import random as rd
import matplotlib.pyplot as plt
import functools
import math
import numpy as np
def sample_generate(n, low, sup, w, e):
X = [[(sup-low) * rd.random() + low if j < len(w)-1 else 1 for j in range(len(w))] for i in range(n)]
Y = [sum([w[j]*X[i][j] for j in range(len(w))])+e*(rd.random()-0.5) for i in range(n)]
return X,Y
def inv_calculate(X, Y):
n = len(X)
X = np.mat(X)
Y = np.mat([[Y[i]] for i in range(len(Y))])
w = np.linalg.inv(X.T*X)*X.T*Y
w = w.tolist()
return [w[i][0] for i in range(len(w))]
def LR_2_plot(X, Y, k, b):
X = [X[i][0] for i in range(len(X))]
x0, x1 = min(X),max(X)
y0, y1 = k*x0+b, k*x1+b
#点、线展示
plt.scatter(X, Y)
plt.plot([x0,x1], [y0,y1], color = 'r')
plt.show()
def f(w, X, Y):
return (w.T*X.T*X*w - 2*Y.T*X*w)[0,0]
def mod(dw):
return math.sqrt(sum([dw[i,0]*dw[i,0] for i in range(dw.size)]))
# r为放缩尺度, step_min为最小步长
def Gradient(X, Y, r = 0.8, step_min = 0.00001):
d = len(X[0])
X = np.mat(X)
Y = np.mat([[Y[i]] for i in range(len(Y))])
w = [[0] for i in range(d)]
w = np.mat(w)
# 先采用放缩法确定寻优区间
while True:
left = 0
right = 1
dw = -X.T * X * w + X.T * Y
while f(w+right*dw, X, Y) < f(w, X, Y):
right = right*(2-r)
mid1 = left*2/3 + right/3
mid2 = left/3 + right*2/3
while abs(left - right)*mod(dw) > step_min:
if f(w+mid1*dw, X, Y) < f(w+mid2*dw, X, Y):
right = mid2
else:
left = mid1
mid1 = left * 2 / 3 + right / 3
mid2 = left / 3 + right * 2 / 3
if left*mod(dw) < step_min:
break
w = w + left * dw
# 由二分法确定寻优步长
w = w.tolist()
return [w[i][0] for i in range(len(w))]
if __name__ == "__main__":
# y = wTx
X, Y = sample_generate(n = 100, low = 10, sup = 20, w = [2,3,4], e = 1)
# 解析解，求逆得到, w = (X.T*X)-1 * X.T * Y
# w = inv_calculate(X,Y)
# print("\nk: ", w[0])
# print("\nb: ", w[1])
# LR_2_plot(X, Y, w[0], w[1])
# 梯度下降法
w = Gradient(X, Y)
print("\nw: ", w)
# print("\nk: ", w[0])
# print("\nb: ", w[1])
# LR_2_plot(X, Y, w[0], w[1])
