Maximize(sum_entries(self.C)), [self.C.T[:,1:3] <= 2, self.C.T[:,0] == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2*[1,2,2])
# Test multiplication on the left by a non-constant.
def test_multiplication_on_left(self):
c = matrix([1,2])
p = Problem(Minimize(c.T*self.A*c), [self.A >= 2])
result = p.solve()
self.assertAlmostEqual(result, 18)
p = Problem(Minimize(self.a*2), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 4)
p = Problem(Minimize(self.x.T*c), [self.x >= 2])
result = p.solve()
self.assertAlmostEqual(result, 6)
p = Problem(Minimize((self.x.T + self.z.T)*c),
[self.x >= 2, self.z >= 1])
result = p.solve()
self.assertAlmostEqual(result, 9)
# Test redundant constraints in cvxopt.
def test_redundant_constraints(self):
obj = Minimize(sum_entries(self.x))
constraints = [self.x == 2, self.x == 2, self.x.T == 2, self.x[0] == 2]
p = Problem(obj, constraints)
result = p.solve(solver=s.CVXOPT)
self.assertAlmostEqual(result, 4)
obj = Minimize(sum_entries(square(self.x)))
constraints = [self.x == self.x]
p = Problem(obj, constraints)
result = p.solve(solver=s.CVXOPT)
self.assertAlmostEqual(result, 0)
# Test that symmetry is enforced.
def test_sdp_symmetry(self):
# TODO should these raise exceptions?
# with self.assertRaises(Exception) as cm:
# lambda_max([[1,2],[3,4]])
# self.assertEqual(str(cm.exception), "lambda_max called on non-symmetric matrix.")
# with self.assertRaises(Exception) as cm:
# lambda_min([[1,2],[3,4]])
# self.assertEqual(str(cm.exception), "lambda_min called on non-symmetric matrix.")
p = Problem(Minimize(lambda_max(self.A)), [self.A >= 2])
result = p.solve()
self.assertItemsAlmostEqual(self.A.value, self.A.value.T)
p = Problem(Minimize(lambda_max(self.A)), [self.A == [[1,2],[3,4]]])
result = p.solve()
self.assertEqual(p.status, s.INFEASIBLE)
# Test SDP
def test_sdp(self):
# Ensure sdp constraints enforce transpose.
obj = Maximize(self.A[1,0] - self.A[0,1])
p = Problem(obj, [lambda_max(self.A) <= 100,
self.A[0,0] == 2,
self.A[1,1] == 2,
self.A[1,0] == 2])
result = p.solve()
self.assertAlmostEqual(result, 0)
# Test getting values for expressions.
def test_expression_values(self):
diff_exp = self.x - self.z
inf_exp = normInf(diff_exp)
sum_entries_exp = 5 + norm1(self.z) + norm1(self.x) + inf_exp
constr_exp = norm2(self.x + self.z)
obj = norm2(sum_entries_exp)
p = Problem(Minimize(obj),
[self.x >= [2,3], self.z <= [-1,-4], constr_exp <= 2])
result = p.solve()
self.assertAlmostEqual(result, 22)
self.assertItemsAlmostEqual(self.x.value, [2,3])
self.assertItemsAlmostEqual(self.z.value, [-1,-4])
# Expression values.
self.assertItemsAlmostEqual(diff_exp.value, self.x.value - self.z.value)
self.assertAlmostEqual(inf_exp.value,
LA.norm(self.x.value - self.z.value, numpy.inf))
self.assertAlmostEqual(sum_entries_exp.value,
5 + LA.norm(self.z.value, 1) + LA.norm(self.x.value, 1) + \
LA.norm(self.x.value - self.z.value, numpy.inf))
self.assertAlmostEqual(constr_exp.value,
LA.norm(self.x.value + self.z.value, 2))
self.assertAlmostEqual(obj.value, result)
def test_mult_by_zero(self):
"""Test multiplication by zero.
"""
exp = 0*self.a
self.assertEqual(exp.value, 0)
obj = Minimize(exp)
p = Problem(obj)
result = p.solve()
self.assertAlmostEqual(result, 0)
assert self.a.value is not None
def test_div(self):
"""Tests a problem with division.
"""
obj = Minimize(normInf(self.A/5))
p = Problem(obj, [self.A >= 5])
result = p.solve()
self.assertAlmostEqual(result, 1)
def test_mul_elemwise(self):
"""Tests problems with mul_elemwise.
"""
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.A)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.A == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
# Test with a sparse matrix.
import cvxopt
interface = intf.get_matrix_interface(cvxopt.spmatrix)
c = interface.const_to_matrix([1,2])
expr = mul_elemwise(c, self.x)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.x == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, 10])
# Test promotion.
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.a)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.a == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
def test_invalid_solvers(self):
"""Tests that errors occur when you use an invalid solver.
"""
with self.assertRaises(Exception) as cm:
Problem(Minimize(-log(self.a))).solve(solver=s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(lambda_max(self.a))).solve(solver=s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(self.a)).solve(solver=s.SCS)
self.assertEqual(str(cm.exception),
"The solver SCS cannot solve the problem.")
def test_reshape(self):
"""Tests problems with reshape.
"""
# Test on scalars.
self.assertEqual(reshape(1, 1, 1).value, 1)
# Test vector to matrix.
x = Variable(4)
mat = matrix([[1,-1], [2, -2]])
vec = matrix([1, 2, 3, 4])
vec_mat = matrix([[1, 2], [3, 4]])
expr = reshape(x, 2, 2)
obj = Minimize(sum_entries(mat*expr))
prob = Problem(obj, [x == vec])
result = prob.solve()
self.assertAlmostEqual(result, sum(mat*vec_mat))
# Test on matrix to vector.
c = [1, 2, 3, 4]
expr = reshape(self.A, 4, 1)
obj = Minimize(expr.T*c)
constraints = [self.A == [[-1, -2], [3, 4]]]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 20)
self.assertItemsAlmostEqual(expr.value, [-1, -2, 3, 4])
self.assertItemsAlmostEqual(reshape(expr, 2, 2).value, [-1, -2, 3, 4])
# Test matrix to matrix.
expr = reshape(self.C, 2, 3)
mat = numpy.matrix([[1,-1], [2, -2]])
C_mat = numpy.matrix([[1, 4], [2, 5], [3, 6]])
obj = Minimize(sum_entries(mat*expr))
prob = Problem(obj, [self.C == C_mat])
result = prob.solve()
reshaped = numpy.reshape(C_mat, (2, 3), 'F')
self.assertAlmostEqual(result, (mat.dot(reshaped)).sum())
self.assertItemsAlmostEqual(expr.value, C_mat)
# Test promoted expressions.
c = matrix([[1,-1], [2, -2]])
expr = reshape(c*self.a, 1, 4)
obj = Minimize(expr*[1, 2, 3, 4])
prob = Problem(obj, [self.a == 2])
result = prob.solve()
self.assertAlmostEqual(result, -6)
self.assertItemsAlmostEqual(expr.value, 2*c)
expr = reshape(c*self.a, 4, 1)
obj = Minimize(expr.T*[1, 2, 3, 4])
prob = Problem(obj, [self.a == 2])
result = prob.solve()
self.assertAlmostEqual(result, -6)
self.assertItemsAlmostEqual(expr.value, 2*c)
def test_vec(self):
"""Tests problems with vec.
"""
c = [1, 2, 3, 4]
expr = vec(self.A)
obj = Minimize(expr.T*c)
constraints = [self.A == [[-1, -2], [3, 4]]]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 20)
self.assertItemsAlmostEqual(expr.value, [-1, -2, 3, 4])
def test_diag_prob(self):
"""Test a problem with diag.
"""
C = Variable(3, 3)
obj = Maximize(C[0, 2])
constraints = [diag(C) == 1,
C[0, 1] == 0.6,
C[1, 2] == -0.3,
C == Semidef(3)]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 0.583151)
def test_presolve_constant_constraints(self):
"""Test that the presolver removes constraints with no variables.
"""
x = Variable()
obj = Maximize(sqrt(x))
prob = Problem(obj)
c, G, h, dims, A, b = prob.get_problem_data(s.ECOS)
for row in range(A.shape[0]):
assert A[row, :].nnz > 0
for row in range(G.shape[0]):
assert G[row, :].nnz > 0
class TestProblem(BaseTest):
""" Unit tests for the expression/expression module. """
def setUp(self):
self.a = Variable(name='a')
self.b = Variable(name='b')
self.c = Variable(name='c')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2, 2, name='A')
self.B = Variable(2, 2, name='B')
self.C = Variable(3, 2, name='C')
def test_to_str(self):
"""Test string representations.
"""
obj = Minimize(self.a)
prob = Problem(obj)
self.assertEqual(repr(prob), "Problem(%s, %s)" % (repr(obj), repr([])))
constraints = [self.x * 2 == self.x, self.x == 0]
prob = Problem(obj, constraints)
self.assertEqual(repr(prob),
"Problem(%s, %s)" % (repr(obj), repr(constraints)))
# Test str.
result = "minimize %(name)s\nsubject to %(name)s == 0\n 0 <= %(name)s" % {
"name": self.a.name()
}
prob = Problem(Minimize(self.a), [self.a == 0, self.a >= 0])
self.assertEqual(str(prob), result)
def test_variables(self):
"""Test the variables method.
"""
p = Problem(Minimize(self.a), [self.a <= self.x, self.b <= self.A + 2])
vars_ = p.variables()
self.assertItemsEqual(vars_, [self.a, self.x, self.b, self.A])
def test_parameters(self):
"""Test the parameters method.
"""
p1 = Parameter()
p2 = Parameter(3, sign="negative")
p3 = Parameter(4, 4, sign="positive")
p = Problem(Minimize(p1), [self.a + p1 <= p2, self.b <= p3 + p3 + 2])
params = p.parameters()
self.assertItemsEqual(params, [p1, p2, p3])
def test_get_problem_data(self):
"""Test get_problem_data method.
