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MathGroup Archive 2007

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Re: Re: Slow Show/Graphics in v6.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81028] Re: [mg80988] Re: [mg80906] Slow Show/Graphics in v6.0
  • From: DrMajorBob <drmajorbob at bigfoot.com>
  • Date: Sat, 8 Sep 2007 03:54:11 -0400 (EDT)
  • References: <200709050653.CAA26889@smc.vnet.net> <377175200709051434pb7ae575gfe4e7574f72f4379@mail.gmail.com> <2275320.1189151752238.JavaMail.root@m35>
  • Reply-to: drmajorbob at bigfoot.com

I suspect (just guessing) that you meant to set finterp equal to the  
Interpolation in your Table; that way the code could actually do  
something. But the Interpolation only wastes time (in version 6):

profr[r_, s_] = E^(Log[0.05]*r^s)

\[ExponentialE]^(-2.99573 r^s)

fonebeam[th_, s_] = profr[Sin[th], s]*Max[0, Cos[th]]

\[ExponentialE]^(-2.99573 Sin[th]^s) Max[0, Cos[th]]

lmax = 10;
Timing[saved = Table[
     NIntegrate[
        fonebeam[th, s]*LegendreP[#1, Cos[th]]*Sin[th], {th, 0, Pi},
        MaxRecursion -> 16] & /@ Range[0, lmax], {s, 1.9, 3., 0.02}];]

{27.453, Null}

Timing[saved2 =
    Table[finterp =
      Interpolation[({#1, fonebeam[#1, s]} &) /@
        Range[0, Pi, Pi/(30.*lmax)]];
     NIntegrate[
        finterp[th]*LegendreP[#1, Cos[th]]*Sin[th], {th, 0, Pi},
        MaxRecursion -> 16] & /@ Range[0, lmax], {s, 1.9, 3., 0.02}];]

{33.609, Null}

saved - saved2 // Abs // Max

2.02138*10^-7

In version 5.2 the timings were 18.5 and 3.1 seconds, so Interpolation DID  
speed things up, and 5.2 does seem faster. (But not unless you write the  
code correctly, of course.)

Back in v6, you can eliminate fonebeam and its Max[0, Cos@th] this way:

Timing[saved = Table[
     NIntegrate[
        profr[th, s]*LegendreP[#1, Cos[th]]*Sin[th], {th, 0, Pi/2},
        MaxRecursion -> 16] & /@ Range[0, lmax], {s, 1.9, 3., 0.02}];]

{6.953, Null}

Can you really try all these things in C or Fortran, in the 30 minutes I  
spent?

Bobby

On Fri, 07 Sep 2007 01:04:29 -0500, Alex Shvydky <ashv at lle.rochester.edu>  
wrote:

