Python 优化非线性方程组-处理复数
我试图解一个非线性方程组。问题是,解决方案很复杂,根据Octave/Matlab,虚部很小。我正试图将这一点转移到python上,但不幸的是,我不确定应该如何优雅地处理这一点 在倍频程中,我可以直接使用fsolve,然后通过“real”函数传递解,得到数字的实部。问题是,它可以轻松地解决问题,而不会返回任何错误 不幸的是,在python中使用numpy在尝试求解方程时会返回错误。以下是用Python编写的方程式:Python 优化非线性方程组-处理复数,python,numpy,complex-numbers,Python,Numpy,Complex Numbers,我试图解一个非线性方程组。问题是,解决方案很复杂,根据Octave/Matlab,虚部很小。我正试图将这一点转移到python上,但不幸的是,我不确定应该如何优雅地处理这一点 在倍频程中,我可以直接使用fsolve,然后通过“real”函数传递解,得到数字的实部。问题是,它可以轻松地解决问题,而不会返回任何错误 不幸的是,在python中使用numpy在尝试求解方程时会返回错误。以下是用Python编写的方程式: import numpy as np from scipy.optimize im
import numpy as np
from scipy.optimize import fsolve
import scipy.io as spio
params = dict()
params['cbeta'] = 0.96
params['cdelta'] = 0.1
params['calpha'] = 0.33
params['cgamma'] = 1.2
params['clambda']= 1.0
params['csigma'] = 0.8
params['etau'] = 0.0
def steady_s(vars0):
# unpacking paramters
cbeta = params['cbeta']
cdelta = params['cdelta']
calpha = params['calpha']
cgamma = params['cgamma']
clambda= params['clambda']
csigma = params['csigma']
# guesses for initial values
c = vars0[0]
y = vars0[1]
k = vars0[2]
g = vars0[3]
r = vars0[4]
# == functions to minimize to find steady states == #
f = np.empty((5,))
# HH Euler
f[0] = (1.0/c)*cbeta*(r + 1.0 - cdelta) - (1.0+g)/c
# Goods market clearing
f[1] = y - c - k*(1.0 + g) + k*(1.0-cdelta)
# Capital Market clearing
f[2] = r - (k)**(calpha-1.0)*calpha**2.0
# production function for final good
f[3] = y - k**calpha
# growth rate
pi = (calpha - 1.0) * k**calpha #small pi, this isnt actual profits
f[4] = g - (cgamma - 1.0) * clambda * (csigma*clambda*pi)**(csigma/(1.0-csigma))
return f
# == Initial Guesses == #
vars0 = np.ones((5,))
# == Solving for Steady State == #
xss = fsolve(steady_s, vars0)
在倍频程中实现同样的功能可以提供以下解决方案:
Columns 1 through 3:
0.7851388 + 0.0000000i 0.8520544 + 0.0000000i 0.6155938 + 0.0000000i
Columns 4 and 5:
0.0087008 - 0.0000000i 0.1507300 - 0.0000000i
我把这个解通过“实”函数的倍频程,得到我想要的结果
特别是,python甚至在一次求解方程时都有困难。特别是,如果我尝试在定义了所有参数的函数外部运行f[4],它将返回一个nan值
任何帮助都将不胜感激
事先向我错过的/格式错误的任何内容道歉。事实上,scipy正在与复数作斗争。然而,一个名为mpmath的项目可以解决您的问题。此处:。它过去常与sympy(sympy.org)一起提供。您可以找到文档:此解决方案适用于我:
from mpmath import findroot
import numpy as np
import scipy.io as spio
params = dict()
params['cbeta'] = 0.96
params['cdelta'] = 0.1
params['calpha'] = 0.33
params['cgamma'] = 1.2
params['clambda']= 1.0
params['csigma'] = 0.8
params['etau'] = 0.0
def steady_s(c,y,k,g,r):
# unpacking paramters
cbeta = params['cbeta']
cdelta = params['cdelta']
calpha = params['calpha']
cgamma = params['cgamma']
clambda= params['clambda']
csigma = params['csigma']
# guesses for initial values
#c = vars0[0]
#y = vars0[1]
#k = vars0[2]
#g = vars0[3]
#r = vars0[4]
# == functions to minimize to find steady states == #
f = [0,0,0,0,0]
# HH Euler
f[0] = (1.0/c)*cbeta*(r + 1.0 - cdelta) - (1.0+g)/c
# Goods market clearing
f[1] = y - c - k*(1.0 + g) + k*(1.0-cdelta)
# Capital Market clearing
f[2] = r - (k)**(calpha-1.0)*calpha**2.0
# production function for final good
f[3] = y - k**calpha
# growth rate
pi = (calpha - 1.0) * k**calpha #small pi, this isnt actual profits
f[4] = g - (cgamma - 1.0) * clambda * (csigma*clambda*pi)**(csigma/(1.0-csigma))
return f
# == Initial Guesses == #
vars0 = list(np.ones((5,)))
# == Solving for Steady State == #
xss = findroot(steady_s, vars0)
工作起来很有魅力!谢谢你