"""
with self.assertRaises(Exception) as cm:
Problem(Maximize(exp(self.a))).get_problem_data(s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
args = Problem(Maximize(exp(self.a) + 2)).get_problem_data(s.SCS)
data, dims = args
self.assertEqual(dims['ep'], 1)
self.assertEqual(data["c"].shape, (2, ))
self.assertEqual(data["A"].shape, (3, 2))
args = Problem(Minimize(norm(self.x) + 3)).get_problem_data(s.ECOS)
c, G, h, dims, A, b = args
self.assertEqual(dims["q"], [3])
self.assertEqual(c.shape, (3, ))
self.assertEqual(A.shape, (0, 3))
self.assertEqual(G.shape, (3, 3))
args = Problem(Minimize(norm(self.x) + 3)).get_problem_data(s.CVXOPT)
c, G, h, dims, A, b = args
self.assertEqual(dims["q"], [3])
self.assertEqual(c.size, (3, 1))
self.assertEqual(A.size, (0, 3))
self.assertEqual(G.size, (3, 3))
# Test silencing and enabling solver messages.
def test_verbose(self):
# From http://stackoverflow.com/questions/5136611/capture-stdout-from-a-script-in-python
# setup the environment
outputs = {True: [], False: []}
backup = sys.stdout
# ####
for verbose in [True, False]:
for solver in [s.ECOS, s.CVXOPT, s.SCS]:
sys.stdout = StringIO() # capture output
p = Problem(Minimize(self.a + self.x[0]),
[self.a >= 2, self.x >= 2])
p.solve(verbose=verbose, solver=solver)
if solver != s.ECOS:
p = Problem(Minimize(self.a), [log(self.a) >= 2])
p.solve(verbose=verbose, solver=solver)
out = sys.stdout.getvalue() # release output
outputs[verbose].append(out.upper())
# ####
sys.stdout.close() # close the stream
sys.stdout = backup # restore original stdout
for output in outputs[True]:
assert len(output) > 0
for output in outputs[False]:
assert len(output) == 0
# Test registering other solve methods.
def test_register_solve(self):
Problem.register_solve("test", lambda self: 1)
p = Problem(Minimize(1))
result = p.solve(method="test")
self.assertEqual(result, 1)
def test(self, a, b=2):
return (a, b)
Problem.register_solve("test", test)
p = Problem(Minimize(0))
result = p.solve(1, b=3, method="test")
self.assertEqual(result, (1, 3))
result = p.solve(1, method="test")
self.assertEqual(result, (1, 2))
result = p.solve(1, method="test", b=4)
self.assertEqual(result, (1, 4))
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, constraints = p.canonicalize()
sym_data = SymData(objective, constraints, SOLVERS[s.ECOS])
# Sort by offset.
vars_ = sorted(sym_data.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(sym_data.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)
# Test removing duplicate constraint objects.
def test_duplicate_constraints(self):
eq = (self.x == 2)
le = (self.x <= 2)
obj = 0
def test(self):
objective, constraints = self.canonicalize()
sym_data = SymData(objective, constraints, SOLVERS[s.ECOS])
return (len(sym_data.constr_map[s.EQ]),
len(sym_data.constr_map[s.LEQ]))
Problem.register_solve("test", test)
p = Problem(Minimize(obj), [eq, eq, le, le])
result = p.solve(method="test")
self.assertEqual(result, (1, 1))
# Internal constraints.
X = Semidef(2)
obj = sum_entries(X + X)
p = Problem(Minimize(obj))
result = p.solve(method="test")
self.assertEqual(result, (1, 1))
# Duplicates from non-linear constraints.
exp = norm(self.x, 2)
prob = Problem(Minimize(0), [exp <= 1, exp <= 2])
result = prob.solve(method="test")
self.assertEqual(result, (0, 4))
# Test the is_dcp method.
def test_is_dcp(self):
p = Problem(Minimize(normInf(self.a)))
self.assertEqual(p.is_dcp(), True)
p = Problem(Maximize(normInf(self.a)))
self.assertEqual(p.is_dcp(), False)
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception),
"Problem does not follow DCP rules.")
p.solve(ignore_dcp=True)
# Test problems involving variables with the same name.
def test_variable_name_conflict(self):
var = Variable(name='a')
p = Problem(Maximize(self.a + var), [var == 2 + self.a, var <= 3])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 1)
self.assertAlmostEqual(var.value, 3)
# Test scalar LP problems.
def test_scalar_lp(self):
p = Problem(Minimize(3 * self.a), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 6)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Maximize(3 * self.a - self.b),
[self.a <= 2, self.b == self.a, self.b <= 5])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 2)
self.assertAlmostEqual(self.b.value, 2)
# With a constant in the objective.
p = Problem(Minimize(3 * self.a - self.b + 100), [
self.a >= 2, self.b + 5 * self.c - 2 == self.a,
self.b <= 5 + self.c
])
result = p.solve()
self.assertAlmostEqual(result, 101 + 1.0 / 6)
self.assertAlmostEqual(self.a.value, 2)
self.assertAlmostEqual(self.b.value, 5 - 1.0 / 6)
self.assertAlmostEqual(self.c.value, -1.0 / 6)
# Test status and value.
exp = Maximize(self.a)
p = Problem(exp, [self.a <= 2])
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.OPTIMAL)
assert self.a.value is not None
assert p.constraints[0].dual_value is not None
# Unbounded problems.
p = Problem(Maximize(self.a), [self.a >= 2])
p.solve(solver=s.ECOS)
self.assertEqual(p.status, s.UNBOUNDED)
assert numpy.isinf(p.value)
assert p.value > 0
assert self.a.value is None
assert p.constraints[0].dual_value is None
p = Problem(Minimize(-self.a), [self.a >= 2])
result = p.solve(solver=s.CVXOPT)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.UNBOUNDED)
assert numpy.isinf(p.value)
assert p.value < 0
# Infeasible problems.
p = Problem(Maximize(self.a), [self.a >= 2, self.a <= 1])
self.a.save_value(2)
p.constraints[0].save_value(2)
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.INFEASIBLE)
assert numpy.isinf(p.value)
assert p.value < 0
assert self.a.value is None
assert p.constraints[0].dual_value is None
p = Problem(Minimize(-self.a), [self.a >= 2, self.a <= 1])
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.INFEASIBLE)
assert numpy.isinf(p.value)
assert p.value > 0
# Test vector LP problems.
def test_vector_lp(self):
c = matrix([1, 2])
p = Problem(Minimize(c.T * self.x), [self.x >= c])
result = p.solve()
self.assertAlmostEqual(result, 5)
self.assertItemsAlmostEqual(self.x.value, [1, 2])
A = matrix([[3, 5], [1, 2]])
I = Constant([[1, 0], [0, 1]])
p = Problem(Minimize(c.T * self.x + self.a), [
A * self.x >= [-1, 1], 4 * I * self.z == self.x, self.z >= [2, 2],
self.a >= 2
])
result = p.solve()
self.assertAlmostEqual(result, 26, places=3)
obj = c.T * self.x.value + self.a.value
self.assertAlmostEqual(obj[0], result)
self.assertItemsAlmostEqual(self.x.value, [8, 8], places=3)
self.assertItemsAlmostEqual(self.z.value, [2, 2], places=3)
def test_ecos_noineq(self):
"""Test ECOS with no inequality constraints.
"""
T = matrix(1, (2, 2))
p = Problem(Minimize(1), [self.A == T])
result = p.solve(solver=s.ECOS)
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, T)
# Test matrix LP problems.
def test_matrix_lp(self):
T = matrix(1, (2, 2))
p = Problem(Minimize(1), [self.A == T])
result = p.solve()
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, T)
T = matrix(2, (2, 3))
c = matrix([3, 4])
p = Problem(Minimize(1),
[self.A >= T * self.C, self.A == self.B, self.C == T.T])
result = p.solve()
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, self.B.value)
self.assertItemsAlmostEqual(self.C.value, T)
assert (self.A.value >= T * self.C.value).all()
# Test variables are dense.
self.assertEqual(type(self.A.value),
intf.DEFAULT_INTERFACE.TARGET_MATRIX)
# Test variable promotion.
def test_variable_promotion(self):
p = Problem(Minimize(self.a), [self.x <= self.a, self.x == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Minimize(self.a),
[self.A <= self.a, self.A == [[1, 2], [3, 4]]])
result = p.solve()
self.assertAlmostEqual(result, 4)
self.assertAlmostEqual(self.a.value, 4)
# Promotion must happen before the multiplication.
p = Problem(Minimize([[1], [1]] * (self.x + self.a + 1)),
[self.a + self.x >= [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 5)
# Test parameter promotion.
def test_parameter_promotion(self):
a = Parameter()
exp = [[1, 2], [3, 4]] * a
a.value = 2
assert not (exp.value - 2 * numpy.array([[1, 2], [3, 4]]).T).any()
def test_parameter_problems(self):
"""Test problems with parameters.
