def loadDataSet(fileName):                 
    """ 加载数据
        解析以tab键分隔的文件中的浮点数
    Returns：
        dataMat ：  feature 对应的数据集
        labelMat ： feature 对应的分类标签，即类别标签

    """
    # 获取样本特征的总数，不算最后的目标变量 
    numFeat = len(open(fileName).readline().split('\t')) - 1 
    dataMat = []
    labelMat = []
    fr = open(fileName)
    for line in fr.readlines():
        # 读取每一行
        lineArr =[]
        # 删除一行中以tab分隔的数据前后的空白符号
        curLine = line.strip().split('\t')
        # i 从0到2，不包括2 
        for i in range(numFeat):
            # 将数据添加到lineArr List中，每一行数据测试数据组成一个行向量           
            lineArr.append(float(curLine[i]))
            # 将测试数据的输入数据部分存储到dataMat 的List中
        dataMat.append(lineArr)
        # 将每一行的最后一个数据，即类别，或者叫目标变量存储到labelMat List中
        labelMat.append(float(curLine[-1]))
    return dataMat,labelMat


def standRegres(xArr,yArr):
    '''
    Description：
        线性回归
    Args:
        xArr ：输入的样本数据，包含每个样本数据的 feature
        yArr ：对应于输入数据的类别标签，也就是每个样本对应的目标变量
    Returns:
        ws：回归系数
    '''

    # mat()函数将xArr，yArr转换为矩阵 mat().T 代表的是对矩阵进行转置操作
    xMat = mat(xArr)
    yMat = mat(yArr).T
    # 矩阵乘法的条件是左矩阵的列数等于右矩阵的行数
    xTx = xMat.T*xMat
    # 因为要用到xTx的逆矩阵，所以事先需要确定计算得到的xTx是否可逆，条件是矩阵的行列式不为0
    # linalg.det() 函数是用来求得矩阵的行列式的，如果矩阵的行列式为0，则这个矩阵是不可逆的，就无法进行接下来的运算                   
    if linalg.det(xTx) == 0.0:
        print "This matrix is singular, cannot do inverse" 
        return
    # 最小二乘法
    # http://cwiki.apachecn.org/pages/viewpage.action?pageId=5505133
    # 书中的公式，求得w的最优解
    ws = xTx.I * (xMat.T*yMat)            
    return ws


def regression1():
    xArr, yArr = loadDataSet("input/8.Regression/data.txt")
    xMat = mat(xArr)
    yMat = mat(yArr)
    ws = standRegres(xArr, yArr)
    fig = plt.figure()
    ax = fig.add_subplot(111)               #add_subplot(349)函数的参数的意思是，将画布分成3行4列图像画在从左到右从上到下第9块
    ax.scatter(xMat[:, 1].flatten(), yMat.T[:, 0].flatten().A[0]) #scatter 的x是xMat中的第二列，y是yMat的第一列
    xCopy = xMat.copy() 
    xCopy.sort(0)
    yHat = xCopy * ws
    ax.plot(xCopy[:, 1], yHat)
    plt.show()

from numpy import *
from bs4 import BeautifulSoup

# 从页面读取数据，生成retX和retY列表
def scrapePage(retX, retY, inFile, yr, numPce, origPrc):

    # 打开并读取HTML文件
    fr = open(inFile)
    soup = BeautifulSoup(fr.read())
    i=1

    # 根据HTML页面结构进行解析
    currentRow = soup.findAll('table', r="%d" % i)
    while(len(currentRow)!=0):
        currentRow = soup.findAll('table', r="%d" % i)
        title = currentRow[0].findAll('a')[1].text
        lwrTitle = title.lower()

        # 查找是否有全新标签
        if (lwrTitle.find('new') > -1) or (lwrTitle.find('nisb') > -1):
            newFlag = 1.0
        else:
            newFlag = 0.0

        # 查找是否已经标志出售，我们只收集已出售的数据
        soldUnicde = currentRow[0].findAll('td')[3].findAll('span')
        if len(soldUnicde)==0:
            print "item #%d did not sell" % i
        else:
            # 解析页面获取当前价格
            soldPrice = currentRow[0].findAll('td')[4]
            priceStr = soldPrice.text
            priceStr = priceStr.replace('$','') #strips out $
            priceStr = priceStr.replace(',','') #strips out ,
            if len(soldPrice)>1:
                priceStr = priceStr.replace('Free shipping', '')
            sellingPrice = float(priceStr)

