从输入文件中读取数组并优化变量Python

时间：2017-05-30 13:49:25

标签： python-2.7 numpy optimization eigenvalue

我有一个简单的Python代码，它从文件中读取两个矩阵，每个矩阵元素包含两个未定义的变量，A和B.读入后，A和B被赋值，字符串使用{{ 1}}（我知道这个安全问题，但这个代码只会被我使用）。为每个矩阵形成eval()阵列，并使用两个矩阵求解一般特征值问题。代码如下：

numpy

这可以工作并输出答案。但是我希望改变参数A和B，以最小化它给我的价值。 （例如）：

from __future__ import division 
from scipy.linalg import eigh
import numpy as np

Mat_size = 4 ## Define matrix size

## Input the two matrices from each side of the generalised eigenvalue problem
HHfile = "Matrix_4x4HH.mat" ## left
SSfile = "Matrix_4x4SS.mat" ## right

## Read matrix files
f1 = open(HHfile, 'r') 
HH_data = f1.read()

f2 = open(SSfile, 'r') 
SS_data = f2.read() 

# Define dictionary of variables
trans = {'A':2.1,
         'B':3,
        }

HHmat = eval(HH_data, trans)
SSmat = eval(SS_data, trans)

## Convert to numpy array
HHmat2 = np.array(HHmat)
SSmat2 = np.array(SSmat)

## Form correct matrix dimensions
shape = ( Mat_size, Mat_size )
HH = HHmat2.reshape( shape )
SS = SSmat2.reshape( shape )  
ev, ew = eigh(HH,SS)

## solve eigenvalue problem
eigenValues,eigenVectors = eigh(HH,SS)
print("Eigenvalue:",eigenValues[0])

我遇到的问题是必须定义A和B才能使def func_min(x): A, B = x ev, ew=eigh(HH,SS) return ev[0] x0 = np.array([2.1, 3]) # Preliminary guess minimize(func_min, x0) 调用工作;因此，由于它们具有指定的值，所以不允许改变A和B，因此不允许优化程序。我已经尝试了几种不同的文件读取方法（pandas，csv，np.genfromtxt等...）但似乎总是留下相同的问题。是否有更好的方法，或对当前代码进行修改以实现此目的？

