def test_div_expression(self):
# Vectors
exp = self.x/2
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(exp.canonical_form[0].size, (2,1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.size, (2,1))
with self.assertRaises(Exception) as cm:
(self.x/[2,2,3])
print cm.exception
self.assertEqual(str(cm.exception), "Can only divide by a scalar constant.")
# Constant expressions.
c = Constant(2)
exp = c/(3 - 5)
self.assertEqual(exp.curvature, u.Curvature.CONSTANT_KEY)
self.assertEqual(exp.size, (1,1))
self.assertEqual(exp.sign, u.Sign.NEGATIVE_KEY)
# Parameters.
p = Parameter(sign="positive")
exp = 2/p
p.value = 2
self.assertEquals(exp.value, 1)
def test_parameters(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.size, (1,1))
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = 1
self.assertEqual(str(cm.exception), "Invalid dimensions (1,1) for Parameter value.")
val = -np.ones((4,3))
val[0,0] = 2
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
p = Parameter(4, 3, sign="negative")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
# No error for unknown sign.
p = Parameter(4, 3)
p.value = val
def test_huber(self):
# Valid.
huber(self.x, 1)
with self.assertRaises(Exception) as cm:
huber(self.x, -1)
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
with self.assertRaises(Exception) as cm:
huber(self.x, [1,1])
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
# M parameter.
M = Parameter(sign="positive")
# Valid.
huber(self.x, M)
M.value = 1
self.assertAlmostEquals(huber(2, M).value, 3)
# Invalid.
M = Parameter(sign="negative")
with self.assertRaises(Exception) as cm:
huber(self.x, M)
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
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_1D_array(self):
"""Test NumPy 1D arrays as constants.
"""
c = np.array([1, 2])
p = Parameter(2)
p.value = [1, 1]
self.assertEqual((c @ p).value, 3)
self.assertEqual((c @ self.x).shape, tuple())
def test_param_copy(self):
"""Test the copy function for Parameters.
"""
x = Parameter((3, 4), name="x", nonneg=True)
y = x.copy()
self.assertEqual(y.shape, (3, 4))
self.assertEqual(y.name(), "x")
self.assertEqual(y.sign, "NONNEGATIVE")
def test_1D_array(self):
"""Test NumPy 1D arrays as constants.
"""
c = np.array([1, 2])
p = Parameter(2)
p.value = [1, 1]
self.assertEqual((c*p).value, 3)
self.assertEqual((c*self.x).size, (1, 1))
def test_param_copy(self):
"""Test the copy function for Parameters.
"""
x = Parameter(3, 4, name="x", sign="positive")
y = x.copy()
self.assertEqual(y.size, (3, 4))
self.assertEqual(y.name(), "x")
self.assertEqual(y.sign, "POSITIVE")
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_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_kron(self):
"""Test the kron atom.
"""
a = np.ones((3,2))
b = Parameter(2, sign='positive')
expr = kron(a, b)
assert expr.is_positive()
self.assertEqual(expr.size, (6, 2))
b = Parameter(2, sign='negative')
expr = kron(a, b)
assert expr.is_negative()
with self.assertRaises(Exception) as cm:
kron(self.x, -1)
self.assertEqual(str(cm.exception),
"The first argument to kron must be constant.")
def test_kron(self):
"""Test the kron atom.
"""
a = np.ones((3, 2))
b = Parameter((2, 1), nonneg=True)
expr = cp.kron(a, b)
assert expr.is_nonneg()
self.assertEqual(expr.shape, (6, 2))
b = Parameter((2, 1), nonpos=True)
expr = cp.kron(a, b)
assert expr.is_nonpos()
with self.assertRaises(Exception) as cm:
cp.kron(self.x, -1)
self.assertEqual(str(cm.exception),
"The first argument to kron must be constant.")
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_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)
def test_quad_form(self):
"""Test quad_form atom.
"""
P = Parameter(2,2)
with self.assertRaises(Exception) as cm:
quad_form(self.x, P)
self.assertEqual(str(cm.exception), "P cannot be a parameter.")
