sum along data with different steps

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Adam 2017-10-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/363843-sum-along-data-with-different-steps

评论： Adam 2017-11-16

采纳的回答： Cedric

在 MATLAB Online 中打开

Dear all;

I have three data sets: This is just an example...

 data1=[1  5  3  4  2  0  1  2  8  2  10  2  1];  %
 data2=[1  10  ....................]
 data3=[4   3  .....................]

I would like to sum by a step of 2 ,3 4 etc.. along data1 file. That means data1 becomes now:

 data1_2 =[6 7 2 3 10 12]    % sum of 2 numbers
 data_3  =[9  6 11 14]       % sum of three numbers, the last number 1 is not included
 data_4  =[13 5 22]          % the last number 1 is again not included
 data_5  =[15 13]            % the last numbers 2 and  1 are not included

I did it and it works..

But I want to improve it to do the following:

Continue the sum calculation till the same length of the original data is reached. That means:

 data1_2 =[6 7 2 3 10 12 12 10 3 2 7 6]; % sum from left to right and then the right to the left till the desired length is reached

The result should be in case of summing 3 numbers for example like this:

data1_3=[9 6 11 14 13 12 3 12 9 6 1 14]

Here is my code:

##########################################
for i=1:1:length(data1);  % sum of events
      step=floor(length(data1)./i);
      for j=1:1:step
          start_idx=i*(j-1)+1;
          end_idx=i+start_idx-1;
          Sum_data1(i,j)=sum(data1(start_idx:end_idx)); 
      end
end
#################################

Thanks you gentlemen for your helps…

Cheers

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Answer 1

Cedric 2017-10-28

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https://ww2.mathworks.cn/matlabcentral/answers/363843-sum-along-data-with-different-steps#answer_288294

编辑：Cedric 2017-10-28

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Interestingly, the following seems to produce what you are looking for:

 >> expandSum = @(x,n) sum(reshape(cell2mat(arrayfun(@(k)rot90(data1(1:n*floor(numel(data1)/n)), 2*(k-1)), 1:n, 'Unif', 0)), n, [])) ;

and with this function defined:

 >> expandSum(data1, 2)
 ans =
     6     7     2     3    10    12    12    10     3     2     7     6
 >> expandSum(data1, 3)
 ans =
     9     6    11    14    14    11     6     9     9     6    11    14
 >> expandSum(data1, 4)
 ans =
    13     5    22    22     5    13    13     5    22    22     5    13

Of course, it may not be that useful given like this as an big ugly one-liner, so here was the thought process:

Q: Are we able to flip/merge the data automatically based on the number of repetitions? A: Yes using ROT90 and setting the number of rotations as twice (multiple of 180) the repetition index minus one (so the first is not rotated).
Q: Are we able to build a cell array of these rotated vectors? A: Yes using ARRAYFUN implicitely iterating from 1 to the number of repetitions (which should be the size of groups for summation).
Q: Are we able to concatenate all rotated vector horizontally without developing as a CSL (necessary for a call to HORZCAT)? A: Yes using CELL2MAT.
Q: Are we able to sum over groups of size n? A: Yes reshaping first the whole thing in a n x m array and summing over dim 1.

PS: I don't guarantee that it is really working in all situations, you'll have to understand and test if you want to follow this approach.

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Cedric 2017-11-3

编辑：Cedric 2017-11-3

在 MATLAB Online 中打开

main_01.m

Assuming that you don't want to skip anything, and that you care more for the efficiency than for the number of lines, I wrote the version attached. You can profile it by setting N large and see in the profiler where the time is spent.

Setting N=1 and looking at result, you can see how it is different from the numbers that you give in the example.

Then we can adapt it or find something more efficient first. One candidate may be a convolution and a permutation of terms.

PS1: for running the code in the profiler (for large Ns), type

profile viewer

in the command window, then type main_01 in the filed "Run this code", and click on [Start profiling]. Clicking on main_01 in the report will give you the detail.

PS2: to illustrate the convolution, set e.g. groupSize=3 and execute:

conv( data1, ones( 1, groupSize ), 'same' )

you will recognize most or all of the terms of the final sum (the one with no skip at least) in a weird order. You should also observe that it is about 10 times faster than what is implemented in the file, which should be faster than the one liner already. What is missing is a reordering operation that could be complex and time consuming, but it is worth investigating if you really need to go fast.

Cedric 2017-11-3

编辑：Cedric 2017-11-3

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The file main_01.m that I attached above does this. You can wrap it into a function if you want:

 function result = expandSum( data, groupSize )
    % - Build alternating "circular buffer".
    data_flr = fliplr( data ) ;
    buffer = repmat( [data, data_flr], 1, floor( groupSize/2 ) ) ;
    if mod( groupSize, 2 )
        buffer = [buffer, data_flr] ;
    end
    % - Truncate to appropriate length for group size.
    len = numel( data ) * groupSize ;
    buffer = buffer(1:len) ;
    % - Reshape for summing along dim 1 and sum.
    result = sum( reshape( buffer, groupSize, [] )) ;
 end

The first question is: does this produce an adequate output? The second is: is it efficient enough? As I explain in my previous comment, if you have only a one-time series of computation to perform with group sizes varying between 2 and 350, it is probably efficient enough because it would take ~3 minutes to go through the whole process. If not, there may be faster alternatives, but you'd have to invest quite a bit of your time for building them (e.g. by studying if it is possible to reorder the output of CONV adequately).

Adam 2017-11-15

在 MATLAB Online 中打开

Yes. it does... The last thing which I have to test now is the randomness. I want to do the same calculation but in a random way. For example. from the previous calculation we get for 2: data1=[1 5 3 4 2 0 1 2 8 2 10 2 1]; %

 >> expandSum(data1, 2)
 ans =
     6     7     2     3    10    12    12    10     3     2     7     6

Now instead of summing 2 (3, 4,...350) numbers successively, the sum should be performed in a random way... Any hints will be greatly welcome...Thanks again

Adam 2017-11-16

I solved it using randperm before performing the sum calculation...I have now to run my calculation with the large amount of data and check the outcome...

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sum along data with different steps

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sum along data with different steps

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