def cos(ad):
"""Returns autodiff instance of cos(x)
INPUTS
=======
ad: autodiff instance
RETURNS
========
anew: autodiff instance
returns a new autodiff instance with updated value and derivative(s)
EXAMPLES
=========
>>> from autodiffpy import autodiffmod as ad
>>> from autodiffpy import autodiff_math as admath
>>> x = ad.autodiff('x', 10)
>>> f1 = admath.cos(x)
>>> print(f1.val, f1.der)
[-0.83907153] {'x': array([0.54402111])}
"""
try:
anew = autodiff.autodiff(name=ad.name, val = np.cos(ad.val), der = ad.der)
anew.lparent = ad
anew.function = cos
for key in ad.der:
if ad.der[key].shape == (-1*np.sin(ad.val)).shape:
anew.der[key] = ad.der[key]*-1*np.sin(ad.val)
else:
anew.der[key] = np.dot(-1*np.sin(ad.val), ad.der[key])
ad.back_partial_der = -1*np.sin(ad.val)
return anew
except AttributeError:
raise AttributeError("Error: input should be autodiff instance only.")
def logistic(ad, A=1.0, k=1.0, x0=0.0):
'''Returns autodiff instance of the logistic function of x
INPUTS
==========
ad: autodiff instance
A: maximum value of this logistic function
k: growth rate (steepness) of the logistic function
x0: x-axis location of the logistic function's midpoint
RETURNS
==========
anew: autodiff instance with updated values and derivatives
EXAMPLES
==========
>>> import numpy as np
>>> from autodiffpy import autodiffmod as autodiff
>>> from autodiffpy import autodiff_math as admath
>>> x = autodiff.autodiff('x', 5)
>>> f1 = admath.logistic(x, A=3, k=4, x0=7)
>>> testresult = 3.0/(1 + np.exp(-4*(5-7)))
>>> print(f1.val == [testresult])
[ True]
>>> print(f1.der['x'] == [12*np.exp(-4*(5 - 7))/1.0/((np.exp(-4*(5 - 7)) + 1)**2)])
[ True]
'''
try:
# Create a new autodiff instance with forward result
anew = autodiff.autodiff(name=ad.name, val = (A/1.0/(1.0 + np.exp(-1.0*k*(ad.val - x0)))), der = ad.der)
anew.function = logistic
anew.lparent = ad
for key in ad.der:
if ad.der[key].shape == (A*k*np.exp(-1.0*k*(ad.val - x0))/1.0/((np.exp(-1.0*k*(ad.val - x0)) + 1.0)**2)).shape:
anew.der[key] = ad.der[key]*A*k*np.exp(-1.0*k*(ad.val - x0))/1.0/((np.exp(-1.0*k*(ad.val - x0)) + 1.0)**2)
else:
anew.der[key] = np.dot(A*k*np.exp(-1.0*k*(ad.val - x0))/1.0/((np.exp(-1.0*k*(ad.val - x0)) + 1.0)**2), ad.der[key])
# Update with the backpropagation derivatives
ad.back_partial_der = (A*k)*np.exp(-1.0*k*(ad.val - x0))/1.0/((np.exp(-1.0*k*(ad.val - x0)) + 1.0)**2)
return anew
except AttributeError: #If non-autodiff instance passed
raise AttributeError("Error: input should be autodiff instance only.")
except TypeError:
raise TypeError("Error: input attributes A, k, and x0 should be numbers.")
def tanh(ad):
'''Returns autodiff instance of tanh(x)
INPUTS
==========
ad: autodiff instance
RETURNS
==========
anew: autodiff instance with updated values and derivatives
EXAMPLES
==========
>>> import numpy as np
>>> from autodiffpy import autodiffmod as autodiff
>>> from autodiffpy import autodiff_math as admath
>>> x = autodiff.autodiff('x', 5)
>>> f1 = admath.tanh(x)
>>> print(f1.val == [np.tanh(5)])
[ True]
>>> print(f1.der['x'] == [(1.0/np.cosh(5))**2])
[ True]
'''
try:
# Create a new autodiff instance with forward result
anew = autodiff.autodiff(name=ad.name, val = np.tanh(ad.val), der = ad.der)
anew.function = tanh
anew.lparent = ad
for key in ad.der:
if ad.der[key].shape == ((1.0/np.cosh(ad.val))**2).shape:
anew.der[key] = ad.der[key]*((1.0/np.cosh(ad.val))**2)
else:
anew.der[key] = np.dot(((1.0/np.cosh(ad.val))**2), ad.der[key])
# Update with the backpropagation derivatives
ad.back_partial_der = ((1.0/np.cosh(ad.val))**2)
return anew
except AttributeError: #If non-autodiff instance passed
raise AttributeError("Error: input should be autodiff instance only.")
