MATLAB: Vectorizing cumsum of table-vectors in a for loop

Question

Dear everyone, I have the following code which works perfectly fine and does what I want: the cumsum of the specified vectors of n vectors from a table in a cell-array vector. Now, I would like to understand if I can, anyhow, vectorialize this cumsum so to speed up the whole process.

The following is the code which works just fine, but I would like to speed up:

% n


n = size(cellarray,2);
% Cell Array Space Preallocation
tot{1,n} = [];
for k = 1:n
    tot{k} = cellarray{1,k}{:,'tot'};
end
tot_s = sum([tot{:}],2);

I have tried this variant, but it seems to increase the total time, rather than decreasing it

% n
n = size(table,2);
for k = 1:n
    tot_s = cumsum(cellarray{1,k}{:,'tot'},2);
end

I was wondering if it could exist a way to not use the loop at all and "vectorialize" this cumsum. I have tried the following code:

% n
n = size(table,2);
tot_s = cumsum(cellarray{1,1:n}{:,'tot'},2);

but I got the following error

% Expected one output from a curly brace or dot indexing expression, but there were 50 results (n = 50 in this particular case).

Any suggestion would be very helpful. For what concern the "data" in input, you can use whatever data you want, it does not matter. The structure is very simple: a table into a vector of cell-array with the name of the variable in each table be 'tot' and all the data in the vector are double.

Answer 1

No, it's not possible to vectorise the loop unless you don't use tables. Even if you were using matrices in the cell array (which would require the table data to be homogeneous), I'm not sure you'd gain much over the loop.

Your first example uses sum instead of cumsum, if it's just the sum you're after, this is probably slightly faster:

tot = cellarray{1}.tot;
for idx = 2:numel(cellarray)
    tot = tot + cellarray{idx}.tot;
end

If you're after cumsum, it may be more efficient to allocate the final matrix directly rather than going through a temporary cell array:

tot = zeros(height(cellarray{1}, numel(cellarray)));
for col = 1:numel(cellarray)
    tot(:, col) = cellarray{col}.tot;
end
tot = cumsum(tot, 2);

Your second example doesn't make sense. You're cumsum'ing a single column at each step of the loop, that doesn't do much, and overwriting tot_s each step.

Also, I believe that dot indexing as I have used above is slightly faster than {} indexing for tables.

Finally, for preallocation:

tot = cell(size(cellarray));

would be clearer than the syntax you use.