def tan(x):
"""
Helper function that calculates the sin of a variable or number.
INPUTS:
x : awesomediff.variable object or a number.
OUTPUT:
awesomediff.variable
"""
try:
# Assume object is a variable:
val = x.val
der = x.der
except:
# If not, treat it as a constant.
try:
float(x)
except:
raise ValueError("{} is not a number.".format(x))
val = x
der = 0 # Derivative of a constant is zero.
# Calculate new value an derivative:
new_val = np.tan(val)
new_der = ((1 / np.cos(val))**2) * der
# Return variable with new value an derivative:
return variable(val=new_val, der=new_der)
def arcsin(x):
"""
Helper function that calculates the arcsine of a variable or number.
INPUTS:
x : awesomediff.variable object or a number.
OUTPUT:
awesomediff.variable
"""
try:
# Assume object is a variable:
val = x.val
der = x.der
except:
# If not, treat it as a constant.
try:
float(x)
except:
raise ValueError("{} is not a number.".format(x))
val = x
der = 0 # Derivative of a constant is zero.
# Calculate new value an derivative:
new_val = np.arcsin(val)
if (np.isnan(new_val)):
raise ValueError("Please enter a number on the unit circle.")
# if (np.sqrt(1-val**2)==0):
# new_der = 0
# else:
# new_der = 1/np.sqrt(1-val**2)*der
# print("new val", new_val)
new_der = 1 / np.sqrt(1 - val**2) * der
# Return variable with new value an derivative:
return variable(val=new_val, der=new_der)
def exp(x):
"""
Helper function that calculates the exponential of a variable or number.
INPUTS:
x : AutoDiff.variable object or a number.
OUTPUT:
AutoDiff.variable
"""
try:
new_val = np.exp(x.val)
new_der = np.exp(x.val) * x.der
return variable(val=new_val, der=new_der)
except:
new_val = np.exp(x)
new_der = 0
return variable(val=new_val, der=new_der)
def sqrt(x):
"""
Helper function that calculates the square root of a variable or number.
INPUTS:
x : AutoDiff.variable object or a number.
OUTPUT:
AutoDiff.variable
"""
try:
new_val = np.sqrt(x.val)
new_der = (0.5 / np.sqrt(x.val)) * x.der
return variable(val=new_val, der=new_der)
except:
new_val = np.sqrt(x)
new_der = 0
return variable(val=new_val, der=new_der)
def logb(x, b):
"""
Helper function that calculates the log of a variable or number with any base.
INPUTS:
x : AutoDiff.variable object or a number.
b: a number
OUTPUT:
AutoDiff.variable
"""
try:
new_val = np.log(x.val) / np.log(b)
new_der = (1 / (np.log(b) * x.val)) * x.der
return variable(val=new_val, der=new_der)
except:
new_val = np.log(x) / np.log(b)
new_der = 0
return variable(val=new_val, der=new_der)
def logistic(x, L=1, k=1, x0=1):
"""
Helper function that calculates the logistic of a variable or number.
INPUTS:
x : AutoDiff.variable object or a number.
OUTPUT:
AutoDiff.variable
"""
try:
val = x.val
der = x.der
logistic = L / (1 + np.exp(-k * (val - x0)))
new_val = logistic
new_der = logistic * (1 - logistic) * der
return variable(val=new_val, der=new_der)
except:
new_val = L / (1 + np.exp(-k * (x - x0)))
new_der = 0
return variable(val=new_val, der=new_der)
def log(x):
"""
Helper function that calculates the natural log of a variable or number.
INPUTS:
x : AutoDiff.variable object or a number.
OUTPUT:
AutoDiff.variable
"""
try:
# x.val = np.log(x.val)
# x.der = (1/x.val)*x.der
new_val = np.log(x.val)
new_der = (1 / x.val) * x.der
# return x
return variable(val=new_val, der=new_der)
except:
new_val = np.log(x)
new_der = 0
return variable(val=new_val, der=new_der)