def log(ad, base = np.e):
'''Returns autodiff instance of log(x)
INPUTS
==========
ad: autodiff instance
base: base of the log. By default, log(x) is natural log.
RETURNS
==========
anew: autodiff instance with updated values and derivatives
EXAMPLES
==========
>>> import numpy as np
>>> from autodiffpy import autodiffmod as autodiff
>>> from autodiffpy import autodiff_math as admath
>>> x = autodiff.autodiff('x', np.exp(2))
>>> f1 = admath.log(x)
>>> print(f1.val)
[2.]
>>> print(f1.der['x'])
[0.13533528]
'''
try:
if np.min(ad.val) <= 0:
raise ValueError('Error: cannot evaluate the log of a nonpositive number.')
anew = autodiff.autodiff(name = ad.name, val = np.log(ad.val)/np.log(base), der = ad.der)
anew.lparent = ad
anew.function = log
for key in ad.der:
if ad.der[key].shape == (ad.val*(np.log(base))).shape:
anew.der[key] = ad.der[key]/(ad.val*(np.log(base)))
else:
anew.der[key] = np.dot(1/(ad.val*(np.log(base))), ad.der[key])
ad.back_partial_der = 1/(ad.val*(np.log(base)))
return anew
except AttributeError:
raise AttributeError("Error: input should be autodiff instance only.")
def sqrt(ad):
"""Returns autodiff instance of sqrt(x)
INPUTS
=======
ad: autodiff instance
RETURNS
========
anew: autodiff instance
returns a new autodiff instance with updated value and derivative(s)
EXAMPLES
=========
>>> from autodiffpy import autodiffmod as autodiff
>>> from autodiffpy import autodiff_math as admath
>>> x = autodiff.autodiff('x', 3)
>>> y = autodiff.autodiff('y', 4)
>>> f1 = admath.sqrt(x*y)
>>> print(f1.val, f1.der)
[3.46410162] {'x': array([0.57735027]), 'y': array([0.4330127])}
"""
try:
# Check that the domain of the square root is valid
if np.min(ad.val) < 0:
raise ValueError('Error: cannot evaluate the square root of a negative number(s).')
# Create a new autodiff instance with forward result
anew = autodiff.autodiff(name = ad.name, val = np.sqrt(ad.val), der = ad.der)
for key in ad.der:
if ad.der[key].shape == (1/(2*np.sqrt(ad.val))).shape:
anew.der[key] = 1/(2*np.sqrt(ad.val))*ad.der[key]
else:
anew.der[key] = np.dot(1/(2*np.sqrt(ad.val)), ad.der[key])
# Update with the backpropagation derivatives
anew.lparent = ad
anew.function = sqrt
ad.back_partial_der = (1/2.0)*((ad.val)**(-1/2.0))
return anew
except AttributeError: #If non-autodiff instance passed
raise AttributeError("Error: input should be autodiff instance only.")
def arcsin(ad):
"""Returns autodiff instance of arcsin(x)
INPUTS
=======
ad: autodiff instance
RETURNS
========
anew: autodiff instance
returns a new autodiff instance with updated value and derivative(s)
EXAMPLES
=========
>>> from autodiffpy import autodiffmod as autodiff
>>> from autodiffpy import autodiff_math as admath
>>> x = autodiff.autodiff('x', 0.1)
>>> f1 = admath.arcsin(x)
>>> print(f1.val, f1.der)
[0.10016742] {'x': array([1.00503782])}
"""
try:
if min(ad.val**2) > 1:
raise ValueError('Error: invalid value encountered while calculating derivatives.')
