基于numpy库concatenate是一个非常好用的数组操作函数。参考：https://blog.csdn.net/brucewong0516/article/details/79158758
Parameters参数
- 传入的参数必须是一个多个数组的元组或者列表
- 另外需要指定拼接的方向，默认是 axis = 0，也就是说对0轴的数组对象进行纵向的拼接（纵向的拼接沿着axis= 1方向）；注：一般axis = 0，就是对该轴向的数组进行操作，操作方向是另外一个轴，即axis=1。
In [23]: a = np.array([[1, 2], [3, 4]])
In [24]: b = np.array([[5, 6]])
In [25]: np.concatenate((a, b), axis=0)
Out[25]:
array([[1, 2],
[3, 4],
[5, 6]])
- 传入的数组必须具有相同的形状，这里的相同的形状可以满足在拼接方向axis轴上数组间的形状一致即可
如果对数组对象进行 axis= 1 轴的拼接，方向是横向0轴，a是一个22维数组，axis= 0轴为2，b是一个12维数组，axis= 0 是1，两者的形状不等，这时会报错
将b进行转置，得到b为2*1维数组：
In [28]: np.concatenate((a,b.T),axis = 1)
Out[28]:
array([[1, 2, 5],
[3, 4, 6]])
- numpy.power(x1, x2);参考：https://blog.csdn.net/lql0716/article/details/52910812
- 数组的元素分别求n次方。x2可以是数字，也可以是数组，但是x1和x2的列数要相同。
>>> x1 = range(6)
>>> x1
[0, 1, 2, 3, 4, 5]
>>> np.power(x1, 3)
array([ 0, 1, 8, 27, 64, 125])
>>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]
>>> np.power(x1, x2)
array([ 0., 1., 8., 27., 16., 5.])
>>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])
>>> x2
array([[1, 2, 3, 3, 2, 1],
[1, 2, 3, 3, 2, 1]])
>>> np.power(x1, x2)
array([[ 0, 1, 8, 27, 16, 5],
[ 0, 1, 8, 27, 16, 5]])
例1：温度预测normal
# coding: utf-8
# linear_regression/test_temperature_normal.py
import regression
from matplotlib import cm
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
import matplotlib.ticker as mtick
import numpy as np
if __name__ == "__main__":
X, y = regression.loadDataSet('data/temperature.txt');
m,n = X.shape
X = np.concatenate((np.ones((m,1)), X), axis=1)
"""
rate 学习率
maxLoop 最大迭代次数
epsilon 收敛精度
"""
rate = 0.0001
maxLoop = 1000
epsilon =0.01
result, timeConsumed = regression.bgd(rate, maxLoop, epsilon, X, y)
theta, errors, thetas = result
# 绘制拟合曲线
fittingFig = plt.figure()
title = 'bgd: rate=%.3f, maxLoop=%d, epsilon=%.3f \n time: %ds'%(rate,maxLoop,epsilon,timeConsumed)
ax = fittingFig.add_subplot(111, title=title)
trainingSet = ax.scatter(X[:, 1].flatten().A[0], y[:,0].flatten().A[0])
xCopy = X.copy()
#？
xCopy.sort(0)
yHat = xCopy*theta
fittingLine, = ax.plot(xCopy[:,1], yHat, color='g')
ax.set_xlabel('temperature')
ax.set_ylabel('yield')
plt.legend([trainingSet, fittingLine], ['Training Set', 'Linear Regression'])
plt.show()
# 绘制误差曲线
errorsFig = plt.figure()
ax = errorsFig.add_subplot(111)
ax.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.4f'))
ax.plot(range(len(errors)), errors)
ax.set_xlabel('Number of iterations')
ax.set_ylabel('Cost J')
plt.show()
例2：温度预测多元
# coding: utf-8
# linear_regression/test_temperature_polynomial.py
import regression
import matplotlib.pyplot as plt
import matplotlib.ticker as mtick
import numpy as np
if __name__ == "__main__":
srcX, y = regression.loadDataSet('data/temperature.txt');
#返回行和列
m,n = srcX.shape
#np.concatenate拼接；np.power()平方
srcX = np.concatenate((srcX[:, 0], np.power(srcX[:, 0], 2)), axis=1)
# 特征缩放
# 标准化
X = regression.standardize(srcX.copy())
# 连接；np.ones((m,1) m行n列，元素值为1
X = np.concatenate((np.ones((m,1)), X), axis=1)
#学习率
rate = 0.1
#迭代次数
maxLoop = 1000
epsilon = 0.01
result, timeConsumed = regression.bgd(rate, maxLoop, epsilon, X, y)
theta, errors, thetas = result
# 打印特征点
fittingFig = plt.figure()
title = 'polynomial with bgd: rate=%.2f, maxLoop=%d, epsilon=%.3f \n time: %ds'%(rate,maxLoop,epsilon,timeConsumed)
ax = fittingFig.add_subplot(111, title=title)
trainingSet = ax.scatter(srcX[:, 0].flatten().A[0], y[:, 0].flatten().A[0])
print(theta)
# 打印拟合曲线
xx = np.linspace(50,100,50)
xx2 = np.power(xx,2)
yHat = []
for i in range(50):
normalizedSize = (xx[i]-xx.mean())/xx.std(0)
normalizedSize2 = (xx2[i]-xx2.mean())/xx2.std(0)
x = np.matrix([[1,normalizedSize, normalizedSize2]])
yHat.append(regression.h(theta, x.T))
fittingLine, = ax.plot(xx, yHat, color='g')
ax.set_xlabel('temperature')
ax.set_ylabel('yield')
plt.legend([trainingSet, fittingLine], ['Training Set', 'Polynomial Regression'])
plt.show()
# 打印误差曲线
errorsFig = plt.figure()
ax = errorsFig.add_subplot(111)
ax.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.2e'))
ax.plot(range(len(errors)), errors)
ax.set_xlabel('Number of iterations')
ax.set_ylabel('Cost J')
plt.show()