            # 去掉不完整的套装价格
            if  sellingPrice > origPrc * 0.5:
                    print "%d\t%d\t%d\t%f\t%f" % (yr,numPce,newFlag,origPrc, sellingPrice)
                    retX.append([yr, numPce, newFlag, origPrc])
                    retY.append(sellingPrice)
        i += 1
        currentRow = soup.findAll('table', r="%d" % i)

# 依次读取六种乐高套装的数据，并生成数据矩阵        
def setDataCollect(retX, retY):
    scrapePage(retX, retY, 'input/8.Regression/setHtml/lego8288.html', 2006, 800, 49.99)
    scrapePage(retX, retY, 'input/8.Regression/setHtml/lego10030.html', 2002, 3096, 269.99)
    scrapePage(retX, retY, 'input/8.Regression/setHtml/lego10179.html', 2007, 5195, 499.99)
    scrapePage(retX, retY, 'input/8.Regression/setHtml/lego10181.html', 2007, 3428, 199.99)
    scrapePage(retX, retY, 'input/8.Regression/setHtml/lego10189.html', 2008, 5922, 299.99)
    scrapePage(retX, retY, 'input/8.Regression/setHtml/lego10196.html', 2009, 3263, 249.99)

# 交叉验证测试岭回归
def crossValidation(xArr,yArr,numVal=10):
    # 获得数据点个数，xArr和yArr具有相同长度
    m = len(yArr)
    indexList = range(m)
    errorMat = zeros((numVal,30))

    # 主循环 交叉验证循环
    for i in range(numVal):
        # 随机拆分数据，将数据分为训练集（90%）和测试集（10%）
        trainX=[]; trainY=[]
        testX = []; testY = []

        # 对数据进行混洗操作
        random.shuffle(indexList)

        # 切分训练集和测试集
        for j in range(m):
            if j < m*0.9: 
                trainX.append(xArr[indexList[j]])
                trainY.append(yArr[indexList[j]])
            else:
                testX.append(xArr[indexList[j]])
                testY.append(yArr[indexList[j]])

        # 获得回归系数矩阵
        wMat = ridgeTest(trainX,trainY)

        # 循环遍历矩阵中的30组回归系数
        for k in range(30):
            # 读取训练集和数据集
            matTestX = mat(testX); matTrainX=mat(trainX)
            # 对数据进行标准化
            meanTrain = mean(matTrainX,0)
            varTrain = var(matTrainX,0)
            matTestX = (matTestX-meanTrain)/varTrain

            # 测试回归效果并存储
            yEst = matTestX * mat(wMat[k,:]).T + mean(trainY)

            # 计算误差
            errorMat[i,k] = ((yEst.T.A-array(testY))**2).sum()

    # 计算误差估计值的均值
    meanErrors = mean(errorMat,0)
    minMean = float(min(meanErrors))
    bestWeights = wMat[nonzero(meanErrors==minMean)]

    # 不要使用标准化的数据，需要对数据进行还原来得到输出结果
    xMat = mat(xArr); yMat=mat(yArr).T
    meanX = mean(xMat,0); varX = var(xMat,0)
    unReg = bestWeights/varX

    # 输出构建的模型
    print "the best model from Ridge Regression is:\n",unReg
    print "with constant term: ",-1*sum(multiply(meanX,unReg)) + mean(yMat)


# predict for lego's price
def regression5():
    lgX = []
    lgY = []

    setDataCollect(lgX, lgY)
    crossValidation(lgX, lgY, 10)

"""Simple tutorial for using TensorFlow to compute a linear regression.
Parag K. Mital, Jan. 2016"""
# %% imports
import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt

# %% Let's create some toy data
plt.ion()
n_observations = 100
fig, ax = plt.subplots(1, 1)
xs = np.linspace(-3, 3, n_observations)
ys = np.sin(xs) + np.random.uniform(-0.5, 0.5, n_observations)
ax.scatter(xs, ys)
fig.show()
plt.draw()

# %% tf.placeholders for the input and output of the network. Placeholders are
# variables which we need to fill in when we are ready to compute the graph.
X = tf.placeholder(tf.float32)
Y = tf.placeholder(tf.float32)

