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MathGroup Archive 2004

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Re: Conditonal sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50309] Re: [mg50263] Conditonal sum
  • From: "David Annetts" <davidannetts at ihug.com.au>
  • Date: Thu, 26 Aug 2004 06:51:01 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Christopher, 

I am new to mathematica and could really need a tip on how to implement a 
conditional sum.  Pseudocode would be something like this


EndSum=a;
if j in Sm:
	EndSum=EndSum+f[j]
end


I have tried doing this by using an If-clause inside the sum-function, but  

this seems little elegant and is nor very suitable for symbolic
calculations.

Any advice would be highly appreciated

--------------------

I suggest looking at Select, then applying Plus to the results of Select.

mylist = Table[Random[Real, {-5, 5}], {100}];
Plus @@ Select[mylist, (# > 0 &)] (* Sum of +ve numbers *)
Plus @@ Select[mylist, (-2 < # < 2) &] (* Sum of numbers in range *)

Another way might be through NestList.  Again, we can apply Plus to the
resulting list.

For example, the code below sums the first 8 powers of 2 ...

Plus @@ NestList[2 # &, 1, 8]

The downside to Select (& NestList, as well as a lot of other functional
programming) is that it is often less intuitive than the Fortran (or C++)
approach of doing things in a loop.  The upside, as far as Mathematica is
concerned, is that the functional approach is often much faster.

Regards,

Dave.


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