我对 Python 比较陌生,正在尝试实现高斯-牛顿方法,特别是维基百科页面上的示例(高斯-牛顿算法 https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm,3个例子)。以下是我到目前为止所做的:
import scipy
import numpy as np
import math
import scipy.misc
from matplotlib import pyplot as plt, cm, colors
S = [0.038,0.194,.425,.626,1.253,2.500,3.740]
rate = [0.050,0.127,0.094,0.2122,0.2729,0.2665,0.3317]
iterations = 5
rows = 7
cols = 2
B = np.matrix([[.9],[.2]]) # original guess for B
Jf = np.zeros((rows,cols)) # Jacobian matrix from r
r = np.zeros((rows,1)) #r equations
def model(Vmax, Km, Sval):
return ((vmax * Sval) / (Km + Sval))
def partialDerB1(B2,xi):
return round(-(xi/(B2+xi)),10)
def partialDerB2(B1,B2,xi):
return round(((B1*xi)/((B2+xi)*(B2+xi))),10)
def residual(x,y,B1,B2):
return (y - ((B1*x)/(B2+x)))
for i in range(0,iterations):
sumOfResid=0
#calculate Jr and r for this iteration.
for j in range(0,rows):
r[j,0] = residual(S[j],rate[j],B[0],B[1])
sumOfResid = sumOfResid + (r[j,0] * r[j,0])
Jf[j,0] = partialDerB1(B[1],S[j])
Jf[j,1] = partialDerB2(B[0],B[1],S[j])
Jft = np.transpose(Jf)
B = B + np.dot((np.dot(Jft,Jf)**-1),(np.dot(Jft,r)))
print B
每次迭代时残差平方和都会增加而不是趋于 0,我的结果B
向量增加。
我无法理解我的问题出在哪里,任何帮助将不胜感激。