def test_atom():
for atom_list, objective_type in atoms:
for atom, size, args, obj_val in atom_list:
for row in range(size[0]):
for col in range(size[1]):
for solver in SOLVERS_TO_TRY:
# Atoms with Constant arguments.
const_args = [Constant(arg) for arg in args]
yield (run_atom, atom,
Problem(
objective_type(atom(*const_args)[row,
col])),
obj_val[row, col].value, solver)
# Atoms with Variable arguments.
variables = []
constraints = []
for idx, expr in enumerate(args):
variables.append(Variable(*intf.size(expr)))
constraints.append(variables[-1] == expr)
objective = objective_type(atom(*variables)[row, col])
yield (run_atom, atom, Problem(objective, constraints),
obj_val[row, col].value, solver)
# Atoms with Parameter arguments.
parameters = []
for expr in args:
parameters.append(Parameter(*intf.size(expr)))
parameters[
-1].value = intf.DEFAULT_INTF.const_to_matrix(
expr)
objective = objective_type(atom(*parameters)[row, col])
yield (run_atom, atom, Problem(objective),
obj_val[row, col].value, solver)
def test_constant_atoms(atom_info, objective_type) -> None:
atom, size, args, obj_val = atom_info
for indexer in get_indices(size):
for solver in SOLVERS_TO_TRY:
# Atoms with Constant arguments.
prob_val = obj_val[indexer].value
const_args = [Constant(arg) for arg in args]
problem = Problem(objective_type(atom(*const_args)[indexer]))
run_atom(atom, problem, prob_val, solver)
# Atoms with Variable arguments.
variables = []
constraints = []
for idx, expr in enumerate(args):
variables.append(Variable(intf.shape(expr)))
constraints.append(variables[-1] == expr)
objective = objective_type(atom(*variables)[indexer])
new_obj_val = prob_val
if objective_type == cp.Maximize:
objective = -objective
new_obj_val = -new_obj_val
problem = Problem(objective, constraints)
run_atom(atom, problem, new_obj_val, solver)
# Atoms with Parameter arguments.
parameters = []
for expr in args:
parameters.append(Parameter(intf.shape(expr)))
parameters[-1].value = intf.DEFAULT_INTF.const_to_matrix(expr)
objective = objective_type(atom(*parameters)[indexer])
run_atom(atom, Problem(objective), prob_val, solver)
def test_atom():
for atom_list, objective_type in atoms:
for atom, obj_val in atom_list:
for row in xrange(atom.size[0]):
for col in xrange(atom.size[1]):
# Atoms with Constant arguments.
yield run_atom, Problem(objective_type(
atom[row, col])), obj_val[row, col].value
# Atoms with Variable arguments.
variables = []
constraints = []
for expr in atom.subexpressions:
variables.append(Variable(*expr.size))
constraints.append(variables[-1] == expr)
atom_func = atom.__class__
objective = objective_type(atom_func(*variables)[row, col])
yield run_atom, Problem(objective,
constraints), obj_val[row,
col].value
# Atoms with Parameter arguments.
parameters = []
for expr in atom.subexpressions:
parameters.append(Parameter(*expr.size))
parameters[-1].value = expr.value
objective = objective_type(
atom_func(*parameters)[row, col])
yield run_atom, Problem(objective), obj_val[row, col].value
def test_partial_optimize_params(self):
"""Test partial optimize with parameters.
"""
x, y = Variable(1), Variable(1)
gamma = Parameter()
# Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
p1 = Problem(Minimize(x+y), [x+y>=gamma, y>=4, x>=5])
gamma.value = 3
p1.solve()
# Solve the two-stage problem via partial_optimize
p2 = Problem(Minimize(y), [x+y>=gamma, y>=4])
g = partial_optimize(p2, [y], [x])
p3 = Problem(Minimize(x+g), [x>=5])
p3.solve()
self.assertAlmostEqual(p1.value, p3.value)
def test_atom():
for atom_list, objective_type in atoms:
for atom, obj_val in atom_list:
for row in xrange(atom.size[0]):
for col in xrange(atom.size[1]):
for solver in [ECOS, SCS, CVXOPT]:
# Atoms with Constant arguments.
yield (run_atom, atom,
Problem(objective_type(atom[row, col])),
obj_val[row, col].value, solver)
# Atoms with Variable arguments.
variables = []
constraints = []
for idx, expr in enumerate(atom.subexpressions):
# Special case for MulExpr because
# can't multiply two variables.
if (idx == 0 and isinstance(atom, MulExpression)):
variables.append(expr)
else:
variables.append(Variable(*expr.size))
constraints.append(variables[-1] == expr)
atom_func = atom.__class__
objective = objective_type(
atom_func(*variables)[row, col])
yield (run_atom, atom, Problem(objective, constraints),
obj_val[row, col].value, solver)
# Atoms with Parameter arguments.
parameters = []
for expr in atom.subexpressions:
parameters.append(Parameter(*expr.size))
parameters[-1].value = expr.value
objective = objective_type(
atom_func(*parameters)[row, col])
yield (run_atom, atom, Problem(objective),
obj_val[row, col].value, solver)
def prox_step(prob, rho_init, scaled=False, spectral=False):
"""Formulates the proximal operator for a given objective, constraints, and step size.
