1、載入必要的庫，生成資料集

import math
import random
import matplotlib.pyplot as plt
import numpy as np
class moon_data_class(object):
    def __init__(self,N,d,r,w):
        self.N=N
        self.w=w
      
        self.d=d
        self.r=r
    
   
    def sgn(self,x):
        if(x>0):
            return 1
 
;
        else:
            return -1;
        
    def sig(self,x):
        return 1.0/(1+np.exp(x))
    
        
    def dbmoon(self):
        N1 = 10*self.N
        N = self.N
        r = self.r
        w2 = self.w/2
        d = self.d
        done = True
        data = np.empty(0)
        while done:
 

            #generate Rectangular data
            tmp_x = 2*(r+w2)*(np.random.random([N1, 1])-0.5)
            tmp_y = (r+w2)*np.random.random([N1, 1])
            tmp = np.concatenate((tmp_x, tmp_y), axis=1)
            tmp_ds = np.sqrt(tmp_x*tmp_x + tmp_y*tmp_y)
            #generate double moon data ---upper
 

            idx = np.logical_and(tmp_ds > (r-w2), tmp_ds < (r+w2))
            idx = (idx.nonzero())[0]
     
            if data.shape[0] == 0:
                data = tmp.take(idx, axis=0)
            else:
                data = np.concatenate((data, tmp.take(idx, axis=0)), axis=0)
            if data.shape[0] >= N:
                done = False
        #print (data)
        db_moon = data[0:N, :]
        #print (db_moon)
        #generate double moon data ----down
        data_t = np.empty([N, 2])
        data_t[:, 0] = data[0:N, 0] + r
        data_t[:, 1] = -data[0:N, 1] - d
        db_moon = np.concatenate((db_moon, data_t), axis=0)
        return db_moon

2、定義啟用函式

def rand(a,b):
    return (b-a)* random.random()+a

def sigmoid(x):
    #return np.tanh(-2.0*x)
    return 1.0/(1.0+math.exp(-x))
def sigmoid_derivate(x):
    #return -2.0*(1.0-np.tanh(-2.0*x)*np.tanh(-2.0*x))
    return x*(1-x) #sigmoid函式的導數

3、定義神經網路

class BP_NET(object):
    def __init__(self):
        self.input_n = 0
        self.hidden_n = 0
        self.output_n = 0
        self.input_cells = []
        self.bias_input_n = []
        self.bias_output = []
        self.hidden_cells = []
        self.output_cells = []
        self.input_weights = []
        self.output_weights = []
        
        self.input_correction = []
        self.output_correction = []
    
    def setup(self, ni,nh,no):
        self.input_n = ni+1#輸入層+偏置項
        self.hidden_n = nh
        self.output_n = no
        self.input_cells = [1.0]*self.input_n
        self.hidden_cells = [1.0]*self.hidden_n
        self.output_cells = [1.0]*self.output_n
        
        self.input_weights = make_matrix(self.input_n,self.hidden_n)
        self.output_weights = make_matrix(self.hidden_n,self.output_n)
        
        for i in range(self.input_n):
            for h in range(self.hidden_n):
                self.input_weights[i][h] = rand(-0.2,0.2)
        
        for h in range(self.hidden_n):
            for o in range(self.output_n):
                self.output_weights[h][o] = rand(-2.0,2.0)
        
        self.input_correction = make_matrix(self.input_n , self.hidden_n)
        self.output_correction = make_matrix(self.hidden_n,self.output_n)
                
    def predict(self,inputs):
        for i in range(self.input_n-1):
            self.input_cells[i] = inputs[i]
        
        for j in range(self.hidden_n):
            total = 0.0
            for i in range(self.input_n):
                total += self.input_cells[i] * self.input_weights[i][j]
            self.hidden_cells[j] = sigmoid(total)
            
        for k in range(self.output_n):
            total = 0.0
            for j in range(self.hidden_n):
               total+= self.hidden_cells[j]*self.output_weights[j][k]# + self.bias_output[k]
               
            self.output_cells[k] = sigmoid(total)
        return self.output_cells[:]
    
    def back_propagate(self, case,label,learn,correct):
        #計算得到輸出output_cells
        self.predict(case)
        output_deltas = [0.0]*self.output_n
        error = 0.0
        #計算誤差 = 期望輸出-實際輸出
        for o in range(self.output_n):
            error = label[o] - self.output_cells[o] #正確結果和預測結果的誤差：0,1，-1
            output_deltas[o]= sigmoid_derivate(self.output_cells[o])*error#誤差穩定在0~1內
 
        hidden_deltas = [0.0] * self.hidden_n
        for j in range(self.hidden_n):
            error = 0.0
            for k in range(self.output_n):
                error+= output_deltas[k]*self.output_weights[j][k]
            hidden_deltas[j] = sigmoid_derivate(self.hidden_cells[j])*error 

        for h in range(self.hidden_n):
            for o in range(self.output_n):
                change = output_deltas[o]*self.hidden_cells[h]
                #調整權重：上一層每個節點的權重學習*變化+矯正率
                self.output_weights[h][o] += learn*change 
        #更新輸入->隱藏層的權重
        for i in range(self.input_n):
            for h in range(self.hidden_n):
                change = hidden_deltas[h]*self.input_cells[i]
                self.input_weights[i][h] += learn*change 
            
            
        error = 0
        for o in range(len(label)):
            for k in range(self.output_n):
                error+= 0.5*(label[o] - self.output_cells[k])**2
            
        return error
        
    def train(self,cases,labels, limit, learn,correct=0.1):

        for i in range(limit):                
            error  = 0.0
           # learn = le.arn_speed_start /float(i+1)        
            for j in range(len(cases)):
                case = cases[j]
                label = labels[j]  
                         
                error+= self.back_propagate(case, label, learn,correct)
            if((i+1)%500==0):
                print("error:",error)
                
    def test(self): #學習異或

        
        N = 200
        d = -4
        r = 10
        width = 6
        
        data_source = moon_data_class(N, d, r, width)
        data = data_source.dbmoon()
        

        
       # x0 = [1 for x in range(1,401)]
        input_cells = np.array([np.reshape(data[0:2*N, 0], len(data)), np.reshape(data[0:2*N, 1], len(data))]).transpose()
        
        labels_pre = [[1.0] for y in range(1, 201)]
        labels_pos = [[0.0] for y in range(1, 201)]
        labels=labels_pre+labels_pos
       
        self.setup(2,5,1) #初始化神經網路：輸入層，隱藏層，輸出層元素個數
        self.train(input_cells,labels,2000,0.05,0.1) #可以更改
       
        test_x = []
        test_y = []
        test_p = []
        
        y_p_old = 0
    
        for x in np.arange(-15.,25.,0.1):

            for y in np.arange(-10.,10.,0.1):
                y_p =self.predict(np.array([x, y]))

                if(y_p_old <0.5 and y_p[0] > 0.5):
                    test_x.append(x)
                    test_y.append(y)
                    test_p.append([y_p_old,y_p[0]])
                y_p_old = y_p[0]
        #畫決策邊界
        plt.plot( test_x, test_y, 'g--')    
        plt.plot(data[0:N, 0], data[0:N, 1], 'r*', data[N:2*N, 0], data[N:2*N, 1], 'b*')
        plt.show()   
                    

if __name__ == '__main__':
    nn = BP_NET()
    nn.test()

4、執行結果