def test_composite():
f1 = AutoDiff(name='x', val=np.pi/4)
f2 = AutoDiff(name='y', val=np.pi / 2)
u = AutoDiffVector((f1, f2))
v = AutoDiffVector([f1, np.pi])
z = AutoDiffVector((f2, -f1))
np.testing.assert_array_almost_equal(ad.cos(ad.sin(u)),
[0.7602445970756302, 0.5403023058681398]), "Composite failed"
J, order = (ad.cos(ad.sin(u))).get_jacobian()
np.testing.assert_array_almost_equal(J, [[-0.4593626849327842, 0], [0, 0]]), "Composite failed"
np.testing.assert_array_almost_equal(ad.cos(ad.sin(v)),
[0.7602445970756302, 1]), "Composite failed"
J, order = (ad.cos(ad.sin(v))).get_jacobian()
np.testing.assert_array_almost_equal(J, [[-0.4593626849327842], [0]]), "Composite failed"
np.testing.assert_array_almost_equal(u*ad.cos(ad.sin(u)),
[0.597094710276033, 0.8487048774164866]), "Composite failed"
J, order = (u*ad.cos(ad.sin(u))).get_jacobian()
np.testing.assert_array_almost_equal(J, [[0.3994619879961, 0], [0, 0.5403023058681397]]), "Composite failed"
np.testing.assert_array_almost_equal(z*ad.cos(ad.sin(u)),
[1.194189420552066, -0.4243524387082433]), "Composite failed"
J, order = (z*ad.cos(ad.sin(u))).get_jacobian()
np.testing.assert_array_almost_equal(J, [[-0.7215652181590587, 0.7602445970756302],
[-0.5403023058681398, 0]]), "Composite failed"
np.testing.assert_array_almost_equal((z*ad.cos(ad.sin(u)))**2,
[1.4260883721584792, 0.18007499223763337]), "Composite failed"
J, order = ((z*ad.cos(ad.sin(u)))**2).get_jacobian()
np.testing.assert_array_almost_equal(J, [[-1.7233710995277831, 1.815752109719],
[0.4585572, 0]]), "Composite failed"
def test_duplicate_instantiation():
f1 = AutoDiff(name='x', val=1)
f2 = AutoDiff(name='x', val=3)
try:
AutoDiffVector((f1, f2))
except Exception:
print("Caught error as expected")
def test_and():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=5)
u = AutoDiffVector((f1, f2))
y = AutoDiffVector((f2, 8))
np.testing.assert_array_equal(u, u) and np.testing.assert_array_equal(
y, y), "And failed"
def test_divide():
x = AutoDiff(name='x', val=6)
y = AutoDiff(name='y', val=-12)
z = AutoDiff(name='z', val=0)
q = AutoDiff(name='b0', val="string")
assert (x / 2) == 3, 'Division failed'
assert (x / 2).trace['d_x'] == (1 / 2), 'Division failed'
assert (18 / x) == 3, 'Division failed'
assert (18 / x).trace['d_x'] == -(1 / 2), 'Division failed'
assert (y / x) == -2, 'Division failed'
assert (y / x).trace['d_x'] == (12 / 36), 'Division failed'
assert (y / x).trace['d_y'] == (1 / 6), 'Division failed'
assert (x / y) == -0.5, 'Division failed'
assert (x / y).trace['d_x'] == (1 / -12), 'Division failed'
assert (x / y).trace['d_y'] == (-6 / 144), 'Division failed'
try:
assert (z / z) == 0
except ZeroDivisionError as e:
print("Caught Zero Division Error")
try:
assert (z / z).trace['d_z'] == 0
except ZeroDivisionError as e:
print("Caught Zero Division Error")
try:
(q / 5)
except TypeError:
print("Caught error as expected")
def test_cot():
f1 = AutoDiff(name='x', val=4)
f2 = AutoDiff(name='y', val=np.pi/8)
u = AutoDiffVector((f1, f2))
np.testing.assert_array_almost_equal(ad.cot(u).val, [0.863691, 2.414214]), 'Cotangent failed'
J, order = (ad.cot(u)).get_jacobian()
np.testing.assert_array_almost_equal(J, [[-1.746, 0], [0, -6.8284]], decimal=4), 'Cotangent failed'
def test_sec():
f1 = AutoDiff(name='x', val=0)
f2 = AutoDiff(name='y', val=np.pi)
u = AutoDiffVector((f1, f2))
np.testing.assert_array_almost_equal(ad.sec(u).val, [1, -1]), 'Secant failed'
J, order = (ad.sec(u)).get_jacobian()
np.testing.assert_array_almost_equal(J, [[0, 0], [0, 0]], decimal=4), 'Secant failed'
def test_round():
x = AutoDiff(name='x', val=5.7)
y = AutoDiff(name='y', val=-4.6)
z = AutoDiff(name='z', val=0)
assert round(x) == 6, "Round failed"
assert -5 == round(y), "Round failed"
assert 0 == round(z), "Round failed"
def test_vec_multiply():
f1 = AutoDiff(name='x', val=-1)
f2 = AutoDiff(name='y', val=3)
u = AutoDiffVector((f1, f2))
v = AutoDiffVector((-f2, f1))
q = [2, 0]
t = [4, 4]
np.testing.assert_array_equal((u * 3).val,