"""
p1 = Parameter()
p2 = Parameter(3, sign="negative")
p3 = Parameter(4, 4, sign="positive")
p = Problem(Maximize(p1 * self.a),
[self.a + p1 <= p2, self.b <= p3 + p3 + 2])
p1.value = 2
p2.value = -numpy.ones((3, 1))
p3.value = numpy.ones((4, 4))
result = p.solve()
self.assertAlmostEqual(result, -6)
# Test problems with normInf
def test_normInf(self):
# Constant argument.
p = Problem(Minimize(normInf(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(normInf(self.a)), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Minimize(3 * normInf(self.a + 2 * self.b) + self.c),
[self.a >= 2, self.b <= -1, self.c == 3])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertAlmostEqual(self.a.value + 2 * self.b.value, 0)
self.assertAlmostEqual(self.c.value, 3)
# Maximize
p = Problem(Maximize(-normInf(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(normInf(self.x - self.z) + 5),
[self.x >= [2, 3], self.z <= [-1, -4]])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertAlmostEqual(
list(self.x.value)[1] - list(self.z.value)[1], 7)
# Test problems with norm1
def test_norm1(self):
# Constant argument.
p = Problem(Minimize(norm1(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(norm1(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, -2)
# Maximize
p = Problem(Maximize(-norm1(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(norm1(self.x - self.z) + 5),
[self.x >= [2, 3], self.z <= [-1, -4]])
result = p.solve()
self.assertAlmostEqual(result, 15)
self.assertAlmostEqual(
list(self.x.value)[1] - list(self.z.value)[1], 7)
# Test problems with norm2
def test_norm2(self):
# Constant argument.
p = Problem(Minimize(norm2(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(norm2(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, -2)
# Maximize
p = Problem(Maximize(-norm2(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(norm2(self.x - self.z) + 5),
[self.x >= [2, 3], self.z <= [-1, -4]])
result = p.solve()
self.assertAlmostEqual(result, 12.61577)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
self.assertItemsAlmostEqual(self.z.value, [-1, -4])
# Row arguments.
p = Problem(Minimize(norm2((self.x - self.z).T) + 5),
[self.x >= [2, 3], self.z <= [-1, -4]])
result = p.solve()
self.assertAlmostEqual(result, 12.61577)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
self.assertItemsAlmostEqual(self.z.value, [-1, -4])
# Test problems with abs
def test_abs(self):
p = Problem(Minimize(sum_entries(abs(self.A))), [-2 >= self.A])
result = p.solve()
self.assertAlmostEqual(result, 8)
self.assertItemsAlmostEqual(self.A.value, [-2, -2, -2, -2])
# Test problems with quad_form.
def test_quad_form(self):
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(self.x, self.A))).solve()
self.assertEqual(
str(cm.exception),
"At least one argument to quad_form must be constant.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(1, self.A))).solve()
self.assertEqual(str(cm.exception),
"Invalid dimensions for arguments.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(self.x, [[-1, 0], [0, 9]]))).solve()
self.assertEqual(str(cm.exception),
"P has both positive and negative eigenvalues.")
P = [[4, 0], [0, 9]]
p = Problem(Minimize(quad_form(self.x, P)), [self.x >= 1])
result = p.solve()
self.assertAlmostEqual(result, 13, places=3)
c = [1, 2]
p = Problem(Minimize(quad_form(c, self.A)), [self.A >= 1])
result = p.solve()
self.assertAlmostEqual(result, 9)
c = [1, 2]
P = [[4, 0], [0, 9]]
p = Problem(Minimize(quad_form(c, P)))
result = p.solve()
self.assertAlmostEqual(result, 40)
# Test combining atoms
def test_mixed_atoms(self):
p = Problem(
Minimize(
norm2(5 + norm1(self.z) + norm1(self.x) +
normInf(self.x - self.z))), [
self.x >= [2, 3], self.z <= [-1, -4],
norm2(self.x + self.z) <= 2
])
result = p.solve()
self.assertAlmostEqual(result, 22)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
self.assertItemsAlmostEqual(self.z.value, [-1, -4])
# Test multiplying by constant atoms.
def test_mult_constant_atoms(self):
p = Problem(Minimize(norm2([3, 4]) * self.a), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertAlmostEqual(self.a.value, 2)
# Test recovery of dual variables.
def test_dual_variables(self):
p = Problem(Minimize(norm1(self.x + self.z)), [
self.x >= [2, 3], [[1, 2], [3, 4]] * self.z == [-1, -4],
norm2(self.x + self.z) <= 100
])
result = p.solve()
self.assertAlmostEqual(result, 4)
self.assertItemsAlmostEqual(self.x.value, [4, 3])
self.assertItemsAlmostEqual(self.z.value, [-4, 1])
# Dual values
self.assertItemsAlmostEqual(p.constraints[0].dual_value, [0, 1])
self.assertItemsAlmostEqual(p.constraints[1].dual_value, [-1, 0.5])
self.assertAlmostEqual(p.constraints[2].dual_value, 0)
T = matrix(2, (2, 3))
c = matrix([3, 4])
p = Problem(Minimize(1),
[self.A >= T * self.C, self.A == self.B, self.C == T.T])
result = p.solve()
# Dual values
self.assertItemsAlmostEqual(p.constraints[0].dual_value, 4 * [0])
self.assertItemsAlmostEqual(p.constraints[1].dual_value, 4 * [0])
self.assertItemsAlmostEqual(p.constraints[2].dual_value, 6 * [0])
# Test problems with indexing.
def test_indexing(self):
# Vector variables
p = Problem(Maximize(self.x[0, 0]),
[self.x[0, 0] <= 2, self.x[1, 0] == 3])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
n = 10
A = matrix(range(n * n), (n, n))
x = Variable(n, n)
p = Problem(Minimize(sum_entries(x)), [x == A])
result = p.solve()
answer = n * n * (n * n + 1) / 2 - n * n
self.assertAlmostEqual(result, answer)
# Matrix variables
p = Problem(
Maximize(sum(self.A[i, i] + self.A[i, 1 - i] for i in range(2))),
[self.A <= [[1, -2], [-3, 4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
self.assertItemsAlmostEqual(self.A.value, [1, -2, -3, 4])
# Indexing arithmetic expressions.
exp = [[1, 2], [3, 4]] * self.z + self.x
p = Problem(Minimize(exp[1, 0]), [self.x == self.z, self.z == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.x.value, self.z.value)
# Test problems with slicing.
def test_slicing(self):
p = Problem(Maximize(sum_entries(self.C)),
[self.C[1:3, :] <= 2, self.C[0, :] == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2 * [1, 2, 2])
p = Problem(Maximize(sum_entries(self.C[0:3:2, 1])),
[self.C[1:3, :] <= 2, self.C[0, :] == 1])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.C.value[0:3:2, 1], [1, 2])
p = Problem(Maximize(sum_entries((self.C[0:2, :] + self.A)[:, 0:2])),
[
self.C[1:3, :] <= 2, self.C[0, :] == 1,
(self.A + self.B)[:, 0] == 3,
(self.A + self.B)[:, 1] == 2, self.B == 1
])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.C.value[0:2, :], [1, 2, 1, 2])
self.assertItemsAlmostEqual(self.A.value, [2, 2, 1, 1])
p = Problem(Maximize([[3], [4]] * (self.C[0:2, :] + self.A)[:, 0]), [
self.C[1:3, :] <= 2, self.C[0, :] == 1, [[1], [2]] *
(self.A + self.B)[:, 0] == 3,
(self.A + self.B)[:, 1] == 2, self.B == 1, 3 * self.A[:, 0] <= 3
])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.C.value[0:2, 0], [1, 2])
self.assertItemsAlmostEqual(self.A.value, [1, -.5, 1, 1])
p = Problem(Minimize(norm2((self.C[0:2, :] + self.A)[:, 0])),
[
self.C[1:3, :] <= 2, self.C[0, :] == 1,
(self.A + self.B)[:, 0] == 3,
(self.A + self.B)[:, 1] == 2, self.B == 1
])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.C.value[0:2, 0], [1, -2])
self.assertItemsAlmostEqual(self.A.value, [2, 2, 1, 1])
# Transpose of slice.
p = Problem(Maximize(sum_entries(self.C)),
[self.C[1:3, :].T <= 2, self.C[0, :].T == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2 * [1, 2, 2])
# Test the vstack atom.
def test_vstack(self):
c = matrix(1, (1, 5))
p = Problem(Minimize(c * vstack(self.x, self.y)),
[self.x == [1, 2], self.y == [3, 4, 5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1, 4))
p = Problem(Minimize(c * vstack(self.x, self.x)), [self.x == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2, 2))
p = Problem(Minimize(sum_entries(vstack(self.A, self.C))),
[self.A >= 2 * c, self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
c = matrix(1, (1, 2))
p = Problem(Minimize(sum_entries(vstack(c * self.A, c * self.B))),
[self.A >= 2, self.B == -2])
result = p.solve()
self.assertAlmostEqual(result, 0)
c = matrix([1, -1])
p = Problem(Minimize(c.T * vstack(square(self.a), sqrt(self.b))),
[self.a == 2, self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception),
"Problem does not follow DCP rules.")
# Test the hstack atom.
def test_hstack(self):
c = matrix(1, (1, 5))
p = Problem(Minimize(c * hstack(self.x.T, self.y.T).T),
[self.x == [1, 2], self.y == [3, 4, 5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1, 4))
p = Problem(Minimize(c * hstack(self.x.T, self.x.T).T),
[self.x == [1, 2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2, 2))
p = Problem(Minimize(sum_entries(hstack(self.A.T, self.C.T))),
[self.A >= 2 * c, self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
D = Variable(3, 3)
expr = hstack(self.C, D)
p = Problem(Minimize(expr[0, 1] + sum_entries(hstack(expr, expr))),
[self.C >= 0, D >= 0, D[0, 0] == 2, self.C[0, 1] == 3])
result = p.solve()
self.assertAlmostEqual(result, 13)
c = matrix([1, -1])
p = Problem(Minimize(c.T * hstack(square(self.a).T,
sqrt(self.b).T).T),
[self.a == 2, self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception),
"Problem does not follow DCP rules.")
def test_bad_objective(self):
"""Test using a cvxpy expression as an objective.
"""
with self.assertRaises(Exception) as cm:
Problem(self.x + 2)
self.assertEqual(str(cm.exception),
"Problem objective must be Minimize or Maximize.")
