def test_merge_two_equations(self):
x, y = initAdArrays([np.array([1]), np.array([2])])
z1 = exp(x) + y
z2 = exp(y) + x
z = concatenate((z1, z2))
val = np.array([np.exp(1) + 2, np.exp(2) + 1])
J = np.array([[np.exp(1), 1], [1, np.exp(2)]])
self.assertTrue(np.allclose(z.val, val) and np.allclose(z.full_jac().A, J))
def test_exp_sparse_jac(self):
val = np.array([1, 2, 3])
J = sps.csc_matrix(np.array([[3, 2, 1], [5, 6, 1], [2, 3, 5]]))
a = Ad_array(val, J)
b = af.exp(a)
jac = np.dot(np.diag(np.exp(val)), J.A)
self.assertTrue(np.all(b.val == np.exp(val)) and np.all(b.jac == jac))
def test_exp_vector(self):
val = np.array([1, 2, 3])
J = np.array([[3, 2, 1], [5, 6, 1], [2, 3, 5]])
a = Ad_array(val, sps.csc_matrix(J))
b = af.exp(a)
jac = np.dot(np.diag(np.exp(val)), J)
self.assertTrue(np.all(b.val == np.exp(val)) and np.all(b.jac == jac))
self.assertTrue(np.all(J == np.array([[3, 2, 1], [5, 6, 1], [2, 3, 5]])))
def test_exp_scalar_times_ad_var(self):
val = np.array([1, 2, 3])
J = sps.diags(np.array([1, 1, 1]))
a = Ad_array(val, J)
c = 2
b = af.exp(c * a)
jac = c * sps.diags(np.exp(c * val)) * J
self.assertTrue(
np.allclose(b.val, np.exp(c * val)) and np.allclose(b.jac.A, jac.A)
)
self.assertTrue(np.all(a.val == [1, 2, 3]) and np.all(a.jac.A == J.A))
def test_exp_scalar_times_ad_var(self):
val = np.array([1, 2, 3])
J = sps.diags(np.array([1, 1, 1]))
a, _, _ = initAdArrays([val, val, val])
c = 2
b = af.exp(c * a)
zero = sps.csc_matrix((3, 3))
jac = sps.hstack([c * sps.diags(np.exp(c * val)) * J, zero, zero])
jac_a = sps.hstack([J, zero, zero])
self.assertTrue(
np.allclose(b.val, np.exp(c * val)) and np.allclose(b.jac.A, jac.A)
)
self.assertTrue(np.all(a.val == [1, 2, 3]) and np.all(a.jac.A == jac_a.A))
def test_exp_advar(self):
a = Ad_array(2, 3)
b = af.exp(a)
self.assertTrue(b.val == np.exp(2) and b.jac == 3 * np.exp(2))
self.assertTrue(a.val == 2 and a.jac == 3)
def test_exp_scalar(self):
a = Ad_array(1, 0)
b = af.exp(a)
self.assertTrue(b.val == np.exp(1) and b.jac == 0)
self.assertTrue(a.val == 1 and a.jac == 0)