#-*- coding: utf-8 -*-
from __future__ import print_function
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
from matplotlib.font_manager import FontProperties
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14) # 解决windows环境下画图汉字乱码问题


def LogisticRegression():
 data = loadtxtAndcsv_data("data2.txt", ",", np.float64) 
 X = data[:,0:-1]
 y = data[:,-1]
 
 plot_data(X,y) # 作图
 
 X = mapFeature(X[:,0],X[:,1]) #映射为多项式
 initial_theta = np.zeros((X.shape[1],1))#初始化theta
 initial_lambda = 0.1 #初始化正则化系数,一般取0.01,0.1,1.....
 
 J = costFunction(initial_theta,X,y,initial_lambda) #计算一下给定初始化的theta和lambda求出的代价J
 
 print(J) #输出一下计算的值,应该为0.693147
 #result = optimize.fmin(costFunction, initial_theta, args=(X,y,initial_lambda)) #直接使用最小化的方法,效果不好
 '''调用scipy中的优化算法fmin_bfgs(拟牛顿法Broyden-Fletcher-Goldfarb-Shanno)
 - costFunction是自己实现的一个求代价的函数,
 - initial_theta表示初始化的值,
 - fprime指定costFunction的梯度
 - args是其余测参数,以元组的形式传入,最后会将最小化costFunction的theta返回 
 '''
 result = optimize.fmin_bfgs(costFunction, initial_theta, fprime=gradient, args=(X,y,initial_lambda)) 
 p = predict(X, result) #预测
 print(u'在训练集上的准确度为%f%%'%np.mean(np.float64(p==y)*100)) # 与真实值比较,p==y返回True,转化为float 
 
 X = data[:,0:-1]
 y = data[:,-1] 
 plotDecisionBoundary(result,X,y) #画决策边界 
 
 

# 加载txt和csv文件
def loadtxtAndcsv_data(fileName,split,dataType):
 return np.loadtxt(fileName,delimiter=split,dtype=dataType)

# 加载npy文件
def loadnpy_data(fileName):
 return np.load(fileName)

# 显示二维图形
def plot_data(X,y):
 pos = np.where(y==1) #找到y==1的坐标位置
 neg = np.where(y==0) #找到y==0的坐标位置
 #作图
 plt.figure(figsize=(15,12))
 plt.plot(X[pos,0],X[pos,1],'ro') # red o
 plt.plot(X[neg,0],X[neg,1],'bo') # blue o
 plt.title(u"两个类别散点图",fontproperties=font)
 plt.show()

# 映射为多项式 
def mapFeature(X1,X2):
 degree = 2; # 映射的最高次方
 out = np.ones((X1.shape[0],1)) # 映射后的结果数组(取代X)
 '''
 这里以degree=2为例,映射为1,x1,x2,x1^2,x1,x2,x2^2
 '''
 for i in np.arange(1,degree+1): 
 for j in range(i+1):
 temp = X1**(i-j)*(X2**j) #矩阵直接乘相当于matlab中的点乘.*
 out = np.hstack((out, temp.reshape(-1,1)))
 return out

# 代价函数
def costFunction(initial_theta,X,y,inital_lambda):
 m = len(y)
 J = 0
 
 h = sigmoid(np.dot(X,initial_theta)) # 计算h(z)
 theta1 = initial_theta.copy() # 因为正则化j=1从1开始,不包含0,所以复制一份,前theta(0)值为0 
 theta1[0] = 0 
 
 temp = np.dot(np.transpose(theta1),theta1)
 J = (-np.dot(np.transpose(y),np.log(h))-np.dot(np.transpose(1-y),np.log(1-h))+temp*inital_lambda/2)/m # 正则化的代价方程
 return J

# 计算梯度
def gradient(initial_theta,X,y,inital_lambda):
 m = len(y)
 grad = np.zeros((initial_theta.shape[0]))
 
 h = sigmoid(np.dot(X,initial_theta))# 计算h(z)
 theta1 = initial_theta.copy()
 theta1[0] = 0

 grad = np.dot(np.transpose(X),h-y)/m+inital_lambda/m*theta1 #正则化的梯度
 return grad

# S型函数 
def sigmoid(z):
 h = np.zeros((len(z),1)) # 初始化,与z的长度一置
 
 h = 1.0/(1.0+np.exp(-z))
 return h


#画决策边界
def plotDecisionBoundary(theta,X,y):
 pos = np.where(y==1) #找到y==1的坐标位置
 neg = np.where(y==0) #找到y==0的坐标位置
 #作图
 plt.figure(figsize=(15,12))
 plt.plot(X[pos,0],X[pos,1],'ro') # red o
 plt.plot(X[neg,0],X[neg,1],'bo') # blue o
 plt.title(u"决策边界",fontproperties=font)
 
 #u = np.linspace(30,100,100)
 #v = np.linspace(30,100,100)
 
 u = np.linspace(-1,1.5,50) #根据具体的数据,这里需要调整
 v = np.linspace(-1,1.5,50)
 
 z = np.zeros((len(u),len(v)))
 for i in range(len(u)):
 for j in range(len(v)):
 z[i,j] = np.dot(mapFeature(u[i].reshape(1,-1),v[j].reshape(1,-1)),theta) # 计算对应的值,需要map
 
 z = np.transpose(z)
 plt.contour(u,v,z,[0,0.01],linewidth=2.0) # 画等高线,范围在[0,0.01],即近似为决策边界
 #plt.legend()
 plt.show()

# 预测
def predict(X,theta):
 m = X.shape[0]
 p = np.zeros((m,1))
 p = sigmoid(np.dot(X,theta)) # 预测的结果,是个概率值
 
 for i in range(m):
 if p[i] > 0.5: #概率大于0.5预测为1,否则预测为0
 p[i] = 1
 else:
 p[i] = 0
 return p


# 测试逻辑回归函数
def testLogisticRegression():
 LogisticRegression()


if __name__ == "__main__":
 testLogisticRegression()