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
>>of costly updates? :
>>
>>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
>>
>>WRI, quo vadis?
>>
>>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