Parikh, Boyd. "Proximal Algorithms."
Parameters
----------
prob : Problem
The objective and constraints associated with the proximal operator.
The sign of the objective function is flipped if `prob` is a maximization problem.
rho_init : float
The initial step size.
scaled : logical, optional
Should the dual variable be scaled?
spectral : logical, optional
Will spectral step sizes be used?
Returns
----------
prox : Problem
The proximal step problem.
vmap : dict
A map of each proximal variable id to a dictionary containing that variable `x`,
the mean variable parameter `xbar`, the associated dual parameter `y`, and the
step size parameter `rho`. If `spectral = True`, the estimated dual parameter
`yhat` is also included.
"""
vmap = {} # Store consensus variables
f = flip_obj(prob).args[0]
# Add penalty for each variable.
for xvar in prob.variables():
xid = xvar.id
shape = xvar.shape
vmap[xid] = {
"x": xvar,
"xbar": Parameter(shape, value=np.zeros(shape)),
"y": Parameter(shape, value=np.zeros(shape)),
"rho": Parameter(value=rho_init[xid], nonneg=True)
}
if spectral:
vmap[xid]["yhat"] = Parameter(shape, value=np.zeros(shape))
dual = vmap[xid]["y"] if scaled else vmap[xid]["y"] / vmap[xid]["rho"]
f += (vmap[xid]["rho"] / 2.0) * sum_squares(xvar - vmap[xid]["xbar"] +
dual)
prox = Problem(Minimize(f), prob.constraints)
return prox, vmap
def test_param(self):
"""Test creating a parameter.
"""
A = Parameter(5, 4)
var = create_param(A, (5, 4))
self.assertEqual(var.size, (5, 4))
self.assertEqual(len(var.args), 0)
self.assertEqual(var.type, PARAM)
def test_1D_array(self):
"""Test NumPy 1D arrays as constants.
"""
c = np.array([1,2])
p = Parameter(2)
with warnings.catch_warnings(record=True) as w:
# Cause all warnings to always be triggered.
warnings.simplefilter("always")
# Trigger a warning.
Constant(c)
self.x + c
p.value = c
# Verify some things
self.assertEqual(len(w), 3)
for warning in w:
self.assertEqual(str(warning.message), "NumPy 1D arrays are treated as column vectors.")
def test_conv(self):
"""Test the conv atom.
"""
a = np.ones((3,1))
b = Parameter(2, sign='positive')
expr = conv(a, b)
assert expr.is_positive()
self.assertEqual(expr.size, (4, 1))
b = Parameter(2, sign='negative')
expr = conv(a, b)
assert expr.is_negative()
with self.assertRaises(Exception) as cm:
conv(self.x, -1)
self.assertEqual(str(cm.exception),
"The first argument to conv must be constant.")
with self.assertRaises(Exception) as cm:
conv([[0,1],[0,1]], self.x)
self.assertEqual(str(cm.exception),
"The arguments to conv must resolve to vectors." )
def test_conv(self):
"""Test the conv atom.
"""
a = np.ones((3, 1))
b = Parameter(2, nonneg=True)
expr = cp.conv(a, b)
assert expr.is_nonneg()
self.assertEqual(expr.shape, (4, 1))
b = Parameter(2, nonpos=True)
expr = cp.conv(a, b)
assert expr.is_nonpos()
with self.assertRaises(Exception) as cm:
cp.conv(self.x, -1)
self.assertEqual(str(cm.exception),
"The first argument to conv must be constant.")
with self.assertRaises(Exception) as cm:
cp.conv([[0, 1], [0, 1]], self.x)
self.assertEqual(str(cm.exception),
"The arguments to conv must resolve to vectors.")
def test_huber(self):
# Valid.
huber(self.x, 1)
with self.assertRaises(Exception) as cm:
huber(self.x, -1)
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
with self.assertRaises(Exception) as cm:
huber(self.x, [1,1])
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
# M parameter.
M = Parameter(sign="positive")
# Valid.
huber(self.x, M)
M.value = 1
self.assertAlmostEquals(huber(2, M).value, 3)
