def loadDataSet():
    dataMat = [] # 列表的列表, 每个小列表包含三个元素[回归系数, 特征1, 特征2]
    labelMat = [] # 每个元素都是分类结果
    fr = open('testSet.txt') # testSet.txt的格式: 特征1, 特征2, 分类结果
    for line in fr.readlines():
        lineArr = line.strip().split()
        dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])]) # 回归系数初始化为1.0
        labelMat.append(int(lineArr[2]))
    return dataMat, labelMat

def sigmoid(inX):
    return 1.0/(1+exp(-inX))

def gradAscent(dataMatIn, classLabels): # dataMatlin: 2维NumPy数组, 一行对应一条数据的特征; classLabels: 类别
    dataMatrix = mat(dataMatIn) # 转换成NumPy矩阵
    labelMat = mat(classLabels).transpose() # 将行向量转换成列向量(转置)
    m, n = shape(dataMatrix) # 计算矩阵的行数和列数
    alpha = 0.001 # 步长
    maxCycles = 500 # 迭代次数
    weights = ones((n, 1)) # n个系数, 每个都初始化为1
    for k in range(maxCycles):
        # 计算真实类别与预测类别的差值
        # 再根据差值的方向调整回归系数
        # 如果差值为正, 则继续往前走一步, 如果差值为负, 则往回走一步
        h = sigmoid(dataMatrix * weights) # h是一个列向量, 元素个数为样本个数
        error = (labelMat - h)
        weights = weights + alpha * dataMatrix.transpose() * error
    return weights

def plotBestFit(wei): # wei是一维矩阵
    import matplotlib.pyplot as plt
    weights = wei.getA() # 将矩阵转换为数组
    dataMat, labelMat = loadDataSet() 
    dataArr = array(dataMat) # 将列表[系数, 特征1, 特征2]转换为数组
    n = shape(dataArr)[0] # 获得矩阵的行数
    xcord1 = []; ycord1 = []
    xcord2 = []; ycord2 = []
    for i in range(n):
        if int(labelMat[i]) == 1: # 将分类结果为1和0的分别存储
            xcord1.append(dataArr[i, 1]); ycord1.append(dataArr[i, 2])
        else:
            xcord2.append(dataArr[i, 1]); ycord2.append(dataArr[i, 2])
    fig = plt.figure() # 生成一个图
    ax = fig.add_subplot(111) # 添加编号为111的子图
    ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
    ax.scatter(xcord2, ycord2, s=30, c='green')
    x = arange(-3.0, 3.0, 0.1) # 以-3.0为起点, 3.0为终点, 步长为0.1
    y = (-weights[0] - weights[1]*x)/weights[2]
    ax.plot(x, y)
    pl.xlabel('X1'); plt.ylabel('X2');
    plt.show()

def stocGradAscent0(dataMatrix, classLabels):
    m, n = shape(dataMatrix)
    alpha = 0.01
    weights = ones(n)
    for i in range(m):
        h = sigmoid(sum(dataMatrix[i] * weights))
        error = classLabels[i] - h
        weights = weights + alpha * error * dataMatrix[i]
    return weights

def stocGradAscent1(dataMatrix, classLabels, numIter=150):
    m, n = shape(dataMatrix)
    weights = ones(n)
    for j in range(numIter):
        dataIndex = range(m) # 0-m
        for i in range(m):
            alpha = 4 / (1.0 + j + i) + 0.01 # 随着迭代次数的增加, 步长不断减小, 但不会减到0, 因为存在常数项
            randIndex = int(random.uniform(0, len(dataIndex))) # 随机选取样本更新回归系数
            h = sigmoid(sum(dataMatrix[randIndex] * weights))
            error = classLabels[randIndex] - h
            weights = weights + alpha * error * dataMatrix[randIndex]
            del(dataIndex[randIndex])
    return weights