sum all combinations of 2d array

So I have an array

a = [1,2,3,4;5,6,7,8;9,10,11,12;13,14,15,16];

now i want to sum every combination. Like a number padlock, i.e

    value1 = a(1,1)+a(2,1)+a(3,1)+a(4,1);
    value2 = a(1,1)+a(2,1)+a(3,1)+a(4,2);
    value3 = a(1,1)+a(2,1)+a(3,1)+a(4,3);
    value4 = a(1,1)+a(2,1)+a(3,1)+a(4,4);

    value5 = a(1,1)+a(2,1)+a(3,2)+a(4,1);
    value6 = a(1,1)+a(2,1)+a(3,2)+a(4,2);
    value7 = a(1,1)+a(2,1)+a(3,2)+a(4,3);
    value8 = a(1,1)+a(2,1)+a(3,2)+a(4,4);

    value9 = a(1,1)+a(2,1)+a(3,3)+a(4,1);
    value10 = a(1,1)+a(2,1)+a(3,3)+a(4,2);
    value11 = a(1,1)+a(2,1)+a(3,3)+a(4,3);
    value12 = a(1,1)+a(2,1)+a(3,3)+a(4,4);

etc etc etc

except I cant figure out the for loops. Espscially with the fact that the array size can change, so I cant just statically place for loops inside of each other, because i dont necessarily know how many rows/columns there will be? Has anyone done anything like this? Thanks

[Alex]

Ahh I did find an answer thanks. it involves mesh grid

[the cyclist]

I'd be curious to see the solution you came up with. There's no harm in posting your own answer.

[Fangjun Jiang]

Are these all the combination or just a sample of examples? What is the logic for picking the numbers? one number from each row (or column)?

[Franc Lever]

Like This, and in C you cna input any operation or function you wish

 a=[1 2 3 4 5];
 b=[1 2 3 5 6];
 [A,B]=meshgrid(a,b);
 C=A+B

 C =

     2     3     4     5     6
     3     4     5     6     7
     4     5     6     7     8
     6     7     8     9    10
     7     8     9    10    11

Answer 1

[Walter Roberson]

by_row = mat2cell(a,ones(1,size(a,1)),size(a,2));
d = numel(by_row);
combos = cell(1,d);
[combos{:}] = ndgrid(by_row{:});
values = sum(cat(d+1,combos{:}),d+1);

The result of this will be that values will be an array, each dimension of which is the number of columns in a, with the number of dimensions being the same as the number of rows in a.

For example, a=rand(3,4) would give a 4 x 4 x 4 result.

(I'll have to recheck whether this is the desirable output size when I have a bit more time.)

[Andrei Bobrov]

values = sum(cat(d+1,combos{:}),d+1);

values = values(:);

Answer 2

[Jos (10584)]

a = [1,2,3,4; 5,6,7,8; 9,10,11,12; 13,14,15,16]; % data
[n,m] = size(a) ;
c = permn(1:m, n) ;  % get all permutations of the column indices
r = repmat(1:n, size(c,1), 1) ;  % create matching row indices
i = sub2ind([n m], r) ;  % transform row and column subindices into linear indices
values = sum(a(i), 2) ;  % sum rows to get the required values

The function PERMN can be downloaded here: https://uk.mathworks.com/matlabcentral/fileexchange/7147-permn-v--n--k-

Answer 3

[Jos (10584)]

And another, faster, solution:

a = [1,2,3,4; 5,6,7,8; 9,10,11,12; 13,14,15,16]; % data
c = mat2cell(a,size(a,1),ones(1,size(a,2))) 
values = sum(allcomb(c{:}),2) ;

The function ALLCOMB can be downloaded from the File Exchange:

https://uk.mathworks.com/matlabcentral/fileexchange/10064-allcomb-varargin-