cs231n作业：Assignment1-Softmax

softmax.py

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_sample = X.shape[0]
  num_class = W.shape[1]
  for i in range(num_sample):
    score_row = X[i].dot(W)
    score_row -= np.max(score_row)
    loss -= np.log(np.exp(score_row[y[i]])/np.sum(np.exp(score_row))) 
    for j in range(num_class):
        P = np.exp(score_row[j])/np.sum(np.exp(score_row))
        if(j == y[i]):
            dW[:,j] += X[i,:].T * (P-1)
        else:
            dW[:,j] += X[i,:].T * P
  loss /= num_sample
  dW /= num_sample
    
  loss += reg*np.sum(W * W)
  dW += 2 * reg * W
  
  #############################################################################
  #                          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!                                                           #
  #############################################################################
  num_sample = X.shape[0]
  score = X.dot(W)
  score -= np.max(score, axis = 1, keepdims = True)
  prob = np.exp(score) / np.sum(np.exp(score), axis = 1, keepdims = True)
  loss = -1 * np.sum(np.log(prob[range(num_sample), y]))
  prob[range(num_sample), y] -= 1
  dW = X.T.dot(prob)

  loss /= num_sample
  dW /= num_sample

  loss += reg * np.sum(W*W)
  dW += 2 * reg * W
  #############################################################################
  #                          END OF YOUR CODE                                 #
  #############################################################################

  return loss, dW