# Invalid.
M = Parameter(sign="negative")
with self.assertRaises(Exception) as cm:
huber(self.x, M)
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
# Test copy with args=None
atom = huber(self.x, 2)
copy = atom.copy()
self.assertTrue(type(copy) is type(atom))
# A new object is constructed, so copy.args == atom.args but copy.args
# is not atom.args.
self.assertEqual(copy.args, atom.args)
self.assertFalse(copy.args is atom.args)
# As get_data() returns a Constant, we have to check the value
self.assertEqual(copy.get_data().value, atom.get_data().value)
# Test copy with new args
copy = atom.copy(args=[self.y])
self.assertTrue(type(copy) is type(atom))
self.assertTrue(copy.args[0] is self.y)
self.assertEqual(copy.get_data().value, atom.get_data().value)
def test_huber(self):
# Valid.
cp.huber(self.x, 1)
with self.assertRaises(Exception) as cm:
cp.huber(self.x, -1)
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
with self.assertRaises(Exception) as cm:
cp.huber(self.x, [1, 1])
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
# M parameter.
M = Parameter(nonneg=True)
# Valid.
cp.huber(self.x, M)
M.value = 1
self.assertAlmostEqual(cp.huber(2, M).value, 3)
# Invalid.
M = Parameter(nonpos=True)
with self.assertRaises(Exception) as cm:
cp.huber(self.x, M)
self.assertEqual(str(cm.exception),
"M must be a non-negative scalar constant.")
# Test copy with args=None
atom = cp.huber(self.x, 2)
copy = atom.copy()
self.assertTrue(type(copy) is type(atom))
# A new object is constructed, so copy.args == atom.args but copy.args
# is not atom.args.
self.assertEqual(copy.args, atom.args)
self.assertFalse(copy.args is atom.args)
# As get_data() returns a Constant, we have to check the value
self.assertEqual(copy.get_data()[0].value, atom.get_data()[0].value)
# Test copy with new args
copy = atom.copy(args=[self.y])
self.assertTrue(type(copy) is type(atom))
self.assertTrue(copy.args[0] is self.y)
self.assertEqual(copy.get_data()[0].value, atom.get_data()[0].value)
def test_multiply(self):
"""Test the multiply atom.
"""
self.assertEqual(cp.multiply([1, -1], self.x).sign, s.UNKNOWN)
self.assertEqual(cp.multiply([1, -1], self.x).curvature, s.AFFINE)
self.assertEqual(cp.multiply([1, -1], self.x).shape, (2,))
pos_param = Parameter(2, nonneg=True)
neg_param = Parameter(2, nonpos=True)
self.assertEqual(cp.multiply(pos_param, pos_param).sign, s.NONNEG)
self.assertEqual(cp.multiply(pos_param, neg_param).sign, s.NONPOS)
self.assertEqual(cp.multiply(neg_param, neg_param).sign, s.NONNEG)
self.assertEqual(cp.multiply(neg_param, cp.square(self.x)).curvature, s.CONCAVE)
# Test promotion.
self.assertEqual(cp.multiply([1, -1], 1).shape, (2,))
self.assertEqual(cp.multiply(1, self.C).shape, self.C.shape)
self.assertEqual(cp.multiply(self.x, [1, -1]).sign, s.UNKNOWN)
self.assertEqual(cp.multiply(self.x, [1, -1]).curvature, s.AFFINE)
self.assertEqual(cp.multiply(self.x, [1, -1]).shape, (2,))
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_mul_elemwise(self):
"""Test the mul_elemwise atom.
"""
self.assertEquals(mul_elemwise([1, -1], self.x).sign, u.Sign.UNKNOWN_KEY)
self.assertEquals(mul_elemwise([1, -1], self.x).curvature, u.Curvature.AFFINE_KEY)
self.assertEquals(mul_elemwise([1, -1], self.x).size, (2, 1))
pos_param = Parameter(2, sign="positive")
neg_param = Parameter(2, sign="negative")
self.assertEquals(mul_elemwise(pos_param, pos_param).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(mul_elemwise(pos_param, neg_param).sign, u.Sign.NEGATIVE_KEY)
self.assertEquals(mul_elemwise(neg_param, neg_param).sign, u.Sign.POSITIVE_KEY)
self.assertEquals(mul_elemwise(neg_param, square(self.x)).curvature, u.Curvature.CONCAVE_KEY)
# Test promotion.
self.assertEquals(mul_elemwise([1, -1], 1).size, (2, 1))
self.assertEquals(mul_elemwise(1, self.C).size, self.C.size)
with self.assertRaises(Exception) as cm:
mul_elemwise(self.x, [1, -1])
self.assertEqual(str(cm.exception),
"The first argument to mul_elemwise must be constant.")
def test_div_expression(self):
# Vectors
exp = self.x/2
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
self.assertEqual(exp.canonical_form[0].size, (2, 1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.size, (2, 1))
with self.assertRaises(Exception) as cm:
(self.x/[2, 2, 3])
print(cm.exception)
self.assertEqual(str(cm.exception), "Can only divide by a scalar constant.")
