- 必要条件:若函数在处取极值,则有
- 其中称为函数的稳定点
- 稳定点 鞍点 在处的Hesse矩阵是不定的 极值点 是一个极小值点,那么在处的Hesse矩阵是半正定的是一个极大值点,那么在处的Hesse矩阵是半负定的在处的Hesse矩阵是正定的, 是一个严格的极小值点 在处的Hesse矩阵是负定的, 是一个严格的极大值点
- Hesse矩阵 在点处的泰勒展开式的矩阵形式
- Numpy 求矩阵的特征值并做判断
import numpy as np a = [[1,0,0],[-2,5,-2],[-2,4,-1]] c = np.linalg.eig(a) eig_values = c[0] p = list(c[0]) positive = 0 negative = 0 null = 0 for i in p: if i > 0: positive += 1 elif i == 0″ null += 1 elif i < 0: negative += 1 if negative > 0 and positive > 0: print(“it is a saddle point”) elif negative > 0 and positive = 0 and null > 0: print(“it is a negative semidefinite matrix”) print(“Warning!!cannot judge!!”) elif negative > 0 and positive = 0 and null = 0: print(“it is a maximum point”) elif negative = 0 and positive > 0 and null = 0: print(“it is a minmum point”) elif negative = 0 and positive > 0 and null > 0: print(“it is a positive semidefinite matrix”) print(“Warning!!cannot judge!!”)import numpy as np a = [[1,0,0],[-2,5,-2],[-2,4,-1]] c = np.linalg.eig(a) eig_values = c[0] p = list(c[0]) positive = 0 negative = 0 null = 0 for i in p: if i > 0: positive += 1 elif i == 0" null += 1 elif i < 0: negative += 1 if negative > 0 and positive > 0: print("it is a saddle point") elif negative > 0 and positive = 0 and null > 0: print("it is a negative semidefinite matrix") print("Warning!!cannot judge!!") elif negative > 0 and positive = 0 and null = 0: print("it is a maximum point") elif negative = 0 and positive > 0 and null = 0: print("it is a minmum point") elif negative = 0 and positive > 0 and null > 0: print("it is a positive semidefinite matrix") print("Warning!!cannot judge!!")
文章出处登录后可见!
已经登录?立即刷新