def test_curvature(self):
x = cp.Variable(3)
expr = cp.length(x)
self.assertEqual(expr.curvature, s.QUASICONVEX)
expr = -cp.length(x)
self.assertEqual(expr.curvature, s.QUASICONCAVE)
expr = cp.ceil(x)
self.assertEqual(expr.curvature, s.QUASILINEAR)
self.assertTrue(expr.is_quasilinear())
def test_length(self):
x = cp.Variable(5)
expr = cp.length(x)
self.assertTrue(expr.is_dqcp())
self.assertTrue(expr.is_quasiconvex())
self.assertFalse(expr.is_quasiconcave())
problem = cp.Problem(cp.Minimize(expr), [x[0] == 2.0, x[1] == 1.0])
problem.solve(SOLVER, qcp=True)
self.assertEqual(problem.objective.value, 2)
np.testing.assert_almost_equal(x.value, np.array([2, 1, 0, 0, 0]))
def test_card_ls(self):
n = 10
np.random.seed(0)
A = np.random.randn(n, n)
x_star = np.random.randn(n)
b = cp.matmul(A, x_star)
epsilon = 1e-3
x = cp.Variable(n)
objective_fn = cp.length(x)
mse = cp.sum_squares(cp.matmul(A, x) - b) / n
problem = cp.Problem(cp.Minimize(objective_fn), [mse <= epsilon])
# smoke test
problem.solve(SOLVER, qcp=True)
def example_min_len_least_squares():
n = 10
np.random.seed(1)
A = np.random.randn(n, n)
x_star = np.random.randn(n)
b = A @ x_star
epsilon = 1e-2
x = cp.Variable(n)
mse = cp.sum_squares(A @ x - b) / n
problem = cp.Problem(cp.Minimize(cp.length(x)), [mse <= epsilon])
print("Is problem DQCP?: ", problem.is_dqcp())
problem.solve(qcp=True)
print("Found a solution, with length: ", problem.value)
def test_length_example(self) -> None:
"""Fix #1760."""
n = 10
np.random.seed(1)
A = np.random.randn(n, n)
x_star = np.random.randn(n)
b = A @ x_star
epsilon = 1e-2
x = cp.Variable(n)
mse = cp.sum_squares(A @ x - b) / n
problem = cp.Problem(cp.Minimize(cp.length(x)), [mse <= epsilon])
assert problem.is_dqcp()
problem.solve(qcp=True)
assert np.isclose(problem.value, 8)
def test_infeasible(self):
x = cp.Variable(2)
problem = cp.Problem(cp.Minimize(cp.length(x)),
[x == -1, cp.ceil(x) >= 1])
problem.solve(SOLVER, qcp=True)
self.assertIn(problem.status, (s.INFEASIBLE, s.INFEASIBLE_INACCURATE))