> Thanks for the input, Ricardo.
>
> They should do something with that. Currently I am running both 5.2 and
> v6.0 side by side
> and for now most of the code is noticeably slower in 6.0! To the point
> it is not usable anymore.
> (Of course I could spent couple of days to optimize its etc. etc., but
> then it would defeat
> the purpose of using Mathematica in the first place - I would rather
> then do it in Fortran
> or C...)
>
> Like e.g.
>
> profr[r_, s_] := E^(Log[0.05]*r^s);
> fonebeam[th_, s_] := profr[Sin[th], s]*Max[0, Cos[th]];
> lmax = 10;
> Table[
>     Interpolation[({#1, fonebeam[#1, s]} &) /@  Range[0, Pi,
> Pi/(30.*lmax)]];
>     NIntegrate[finterp[th]*LegendreP[#1, Cos[th]]*Sin[th], {th, 0, Pi},
> MaxRecursion -> 16] & /@ Range[0, lmax],
> {s, 1.9, 3., 0.02}];
>
> took 3.78sec in Mathematica V5.2 and 39.97sec in V6.0.
>
> There is again an order of magnitude slow down!
>
> I am observing this across the board. Whatever the "improvement" they
> introduce in
> my view can not justify an order of magnitude slow down!
> I hope they work on that and v6.xx will be faster.
>
> It is like a new version or a C or Fortran compiler would come with 10
> times larger libraries and features,
> but the code it would generate from your old programs would run 10 times
> slower.
>
> Alex
>
>
>
>
> Ricardo Samad wrote:
>> Dear Alex,
>>
>> I confirm that some graphic functions rendering became slower in
>> Mathematica 6.0.
>> I am having a similar problem when trying to display a 480 x 640 data
>> array using ListContourPlot or ListPlot3D; In Mathematica 5.2 it took
>> a few seconds, in 6.0 it takes minutes, and eventually the Kernel hangs.
>> I also would like to know if there´s a setting to speed the rendering  
>> up.
>>
>> Ricardo Samad
>>
>>
>>
>> On 9/5/07, *Alex Shvydky* <ashv at lle.rochester.edu
>> <mailto:ashv at lle.rochester.edu>> wrote:
>>
>>     Hello,
>>
>>     Just wanted to share my puzzlement (utter disappointment/
>>     frastration) with a ridiculously slow speed of Show/Graphics
>>     routines in the v6.0 of Mathematica as compared to 5.2,
>>     which to me at this point makes v6.0 plain unusable.
>>
>>     Working with hydrodynamic simulations I need to
>>     visualize the computational grid. So I wrote
>>     simple Mathematica routines to draw a simulation grid.
>>     In 5.2 they worked fabulously for the past couple of
>>     years.
>>
>>     Here's an example.
>>     First, set up two 2dimensional x- and y-coordinate
>>     arrays.
>>
>>     Timing[
>>        mr = 350;
>>        mt = 350;
>>        xar = Table[((ir - 1.)/(mr - 1.))*Cos[Pi*((it - 1.)/(mt - 1.))],
>>                    {it, 1, mt}, {ir, 1, mr}];
>>        yar = Table[((ir - 1.)/(mr - 1.))*Sin[Pi*((it - 1.)/(mt - 1.))],
>>                    {it, 1, mt}, {ir, 1, mr}];
>>     ]
>>
>>     In v6.0 it took
>>     Out[3]= {2.312, Null}
>>     In v5.2 it took
>>     {0.281 Second, Null}
>>
>>     Which is an order of magnitude difference, but hold on.
>>     Now let's plot the mesh by simply constructing table
>>     of edges of all the cells (I am aware that the algorithm
>>     below is very unoptimized and can be made faster etc. etc.
>>     It was not my intention to discuss here what should be the
>>     fastest algorithm to plot a 2-d mesh,
>>     nor was it my intention to debate the issue why one
>>     would need to plot such a large mesh in the first place...,
>>     but rather to compare the execution time for an IDENTICAL
>>     code on v6.0 and v5.2. and get some confirmation/explanation
>>     of such a suspiciously slow execution speed!).:
>>
>>     Timing[
>>     Show[
>>         Graphics[{Hue[ 0.7], AbsoluteThickness[0.1],
>>             Table[{Line[{{xar[[it,ir]], yar[[it,ir]]},
>>                           {xar[[it,ir + 1]],yar[[it,ir + 1]]},
>>                           {xar[[it + 1,ir + 1]], yar[[it + 1,ir + 1]]},
>>                           {xar[[it + 1,ir]], yar[[it + 1,ir]]}}]},
>>              {ir, 1, mr - 1}, {it, 1, mt - 1}]
>>         }],
>>     PlotRange -> {{-1, 1}, {0, 1}}, AspectRatio -> 1/2, Axes -> True,
>>     DisplayFunction -> $DisplayFunction, ImageSize -> 800]]
>>
>>     While the timing as, it is returned by the Timing[] function,
>>     is smaller in the v6.0:
>>     {1.703, <Here goes the actual graphics>}
>>     vs.
>>     {2.094 Second, -Graphics-}
>>     in v5.2
>>
>>
>>     The actual cell evaluation time in v.6.0 is 124.11 seconds
>>     vs. 2.22 seconds in v 5.2. ???!!!!!!!
>>
>>     Could anybody please confirm this. Also it would be helpful
>>     if someone from Wolfram Research would explain if
>>     that is intended (unavoidable) by design or maybe
>>     a simple setting (which I am unaware of) or a future patch
>>     will be able to fix it.
>>
>>     Also, it is horribly slow to resize the above graphics
>>     in v5.2 you just grab the corned and drag. In v6.0 you
>>     must do it 10-100 times slower (is it possible
>>     that I just have a very poor graphics card?).
>>
>>
>>     Thanks,
>>     Alex Shvydky
>>
>>
>>
>>
>> --
>> ____________________________________
>> Ricardo Elgul Samad
>>
>> tel: (+55 11) 3816-9314
>> fax: (+55 11) 3816-9315
>>
>> Centro de Lasers e Aplicações
>> IPEN/CNEN-SP
>> AV. Prof. Lineu Prestes 2242
>> Cidade Universitária
>> 05508-000
>> São Paulo - SP
>> Brazil
>> ____________________________________
>
> --
> _______________________________________________________________
>
> Alex Shvydky                           <ashv at lle.rochester.edu>
>
> Research Associate
> Computational Design Group
>
> Laboratory for Laser Energetics        Office:  1423 COI
> University of Rochester                Phone:  (585) 275-9539
> 250 East River Road                    FAX:    (585) 275-5960
> Rochester NY  14623
> _______________________________________________________________
>
>
>



-- 
DrMajorBob at bigfoot.com


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