NaN-toolbox much faster now

[Alois Schlögl]

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The following improvements have been included in the NaN-toolbox.

- - sumskipnan_mex.mex has been optimized for speed (minimizing cache
missing, reducing loop overhead)

- - a flag is set if some NaN occures in the data. The flag can be checked
(and reset) with function FLAG_NANS_OCCURED(). This enables a flexible
control on checks for NaN. (You can check after every call, or only at
the end of your script).

- - the performance of var, std, and meansq has been improved.

A performance between the NaN-toolbox and corresponding standard octave
functions (see script below) show the following results (time in [s]):


with NaN-tb     w/o NaN-tb      ratio   
    0.25884    3.56726   13.78183       mean(x,1)/nanmean(x,1)
    0.36784    3.32899    9.05020       mean(x,2)/nanmean(x,2)
    0.30019    6.62467   22.06789       std(x,0,1)
    0.40114    2.23262    5.56561       std(x,0,2)
    0.28681    6.40276   22.32407       var(x,0,1)
    0.40269    2.18056    5.41505       var(x,0,2)
    0.28175    4.05612   14.39598       meansq(x,1)
    0.40703    4.19346   10.30248       meansq(x,2)
    0.25930    0.19884    0.76683       sumskipnan(x,1)/sum(x,1)
    0.30624    0.24179    0.78955       sumskipnan(x,2)/sum(x,2)


A performance improvement by factors as high as 22 can be seen, and
sumskipnan() is only about 25% slower than sum().

Of course, sumskipnan could also improve the speed of functions like
nanmean, nanstd, etc. Maybe you want to consider including sumskipnan in
standard octave.


Cheers,
   Alois



======== script of for the performance test ===
The machine has 4 GB of RAM (no swapping took place) AMD64, Ubuntu 8.


x=randn(1e4); %%!!! 800 MBytes

        
%%      add path to .../octave-forge/extra/NaN/src
        mex .../octave-forge/extra/NaN/src/sumskipnan_mex.cpp
%%      add path to .../octave-forge/extra/NaN/inst
        k=1;

        t=cputime();tic; m = mean(x,1); T(k,1)=toc;V(k,1)=cputime()-t;
        t=cputime();tic; m = mean(x,2); T(k,2)=toc;V(k,2)=cputime()-t;

        t=cputime();tic; m = std(x,0,1); T(k,3)=toc;V(k,3)=cputime()-t;
        t=cputime();tic; m = std(x,0,2); T(k,4)=toc;V(k,4)=cputime()-t;

        t=cputime();tic; m = var(x,0,1); T(k,5)=toc;V(k,5)=cputime()-t;
        t=cputime();tic; m = var(x,0,2); T(k,6)=toc;V(k,6)=cputime()-t;

        t=cputime();tic; m = meansq(x,1); T(k,7)=toc;V(k,7)=cputime()-t;
        t=cputime();tic; m = meansq(x,2); T(k,8)=toc;V(k,8)=cputime()-t;

        t=cputime();tic; m = sumskipnan(x,1); T(k,9)=toc;V(k,9)=cputime()-t;
        t=cputime();tic; m = sumskipnan(x,2); T(k,10)=toc;V(k,10)=cputime()-t;

%%      remove path to .../octave-forge/extra/NaN/src
%%      remove path to .../octave-forge/extra/NaN/inst

        k = 2;
        t=cputime();tic; n=sum(~isnan(x),1);x(isnan(x))=0;
m = sum(x,1)./n; T(k,1)=toc;V(k,1)=cputime()-t;         %% nanmean
        t=cputime();tic; n=sum(~isnan(x),2);x(isnan(x))=0;
m = sum(x,2)./n; T(k,2)=toc;V(k,2)=cputime()-t;         %% nanmean

        t=cputime();tic; m = std(x,0,1); T(k,3)=toc;V(k,3)=cputime()-t;
        t=cputime();tic; m = std(x,0,2); T(k,4)=toc;V(k,4)=cputime()-t;

        t=cputime();tic; m = var(x,0,1); T(k,5)=toc;V(k,5)=cputime()-t;
        t=cputime();tic; m = var(x,0,2); T(k,6)=toc;V(k,6)=cputime()-t;

        t=cputime();tic; m = meansq(x,1); T(k,7)=toc;V(k,7)=cputime()-t;
        t=cputime();tic; m = meansq(x,2); T(k,8)=toc;V(k,8)=cputime()-t;

        t=cputime();tic; m = sum(x,1); T(k,9)=toc;V(k,9)=cputime()-t;
        t=cputime();tic; m = sum(x,2); T(k,10)=toc;V(k,10)=cputime()-t;

 [V',V(2,:)'./V(1,:)']


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