Re: Another Out of Memory Problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg91311] Re: Another Out of Memory Problem*From*: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>*Date*: Fri, 15 Aug 2008 06:52:33 -0400 (EDT)*References*: <g8137j$19$1@smc.vnet.net> <48A42D4D.7060504@gmail.com>

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