[-3, 9]), 'Multiplication failed'
J, order = (u * 3).get_jacobian()
np.testing.assert_array_equal(J, [[3, 0], [0, 3]]), "Multiplication failed"
np.testing.assert_array_equal((-4 * u).val,
[4, -12]), 'Multiplication failed'
np.testing.assert_array_equal((u * q).val,
[-2, 0]), 'Multiplication failed'
np.testing.assert_array_equal((q * u).val,
[-2, 0]), 'Multiplication failed'
J, order = (u * t).get_jacobian()
np.testing.assert_array_equal(J, [[4, 0], [0, 4]]), "Multiplication failed"
J, order = (u * q).get_jacobian()
np.testing.assert_array_equal(J, [[2, 0], [0, 0]]), 'Multiplication failed'
J, order = (q * u).get_jacobian()
np.testing.assert_array_equal(J, [[2, 0], [0, 0]]), 'Multiplication failed'
J, order = (u * v).get_jacobian()
np.testing.assert_array_equal(J,
[[-3, 1], [3, -1]]), 'Multiplication failed'
J, order = (v * u).get_jacobian()
np.testing.assert_array_equal(J,
[[-3, 1], [3, -1]]), 'Multiplication failed'
def test_csc():
f1 = AutoDiff(name='x', val=-2)
f2 = AutoDiff(name='y', val=np.pi / 8)
u = AutoDiffVector((f1, f2))
np.testing.assert_array_almost_equal(ad.csc(u).val, [-1.09975, 2.613126]), 'Cosecant failed'
J, order = (ad.csc(u)).get_jacobian()
np.testing.assert_array_almost_equal(J, [[0.5033, 0], [0, -6.3086]], decimal=4), 'Cosecant failed'
def test_eq():
x = AutoDiff(name='x', val=2)
y = AutoDiff(name='x', val=2)
assert 2 == x, "Equals failed"
assert x == 2, "Equals failed"
assert x == y, "Equals failed"
assert y == x, "Equals failed"
def test_str():
f1 = AutoDiff(name='x', val=3.3333)
f2 = AutoDiff(name='y', val=-5.888)
u = AutoDiffVector((f1, f2))
assert str(
u
) == "[{'val': 3.3333, 'd_x': 1},{'val': -5.888, 'd_y': 1}]", "Str failed"
def test_or():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=5)
u = AutoDiffVector((f1, f2))
y = AutoDiffVector((f2, 8))
assert u == [3, 5] or y == [0, 0], "Or failed"
assert u == [3, 5] or y == [5, 8], "Or failed"
def test_exponentiation():
x = AutoDiff(name='x', val=3)
y = AutoDiff(name='y', val=0)
z = AutoDiff(name='z', val=-2)
q = AutoDiff(name='b0', val="string")
r = AutoDiff(name='r', val=5)
assert (x**2) == 9, "Exponentiation failed"
assert (x**2).trace['d_x'] == 6, "Exponentiation failed"
assert (2**x) == 8, "Exponentiation failed"
assert np.allclose((2**x).trace['d_x'], 5.545177444479562,
atol=1e-12) is True, "Exponentiation failed"
assert (x**0) == 1, "Exponentiation failed"
assert (x**0).trace['d_x'] == 0, "Exponentiation failed"
assert (x**-2) == (1 / 9), "Exponentiation failed"
assert (x**-2).trace['d_x'] == -2 / (3**3), "Exponentiation failed"
assert (z**2) == 4, "Exponentiation failed"
assert (z**2).trace['d_z'] == -4, "Exponentiation failed"
assert (z**3) == -8, "Exponentiation failed"
assert (z**3).trace['d_z'] == 12, "Exponentiation failed"
assert (y**2) == 0, "Exponentiation failed"
assert (y**2).trace['d_y'] == 0, "Exponentiation failed"
assert (x**x) == 27, "Exponentiation failed"
assert (r**x) == 125, "Exponentiation failed"
try:
(q**5)
except TypeError:
print("Caught error as expected")
def test_bool():
f1 = AutoDiff(name='x', val=0)
f2 = AutoDiff(name='y', val=0)
u = AutoDiffVector((f1, f2))
try:
bool(u)
except TypeError:
print("Caught error as expected")
def test_shift():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=4)
u = AutoDiffVector((f1, f2))
np.testing.assert_array_equal(u >> 2, [16, 32]), "Shift failed"
np.testing.assert_array_equal(u << 2, [12, 16]), "Shift failed"
np.testing.assert_array_equal(3 >> u, [24, 32]), "Shift failed"
np.testing.assert_array_equal(3 << u, [24, 48]), "Shift failed"
def test_contains():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=4)
u = AutoDiffVector((f1, f2))
try:
assert 2 in u
except NotImplementedError:
print("Caught error as expected")
def test_ne():
x = AutoDiff(name='x', val=10)
y = AutoDiff(name='y', val=100)
q = AutoDiff(name='b0', val="string")
assert x != 11, "Not equal failed"
assert 11 != x, "Not equal failed"
assert x != y, "Not equal failed"
assert 12 != q, "Not equal failed"
