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Tagged list processing

• To: mathgroup at smc.vnet.net
• Subject: [mg86891] Tagged list processing
• From: carlos at colorado.edu
• Date: Tue, 25 Mar 2008 01:17:08 -0500 (EST)

This is related to a recent question. Best stated through an example.
I have two flat lists of equal length:

tag={0,0,1,0,0,  -3,0,0,0,0,          2,4,1,0,0};
val={0,0,4,5,6,  P,1/2,0,-3.0,a+4, 8,16.4,0,Sin[ang],Cos[ang]};

tag contains only integers whereas val can have numbers or
expressions that will (eventually) evaluate to a number.

Task. Generate a pointer list to all nz values in tag, and a
corresponding list of values:

nztag={3,6,11,12,13};   (* may be empty *)
nzval={4,P,8,16.4,0};   (* may be empty *)

and also build the complementary lists

ztag={1,2,4,5,7,8,9,10,14,15};
zval={0,0,5,6,1/2,0,-3.0,a+4, Sin[ang],Cos[ang]};

Obviously ztag=Position[tag,0]; but which
form argument do I use for nztag in Position[tag,form]?
Can I build zval  and nzval with Table for speed ?
(lists may contain 10^4 to 10^6  items)

Constraint: must work in 4.0 thru 6.0 since some of my
remote students have legacy academic versions. Thanks.

• Follow-Ups:
  • Re: Tagged list processing
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Tagged list processing
    • From: János <janos.lobb@yale.edu>
  • Re: Tagged list processing
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>