# Constant expressions.
c = Constant(2)
exp = c/(3 - 5)
self.assertEqual(exp.curvature, s.CONSTANT)
self.assertEqual(exp.size, (1, 1))
self.assertEqual(exp.sign, s.NEGATIVE)
# Parameters.
p = Parameter(sign="positive")
exp = 2/p
p.value = 2
self.assertEqual(exp.value, 1)
rho = Parameter(sign="positive")
rho.value = 1
self.assertEqual(rho.sign, s.POSITIVE)
self.assertEqual(Constant(2).sign, s.POSITIVE)
self.assertEqual((Constant(2)/Constant(2)).sign, s.POSITIVE)
self.assertEqual((Constant(2)*rho).sign, s.POSITIVE)
self.assertEqual((rho/2).sign, s.POSITIVE)
def test_div_expression(self):
# Vectors
exp = self.x/2
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.shape, (2,))
with self.assertRaises(Exception) as cm:
(self.x/[2, 2, 3])
print(cm.exception)
self.assertRegexpMatches(str(cm.exception),
"Incompatible shapes for division.*")
c = Constant([3.0, 4.0, 12.0])
self.assertItemsAlmostEqual(
(c / Constant([1.0, 2.0, 3.0])).value, np.array([3.0, 2.0, 4.0]))
# Constant expressions.
c = Constant(2)
exp = c/(3 - 5)
self.assertEqual(exp.curvature, s.CONSTANT)
self.assertEqual(exp.shape, tuple())
self.assertEqual(exp.sign, s.NONPOS)
# Parameters.
p = Parameter(nonneg=True)
exp = 2/p
p.value = 2
self.assertEqual(exp.value, 1)
rho = Parameter(nonneg=True)
rho.value = 1
self.assertEqual(rho.sign, s.NONNEG)
self.assertEqual(Constant(2).sign, s.NONNEG)
self.assertEqual((Constant(2)/Constant(2)).sign, s.NONNEG)
self.assertEqual((Constant(2)*rho).sign, s.NONNEG)
self.assertEqual((rho/2).sign, s.NONNEG)
# Broadcasting.
x = cp.Variable((3, 3))
c = np.arange(1, 4)[:, None]
expr = x / c
self.assertEqual((3, 3), expr.shape)
x.value = np.ones((3, 3))
A = np.ones((3, 3)) / c
self.assertItemsAlmostEqual(A, expr.value)
with self.assertRaises(Exception) as cm:
(x/c[:, 0])
print(cm.exception)
self.assertRegexpMatches(str(cm.exception),
"Incompatible shapes for division.*")
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)
def test_div_expression(self):
# Vectors
exp = self.x / 2
self.assertEqual(exp.curvature, u.Curvature.AFFINE_KEY)
self.assertEqual(exp.sign, u.Sign.UNKNOWN_KEY)
self.assertEqual(exp.canonical_form[0].size, (2, 1))
self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.size, (2, 1))
with self.assertRaises(Exception) as cm:
(self.x / [2, 2, 3])
print(cm.exception)
self.assertEqual(str(cm.exception),
"Can only divide by a scalar constant.")
# Constant expressions.
c = Constant(2)
exp = c / (3 - 5)
self.assertEqual(exp.curvature, u.Curvature.CONSTANT_KEY)
self.assertEqual(exp.size, (1, 1))
self.assertEqual(exp.sign, u.Sign.NEGATIVE_KEY)
# Parameters.
p = Parameter(sign="positive")
exp = 2 / p
p.value = 2
self.assertEquals(exp.value, 1)
rho = Parameter(sign="positive")
rho.value = 1
self.assertEquals(rho.sign, u.Sign.POSITIVE_KEY)
self.assertEquals(Constant(2).sign, u.Sign.POSITIVE_KEY)
self.assertEquals((Constant(2) / Constant(2)).sign,
u.Sign.POSITIVE_KEY)
self.assertEquals((Constant(2) * rho).sign, u.Sign.POSITIVE_KEY)
self.assertEquals((rho / 2).sign, u.Sign.POSITIVE_KEY)
def test_div_expression(self):
# Vectors
exp = self.x / 2
self.assertEqual(exp.curvature, s.AFFINE)
self.assertEqual(exp.sign, s.UNKNOWN)
# self.assertEqual(exp.canonical_form[0].shape, (2, 1))
# self.assertEqual(exp.canonical_form[1], [])
# self.assertEqual(exp.name(), c.name() + " * " + self.x.name())
self.assertEqual(exp.shape, (2, ))
with self.assertRaises(Exception) as cm:
(self.x / [2, 2, 3])
print(cm.exception)
self.assertEqual(str(cm.exception),
"Can only divide by a scalar constant.")
