def test_invalid_variable(self):
x = cvx.Variable(shape=(2, 2), symmetric=True)
try:
cvx.suppfunc(x, []) # dead-store
assert False
except ValueError as e:
assert 'attributes' in e.args[0]
pass
def test_invalid_constraint(self):
x = cvx.Variable(shape=(3, ))
a = cvx.Parameter(shape=(3, ))
cons = [a @ x == 1]
try:
cvx.suppfunc(x, cons) # dead-store
assert False
except ValueError as e:
assert 'Parameter' in e.args[0]
pass
def test_invalid_solver(self) -> None:
n = 3
x = cp.Variable(shape=(n,))
sigma = cp.suppfunc(x, [cp.norm(x - np.random.randn(n,), 2) <= 1])
y_var = cp.Variable(shape=(n,))
prob = cp.Problem(cp.Minimize(sigma(y_var)), [np.random.randn(n,) == y_var])
with self.assertRaisesRegex(
SolverError, ".*could not be reduced to a QP.*"):
prob.solve(solver='OSQP')
def test_expcone_1(self):
x = cvx.Variable(shape=(1, ))
tempcons = [cvx.exp(x[0]) <= np.exp(1), cvx.exp(-x[0]) <= np.exp(1)]
sigma = cvx.suppfunc(x, tempcons)
y = cvx.Variable(shape=(1, ))
obj_expr = y[0]
cons = [sigma(y) <= 1]
# ^ That just means -1 <= y[0] <= 1
prob = cvx.Problem(cvx.Minimize(obj_expr), cons)
prob.solve(solver='ECOS')
viol = cons[0].violation()
assert viol <= 1e-6
assert abs(y.value - (-1)) <= 1e-6
def test_invalid_solver(self):
n = 3
x = cvx.Variable(shape=(n, ))
sigma = cvx.suppfunc(x, [cvx.norm(x - np.random.randn(n, ), 2) <= 1])
y_var = cvx.Variable(shape=(n, ))
prob = cvx.Problem(cvx.Minimize(sigma(y_var)),
[np.random.randn(n, ) == y_var])
try:
prob.solve(solver='OSQP')
assert False
except SolverError as e:
assert 'could not be reduced to a QP' in e.args[0]
pass
def test_expcone_1(self) -> None:
x = cp.Variable(shape=(1, ))
tempcons = [cp.exp(x[0]) <= np.exp(1), cp.exp(-x[0]) <= np.exp(1)]
sigma = cp.suppfunc(x, tempcons)
y = cp.Variable(shape=(1, ))
obj_expr = y[0]
cons = [sigma(y) <= 1]
# ^ That just means -1 <= y[0] <= 1
prob = cp.Problem(cp.Minimize(obj_expr), cons)
prob.solve(solver='ECOS')
viol = cons[0].violation()
self.assertLessEqual(viol, 1e-6)
self.assertLessEqual(abs(y.value - (-1)), 1e-6)
def test_vector2norm(self) -> None:
n = 3
np.random.seed(1)
a = np.random.randn(n, )
x = cp.Variable(shape=(n, ))
sigma = cp.suppfunc(x, [cp.norm(x - a, 2) <= 1])
y = np.random.randn(n, )
y_var = cp.Variable(shape=(n, ))
prob = cp.Problem(cp.Minimize(sigma(y_var)), [y == y_var])
prob.solve(solver='ECOS')
actual = prob.value
expected = a @ y + np.linalg.norm(y, ord=2)
self.assertLessEqual(abs(actual - expected), 1e-6)
self.assertLessEqual(abs(prob.objective.expr.value - prob.value), 1e-6)
def test_largest_singvalue(self) -> None:
np.random.seed(3)
rows, cols = 3, 4
A = np.random.randn(rows, cols)
A_sv = np.linalg.svd(A, compute_uv=False)
X = cp.Variable(shape=(rows, cols))
sigma = cp.suppfunc(X, [cp.sigma_max(X) <= 1])
Y = cp.Variable(shape=(rows, cols))
cons = [Y == A]
prob = cp.Problem(cp.Minimize(sigma(Y)), cons)
prob.solve(solver='SCS', eps=1e-8)
actual = prob.value
expect = np.sum(A_sv)
self.assertLessEqual(abs(actual - expect), 1e-6)
def test_vector1norm(self):
n = 3
np.random.seed(1)
a = np.random.randn(n, )
x = cvx.Variable(shape=(n, ))
sigma = cvx.suppfunc(x, [cvx.norm(x - a, 1) <= 1])
y = np.random.randn(n, )
y_var = cvx.Variable(shape=(n, ))
prob = cvx.Problem(cvx.Minimize(sigma(y_var)), [y == y_var])
prob.solve(solver='ECOS')
actual = prob.value
expected = a @ y + np.linalg.norm(y, ord=np.inf)
assert abs(actual - expected) <= 1e-6
assert abs(prob.objective.expr.value - prob.value) <= 1e-6
def test_psd_dualcone(self) -> None:
np.random.seed(5)
n = 3
X = cp.Variable(shape=(n, n))
sigma = cp.suppfunc(X, [X >> 0])
A = np.random.randn(n, n)
Y = cp.Variable(shape=(n, n))
objective = cp.Minimize(cp.norm(A.ravel(order='F') + Y.flatten()))
cons = [sigma(Y) <= 0] # Y is negative definite.
