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_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_cos():
x = AutoDiff(5.0, 1.0, "x")
f1 = 3 * x + 2
f2 = AutoDiff.cos(f1)
assert f2.val == np.cos(17)
assert f2.der["x"] == -3 * np.sin(17)