求解非负最小二乘问题“xA = b”

Question

我想找到“xA = b”的非负最小二乘解。我很高兴在Python，Matlab或R中得到答案。

A是一个6 * 10矩阵，而b是8192 * 10矩阵。

我发现了一些函数：Python中的least_squares和nnls以及Matlab中的lsqnonneg。

nnls和lsqnonneg仅用于Ax=b。

我的least_squares执行给我一个错误：

import numpy as np 
import pandas as pd 
from matplotlib import pyplot as plt 

from scipy.optimize import least_squares 

spec=pd.read_csv('spec.csv',sep=',',header=None) 
y=pd.read_csv('y.csv',sep=',',header=None) 

spec=np.array(spec).T 
y=np.array(y) 

spec=spec[(0,1,2,3,4,5,6,9),:] 
y=y[(0,1,2,3,4,5,6,9),:] 

print(spec.shape,y.shape) 

def fun(a, x, y): 
    return a*x-y 

a0=np.ones((8192,6)) 
a=least_squares(fun, a0, args=(y.T[:,0], spec.T[:,0]), 
          bounds=([np.zeros((8192,6)), 
          np.ones((8192,6))*np.inf])) 

runfile('C:/Users/Documents/lsq.py', wdir='C:/Users/Documents') (8, 8192) (8, 6) Traceback (most recent call last):

File "", line 1, in runfile('C:/Users/wangm/Documents/lsq.py', wdir='C:/Users/Documents')

File "C:\Anaconda3\lib\site-packages\spyderlib\widgets\externalshell\sitecustomize.py", line 714, in runfile execfile(filename, namespace)

File "C:\Anaconda3\lib\site-packages\spyderlib\widgets\externalshell\sitecustomize.py", line 89, in execfile exec(compile(f.read(), filename, 'exec'), namespace)

File "C:/Users/Documents/lsq.py", line 30, in np.ones((8192,6))*np.inf]))

File "C:\Anaconda3\lib\site-packages\scipy\optimize_lsq\least_squares.py", line 742, in least_squares raise ValueError("x0 must have at most 1 dimension.")

ValueError: x0 must have at most 1 dimension.

Answer 1

这是这样一个共同的矩阵问题，你可以使用mrdivide做在一个字符在Matlab。

从文档：

mrdivide , / : Solve systems of linear equations xA = B for x

% Option 1, shorthand: 
x = B/A; 
% Option 2, longhand: 
x = mrdivide(B,A);