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Re: choose elements from list based on elements in different list

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86734] Re: choose elements from list based on elements in different list
  • From: "David Park" <djmpark at comcast.net>
  • Date: Thu, 20 Mar 2008 02:50:34 -0500 (EST)
  • References: <frqpnb$4vl$1@smc.vnet.net>

Whenever one wants to do operations on two equal length structures the Inner 
statement is a good choice.

Reihe1 = {22, 33, 44, 0, 0, 16, 5, 0, 0, 0};
Reihe2 = {16, 27, 0, 0, 5, 11, 5, 0, 0, 12};

Here we do the two tests and either insert the nonzero number in a new list, 
or insert an empty Sequence. The empty Sequence must be Unevaluated in the 
If statement or it would simply disappear for there.

Inner[If[#1 == 0 \[And] #2 != 0, #2,
   Unevaluated@Sequence[]] &, Reihe1, Reihe2, List]
{5, 12}

Inner[If[#2 == 0 \[And] #1 != 0, #1,
   Unevaluated@Sequence[]] &, Reihe1, Reihe2, List]
{44}

This construction is also useful for the combination of equations.

eqn1 = x == a + b;
eqn2 = y == a - b;

Inner[#1 + #2 &, eqn1, eqn2, Equal]
x + y == 2 a

Inner[Expand[2 #1 - #2] &, eqn1, eqn2, Equal]
2 x - y == a + 3 b

-- 
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/


"Claus" <clausenator at gmail.com> wrote in message 
news:frqpnb$4vl$1 at smc.vnet.net...
> Hi,
> I'm trying to choose elements from list based on elements in different
> list and I came up with the ideas listed below. It seems to me that
> there are a few too many steps involved here, and I need to run this on
> larger lists (~20000 entries).
> Are there ways to improve this?
> Thanks,
> Claus
>
> Here is the mathematica code:
>
> Reihe1={22,33,44,0,0,16,5,0,0,0}
> Reihe2={16,27,0,0,5,11,5,0,0,12}
>
> {22, 33, 44, 0, 0, 16, 5, 0, 0, 0}
>
> {16, 27, 0, 0, 5, 11, 5, 0, 0, 12}
>
> (*Find out where in Reihe1 and in Reihe2 are Zeros and notZeros*)
>
> Reihe1Is0 = Thread[Reihe1 == 0]
> Reihe1Not0 = Thread[Reihe1 != 0]
> Reihe2Is0 = Thread[Reihe2 == 0]
> Reihe2Not0 = Thread[Reihe2 != 0]
>
> {False, False, False, True, True, False, False, True, True, True}
>
> {True, True, True, False, False, True, True, False, False, False}
>
> {False, False, True, True, False, False, False, True, True, False}
>
> {True, True, False, False, True, True, True, False, False, True}
>
> (*Select the values of Reihe1 and Reihe2 which are of interest
>
> There are 4 Cases (not all of them calculated later) :
>  Case1 :  Reihe1 and Reihe2 are 0
>  Case2 :  Reihe1 and Reihe2 are NOT 0
>  Case3 : (Reihe2 is NOT 0) AND (Reihe1 is 0)
>  Case4 : (Reihe1 is NOT 0) AND (Reihe2 is 0)*)
>
> PreCase3=Pick[Reihe2,Reihe1Is0]
> PreCase4=Pick[Reihe1,Reihe2Is0]
>
> {0, 5, 0, 0, 12}
>
> {44, 0, 0, 0}
>
> Case3=Select[PreCase3,#>0&]
> Case4=Select[PreCase4,#>0&]
>
> {5, 12}
>
> {44}
> 



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