# Test variable transpose.
def test_transpose(self):
p = Problem(Minimize(sum_entries(self.x)),
[self.x.T >= matrix([1, 2]).T])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.x.value, [1, 2])
p = Problem(Minimize(sum_entries(self.C)),
[matrix([1, 1]).T * self.C.T >= matrix([0, 1, 2]).T])
result = p.solve()
value = self.C.value
constraints = [
1 * self.C[i, 0] + 1 * self.C[i, 1] >= i for i in range(3)
]
p = Problem(Minimize(sum_entries(self.C)), constraints)
result2 = p.solve()
self.assertAlmostEqual(result, result2)
self.assertItemsAlmostEqual(self.C.value, value)
p = Problem(Minimize(self.A[0, 1] - self.A.T[1, 0]),
[self.A == [[1, 2], [3, 4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
exp = (-self.x).T
p = Problem(Minimize(sum_entries(self.x)), [(-self.x).T <= 1])
result = p.solve()
self.assertAlmostEqual(result, -2)
c = matrix([1, -1])
p = Problem(Minimize(max_elemwise(c.T, 2, 2 + c.T)[1]))
result = p.solve()
self.assertAlmostEqual(result, 2)
c = matrix([[1, -1, 2], [1, -1, 2]])
p = Problem(Minimize(sum_entries(max_elemwise(c, 2, 2 + c).T[:, 0])))
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix([[1, -1, 2], [1, -1, 2]])
p = Problem(Minimize(sum_entries(square(c.T).T[:, 0])))
result = p.solve()
self.assertAlmostEqual(result, 6)
# Slice of transpose.
p = Problem(Maximize(sum_entries(self.C)),
[self.C.T[:, 1:3] <= 2, self.C.T[:, 0] == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2 * [1, 2, 2])
# Test multiplication on the left by a non-constant.
def test_multiplication_on_left(self):
c = matrix([1, 2])
p = Problem(Minimize(c.T * self.A * c), [self.A >= 2])
result = p.solve()
self.assertAlmostEqual(result, 18)
p = Problem(Minimize(self.a * 2), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 4)
p = Problem(Minimize(self.x.T * c), [self.x >= 2])
result = p.solve()
self.assertAlmostEqual(result, 6)
p = Problem(Minimize((self.x.T + self.z.T) * c),
[self.x >= 2, self.z >= 1])
result = p.solve()
self.assertAlmostEqual(result, 9)
# Test redundant constraints in cvxopt.
def test_redundant_constraints(self):
obj = Minimize(sum_entries(self.x))
constraints = [self.x == 2, self.x == 2, self.x.T == 2, self.x[0] == 2]
p = Problem(obj, constraints)
result = p.solve(solver=s.CVXOPT)
self.assertAlmostEqual(result, 4)
obj = Minimize(sum_entries(square(self.x)))
constraints = [self.x == self.x]
p = Problem(obj, constraints)
result = p.solve(solver=s.CVXOPT)
self.assertAlmostEqual(result, 0)
# Test that symmetry is enforced.
def test_sdp_symmetry(self):
# TODO should these raise exceptions?
# with self.assertRaises(Exception) as cm:
# lambda_max([[1,2],[3,4]])
# self.assertEqual(str(cm.exception), "lambda_max called on non-symmetric matrix.")
# with self.assertRaises(Exception) as cm:
# lambda_min([[1,2],[3,4]])
# self.assertEqual(str(cm.exception), "lambda_min called on non-symmetric matrix.")
p = Problem(Minimize(lambda_max(self.A)), [self.A >= 2])
result = p.solve()
self.assertItemsAlmostEqual(self.A.value, self.A.value.T)
p = Problem(Minimize(lambda_max(self.A)), [self.A == [[1, 2], [3, 4]]])
result = p.solve()
self.assertEqual(p.status, s.INFEASIBLE)
# Test SDP
def test_sdp(self):
# Ensure sdp constraints enforce transpose.
obj = Maximize(self.A[1, 0] - self.A[0, 1])
p = Problem(obj, [
lambda_max(self.A) <= 100, self.A[0, 0] == 2, self.A[1, 1] == 2,
self.A[1, 0] == 2
])
result = p.solve()
self.assertAlmostEqual(result, 0)
# Test getting values for expressions.
def test_expression_values(self):
diff_exp = self.x - self.z
inf_exp = normInf(diff_exp)
sum_entries_exp = 5 + norm1(self.z) + norm1(self.x) + inf_exp
constr_exp = norm2(self.x + self.z)
obj = norm2(sum_entries_exp)
p = Problem(Minimize(obj),
[self.x >= [2, 3], self.z <= [-1, -4], constr_exp <= 2])
result = p.solve()
self.assertAlmostEqual(result, 22)
self.assertItemsAlmostEqual(self.x.value, [2, 3])
self.assertItemsAlmostEqual(self.z.value, [-1, -4])
# Expression values.
self.assertItemsAlmostEqual(diff_exp.value,
self.x.value - self.z.value)
self.assertAlmostEqual(inf_exp.value,
LA.norm(self.x.value - self.z.value, numpy.inf))
self.assertAlmostEqual(sum_entries_exp.value,
5 + LA.norm(self.z.value, 1) + LA.norm(self.x.value, 1) + \
LA.norm(self.x.value - self.z.value, numpy.inf))
self.assertAlmostEqual(constr_exp.value,
LA.norm(self.x.value + self.z.value, 2))
self.assertAlmostEqual(obj.value, result)
def test_mult_by_zero(self):
"""Test multiplication by zero.
"""
exp = 0 * self.a
self.assertEqual(exp.value, 0)
obj = Minimize(exp)
p = Problem(obj)
result = p.solve()
self.assertAlmostEqual(result, 0)
assert self.a.value is not None
def test_div(self):
"""Tests a problem with division.
"""
obj = Minimize(normInf(self.A / 5))
p = Problem(obj, [self.A >= 5])
result = p.solve()
self.assertAlmostEqual(result, 1)
def test_mul_elemwise(self):
"""Tests problems with mul_elemwise.
"""
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.A)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.A == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
# Test with a sparse matrix.
import cvxopt
interface = intf.get_matrix_interface(cvxopt.spmatrix)
c = interface.const_to_matrix([1, 2])
expr = mul_elemwise(c, self.x)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.x == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, 10])
# Test promotion.
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.a)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.a == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
def test_invalid_solvers(self):
"""Tests that errors occur when you use an invalid solver.
"""
with self.assertRaises(Exception) as cm:
Problem(Minimize(-log(self.a))).solve(solver=s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(lambda_max(self.a))).solve(solver=s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(self.a)).solve(solver=s.SCS)
self.assertEqual(str(cm.exception),
"The solver SCS cannot solve the problem.")
def test_reshape(self):
"""Tests problems with reshape.
"""
# Test on scalars.
self.assertEqual(reshape(1, 1, 1).value, 1)
# Test vector to matrix.
x = Variable(4)
mat = matrix([[1, -1], [2, -2]])
vec = matrix([1, 2, 3, 4])
vec_mat = matrix([[1, 2], [3, 4]])
expr = reshape(x, 2, 2)
obj = Minimize(sum_entries(mat * expr))
prob = Problem(obj, [x == vec])
result = prob.solve()
self.assertAlmostEqual(result, sum(mat * vec_mat))
# Test on matrix to vector.
c = [1, 2, 3, 4]
expr = reshape(self.A, 4, 1)
obj = Minimize(expr.T * c)
constraints = [self.A == [[-1, -2], [3, 4]]]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 20)
self.assertItemsAlmostEqual(expr.value, [-1, -2, 3, 4])
self.assertItemsAlmostEqual(reshape(expr, 2, 2).value, [-1, -2, 3, 4])
# Test matrix to matrix.
expr = reshape(self.C, 2, 3)
mat = numpy.matrix([[1, -1], [2, -2]])
C_mat = numpy.matrix([[1, 4], [2, 5], [3, 6]])
obj = Minimize(sum_entries(mat * expr))
prob = Problem(obj, [self.C == C_mat])
result = prob.solve()
reshaped = numpy.reshape(C_mat, (2, 3), 'F')
self.assertAlmostEqual(result, (mat.dot(reshaped)).sum())
self.assertItemsAlmostEqual(expr.value, C_mat)
# Test promoted expressions.
c = matrix([[1, -1], [2, -2]])
expr = reshape(c * self.a, 1, 4)
obj = Minimize(expr * [1, 2, 3, 4])
prob = Problem(obj, [self.a == 2])
result = prob.solve()
self.assertAlmostEqual(result, -6)
self.assertItemsAlmostEqual(expr.value, 2 * c)
expr = reshape(c * self.a, 4, 1)
obj = Minimize(expr.T * [1, 2, 3, 4])
prob = Problem(obj, [self.a == 2])
result = prob.solve()
self.assertAlmostEqual(result, -6)
self.assertItemsAlmostEqual(expr.value, 2 * c)
def test_vec(self):
"""Tests problems with vec.
"""
c = [1, 2, 3, 4]
expr = vec(self.A)
obj = Minimize(expr.T * c)
constraints = [self.A == [[-1, -2], [3, 4]]]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 20)
self.assertItemsAlmostEqual(expr.value, [-1, -2, 3, 4])
def test_diag_prob(self):
"""Test a problem with diag.
"""
C = Variable(3, 3)
obj = Maximize(C[0, 2])
constraints = [
diag(C) == 1, C[0, 1] == 0.6, C[1, 2] == -0.3, C == Semidef(3)
]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 0.583151)
def test_presolve_constant_constraints(self):
"""Test that the presolver removes constraints with no variables.
"""
x = Variable()
obj = Maximize(sqrt(x))
prob = Problem(obj)
c, G, h, dims, A, b = prob.get_problem_data(s.ECOS)
for row in range(A.shape[0]):
assert A[row, :].nnz > 0
for row in range(G.shape[0]):
assert G[row, :].nnz > 0
def test_presolve_parameters(self):
"""Test presolve with parameters.
"""
# Test with parameters.
gamma = Parameter(sign="positive")
x = Variable()
obj = Minimize(x)
prob = Problem(obj, [gamma == 1, x >= 0])
gamma.value = 0
prob.solve(solver=s.SCS)
self.assertEqual(prob.status, s.INFEASIBLE)
gamma.value = 1
prob.solve(solver=s.CVXOPT)
self.assertEqual(prob.status, s.OPTIMAL)
class TestProblem(BaseTest):
""" Unit tests for the expression/expression module. """
def setUp(self):
self.a = Variable(name='a')
self.b = Variable(name='b')
self.c = Variable(name='c')
self.x = Variable(2, name='x')
self.y = Variable(3, name='y')
self.z = Variable(2, name='z')
self.A = Variable(2,2,name='A')
self.B = Variable(2,2,name='B')
self.C = Variable(3,2,name='C')
def test_to_str(self):
"""Test string representations.