prob = cp.Problem(objective, cons)
prob.solve(solver='SCS', eps=1e-8)
viol = cons[0].violation()
self.assertLessEqual(viol, 1e-6)
eigs = np.linalg.eigh(Y.value)[0]
self.assertLessEqual(np.max(eigs), 1e-6)
def test_rectangular_variable(self) -> None:
np.random.seed(2)
rows, cols = 4, 2
a = np.random.randn(rows, cols)
x = cp.Variable(shape=(rows, cols))
sigma = cp.suppfunc(x, [x[:, 0] == 0])
y = cp.Variable(shape=(rows, cols))
cons = [sigma(y - a) <= 0]
objective = cp.Minimize(cp.sum_squares(y.flatten()))
prob = cp.Problem(objective, cons)
prob.solve(solver='ECOS')
expect = np.hstack([np.zeros(shape=(rows, 1)), a[:, [1]]])
actual = y.value
self.assertLessEqual(np.linalg.norm(actual - expect, ord=2), 1e-6)
viol = cons[0].violation()
self.assertLessEqual(viol, 1e-6)
def test_basic_lmi(self) -> None:
np.random.seed(4)
n = 3
A = np.random.randn(n, n)
A = A.T @ A
X = cp.Variable(shape=(n, n)) # will fail if you try PSD=True, or symmetric=Trues
sigma = cp.suppfunc(X, [0 << X, cp.lambda_max(X) <= 1])
Y = cp.Variable(shape=(n, n))
cons = [Y == A]
expr = sigma(Y)
prob = cp.Problem(cp.Minimize(expr), cons) # opt value of support func would be at X=I.
prob.solve(solver='SCS', eps=1e-8)
actual1 = prob.value # computed with epigraph
actual2 = expr.value # computed by evaluating support function, as a maximization problem.
self.assertLessEqual(abs(actual1 - actual2), 1e-6)
expect = np.trace(A)
self.assertLessEqual(abs(actual1 - expect), 1e-4)
def test_expcone_2(self) -> None:
x = cp.Variable(shape=(3,))
tempcons = [cp.sum(x) <= 1.0, cp.sum(x) >= 0.1, x >= 0.01,
cp.kl_div(x[1], x[0]) + x[1] - x[0] + x[2] <= 0]
sigma = cp.suppfunc(x, tempcons)
y = cp.Variable(shape=(3,))
a = np.array([-3, -2, -1]) # this is negative of objective in mosek_conif.py example
expr = -sigma(y)
objective = cp.Maximize(expr)
cons = [y == a]
prob = cp.Problem(objective, cons)
prob.solve(solver='ECOS')
# Check for expected objective value
epi_actual = prob.value
direct_actual = expr.value
expect = 0.235348211
self.assertLessEqual(abs(epi_actual - expect), 1e-6)
self.assertLessEqual(abs(direct_actual - expect), 1e-6)
def test_Rn(self) -> None:
np.random.seed(0)
n = 5
x = cp.Variable(shape=(n, ))
sigma = cp.suppfunc(x, [])
a = np.random.randn(n, )
y = cp.Variable(shape=(n, ))
cons = [sigma(y - a) <= 0] # "<= num" for any num >= 0 is valid.
objective = cp.Minimize(a @ y)
prob = cp.Problem(objective, cons)
prob.solve(solver='ECOS')
actual = prob.value
expected = np.dot(a, a)
self.assertLessEqual(abs(actual - expected), 1e-6)
actual = y.value
expected = a
self.assertLessEqual(np.linalg.norm(actual - expected, ord=2), 1e-6)
viol = cons[0].violation()
self.assertLessEqual(viol, 1e-8)
def test_Rn(self):
np.random.seed(0)
n = 5
x = cvx.Variable(shape=(n, ))
sigma = cvx.suppfunc(x, [])
a = np.random.randn(n, )
y = cvx.Variable(shape=(n, ))
cons = [sigma(y - a) <= 0] # "<= num" for any num >= 0 is valid.
objective = cvx.Minimize(a @ y)
prob = cvx.Problem(objective, cons)
prob.solve(solver='ECOS')
actual = prob.value
expected = np.dot(a, a)
assert abs(actual - expected) <= 1e-6
actual = y.value
expected = a
assert np.linalg.norm(actual - expected, ord=2) <= 1e-6
viol = cons[0].violation()
assert viol <= 1e-8
def test_invalid_constraint(self) -> None:
x = cp.Variable(shape=(3, ))
a = cp.Parameter(shape=(3, ))
cons = [a @ x == 1]
with self.assertRaises(ValueError):
cp.suppfunc(x, cons)
def test_invalid_variable(self) -> None:
x = cp.Variable(shape=(2, 2), symmetric=True)
with self.assertRaises(ValueError):
cp.suppfunc(x, [])
