In [2]:

    

import numpy as np
import matplotlib.pyplot as plt

%matplotlib inline


    

In [54]:

    

def sigmoid(z):
    return 1 / (1 + np.exp(-z))

z = np.linspace(-10, 10, 1000)
a = sigmoid(z)


    

In [55]:

    

plt.plot(z, a)
plt.xlabel("Z")
plt.ylabel("g(z)")
plt.title("Sigmoid")
plt.grid(True)


    

In [56]:

    

dz = a*(1-a)
plt.plot(z, dz)
plt.xlabel("Z")
plt.ylabel("g'(z)")
plt.title("Derivative of Sigmoid function")
plt.grid(True)


    

In [57]:

    

def tanh(z):
    return (np.exp(z) - np.exp(-z)) / (np.exp(z) + np.exp(-z))

z = np.linspace(-10, 10, 1000)
a = tanh(z)


    

In [58]:

    

plt.plot(z, a)
plt.xlabel("Z")
plt.ylabel("g(z)")
plt.title("tanh")
plt.grid(True)


    

In [59]:

    

dz = 1 - (a ** 2)
plt.plot(z, dz)
plt.xlabel("Z")
plt.ylabel("g'(z)")
plt.title("Derivative of tanh")
plt.grid(True)


    

In [60]:

    

def relu(z):
    return np.maximum(0, z)

z = np.linspace(-10, 10, 1000)
a = relu(z)


    

In [61]:

    

plt.plot(z, a)
plt.xlabel("Z")
plt.ylabel("g(z)")
plt.title("relu")
plt.grid(True)


    

In [62]:

    

dz = np.where(z <=0, 0, 1)
plt.plot(z, dz)
plt.xlabel("Z")
plt.ylabel("g'(z)")
plt.title("Derivative of relu")
plt.grid(True)


    

In [65]:

    

def weak_relu(z):
    return np.maximum(0.01 * z, z)

z = np.linspace(-10, 10, 1000)
a = weak_relu(z)


    

In [66]:

    

plt.plot(z, a)
plt.xlabel("Z")
plt.ylabel("g(z)")
plt.title("Weak relu")
plt.grid(True)


    

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