def test_ge():
x = AutoDiff(2.0, 10.0)
y = AutoDiff(2.0, 8.0)
assert y >= x
x = AutoDiff([1.0, 2.0], 10.0)
y = AutoDiff([2.0, 2.0], 10.0)
assert np.array_equal(y >= x, np.array([True, True]))
x = AutoDiff([3.0, 1.0], 3.0)
y = AutoDiff([2.0, 2.0], 10.0)
assert np.array_equal(x >= y, np.array([True, False]))
x = AutoDiff(1.0, 10.0)
assert x >= 0
# Test for raising TypeError
with pytest.raises(TypeError):
x = AutoDiff([1.0, 2.0], 10.0)
y = AutoDiff([2.0], 10.0)
x >= y
# Test for raising TypeError
with pytest.raises(TypeError):
x = AutoDiff([1.0, 2.0], 10.0)
y = 2
x >= y
def test_le():
x = AutoDiff(1.0, 10.0)
y = AutoDiff(2.0, 10.0)
assert x <= y
x = AutoDiff(2.0, 10.0)
y = AutoDiff(2.0, 10.0)
assert x <= y
x = AutoDiff([1.0, 2.0], 10.0)
y = AutoDiff([2.0, 2.0], 10.0)
assert np.array_equal(x <= y, np.array([True, True]))
x = AutoDiff(1.0, 10.0)
assert x < 2
# Test for raising TypeError
with pytest.raises(TypeError):
x = AutoDiff([1.0, 2.0], 10.0)
y = AutoDiff([2.0], 10.0)
x <= y
# Test for raising TypeError
with pytest.raises(TypeError):
x = AutoDiff([1.0, 2.0], 10.0)
y = 2
x <= y
def test_rmul():
x = AutoDiff([8, 4], name='x')
y = AutoDiff([9, 12], name='y')
f1 = y * x
assert np.array_equal(f1.val, np.array([72, 48]))
assert np.array_equal(f1.der["x"], np.array([9, 12]))
assert np.array_equal(f1.der["y"], np.array([8, 4]))
def test_equal():
x = AutoDiff(2.0, 10.0, "x")
y = AutoDiff(2.0, 10.0, "y")
assert x == y
x = AutoDiff(2.0, name="x")
y = 2
assert x == y
def test_sin():
x = AutoDiff(2, name="x")
x1 = AutoDiff.sin(x)
assert x1.val == [np.sin(2)]
assert x1.der['x'] == [np.cos(2)]
x = AutoDiff(2.0, 1.0, "x")
f1 = AutoDiff.sin(3 * x + 2)
assert f1.val == np.sin(8.0)
assert f1.der["x"] == 3 * np.cos(8.0)
def test_exp_base():
x = AutoDiff(5.0, 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.exp_base(f1, 4)
assert f2.val == 4**17
assert f2.der["x"] == (4**17) * 3 * np.log(4)
x = AutoDiff([-5.0, -1], 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.exp_base(f1, 4)
assert np.array_equal(f2.val, np.array([4**(-13), 0.25]))
assert np.array_equal(
f2.der["x"], np.array([4**(-13) * np.log(4) * 3,
0.25 * np.log(4) * 3]))
def test_truediv():
x = AutoDiff(4, 3, "x")
f1 = x / 2.0
assert f1.val == 2.0
assert f1.der["x"] == 1.5
x = AutoDiff(2, name="x")
f2 = x / x
assert f2.val == [1]
assert f2.der['x'] == [0]
x = AutoDiff([16, 0], name="x")
y = AutoDiff([8, -1], name="y")
f3 = x / y
assert np.array_equal(f3.val, np.array([2, 0]))
assert np.array_equal(f3.der['x'], np.array([0.125, -1.0]))
assert np.array_equal(f3.der['y'], np.array([-0.25, -0.0]))
def test_vector():
# handling multiple input; each input is a vector; multiple functions
x = AutoDiff([3, 1, 9], name='x')
y = AutoDiff([5, 2, 4], name='y')
