Re: MMA 5.1 Integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg52838] Re: MMA 5.1 Integrals
• From: Urijah Kaplan <uak at sas.upenn.edu>
• Date: Tue, 14 Dec 2004 05:59:41 -0500 (EST)
• Organization: University of Pennsylvania
• References: <cpauqc\$ipm\$1@smc.vnet.net> <cpjnj9\$n7r\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```nospam nospam wrote:
> Egbert Kankeleit wrote:
>
>
>>Someone with  elitist "insight" can understand  the philosophy
>>
>>Example (win2000, 850 MHz):
>>
>>i)     Timing[ FourierTransform[Exp[-(x + 1)^2] , x, X];]
>>
>>ii)     Timing[ Integrate[Exp[-(x + 1)^2 + I *x *X],
>>        {x, -\[Infinity],\[Infinity]}];]
>>
>>iii)     Timing[ LaplaceTransform[Exp[-(x + 1)^2], x, X];]
>>
>>results respectively:
>>         MMA 4.2,                  MMA 5.0            MMA5.1
>>
>>i)         1.4                    Infinity          117.       seconds
>>ii)        1.0                    45.                     1.9
>>iii)       0.15                    1.0                   1.0
>>
>>
>>kankel
>>
>>
>
>
>
> You must have very old PC or something?
> I am running XP, and I tried the third test, and I get (my
> PC is almost 3 years old), this is Mathematica 5.1
>
> d = Table[Timing[LaplaceTransform[Exp[-(x + 1)^2], x, X]][[1, 1]]
>      , {i, 100}];
>
> Mean[d]
> 0.10094
>
> Min[d]
> 0.078
>
> Max[d]
> 0.11
>
> so I get something faster than 4.2
>
> You have to understand that the FIRST time you run the
> command, it can take as much as 10 times longer, since
> it will load the code to memory when needed. so get
> an accourate test, try the command once, then the
> second time will be the actual timing results you want to
> look at.
>
> I found Mathematica to be very fast actually.
>
>
>
>
>
I don't think that's what's is going on. I believe Mathematica is caching
some of the intermediate results, so Mathematica is not actually
completely recalculating the result. In order to prevent that, you should
use ClearCache[]. On an Athlon XP 1700+ and Mathematica 5.1;

d = Table[Developer`ClearCache[];
Timing[LaplaceTransform[Exp[-(x + 1)^2], x, X]][[
1,1]], {i, 100}];

{Mean[d], Min[d], Max[d]}

{0.47169,0.437,0.547}

--Urijah Kaplan

```

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