# Constant expressions.
c = Constant(2)
exp = c / (3 - 5)
self.assertEqual(exp.curvature, s.CONSTANT)
self.assertEqual(exp.shape, tuple())
self.assertEqual(exp.sign, s.NONPOS)
# Parameters.
p = Parameter(nonneg=True)
exp = 2 / p
p.value = 2
self.assertEqual(exp.value, 1)
rho = Parameter(nonneg=True)
rho.value = 1
self.assertEqual(rho.sign, s.NONNEG)
self.assertEqual(Constant(2).sign, s.NONNEG)
self.assertEqual((Constant(2) / Constant(2)).sign, s.NONNEG)
self.assertEqual((Constant(2) * rho).sign, s.NONNEG)
self.assertEqual((rho / 2).sign, s.NONNEG)
def test_get_coefficients(self):
"""Test the get_coefficients function.
"""
size = (5, 4)
# Eye
x = create_var(size)
coeffs = get_coefficients(x)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(id_, x.data)
self.assertItemsAlmostEqual(mat.todense(), sp.eye(20).todense())
# Eye with scalar mult.
x = create_var(size)
A = create_const(5, (1, 1))
coeffs = get_coefficients(mul_expr(A, x, size))
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertItemsAlmostEqual(mat.todense(), 5*sp.eye(20).todense())
# Promoted
x = create_var((1, 1))
coeffs = get_coefficients(promote(x, size))
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (20, 1))
self.assertItemsAlmostEqual(mat, np.ones((20, 1)))
# Normal
size = (5, 5)
x = create_var((5, 1))
A = create_const(np.ones(size), size)
coeffs = get_coefficients(mul_expr(A, x, (5, 1)))
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (5, 5))
self.assertItemsAlmostEqual(mat.todense(), A.data)
# Blocks
size = (5, 5)
x = create_var(size)
A = create_const(np.ones(size), size)
coeffs = get_coefficients(mul_expr(A, x, size))
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (25, 25))
self.assertItemsAlmostEqual(mat.todense(),
sp.block_diag(5*[np.ones(size)]).todense())
# Scalar constant
size = (1, 1)
A = create_const(5, size)
coeffs = get_coefficients(A)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(intf.size(mat), (1, 1))
self.assertEqual(mat, 5)
# Dense constant
size = (5, 4)
A = create_const(np.ones(size), size)
coeffs = get_coefficients(A)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (size[0]*size[1], 1))
self.assertItemsAlmostEqual(mat, np.ones(size))
# Sparse constant
size = (5, 5)
A = create_const(sp.eye(5), size)
coeffs = get_coefficients(A)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (size[0]*size[1], 1))
self.assertItemsAlmostEqual(mat, sp.eye(5).todense())
# Parameter
size = (5, 4)
param = Parameter(*size)
param.value = np.ones(size)
A = create_param(param, size)
coeffs = get_coefficients(A)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (size[0]*size[1], 1))
self.assertItemsAlmostEqual(mat, param.value)
def test_parameters(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.size, (1,1))
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = 1
self.assertEqual(str(cm.exception), "Invalid dimensions (1, 1) for Parameter value.")
val = -np.ones((4,3))
val[0,0] = 2
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
p = Parameter(4, 3, sign="negative")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
# No error for unknown sign.
p = Parameter(4, 3)
p.value = val
# Initialize a parameter with a value.
p = Parameter(value=10)
self.assertEqual(p.value, 10)
with self.assertRaises(Exception) as cm:
p = Parameter(2, 1, sign="negative", value=[2,1])
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
with self.assertRaises(Exception) as cm:
p = Parameter(4, 3, sign="positive", value=[1,2])
self.assertEqual(str(cm.exception), "Invalid dimensions (2, 1) for Parameter value.")
# Test repr.
p = Parameter(4, 3, sign="negative")
self.assertEqual(repr(p), 'Parameter(4, 3, sign="NEGATIVE")')
def test_quad_form(self) -> None:
"""Test quad_form atom.