anew = autodiff.autodiff(name=ad.name, val = np.arcsin(ad.val), der = ad.der)
anew.function = arcsin
anew.lparent = ad
for key in ad.der:
if ad.der[key].shape == (1/np.sqrt(1 - ad.val**2)).shape:
anew.der[key] = 1/np.sqrt(1 - ad.val**2)*ad.der[key]
else:
anew.der[key] = np.dot(1/np.sqrt(1 - ad.val**2), ad.der[key])
ad.back_partial_der = 1/np.sqrt(1 - ad.val**2)
return anew
except AttributeError:
raise AttributeError("Error: input should be autodiff instance only.")
def arctan(ad):
"""Returns autodiff instance of arctan(x)
INPUTS
=======
ad: autodiff instance
RETURNS
========
anew: autodiff instance
returns a new autodiff instance with updated value and derivative(s)
EXAMPLES
=========
>>> from autodiffpy import autodiffmod as autodiff
>>> from autodiffpy import autodiff_math as admath
>>> x = autodiff.autodiff('x', 0.2)
>>> f1 = admath.arctan(x)
>>> print(f1.val, f1.der)
[0.19739556] {'x': array([0.96153846])}
"""
try:
anew = autodiff.autodiff(name=ad.name, val = np.arctan(ad.val), der = ad.der)
anew.function = arctan
anew.lparent = ad
for key in ad.der:
if ad.der[key].shape == (1/(1+ad.val**2)).shape:
anew.der[key] = 1/(1+ad.val**2)*ad.der[key]
else:
anew.der[key] = np.dot(1/(1+ad.val**2), ad.der[key])
ad.back_partial_der = 1/(1+ad.val**2)
return anew
except AttributeError:
raise AttributeError("Error: input should be autodiff instance only.")
def exp(ad):
'''Returns autodiff instance of exp(x)
INPUTS
==========
ad: autodiff instance
RETURNS
==========
anew: autodiff instance with updated values and derivatives
EXAMPLES
==========
>>> import numpy as np
>>> from autodiffpy import autodiffmod as autodiff
>>> from autodiffpy import autodiff_math as admath
>>> x = autodiff.autodiff('x', 10)
>>> f1 = admath.exp(x)
>>> print(f1.val == [np.exp(10)])
[ True]
>>> print(f1.der['x'] == [np.exp(10)])
[ True]
'''
try:
anew = autodiff.autodiff(name=ad.name, val = np.exp(ad.val), der = ad.der)
anew.lparent = ad
anew.function = exp
for key in ad.der:
if ad.der[key].shape == anew.val.shape:
anew.der[key] = ad.der[key]*anew.val
else:
anew.der[key] = np.dot(anew.val, ad.der[key])
ad.back_partial_der = anew.val
return anew
except AttributeError:
raise AttributeError("Error: input should be autodiff instance only.")
def tan(ad):
"""Returns autodiff instance of tan(x)
INPUTS
=======
ad: autodiff instance
RETURNS
========
anew: autodiff instance
returns a new autodiff instance with updated value and derivative(s)
EXAMPLES
=========
>>> from autodiffpy import autodiffmod as autodiff
>>> from autodiffpy import autodiff_math as admath
>>> x = autodiff.autodiff('x', 10)
>>> f1 = admath.tan(x)
>>> print(f1.val, f1.der)
[0.64836083] {'x': array([1.42037176])}
"""
try:
anew = autodiff.autodiff(name=ad.name, val = np.tan(ad.val), der = ad.der)
anew.lparent = ad
anew.function = tan
for key in ad.der:
if ad.der[key].shape == (1/(np.cos(ad.val))**2).shape:
anew.der[key] = 1/(np.cos(ad.val))**2*ad.der[key]
else:
anew.der[key] = np.dot(1/(np.cos(ad.val))**2, ad.der[key])
ad.back_partial_der = 1/(np.cos(ad.val))**2
return anew
except AttributeError:
raise AttributeError("Error: input should be autodiff instance only.")