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Re: Another Out of Memory Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91323] Re: Another Out of Memory Problem
  • From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
  • Date: Fri, 15 Aug 2008 06:54:46 -0400 (EDT)
  • References: <g8137j$19$1@smc.vnet.net> <48A42D4D.7060504@gmail.com> <48A42E5D.2060407@umbc.edu> <22d35c5a0808140905r7b7483bdi89c0485a0f0f95cd@mail.gmail.com>

Jean-Marc,

Thanks for the detailed analysis. I am not sure what I will do about it. I guess I can rationalize the coefficients.

Kevin



Jean-Marc Gulliet wrote:
> On Thu, Aug 14, 2008 at 3:08 PM, Kevin J. McCann wrote:
>
>   
>> Thanks, Jean-Marc. I still find it strange that it runs out of memory and so
>> fast. The error message comes up within less than 1 second.
>>     
>
> [... Cross-posted on MathGroup ...]
>
> Kevin,
>
> I have just tried to do the integration with approximate coefficient
> on my system (64-bit Intel Core 2 Duo 4 GB RAM Mac OS X Leopard 1.5.4
> Mathematica 6.0.3).
>
> . On this 64-bit platform, the kernel does not crash: the expression
> returns unevaluated after about four minutes elapsed-time (or about
> two minutes cpu-time)
>
> . However, the computation takes up to about 2.2 GB of memory, which
> is fine on a 64-bit system but is too much on a standard 32-bit
> platform
>
> . Also, I have observed thanks to the command Top (UNIX/Mac OS X shell
> command) that the memory consumption varies/oscillates quickly from
> nearly nothing (few dozens of MB) to one or two GB in a fraction of
> second
>
> . OTOH, with exact coeffiecients, the integration consumes about 200
> MB of memory (steady increase from the beginning to the end, no wild
> variations, as far as I can tell), though the process is seven time
> slower
>
> So it seems that the algorithm goes wild when used with approximate
> numbers, for reasons I am clueless about.
>
> (* Timing and memory consumption with *floating-point* coefficients *)
>
> In[1]:= Integrate[Cos[2.5*x]*Exp[I*z*Cos[x]], {x, -Pi, Pi}] // Timing
>
> Out[1]=
>                      I z Cos[x]
> {112.795, Integrate[E           Cos[2.5 x], {x, -Pi, Pi}]}
>
> In[2]:= MaxMemoryUsed[]/2.^30 GB
>
> Out[2]= 2.19748 GB
>
> In[3]:= $Version
>
> Out[3]= "6.0 for Mac OS X x86 (64-bit) (May 21, 2008)"
>
> (* Timing and memory consumption with *exact* coefficients *)
>
> In[1]:= Integrate[Cos[5/2*x]*Exp[I*z*Cos[x]], {x, -Pi, Pi}] // Timing
>
> Out[1]=
>                      I z Cos[x]     5 x
> {705.092, Integrate[E           Cos[---], {x, -Pi, Pi}]}
>                                      2
>
> In[2]:= MaxMemoryUsed[]/2.^30 GB
>
> Out[2]= 0.191426 GB
>
> In[3]:= $Version
>
> Out[3]= "6.0 for Mac OS X x86 (64-bit) (May 21, 2008)"
>
> Best regards,
> -- Jean-Marc
>
>   
>> Kevin
>>
>> Jean-Marc Gulliet wrote:
>>     
>>> Kevin J. McCann wrote:
>>>
>>>       
>>>> I can do the following:
>>>>
>>>> Integrate[Cos[2*x]*
>>>>      Exp[I*z*Cos[x]],
>>>>    {x, -Pi, Pi}]
>>>>
>>>>
>>>> which produces a Bessel function answer; however if I change the
>>>> argument in the cosine to 2.5 as in:
>>>>
>>>> Integrate[Cos[2.5*x]*
>>>>      Exp[I*z*Cos[x]],
>>>>    {x, -Pi, Pi}]
>>>>
>>>> I almost immediately get this:
>>>>
>>>> No more memory available.
>>>> Mathematica kernel has shut down.
>>>> Try quitting other applications and then retry.
>>>>
>>>> Any ideas why? I am running XP with 2Gb of memory.
>>>>         
>>> When using symbolic function (i.e. Integrate rather than NIntegrate, Solve
>>> rather than NSolve, etc.) it is always a good idea to feed the function with
>>> *exact* (infinite precision) numbers, thus 5/2 rather 2.5 in your case.
>>> (Mathematica does not find any closed form for your integrand. Note that it
>>> take a while to compute but memory consumption is under control.)
>>>
>>> In[1]:= Integrate[Cos[5/2*x]*Exp[I*z*Cos[x]], {x, -Pi, Pi}]
>>>
>>> Out[1]=
>>>
>>>           I z Cos[x]     5 x
>>> Integrate[E           Cos[---], {x, -Pi, Pi}]
>>>                           2
>>>       
>
>
>   

-- 


Kevin J. McCann
Research Associate Professor
JCET/Physics
University of Maryland, Baltimore County (UMBC)
1000 Hilltop Circle
Baltimore, MD 21250



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