Filling in array with specific numbers

Hi, So I have 3 arrays that I would like to combine in a specific order like so:

A = [1;2;3];
B = [a;b;c;d];
C = [I,II,III];
ie:
A = 1     B = a       C = I
    2         b           II
    3         c           III
              d

and want them to be sorted like so:
M = [1,a,I;1,b,I;1,c,I;1,d,I;2,a,I;2,b,I;2,c,I;2,d,I;3,a,I;....etc until... 1,a,II;1,b,II;..etc];
ie: Want to fill the matrix with every combination of the 3 matrices in order like so:

 M = 1 a I
     1 b I
     1 c I
     1 d I
     2 a I
     2 b I
     2 c I
     2 d I
     3 a I
     3 b I
     3 c I
     3 d I
     1 a II
     1 b II
     1 c II
     1 d II
     2 a II
.. and so on.

Maple has a Fill function which I could use to do this easily, however I couldn't find a similar function in Matlab so I was wondering what the most efficient way of doing it would be.

Thanks in advance.

[Stephen23]

You might like to have a look at my FEX submission natsrtorows:

http://www.mathworks.com/matlabcentral/fileexchange/47433-natural-order-row-sort

This function sorts a cell array of strings into order, taking into account the values of any numeric in the strings. And just like MATLAB's sortrows you can tell it which columns you want to sort by.

So given an input matrix M containing all of the required rows, but in the wrong order, we can simply call natsortrows to sort them into the required order:

N = cellfun(@num2str,M,'UniformOutput',false);
[~,idx] = natsortrows(N,[3,1,2]);
M = M(idx,:);

which sorts by the third, then the first and second columns.

Answer 1

[Star Strider]

The only way I can see to do this is with nested for loops:

A = {1;2;3};
B = {'a';'b';'c';'d'};
C = {'I','II','III'};

k = 0;
for k1 = 1:length(C)
    for k2 = 1:length(A)
        for k3 = 1:length(B)
            k = k + 1;
            M{k} = {A(k2) B(k3) C(k1)};
        end
    end
end

Q = M(1:10)'        % Sample Output
celldisp(Q)         % Display Sample Output

[John Andrews]

Thanks, that's what I ended up doing. Was hoping there was a more efficient(?) way of doing it.

[Star Strider]

My pleasure.

Unfortunately, since you have a mix of numeric (‘A’) and character (‘B’,‘C’) arrays, you have to use cell arrays. The repmat function will work on those, so David Young may have the more efficient solution.

Give him a vote. I did.

[David Young]

Thanks!

[Star Strider]

@David — Well earned! I went back and ran your code with my cell arrays and it worked as it should. So many functions don’t work and play well with cell arrays, I didn’t try repmat. It turns out repmat doesn’t care what the data type is, so long as the dimensions are compatible.

Answer 2

[David Young]

One way, using repmat to make the repeated values:

% test data
A = [1;2;3];
B = [11;12;13;14];
C = [21;22;23];

% compute combination matrix 
nA = length(A);
nB = length(B);
nC = length(C);
Acol = repmat(A.', nB, nC);
Bcol = repmat(B, nA*nC, 1);
Ccol = repmat(C.', nA*nB, 1);
M = [Acol(:) Bcol(:) Ccol(:)];