Python中的二维优化(最小化)(使用scipy.optimize) [英] Two dimensional Optimization (minimization) in Python (using scipy.optimize)

问题描述

我正在尝试优化(最小化)如下定义的二维函数E(n,k):

I am trying to optimize (minimize) a two dimensional function E(n,k) defined as follows:

error=lambda x,y,w: (math.log(abs(Tformulated(x,y,w))) - math.log(abs(Tw[w])))**2 + (math.atan2(Tformulated(x,y,w).imag,Tformulated(x,y,w).real) - math.atan2(Tw[w].imag,Tw[w].real))**2

其中Tformulated的获取方式如下:

def Tformulated(n,k,w):
    z=1j
    L=1
    C=0.1
    RC=(w*L)/C
    n1=complex(1,0)
    n3=complex(1,0)
    n2=complex(n,k)
    FP=1/(1-(((n2-n1)/(n2+n1))*((n2-n3)/(n2+n3))*math.exp(-2*z*n2*RC)))
    Tform=((2*n2*(n1+n3))/((n2+n1)*(n2+n3)))*(math.exp(-z*(n2-n1)*RC))*FP
    return Tform

和Tw是先前计算的具有复杂值元素的列表. 我确切想做的是针对w的每个值(用于错误x，y，w ....").我想将x&的值的函数错误"最小化. y. w的范围是1到2048.因此，它基本上是一个2D最小化问题.我曾经尝试过编程(尽管我被困在使用哪种方法以及如何使用它)上；我的代码如下:

and Tw is a list previously calculated having complex valued elements. What I am exactly trying to do is for each value of w (used in "error x,y,w ....") I want to minimize the function "error" for the values of x & y. w ranges from 1 to 2048. So, it is basically a 2D minimization problem. I have tried programming on my part (though I am getting stuck at what method to use and how to use it); my code is as follows :

temp=[]
i=range(5)
retval = fmin_powell(error , x ,y, args=(i) , maxiter=100 ,maxfun=100)
temp.append(retval)

即使fmin_powell是正确的方法，我也不确定.

I am not sure even if fmin_powell is the correct way to go.

推荐答案

这是最简单的示例:

from scipy.optimize import fmin

def minf(x):
  return x[0]**2 + (x[1]-1.)**2

print fmin(minf,[1,2])

[输出]:

Optimization terminated successfully.
         Current function value: 0.000000
         Iterations: 44
         Function evaluations: 82
[ -1.61979362e-05   9.99980073e-01]

这里可能的陷阱是最小化例程期望列表作为参数.有关所有详细信息，请参见文档.不知道是否可以直接最小化复数值函数，可能需要分别考虑实部和虚部.

A possible gotcha here is that the minimization routines are expecting a list as an argument. See the docs for all the gory details. Not sure if you can minimize complex-valued functions directly, you might need to consider the real and imaginary parts separately.

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