def test_gmatmul(self):
x = cp.Variable(2, pos=True)
A = cp.Parameter(shape=(2, 2))
A.value = np.array([[-5, 2], [1, -3]])
b = np.array([3, 2])
expr = cp.gmatmul(A, x)
problem = cp.Problem(cp.Minimize(1.0), [expr == b])
self.assertTrue(problem.is_dgp(dpp=True))
problem.solve(gp=True, enforce_dpp=True)
sltn = np.exp(np.linalg.solve(A.value, np.log(b)))
self.assertItemsAlmostEqual(x.value, sltn)
x_par = cp.Parameter(2, pos=True)
expr = cp.gmatmul(A, x_par)
self.assertFalse(expr.is_dgp(dpp=True))
self.assertTrue(expr.is_dgp(dpp=False))
def test_gmatmul(self):
x = cvxpy.Variable(2, pos=True)
A = np.array([[-5., 2.], [1., -3.]])
b = np.array([3, 2])
expr = cvxpy.gmatmul(A, x)
x.value = b
self.assertItemsAlmostEqual(expr.value, [3**-5 * 2**2, 3. / 8])
A_par = cvxpy.Parameter((2, 2), value=A)
self.assertItemsAlmostEqual(
cvxpy.gmatmul(A_par, x).value, [3**-5 * 2**2, 3. / 8])
x.value = None
prob = cvxpy.Problem(cvxpy.Minimize(1.0), [expr == b])
prob.solve(gp=True)
sltn = np.exp(np.linalg.solve(A, np.log(b)))
self.assertItemsAlmostEqual(x.value, sltn)
def test_gmatmul(self):
x = cvxpy.Variable(2, pos=True)
A = cvxpy.Variable((2, 2))
with self.assertRaises(Exception) as cm:
cvxpy.gmatmul(A, x)
self.assertTrue(str(cm.exception) ==
"gmatmul(A, X) requires that A be constant.")
x = cvxpy.Variable(2)
A = np.ones((4, 2))
with self.assertRaises(Exception) as cm:
cvxpy.gmatmul(A, x)
self.assertTrue(str(cm.exception) ==
"gmatmul(A, X) requires that X be positive.")
x = cvxpy.Variable(3, pos=True)
A = np.ones((4, 3))
gmatmul = cvxpy.gmatmul(A, x)
self.assertTrue(gmatmul.is_dgp())
self.assertTrue(gmatmul.is_log_log_affine())
self.assertTrue(gmatmul.is_log_log_convex())
self.assertTrue(gmatmul.is_log_log_concave())
self.assertTrue(gmatmul.is_nonneg())
self.assertTrue(gmatmul.is_incr(0))
self.assertTrue(cvxpy.gmatmul(-A, x).is_decr(0))
x = cvxpy.Variable((2, 3), pos=True)
A = np.array([[2., -1.], [0., 3.]])
gmatmul = cvxpy.gmatmul(A, x)
self.assertTrue(gmatmul.is_dgp())
self.assertTrue(gmatmul.is_log_log_affine())
self.assertTrue(gmatmul.is_log_log_convex())
self.assertTrue(gmatmul.is_log_log_concave())
self.assertFalse(gmatmul.is_incr(0))
self.assertFalse(gmatmul.is_decr(0))
