Concatenate subcells through one dimension of a cell array without using loops in MATLAB

Question

I have a cell array. Each cell contains a vector of variable length. For example:

example_cell_array=cellfun(@(x)x.*rand([length(x),1]),cellfun(@(x)ones(x,1), num2cell(ceil(10.*rand([7,4]))), 'UniformOutput', false), 'UniformOutput', false)

I need to concatenate the contents of the cells down through one dimension then perform an operation on each concatenated vector generating scalar for each column in my cell array (like sum() for example - the actual operation is complex, time consuming, and not naturally vectorisable - especially for diffent length vecotrs).

I can do this with loops easily (for my concatenated vector sum example) as follows:

[M N]=size(example_cell_array);
result=zeros(1,N);
cat_cell_array=cell(1,N);
for n=1:N
    cat_cell_array{n}=[];
    for m=1:M
        cat_cell_array{n}=[cat_cell_array{n};example_cell_array{m,n}];
    end
end
result=cell2mat(cellfun(@(x)sum(x), cat_cell_array, 'UniformOutput', false))

Unfortunately this is WAY too slow. (My cell array is 1Mx5 with vectors in each cell ranging in length from 100-200)

Is there a simple way to produce the concatenated cell array where the vectors contained in the cells have been concatenated down one dimension?

Something like:

dim=1;
cat_cell_array=(?concatcells?(dim,example_cell_array);

Edit: Since so many people have been testing the solutions: Just FYI, the function I'm applying to each concatenated vector is circ_kappa(x) available from Circular Statistics Toolbox

Answer 1

Some approaches might suggest you to unpack the numeric data from example_cell_array using {..} and then after concatenation pack it back into bigger sized cells to form your cat_cell_array. Then, again you need to unpack numeric data from that concatenated cell array to perform your operation on each cell.

Now, in my view, this multiple unpacking and packing approaches won't be efficient ones if example_cell_array isn't one of your intended outputs. So, considering all these, let me suggest two approaches here.

---

Loopy approach

The first one is a for-loop code -

data1 =  vertcat(example_cell_array{:}); %// extract all numeric data for once
starts = [1 sum(cellfun('length',example_cell_array),1)]; %// intervals lengths
idx = cumsum(starts); %// get indices to work on intervals basis
result  = zeros(1,size(example_cell_array,2)); 
%// replace this with "result(size(example_cell_array,2))=0;" for performance
for k1 = 1:numel(idx)-1
    result(k1) = sum(data1(idx(k1):idx(k1+1)-1));
end

So, you need to edit sum with your actual operation.

---

Almost-vectorized approach

If example_cell_array has a lot of columns, my second suggestion would be an almost vectorized approach, though it doesn't perform badly either with a small number of columns. Now this code uses cellfun at the first line to get the lengths for each cell in concatenated version. cellfun is basically a wrapper to a loop code, but this is not very expensive in terms of runtime and that's why I categorized this approach as an almost vectorized one.

The code would be -

lens = sum(cellfun('length',example_cell_array),1); %// intervals lengths
maxlens = max(lens);
numlens = numel(lens);
array1(maxlens,numlens)=0;
array1(bsxfun(@ge,lens,[1:maxlens]')) = vertcat(example_cell_array{:}); %//'
result = sum(array1,1);

The thing you need to do now, is to make your operation run on column basis with array1 using the mask created by the bsxfun implementation. Thus, if array1 is a M x 5 sized array, you need to select the valid elements from each column using the mask and then do the operation on those elements. Let me know if you need more info on the masking issue.

Hope one of these approaches would work for you!

---

Quick Tests: Using a 250000x5 sized example_cell_array, quick tests show that both these approaches for the sum operation perform very well and give about 400x speedup over the code in the question at my end.

Answer 2

For the concatenation itself, it sounds like you might want the functional form of cat:

for n=1:N
    cat_cell_array{n} = cat(1, example_cell_array{:,n});
end

This will concatenate all the arrays in the cells in each column in the original input array.

Answer 3

You can define a function like this:

cellcat = @(C) arrayfun(@(k) cat(1, C{:, k}), 1:size(C,2), 'uni', 0);

And then just use

>> cellcat(example_cell_array)
ans = 
    [42x1 double]    [53x1 double]    [51x1 double]    [47x1 double]

Answer 4

I think you are looking to generate cat_cell_array without using for loops. If so, you can do it as follows:

cat_cell_array=cellfun(@(x) cell2mat(x),num2cell(example_cell_array,1),'UniformOutput',false);

The above line can replace your entire for loop according to me. Then you can calculate your complex function over this cat_cell_array.

If only result is important to you and you do not want to store cat_cell_array, then you can do everything in a single line (not recommended for readability):

result=cell2mat(cellfun(@(x)sum(x), cellfun(@(x) cell2mat(x),num2cell(example_cell_array,1),'Uni',false), 'Uni', false));