Two variable Cumulative Sum calculation

I am having 5 by 5 matrix. I want to make a cumulative sum from each variable As an example:

The A(3,2) Argument would be the sum of all the arguemts before this argument and this argument, like:

A(3,2)=A(1,1)+A(2,1)+A(3,1)+A(1,2)+A(2,2)+A(3,2)

I want to make a for loop to go on each argument

for i = 1:5

For j=1:5

Any ideas on how I can do that?

Answer 1

[Jon]

If I understand your description corrrectly, I think this does what you want, no loops needed.

B = cumsum(cumsum(A,1),2)

[frankovaT]

Yes Jonathan!

That is exactly what I wanted.

Do you have any ideas of how to do it by for loop as well?

I might have to do sth like this along the way, So I d like to have an idea of how to make that for loop.

[Jon]

If this one line of MATLAB code computes what you want I don't know why you would want to do it within a double loop. Generally MATLAB's performance is better when things are done in a vectorized fashion. Also one of the great powers of MATLAB is to be able to deal directly with matrices and vectors which makes it much easier to follow the math, than when things are buried in loops. For this reason loops are generally discouraged unless they are really needed.

[frankovaT]

haha Thanks

[Jon]

As you were interested, I've attached a function which I just wrote that computes the cumulative 2d sum using for loops. I did a little bit of testing to compare run times (using tic,toc) for a large array (10^4 x 10^4) using this double loop compared to the one line B = cumsum(cumsum(A,1),2). It seemed that it took almost twice as long using the double loop.

function B = cumsum2d(A)
%CUMSUM2D Compute cumulative sum over 2d array
%   B = cumsum2d(A) computes 2-d matrix B whose elements are
%       the cumulative sum over elements of 2-d matrix A
%       such that B(i,j) is the sum of all elements of A whose row and
%       column indices are less than or equal to i and j respectively

% get the total number of rows and columns, we need these for end condition
% on loops
[numRows,numCols] = size(A);

% preallocate matrix the same size as A to hold result
B = zeros(numRows,numCols);


% loop through rows and columns accumulating totals
for jCol = 1:numCols
    % initialize cumulative sum of elements in this column
    sumThisCol = 0;
    for iRow = 1:numRows
        % update the sum of elements in the current column
        sumThisCol = sumThisCol + A(iRow,jCol);
        
        % update the cumulative sum of all of the elements to the left and
        % above this element (inclusive)
        % (need branch to handle special case of first column since there
        % isn't anything to the left of that)
        if jCol > 1
            % in the interior, there is a column to the left of this one
            B(iRow,jCol) = B(iRow,jCol - 1) + sumThisCol;
        else
            % this is the first column, there is nothing to the left of it
            % to add
            B(iRow,jCol) = sumThisCol;
        end
    end
end

[frankovaT]

Dear Jonathan

Thank you very much for sending me this as well. I truly appreciate your effort. This helps alot.

Best