def load_data(filename,dataType):

    return np.loadtxt(filename,delimiter=",",dtype = dataType)

def read_data():

    data = load_data("data2.txt",np.float64)

    X = data[:,0:-1]

    y = data[:,-1]

    return X,y 

def plot_data(x,y):

    pos = np.where(y==1) # 找到标签为1的位置

    neg = np.where(y==0) #找到标签为0的位置

    plt.figure(figsize=(8,6))

    plt.plot(x[pos,0],x[pos,1],'ro')

    plt.plot(x[neg,0],x[neg,1],'bo')

    plt.title("raw data")

    plt.show() 

X,y = read_data()

plot_data(X,y)

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） 

    for i in np.arange(1,degree+1):

        for j in range(i+1):

            temp = x1 ** (i-j) * (x2**j)

            out = np.hstack((out,temp.reshape(-1,1)))

    return out 

def sigmoid(x):

    return 1.0 / (1.0+np.exp(-x))

def CrossEntropy_loss(initial_theta,X,y,inital_lambda):   #定义交叉熵损失函数

    m = len(y)

    h = sigmoid(np.dot(X,initial_theta))

    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)

    loss = (-np.dot(np.transpose(y),np.log(h)) - np.dot(np.transpose(1-y),np.log(1-h)) + temp*inital_lambda/2) / m

    return loss 

def gradientDescent(initial_theta,X,y,initial_lambda,lr,num_iters):

    m = len(y)

    theta1 = initial_theta.copy()

    theta1[0] = 0

    J_history = np.zeros((num_iters,1)) 

    for i in range(num_iters):

        h = sigmoid(np.dot(X,theta1))

        grad = np.dot(np.transpose(X),h-y)/m + initial_lambda * theta1/m

        theta1 = theta1 - lr*grad

        #print(theta1)

        J_history[i] = CrossEntropy_loss(theta1,X,y,initial_lambda)

    return theta1,J_history

def plotLoss(J_history,num_iters):

    x = np.arange(1,num_iters+1)

    plt.plot(x,J_history)

    plt.xlabel("num_iters")

    plt.ylabel("loss")

    plt.title("Loss value changes with the number of iterations")

    plt.show()

def plotDecisionBoundary(theta,x,y):

    pos = np.where(y==1)  #找到标签为1的位置

    neg = np.where(y==0)  #找到标签为2的位置

    plt.figure(figsize=(8,6))

    plt.plot(x[pos,0],x[pos,1],'ro')

    plt.plot(x[neg,0],x[neg,1],'bo')

    plt.title("Decision Boundary")

    #生成和原数据类似的数据

    u = np.linspace(-1,1.5,50)

    v = np.linspace(-1,1.5,50)

    z = np.zeros((len(u),len(v)))

    #利用训练好的参数做预测

    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)

    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()

if __name__ == "__main__":

    #数据的加载

    x,y = read_data()

    X = mapFeature(x[:,0],x[:,1])

    Y = y.reshape((-1,1))

    #参数的初始化

    num_iters = 400

    lr = 0.1

    initial_theta = np.zeros((X.shape[1],1))  #初始化参数theta

    initial_lambda = 0.1 #初始化正则化系数

    #迭代优化

    theta,loss = gradientDescent(initial_theta,X,Y,initial_lambda,lr,num_iters)

    plotLoss(loss,num_iters)

    plotDecisionBoundary(theta,x,y)