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 *
> Psychology Building                *                           *
> Bloomington, 47405                 *****************************
>
> Office: (812) 856-5217             Fax:    (812) 855-1086
> E-mail: decousin at indiana.edu
http://Prelude.PSY.UMontreal.CA/~cousined
>

```

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