How to find every combination of values in a cell array?

Hi, I have a cell array with a variable number of values inside each cell, something like this:

M=

{1,2,3} {4,5,6}{7,8,9}

{10,11}{12,13}{14,15}

{16,17,18,19,20}{21,22,23,24}{25,26,27,28}

I want to create every possible combination of cell arrays contanining one value of each cell, something like this:

m1= m2= m3= m4=

{1}{4}{7} | {2}{4}{7} | {3}{4}{7} | {1}{5}{7}

{10}{12}{14} | {10}{12}{14} | {10}{12}{14} | {10}{12}{14}

{16}{21}{25} | {16}{21}{25} | {16}{21}{25} | {16}{21}{25}

---

and so on.

Is it possible to do it? Tried with nchoosek and cell2mat, but the vary in length of array is a problem I couldn't resolve.

Answer 1

[Stephan]

One way, using allcomb:

M = {[1,2,3], [4,5,6],[7,8,9];
[10,11],[12,13],[14,15];
[16,17,18,19,20],[21,22,23,24],[25,26,27,28]};

res = {allcomb(M{1,1:3}, M{2,1:3}, M{3,1:3})};
res = permute(reshape(res{:}',3,3,[]),[2 1 3]);

The order of the results is a bit different then you wanted, but always only one value is changed:

>> res(:,:,1:5)

ans(:,:,1) =

     1     4     7
    10    12    14
    16    21    25


ans(:,:,2) =

     1     4     7
    10    12    14
    16    21    26


ans(:,:,3) =

     1     4     7
    10    12    14
    16    21    27


ans(:,:,4) =

     1     4     7
    10    12    14
    16    21    28


ans(:,:,5) =

     1     4     7
    10    12    14
    16    22    25

[asobrado]

Works perfect! It's quite a pity Matlab can't handle the size of the real cell array I am using, but the solution is very straightforward. Thank you.