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MathGroup Archive 1996

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Re: Array[] building speed

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5242] Re: Array[] building speed
  • From: News at rrze.uni-erlangen.de
  • Date: Fri, 15 Nov 1996 03:33:55 -0500
  • Organization: Institute for Biomedical Engineering at the FAU Erlangen
  • Sender: owner-wri-mathgroup at wolfram.com

Rich Klopp wrote:
From: news at MailHub.rrze.uni-erlangen.de
To: mathgroup at smc.vnet.net

> 
> I am faking a 600x400 pixel 8-bit gray-scale image by defining
> 
>    grayfield[x_, y_] := Floor[ 256 *
>       (1/2 +
>       1/4 N[Sin[2 Pi (x/100 + y/1800)]] +
>       1/4 N[Sin[2 Pi (x/4 + y/600)]])
>       ]
> 
> and then evaluating
> 
>    grayimage = Array[
>       grayfield[ #1, #2 ]&,
>    {600, 400}];
> 
> However, the latter takes bloody forever. (Well, how about 15 minutes on a
> Power Mac 7100.)   Am I doing something wrong? I note that
> Show[]ing the DensityGraphics[] of grayimage ain't very speedy either.
> 
> --
> Rich Klopp

Hi Rich! 

There are several stages of improving your algorithm.
Take a look at the little benchmark below.

Here we use to much exact arithmetic:

In[1]:
  grayfield[x_, y_] := Floor[ 256 *
      (1/2 +
      1/4 N[Sin[2 Pi (x/100 + y/1800)]] +
      1/4 N[Sin[2 Pi (x/4 + y/600)]])
      ];
  grayimage = Array[
      grayfield[ #1, #2 ]&,
   {60, 40}];//Timing
Out[1]:
  {29.928 Second, Null}

First Step: Try to use as much real arithmetic as possible:

In[2]:
  ClearAll[grayfield,grayimage];
  grayfield[x_, y_] := Floor[ 256 *
      (0.5 +
      0.25 N[Sin[2 N[Pi] (x/100. + y/1800.)]] +
      0.25 N[Sin[2 N[Pi] (x/4. + y/600.)]])
      ];
  grayimage = Array[
      grayfield[ #1, #2 ]&,
   {60, 40}];//Timing
Out[2]:
  {17.256 Second, Null}

This one was better but there is still place for improvement:

In[3]:
  ClearAll[grayfieldcompiled,grayimage];
  grayfieldcompiled= Compile[{{x,_Integer},{y,_Integer}},Floor[ 256 *
      (0.5 +
      0.25 N[Sin[2 N[Pi] (x 0.01 + y/1800.)]] +
      0.25 N[Sin[2 N[Pi] (x 0.25 + y/600.)]])
      ]];
  grayimage = Array[
      grayfieldcompiled[ #1, #2]&,
   {60,40}];//Timing
Out[3]:
  {1.419 Second, Null}

That is quite fast compared to the beginning!!

I hope this helps.

-- 
Jens Potschadtke

Institute for biomedical engineering at the FAU Erlangen (germany).

mailto:Jens.Potschadtke at stud.uni-erlangen.de
http://www.uni-erlangen.de/~sz0438/


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