f1 = (2 * x ** (-2)) + (3 * y ** 4)
f2 = AutoDiff.cos(x + (4 * y ** 2))
v = Vector_Forward([f1, f2])
assert np.array_equal(v.val()[0], np.array([16877/9, np.cos(103)]))
assert np.array_equal(v.val()[1], np.array([50, np.cos(17)]))
assert np.array_equal(v.val()[2], np.array([62210/81, np.cos(73)]))
index_x = v.jacobian()[0].index("x")
index_y = v.jacobian()[0].index("y")
assert np.array_equal(v.jacobian()[1][0][:, index_x], np.array([-4/27, -np.sin(103)]))
assert np.array_equal(v.jacobian()[1][1][:, index_x], np.array([-4, -np.sin(17)]))
assert np.array_equal(v.jacobian()[1][2][:, index_x], np.array([-4/729, -np.sin(73)]))
assert np.array_equal(v.jacobian()[1][0][:, index_y], np.array([12*(5**3), -40*np.sin(103)]))
assert np.array_equal(v.jacobian()[1][1][:, index_y], np.array([96, -16*np.sin(17)]))
assert np.array_equal(v.jacobian()[1][2][:, index_y], np.array([12*(4**3), -32*np.sin(73)]))
def test_sub():
x = AutoDiff(5, 10, "x")
f1 = x - 100
assert f1.val == -95
assert f1.der["x"] == 10
x = AutoDiff(5, [10, 11], "x")
f1 = x - 100
assert f1.val == -95
assert np.array_equal(f1.der["x"], np.array([10, 11]))
x = AutoDiff([8, 4], [10, 11], 'x')
y = AutoDiff([9, 12], [20, 33], 'y')
f1 = x - y
assert np.array_equal(f1.val, np.array([-1, -8]))
assert np.array_equal(f1.der["x"], np.array([10, 11]))
assert np.array_equal(f1.der["y"], np.array([-20, -33]))
# Test TypeError
with pytest.raises(TypeError):
x = AutoDiff(5, 10, "x")
f1 = x - 'InvalidInput'
def test_add():
x = AutoDiff(5, 10, "x")
f1 = x + 100
assert f1.val == 105
assert f1.der["x"] == 10
x = AutoDiff(5, [10, 11], "x")
f1 = x + 100
assert f1.val == 105
assert np.array_equal(f1.der["x"], np.array([10, 11]))
x = AutoDiff([8, 4], [10, 11], 'x')
y = AutoDiff([9, 12], [20, 33], 'y')
f1 = x + y
assert np.array_equal(f1.val, np.array([17, 16]))
assert np.array_equal(f1.der["x"], np.array([10, 11]))
assert np.array_equal(f1.der["y"], np.array([20, 33]))
# Test TypeError
with pytest.raises(TypeError):
x = AutoDiff(5, 10, "x")
f1 = x + 'InvalidInput'
def test_unequal():
x = AutoDiff(4.0, 10.0)
y = AutoDiff(2.0, 10.0)
assert x != y
x = AutoDiff(4.0, 10.0)
assert x != 2
x = AutoDiff([2.0, 2.0], 10.0)
y = AutoDiff(2.0, 10.0)
assert x != y
x = AutoDiff([1.0, 2.0], 10.0)
y = AutoDiff([2.0, 3, 4], 10.0)
assert x != y
def test_complicated_func():
tol = 1e-4
x = AutoDiff(2.0, name="x")
f1 = AutoDiff.sin((AutoDiff.cos(x)**2.0 + x**2.0)**0.5)
assert abs(f1.val - 0.890643) < tol
assert abs(f1.der["x"] - (-0.529395)) < tol
x = AutoDiff([1.0, 3.0, 5.0, 7.0], name="x")
f2 = AutoDiff.sin(AutoDiff.ln(x) + (3 * x**2) + (2 * x) + 7)
assert np.array_equal(
f2.val,
np.array([
np.sin(12),
np.sin(40 + np.log(3)),
np.sin(92 + np.log(5)),
np.sin(168 + np.log(7))
]))
assert np.array_equal(
