def logb(b, N):
"""
input:
b:base,a integer or float
N:node,node_b or scalar
the log function for any base
If the input is a Node instance return Node
if the input is a Node_b instance return Node_b
if a scalar n return logb(n)
else raise an error
"""
try:
float(b)
if isinstance(N, Node):
new_val = np.log(N.val) / np.log(b)
new_der = (1 / (np.log(b) * N.val)) * N.der
return Node(val=new_val, der=new_der)
if isinstance(N, Node_b):
z = Node_b(np.log(N.val) / np.log(b))
z.parents = [(N, (1 / (np.log(b) * N.val)))]
return z
try:
float(N)
new_val = np.log(N) / np.log(b)
return new_val
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
except:
raise ValueError("the base of a logb should be an int or a float")
def power(b, N):
"""
input:
b:base,a integer or float
N:node,node_b or scalar
the exponential unction for any base
If the input is a Node instance return Node
if the input is a Node_b instance return Node_b
if a scalar n return b**n
else raise an error
"""
try:
float(b)
if isinstance(N, Node):
val = b**N.val
der = val * log(b) * N.der
return Node(val, der)
if isinstance(N, Node_b):
val = b**N.val
z = Node_b(val)
z.parents = [(N, val * log(b))]
return z
try:
float(N)
return b**N
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
except:
raise ValueError("the base of a power should be an int or a float")
def arccos(N):
"""
the arccos() function
If the input is a Node instance return Node
if the input is a Node_b instance return Node_b
if a scalar n return arccos(n)
else raise an error
Pay attention that arccos only accept value between -1 and 1
"""
if isinstance(N, Node):
if N.val > 1 or N.val < -1:
raise ValueError(
"{} should have values and derivatives -1 <= x <= 1 for arccos use"
.format(N))
val = np.arccos(N.val)
der = (-1 / np.sqrt(1 - N.val**2)) * N.der
return Node(val, der)
if isinstance(N, Node_b):
if N.val > 1 or N.val < -1:
raise ValueError(
"{} should have values and derivatives -1 <= x <= 1 for arcsin use"
.format(N))
z = Node_b(np.arccos(N.val))
z.parents = [(N, (-1 / np.sqrt(1 - N.val**2)))]
return z
try:
float(N)
return np.arccos(N)
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
def arccos(N):
if isinstance(N, Node):
if N.val > 1 or N.val < -1:
raise ValueError(
"{} should have values and derivatives -1 <= x <= 1 for arccos use"
.format(N))
val = np.arccos(N.val)
der = (-1 / np.sqrt(1 - N.val**2)) * N.der
return Node(val, der)
if isinstance(N, Node_b):
if N.val > 1 or N.val < -1:
raise ValueError(
"{} should have values and derivatives -1 <= x <= 1 for arcsin use"
.format(N))
z = Node_b(np.arccos(N.val))
z.parents = [(N, (-1 / np.sqrt(1 - N.val**2)))]
return z
try:
float(N)
return np.arccos(N)
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
def exp(N):
if isinstance(N, Node):
val = np.exp(N.val)
der = np.exp(N.val) * N.der
return Node(val, der)
if isinstance(N, Node_b):
z = Node_b(np.exp(N.val))
z.parents = [(N, np.exp(N.val))]
return z
try:
float(N)
return np.exp(N)
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
def logistic(N):
if isinstance(N, Node):
val = np.exp(N.val) / (np.exp(N.val) + 1)
der = (np.exp(-N.val) / (1 + np.exp(-N.val))**2) * N.der
return Node(val, der)
if isinstance(N, Node_b):
z = Node_b(np.exp(N.val) / (np.exp(N.val) + 1))
z.parents = [(N, (np.exp(-N.val) / (1 + np.exp(-N.val))**2))]
return z
try:
float(N)
return np.exp(N) / (np.exp(N) + 1)
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
def power(b, N):
try:
float(b)
if isinstance(N, Node):
val = b**N.val
der = val * log(b) * N.der
return Node(val, der)
if isinstance(N, Node_b):
val = b**N.val
z = Node_b(val)
z.parents = [(N, val * log(b))]
return z
try:
float(N)
return b**N
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
except:
raise ValueError("the base of a power should be an int or a float")
def logb(b, N):
try:
float(b)
if isinstance(N, Node):
new_val = np.log(N.val) / np.log(b)
new_der = (1 / (np.log(b) * N.val)) * N.der
return Node(val=new_val, der=new_der)
if isinstance(N, Node_b):
z = Node_b(np.log(N.val) / np.log(b))
z.parents = [(N, (1 / (np.log(b) * N.val)))]
return z
try:
float(N)
new_val = np.log(N) / np.log(b)
return new_val
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
except:
raise ValueError("the base of a logb should be an int or a float")
def exp(N):
"""
the exp() function
If the input is a Node instance return Node
if the input is a Node_b instance return Node_b
if a scalar n return sin(n)
else raise an error
"""
if isinstance(N, Node):
val = np.exp(N.val)
der = np.exp(N.val) * N.der
return Node(val, der)
if isinstance(N, Node_b):
z = Node_b(np.exp(N.val))
z.parents = [(N, np.exp(N.val))]
return z
try:
float(N)
return np.exp(N)
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
def logistic(N):
"""
the sigmoid function
If the input is a Node instance return Node
if the input is a Node_b instance return Node_b
if a scalar n return logistic(n)
else raise an error
"""
if isinstance(N, Node):
val = np.exp(N.val) / (np.exp(N.val) + 1)
der = (np.exp(-N.val) / (1 + np.exp(-N.val))**2) * N.der
return Node(val, der)
if isinstance(N, Node_b):
z = Node_b(np.exp(N.val) / (np.exp(N.val) + 1))
z.parents = [(N, (np.exp(-N.val) / (1 + np.exp(-N.val))**2))]
return z
try:
float(N)
return np.exp(N) / (np.exp(N) + 1)
except:
raise ValueError(
"{}should either be a Node instance or a number".format(N))
