how to generate random matrix with known matrix

Hello Everyone, For example I have; a=[1 2 3]; b=[4 5]; s=8;

I can create matrix(es?) like this; matrix1=[a b s]; (ans=[1 2 3 4 5 8]) matrix2=[a s b]; (ans=[1 2 3 8 4 5]) matrix3=[s b a]; (ans=[8 4 5 1 2 3]) etc...

But how can I make Matlab generate all the possible (3!) combinations without writing them manually myself? Is it even possible? I am aware that it is not that hard to do with 6 different outcomes but I have (15!) combinations that I have to generate. I appriciate all answers. Thank you.

[David Goodmanson]

Hello Melike,

The perms function will give all possible permutations of the elements of a vector, and you could use that as a building block to get concatenated permutations of small row vectors. However, maybe you should think about the final result. 15! is approximately 1.31e12. Suppose the the average length of the small vectors is 2 and you generated all the results at once as implied above. Then even with everything stored as uint8, it takes39000 Gbytes of memory. That's a lot of memory.

If you only wanted to generate a few million of them or whatever at random, that's doable with the help of the randperm function.

[Melike Öztürk]

Thank you David :) I didn't consider the memory aspect, I will think about alternative approaches.

Answer 1

[Jos (10584)]

Indeed, as David warned, seriously reconsider your approach before trying the following with 15 matrices:

a=[1 2 3]; b=[4 5]; s=8; % your data, row vectors
C = {a b s}              % store them in a cell array for easy access
p = perms(1:numel(C))    % get all permutations
matrix = arrayfun(@(k) [C{p(k,:)}], 1:size(p,1), 'un', 0)  % concatenate the permutations
% matrix{k} now holds the k-th permutation of the three arrays (a, b, and s)

[Melike Öztürk]

Thank you Jos. I didn't realize it would be this easy :) I will consider my approach with memory problem in mind...