def train(x, y, learning_rate = 1e-3, reg = 1e-5, num_iters = 100, batch_size = 200, verbose = False):

    num_train, dim = x.shape
    ## assuming that there will be atleast one example of class (k - 1) when there are k classes from (0) to (k-1)
    num_classes = np.max(y) + 1

    ## intializing parameters
    W = 0.001 * np.random.randn(dim, num_classes)

    loss_history = []

    for it in range(num_iters):
        ## sampling some random indices
        sample_indices = np.random.choice(np.arange(num_train), batch_size)

        ## creating the batches
        x_batch = x[sample_indices]
        y_batch = y[sample_indices]

        ## evaluating loss and gradient
        loss, grad = softmax_loss_vectorized(W, x_batch, y_batch, reg)
        loss_history.append(loss)

        ## changing the weights
        W = W - learning_rate * grad

        ## printing is verbose is true
        if(verbose==True and it%100==0):
            print('Iteration {}/{} : Loss {}'.format(it,num_iters,loss))

    return loss_history, W

## calling the train function
loss_hist, new_W = train(x_train, y_train, learning_rate = 1e-7, reg = 2.5e4, num_iters = 1500, verbose = True)

## making new_W equal to W
W = new_W