# %% We will try to optimize min_(W,b) ||(X*w + b) - y||^2
# The `Variable()` constructor requires an initial value for the variable,
# which can be a `Tensor` of any type and shape. The initial value defines the
# type and shape of the variable. After construction, the type and shape of
# the variable are fixed. The value can be changed using one of the assign
# methods.
W = tf.Variable(tf.random_normal([1]), name='weight')
b = tf.Variable(tf.random_normal([1]), name='bias')
Y_pred = tf.add(tf.multiply(X, W), b)

# %% Loss function will measure the distance between our observations
# and predictions and average over them.
cost = tf.reduce_sum(tf.pow(Y_pred - Y, 2)) / (n_observations - 1)

# %% if we wanted to add regularization, we could add other terms to the cost,
# e.g. ridge regression has a parameter controlling the amount of shrinkage
# over the norm of activations. the larger the shrinkage, the more robust
# to collinearity.
# cost = tf.add(cost, tf.mul(1e-6, tf.global_norm([W])))

# %% Use gradient descent to optimize W,b
# Performs a single step in the negative gradient
learning_rate = 0.01
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

# %% We create a session to use the graph
n_epochs = 1000
with tf.Session() as sess:
    # Here we tell tensorflow that we want to initialize all
    # the variables in the graph so we can use them
    sess.run(tf.global_variables_initializer())

    # Fit all training data
    prev_training_cost = 0.0
    for epoch_i in range(n_epochs):
        for (x, y) in zip(xs, ys):
            sess.run(optimizer, feed_dict={X: x, Y: y})

        training_cost = sess.run(
            cost, feed_dict={X: xs, Y: ys})
        print(training_cost)

        if epoch_i % 20 == 0:
            ax.plot(xs, Y_pred.eval(
                feed_dict={X: xs}, session=sess),
                    'k', alpha=epoch_i / n_epochs)
            fig.show()
            plt.draw()

        # Allow the training to quit if we've reached a minimum
        if np.abs(prev_training_cost - training_cost) < 0.000001:
            break
        prev_training_cost = training_cost
fig.show()
plt.waitforbuttonpress()

#Import Library
#Import other necessary libraries like pandas, numpy...
from sklearn import linear_model
 
#Load Train and Test datasets
#Identify feature and response variable(s) and values must be numeric and numpy arrays
x_train=input_variables_values_training_datasets
y_train=target_variables_values_training_datasets
x_test=input_variables_values_test_datasets
 
# Create linear regression object
linear = linear_model.LinearRegression()
 
# Train the model using the training sets and check score
linear.fit(x_train, y_train)
linear.score(x_train, y_train)
 
#Equation coefficient and Intercept
print('Coefficient: n', linear.coef_)
print('Intercept: n', linear.intercept_)
 
#Predict Output
predicted= linear.predict(x_test)

import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt


# Hyper-parameters
input_size = 1
output_size = 1
num_epochs = 60
learning_rate = 0.001

# Toy dataset
x_train = np.array([[3.3], [4.4], [5.5], [6.71], [6.93], [4.168], 
                    [9.779], [6.182], [7.59], [2.167], [7.042], 
                    [10.791], [5.313], [7.997], [3.1]], dtype=np.float32)

y_train = np.array([[1.7], [2.76], [2.09], [3.19], [1.694], [1.573], 
                    [3.366], [2.596], [2.53], [1.221], [2.827], 
                    [3.465], [1.65], [2.904], [1.3]], dtype=np.float32)

# Linear regression model
model = nn.Linear(input_size, output_size)

# Loss and optimizer
criterion = nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)  

# Train the model
for epoch in range(num_epochs):
    # Convert numpy arrays to torch tensors
    inputs = torch.from_numpy(x_train)
    targets = torch.from_numpy(y_train)

    # Forward pass
    outputs = model(inputs)
    loss = criterion(outputs, targets)
    
    # Backward and optimize
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    
    if (epoch+1) % 5 == 0:
        print ('Epoch [{}/{}], Loss: {:.4f}'.format(epoch+1, num_epochs, loss.item()))

# Plot the graph
predicted = model(torch.from_numpy(x_train)).detach().numpy()
plt.plot(x_train, y_train, 'ro', label='Original data')
plt.plot(x_train, predicted, label='Fitted line')
plt.legend()
plt.show()

# Save the model checkpoint
torch.save(model.state_dict(), 'model.ckpt')