def test_jacobian_exception():
x = AD.AD(3.0)
y = AD.AD(2.0, [0.0, 1.0])
with pytest.raises(Exception, match="Incorrect dimension"):
assert AD.AD.get_jacobian([x, y])
with pytest.raises(TypeError, match="Invalid input type: not a function"):
assert AD.AD.get_jacobian([x, 3.0])
with pytest.raises(Exception, match="Empty list of functions"):
assert AD.AD.get_jacobian([])
def test_jacobian():
x = AD.AD(3.0, [1.0, 0.0, 0.0])
y = AD.AD(2.0, [0.0, 1.0, 0.0])
z = AD.AD(1.0, [0.0, 0.0, 1.0])
vals, ders = AD.AD.get_jacobian([x * y, x + y, z, unary.sin(x)])
test_jac = np.array([[2.0, 3.0, 0.0], [1.0, 1.0, 0.0], [0.0, 0.0, 1.0],
[np.cos(3.0), 0.0, 0.0]])
assert (vals[0] == 6.0)
assert (vals[2] == 1.0)
assert (np.array_equal(ders, test_jac))
def test_add_radd_mult_rmult():
x = AD.AD(2.0)
alpha = 2.0
beta = 3.0
functions = []
functions.append(('alpha * x + beta', alpha * x + beta))
functions.append(('x * alpha + beta', x * alpha + beta))
functions.append(('beta + alpha * x', beta + alpha * x))
functions.append(('beta + x * alpha', beta + x * alpha))
for (name, val) in functions:
assert (val.val == 7)
assert (val.der == 2)
def tanh(x):
""" Calculate hyperbolic tangent of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or float
RETURNS
========
result: hyperbolic tangent of x
EXAMPLES
=========
>>> x = ad.AD(2.0, [1.0,0.0])
>>> print(tanh(x))
AD(0.9640275800758169, [0.07065082 0. ])
"""
try:
return ad.AD(np.tanh(x.val), x.der/np.cosh(x.val)**2)
except AttributeError:
return np.tanh(x)
def arctan(x):
""" Calculate inverse tangent of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or float
RETURNS
========
result: inverse tangent of x
EXAMPLES
=========
>>> x = ad.AD(2)
>>> print(arctan(x))
AD(1.1071487177940906, [0.2])
"""
try:
return ad.AD(np.arctan(x.val), x.der/(1+x.val**2))
except AttributeError:
return np.arctan(x)
def logistic(x):
""" Return the logistic of an AD object, integer, or float
INPUTS
=======
x: the AD object, int, or float
RETURNS
========
result: 1/(1+e^(-x))
EXAMPLES
=========
>>> x = ad.AD(4.0)
>>> print(logistic(x))
AD(0.9820137900379085, [0.0183095])
"""
try:
return ad.AD(1/(1+np.exp(-x.val)), np.exp(-x.val)*x.der/(1+np.exp(-x.val))**2)
except AttributeError:
return 1/(1+np.exp(-x))
def log(x, base):
""" Calculate the logarithm of an AD object, integer, or float of given base
INPUTS
=======
x: the AD object, int, or float
base: logarithm base
RETURNS
========
result: given base logarithm of x
EXAMPLES
=========
>>> x = ad.AD(4.0)
>>> print(log(x,2))
AD(2.0, [0.36067376])
"""
try:
return ad.AD(math.log(x.val, base), x.der/(x.val*np.log(base)))
except AttributeError:
return math.log(x,base)
def ln(x):
""" Calculate the natural base logarithm of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or float
RETURNS
========
result: natural logarithm of x
EXAMPLES
=========
>>> x = ad.AD(2.0, [1.0,0.0])
>>> y = ad.AD(3.0, [0.0,1.0])
>>> print(ln(x*y))
AD(1.791759469228055, [0.5 0.33333333])
"""
try:
return ad.AD(np.log(x.val), x.der/x.val)
except AttributeError:
return np.log(x)
def cosh(x):
""" Calculate hyperbolic cosine of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or float
RETURNS
========
result: hyperbolic cosine of x
EXAMPLES
=========
>>> x = ad.AD(2.0, [1.0,0.0])
>>> y = ad.AD(3.0, [0.0,1.0])
>>> print(cosh(x*y))
AD(201.7156361224559, [605.13947211 403.42631474])
"""
try:
return ad.AD(np.cosh(x.val), x.der*np.sinh(x.val))
except AttributeError:
return np.cosh(x)
def sinh(x):