"""
P = Parameter((2, 2), symmetric=True)
expr = cp.quad_form(self.x, P)
assert not expr.is_dcp()
def test_readme_examples(self):
import cvxopt
import numpy
# Problem data.
m = 30
n = 20
A = cvxopt.normal(m,n)
b = cvxopt.normal(m)
# Construct the problem.
x = Variable(n)
objective = Minimize(sum(square(A*x - b)))
constraints = [0 <= x, x <= 1]
p = Problem(objective, constraints)
# The optimal objective is returned by p.solve().
result = p.solve()
# The optimal value for x is stored in x.value.
print x.value
# The optimal Lagrange multiplier for a constraint
# is stored in constraint.dual_value.
print constraints[0].dual_value
####################################################
# Scalar variable.
a = Variable()
# Column vector variable of length 5.
x = Variable(5)
# Matrix variable with 4 rows and 7 columns.
A = Variable(4,7)
####################################################
# Positive scalar parameter.
m = Parameter(sign="positive")
# Column vector parameter with unknown sign (by default).
c = Parameter(5)
# Matrix parameter with negative entries.
G = Parameter(4,7,sign="negative")
# Assigns a constant value to G.
G.value = -numpy.ones((4,7))
# Raises an error for assigning a value with invalid sign.
with self.assertRaises(Exception) as cm:
G.value = numpy.ones((4,7))
self.assertEqual(str(cm.exception), "Invalid sign for Parameter value.")
####################################################
a = Variable()
x = Variable(5)
# expr is an Expression object after each assignment.
expr = 2*x
expr = expr - a
expr = sum(expr) + norm2(x)
####################################################
import numpy as np
import cvxopt
from multiprocessing import Pool
# Problem data.
n = 10
m = 5
A = cvxopt.normal(n,m)
b = cvxopt.normal(n)
gamma = Parameter(sign="positive")
# Construct the problem.
x = Variable(m)
objective = Minimize(sum(square(A*x - b)) + gamma*norm1(x))
p = Problem(objective)
# Assign a value to gamma and find the optimal x.
def get_x(gamma_value):
gamma.value = gamma_value
result = p.solve()
return x.value
gammas = np.logspace(-1, 2, num=2)
# Serial computation.
x_values = [get_x(value) for value in gammas]
####################################################
n = 10
mu = cvxopt.normal(1, n)
sigma = cvxopt.normal(n,n)
sigma = sigma.T*sigma
gamma = Parameter(sign="positive")
gamma.value = 1
x = Variable(n)
# Constants:
# mu is the vector of expected returns.
# sigma is the covariance matrix.
# gamma is a Parameter that trades off risk and return.
# Variables:
# x is a vector of stock holdings as fractions of total assets.
expected_return = mu*x
risk = quad_form(x, sigma)
objective = Maximize(expected_return - gamma*risk)
p = Problem(objective, [sum(x) == 1])
result = p.solve()
# The optimal expected return.
print expected_return.value
# The optimal risk.
print risk.value
# # Risk return tradeoff curve
# def test_risk_return_tradeoff(self):
# from math import sqrt
# from cvxopt import matrix
# from cvxopt.blas import dot
# from cvxopt.solvers import qp, options
# import scipy
# n = 4
# S = matrix( [[ 4e-2, 6e-3, -4e-3, 0.0 ],
# [ 6e-3, 1e-2, 0.0, 0.0 ],
# [-4e-3, 0.0, 2.5e-3, 0.0 ],
# [ 0.0, 0.0, 0.0, 0.0 ]] )
# pbar = matrix([.12, .10, .07, .03])
# N = 100
# # CVXPY
# Sroot = numpy.asmatrix(scipy.linalg.sqrtm(S))
# x = Variable(n, name='x')
# mu = Parameter(name='mu')
# mu.value = 1 # TODO Parameter("positive")
# objective = Minimize(-pbar*x + mu*quad_over_lin(Sroot*x,1))
# constraints = [sum(x) == 1, x >= 0]
# p = Problem(objective, constraints)
# mus = [ 10**(5.0*t/N-1.0) for t in range(N) ]
# xs = []
# for mu_val in mus:
# mu.value = mu_val
# p.solve()
# xs.append(x.value)
# returns = [ dot(pbar,x) for x in xs ]
# risks = [ sqrt(dot(x, S*x)) for x in xs ]
# # QP solver
def test_parameters(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.size, (1, 1))
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = 1
self.assertEqual(str(cm.exception),
"Invalid dimensions (1, 1) for Parameter value.")
val = -np.ones((4, 3))
val[0, 0] = 2
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception),
"Invalid sign for Parameter value.")
p = Parameter(4, 3, sign="negative")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception),
"Invalid sign for Parameter value.")
# No error for unknown sign.
p = Parameter(4, 3)
p.value = val
# Initialize a parameter with a value.
p = Parameter(value=10)
self.assertEqual(p.value, 10)
# Test assigning None.
p.value = 10
p.value = None
assert p.value is None
with self.assertRaises(Exception) as cm:
p = Parameter(2, 1, sign="negative", value=[2, 1])
self.assertEqual(str(cm.exception),
"Invalid sign for Parameter value.")
with self.assertRaises(Exception) as cm:
p = Parameter(4, 3, sign="positive", value=[1, 2])
self.assertEqual(str(cm.exception),
"Invalid dimensions (2, 1) for Parameter value.")