"""
obj = Minimize(self.a)
prob = Problem(obj)
self.assertEqual(repr(prob), "Problem(%s, %s)" % (repr(obj), repr([])))
constraints = [self.x*2 == self.x, self.x == 0]
prob = Problem(obj, constraints)
self.assertEqual(repr(prob), "Problem(%s, %s)" % (repr(obj), repr(constraints)))
# Test str.
result = "minimize %(name)s\nsubject to %(name)s == 0\n 0 <= %(name)s" % {"name": self.a.name()}
prob = Problem(Minimize(self.a), [self.a == 0, self.a >= 0])
self.assertEqual(str(prob), result)
def test_variables(self):
"""Test the variables method.
"""
p = Problem(Minimize(self.a), [self.a <= self.x, self.b <= self.A + 2])
vars_ = p.variables()
ref = [self.a, self.x, self.b, self.A]
if PY2:
self.assertItemsEqual(vars_, ref)
else:
self.assertCountEqual(vars_, ref)
def test_parameters(self):
"""Test the parameters method.
"""
p1 = Parameter()
p2 = Parameter(3, sign="negative")
p3 = Parameter(4, 4, sign="positive")
p = Problem(Minimize(p1), [self.a + p1 <= p2, self.b <= p3 + p3 + 2])
params = p.parameters()
ref = [p1, p2, p3]
if PY2:
self.assertItemsEqual(params, ref)
else:
self.assertCountEqual(params, ref)
def test_get_problem_data(self):
"""Test get_problem_data method.
"""
with self.assertRaises(Exception) as cm:
Problem(Maximize(exp(self.a))).get_problem_data(s.ECOS)
self.assertEqual(str(cm.exception), "The solver ECOS cannot solve the problem.")
data = Problem(Maximize(exp(self.a) + 2)).get_problem_data(s.SCS)
dims = data["dims"]
self.assertEqual(dims['ep'], 1)
self.assertEqual(data["c"].shape, (2,))
self.assertEqual(data["A"].shape, (3, 2))
data = Problem(Minimize(norm(self.x) + 3)).get_problem_data(s.ECOS)
dims = data["dims"]
self.assertEqual(dims["q"], [3])
self.assertEqual(data["c"].shape, (3,))
self.assertEqual(data["A"].shape, (0, 3))
self.assertEqual(data["G"].shape, (3, 3))
data = Problem(Minimize(norm(self.x) + 3)).get_problem_data(s.CVXOPT)
dims = data["dims"]
self.assertEqual(dims["q"], [3])
self.assertEqual(data["c"].size, (3, 1))
self.assertEqual(data["A"].size, (0, 3))
self.assertEqual(data["G"].size, (3, 3))
def test_unpack_results(self):
"""Test unpack results method.
"""
with self.assertRaises(Exception) as cm:
Problem(Minimize(exp(self.a))).unpack_results("blah", None)
self.assertEqual(str(cm.exception), "Unknown solver.")
prob = Problem(Minimize(exp(self.a)), [self.a == 0])
args = prob.get_problem_data(s.SCS)
data = {"c": args["c"], "A": args["A"], "b": args["b"]}
results_dict = scs.solve(data, args["dims"])
prob = Problem(Minimize(exp(self.a)), [self.a == 0])
prob.unpack_results(s.SCS, results_dict)
self.assertAlmostEqual(self.a.value, 0, places=3)
self.assertAlmostEqual(prob.value, 1, places=3)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
args = prob.get_problem_data(s.ECOS)
results_dict = ecos.solve(args["c"], args["G"], args["h"],
args["dims"], args["A"], args["b"])
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
prob.unpack_results(s.ECOS, results_dict)
self.assertItemsAlmostEqual(self.x.value, [0,0])
self.assertAlmostEqual(prob.value, 0)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
args = prob.get_problem_data(s.CVXOPT)
results_dict = cvxopt.solvers.conelp(args["c"], args["G"], args["h"],
args["dims"], args["A"], args["b"])
prob = Problem(Minimize(norm(self.x)), [self.x == 0])
prob.unpack_results(s.CVXOPT, results_dict)
self.assertItemsAlmostEqual(self.x.value, [0,0])
self.assertAlmostEqual(prob.value, 0)
self.assertAlmostEqual(prob.status, s.OPTIMAL)
# Test silencing and enabling solver messages.
def test_verbose(self):
import sys
# From http://stackoverflow.com/questions/5136611/capture-stdout-from-a-script-in-python
# setup the environment
outputs = {True: [], False: []}
backup = sys.stdout
# ####
for verbose in [True, False]:
for solver in installed_solvers():
# Don't test GLPK because there's a race
# condition in setting CVXOPT solver options.
if solver in ["GLPK", "GLPK_MI"]:
continue
# if solver == "GLPK":
# # GLPK's stdout is separate from python,
# # so we have to do this.
# # Note: This probably breaks (badly) on Windows.
# import os
# import tempfile
# stdout_fd = 1
# tmp_handle = tempfile.TemporaryFile(bufsize = 0)
# os.dup2(tmp_handle.fileno(), stdout_fd)
# else:
sys.stdout = StringIO() # capture output
p = Problem(Minimize(self.a + self.x[0]),
[self.a >= 2, self.x >= 2])
if SOLVERS[solver].MIP_CAPABLE:
p.constraints.append(Bool() == 0)
p.solve(verbose=verbose, solver=solver)
if SOLVERS[solver].EXP_CAPABLE:
p = Problem(Minimize(self.a), [log(self.a) >= 2])
p.solve(verbose=verbose, solver=solver)
# if solver == "GLPK":
# # GLPK's stdout is separate from python,
# # so we have to do this.
# tmp_handle.seek(0)
# out = tmp_handle.read()
# tmp_handle.close()
# else:
out = sys.stdout.getvalue() # release output
outputs[verbose].append((out, solver))
# ####
sys.stdout.close() # close the stream
sys.stdout = backup # restore original stdout
for output, solver in outputs[True]:
print(solver)
assert len(output) > 0
for output, solver in outputs[False]:
print(solver)
assert len(output) == 0
# Test registering other solve methods.
def test_register_solve(self):
Problem.register_solve("test",lambda self: 1)
p = Problem(Minimize(1))
result = p.solve(method="test")
self.assertEqual(result, 1)
def test(self, a, b=2):
return (a,b)
Problem.register_solve("test", test)
p = Problem(Minimize(0))
result = p.solve(1,b=3,method="test")
self.assertEqual(result, (1,3))
result = p.solve(1,method="test")
self.assertEqual(result, (1,2))
result = p.solve(1,method="test",b=4)
self.assertEqual(result, (1,4))
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, constraints = p.canonicalize()
sym_data = SymData(objective, constraints, SOLVERS[s.ECOS])
# Sort by offset.
vars_ = sorted(sym_data.var_offsets.items(),
key=lambda key_val: key_val[1])
vars_ = [var_id for (var_id, offset) in vars_]
vars_lists.append(vars_)
ineqs_lists.append(sym_data.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)
# Test removing duplicate constraint objects.
def test_duplicate_constraints(self):
eq = (self.x == 2)
le = (self.x <= 2)
obj = 0
def test(self):
objective, constraints = self.canonicalize()
sym_data = SymData(objective, constraints, SOLVERS[s.CVXOPT])
return (len(sym_data.constr_map[s.EQ]),
len(sym_data.constr_map[s.LEQ]))
Problem.register_solve("test", test)
p = Problem(Minimize(obj),[eq,eq,le,le])
result = p.solve(method="test")
self.assertEqual(result, (1, 1))
# Internal constraints.
X = Semidef(2)
obj = sum_entries(X + X)
p = Problem(Minimize(obj))
result = p.solve(method="test")
self.assertEqual(result, (0, 1))
# Duplicates from non-linear constraints.
exp = norm(self.x, 2)
prob = Problem(Minimize(0), [exp <= 1, exp <= 2])
result = prob.solve(method="test")
self.assertEqual(result, (0, 4))
# Test the is_dcp method.
def test_is_dcp(self):
p = Problem(Minimize(normInf(self.a)))
self.assertEqual(p.is_dcp(), True)
p = Problem(Maximize(normInf(self.a)))
self.assertEqual(p.is_dcp(), False)
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception), "Problem does not follow DCP rules.")
p.solve(ignore_dcp=True)
# Test problems involving variables with the same name.
def test_variable_name_conflict(self):
var = Variable(name='a')
p = Problem(Maximize(self.a + var), [var == 2 + self.a, var <= 3])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 1)
self.assertAlmostEqual(var.value, 3)
# Test scalar LP problems.
def test_scalar_lp(self):
p = Problem(Minimize(3*self.a), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 6)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Maximize(3*self.a - self.b),
[self.a <= 2, self.b == self.a, self.b <= 5])
result = p.solve()
self.assertAlmostEqual(result, 4.0)
self.assertAlmostEqual(self.a.value, 2)
self.assertAlmostEqual(self.b.value, 2)
# With a constant in the objective.
p = Problem(Minimize(3*self.a - self.b + 100),
[self.a >= 2,
self.b + 5*self.c - 2 == self.a,
self.b <= 5 + self.c])
result = p.solve()
self.assertAlmostEqual(result, 101 + 1.0/6)
self.assertAlmostEqual(self.a.value, 2)
self.assertAlmostEqual(self.b.value, 5-1.0/6)
self.assertAlmostEqual(self.c.value, -1.0/6)
# Test status and value.
exp = Maximize(self.a)
p = Problem(exp, [self.a <= 2])
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.OPTIMAL)
assert self.a.value is not None
assert p.constraints[0].dual_value is not None
# Unbounded problems.
p = Problem(Maximize(self.a), [self.a >= 2])
p.solve(solver=s.ECOS)
self.assertEqual(p.status, s.UNBOUNDED)
assert numpy.isinf(p.value)
assert p.value > 0
assert self.a.value is None
assert p.constraints[0].dual_value is None
p = Problem(Minimize(-self.a), [self.a >= 2])
result = p.solve(solver=s.CVXOPT)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.UNBOUNDED)
assert numpy.isinf(p.value)
assert p.value < 0
# Infeasible problems.
p = Problem(Maximize(self.a), [self.a >= 2, self.a <= 1])
self.a.save_value(2)
p.constraints[0].save_value(2)
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.INFEASIBLE)
assert numpy.isinf(p.value)
assert p.value < 0
assert self.a.value is None
assert p.constraints[0].dual_value is None
p = Problem(Minimize(-self.a), [self.a >= 2, self.a <= 1])
result = p.solve(solver=s.ECOS)
self.assertEqual(result, p.value)
self.assertEqual(p.status, s.INFEASIBLE)
assert numpy.isinf(p.value)
assert p.value > 0
# Test vector LP problems.
def test_vector_lp(self):
c = matrix([1,2])
p = Problem(Minimize(c.T*self.x), [self.x >= c])
result = p.solve()
self.assertAlmostEqual(result, 5)
self.assertItemsAlmostEqual(self.x.value, [1,2])
A = matrix([[3,5],[1,2]])
I = Constant([[1,0],[0,1]])
p = Problem(Minimize(c.T*self.x + self.a),
[A*self.x >= [-1,1],
4*I*self.z == self.x,
self.z >= [2,2],
self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 26, places=3)
obj = c.T*self.x.value + self.a.value
self.assertAlmostEqual(obj[0,0], result)
self.assertItemsAlmostEqual(self.x.value, [8,8], places=3)
self.assertItemsAlmostEqual(self.z.value, [2,2], places=3)
def test_ecos_noineq(self):
"""Test ECOS with no inequality constraints.
