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)

rahnema1 · Accepted Answer · 2017-11-30 10:56:55Z

2

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

edited Nov 30, 2017 at 10:56

answered Nov 29, 2017 at 11:31

rahnema1

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6 Comments

Andi Over a year ago

That doesn't look like an easy solution. It's working but in imho it makes the accumarray function less readable. In that case, I think I prefer a simple for-loop solution. <br/> for i = 1 : size(vals2, 2) result2(:,i) = accumarray(subs, vals2(:,i), [], @(x) prod(1+x) -1); end

rahnema1 Over a year ago

for-loop solution may be inefficient when number of columns is high.

Andi Over a year ago

Hmm, in my case, number of columns can be as high as 10,000.

Turbo Over a year ago

@rahnema1 I think the for loop solution posted by OP is not efficient. I implemented an improved for loop without accumarray which is performing as fast as the cell2mat. I modified your script and added the improved for loop solution. Run it a few times and you will see the perf is similar to cell2mat. rextester.com/RLYKA32361 . Honestly, I am a bit surprised that the simple for loop is matching accumarray. Let me know if I am missing something.

rahnema1 Over a year ago

@Turbo Here I edited the code and used a random data set for subs. There are 1500 unique categories each repeated at most 500 times. I commented out ndgrid because it requires much of memory. The improved loop is better than non improved loop but it cannot outperform cell2mat. It would be better to use repelem to create the data-set but that version of Octave doesn't contain repelem.

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gnovice · Accepted Answer · 2017-11-29 16:09:21Z

0

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

answered Nov 29, 2017 at 16:09

gnovice

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2 Comments

Andi Over a year ago

How would you define the output arguments of ngrid if the number of columns in vals2 is variable?

gnovice Over a year ago

@Andi: That's exactly what I do in the above code. Note that the second argument to ndgrid is a vector from 1 to size(vals2, 2) (i.e. the number of columns in vals2).

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