Re: RE Map

*To*: mathgroup at smc.vnet.net*Subject*: [mg29740] Re: RE Map*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Fri, 6 Jul 2001 03:24:35 -0400 (EDT)*References*: <9i06i3$h19$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Ranko, > b={{1, 5, 10},{25, 0, {1,2,3,4}},{55, 5, 2001} > > If we try to apply a function g to levels 2 and 3 we get > > ClearAll[g] > Map[g,b,{2,3}] > {{g[1],g[5],g[10]},{g[25],g[0],g[{g[1],g[2],g[3],g[4]}]},{g[55],g[5],g[2001] }} > > but this is clearly not what we wanted because of the term > g[{g[1],g[2],g[3],g[4]}]} > > The only way to obtain the correct result in this case is to make g > listable Not in this case: b={{1, 5, 10},{25, 0, {1,2,3,4}},{55, 5, 2001}} {{1,5,10},{25,0,{1,2,3,4}},{55,5,2001}} Map[g,b,{-1}] {{g[1],g[5],g[10]},{g[25],g[0],{g[1],g[2],g[3],g[4]}},{g[55],g[5],g[2001]}} -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Ranko Bojanic" <bojanic at math.ohio-state.edu> wrote in message news:9i06i3$h19$1 at smc.vnet.net... > > > > Benedetto Bongiorno wanted to convert the list > a={{1, 5, 10},{25, 0, 2000},{55, 5, 2001} > into the list > {{01, 05,10},{25, 00, 2000},{55, 05, 2001} > His program > > Map[If[#<10,(StringJoin[ToString[0],ToString[#]]),#]&,a] > > did not work but, as several readers pointed out, this could be > easily corrected by adding the correct level specification: > > Map[If[#<10,(StringJoin[ToString[0],ToString[#]]),#]&,a,{2}] > {{01,05,10},{25,00,2000},{55,05,2001}} > > One potential problem I see here is that the result is a list of > strings and integers > > Map[Head, %,{2}] > {{String,String,Integer},{Integer,String,Integer},{Integer,String,Integer}} > > This can be also easily corrected by writing: > > Map[If[#<10,(StringJoin[ToString[0],ToString[#]]),ToString[#]]&,a,{2}] > > The main reason I am writing this letter is that Map with level > specifications does not seem to work in a slightly more complicated cases, > for instance when > > b={{1, 5, 10},{25, 0, {1,2,3,4}},{55, 5, 2001} > > If we try to apply a function g to levels 2 and 3 we get > > ClearAll[g] > Map[g,b,{2,3}] > {{g[1],g[5],g[10]},{g[25],g[0],g[{g[1],g[2],g[3],g[4]}]},{g[55],g[5],g[2001] }} > > but this is clearly not what we wanted because of the term > g[{g[1],g[2],g[3],g[4]}]} > > The only way to obtain the correct result in this case is to make g listable: > > SetAttributes[g,Listable] > g[b] > {{g[1],g[5],g[10]},{g[25],g[0],{g[1],g[2],g[3],g[4]}},{g[55],g[5],g[2001]}} > > This suggests the following approach to Bongiorno's problem. Define > > f[x_] :=If[x<10,(StringJoin[ToString[0],ToString[x]]),ToString[x]]; > > and make it Listable > > SetAttributes[f,Listable] > > We obtain then > > f[a] > {{01 ,05, 10},{25, 00, 2000},{55, 05, 2001}} > f[b] > {{01,05,10},{25,00,{01,02,03,04}},{55,05,2001}} > > Ranko > > >