MATLAB: accumarray with matrix as values (second input parameter)

Question

I have a matrix with percantage values where every row represents an individual observation. I need to compute the cumulative product where these values correspond to the same subscript. I tried to use the accumarray function, which works fine and as expected as long I use a column vector as values (rather than a matrix). I am wondering what is the best way to solve my problem without looping through the individual columns of my value matrix?

Here's my sample code:

subs = [1;1;1;2;2;2;2;2;3;3;4;4;4];
vals1 = [0.1;0.05;0.2;0.02;0.09;0.3;0.01;0.21;0.12;0.06;0.08;0.12;0.05];

% This is working as expected
result1 = accumarray(subs,vals1, [], @(x) prod(1+x) -1)


vals2 = [vals1,vals1];

% This is not working as the second input parameter of accumarray
% apperently must be a vector (rather than a matrix)
result2 = accumarray(subs, vals2, [], @(x) prod(1+x) -1)

Answer 1

For vals you can set it as 1:size(vals2,1) and use it to extract rows of vals2. Also it is required for the function to return cell.

result2 = accumarray(subs, 1:size(vals2,1), [], @(x) {prod(1+vals2(x,:),1)-1})

You can concatenate cell elements:

result3 = vertcat(result2{:})

Or all in one line:

result3 = cell2mat( accumarray(subs, 1:size(vals2,1), [], @(x) {prod(1+vals2(x,:),1)-1}))

result3 =

   0.38600   0.38600
   0.76635   0.76635
   0.18720   0.18720
   0.27008   0.27008

Result of a test in Octave comparing three proposed methods using a [10000 x 200] matrix as input:

subs = randi(1000,10000,1);
vals2 = rand(10000,200);

=========CELL2MAT========
Elapsed time is 0.130961 seconds.
=========NDGRID========
Elapsed time is 3.96383 seconds.
=========FOR LOOP========
Elapsed time is 6.16265 seconds.

Online Demo

Answer 2

You need to add a second set of subscripts to subs (so that it is N-by-2) to handle your 2D data, which still has to be passed as an N-element vector (i.e. one element for each row in subs). You can generate the new set of 2D subscripts using ndgrid:

[subs1, subs2] = ndgrid(subs, 1:size(vals2, 2));
result2 = accumarray([subs1(:) subs2(:)], vals2(:), [], @(x) prod(1+x) -1)

And the result with your sample data:

result2 =

    0.3860    0.3860
    0.7664    0.7664
    0.1872    0.1872
    0.2701    0.2701