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Cat vs Non-cat Classifier - Defining some utility functions - Forward Propagation

In forward propagation, we aim to calculate the activations and cost.

To calculate activations, we need to follow 2 steps for that:

  • Calculate the dot product of X and w.T, add then b.

  • Pass the above-obtained result to the sigmoid function.

To compute the cost, we:

  1. Calculate the product of Y and np.log(A)
  2. Calculate the product of (1-Y) and np.log(1-A)
  3. Add the results of the above 2 steps.
  4. Divide the negative of the result obtained in the third step with m, the total samples of the trainset.

Note:

  • np.log calculates the natural logarithm of all the elements in the array.

  • np.dot(a,b) calculates the dot product of the two vectors a and b.

  • np.sum(x) calculates the sum of elements in the input array.

INSTRUCTIONS
  • Create a list x with elements 1,2,3.

    x = << your code comes here >>
    
  • Calculate the natural logarithm of all the elements in x, using np.log function, store it in x_log.

    x_log = << your code comes here >>(x)
    
  • Calculate the dot product of vectors a and b using np.dot() function, store the result in c.

    a = np.array([[1,2],[3,4]]) 
    b = np.array([[10,20],[30,40]]) 
    
    c = << your code comes here >>(a,b)
    print(c)
    
  • Use np.ones() to create a NumPy array containing 1 as all of its elements, and shape (4,4).

    ones_array = << your code comes here >>(shape=(4,4))
    
  • Calculate the sum of the elements of ones_array using np.sum() function.

    sum_of_ones_array = << your code comes here >>(ones_array)
    
  • The forward_prop function below, calculates the activations A and the cross-entropy cost cost. Copy-paste the following function.

    def forward_prop(w, b, X, Y):
    
        # calculate activations
        z = np.dot(w.T, X) + b
        A = sigmoid(z)
    
        # calculate cost
        m = X.shape[1]
        cost = (-1/m) * np.sum(Y * np.log(A) + (1-Y) * (np.log(1-A)))
        cost = np.squeeze(cost)
    
        return A, cost
    

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