""" Calculate hyperbolic sine of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or float
RETURNS
========
result: hyperbolic sine of x
EXAMPLES
=========
>>> x = ad.AD(2.0, [1.0,0.0])
>>> y = ad.AD(3.0, [0.0,1.0])
>>> print(sinh(x+y))
AD(74.20321057778875, [74.20994852 74.20994852])
"""
try:
return ad.AD(np.sinh(x.val), x.der*np.cosh(x.val))
except AttributeError:
return np.sinh(x)
def sin(x):
""" Calculate sine of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or float
RETURNS
========
result: sine of x
EXAMPLES
=========
>>> x = ad.AD(2.0, [1.0,0.0])
>>> y = ad.AD(3.0, [0.0,1.0])
>>> print(sin(x*y))
AD(-0.27941549819892586, [2.88051086 1.92034057])
"""
try:
return ad.AD(np.sin(x.val), x.der*np.cos(x.val))
except AttributeError:
return np.sin(x)
def cos(x):
""" Calculate cosine of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or float
RETURNS
========
result: cosine of x
EXAMPLES
=========
>>> x = ad.AD(2.0, [1.0,0.0])
>>> y = ad.AD(3.0, [0.0,1.0])
>>> print(cos(x*y))
AD(0.9601702866503661, [0.83824649 0.558831 ])
"""
try:
return ad.AD(np.cos(x.val), -x.der*np.sin(x.val))
except AttributeError:
return np.cos(x)
def arccos(x):
""" Calculate inverse cosine of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or float
RETURNS
========
result: inverse cosine of x
EXAMPLES
=========
>>> x = ad.AD(0.5)
>>> print(arccos(x))
AD(1.0471975511965976, [-1.15470054])
"""
try:
if x.val<=-1 or x.val>=1:
raise Exception("X out of domain")
return ad.AD(np.arccos(x.val), -x.der/np.sqrt(1-x.val**2))
except AttributeError:
return np.arccos(x)
def exp(x):
""" Calculate the exponential of the input AD object, integer, or float
INPUTS
=======
x: input value, an AD object, int, or flot
RETURNS
========
result: exponential of x
EXAMPLES
=========
>>> x = ad.AD(2.0, [1.0,0.0])
>>> y = ad.AD(3.0, [0.0,1.0])
>>> print(exp(x))
AD(7.38905609893065, [7.3890561 0. ])
>>> print(exp(x*y))
AD(403.4287934927351, [1210.28638048 806.85758699])
"""
try:
return ad.AD(np.exp(x.val), np.exp(x.val)*x.der)
except AttributeError:
return np.exp(x)
def test_add_reg_AD():
x = 2 + AD.AD(1.0)
y = AD.AD(3.0, 1.0)
assert (x == y)
def test_add_AD_reg():
x = AD.AD(2.0) + 3
y = AD.AD(5.0, 1.0)
assert (x == y)
def test_add_AD_AD():
x = AD.AD(2.0) + AD.AD(3.0)
y = AD.AD(5.0, 2.0)
assert (x == y)
def test_identity():
x = AD.AD(3.0)
eq = (2 * x) / (2 * x)
y = AD.AD(1.0, 0.0)
assert (eq == y)
def test_mult_reg_AD():
x = 2 * AD.AD(1.0)
y = AD.AD(2.0, 2.0)
assert (x == y)
def test_invalid_init():
x = AD.AD(3.0)
with pytest.raises(TypeError, match="Invalid input type"):
assert AD.AD(x)
def test_sub_AD_reg():
x = AD.AD(2.0) - 1.0
y = AD.AD(1.0, 1.0)
assert (x == y)
def test_mult_AD_AD():
x = AD.AD(2.0) * AD.AD(1.0)
y = AD.AD(2.0, 3.0)
assert (x == y)
def test_sub_AD_AD():
x = AD.AD(2.0) - AD.AD(1.0)
y = AD.AD(1.0, 0.0)
assert (x == y)
def test_eq():
x = AD.AD(3.0)
y = 3.0
assert (x == y)
def test_sub_reg_AD():
x = 2 - AD.AD(1.0)
y = AD.AD(1.0, -1.0)
assert (x == y)
def test_ne():
x = AD.AD(3.0, [1.0, 0.0])
y = AD.AD(3.0)
assert (x != y)
def test_mult_AD_reg():
x = AD.AD(2.0) * 2.0
y = AD.AD(4.0, 2.0)
assert (x == y)
def test_neg():
x = AD.AD(3.0, [1.0, 0.0])
y = AD.AD(2.0, [0.0, 1.0])
f = -x * y
assert (f.val == -6.0)
assert (np.array_equal(f.der, np.array([-2.0, -3.0])))
def test_truediv_AD_AD():
x = AD.AD(6.0) / AD.AD(3.0)
y = AD.AD(2.0, -1 / 3)
assert (x == y)
def test_linear_combos():
x = AD.AD(3.0)
eq = x**2 + x
y = AD.AD(12.0, 7.0)
assert (eq == y)