Python Powell 最小化求解器 : type error - subtracting 'list' and 'list'

Question

我尝试使用 Python 求解/最小化一组多项式(Winterstein-Jensen LTE 计算的一部分)。

我正在使用 SciPy 的最小化求解器 fmin_Powell。见以下代码:

import numpy as np
import scipy as sp
import scipy.optimize as spo

#start parameters and initial estimates:
average  = 128.96530977973006
Stdevv   = 355.72971228985256
Skewv    = 12913.846528570562
Kurtv    = 3.0009847038644031
Exckurtv = 0.00098470386440308033
c    = np.zeros (4)
h30  = Skewv / (4.0 + 2.0 * (np.power(abs(1.0 + 1.5 * Exckurtv), 0.5)))
h40  = (np.sqrt((abs(1.0 + 1.5 * Exckurtv))) - 1.0) / 18.0
K0   = np.power((1.0 + 2.0 * (np.power(h30,2.0)) + 6.0 * np.power(h40,2.0)), -0.5 )
c[1] = Stdevv * K0 * (1.0 - 3.0 * h40)
c[2] = Stdevv * K0 * h30
c[3] = Stdevv * K0 * h40

#multi polynomials
def wj_f(p):
     f1   = (np.power(p[0],2.0) + 6.0 * p[0] * p[2] + 2.0 * np.power(p[1],2.0) + 
            15.0 * np.power(p[2],2.0) - np.power(Stdevv,2.0))
     f2   = (p[1] * (6.0 * np.power(p[0],2.0) + 8.0 * np.power(p[1],2.0) + 72.0 * p[0] * p[2] + 270.0 * np.power(p[2],2.0))
            - np.power(Stdevv,3.0) * Skewv)
     f3   = (60.0 * np.power(p[1],4.0) + 3.0 * np.power(p[0],4.0) + 10395.0 * np.power(p[2],4.0) 
            + 60.0 * np.power(p[0],2.0) * np.power(p[1],2.0) + 4500.0 * np.power(p[1],2.0) * np.power(p[2],2.0)
            + 630.0 * np.power(p[0],2.0) * np.power(p[2],2.0) + 936.0 * p[0] * np.power(p[1],2.0) * p[2]
            + 3780.0 * p[0] * np.power(p[2],3.0) + 60.0 * np.power(p[0],3.0) * p[2] - np.power(Stdevv,4.0) * Kurtv)
     wj_f = [f1,f2,f3]
     return(wj_f)

print('Start solving') 
#solver
xopt = spo.fmin_powell(wj_f,c[1:],args=(),xtol=1e-06,ftol=1e-   06,maxiter=None,maxfun=None,full_output=1,disp=1,retall=1,callback=None,direc=None)

print('Solved')

但是，我收到以下错误:

Traceback (most recent call last):


File "<pyshell#22>", line 1, in <module>
    execfile('wj_in_python.py')
  File "wj_in_python.py", line 85, in <module>
    xopt = spo.fmin_powell(wj_f,c[1:],args=(),xtol=1e-06,ftol=1e-06,maxiter=None,maxfun=None,full_output=1,disp=1,retall=1,callback=None,direc=None)
  File "C:\Program Files (x86)\Python\2.7.3\lib\site-packages\scipy\optimize\optimize.py", line 2227, in fmin_powell
    res = _minimize_powell(func, x0, args, callback=callback, **opts)
  File "C:\Program Files (x86)\Python\2.7.3\lib\site-packages\scipy\optimize\optimize.py", line 2299, in _minimize_powell
    tol=xtol * 100)
  File "C:\Program Files (x86)\Python\2.7.3\lib\site-packages\scipy\optimize\optimize.py", line 2120, in _linesearch_powell
    alpha_min, fret, iter, num = brent(myfunc, full_output=1, tol=tol)
  File "C:\Program Files (x86)\Python\2.7.3\lib\site-packages\scipy\optimize\optimize.py", line 1885, in brent
    res = _minimize_scalar_brent(func, brack, args, **options)
  File "C:\Program Files (x86)\Python\2.7.3\lib\site-packages\scipy\optimize\optimize.py", line 1901, in _minimize_scalar_brent
    brent.optimize()
  File "C:\Program Files (x86)\Python\2.7.3\lib\site-packages\scipy\optimize\optimize.py", line 1757, in optimize
    tmp1 = (x - w) * (fx - fv)
TypeError: unsupported operand type(s) for -: 'list' and 'list'

错误本身很明显:列表不能彼此相减。

问题是:为什么 Python/SciPy 脚本创建两个或更多列表而不是数字或整数？

Answer 1

应该将三个函数的结果合并为一个大和 (wj_f = f1 + f2 + f3)。

求解器无法处理列表/矩阵/向量。