text: import numpy as np
  from random import shuffle
  
  def softmax_loss_naive(W, X, y, reg):
    """
    Softmax loss function, naive implementation (with loops)
  
    Inputs have dimension D, there are C classes, and we operate on minibatches
    of N examples.
  
    Inputs:
    - W: A numpy array of shape (D, C) containing weights.
    - X: A numpy array of shape (N, D) containing a minibatch of data.
    - y: A numpy array of shape (N,) containing training labels; y[i] = c means
      that X[i] has label c, where 0 <= c < C.
    - reg: (float) regularization strength
  
    Returns a tuple of:
    - loss as single float
    - gradient with respect to weights W; an array of same shape as W
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)
    
    #############################################################################
    # TODO: Compute the softmax loss and its gradient using explicit loops.     #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    num_train = X.shape[0]
    for i in xrange(num_train):
      z = X[i].dot(W)
      z_exp = np.exp(z) 
      scores = z_exp / np.sum(z_exp)
      
    
    #############################################################################
    #                          END OF YOUR CODE                                 #
    #############################################################################
  
    return loss, dW
  
  
  def softmax_loss_vectorized(W, X, y, reg):
    """
    Softmax loss function, vectorized version.
  
    Inputs and outputs are the same as softmax_loss_naive.
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)
  
    #############################################################################
    # TODO: Compute the softmax loss and its gradient using no explicit loops.  #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    pass
    #############################################################################
    #                          END OF YOUR CODE                                 #
    #############################################################################
  
    return loss, dW
  
  