def crossValidation(xArr,yArr,numVal = 10):"""numVal：交叉验证的次数"""m = len(yArr)indexList = range(m)errorMat = np.zeros((numVal,30))for i in range(numVal):trainX = []trainY = []testX = []testY = []random.shuffle(indexList)   #实现训练和测试数据的随机抽取#分为训练集和测试集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]])wMat = ridgeTest(trainX,trainY)for k in range(30):#用训练时的参数将测试数据标准化matTestX = np.mat(testX)matTrainX = np.mat(trainX)meanTrain = np.mean(matTrainX,0)varTrain = np.var(matTrainX,0)matTestX = (matTestX - meanTrain)/varTrainyEst = matTestX*np.mat(wMat[k,:]).T+np.mean(trainY)errorMat[i,k] = rssError(yEst.T.A,np.array(testY))meanErrors = np.mean(errorMat,0)minMean = float(min(meanErrors))bestWeights = wMat[np.nonzero(meanErrors==minMean)]print("the best regression params :",bestWeights)xMat = np.mat(xArr)yMat = np.mat(yArr).TmeanX = np.mean(xMat,0)varX = np.var(xMat,0)#数据还原-便于与其他的算法模型拟合结果进行比较unReg = bestWeights/varXprint('the best model from Ridge Regression is:\n',unReg)print('with constant term',-1*sum(np.multiply(meanX,unReg))+np.mean(yMat))