def test_advar_init_cross_jacobi(self):
x, y = initAdArrays([np.array([-1, 4]), np.array([1, 5])])
z = x * y
J = np.array([[1, 0, -1, 0], [0, 5, 0, 4]])
self.assertTrue(np.all(z.val == [-1, 20]))
self.assertTrue(np.all((z.jac == J).A))
def test_vector_quadratic(self):
x, y = initAdArrays([np.array([1, 1]), np.array([2, 3])])
z = 1 * x + 2 * y + 3 * x * y + 4 * x * x + 5 * y * y
val = np.array([35, 65])
J = np.array([[15, 0, 25, 0], [0, 18, 0, 35]])
self.assertTrue(np.all(z.val == val) and np.sum(z.full_jac() != J) == 0)
def test_mul_sps_advar_init(self):
x = initAdArrays(np.array([1, 2, 3]))
A = sps.csc_matrix(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
f = A * x
self.assertTrue(np.all(f.val == [14, 32, 50]))
self.assertTrue(np.all((f.jac == A).A))
def test_add_scal_with_var_init(self):
a = initAdArrays(3)
b = 3
c = b + a
self.assertTrue(np.allclose(c.val, 6) and np.allclose(c.jac.A, 1))
self.assertTrue(a.val == 3 and np.allclose(a.jac.A, 1))
self.assertTrue(b == 3)
def test_mul_scal_ad_var_init(self):
a, b = initAdArrays([np.array(3), np.array(2)])
d = 3
c = d * a
self.assertTrue(c.val == 9 and np.all(c.jac.A == [3, 0]))
self.assertTrue(a.val == 3 and np.all(a.jac.A == [1, 0]))
self.assertTrue(b.val == 2 and np.all(b.jac.A == [0, 1]))
def test_sub_scal_with_var_init(self):
a = initAdArrays(3)
b = 3
c = b - a
self.assertTrue(np.allclose(c.val, 0) and np.allclose(c.jac.A, -1))
self.assertTrue(a.val == 3 and a.jac.A == 1)
self.assertTrue(b == 3)
def test_power_advar_advar_init(self):
a, b = initAdArrays([np.array(4.0), np.array(-8)])
c = a**b
jac = np.array([-8 * (4**-9), 4**-8 * np.log(4)])
self.assertTrue(np.allclose(c.val, 4**-8))
self.assertTrue(np.all(np.abs(c.jac.A - jac) < 1e-6))
def test_mapping_m_to_n(self):
x, y = initAdArrays([np.array([1, 1, 3]), np.array([2, 3])])
A = sps.csc_matrix(np.array([[1, 2, 1], [2, 3, 4]]))
z = y * (A * x)
val = np.array([12, 51])
J = np.array([[2, 4, 2, 6, 0], [6, 9, 12, 0, 17]])
self.assertTrue(np.all(z.val == val) and np.sum(z.full_jac() != J) == 0)
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_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_advar_init_diff_len(self):
a, b = initAdArrays([np.array([1, 2, 3]), np.array([1, 2])])
A = sps.csc_matrix(np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
B = sps.csc_matrix(np.array([[1, 2], [4, 5]]))
f = A * a
g = B * b
zero_32 = sps.csc_matrix((3, 2))
zero_23 = sps.csc_matrix((2, 3))
jac_f = sps.hstack((A, zero_32))
jac_g = sps.hstack((zero_23, B))
self.assertTrue(np.all(f.val == [14, 32, 50]))
self.assertTrue(np.all((f.jac == jac_f).A))
self.assertTrue(np.all(g.val == [5, 14]))
self.assertTrue(np.all((g.jac == jac_g).A))
def test_quadratic_function(self):
x, y = initAdArrays([np.array(1), np.array(2)])
z = 1 * x + 2 * y + 3 * x * y + 4 * x * x + 5 * y * y
val = 35
self.assertTrue(z.val == val and np.all(z.jac.A == [15, 25]))
def test_mul_ad_var_init(self):
a, b = initAdArrays([np.array(3), np.array(2)])
c = a * b
self.assertTrue(c.val == 6 and np.all(c.jac.A == [2, 3]))
self.assertTrue(a.val == 3 and np.all(a.jac.A == [1, 0]))
self.assertTrue(b.val == 2 and np.all(b.jac.A == [0, 1]))
def test_sub_var_init_with_var_init(self):
a, b = initAdArrays([np.array(3), np.array(2)])
c = b - a
self.assertTrue(np.allclose(c.val, -1) and np.all(c.jac.A == [-1, 1]))
self.assertTrue(a.val == 3 and np.all(a.jac.A == [1, 0]))
self.assertTrue(b.val == 2 and np.all(b.jac.A == [0, 1]))
def test_add_two_ad_variables_init(self):
a, b = initAdArrays([np.array(1), np.array(-10)])
c = a + b
self.assertTrue(c.val == -9 and np.all(c.jac.A == [1, 1]))
self.assertTrue(a.val == 1 and np.all(a.jac.A == [1, 0]))
self.assertTrue(b.val == -10 and np.all(b.jac.A == [0, 1]))