all submatrices of given order of a given matrix

I am new in matlab. Is it possible to compute the all submatrices of given order of a given matrix M? For example suppose we have a matrix M of order m by n, and want to compute the all submatrices of order k by n, for some k <= m.

thanks

[John D'Errico]

By the way, expect this to be HUGE for even reasonable values for your matrix sizes.

m = 50;
n = 25;
nchoosek(m,n)
ans =
   1.2641e+14

So there are roughly 126 trillion such sub-matrices. If you will store them too, it will take a serious amount of memory. Just the work to generate them all will be immense, even if done in a loop rather than all at once.

Answer 1

[Guillaume]

Use nchoosek(1:m, k) to find all the possible combination of rows to pick in your matrix, and pick these rows:

%random demo data
m = 5; n = 4;
mx = reshape(1:m*n, m, n);
k = 3;

subrows = num2cell(nchoosek(1:m, k), 2);
subm = cellfun(@(rows) mx(rows, :), subrows, 'UniformOutput', false)

[Raj]

Thanks @ Guillaume for replying. I couldn't understand the nchoosek(1:m,k), i mean where is the role of the given matrix M? When i am running the code, which you have give , the output is: subm =

    [3x4 double]
    [3x4 double]
    [3x4 double]
    [3x4 double]
    [3x4 double]
    [3x4 double]
    [3x4 double]
    [3x4 double]
    [3x4 double]
    [3x4 double]

what is meaning of this? could you please explane little bit.

[Guillaume]

nchoosek(1:m, k) gives you all possible combinations of picking k rows out of m rows. I use these combinations to generate all possible submatrices and put them into a cell array.

Each element of the cell array subm is one of these submatrix. You can see individual element of the cell array with {} brackets:

subm{1} %first submatrix
subm{end} %last submatrix

Or display all of them with:

celldisp(subm)

[Raj]

Thank you so much Guillaume.

[Daniel Wilson-NUnn]

Hi Guillaume, I have been looking at this answer, and I would like to be able to use this code to select all 2x2 matrices of a bigger nxn matrix. Would you be able to advise as to how to do this?

Many thanks

[Guillaume]

Daniel, please start a new question. You'll get more people to contribute that way