Re: [slightly OT]: Octave featured in Free Software magazine

[Alexander Barth]

Hi Jordi,
Thank you for pointing this benchmark out.

Octave's speed can be improved quite significantly if lines like:

    qgtfive= find(qRe > 5.);
    zRe(qgtfive)=5.;

are replaced by:

    zRe(qRe > 5.)=5.;

The code is also much clearer this way.
On my machine (AMD Opteron 244):

octave:1> tic; fractal_benchmark; toc
Elapsed time is 24.935944 seconds.
octave:2> tic; fractal_benchmark2; toc
Elapsed time is 14.843300 seconds.

In addition to this, the complex type can be used instead of real and imaginary 
part separately.

Alex

Jordi Gutierrez Hermoso wrote:
> This isn't a question about help, but it's nice to see that Octave got
> mentioned in Free Software Magazine and was quite favourably compared
> as "an almost perfect clone of MATLAB."
>      
> http://www.freesoftwaremagazine.com/articles/cool_fractals_with_perl_pdl_a_benchmark?page=0%2C4
> 
> The code provided in the page, written somewhat in a Matlab-style,
> works in 2.9.12. Unfortunately, Octave was also the slowest one to
> generate a Mandelbro  fractal, at least with the given code:
> 
>      
> http://www.freesoftwaremagazine.com/articles/cool_fractals_with_perl_pdl_a_benchmark?page=0%2C6
> 
> I haven't grokked the code yet, but I do wonder if it's possible to
> vectorise that for-loop out... I doubt it, though. Loops that use the
> information from the previous iteration for the next iteration are the
> one kind of loop I have never been able to vectorise out.
> 
> Hope this was interesting.
> 
> - Jordi G. H.
> _______________________________________________
> Help-octave mailing list
> address@hidden
> https://www.cae.wisc.edu/mailman/listinfo/help-octave
> 


-- 
_______________________________________________________________

  Alexander Barth

  Ocean Circulation Group
  University of South Florida
  College of Marine Science
  140 Seventh Avenue South
  St. Petersburg, Florida  33701
  USA

  Phone: +1-727-553-3508     FAX:   +1-727-553-1189

_______________________________________________________________

% MATLAB and Octave code to generate a Mandelbrot fractal

% Number of points in side of image and
% number of iterations in the Mandelbrot
% fractal calculation
npts=1000;
niter=51;
% Generating z = 0 (real and
% imaginary part)
zRe=zeros(npts,npts);
zIm=zeros(npts,npts);
% Generating the constant k (real and
% imaginary part)
kRe=repmat(linspace(-1.5,0.5,npts),npts,1);
kIm=repmat(linspace(-1,1,npts)',1,npts);

% Iterating 
for j=1:niter
    % Calculating q = z*z + k in complex space
    % q is a temporary variable to store the result
    qRe=zRe.*zRe-zIm.*zIm+kRe;
    qIm=2.*zRe.*zIm+kIm;
    % Assigning the q values to z constraining between
    % -5 and 5 to avoid numerical divergences
    zRe=qRe;
    qgtfive= find(qRe > 5.);
    zRe(qgtfive)=5.;
    qltmfive=find(qRe<-5.);
    zRe(qltmfive)=-5.;
    zIm=qIm;
    hgtfive=find(qIm>5.);
    zIm(hgtfive)=5.;
    hltmfive=find(qIm<-5.);
    zIm(hltmfive)=-5.;
end

% MATLAB and Octave code to generate a Mandelbrot fractal

% Number of points in side of image and
% number of iterations in the Mandelbrot
% fractal calculation
npts=1000;
niter=51;
% Generating z = 0 (real and
% imaginary part)
zRe=zeros(npts,npts);
zIm=zeros(npts,npts);
% Generating the constant k (real and
% imaginary part)
kRe=repmat(linspace(-1.5,0.5,npts),npts,1);
kIm=repmat(linspace(-1,1,npts)',1,npts);

% Iterating 
for j=1:niter
    % Calculating q = z*z + k in complex space
    % q is a temporary variable to store the result
    qRe=zRe.*zRe-zIm.*zIm+kRe;
    qIm=2.*zRe.*zIm+kIm;
    % Assigning the q values to z constraining between
    % -5 and 5 to avoid numerical divergences
    zRe=qRe;
    zRe(qRe > 5.)=5.;
    zRe(qRe<-5.)=-5.;
    zIm=qIm;
    zIm(qIm>5.)=5.;
    zIm(qIm<-5.)=-5.;
end