backward_pass.py

def conv_backward(dH, cache):
    '''
    The backward computation for a convolution function
    
    Arguments:
    dH -- gradient of the cost with respect to output of the conv layer (H), numpy array of shape (n_H, n_W) assuming channels = 1
    cache -- cache of values needed for the conv_backward(), output of conv_forward()
    
    Returns:
    dX -- gradient of the cost with respect to input of the conv layer (X), numpy array of shape (n_H_prev, n_W_prev) assuming channels = 1
    dW -- gradient of the cost with respect to the weights of the conv layer (W), numpy array of shape (f,f) assuming single filter
    '''
    
    # Retrieving information from the "cache"
    (X, W) = cache
    
    # Retrieving dimensions from X's shape
    (n_H_prev, n_W_prev) = X.shape
    
    # Retrieving dimensions from W's shape
    (f, f) = W.shape
    
    # Retrieving dimensions from dH's shape
    (n_H, n_W) = dH.shape
    
    # Initializing dX, dW with the correct shapes
    dX = np.zeros(X.shape)
    dW = np.zeros(W.shape)
    
    # Looping over vertical(h) and horizontal(w) axis of the output
    for h in range(n_H):
        for w in range(n_W):
            dX[h:h+f, w:w+f] += W * dH(h,w)
            dW += X[h:h+f, w:w+f] * dH(h,w)
    
    return dX, dW