以下是文件的输入。我不确定如何包含它们，但如果更好的话，我可以使用文件上传服务。

来自Matrix_4x4HH.mat的输入

eval

来自Matrix_4x4SS.mat的输入

-.7500000000000000/B**3*A**5/(A+B)**6-4.500000000000000/B**2*A**4/(A+B)**6-12./B*A**3/(A+B)**6-19.50000000000000*A**2/(A+B)**6-118.5000000000000*B*A/(A+B)**6-19.50000000000000*B**2/(A+B)**6-12.*B**3/A/(A+B)**6-4.500000000000000*B**4/A**2/(A+B)**6-.7500000000000000*B**5/A**3/(A+B)**6+2./B**3*A**4/(A+B)**6+13./B**2*A**3/(A+B)**6+36./B*A**2/(A+B)**6+165.*A/(A+B)**6+165.*B/(A+B)**6+36.*B**2/A/(A+B)**6+13.*B**3/A**2/(A+B)**6+2.*B**4/A**3/(A+B)**6,-.3750000000000000/B**3*A**5/(A+B)**6-2.125000000000000/B**2*A**4/(A+B)**6-4.750000000000000/B*A**3/(A+B)**6-23.87500000000000*A**2/(A+B)**6-1.750000000000000*B*A/(A+B)**6-23.87500000000000*B**2/(A+B)**6-4.750000000000000*B**3/A/(A+B)**6-2.125000000000000*B**4/A**2/(A+B)**6-.3750000000000000*B**5/A**3/(A+B)**6-1.500000000000000/B**2*A**3/(A+B)**6-5.500000000000000/B*A**2/(A+B)**6-25.*A/(A+B)**6-25.*B/(A+B)**6-5.500000000000000*B**2/A/(A+B)**6-1.500000000000000*B**3/A**2/(A+B)**6,1.500000000000000/B**3*A**6/(A+B)**7+10.12500000000000/B**2*A**5/(A+B)**7+29.12500000000000/B*A**4/(A+B)**7+45.25000000000000*A**3/(A+B)**7-135.1250000000000*B*A**2/(A+B)**7+298.7500000000000*B**2*A/(A+B)**7+14.87500000000000*B**3/(A+B)**7-5.750000000000000*B**4/A/(A+B)**7-2.375000000000000*B**5/A**2/(A+B)**7-.3750000000000000*B**6/A**3/(A+B)**7-4./B**3*A**5/(A+B)**7-27./B**2*A**4/(A+B)**7-76.50000000000000/B*A**3/(A+B)**7-9.500000000000000*A**2/(A+B)**7-305.*B*A/(A+B)**7-362.*B**2/(A+B)**7-14.50000000000000*B**3/A/(A+B)**7-1.500000000000000*B**4/A**2/(A+B)**7,-.3750000000000000/B**3*A**6/(A+B)**7-2.375000000000000/B**2*A**5/(A+B)**7-5.750000000000000/B*A**4/(A+B)**7+14.87500000000000*A**3/(A+B)**7+298.7500000000000*B*A**2/(A+B)**7-135.1250000000000*B**2*A/(A+B)**7+45.25000000000000*B**3/(A+B)**7+29.12500000000000*B**4/A/(A+B)**7+10.12500000000000*B**5/A**2/(A+B)**7+1.500000000000000*B**6/A**3/(A+B)**7-1.500000000000000/B**2*A**4/(A+B)**7-14.50000000000000/B*A**3/(A+B)**7-362.*A**2/(A+B)**7-305.*B*A/(A+B)**7-9.500000000000000*B**2/(A+B)**7-76.50000000000000*B**3/A/(A+B)**7-27.*B**4/A**2/(A+B)**7-4.