Matlab large array (1e6 values) computation speed -

i trying optimize matlab code statistic calculation large array of data (1e6 values). tried several methods, loops or fun functions, diff or basic math. need calculate accumulation set of data , standard deviation it.

i cannot running under 24 seconds. there way improve code, without using additional toolboxes?

here tried until now:

clear close mydata = rand(1e5, 1)/5e6;  m = 1000; n = length(mydata)-m;  pkpk  = nan(m, 1); std  = nan(m, 1); mymat = nan (1, n);   %%%%%%%%%%%%%%%%%%%%%%%%%% peak2peak part of  signal processing toolbox: %%%%%%%%%%%%%%%%%%%%%%%%%% can use max()-min() tic x = 1  : m      mymat =    diff( (reshape(mydata(1:x*floor(n/x)),x,floor(n/x)))')   ;     pkpk (x) = peak2peak(mymat(:)) ;     std(x) = sqrt(sum(sum((mymat-mean(mymat(:))).^2))/numel(mymat)); end time1 = toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% tic x = 1  : m     mymat =  bsxfun(@minus,  mydata(x+1 : x+n) , mydata(1:n)) '; % edit here: transpose     pkpk (x) = peak2peak(mymat(:)) ; % max - min     std(x) = sqrt(sum(sum((mymat-mean(mymat(:))).^2))/numel(mymat)); % std end time2 = toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% tic x = 1  : m     mymat =   mydata(x+1 : x+n) - mydata(1:n);%     pkpk (x) = peak2peak(mymat(:)) ; % max - min     std(x) = sqrt(sum(sum((mymat-mean(mymat(:))).^2))/numel(mymat)); % std end time3 = toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% tic  x = 1  : m std(x) = std( reshape( diff(reshape( mydata(1:x*floor(n/x))  , x ,floor(n/x))'),  floor(n/x)' * x -x, 1    )  ) ; pkpk(x) = peak2peak( reshape( diff(reshape( mydata(1:x*floor(n/x))  , x ,floor(n/x))'),  floor(n/x)' * x -x, 1    )  );  end time4 =toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% tic x = 1  : m pkpk (m) = peak2peak( mydata(x+1 : x+n) - mydata(1:n)) ; std(m) = std( mydata(x+1 : x+n) - mydata(1:n)) ; end time5 =toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% tic  pkpk = (cellfun(@(x)  peak2peak( reshape( diff(reshape( mydata(1:x*floor(n/x))  , x ,floor(n/x))'),  floor(n/x)' * x -x, 1    )  )  ,  num2cell(1:m)   )); std = (cellfun(@(x)  std( reshape( diff(reshape( mydata(1:x*floor(n/x))  , x ,floor(n/x))'),  floor(n/x)' * x -x, 1    )  )  ,  num2cell(1:m)   )); time6 =toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% tic   pkpk = cellfun( @(x)  peak2peak(    mydata(x:n+x-1) - mydata(1:n)     )    ,  num2cell(1:m) )  ; std = cellfun( @(x)  std(    mydata(x:n+x-1) - mydata(1:n)     )    ,  num2cell(1:m) )  ; time7 =toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%  tic  std = cellfun( @(x)  std( mydata(x+1 : x+n) - mydata(1:n)), num2cell(1:m) ) ; pkpk  = cellfun( @(x)  max( mydata(x+1 : x+n) - mydata(1:n)) - min( mydata(x+1 : x+n) - mydata(1:n)) , num2cell(1:m) ); time8 =toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% tic std = arrayfun( @(x)  std( mydata(x+1 : x+n) - mydata(1:n)), (1:m) ) ; pkpk  = arrayfun( @(x)  peak2peak( mydata(x+1 : x+n) - mydata(1:n))  , (1:m) ); time9 =toc; %%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% 

and here time results(in seconds):

time1: 24.47 time2: 23.56 time3: 25.20 time4: 45.44 time5: 42.99 time6: 46.27 time7: 43.62 time8: 62.49 time9: 41.69 

thank you!

i took second solution (the fastest on benchmark) , did modifications.

a performance improvement can achieved if stop acessing mydata(1:n) every loop iteration , assign array before loop, this:

tic mydata1ton = mydata(1:n); x = 1  : m     mymat =  bsxfun(@minus,  mydata(x+1 : x+n) , mydata1ton);     pkpk (x) = peak2peak(mymat(:)) ; % max - min     std(x) = sqrt(sum(sum((mymat-mean(mymat(:))).^2))/numel(mymat)); % std end clear mydata1ton; time2 = toc 

time before:

time2: 20.5618 

time after:

time2: 14.2260 

another modification: sum(sum(... can changed sum(..., because outer sum summing single value.

time after:

time2: 11.6573 

by way, numel(mymat) can replaced n, didn't note performance improvement.