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Re: "Accumulate" in Mathematica 6

• To: mathgroup at smc.vnet.net
• Subject: [mg82837] Re: "Accumulate" in Mathematica 6
• From: "Oskar Itzinger" <oskar at opec.org>
• Date: Thu, 1 Nov 2007 05:09:28 -0500 (EST)
• References: <200710301049.FAA20459@smc.vnet.net> <fg9o2k$lv7$1@smc.vnet.net>

Taken - so it's speed. Does that imply we can expect in the future a whole
bunch of

speed-optimized functions for doing a similar thing for, say, Times, Divide,
or

any other function one can dream of?

BTW, your mileage may vary - but in my code I've certainly much more
occasions to

use Fold/FoldList with other functions than Plus [as per the new
Accumulate]. So,

since Fold/FoldList plays a reasonably important role in functional
programming,

wouldn't speeding *them* up be more useful in general than providing just
individually

optimized functions?

Thanks.

/oskar

"Andrzej Kozlowski" <akoz at mimuw.edu.pl> wrote in message
news:fg9o2k$lv7$1 at smc.vnet.net...
> On 30 Oct 2007, at 19:49, Oskar Itzinger wrote:
>
> > Very sadly, Mathematica 6 is not supported under Irix - so I can't
> > play with
> > it practically - but I noticed in the online
> >
> > documentation that there is a new function "Accumulate[list]",
> > defined to be
> > equivalent to "Rest[FoldList[Plus, 0, list]]",
> >
> > giving a list of the successive accumulated totals of the elements in
> > <list>.
> >
> > Funny. While it was considered obsolete and superseded by
> > "FoldList" in
> > Mathematica 2, Mathematica 1 (!) already did
> >
> > have a function "Accumulate", defined as
> >
> > Accumulate[f, g[e1, e2, e3, ...]] <==> g[e1, f[e1, e2], f[f[e1,
> > e2], e3],
> > ...]
> >
> > so that
> >
> > Accumulate[Plus, Range[5]] <==> {1, 3, 6, 10, 15}
> >
> > However, "Accumulate" in Mathematica 1 clearly was not restricted
> > to "Plus"
> > but rather specifically intended for dealing
> >
> > with functions that take exactly two arguments - so, I believe that
> > "Accumulate" in Mathematica 6 is much less usable
> >
> > than the former in Mathematica 1.
> >
> > Maybe I'm missing something here - but what was the rationale behind
> > re-implementing "Accumulate" in such a restricted
> >
> > version now?
> >
> > Thanks.
> >
> > /oskar
> >
> >
> >
> >
>
> You are missing just one thing - performance. Accumulate in this
> restricted sense is incredibly fast - and extremly useful.
>
> Andrzej Kozlowski
>

• Follow-Ups:
  • Re: Re: "Accumulate" in Mathematica 6
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>