f2.der["x"],
np.array([
9 * np.cos(12), 61 / 3 * np.cos(40 + np.log(3)),
161 / 5 * np.cos(92 + np.log(5)), 309 / 7 * np.cos(168 + np.log(7))
]))
x = AutoDiff([-1.0, -3.0, -5.0, -7.0, 0.1], name="x")
f3 = AutoDiff.logistic(AutoDiff.tan(x) + (3 * x**(-2)) + (2 * x) + 7)
assert np.less(
abs(f3.val - np.array([
1 / (1 + np.exp(np.tan(1) - 8)), 1 /
(1 + np.exp(np.tan(3) - 4 / 3)), 1 /
(1 + np.exp(np.tan(5) + 72 / 25)), 1 /
(1 + np.exp(np.tan(7) + 340 / 49)), 1
])),
np.ones((5, 1)) * tol).all()
assert np.less(
abs(f3.der["x"] -
np.array([0.018135, 0.49104, 3.40145666, 0.001531, 0])),
np.ones((5, 1)) * tol).all()
def test_mul():
x = AutoDiff(5, 30, "x")
f1 = x * 5
assert f1.val == 25
assert f1.der["x"] == 150
x = AutoDiff(5, 15, "x")
y = AutoDiff(2, 3, "y")
result = x * y
assert result.val == 10
assert result.der["x"] == 30
assert result.der["y"] == 15
x = AutoDiff([8, 4], name='x')
y = AutoDiff([9, 12], name='y')
f1 = x * y
assert np.array_equal(f1.val, np.array([72, 48]))
assert np.array_equal(f1.der["x"], np.array([9, 12]))
assert np.array_equal(f1.der["y"], np.array([8, 4]))
# Test TypeError
with pytest.raises(TypeError):
x = AutoDiff(5, 10, "x")
f1 = x * 'InvalidInput'
def test_logistic():
tol = 1e-6
x = AutoDiff(2, name="x")
f = AutoDiff.logistic(x)
assert f.val == [1 / (1 + np.exp(-2))]
assert abs(f.der['x'] - np.exp(2) / ((1 + np.exp(2))**2)) < tol
def test_pow():
x = AutoDiff(2, 5, "x")
f1 = x**2
assert f1.val == 4.0
assert f1.der["x"] == 20.0
x = AutoDiff(2, 1, "x")
f2 = x**x
assert f2.val == 4
assert f2.der["x"] == 4.0 * (np.log(x.val) + 1)
x = AutoDiff(2, name="x")
y = AutoDiff(4, name='y')
f2 = x**y
assert f2.val == 16
assert f2.der["x"] == 32
assert f2.der["y"] == 16 * np.log(2)
x = AutoDiff(3, name='x')
y = AutoDiff(4, name='y')
f3 = (x**2) * (y**3)
assert np.array_equal(f3.val, np.array([576]))
assert np.array_equal(f3.der['x'], np.array([384]))
assert np.array_equal(f3.der['y'], np.array([432]))
tol = 1e-6
x = AutoDiff([3, 2], name='x')
y = AutoDiff([-2, -5], name='y')
f3 = (x**y)
assert np.array_equal(f3.val, np.array([1 / 9, 2**(-5)]))
assert np.array_equal(f3.der['x'],
np.array([-2 * (3)**(-3), (-5) * (2)**(-6)]))
assert np.less(
abs(f3.der['y'] - np.array([1 / 9 * np.log(3), 2**(-5) * np.log(2)])),
np.ones((2, 1)) * tol).all()
tol = 1e-6
x = AutoDiff([3, 2], name='x')
y = AutoDiff([-2], name='y')
f3 = (x**y)
assert np.array_equal(f3.val, np.array([1 / 9, 2**(-2)]))
assert np.array_equal(f3.der['x'],
np.array([-2 * (3)**(-3), (-2) * (2)**(-3)]))
assert np.less(
abs(f3.der['y'] - np.array([1 / 9 * np.log(3), 2**(-2) * np.log(2)])),
np.ones((2, 1)) * tol).all()
x = AutoDiff([8, 4], name='x')
y = AutoDiff([9, 12], name='y')
f4 = (x**2) * (y**3)
assert np.array_equal(f4.val, np.array([46656, 27648]))
