#!usr/bin/env python3# -*- coding:utf-8 -*-import numpy as npimport math# definition of sigmoid funtion# numpy.exp work for arrays.def sigmoid(x):  return 1 / (1 + np.exp(-x))# definition of sigmoid derivative funtion# input must be sigmoid function's resultdef sigmoid_output_to_derivative(result):  return result*(1-result)# init training setdef getTrainingSet(nameOfSet):  setDict = {    "sin": getSinSet(),    }  return setDict[nameOfSet]def getSinSet():  x = 6.2 * np.random.rand(1) - 3.14  x = x.reshape(1,1)  # y = np.array([5 *x]).reshape(1,1)  # y = np.array([math.sin(x)]).reshape(1,1)  y = np.array([math.sin(x),1]).reshape(1,2)  return x, ydef getW(synapse, delta):  resultList = []  # 遍歷隱藏層每個(gè)隱藏單元對每個(gè)輸出的權(quán)值，比如8個(gè)隱藏單元，每個(gè)隱藏單元對兩個(gè)輸出各有2個(gè)權(quán)值  for i in range(synapse.shape[0]):    resultList.append(      (synapse[i,:] * delta).sum()      )  resultArr = np.array(resultList).reshape(1, synapse.shape[0])  return resultArrdef getT(delta, layer):  result = np.dot(layer.T, delta)  return resultdef backPropagation(trainingExamples, etah, input_dim, output_dim, hidden_dim, hidden_num):  # 可行條件  if hidden_num < 1:    print("隱藏層數(shù)不得小于1")    return  # 初始化網(wǎng)絡(luò)權(quán)重矩陣，這個(gè)是核心  synapseList = []  # 輸入層與隱含層1  synapseList.append(2*np.random.random((input_dim,hidden_dim)) - 1)  # 隱含層1與隱含層2, 2->3,,,,,,n-1->n  for i in range(hidden_num-1):    synapseList.append(2*np.random.random((hidden_dim,hidden_dim)) - 1)  # 隱含層n與輸出層  synapseList.append(2*np.random.random((hidden_dim,output_dim)) - 1)  iCount = 0  lastErrorMax = 99999  # while True:  for i in range(10000):    errorMax = 0    for x, y in trainingExamples:      iCount += 1      layerList = []      # 正向傳播      layerList.append(        sigmoid(np.dot(x,synapseList[0]))        )      for j in range(hidden_num):        layerList.append(          sigmoid(np.dot(layerList[-1],synapseList[j+1]))          )      # 對于網(wǎng)絡(luò)中的每個(gè)輸出單元k，計(jì)算它的誤差項(xiàng)      deltaList = []      layerOutputError = y - layerList[-1]      # 收斂條件      errorMax = layerOutputError.sum() if layerOutputError.sum() > errorMax else errorMax      deltaK = sigmoid_output_to_derivative(layerList[-1]) * layerOutputError      deltaList.append(deltaK)      iLength = len(synapseList)      for j in range(hidden_num):        w = getW(synapseList[iLength - 1 - j], deltaList[j])        delta = sigmoid_output_to_derivative(layerList[iLength - 2 - j]) * w        deltaList.append(delta)      # 更新每個(gè)網(wǎng)絡(luò)權(quán)值w(ji)      for j in range(len(synapseList)-1, 0, -1):        t = getT(deltaList[iLength - 1 -j], layerList[j-1])        synapseList[j] = synapseList[j] + etah * t      t = getT(deltaList[-1], x)      synapseList[0] = synapseList[0] + etah * t    print("最大輸出誤差:")    print(errorMax)    if abs(lastErrorMax - errorMax) < 0.0001:      print("收斂了")      print("####################")      break    lastErrorMax = errorMax  # 測試訓(xùn)練好的網(wǎng)絡(luò)  for i in range(5):    xTest, yReal = getSinSet()    layerTmp = sigmoid(np.dot(xTest,synapseList[0]))    for j in range(1, len(synapseList), 1):      layerTmp = sigmoid(np.dot(layerTmp,synapseList[j]))    yTest = layerTmp    print("x:")    print(xTest)    print("實(shí)際的y:")    print(yReal)    print("神經(jīng)元網(wǎng)絡(luò)輸出的y:")    print(yTest)    print("最終輸出誤差:")    print(np.abs(yReal - yTest))    print("#####################")  print("迭代次數(shù):")  print(iCount)if __name__ == '__main__':  import datetime  tStart = datetime.datetime.now()  # 使用什么樣的訓(xùn)練樣例  nameOfSet = "sin"  x, y = getTrainingSet(nameOfSet)  # setting of parameters  # 這里設(shè)置了學(xué)習(xí)速率。  etah = 0.01  # 隱藏層數(shù)  hidden_num = 2  # 網(wǎng)絡(luò)輸入層的大小  input_dim = x.shape[1]  # 隱含層的大小  hidden_dim = 100  # 輸出層的大小  output_dim = y.shape[1]  # 構(gòu)建訓(xùn)練樣例  trainingExamples = []  for i in range(10000):    x, y = getTrainingSet(nameOfSet)    trainingExamples.append((x, y))  # 開始用反向傳播算法訓(xùn)練網(wǎng)絡(luò)  backPropagation(trainingExamples, etah, input_dim, output_dim, hidden_dim, hidden_num)  tEnd = datetime.datetime.now()  print("time cost:")  print(tEnd - tStart)