*B**5/A**3/(A+B)**7,-.3750000000000000/B**3*A**5/(A+B)**6-2.125000000000000/B**2*A**4/(A+B)**6-4.750000000000000/B*A**3/(A+B)**6-23.87500000000000*A**2/(A+B)**6-1.750000000000000*B*A/(A+B)**6-23.87500000000000*B**2/(A+B)**6-4.750000000000000*B**3/A/(A+B)**6-2.125000000000000*B**4/A**2/(A+B)**6-.3750000000000000*B**5/A**3/(A+B)**6-1.500000000000000/B**2*A**3/(A+B)**6-5.500000000000000/B*A**2/(A+B)**6-25.*A/(A+B)**6-25.*B/(A+B)**6-5.500000000000000*B**2/A/(A+B)**6-1.500000000000000*B**3/A**2/(A+B)**6,-1.500000000000000/B**3*A**5/(A+B)**6-10.50000000000000/B**2*A**4/(A+B)**6-35./B*A**3/(A+B)**6-101.5000000000000*A**2/(A+B)**6-343.*B*A/(A+B)**6-101.5000000000000*B**2/(A+B)**6-35.*B**3/A/(A+B)**6-10.50000000000000*B**4/A**2/(A+B)**6-1.500000000000000*B**5/A**3/(A+B)**6+2./B**3*A**4/(A+B)**6+16./B**2*A**3/(A+B)**6+45./B*A**2/(A+B)**6+201.*A/(A+B)**6+201.*B/(A+B)**6+45.*B**2/A/(A+B)**6+16.*B**3/A**2/(A+B)**6+2.*B**4/A**3/(A+B)**6,.7500000000000000/B**3*A**6/(A+B)**7+5.625000000000000/B**2*A**5/(A+B)**7+18.87500000000000/B*A**4/(A+B)**7+19.62500000000000*A**3/(A+B)**7+170.3750000000000*B*A**2/(A+B)**7+73.87500000000000*B**2*A/(A+B)**7+57.62500000000000*B**3/(A+B)**7+4.875000000000000*B**4/A/(A+B)**7+.3750000000000000*B**5/A**2/(A+B)**7+1.500000000000000/B**2*A**4/(A+B)**7+7.500000000000000/B*A**3/(A+B)**7-1.*A**2/(A+B)**7+39.*B*A/(A+B)**7+47.50000000000000*B**2/(A+B)**7+1.500000000000000*B**3/A/(A+B)**7,.3750000000000000/B**2*A**5/(A+B)**7+4.875000000000000/B*A**4/(A+B)**7+57.62500000000000*A**3/(A+B)**7+73.87500000000000*B*A**2/(A+B)**7+170.3750000000000*B**2*A/(A+B)**7+19.62500000000000*B**3/(A+B)**7+18.87500000000000*B**4/A/(A+B)**7+5.625000000000000*B**5/A**2/(A+B)**7+.7500000000000000*B**6/A**3/(A+B)**7+1.500000000000000/B*A**3/(A+B)**7+47.50000000000000*A**2/(A+B)**7+39.*B*A/(A+B)**7-1.*B**2/(A+B)**7+7.500000000000000*B**3/A/(A+B)**7+1.500000000000000*B**4/A**2/(A+B)**7,1.500000000000000/B**3*A**6/(A+B)**7+10.12500000000000/B**2*A**5/(A+B)**7+29.12500000000000/B*A**4/(A+B)**7+45.25000000000000*A**3/(A+B)**7-135.1250000000000*B*A**2/(A+B)**7+298.7500000000000*B**2*A/(A+B)**7+14.87500000000000*B**3/(A+B)**7-5.750000000000000*B**4/A/(A+B)**7-2.375000000000000*B**5/A**2/(A+B)**7-.3750000000000000*B**6/A**3/(A+B)**7-4./B**3*A**5/(A+B)**7-27./B**2*A**4/(A+B)**7-76.50000000000000/B*A**3/(A+B)**7-9.500000000000000*A**2/(A+B)**7-305.