assert np.array_equal(f4.der['x'], np.array([11664, 13824]))
assert np.array_equal(f4.der['y'], np.array([15552, 6912]))
# Test TypeError
with pytest.raises(TypeError):
x = AutoDiff(5, 10, "x")
f1 = x**'InvalidInput'
def test_exp():
x = AutoDiff(5.0, 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.exp(f1)
assert f2.val == np.exp(17)
assert f2.der["x"] == 3 * np.exp(17)
def test_log():
x = AutoDiff(5.0, 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.log(f1, 4)
assert f2.val == np.log(17) / np.log(4)
assert f2.der["x"] == 3 / (np.log(4) * (17))
def test_tanh():
x = AutoDiff(5.0, 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.tanh(f1)
assert f2.val == np.tanh(17)
assert f2.der["x"] == 3 / ((np.cosh(17))**2)
def test_rsub():
x = AutoDiff(5, 1, "x")
f1 = 100 - x
assert f1.val == 95
assert f1.der["x"] == -1
def test_rpow():
x = AutoDiff(2, name="x")
f1 = 2**x
assert f1.val == 4.0
assert f1.der["x"] == 4.0 * np.log(2)
x = AutoDiff(2, name="x")
y = AutoDiff(5, name="y")
# use ** for two AutoDiff
f2 = x.__rpow__(y)
assert f2.val == 25.0
assert f2.der["x"] == 25.0 * np.log(5)
assert f2.der["y"] == 10.0
x = AutoDiff([3, 2], name='x')
y = AutoDiff([2], name='y')
# use ** for two AutoDiff
f3 = x.__rpow__(y)
assert np.array_equal(f3.val, np.array([(2)**3, 4]))
assert np.array_equal(f3.der['x'],
np.array([(2)**3 * np.log(2), 4 * np.log(2)]))
assert np.array_equal(f3.der['y'], np.array([12, 4]))
# Test TypeError
with pytest.raises(TypeError):
x = AutoDiff(5, 10, "x")
f1 = 'InvalidInput'**x
def test_rtruediv():
x_val = 2.0
x = AutoDiff(x_val, name="x")
f1 = 2.0 / x
assert f1.val == 2.0 / x_val
assert f1.der["x"] == -0.5
def test_arccos():
tol = 1e-6
x = AutoDiff(0.5, name="x")
f = AutoDiff.arccos(x)
assert f.val == np.arccos(0.5)
assert abs(f.der["x"] + 1.1547) < tol
def test_sqrt():
x = AutoDiff(5.0, 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.sqrt(f1)
assert f2.val == (17)**0.5
assert f2.der["x"] == 3 / (2 * (17**0.5))
def test_arctan():
tol = 1e-6
x = AutoDiff(0.5, name="x")
f = AutoDiff.arctan(x)
assert f.val == np.arctan(0.5)
assert abs(f.der["x"] - 0.8) < tol
def test_ln():
x = AutoDiff(5.0, 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.ln(f1)
assert f2.val == np.log(17)
assert f2.der["x"] == (1 / 17) * 3
def test_radd():
x = AutoDiff(3, 10, "x")
f1 = 100 + x
assert f1.val == 103
assert f1.der["x"] == 10
def test_neg():
x = AutoDiff(2.0, 10.0, "x")
f1 = -x
assert f1.val == -2.0
assert f1.der["x"] == -10.0
def test_cosh():
x = AutoDiff(5.0, 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.cosh(f1)
assert f2.val == np.cosh(17)
assert f2.der["x"] == 3 * np.sinh(17)
def test_init_fail():
with pytest.raises(TypeError):
x = AutoDiff('InvalidInput')