Re: Why so slow and not getting faster
- To: mathgroup at smc.vnet.net
- Subject: [mg113261] Re: Why so slow and not getting faster
- From: David Bailey <dave at removedbailey.co.uk>
- Date: Thu, 21 Oct 2010 07:01:31 -0400 (EDT)
- References: <i9m7vi$j5c$1@smc.vnet.net>
On 20/10/10 09:07, Sam Takoy wrote:
> Hi,
>
> I ran the following code on two machines (linux and windows) under
> identical versions - 7.0.1.0.
>
> On the windows machine, the code takes 10-15 seconds on each run.
>
> On the linux maxhine, the first run took 6 seconds and all subsequent
> runs are nearly instantaneous (< 1/10 sec).
>
> 1. I accept that my windows machine is slower, but why doesn't it show
> similar acceleration in subsequent runs?
>
> 2. Even 6 seconds I think is too high. Are these very simple
> integrations for Mathematica?
>
> Many thanks in advance,
>
> Sam
>
>
> FourierCoefficients[f_, order_] := Module[{first, reim},
> first = 1/(2 \[Pi]) Integrate[f[a], {a, -\[Pi], \[Pi]}];
> Print[first];
> reim = Table[(Print[n];
> 1/\[Pi] Integrate[f[a]*E^(I*n*a), {a, -\[Pi], \[Pi]}]), {n, 1,
> order}];
> Join[{first}, Map[ComplexExpand[{Re[#], Im[#]}]&, reim]]]
>
> g[a_] := 1/32 (7 - 11 Cos[2 a] - 8 Cos[4 a] - 3 Cos[6 a])
> FourierCoefficients[g, 5]
>
Integrate (as opposed to NIntegrate) is a complicated symbolic
operation, and you can't expect lightening speed. A lot of checks are
performed to avoid returning invalid results of various sorts.
Integrate will sometimes store results for re-use (a process known as
caching) and this is almost certainly responsible for the speed up when
you repeat the calculation. The exact decision as to when to keep a
result, and when to discard it is obviously somewhat arbitrary, and
Mathematica may store more results if more memory is available - which
could account for the difference between your two machines.
David Bailey
http://www.dbaileyconsultancy.co.uk