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# coding: utf-8
import numpy as np
def identity_function ( x ) :
return x
def step_function ( x ) :
return np . array ( x > 0 , dtype = np . int )
def sigmoid ( x ) :
return 1 / ( 1 + np . exp ( - x ) )
def sigmoid_grad ( x ) :
return ( 1.0 - sigmoid ( x ) ) * sigmoid ( x )
def relu ( x ) :
return np . maximum ( 0 , x )
def relu_grad ( x ) :
grad = np . zeros ( x )
grad [ x > = 0 ] = 1
return grad
def softmax ( x ) :
if x . ndim == 2 :
x = x . T
x = x - np . max ( x , axis = 0 )
y = np . exp ( x ) / np . sum ( np . exp ( x ) , axis = 0 )
return y . T
x = x - np . max ( x ) # 溢出对策
return np . exp ( x ) / np . sum ( np . exp ( x ) )
def mean_squared_error ( y , t ) :
return 0.5 * np . sum ( ( y - t ) * * 2 )
def cross_entropy_error ( y , t ) :
if y . ndim == 1 :
t = t . reshape ( 1 , t . size )
y = y . reshape ( 1 , y . size )
# 监督数据是one-hot-vector的情况下，
if t . size == y . size :
t = t . argmax ( axis = 1 )
batch_size = y . shape [ 0 ]
return - np . sum ( np . log ( y [ np . arange ( batch_size ) , t ] + 1e-7 ) ) / batch_size
def softmax_loss ( X , t ) :
y = softmax ( X )
return cross_entropy_error ( y , t )
