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Re: Re: "Accumulate" in Mathematica 6

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82949] Re: [mg82837] Re: "Accumulate" in Mathematica 6
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 4 Nov 2007 06:12:42 -0500 (EST)
  • References: <200710301049.FAA20459@smc.vnet.net> <fg9o2k$lv7$1@smc.vnet.net> <200711011009.FAA07420@smc.vnet.net>

It is in the nature of things that specialized tools can be better  
optimized than more general ones. In particular, this is true of  
computer programs.

As for usefulness: I will give just one example. This graphic  
represents one of the most important objects in mathematics.

With[{m = 500, n = 20},
  ListPlot[
   Accumulate /@
    Map[Prepend[#, 0] &,
     RandomReal[NormalDistribution[0, N[Sqrt[1/m]]], {n, m}]], Joined  
-> True,
   DataRange -> {0, 1}]]

I think the speed of generating this alone justifies the existence of  
Accumulate.

Andrzej Kozlowski



On 1 Nov 2007, at 19:09, Oskar Itzinger wrote:

> 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 While it was considered obsolete and superseded by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
>>
>
>
>



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