*B*A/(A+B)**7-362.*B**2/(A+B)**7-14.50000000000000*B**3/A/(A+B)**7-1.500000000000000*B**4/A**2/(A+B)**7,.7500000000000000/B**3*A**6/(A+B)**7+5.625000000000000/B**2*A**5/(A+B)**7+18.87500000000000/B*A**4/(A+B)**7+19.62500000000000*A**3/(A+B)**7+170.3750000000000*B*A**2/(A+B)**7+73.87500000000000*B**2*A/(A+B)**7+57.62500000000000*B**3/(A+B)**7+4.875000000000000*B**4/A/(A+B)**7+.3750000000000000*B**5/A**2/(A+B)**7+1.500000000000000/B**2*A**4/(A+B)**7+7.500000000000000/B*A**3/(A+B)**7-1.*A**2/(A+B)**7+39.*B*A/(A+B)**7+47.50000000000000*B**2/(A+B)**7+1.500000000000000*B**3/A/(A+B)**7,-5.250000000000000/B**3/(A+B)**8*A**7-40.50000000000000/B**2/(A+B)**8*A**6-138.7500000000000/B/(A+B)**8*A**5-280.7500000000000/(A+B)**8*A**4-629.7500000000000*B/(A+B)**8*A**3+770.2500000000000*B**2/(A+B)**8*A**2-836.7500000000000*B**3/(A+B)**8*A-180.2500000000000*B**4/(A+B)**8-52.*B**5/(A+B)**8/A-12.75000000000000*B**6/(A+B)**8/A**2-1.500000000000000*B**7/(A+B)**8/A**3+14./B**3/(A+B)**8*A**6+107./B**2/(A+B)**8*A**5+355./B/(A+B)**8*A**4+778./(A+B)**8*A**3+284.*B/(A+B)**8*A**2+597.*B**2/(A+B)**8*A+911.*B**3/(A+B)**8+100.*B**4/(A+B)**8/A+20.*B**5/(A+B)**8/A**2+2.*B**6/(A+B)**8/A**3,.7500000000000000/B**3/(A+B)**8*A**7+5.625000000000000/B**2/(A+B)**8*A**6+18.25000000000000/B/(A+B)**8*A**5+52.50000000000000/(A+B)**8*A**4+397.*B/(A+B)**8*A**3-2356.250000000000*B**2/(A+B)**8*A**2+397.*B**3/(A+B)**8*A+52.50000000000000*B**4/(A+B)**8+18.25000000000000*B**5/(A+B)**8/A+5.625000000000000*B**6/(A+B)**8/A**2+.7500000000000000*B**7/(A+B)**8/A**3+1.500000000000000/B**2/(A+B)**8*A**5+10.50000000000000/B/(A+B)**8*A**4-276.5000000000000/(A+B)**8*A**3+1848.500000000000*B/(A+B)**8*A**2+1848.500000000000*B**2/(A+B)**8*A-276.5000000000000*B**3/(A+B)**8+10.50000000000000*B**4/(A+B)**8/A+1.500000000000000*B**5/(A+B)**8/A**2,-.3750000000000000/B**3*A**6/(A+B)**7-2.375000000000000/B**2*A**5/(A+B)**7-5.750000000000000/B*A**4/(A+B)**7+14.87500000000000*A**3/(A+B)**7+298.7500000000000*B*A**2/(A+B)**7-135.1250000000000*B**2*A/(A+B)**7+45.25000000000000*B**3/(A+B)**7+29.12500000000000*B**4/A/(A+B)**7+10.12500000000000*B**5/A**2/(A+B)**7+1.500000000000000*B**6/A**3/(A+B)**7-1.500000000000000/B**2*A**4/(A+B)**7-14.50000000000000/B*A**3/(A+B)**7-362.