def test_convexify_deg_2_negative_hessian(self):
f = lambda x: -x**2
f_hess = np.array([[-2.0]])
e = Expr(f)
quad_e = e.convexify(np.zeros((1, 1)), degree=2)
self.assertIsInstance(quad_e, QuadExpr)
Q = quad_e.Q
self.assertTrue(np.allclose(Q, np.zeros((1, 1))))
def test_convexify_deg_2_multi_dim(self):
x0 = np.array([[5.0], [5.0]])
f = lambda x: np.vstack((\
x[0,0]**2 + x[1,0]**2 - 4, \
-((x[0,0]-1)**2 +(x[1,0]**2-1)**2 - 0.25), \
-((x[0,0]+1)**2 +(x[1,0]**2-1)**2 - 0.25), \
-((x[0,0])**2 + 7*(x[1,0]+1-x[0,0]**2/2)**2 - 0.8)))
e = Expr(f)
aff_e = e.convexify(x0)
self.assertTrue(aff_e.A.shape[0] == aff_e.b.shape[0])
def test_convexify_deg_1(self):
for f, fder, _ in fs:
e = Expr(f)
for x in xs:
y = f(x)
y_prime = fder(x)
aff_e = e.convexify(x, degree=1)
self.assertIsInstance(aff_e, AffExpr)
A = aff_e.A
b = aff_e.b
self.assertTrue(np.allclose(A, fder(x)))
self.assertTrue(np.allclose(b, f(x) - A.dot(x)))
self.assertTrue(np.allclose(aff_e.eval(x), f(x)))
def test_convexify_deg_2(self):
for f, fder, fhess in fs:
e = Expr(f)
for x in xs:
y = f(x)
y_prime = fder(x)
y_d_prime = fhess(x)
y_d_prime = np.maximum(y_d_prime, np.zeros((1, 1)))
quad_e = e.convexify(x, degree=2)
self.assertIsInstance(quad_e, QuadExpr)
Q = np.maximum(quad_e.Q, np.zeros((1, 1)))
A = quad_e.A
b = quad_e.b
self.assertTrue(np.allclose(Q, y_d_prime))
self.assertTrue(np.allclose(A, \
y_prime -np.transpose(x).dot(y_d_prime)))
self.assertTrue(np.allclose(b, \
np.array(0.5*np.transpose(x).dot(y_d_prime)).dot(x) \
- y_prime.dot(x) + y))
self.assertTrue(np.allclose(quad_e.eval(x), y))
