from matplotlib.font_manager import FontProperties
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl

# 預處理data1.txt
def loaddata():
    data = np.loadtxt('data1.txt',delimiter=',')
    n = data.shape[1] - 1  # 特徵數
    X = data[:, 0:n]
    y = data[:, -1].reshape(-1, 1)
    return X, y

# 將data1.txt繪製
def plot(X,y):
    pos = np.where(y==1)
    neg = np.where(y==0)
    plt.scatter(X[pos[0],0],X[pos[0],1],marker='x')
    plt.scatter(X[neg[0], 0], X[neg[0], 1], marker='o')
    plt.xlabel('Exam 1 score')
    plt.ylabel('Exam 2 score')
    plt.show()

X,y = loaddata()
plot(X,y)
# sigmoid函式：1/( 1+pow(e,(-z)) )
def sigmoid(z):
    r = 1/(1+np.exp(-z))
    return r
# 返回邏輯迴歸函式（線性迴歸函式的結果y，放到sigmod函式中去）
def hypothesis(X,theta):
    z=np.dot(X,theta)
    return sigmoid(z)
# 計算代價函式的程式碼
# l(θ)=ln(L(θ))=∑m(i=1)(yi*ln(gθ(xi))+(1−yi)ln(1−gθ(xi)))
# ln(L(θ)) * (-m)為代價函式
# 代價函式：-y*log(hypothesis+正規化因子)-(1-y)*log(1-hypothesis+正規化因子)
# 用梯度下降法求出使得損失最小對應的引數θ
def computeCost(X,y,theta):
    m = X.shape[0]
    #補充計算代價的程式碼；
    z = -y * np.log(hypothesis(X,theta) + 1e-6) - (1 - y) * np.log(1 - hypothesis(X,theta) + 1e-6)
    return np.sum(z)/m 

diff = []
#梯度下降法
def gradientDescent(X,y,theta,iterations,alpha):
    #取資料條數
    m = X.shape[0]
    #在x最前面插入全1的列
    X = np.hstack((np.ones((m, 1)), X))
    for i in range(iterations):
    #補充引數更新程式碼；
        theta_temp = theta - alpha * np.dot(X.T,hypothesis(X,theta) - y) / m
        # 梯度下降公式如下：
        # theta = theta - 學習率 * 損失函式
        theta = theta_temp
        # 對應到每個權重公式為：
        # w = w - 學習率 * (損失函式對wi求偏導)
        # 每迭代1000次輸出一次損失值
        if(i%10000==0):
            diff.append([i,computeCost(X,y,theta)])
            # 將每個10000*k次迭代的損失函式的值送進diff[]
            print('第',i,'次迭代，當前損失為：',computeCost(X,y,theta),'theta=',theta)
    return theta

# 預測函式
def predict(X):
    # 在x最前面插入全1的列
    c = np.ones(X.shape[0]).transpose()
    X = np.insert(X, 0, values=c, axis=1)
    #求解假設函式的值
    h = hypothesis(X,theta)
    #根據概率值決定最終的分類,>=0.5為1類，<0.5為0類
    h[h>=0.5]=1
    h[h<0.5]=0
    return h

X,y = loaddata()
n = X.shape[1]#特徵數
theta = np.zeros(n+1).reshape(n+1, 1)
# theta是列向量,+1是因為求梯度時X前會增加一個全1列
theta_temp = np.zeros(n+1).reshape(n+1, 1)
iterations = 250000
alpha = 0.008   # 學習率

theta = gradientDescent(X,y,theta,iterations,alpha)
print('theta=\n',theta)

def plotDescisionBoundary(X,y,theta):
    cm_dark = mpl.colors.ListedColormap(['g', 'r'])
    plt.xlabel('Exam 1 score')
    plt.ylabel('Exam 2 score')
    plt.scatter(X[:,0],X[:,1],c=np.array(y).squeeze(),cmap=cm_dark,s=30)
    #補充畫決策邊界程式碼；
    x1 = np.linspace(0,150,500)
    x2 = (-theta[0] - theta[1] * x1) / theta[2]
    plt.plot(x1,x2)
    plt.show()

def plotLoss():
    d = np.array(diff)
    x = d[:,0]
    y = d[:,1]
    plt.plot(x,y)
    plt.title("損失函式變化圖",fontsize = 20,fontproperties = "kaiti")
    plt.show()

def plotPred():
    test_x = []
    for i in range(233):
        tx = np.random.uniform(0.0,100.0)
        ty = np.random.uniform(0.0,100.0)
        test_x.append([tx,ty])
    test_x = np.array(test_x)
    test_y = predict(test_x)
    cm_dark = mpl.colors.ListedColormap(['b', 'pink'])
    plt.scatter(test_x[:, 0], test_x[:, 1], c=np.array(test_y).squeeze(), cmap=cm_dark, s=30)
    x1 = np.linspace(0, 150, 500)
    x2 = (- theta[0] - theta[1] * x1) / theta[2]
    plt.plot(x1,x2)
    plt.title("預測",fontproperties = 'kaiti',fontsize = 20)
    plt.show()

plotDescisionBoundary(X,y,theta)
plotLoss()
plotPred()