*A**2/(A+B)**7-305.*B*A/(A+B)**7-9.500000000000000*B**2/(A+B)**7-76.50000000000000*B**3/A/(A+B)**7-27.*B**4/A**2/(A+B)**7-4.*B**5/A**3/(A+B)**7,.3750000000000000/B**2*A**5/(A+B)**7+4.875000000000000/B*A**4/(A+B)**7+57.62500000000000*A**3/(A+B)**7+73.87500000000000*B*A**2/(A+B)**7+170.3750000000000*B**2*A/(A+B)**7+19.62500000000000*B**3/(A+B)**7+18.87500000000000*B**4/A/(A+B)**7+5.625000000000000*B**5/A**2/(A+B)**7+.7500000000000000*B**6/A**3/(A+B)**7+1.500000000000000/B*A**3/(A+B)**7+47.50000000000000*A**2/(A+B)**7+39.*B*A/(A+B)**7-1.*B**2/(A+B)**7+7.500000000000000*B**3/A/(A+B)**7+1.500000000000000*B**4/A**2/(A+B)**7,.7500000000000000/B**3/(A+B)**8*A**7+5.625000000000000/B**2/(A+B)**8*A**6+18.25000000000000/B/(A+B)**8*A**5+52.50000000000000/(A+B)**8*A**4+397.*B/(A+B)**8*A**3-2356.250000000000*B**2/(A+B)**8*A**2+397.*B**3/(A+B)**8*A+52.50000000000000*B**4/(A+B)**8+18.25000000000000*B**5/(A+B)**8/A+5.625000000000000*B**6/(A+B)**8/A**2+.7500000000000000*B**7/(A+B)**8/A**3+1.500000000000000/B**2/(A+B)**8*A**5+10.50000000000000/B/(A+B)**8*A**4-276.5000000000000/(A+B)**8*A**3+1848.500000000000*B/(A+B)**8*A**2+1848.500000000000*B**2/(A+B)**8*A-276.5000000000000*B**3/(A+B)**8+10.50000000000000*B**4/(A+B)**8/A+1.500000000000000*B**5/(A+B)**8/A**2,-1.500000000000000/B**3/(A+B)**8*A**7-12.75000000000000/B**2/(A+B)**8*A**6-52./B/(A+B)**8*A**5-180.2500000000000/(A+B)**8*A**4-836.7500000000000*B/(A+B)**8*A**3+770.2500000000000*B**2/(A+B)**8*A**2-629.7500000000000*B**3/(A+B)**8*A-280.7500000000000*B**4/(A+B)**8-138.7500000000000*B**5/(A+B)**8/A-40.50000000000000*B**6/(A+B)**8/A**2-5.250000000000000*B**7/(A+B)**8/A**3+2./B**3/(A+B)**8*A**6+20./B**2/(A+B)**8*A**5+100./B/(A+B)**8*A**4+911./(A+B)**8*A**3+597.*B/(A+B)**8*A**2+284.*B**2/(A+B)**8*A+778.*B**3/(A+B)**8+355.*B**4/(A+B)**8/A+107.*B**5/(A+B)**8/A**2+14.*B**6/(A+B)**8/A**3

