Re: Inner product can be modified?
- To: mathgroup at smc.vnet.net
- Subject: [mg21473] Re: Inner product can be modified?
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Tue, 11 Jan 2000 04:17:52 -0500 (EST)
- References: <85cmmt$lgk@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Denis,
General point: Mathematica has a programming language that is not tied to
Mathematics - if you can use the generality to get what you need efficiently
then use it.
I have certainly made use of Inner to generalize Dot, but I can't trace
this at the moment. However, consider finding the volume of a hypercube in
n-space with edges parallel to the axes and with the ends ot the principle
diagonal given by v1 and v2:
v1 = {a, b, c};
v2 = {A, B, C};
Inner[Subtract, v1, v2, Times]
(a - A) (b - B) (c - C)
Times @@ (v1 - v2)
(a - A) (b - B) (c - C)
The "Inner " form looks cumbersome, but it is faster, certainly for higher
dimensions
v1 = Table[Random, {100}];
v2 = Table[Random, {100}];
Do[Inner[Subtract, v1, v2, Times],
{100}] // Timing
{0.38 Second, Null}
Do[Times @@ (v1 - v2), {100}] // Timing
{1.15 Second, Null}
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"Denis Cousineau" <decousin at indiana.edu> wrote in message
news:85cmmt$lgk at smc.vnet.net...
> Hi,
>
> I've seen in the documentation that the command
> Inner[]
> can be modified so that it is not necessarily the
> sum (Plus) that is executed on the elements.
>
> Is is done frequently in mathematics? I discover that
> I needed to do that in my own application, but though
> I was doing a crazy thing, so if other did, I would
> like to know.
>
> What kind of application requires a different aggregate
> operation than Plus?
> Is is well-known?
> Do you have an easy-to-access reference where this
> is done?
>
> Thank you for your help.
> Denis
>
> P.S. mail and post reply appreciated.
> --
>
> Denis Cousineau, Postdoc *****************************
> Cognitive psychology * *
> Indiana University * Etudiant devant l'eternel *
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> E-mail: decousin at indiana.edu
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>