Week3-backpropagation.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun Jul  8 20:52:02 2018

@author: wzy
"""

# GRADED FUNCTION

# Jacobian for the third layer weights. There is no need to edit this function.
def J_W3 (x, y) :
    # First get all the activations and weighted sums at each layer of the network.
    a0, z1, a1, z2, a2, z3, a3 = network_function(x)
    # We'll use the variable J to store parts of our result as we go along, updating it in each line.
    # Firstly, we calculate dC/da3, using the expressions above.
    J = 2 * (a3 - y)
    # Next multiply the result we've calculated by the derivative of sigma, evaluated at z3.
    J = J * d_sigma(z3)
    # Then we take the dot product (along the axis that holds the training examples) with the final partial derivative,
    # i.e. dz3/dW3 = a2
    # and divide by the number of training examples, for the average over all training examples.
    J = J @ a2.T / x.size
    # Finally return the result out of the function.
    return J

# In this function, you will implement the jacobian for the bias.
# As you will see from the partial derivatives, only the last partial derivative is different.
# The first two partial derivatives are the same as previously.
# ===YOU SHOULD EDIT THIS FUNCTION===
def J_b3 (x, y) :
    # As last time, we'll first set up the activations.
    a0, z1, a1, z2, a2, z3, a3 = network_function(x)
    # Next you should implement the first two partial derivatives of the Jacobian.
    # ===COPY TWO LINES FROM THE PREVIOUS FUNCTION TO SET UP THE FIRST TWO JACOBIAN TERMS===
    J =2 * (a3 - y)
    J =J * d_sigma(z3)
    # For the final line, we don't need to multiply by dz3/db3, because that is multiplying by 1.
    # We still need to sum over all training examples however.
    # There is no need to edit this line.
    J = np.sum(J, axis=1, keepdims=True) / x.size
    return J

# GRADED FUNCTION

# Compare this function to J_W3 to see how it changes.
# There is no need to edit this function.
def J_W2 (x, y) :
    #The first two lines are identical to in J_W3.
    a0, z1, a1, z2, a2, z3, a3 = network_function(x)    
    J = 2 * (a3 - y)
    # the next two lines implement da3/da2, first σ' and then W3.
    J = J * d_sigma(z3)
    J = (J.T @ W3).T
    # then the final lines are the same as in J_W3 but with the layer number bumped down.
    J = J * d_sigma(z2)
    J = J @ a1.T / x.size
    return J

# As previously, fill in all the incomplete lines.
# ===YOU SHOULD EDIT THIS FUNCTION===
def J_b2 (x, y) :
    a0, z1, a1, z2, a2, z3, a3 = network_function(x)
    J = 2 * (a3 - y)
    J =J * d_sigma(z3)
    J =(J.T @ W3).T
    J =J * d_sigma(z2)
    J = np.sum(J, axis=1, keepdims=True) / x.size
    return J

# GRADED FUNCTION

# Fill in all incomplete lines.
# ===YOU SHOULD EDIT THIS FUNCTION===
def J_W1 (x, y) :
    a0, z1, a1, z2, a2, z3, a3 = network_function(x)
    J =2 * (a3 - y)
    J =J * d_sigma(z3)
    J =(J.T @ W3).T
    J =J * d_sigma(z2)
    J =(J.T @ W2).T
    J =J * d_sigma(z1)
    J = J @ a0.T / x.size
    return J

# Fill in all incomplete lines.
# ===YOU SHOULD EDIT THIS FUNCTION===
def J_b1 (x, y) :
    a0, z1, a1, z2, a2, z3, a3 = network_function(x)
    J =2 * (a3 - y)
    J =J * d_sigma(z3)
    J =(J.T @ W3).T
    J =J * d_sigma(z2)
    J =(J.T @ W2).T
    J =J * d_sigma(z1)
    J = np.sum(J, axis=1, keepdims=True) / x.size
    return J