How to vectorize for loop when iterator is used to access data?

Question

Let's say I have

data = rand(10000,1); % 10000x1 double
x = 8;
y = 10;
offset = 5000; % x,y and offset are scalar.

Currently, I have implemented my logic as follows:

tempData=zeros(x,y)
for i=1:x
    tempData(i,:)=data(offset+i-1:x:offset + (x*y) -1)
end

I have implemented the logic to get equally spaced data of length y beginning from offset and dividing them into x buckets. Is it possible to vectorize this code?

If yes, then I want to vectorize case where x, y and offset are vectors themselves of equal length and each corresponding set of x, y and offset values gives different tempData. I am thinking size of tempData should be zeros(A,max(X),max(Y)), where A is common length of vectors x, y and offset, which will accomodate all ranges of data. But I am not sure how to implement this logic as well.

HansHirse · Accepted Answer · 2019-11-07T12:14:51.710

Using implicit expansion (or broadcasting), the needed indices can be pre-calculated, and then data can be accessed with these indices in one step. For MATLAB versions before R2016b, this has to be explicitly done by using the bsxfun method.

Here's one possible vectorization of the given code:

data = rand(10000, 1);
x = 8;
y = 10;
offset = 5000;

tempData = zeros(x, y);
for ii = 1:x
    tempData(ii, :) = data(offset+ii-1:x:offset+(x*y)-1);
end
tempData

% MATLAB versions R2016b and newer
idx = [0:x-1].' + offset + [0:x:(x*y)-1];

% MATLAB versions before R2016b
%idx = bsxfun(@plus, bsxfun(@plus, [0:x-1].', offset), [0:x:(x*y)-1]);

tempData2 = data(idx)

disp(['Number of different array elements: ', ...
      num2str(numel(find(tempData ~= tempData2)))]);

Output:

tempData =
   0.8066402   0.6572843   0.9425518   0.9663419   0.9700796   0.2132531   0.0562514   0.7089385   0.1911747   0.9513211
   0.3150179   0.4987158   0.5472079   0.3804589   0.6569250   0.9619353   0.1204870   0.6133104   0.7718005   0.8298695
   0.5942941   0.2964820   0.5767488   0.2801063   0.4969586   0.6939726   0.6652277   0.9043894   0.8220853   0.6501431
   0.5398818   0.0067256   0.5347702   0.0935663   0.9080668   0.2440419   0.5053460   0.2064903   0.9822692   0.0440910
   0.2567786   0.2294226   0.8511809   0.6516491   0.1073913   0.8241950   0.9817716   0.8543800   0.3400275   0.9529938
   0.5700380   0.9455092   0.5102088   0.5539329   0.0058831   0.6627464   0.3184132   0.6538248   0.5766122   0.8352150
   0.4384866   0.9618210   0.6841067   0.4880946   0.3056896   0.8244916   0.6240189   0.5447771   0.0317932   0.4269364
   0.0054480   0.9978763   0.7917681   0.6482806   0.5933597   0.4203822   0.3880279   0.8687756   0.7550784   0.6491559

tempData2 =
   0.8066402   0.6572843   0.9425518   0.9663419   0.9700796   0.2132531   0.0562514   0.7089385   0.1911747   0.9513211
   0.3150179   0.4987158   0.5472079   0.3804589   0.6569250   0.9619353   0.1204870   0.6133104   0.7718005   0.8298695
   0.5942941   0.2964820   0.5767488   0.2801063   0.4969586   0.6939726   0.6652277   0.9043894   0.8220853   0.6501431
   0.5398818   0.0067256   0.5347702   0.0935663   0.9080668   0.2440419   0.5053460   0.2064903   0.9822692   0.0440910
   0.2567786   0.2294226   0.8511809   0.6516491   0.1073913   0.8241950   0.9817716   0.8543800   0.3400275   0.9529938
   0.5700380   0.9455092   0.5102088   0.5539329   0.0058831   0.6627464   0.3184132   0.6538248   0.5766122   0.8352150
   0.4384866   0.9618210   0.6841067   0.4880946   0.3056896   0.8244916   0.6240189   0.5447771   0.0317932   0.4269364
   0.0054480   0.9978763   0.7917681   0.6482806   0.5933597   0.4203822   0.3880279   0.8687756   0.7550784   0.6491559

Number of different array elements: 0

EDIT: Regarding the extension to multiple parameters, there is also the possibility to pre-calculate the needed indices using a vectorized approach (cf. Divakar's answer here), but the code then gets absolutely unreadable. So, at least in my opinion, using a for loop with the before presented vectorized code is suitable. I also extended your initial loop code for comparison:

data = rand(10000, 1);
x = [6, 8];
y = [10, 9];
offset = [3000, 5000];
A = numel(x);

tempData = zeros(max(x), max(y), A);
for jj = 1:A
  for ii = 1:x(jj)
    X = x(jj);
    Y = y(jj);
    off = offset(jj);
    tempData(ii, 1:Y, jj) = data(off+ii-1:X:off+(X*Y)-1);
  end
end
tempData

tempData2 = zeros(max(x), max(y), A);
for jj = 1:A
  X = x(jj);
  Y = y(jj);
  off = offset(jj);

  % MATLAB versions R2016b and newer
  idx = [0:X-1].' + off + [0:X:(X*Y)-1];

  % MATLAB versions before R2016b
  %idx = bsxfun(@plus, bsxfun(@plus, [0:X-1].', off), [0:X:(X*Y)-1]);

  tempData2(1:X, 1:Y, jj) = data(idx); 
end
tempData2

disp(['Number of different array elements: ', ...
      num2str(numel(find(tempData ~= tempData2)))]);

Output (shortened):

tempData =

ans(:,:,1) =
   0.70758   0.71552   0.54604   0.73202   0.72717   0.16028   0.63080   0.48345   0.93159   0.96625
   0.00320   0.11202   0.00179   0.90887   0.21830   0.91380   0.12110   0.31074   0.72834   0.52315
   [...]
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000

ans(:,:,2) =
   0.11960   0.35942   0.62390   0.45457   0.63471   0.23471   0.75660   0.34019   0.06892   0.00000
   0.46443   0.21113   0.55479   0.51218   0.83697   0.30117   0.13935   0.81838   0.80042   0.00000
   [...]

tempData2 =

ans(:,:,1) =
   0.70758   0.71552   0.54604   0.73202   0.72717   0.16028   0.63080   0.48345   0.93159   0.96625
   0.00320   0.11202   0.00179   0.90887   0.21830   0.91380   0.12110   0.31074   0.72834   0.52315
   [...]
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000

ans(:,:,2) =
   0.11960   0.35942   0.62390   0.45457   0.63471   0.23471   0.75660   0.34019   0.06892   0.00000
   0.46443   0.21113   0.55479   0.51218   0.83697   0.30117   0.13935   0.81838   0.80042   0.00000
   [...]

Number of different array elements: 0

Nice. +1 even just for giving the 2 options for broadcasting (the new implicit one and a method with `bsxfun` for those poor folks like me who do not have the latest MATLAB). — Hoki, Nov 07 '19 at 11:48
Thank you very much. This is precisely what I required. Thank you for sharing exhaustive details so that I may understand how to solve this myself. — lonstud, Nov 07 '19 at 16:55

How to vectorize for loop when iterator is used to access data?

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