"""
T = matrix(1, (2, 2))
p = Problem(Minimize(1), [self.A == T])
result = p.solve(solver=s.ECOS)
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, T)
# Test matrix LP problems.
def test_matrix_lp(self):
T = matrix(1, (2, 2))
p = Problem(Minimize(1), [self.A == T])
result = p.solve()
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, T)
T = matrix(2,(2,3))
c = matrix([3,4])
p = Problem(Minimize(1), [self.A >= T*self.C,
self.A == self.B, self.C == T.T])
result = p.solve()
self.assertAlmostEqual(result, 1)
self.assertItemsAlmostEqual(self.A.value, self.B.value)
self.assertItemsAlmostEqual(self.C.value, T)
assert (self.A.value >= T*self.C.value).all()
# Test variables are dense.
self.assertEqual(type(self.A.value), intf.DEFAULT_INTERFACE.TARGET_MATRIX)
# Test variable promotion.
def test_variable_promotion(self):
p = Problem(Minimize(self.a), [self.x <= self.a, self.x == [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Minimize(self.a),
[self.A <= self.a,
self.A == [[1,2],[3,4]]
])
result = p.solve()
self.assertAlmostEqual(result, 4)
self.assertAlmostEqual(self.a.value, 4)
# Promotion must happen before the multiplication.
p = Problem(Minimize([[1],[1]]*(self.x + self.a + 1)),
[self.a + self.x >= [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 5)
# Test parameter promotion.
def test_parameter_promotion(self):
a = Parameter()
exp = [[1,2],[3,4]]*a
a.value = 2
assert not (exp.value - 2*numpy.array([[1,2],[3,4]]).T).any()
def test_parameter_problems(self):
"""Test problems with parameters.
"""
p1 = Parameter()
p2 = Parameter(3, sign="negative")
p3 = Parameter(4, 4, sign="positive")
p = Problem(Maximize(p1*self.a), [self.a + p1 <= p2, self.b <= p3 + p3 + 2])
p1.value = 2
p2.value = -numpy.ones((3,1))
p3.value = numpy.ones((4, 4))
result = p.solve()
self.assertAlmostEqual(result, -6)
# Test problems with normInf
def test_normInf(self):
# Constant argument.
p = Problem(Minimize(normInf(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(normInf(self.a)), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, 2)
p = Problem(Minimize(3*normInf(self.a + 2*self.b) + self.c),
[self.a >= 2, self.b <= -1, self.c == 3])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertAlmostEqual(self.a.value + 2*self.b.value, 0)
self.assertAlmostEqual(self.c.value, 3)
# Maximize
p = Problem(Maximize(-normInf(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(normInf(self.x - self.z) + 5),
[self.x >= [2,3], self.z <= [-1,-4]])
result = p.solve()
self.assertAlmostEqual(float(result), 12)
self.assertAlmostEqual(float(list(self.x.value)[1] - list(self.z.value)[1]), 7)
# Test problems with norm1
def test_norm1(self):
# Constant argument.
p = Problem(Minimize(norm1(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(norm1(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, -2)
# Maximize
p = Problem(Maximize(-norm1(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(norm1(self.x - self.z) + 5),
[self.x >= [2,3], self.z <= [-1,-4]])
result = p.solve()
self.assertAlmostEqual(float(result), 15)
self.assertAlmostEqual(float(list(self.x.value)[1] - list(self.z.value)[1]), 7)
# Test problems with norm2
def test_norm2(self):
# Constant argument.
p = Problem(Minimize(norm2(-2)))
result = p.solve()
self.assertAlmostEqual(result, 2)
# Scalar arguments.
p = Problem(Minimize(norm2(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertAlmostEqual(self.a.value, -2)
# Maximize
p = Problem(Maximize(-norm2(self.a)), [self.a <= -2])
result = p.solve()
self.assertAlmostEqual(result, -2)
self.assertAlmostEqual(self.a.value, -2)
# Vector arguments.
p = Problem(Minimize(norm2(self.x - self.z) + 5),
[self.x >= [2,3], self.z <= [-1,-4]])
result = p.solve()
self.assertAlmostEqual(result, 12.61577)
self.assertItemsAlmostEqual(self.x.value, [2,3])
self.assertItemsAlmostEqual(self.z.value, [-1,-4])
# Row arguments.
p = Problem(Minimize(norm2((self.x - self.z).T) + 5),
[self.x >= [2,3], self.z <= [-1,-4]])
result = p.solve()
self.assertAlmostEqual(result, 12.61577)
self.assertItemsAlmostEqual(self.x.value, [2,3])
self.assertItemsAlmostEqual(self.z.value, [-1,-4])
# Test problems with abs
def test_abs(self):
p = Problem(Minimize(sum_entries(abs(self.A))), [-2 >= self.A])
result = p.solve()
self.assertAlmostEqual(result, 8)
self.assertItemsAlmostEqual(self.A.value, [-2,-2,-2,-2])
# Test problems with quad_form.
def test_quad_form(self):
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(self.x, self.A))).solve()
self.assertEqual(str(cm.exception), "At least one argument to quad_form must be constant.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(1, self.A))).solve()
self.assertEqual(str(cm.exception), "Invalid dimensions for arguments.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(quad_form(self.x, [[-1, 0], [0, 9]]))).solve()
self.assertEqual(str(cm.exception), "P has both positive and negative eigenvalues.")
P = [[4, 0], [0, 9]]
p = Problem(Minimize(quad_form(self.x, P)), [self.x >= 1])
result = p.solve()
self.assertAlmostEqual(result, 13, places=3)
c = [1,2]
p = Problem(Minimize(quad_form(c, self.A)), [self.A >= 1])
result = p.solve()
self.assertAlmostEqual(result, 9)
c = [1,2]
P = [[4, 0], [0, 9]]
p = Problem(Minimize(quad_form(c, P)))
result = p.solve()
self.assertAlmostEqual(result, 40)
# Test combining atoms
def test_mixed_atoms(self):
p = Problem(Minimize(norm2(5 + norm1(self.z)
+ norm1(self.x) +
normInf(self.x - self.z) ) ),
[self.x >= [2,3], self.z <= [-1,-4], norm2(self.x + self.z) <= 2])
result = p.solve()
self.assertAlmostEqual(result, 22)
self.assertItemsAlmostEqual(self.x.value, [2,3])
self.assertItemsAlmostEqual(self.z.value, [-1,-4])
# Test multiplying by constant atoms.
def test_mult_constant_atoms(self):
p = Problem(Minimize(norm2([3,4])*self.a), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertAlmostEqual(self.a.value, 2)
# Test recovery of dual variables.
def test_dual_variables(self):
p = Problem(Minimize( norm1(self.x + self.z) ),
[self.x >= [2,3],
[[1,2],[3,4]]*self.z == [-1,-4],
norm2(self.x + self.z) <= 100])
result = p.solve()
self.assertAlmostEqual(result, 4)
self.assertItemsAlmostEqual(self.x.value, [4,3])
self.assertItemsAlmostEqual(self.z.value, [-4,1])
# Dual values
self.assertItemsAlmostEqual(p.constraints[0].dual_value, [0, 1])
self.assertItemsAlmostEqual(p.constraints[1].dual_value, [-1, 0.5])
self.assertAlmostEqual(p.constraints[2].dual_value, 0)
T = matrix(2, (2, 3))
c = matrix([3,4])
p = Problem(Minimize(1),
[self.A >= T*self.C,
self.A == self.B,
self.C == T.T])
result = p.solve()
# Dual values
self.assertItemsAlmostEqual(p.constraints[0].dual_value, 4*[0])
self.assertItemsAlmostEqual(p.constraints[1].dual_value, 4*[0])
self.assertItemsAlmostEqual(p.constraints[2].dual_value, 6*[0])
# Test problems with indexing.
def test_indexing(self):
# Vector variables
p = Problem(Maximize(self.x[0,0]), [self.x[0,0] <= 2, self.x[1,0] == 3])
result = p.solve()
self.assertAlmostEqual(result, 2)
self.assertItemsAlmostEqual(self.x.value, [2,3])
n = 10
A = matrix(range(n*n), (n,n))
x = Variable(n,n)
p = Problem(Minimize(sum_entries(x)), [x == A])
result = p.solve()
answer = n*n*(n*n+1)/2 - n*n
self.assertAlmostEqual(result, answer)
# Matrix variables
p = Problem(Maximize( sum(self.A[i,i] + self.A[i,1-i] for i in range(2)) ),
[self.A <= [[1,-2],[-3,4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
self.assertItemsAlmostEqual(self.A.value, [1,-2,-3,4])
# Indexing arithmetic expressions.
exp = [[1,2],[3,4]]*self.z + self.x
p = Problem(Minimize(exp[1,0]), [self.x == self.z, self.z == [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.x.value, self.z.value)
