'n' number of nested for loops

I have a cell array M with 4 cell elements and each cell element has a 8x2 matrix.

I'm trying to making different combinations using nested for loops as

n = length(M);
[s,d]  = cellfun(@size,M);
ncombs = prod(s);

P = cell(1,ncombs);

k = 0;
for i = 1:size(M{1},1)
    for j = 1:size(M{2},1)
        for x = 1:size(M{3},1)
            for y = 1:size(M{4},1)
                k = k+1;
                P{k} = [M{1}(i,:);M{2}(j,:);M{3}(x,:);M{4}(y,:)];
            end
        end
    end
end

Now in this case, I have n = 4 and hence 4 nested loops. Can I generalize this thing with any n? For example like for n = 2, 2 nested loops and correspondingly P{k} becomes [M{1}(i,:),M{2}(j,:)]

[Matt J]

I have a cell array M with 4 cell elements and each cell element has a 8x2 matrix.

It doesn't make much sense for them to be a cell array in that case. You could have an 8x2x4 matrix.

[Fawad Khan]

You're right, they could be a 3-dimensional matrix but I pass the cell element to another library function which uses it as elements of a cell array.

Answer 1

[Matt J]

[c{1:n}]=ndgrid(1:8);
c=reshape(cat(n+1,c{:})  [],n);

K=size(c,1);

Q=cell(n,1);
for i=1:n

    Q{i}=reshape(M{i}( c(:,n+1-i),: ), 1,[],K);
    
end

P=num2cell(vertcat(Q{:}), [1,2]);

[Fawad Khan]

Thank you for the help. However, the results aren't matching. All elements of the P cell array are supposed to be 4x2 matrices. But with your method I'm getting 4x1 matrices. Could you please help with that?

I ran a test script for it for n = 2 which would return 2x2 matrices. Maybe you can check that as well?

%% 

M{1} = ones(4,2)*rand;
M{2} = ones(4,2)*rand;

%% Method 01 

n = length(M);
[s,d]  = cellfun(@size,M);
ncombs = prod(s);
P = cell(ncombs,1);

k = 0;

for i = 1:size(M{1},1)
    for j = 1:size(M{2},1)
                k = k+1;
                P{k} = [M{1}(i,:);M{2}(j,:)];
    end
end

%% Method 02

c = cell(1,n);
[c{1:n}] = ndgrid(1:size(M{1},1));

c = reshape(cat(n+1,c{:}),  [],n);
K = size(c,1);
Q = cell(n,1);

for i=1:n
    Q{i} = reshape(M{i}( c(:,n+1-i) ), 1,[],K);
    
end
P2 = num2cell(vertcat(Q{:}), [1,2]);

[Matt J]

Should be

 Q{i} = reshape(M{i}( c(:,n+1-i) , : ), 1,[],K);

[Fawad Khan]

Yes that works. Thanks a lot

[Fawad Khan]

Sorry to bother you again @Matt J. But I think I'm still not getting the correct results. It'd be a great help if you could take a look at the test script I'm trying to run.

%% 

M{1} = rand(8,2);
M{2} = rand(8,2);

%% Method 01 

n = length(M);
[s,d]  = cellfun(@size,M);
ncombs = prod(s);
P = cell(ncombs,1);

k = 0;
for i = 1:size(M{1},1)
    for j = 1:size(M{2},1)
                k = k+1;
                P{k} = [M{1}(i,:);M{2}(j,:)];
    end
end

%% Method 02

c = cell(1,n);
[c{1:n}] = ndgrid(1:size(M{1},1));

c = reshape(cat(n+1,c{:}),  [],n);
K = size(c,1);
Q = cell(n,1);

for i=1:n
    Q{i} = reshape(M{i}( c(:,n+1-i) , : ), 1,[],K);
end
P2 = num2cell(vertcat(Q{:}), [1,2]);

In this case, P{1} and P2{1} should match. But in P2, all the P2{i}(1,1) are equal to P2{i}(1,2) which doesn't quite seem right.

[Fawad Khan]

I found the error in my code. I had to take transpose there

 Q{i} = reshape(M{i}( c(:,n+1-i) , : )', 1,[],K);

instead of

 Q{i} = reshape(M{i}( c(:,n+1-i) , : ), 1,[],K);

Thanks a lot for the help.