def test_le():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=5)
u = AutoDiffVector((f1, f2))
y = AutoDiffVector((f2, 8))
assert [3, 5] <= u, "Less than failed"
assert u <= [100, 100], "Less than failed"
assert u <= y, "Less than failed"
def test_lt():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=5)
u = AutoDiffVector((f1, f2))
y = AutoDiffVector((f2, 8))
assert [0, 0] < u, "Less than failed"
assert u < [100, 100], "Less than failed"
assert u < y, "Less than failed"
def test_gt():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=5)
u = AutoDiffVector((f1, f2))
y = AutoDiffVector((f2, 8))
assert u > [0, 0], "Greater than failed"
assert [100, 100] > u, "Greater than failed"
assert y > u, "Greater than failed"
def test_ge():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=5)
u = AutoDiffVector((f1, f2))
y = AutoDiffVector((f2, 8))
assert u >= [0, 0], "Greater than or equal to failed"
assert u >= [3, 5], "Greater than or equal to failed"
assert [100, 100] >= u, "Greater than or equal to failed"
assert y >= u, "Greater than or equal to failed"
def test_instantiation_zero():
f1 = AutoDiff(name='x', val=0)
f2 = AutoDiff(name='y', val=0)
u = AutoDiffVector((f1, f2))
np.testing.assert_array_equal(u.val,
[0, 0]), "Positive instantiation failed"
J, order = u.get_jacobian()
np.testing.assert_array_equal(
J, [[1, 0], [0, 1]]), "Positive instantiation failed"
def test_get_gradient():
x = AutoDiff(name='x', val=3)
grad1, varnames = x.get_gradient()
grad2, _ = (8 * x).get_gradient()
grad3, _ = x.gradient
assert np.allclose(grad1, np.array([1.])), "Get gradient failed"
assert np.allclose(grad2, np.array([8.])), "Get gradient failed"
assert np.allclose(grad3, np.array([1.])), "Get gradient property failed"
def test_ne():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=5)
u = AutoDiffVector((f1, f2))
y = AutoDiffVector((f2, 8))
q = AutoDiff(name='b0', val="string")
assert u != 11, "Not equal failed"
assert 11 != u, "Not equal failed"
assert u != y, "Not equal failed"
assert y != q, "Not equal failed"
def test_xor():
x = AutoDiff(name='x', val=0)
y = AutoDiff(name='y', val=1)
assert (x ^ y) == 1, "Xor failed"
assert (x ^ 1) == 1, "Xor failed"
assert (1 ^ x) == 1, "Xor failed"
try:
assert x ^ x == 1
except AssertionError:
print("Caught Error as expected")
def test_sin():
f1 = AutoDiff(name='x', val=0)
f2 = AutoDiff(name='y', val=np.pi/2)
u = AutoDiffVector((f1, f2))
v = AutoDiffVector([0, np.pi/2])
np.testing.assert_array_almost_equal(ad.sin(u), [0, 1]), 'Sine failed'
J, order = (ad.sin(u)).get_jacobian()
np.testing.assert_array_almost_equal(J, [[1, 0], [0, 0]]), 'Sine failed'
np.testing.assert_array_almost_equal(ad.sin(v), [0, 1]), 'Sine failed'
J, order = (ad.sin(v)).get_jacobian()
np.testing.assert_array_almost_equal(J, [[0], [0]]), 'Sine failed'
def test_xor():
f1 = AutoDiff(name='x', val=3)
f2 = AutoDiff(name='y', val=5)
u = AutoDiffVector((f1, f2))
y = AutoDiffVector((f2, 8))
np.testing.assert_array_equal(u ^ y, [6, 13]), "Xor failed"
np.testing.assert_array_equal(y ^ u, [6, 13]), "Xor failed"
try:
assert (u ^ y) == 1, "Xor failed"
except ValueError:
print("Caught error as expected")
def test_lt():
x = AutoDiff(name='x', val=10)
y = AutoDiff(name='y', val=100)
q = AutoDiff(name='b0', val="string")
assert 2 < x, "Less than failed"
assert x < 20, "Less than failed"
assert x < y, "Less than failed"
try:
(12 < q)
except TypeError:
print("Caught error as expected")
def test_gt():
x = AutoDiff(name='x', val=10)
y = AutoDiff(name='y', val=100)
q = AutoDiff(name='b0', val="string")
assert x > 2, "Greater than failed"
assert 20 > x, "Greater than failed"
assert y > x, "Greater than failed"
try:
(12 > q)
except TypeError:
print("Caught error as expected")
def test_double_instantiation():
try:
AutoDiffVector(name='x', val=3, trace=3)
except TypeError:
print("Caught error as expected")
f1 = AutoDiff(name='x', val=1)
f2 = AutoDiff(name='y', val=3)
try:
AutoDiffVector((f1, f2), f1)
except TypeError:
print("Caught error as expected")
