def test_round_attr(self):
"""Test rounding for attributes.
"""
# Nonpos
v = Variable(1, nonpos=True)
self.assertAlmostEqual(v.project(1), 0)
v = Variable(2, nonpos=True)
self.assertItemsAlmostEqual(v.project(np.array([1, -1])), [0, -1])
# Nonneg
v = Variable(1, nonneg=True)
self.assertAlmostEqual(v.project(-1), 0)
v = Variable(2, nonneg=True)
self.assertItemsAlmostEqual(v.project(np.array([1, -1])), [1, 0])
# Boolean
v = Variable((2, 2), boolean=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, 0]]).T),
[1, 0, 1, 0])
# Integer
v = Variable((2, 2), integer=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1.6], [1, 0]]).T),
[1, -2, 1, 0])
# Symmetric
v = Variable((2, 2), symmetric=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, 0]])),
[1, 0, 0, 0])
# PSD
v = Variable((2, 2), PSD=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, -1]])),
[1, 0, 0, 0])
# NSD
v = Variable((2, 2), NSD=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1], [1, -1]])),
[0, 0, 0, -1])
# diag
v = Variable((2, 2), diag=True)
self.assertItemsAlmostEqual(
v.project(np.array([[1, -1], [1, 0]])).todense(), [1, 0, 0, 0])
# Hermitian
v = Variable((2, 2), hermitian=True)
self.assertItemsAlmostEqual(v.project(np.array([[1, -1j], [1, 0]])),
[1, 0.5 + 0.5j, 0.5 - 0.5j, 0])
A = Constant(np.array([[1.0]]))
self.assertEqual(A.is_psd(), True)
self.assertEqual(A.is_nsd(), False)
A = Constant(np.array([[-1.0]]))
self.assertEqual(A.is_psd(), False)
self.assertEqual(A.is_nsd(), True)
A = Constant(np.array([[0.0]]))
self.assertEqual(A.is_psd(), True)
self.assertEqual(A.is_nsd(), True)
def test_constant_psd_nsd(self):
n = 5
np.random.randn(0)
U = np.random.randn(n, n)
U = U @ U.T
(evals, U) = np.linalg.eigh(U) # U is now an orthogonal matrix
# Try four indefinite matrices with different eigenvalue
# spread around the origin.
v1 = np.array([3, 2, 1, 1e-8, -1])
P = Constant(U @ np.diag(v1) @ U.T)
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
v2 = np.array([3, 2, 2, 1e-6, -1])
P = Constant(U @ np.diag(v2) @ U.T)
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
v3 = np.array([3, 2, 2, 1e-4, -1e-6])
P = Constant(U @ np.diag(v3) @ U.T)
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
v4 = np.array([-1, 3, 0, 0, 0])
P = Constant(U @ np.diag(v4) @ U.T)
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
# Try a test case given in GitHub issue 1451.
# (Should be equivalent to v4 above).
P = Constant(np.array([[1, 2], [2, 1]]))
x = Variable(shape=(2, ))
expr = cp.quad_form(x, P)
self.assertFalse(expr.is_dcp())
self.assertFalse((-expr).is_dcp())
self.assertFalse(gershgorin_psd_check(P.value, tol=0.99))
# Useful Gershgorin disc check
P = Constant(np.array([[2, 1], [1, 2]]))
self.assertTrue(gershgorin_psd_check(P.value, tol=0.0))
# Verify good behavior for large eigenvalues
P = Constant(np.diag(9 * [1e-4] + [-1e4]))
self.assertFalse(P.is_psd())
self.assertFalse(P.is_nsd())
# Check a case when the matrix is in fact PSD.
P = Constant(np.ones(shape=(5, 5)))
self.assertTrue(P.is_psd())
self.assertFalse(P.is_nsd())
# Check with sparse inputs
P = Constant(sp.eye(10))
self.assertTrue(gershgorin_psd_check(P.value, s.EIGVAL_TOL))
self.assertTrue(P.is_psd())
self.assertTrue((-P).is_nsd())
Q = -s.EIGVAL_TOL / 2 * P
self.assertTrue(gershgorin_psd_check(Q.value, s.EIGVAL_TOL))
Q = -1.1 * s.EIGVAL_TOL * P
self.assertFalse(gershgorin_psd_check(Q.value, s.EIGVAL_TOL))
self.assertFalse(Q.is_psd())