# Test problems with slicing.
def test_slicing(self):
p = Problem(Maximize(sum_entries(self.C)), [self.C[1:3,:] <= 2, self.C[0,:] == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2*[1,2,2])
p = Problem(Maximize(sum_entries(self.C[0:3:2,1])),
[self.C[1:3,:] <= 2, self.C[0,:] == 1])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.C.value[0:3:2,1], [1,2])
p = Problem(Maximize(sum_entries( (self.C[0:2,:] + self.A)[:,0:2] )),
[self.C[1:3,:] <= 2, self.C[0,:] == 1,
(self.A + self.B)[:,0] == 3, (self.A + self.B)[:,1] == 2,
self.B == 1])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.C.value[0:2,:], [1,2,1,2])
self.assertItemsAlmostEqual(self.A.value, [2,2,1,1])
p = Problem(Maximize( [[3],[4]]*(self.C[0:2,:] + self.A)[:,0] ),
[self.C[1:3,:] <= 2, self.C[0,:] == 1,
[[1],[2]]*(self.A + self.B)[:,0] == 3, (self.A + self.B)[:,1] == 2,
self.B == 1, 3*self.A[:,0] <= 3])
result = p.solve()
self.assertAlmostEqual(result, 12)
self.assertItemsAlmostEqual(self.C.value[0:2,0], [1,2])
self.assertItemsAlmostEqual(self.A.value, [1,-.5,1,1])
p = Problem(Minimize(norm2((self.C[0:2,:] + self.A)[:,0] )),
[self.C[1:3,:] <= 2, self.C[0,:] == 1,
(self.A + self.B)[:,0] == 3, (self.A + self.B)[:,1] == 2,
self.B == 1])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.C.value[0:2,0], [1,-2])
self.assertItemsAlmostEqual(self.A.value, [2,2,1,1])
# Transpose of slice.
p = Problem(Maximize(sum_entries(self.C)), [self.C[1:3,:].T <= 2, self.C[0,:].T == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2*[1,2,2])
# Test the vstack atom.
def test_vstack(self):
c = matrix(1, (1,5))
p = Problem(Minimize(c * vstack(self.x, self.y)),
[self.x == [1,2],
self.y == [3,4,5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1,4))
p = Problem(Minimize(c * vstack(self.x, self.x)),
[self.x == [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2,2))
p = Problem( Minimize( sum_entries(vstack(self.A, self.C)) ),
[self.A >= 2*c,
self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
c = matrix(1, (1,2))
p = Problem( Minimize( sum_entries(vstack(c*self.A, c*self.B)) ),
[self.A >= 2,
self.B == -2])
result = p.solve()
self.assertAlmostEqual(result, 0)
c = matrix([1,-1])
p = Problem( Minimize( c.T * vstack(square(self.a), sqrt(self.b))),
[self.a == 2,
self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception), "Problem does not follow DCP rules.")
# Test the hstack atom.
def test_hstack(self):
c = matrix(1, (1,5))
p = Problem(Minimize(c * hstack(self.x.T, self.y.T).T),
[self.x == [1,2],
self.y == [3,4,5]])
result = p.solve()
self.assertAlmostEqual(result, 15)
c = matrix(1, (1,4))
p = Problem(Minimize(c * hstack(self.x.T, self.x.T).T),
[self.x == [1,2]])
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix(1, (2,2))
p = Problem( Minimize( sum_entries(hstack(self.A.T, self.C.T)) ),
[self.A >= 2*c,
self.C == -2])
result = p.solve()
self.assertAlmostEqual(result, -4)
D = Variable(3, 3)
expr = hstack(self.C, D)
p = Problem( Minimize( expr[0,1] + sum_entries(hstack(expr, expr)) ),
[self.C >= 0,
D >= 0, D[0,0] == 2, self.C[0,1] == 3])
result = p.solve()
self.assertAlmostEqual(result, 13)
c = matrix([1,-1])
p = Problem( Minimize( c.T * hstack(square(self.a).T, sqrt(self.b).T).T),
[self.a == 2,
self.b == 16])
with self.assertRaises(Exception) as cm:
p.solve()
self.assertEqual(str(cm.exception), "Problem does not follow DCP rules.")
def test_bad_objective(self):
"""Test using a cvxpy expression as an objective.
"""
with self.assertRaises(Exception) as cm:
Problem(self.x+2)
self.assertEqual(str(cm.exception), "Problem objective must be Minimize or Maximize.")
# Test variable transpose.
def test_transpose(self):
p = Problem(Minimize(sum_entries(self.x)), [self.x.T >= matrix([1,2]).T])
result = p.solve()
self.assertAlmostEqual(result, 3)
self.assertItemsAlmostEqual(self.x.value, [1,2])
p = Problem(Minimize(sum_entries(self.C)), [matrix([1,1]).T*self.C.T >= matrix([0,1,2]).T])
result = p.solve()
value = self.C.value
constraints = [1*self.C[i,0] + 1*self.C[i,1] >= i for i in range(3)]
p = Problem(Minimize(sum_entries(self.C)), constraints)
result2 = p.solve()
self.assertAlmostEqual(result, result2)
self.assertItemsAlmostEqual(self.C.value, value)
p = Problem(Minimize(self.A[0,1] - self.A.T[1,0]),
[self.A == [[1,2],[3,4]]])
result = p.solve()
self.assertAlmostEqual(result, 0)
exp = (-self.x).T
p = Problem(Minimize(sum_entries(self.x)), [(-self.x).T <= 1])
result = p.solve()
self.assertAlmostEqual(result, -2)
c = matrix([1,-1])
p = Problem(Minimize(max_elemwise(c.T, 2, 2 + c.T)[1]))
result = p.solve()
self.assertAlmostEqual(result, 2)
c = matrix([[1,-1,2],[1,-1,2]])
p = Problem(Minimize(sum_entries(max_elemwise(c, 2, 2 + c).T[:,0])))
result = p.solve()
self.assertAlmostEqual(result, 6)
c = matrix([[1,-1,2],[1,-1,2]])
p = Problem(Minimize(sum_entries(square(c.T).T[:,0])))
result = p.solve()
self.assertAlmostEqual(result, 6)
# Slice of transpose.
p = Problem(Maximize(sum_entries(self.C)), [self.C.T[:,1:3] <= 2, self.C.T[:,0] == 1])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(self.C.value, 2*[1,2,2])
# Test multiplication on the left by a non-constant.
def test_multiplication_on_left(self):
c = matrix([1,2])
p = Problem(Minimize(c.T*self.A*c), [self.A >= 2])
result = p.solve()
self.assertAlmostEqual(result, 18)
p = Problem(Minimize(self.a*2), [self.a >= 2])
result = p.solve()
self.assertAlmostEqual(result, 4)
p = Problem(Minimize(self.x.T*c), [self.x >= 2])
result = p.solve()
self.assertAlmostEqual(result, 6)
p = Problem(Minimize((self.x.T + self.z.T)*c),
[self.x >= 2, self.z >= 1])
result = p.solve()
self.assertAlmostEqual(result, 9)
# Test redundant constraints in cvxopt.
def test_redundant_constraints(self):
obj = Minimize(sum_entries(self.x))
constraints = [self.x == 2, self.x == 2, self.x.T == 2, self.x[0] == 2]
p = Problem(obj, constraints)
result = p.solve(solver=s.CVXOPT)
self.assertAlmostEqual(result, 4)
obj = Minimize(sum_entries(square(self.x)))
constraints = [self.x == self.x]
p = Problem(obj, constraints)
result = p.solve(solver=s.CVXOPT)
self.assertAlmostEqual(result, 0)
# Test that symmetry is enforced.
def test_sdp_symmetry(self):
# TODO should these raise exceptions?
# with self.assertRaises(Exception) as cm:
# lambda_max([[1,2],[3,4]])
# self.assertEqual(str(cm.exception), "lambda_max called on non-symmetric matrix.")
# with self.assertRaises(Exception) as cm:
# lambda_min([[1,2],[3,4]])
# self.assertEqual(str(cm.exception), "lambda_min called on non-symmetric matrix.")
p = Problem(Minimize(lambda_max(self.A)), [self.A >= 2])
result = p.solve()
self.assertItemsAlmostEqual(self.A.value, self.A.value.T)
p = Problem(Minimize(lambda_max(self.A)), [self.A == [[1,2],[3,4]]])
result = p.solve()
self.assertEqual(p.status, s.INFEASIBLE)
# Test SDP
def test_sdp(self):
# Ensure sdp constraints enforce transpose.
obj = Maximize(self.A[1,0] - self.A[0,1])
p = Problem(obj, [lambda_max(self.A) <= 100,
self.A[0,0] == 2,
self.A[1,1] == 2,
self.A[1,0] == 2])
result = p.solve()
self.assertAlmostEqual(result, 0)
# Test getting values for expressions.
def test_expression_values(self):
diff_exp = self.x - self.z
inf_exp = normInf(diff_exp)
sum_entries_exp = 5 + norm1(self.z) + norm1(self.x) + inf_exp
constr_exp = norm2(self.x + self.z)
obj = norm2(sum_entries_exp)
p = Problem(Minimize(obj),
[self.x >= [2,3], self.z <= [-1,-4], constr_exp <= 2])
result = p.solve()
self.assertAlmostEqual(result, 22)
self.assertItemsAlmostEqual(self.x.value, [2,3])
self.assertItemsAlmostEqual(self.z.value, [-1,-4])
# Expression values.
self.assertItemsAlmostEqual(diff_exp.value, self.x.value - self.z.value)
self.assertAlmostEqual(inf_exp.value,
LA.norm(self.x.value - self.z.value, numpy.inf))
self.assertAlmostEqual(sum_entries_exp.value,
5 + LA.norm(self.z.value, 1) + LA.norm(self.x.value, 1) + \
LA.norm(self.x.value - self.z.value, numpy.inf))
self.assertAlmostEqual(constr_exp.value,
LA.norm(self.x.value + self.z.value, 2))
self.assertAlmostEqual(obj.value, result)
def test_mult_by_zero(self):
"""Test multiplication by zero.
