def test_logsqrt():
x = ad.AutoDiff(2)
func = ad.sqrt(ad.log(x))
assert (func.val, func.der,
func.Jacobian()) == (np.sqrt(np.log(2)),
.25 * (1 / (np.sqrt(np.log(2)))),
.25 * (1 / (np.sqrt(np.log(2)))))
def test_trig2():
x = ad.AutoDiff(2)
func = ad.sin(x) + 2 * ad.cosh(x) + 3 * ad.atan(x**2)
assert (func.val, func.der,
func.Jacobian()) == (np.sin(2) + 2 * np.cosh(2) + 3 * np.arctan(4),
np.cos(2) + 2 * np.sinh(2) + 12 / 17,
np.cos(2) + 2 * np.sinh(2) + 12 / 17)
def test_logistic():
x = ad.AutoDiff(2)
func = ad.logistic(x)
assert (func.val,
func.der, func.Jacobian()) == (np.exp(2) / (np.exp(2) + 1),
np.exp(2) / ((np.exp(2) + 1)**2),
np.exp(2) / ((np.exp(2) + 1)**2))
def test_trig3():
x = ad.AutoDiff(1)
func = ad.tan(x) - ad.asin((x / 2)) + ad.sinh((6 / x))
assert (func.val, func.der,
func.Jacobian()) == (np.tan(1) - np.arcsin((1 / 2)) + np.sinh(
(6 / 1)), 1 / (np.cos(1)**2) - .5 / np.sqrt(.75) -
6 * np.cosh(6), 1 / (np.cos(1)**2) -
.5 / np.sqrt(.75) - 6 * np.cosh(6))
def test_trig4():
x = ad.AutoDiff(.5)
func = ad.acos(x) * ad.tanh(x)
assert np.isclose(func.val, np.arccos(.5) * np.tanh(.5))
assert np.isclose(
func.der,
np.arccos(.5) / (np.cosh(.5)**2) - np.tanh(.5) / (np.sqrt(.75)))
assert np.isclose(
func.Jacobian(),
np.arccos(.5) / (np.cosh(.5)**2) - np.tanh(.5) / (np.sqrt(.75)))
def __init__(self, *args, **kwargs):
"""Instantiates multiple AutoDiff objects
INPUTS
=======
User defined variables and assigned values
(for example, you might input all of the variables in a multivariate function)
RETURNS
========
Returns len(kwargs) number of AutoDiff class objects with an associated derivative (seed) as an np.array
NOTE:
========
This class acts as a helper function to allow the user to create multiple
AutoDiff objects conveniently (instead of manually creating each AutoDiff object)
These multiple AutoDiff objects may be useful in the evaluation of a multivariate function
EXAMPLES
=========
>>> X,Y = Multi_AutoDiff_Creator(X = 2, Y = 4).Vars
>>> X.val
2
>>> X.der
array([1., 0.])
>>> Y.val
4
>>> Y.der
array([0., 1.])
"""
deri = np.identity(len(kwargs))
i = 0
self.Vars = []
for key, value in kwargs.items():
self.Vars.append(ad.AutoDiff(value, deri[i]))
i += 1
def __init__(self, Vals):
"""Instantiates multiple AutoDiff objects (for use in multivariate functions)
INPUTS
=======
User defined variables and assigned values
(for example, you might input all of the variables in a multivariate function)
RETURNS
========
Returns len(kwargs) number of AutoDiff class objects with an associated derivative (seed) as an np.array
NOTE:
========
This class acts as a helper function to create multiple AutoDiff objects conveniently
These multiple AutoDiff objects may be useful in the evaluation of a multivariate function
"""
deri = np.identity(len(Vals))
self.Vars = []
for i in range(len(Vals)):
self.Vars.append(ad.AutoDiff(Vals[i], deri[i]))
def test_exp():
x = ad.AutoDiff(3)
func = ad.exp(x)
assert (func.val, func.der, func.Jacobian()) == (np.exp(3), np.exp(3),
np.exp(3))
def test_revpower():
x = ad.AutoDiff(2)
func = 2 - 2**x
assert (func.val, func.der, func.Jacobian()) == (-2, -4 * np.log(2),
-4 * np.log(2))
def test_trig1():
x = ad.AutoDiff(4)
func = ad.cos(x) - 1
assert (func.val, func.der, func.Jacobian()) == (np.cos(4) - 1, -np.sin(4),
-np.sin(4))
def test_powers():
x = ad.AutoDiff(2)
func = x**x
assert (func.val, func.der, func.Jacobian()) == (4, 4 * (np.log(2) + 1),
4 * (np.log(2) + 1))
def test_log_base10():
x = ad.AutoDiff(2)
func = ad.log(x, 10)
assert np.isclose(func.val, np.log10(2))
assert np.isclose(func.der, 1 / (np.log(10) * 2))
assert np.isclose(func.Jacobian(), 1 / (np.log(10) * 2))
def test_jacobian():
x = ad.AutoDiff(5, np.array([1, 0]))
y = ad.AutoDiff(3, np.array([0, 1]))
func = 5 * x + 3 * y
assert np.all(func.Jacobian() == [5, 3])
def test_submulti():
x = ad.AutoDiff(3)
func = 1 + x * 5 - 2 * x
assert (func.val, func.der, func.Jacobian()) == (10, 3, 3)
def test_addnegexp():
x = ad.AutoDiff(5)
func = -x + 2 * x**2 + 2
assert (func.val, func.der, func.Jacobian()) == (47, 19, 19)
def test_ne():
x = ad.AutoDiff(20, 1)
func1 = x / 2 - 25
func2 = x / 3 - 25
assert (func1.val, func1.der, func1.Jacobian()) != (func2.val, func2.der,
func2.Jacobian())
def test_eq():
x = ad.AutoDiff(20, 1)
func1 = x / 2 - 25
func2 = func1
assert (func1.val, func1.der, func1.Jacobian()) == (func2.val, func2.der,
func2.Jacobian())
def test_str():
x = ad.AutoDiff(5)
func = 1 / x
assert str(func) == "f(x) = 0.20, f'(x) = -0.04"