修改

我想这个问题的重要部分是如何从一个文件读入一个numpy数组中的方程组，并且能够在不需要1./B**3*A**3/(A+B)**6+6./B**2*A**2/(A+B)**6+15./B*A/(A+B)**6+84./(A+B)**6+15.*B/A/(A+B)**6+6.*B**2/A**2/(A+B)**6+1.*B**3/A**3/(A+B)**6,-.5000000000000000/B**3*A**3/(A+B)**6-3.500000000000000/B**2*A**2/(A+B)**6-9.500000000000000/B*A/(A+B)**6-53./(A+B)**6-9.500000000000000*B/A/(A+B)**6-3.500000000000000*B**2/A**2/(A+B)**6-.5000000000000000*B**3/A**3/(A+B)**6,-2./B**3*A**4/(A+B)**7-12.50000000000000/B**2*A**3/(A+B)**7-32.50000000000000/B*A**2/(A+B)**7+18.50000000000000*A/(A+B)**7-253.*B/(A+B)**7-17.50000000000000*B**2/A/(A+B)**7-4.500000000000000*B**3/A**2/(A+B)**7-.5000000000000000*B**4/A**3/(A+B)**7,-.5000000000000000/B**3*A**4/(A+B)**7-4.500000000000000/B**2*A**3/(A+B)**7-17.50000000000000/B*A**2/(A+B)**7-253.*A/(A+B)**7+18.50000000000000*B/(A+B)**7-32.50000000000000*B**2/A/(A+B)**7-12.50000000000000*B**3/A**2/(A+B)**7-2.*B**4/A**3/(A+B)**7,-.5000000000000000/B**3*A**3/(A+B)**6-3.500000000000000/B**2*A**2/(A+B)**6-9.500000000000000/B*A/(A+B)**6-53./(A+B)**6-9.500000000000000*B/A/(A+B)**6-3.500000000000000*B**2/A**2/(A+B)**6-.5000000000000000*B**3/A**3/(A+B)**6,2./B**3*A**3/(A+B)**6+14./B**2*A**2/(A+B)**6+38./B*A/(A+B)**6+212./(A+B)**6+38.*B/A/(A+B)**6+14.*B**2/A**2/(A+B)**6+2.*B**3/A**3/(A+B)**6,1./B**3*A**4/(A+B)**7+6.500000000000000/B**2*A**3/(A+B)**7+16.50000000000000/B*A**2/(A+B)**7-19.*A/(A+B)**7+118.*B/(A+B)**7+4.500000000000000*B**2/A/(A+B)**7+.5000000000000000*B**3/A**2/(A+B)**7,.5000000000000000/B**2*A**3/(A+B)**7+4.500000000000000/B*A**2/(A+B)**7+118.*A/(A+B)**7-19.*B/(A+B)**7+16.50000000000000*B**2/A/(A+B)**7+6.500000000000000*B**3/A**2/(A+B)**7+1.*B**4/A**3/(A+B)**7,-2./B**3*A**4/(A+B)**7-12.50000000000000/B**2*A**3/(A+B)**7-32.50000000000000/B*A**2/(A+B)**7+18.50000000000000*A/(A+B)**7-253.*B/(A+B)**7-17.50000000000000*B**2/A/(A+B)**7-4.500000000000000*B**3/A**2/(A+B)**7-.5000000000000000*B**4/A**3/(A+B)**7,1./B**3*A**4/(A+B)**7+6.500000000000000/B**2*A**3/(A+B)**7+16.50000000000000/B*A**2/(A+B)**7-19.*A/(A+B)**7+118.*B/(A+B)**7+4.500000000000000*B**2/A/(A+B)**7+.5000000000000000*B**3/A**2/(A+B)**7,7./B**3/(A+B)**8*A**5+50./B**2/(A+B)**8*A**4+154./B/(A+B)**8*A**3+331./(A+B)**8*A**2-147.*B/(A+B)**8*A+848.*B**2/(A+B)**8+80.*B**3/(A+B)**8/A+19.*B**4/(A+B)**8/A**2+2.*B**5/(A+B)**8/A**3,1./B**3/(A+B)**8*A**5+8.500000000000000/B**2/(A+B)**8*A**4+31./B/(A+B)**8*A**3-152.5000000000000/(A+B)**8*A**2+1568.*B/(A+B)**8*A-152.5000000000000*B**2/(A+B)**8+31.*B**3/(A+B)**8/A+8.500000000000000*B**4/(A+B)**8/A**2+1.*B**5/(A+B)**8/A**3,-.5000000000000000/B**3*A**4/(A+B)**7-4.500000000000000/B**2*A**3/(A+B)**7-17.50000000000000/B*A**2/(A+B)**7-253.*A/(A+B)**7+18.50000000000000*B/(A+B)**7-32.50000000000000*B**2/A/(A+B)**7-12.50000000000000*B**3/A**2/(A+B)**7-2.*B**4/A**3/(A+B)**7,.5000000000000000/B**2*A**3/(A+B)**7+4.500000000000000/B*A**2/(A+B)**7+118.*A/(A+B)**7-19.*B/(A+B)**7+16.50000000000000*B**2/A/(A+B)**7+6.500000000000000*B**3/A**2/(A+B)**7+1.*B**4/A**3/(A+B)**7,1./B**3/(A+B)**8*A**5+8.500000000000000/B**2/(A+B)**8*A**4+31./B/(A+B)**8*A**3-152.5000000000000/(A+B)**8*A**2+1568.*B/(A+B)**8*A-152.5000000000000*B**2/(A+B)**8+31.*B**3/(A+B)**8/A+8.500000000000000*B**4/(A+B)**8/A**2+1.*B**5/(A+B)**8/A**3,2./B**3/(A+B)**8*A**5+19./B**2/(A+B)**8*A**4+80./B/(A+B)**8*A**3+848./(A+B)**8*A**2-147.*B/(A+B)**8*A+331.*B**2/(A+B)**8+154.*B**3/(A+B)**8/A+50.*B**4/(A+B)**8/A**2+7.*B**5/(A+B)**8/A**3 的情况下为变量赋值。作为使用numpy通常可以做的事情的一个例子：

eval

这给出了：

import numpy as np
A = 1
B = 1
arr = np.array([[A+2*B,2],[2,B+6*(B+A)]])
print arr

numpy数组包含代数项，并且在打印时插入了A和B的指定值。这可能是从一个文件读入一个numpy数组的方程吗？我查看了numpy文档，是否与正在读入的数据类型有关？即我不能将dtype指定为int或float，因为每个数组元素都包含int，float和text。我觉得Python缺少一个非常简单的方面可以做到这一点。

0 个答案:

没有答案
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