"""
exp = 0*self.a
self.assertEqual(exp.value, 0)
obj = Minimize(exp)
p = Problem(obj)
result = p.solve()
self.assertAlmostEqual(result, 0)
assert self.a.value is not None
def test_div(self):
"""Tests a problem with division.
"""
obj = Minimize(normInf(self.A/5))
p = Problem(obj, [self.A >= 5])
result = p.solve()
self.assertAlmostEqual(result, 1)
def test_mul_elemwise(self):
"""Tests problems with mul_elemwise.
"""
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.A)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.A == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
# Test with a sparse matrix.
import cvxopt
interface = intf.get_matrix_interface(cvxopt.spmatrix)
c = interface.const_to_matrix([1,2])
expr = mul_elemwise(c, self.x)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.x == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, 10])
# Test promotion.
c = [[1, -1], [2, -2]]
expr = mul_elemwise(c, self.a)
obj = Minimize(normInf(expr))
p = Problem(obj, [self.a == 5])
result = p.solve()
self.assertAlmostEqual(result, 10)
self.assertItemsAlmostEqual(expr.value, [5, -5] + [10, -10])
def test_invalid_solvers(self):
"""Tests that errors occur when you use an invalid solver.
"""
with self.assertRaises(Exception) as cm:
Problem(Minimize(-log(self.a))).solve(solver=s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(lambda_max(self.a))).solve(solver=s.ECOS)
self.assertEqual(str(cm.exception),
"The solver ECOS cannot solve the problem.")
with self.assertRaises(Exception) as cm:
Problem(Minimize(self.a)).solve(solver=s.SCS)
self.assertEqual(str(cm.exception),
"The solver SCS cannot solve the problem.")
def test_reshape(self):
"""Tests problems with reshape.
"""
# Test on scalars.
self.assertEqual(reshape(1, 1, 1).value, 1)
# Test vector to matrix.
x = Variable(4)
mat = matrix([[1,-1], [2, -2]])
vec = matrix([1, 2, 3, 4])
vec_mat = matrix([[1, 2], [3, 4]])
expr = reshape(x, 2, 2)
obj = Minimize(sum_entries(mat*expr))
prob = Problem(obj, [x == vec])
result = prob.solve()
self.assertAlmostEqual(result, sum(mat*vec_mat))
# Test on matrix to vector.
c = [1, 2, 3, 4]
expr = reshape(self.A, 4, 1)
obj = Minimize(expr.T*c)
constraints = [self.A == [[-1, -2], [3, 4]]]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 20)
self.assertItemsAlmostEqual(expr.value, [-1, -2, 3, 4])
self.assertItemsAlmostEqual(reshape(expr, 2, 2).value, [-1, -2, 3, 4])
# Test matrix to matrix.
expr = reshape(self.C, 2, 3)
mat = numpy.matrix([[1,-1], [2, -2]])
C_mat = numpy.matrix([[1, 4], [2, 5], [3, 6]])
obj = Minimize(sum_entries(mat*expr))
prob = Problem(obj, [self.C == C_mat])
result = prob.solve()
reshaped = numpy.reshape(C_mat, (2, 3), 'F')
self.assertAlmostEqual(result, (mat.dot(reshaped)).sum())
self.assertItemsAlmostEqual(expr.value, C_mat)
# Test promoted expressions.
c = matrix([[1,-1], [2, -2]])
expr = reshape(c*self.a, 1, 4)
obj = Minimize(expr*[1, 2, 3, 4])
prob = Problem(obj, [self.a == 2])
result = prob.solve()
self.assertAlmostEqual(result, -6)
self.assertItemsAlmostEqual(expr.value, 2*c)
expr = reshape(c*self.a, 4, 1)
obj = Minimize(expr.T*[1, 2, 3, 4])
prob = Problem(obj, [self.a == 2])
result = prob.solve()
self.assertAlmostEqual(result, -6)
self.assertItemsAlmostEqual(expr.value, 2*c)
def test_vec(self):
"""Tests problems with vec.
"""
c = [1, 2, 3, 4]
expr = vec(self.A)
obj = Minimize(expr.T*c)
constraints = [self.A == [[-1, -2], [3, 4]]]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 20)
self.assertItemsAlmostEqual(expr.value, [-1, -2, 3, 4])
def test_diag_prob(self):
"""Test a problem with diag.
"""
C = Variable(3, 3)
obj = Maximize(C[0, 2])
constraints = [diag(C) == 1,
C[0, 1] == 0.6,
C[1, 2] == -0.3,
C == Semidef(3)]
prob = Problem(obj, constraints)
result = prob.solve()
self.assertAlmostEqual(result, 0.583151)
def test_presolve_constant_constraints(self):
"""Test that the presolver removes constraints with no variables.
"""
x = Variable()
obj = Maximize(sqrt(x))
prob = Problem(obj)
data = prob.get_problem_data(s.ECOS)
A = data["A"]
G = data["G"]
for row in range(A.shape[0]):
assert A[row, :].nnz > 0
for row in range(G.shape[0]):
assert G[row, :].nnz > 0
def test_presolve_parameters(self):
"""Test presolve with parameters.
"""
# Test with parameters.
gamma = Parameter(sign="positive")
x = Variable()
obj = Minimize(x)
prob = Problem(obj, [gamma == 1, x >= 0])
gamma.value = 0
prob.solve(solver=s.SCS)
self.assertEqual(prob.status, s.INFEASIBLE)
gamma.value = 1
prob.solve(solver=s.CVXOPT)
self.assertEqual(prob.status, s.OPTIMAL)
def test_parameter_expressions(self):
"""Test that expressions with parameters are updated properly.
"""
x = Variable()
y = Variable()
x0 = Parameter()
xSquared = x0*x0 + 2*x0*(x - x0)
# initial guess for x
x0.value = 2
# make the constraint x**2 - y == 0
g = xSquared - y
# set up the problem
obj = abs(x - 1)
prob = Problem( Minimize( obj ), [ g == 0 ] )
prob.solve()
x0.value = 1
prob.solve()
self.assertAlmostEqual(g.value, 0)
# Test multiplication.
prob = Problem( Minimize( x0*x ), [ x == 1 ] )
x0.value = 2
prob.solve()
x0.value = 1
prob.solve()
self.assertAlmostEqual(prob.value, 1)
def test_geo_mean(self):
import numpy as np
x = Variable(2)
cost = geo_mean(x)
prob = Problem(Maximize(cost), [x <= 1])
prob.solve()
self.assertAlmostEqual(prob.value, 1)
prob = Problem(Maximize(cost), [sum(x) <= 1])
prob.solve()
self.assertItemsAlmostEqual(x.value, [.5, .5])
x = Variable(3, 3)
self.assertRaises(ValueError, geo_mean, x)
x = Variable(3, 1)
g = geo_mean(x)
self.assertSequenceEqual(g.w, [Fraction(1, 3)]*3)
x = Variable(1, 5)
g = geo_mean(x)
self.assertSequenceEqual(g.w, [Fraction(1, 5)]*5)
# check that we get the right answer for
# max geo_mean(x) s.t. sum(x) <= 1
p = np.array([.07, .12, .23, .19, .39])
def short_geo_mean(x, p):
p = np.array(p)/sum(p)
x = np.array(x)
return np.prod(x**p)
x = Variable(5)
prob = Problem(Maximize(geo_mean(x, p)), [sum(x) <= 1])
prob.solve()
x = np.array(x.value).flatten()
x_true = p/sum(p)
self.assertTrue(np.allclose(prob.value, geo_mean(list(x), p).value))
self.assertTrue(np.allclose(prob.value, short_geo_mean(x, p)))
self.assertTrue(np.allclose(x, x_true, 1e-3))
# check that we get the right answer for
# max geo_mean(x) s.t. norm(x) <= 1
x = Variable(5)
prob = Problem(Maximize(geo_mean(x, p)), [norm(x) <= 1])
prob.solve()
x = np.array(x.value).flatten()
x_true = np.sqrt(p/sum(p))
self.assertTrue(np.allclose(prob.value, geo_mean(list(x), p).value))
self.assertTrue(np.allclose(prob.value, short_geo_mean(x, p)))
self.assertTrue(np.allclose(x, x_true, 1e-3))
def test_pnorm(self):
import numpy as np
x = Variable(3, name='x')
a = np.array([1.0, 2, 3])
# todo: add -1, .5, .3, -2.3 and testing positivity constraints
for p in (1, 1.6, 1.3, 2, 1.99, 3, 3.7, np.inf):
prob = Problem(Minimize(pnorm(x, p=p)), [x.T*a >= 1])
prob.solve()
# formula is true for any a >= 0 with p > 1
if p == np.inf:
x_true = np.ones_like(a)/sum(a)
elif p == 1:
# only works for the particular a = [1,2,3]
x_true = np.array([0, 0, 1.0/3])
else:
x_true = a**(1.0/(p-1))/a.dot(a**(1.0/(p-1)))
x_alg = np.array(x.value).flatten()
self.assertTrue(np.allclose(x_alg, x_true, 1e-3), 'p = {}'.format(p))
self.assertTrue(np.allclose(prob.value, np.linalg.norm(x_alg, p)))
self.assertTrue(np.allclose(np.linalg.norm(x_alg, p), pnorm(x_alg, p).value))
def test_pnorm_concave(self):
import numpy as np
x = Variable(3, name='x')
# test positivity constraints
a = np.array([-1.0, 2, 3])
for p in (-1, .5, .3, -2.3):
prob = Problem(Minimize(sum_entries(abs(x-a))), [pnorm(x, p) >= 0])
prob.solve()
self.assertTrue(np.allclose(prob.value, 1))
a = np.array([1.0, 2, 3])
for p in (-1, .5, .3, -2.3):
prob = Problem(Minimize(sum_entries(abs(x-a))), [pnorm(x, p) >= 0])
prob.solve()
self.assertTrue(np.allclose(prob.value, 0))
def test_power(self):
x = Variable()
prob = Problem(Minimize(power(x, 1.7) + power(x, -2.3) - power(x, .45)))
prob.solve()
x = x.value
self.assertTrue(__builtins__['abs'](1.7*x**.7 - 2.3*x**-3.3 - .45*x**-.55) <= 1e-3)
