All Possible Matrix Permutations

I am trying to write a program that takes integers (or any value, really) and square matrix size m as inputs and returns all possible mxm matrices with those inputs as matrix entries. It would look something like this example input:

allMatrices([0 1],2)

Which would return all 2x2 matrices with 0 and 1 as matrix entries ([0 0; 0 0], [0 0; 0 1], [0 0; 1 1], etc). I would also like to store the matrices so that they can be called individually (M_1, M_2, and so on).

My current strategy is to use

A = unique(nchoosek(repmat('10', 1,4), 4), 'rows')

This lets me index the values A(1:4) as characters for the first 4 entries in a 2x2 matrix, at which point I can use a for-loop to index the remaining entries.

I need to know how to go from my 4 character array ('0000') to a 2x2 matrix ([0 0;0 0]).

And, as always, if there is a more elegant way to do this, please let me know.

Thanks!

Answer 1

[Ameer Hamza]

Starting with char array '10' to create such matrices does not seems to be a good strategy. It is possible, but better to use numeric datatypes from the beginning.

The following code creates a 3D matrix with all possible permutation along the 3rd dimension.

N = 2;
n2 = N^2;

x = repmat({[0, 1]}, 1, n2);
M = reshape(combvec(x{:}), 2, 2, []);

Result

>> M(:,:,1)
ans =
     0     0
     0     0
>> M(:,:,2)
ans =
     1     0
     0     0
>> M(:,:,5)
ans =
     0     1
     0     0
>> M(:,:,end)
ans =
     1     1
     1     1

It shows a few permutations of the matrix.

[Shawn Cooper]

I appreciate it. That works great.

[Ameer Hamza]

I am glad to be of help!

[Akira Agata]

+1

If you don't have Deep Learning Toolbox, one possible workaround will be like this:

[p,q,r,s] = ndgrid([0 1]);
C = mat2cell([p(:),q(:),r(:),s(:)],ones(numel(p),1));
M = cellfun(@(x) reshape(x,[2 2]),C,'UniformOutput',false);

Result is:

>> M{1}
ans =
     0     0
     0     0
>> M{2}
ans =
     1     0
     0     0
...
>> M{end}
ans =
     1     1
     1     1