Re: argMax

*To*: mathgroup at smc.vnet.net*Subject*: [mg51328] Re: argMax*From*: "Peltio" <peltio at twilight.zone>*Date*: Thu, 14 Oct 2004 06:37:10 -0400 (EDT)*References*: <ckaj3i$m3r$1@smc.vnet.net> <200410110525.BAA05047@smc.vnet.net> <ckfrv9$ise$1@smc.vnet.net>*Reply-to*: "Peltio" <peltioNOSP at Mdespammed.com.invalid>*Sender*: owner-wri-mathgroup at wolfram.com

"DrBob" wrote >The dichotomy isn't really one-dimensional versus multi-dimensional, I think; it's values versus positions. Since the OP was looking for a fast procedure I thought it would have been better to use 'dedicated' functions for each special case in order to keep the overhead to a minimum. I got my second procedure totally wrong though. Yours is fine, instead, but... > positions[f_,arglist_List]:= > Module[ > {spectrum=Map[f,arglist,-1]}, > Position[spectrum,Max[spectrum]] > ] > values[f_,arglist_List]:=Extract[arglist,positions[f,arglist]] I think you had a 'lapsus digitae' after reading my mistake. : ) In fact Map[f,arglist,-1] should read Map[f,arglist,{-1}] (with onedimensional lists and Identity there are no differences since either there is no nesting or when there is nesting, nesting Identity won't change anything). I was thinking about a way to make the procedure a little faster, but I fear there is little room for improvement (at least without a real breakthrough - such as an undocumented function that does just that : )))). For a start: if the function f to be applied is rather complicated, it could be advisable to use N. Also, when the procedure ArgMax is called many times. using With instead of Module could reduce its overhead (or at least I think so [1]). I am not sure if, when the original data structure is very complex, there could be any improvement in processing the flattened structure (but I guess it's unlikely to have data in a form that is not a neat list, matrix or tensor...) Should that be true, this proc should have a ( theoretical : ) ) edge in case ArgMax is called very many times feeding it complex data structures and timeconsuming functions: argMax[f_, arglist_List] := With[ {newarg = Flatten[N[arglist]]}, spectrum = Map[f, newarg]; Extract[newarg, Position[spectrum, Max[spectrum]] ] ] But it's very likely it won't show any sensible -practical- improvement over the original (corrected) multidimensional version. Moreover, Flatten is useless when the list is onedimensional, so if the other tricks have any effect whatsoever, it'd be better to use a dedicated proc for onedimensional lists. [1] I recall a discussion on Bahder's book (Mathematica for Scientist and Engineers [2]) about different versions of a procedure called trapIntegrate. [2] Wouldn't it be nice to have that book updated? cheers, Peltio Invalid address in reply-to. Crafty demunging required to mail me.

**Follow-Ups**:**Re: Re: argMax***From:*DrBob <drbob@bigfoot.com>

**References**:**Re: argMax***From:*"Peltio" <peltio@twilight.zone>