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Re: Tagged list processing

• To: mathgroup at smc.vnet.net
• Subject: [mg86914] Re: [mg86891] Tagged list processing
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 26 Mar 2008 04:52:33 -0500 (EST)
• References: <200803250617.BAA10618@smc.vnet.net>

carlos at colorado.edu wrote:
> 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.

This will work for versions 5.0 through present, but not in 4.x.

tagsAndValues[tag_List,val_List] := Module[
   {n=Length[tag]},
   Map[First,Reap[Do[If[tag[[j]]==0,
     Sow[j,ztag]; Sow[val[[j]],zval],
     Sow[j,nztag]; Sow[val[[j]],nzval]]
     , {j,n}],
	{nztag,nzval,ztag,zval}][[2]]]
   ]

Example:

{nztag,nzval,ztag,zval} = tagsAndValues[tag,val]

In[4]:= InputForm[
   {nztag,nzval,ztag,zval} = tagsAndValues[tag,val]]

Out[4]//InputForm=
{{3, 6, 11, 12, 13}, {4, P, 8, 16.4, 0},
  {1, 2, 4, 5, 7, 8, 9, 10, 14, 15},
  {0, 0, 5, 6, 1/2, 0, -3., 4 + a, Sin[ang], Cos[ang]}}

For prior versions I'd suggest either using Position, or else emulating 
Sow/Reap using DownValue assignment. Other approaches will likely be 
noticeably slow, for lists in the size range you require.

Daniel Lichtblau
Wolfram Research

• Follow-Ups:
  • Re: Re: Tagged list processing
    • From: Daniel Lichtblau <danl@wolfram.com>

• References:
  • Tagged list processing
    • From: carlos@colorado.edu