Gradient Descent Function in Machine Learning

Question

I am enrolled in the Machine Learning Specialization course by Andrew Ng on Coursera, where I encountered this function implementing the Gradient descent algorithm.

def gradient_descent(x, y, w_in, b_in, alpha, num_iters, cost_function, gradient_function): 

    w = copy.deepcopy(w_in) # avoid modifying global w_in
# An array to store cost J and w's at each iteration primarily for graphing later
    J_history = []
    p_history = []
    b = b_in
    w = w_in

    for i in range(num_iters):

        # Calculate the gradient and update the parameters using gradient_function
        dj_dw, dj_db = gradient_function(x, y, w , b)  

        # Update Parameters using equation (3) above
        b = b - alpha * dj_db                            
        w = w - alpha * dj_dw 
                       
        # Save cost J at each iteration
        if i<100000:      # prevent resource exhaustion 
            J_history.append( cost_function(x, y, w , b))
            p_history.append([w,b])

        # Print cost every at intervals 10 times or as many iterations if < 10
        if i% math.ceil(num_iters/10) == 0:
            print(f"Iteration {i:4}: Cost {J_history[-1]:0.2e} ",
                  f"dj_dw: {dj_dw: 0.3e}, dj_db: {dj_db: 0.3e}  ",
                  f"w: {w: 0.3e}, b:{b: 0.5e}")
    return w, b, J_history, p_history #return w and J,w history for graphing`

Could anyone please explain to me the second if statement within the for-loop?

I am getting the actual purpose of that conditional statement? I do understand that it is to print something out on the console, but what does the following condition signify in this case? if i% math.ceil(num_iters/10) == 0:

Answer 1

If you deconstruct i% math.ceil(num_iters/10) == 0:

• num_iters/10 is the number of iterations divided by 10.
• math.ceil returns the rounded-up number, in order for it to be an integer.
• % is the modulo operator, so it returns the remainder of the division.
• == 0, if the remainder of the division is 0, it means i is a multiple of num_iters/10.

Overall, this expression is True when i is at a decile of num_iters.

For example if num_iters = 200, this will print ten times, when i = 20, 40, 60, ... , 180, 200