# Test repr.
p = Parameter(4, 3, sign="negative")
self.assertEqual(repr(p), 'Parameter(4, 3, sign="NEGATIVE")')
def test_parameters(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.size, (1, 1))
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = 1
self.assertEqual(str(cm.exception),
"Invalid dimensions (1,1) for Parameter value.")
val = -np.ones((4, 3))
val[0, 0] = 2
p = Parameter(4, 3, sign="positive")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception),
"Invalid sign for Parameter value.")
p = Parameter(4, 3, sign="negative")
with self.assertRaises(Exception) as cm:
p.value = val
self.assertEqual(str(cm.exception),
"Invalid sign for Parameter value.")
# No error for unknown sign.
p = Parameter(4, 3)
p.value = val
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_quad_form(self):
"""Test quad_form atom.
"""
P = Parameter((2, 2))
expr = cp.quad_form(self.x, P)
assert not expr.is_dcp()
def test_parameters(self):
p = Parameter(name='p')
self.assertEqual(p.name(), "p")
self.assertEqual(p.size, (1,1))
def test_index(self):
"""Test the get_coefficients function for index.
"""
size = (5, 4)
# Eye
key = (slice(0,2,None), slice(0,2,None))
x = create_var(size)
expr = index(x, (2, 2), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(id_, x.data)
self.assertEqual(mat.shape, (4, 20))
test_mat = np.mat(range(20)).T
self.assertItemsAlmostEqual((mat*test_mat).reshape((2, 2), order='F'),
test_mat.reshape(size, order='F')[key])
# Eye with scalar mult.
key = (slice(0,2,None), slice(0,2,None))
x = create_var(size)
A = create_const(5, (1, 1))
expr = mul_expr(A, x, size)
expr = index(expr, (2, 2), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
test_mat = np.mat(range(20)).T
self.assertItemsAlmostEqual((mat*test_mat).reshape((2, 2), order='F'),
5*test_mat.reshape(size, order='F')[key])
# Promoted
key = (slice(0,2,None), slice(0,2,None))
x = create_var((1, 1))
value = np.array(range(20)).reshape(size)
A = create_const(value, size)
prom_x = promote(x, (size[1], 1))
expr = mul_expr(A, diag_vec(prom_x), size)
expr = index(expr, (2, 2), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (4, 1))
self.assertItemsAlmostEqual(mat, value[key])
# Normal
size = (5, 5)
key = (slice(0,2,None), slice(0,1,None))
x = create_var((5, 1))
A = create_const(np.ones(size), size)
expr = mul_expr(A, x, (5, 1))
expr = index(expr, (2, 1), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (2, 5))
self.assertItemsAlmostEqual(mat.todense(), A.data[slice(0,2,None)])
# Blocks
size = (5, 5)
key = (slice(0,2,None), slice(0,2,None))
x = create_var(size)
value = np.array(range(25)).reshape(size)
A = create_const(value, size)
expr = mul_expr(A, x, size)
expr = index(expr, (2, 2), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (4, 25))
test_mat = np.mat(range(25)).T
self.assertItemsAlmostEqual((mat*test_mat).reshape((2, 2), order='F'),
(A.data*test_mat.reshape(size, order='F'))[key])
# Scalar constant
size = (1, 1)
A = create_const(5, size)
key = (slice(0,1,None), slice(0,1,None))
expr = index(A, (1, 1), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(intf.size(mat), (1, 1))
self.assertEqual(mat, 5)
# Dense constant
size = (5, 4)
key = (slice(0,2,None), slice(0,1,None))
value = np.array(range(20)).reshape(size)
A = create_const(value, size)
expr = index(A, (2, 1), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (2, 1))
self.assertItemsAlmostEqual(mat, value[key])
# Sparse constant
size = (5, 5)
key = (slice(0,2,None), slice(0,1,None))
A = create_const(sp.eye(5), size)
expr = index(A, (2, 1), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (2, 1))
self.assertItemsAlmostEqual(mat, sp.eye(5).todense()[key])
# Parameter
size = (5, 4)
key = (slice(0,2,None), slice(0,1,None))
param = Parameter(*size)
value = np.array(range(20)).reshape(size)
param.value = value
A = create_param(param, size)
expr = index(A, (2, 1), key)
coeffs = get_coefficients(expr)
assert len(coeffs) == 1
id_, mat = coeffs[0]
self.assertEqual(mat.shape, (2, 1))
self.assertItemsAlmostEqual(mat, param.value[key])