Select mxm matrix from mxn matrix and solve systems of linear equations

Question

Thuy Tran 2020-2-27

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/507841-select-mxm-matrix-from-mxn-matrix-and-solve-systems-of-linear-equations

评论： Thuy Tran 2020-2-28

Hi everyone, 
I has started using Matlab recently. There are two problems in my following code:
+ Firstly, I would like to choose different sets of m columns from n columns matrix. e.g,5 columns from 10 columns. 
There must be 252 sets, however, my code randomly select so there are some sets are the same (only the position of the columns are changed).
+ Secondly, when solving the systems of linear equations with matrix: a=xb then x=a\b, there appears error "Warning: Matrix is close to singular 
or badly scaled.Results may be inaccurate" since the det(a)~0. I have set "if (det(a)<=-1e-12) | (det(a)>=1e-12)" but it seems not so good.
Hope to receive your help. Thank you so much in advance.
A =[ 0     0     2     2     6     3     4     5     2     1
     2     2     0     0     0     1     0     0     0     1
     0     2     0     1     2     0     1     0     0     1
     0     0     0     0     0     0     0     1     1     0
     3     7     1     3     7     3     4     4     3     4 ];
 %choose different sets of 5 columns from 10 columns: 10!/(5!5!)=252 sets
for i=1:252
    c=randperm(length(A),5); 
    a=A(:,c);
b=[5.8; 2.4; 1.6; 0.2; 10];
%Error "Warning: Matrix is close to singular or badly scaled" 
%if det(a)~=0
if (det(a)<=-1e-12) | (det(a)>=1e-12)
   x=a\b;
%Find non-negative and non-Infinities x values
    if (x(:,:)>=0) & (x(:,:)~=Inf) 
        disp(x)
        disp(a)
    end
end
end

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

J. Alex Lee 2020-2-27

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/507841-select-mxm-matrix-from-mxn-matrix-and-solve-systems-of-linear-equations#answer_417607

Does this help with first problem: https://www.mathworks.com/help/matlab/ref/nchoosek.html

Second problem, maybe make tolerance more stringent?

3 个评论
显示 1更早的评论隐藏 1更早的评论

J. Alex Lee 2020-2-28

在 MATLAB Online 中打开

I'm not sure I understand your examples, which are 2x2...but it sounds like you are confirming that you wish to find ALL the unique combinations of K columns of a matrix that has N columns. In this case, nchoosek() should do exactly what you need

clc;
clear;
A =[ 0     0     2     2     6     3     4     5     2     1
	2     2     0     0     0     1     0     0     0     1
	0     2     0     1     2     0     1     0     0     1
	0     0     0     0     0     0     0     1     1     0
	3     7     1     3     7     3     4     4     3     4 ];
K = 5
N = size(A,2)
colsets = nchoosek(1:N,K);
b = [5.8; 2.4; 1.6; 0.2; 10];
% confirm that you have the right number of combinations
nCombinations = size(colsets,1)
for i = 1:nCombinations
	
	ASub = A(:,colsets(i,:));
	
	if rank(ASub) < K
		fprintf('skip combination %3d\n',i)
	else
		x = ASub \ b;
	end
end