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MathGroup Archive 2007

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Re: ListDimension function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72578] Re: ListDimension function
  • From: carlos at colorado.edu
  • Date: Thu, 11 Jan 2007 02:28:24 -0500 (EST)
  • References: <eo25ue$as5$1@smc.vnet.net>

Many thanks to all of you who sent me solutions by direct email.
For testing purposes I organized them into 7 functions:

ListDim1[v_]:=If[Head[v]===List,1+Max[Map[ListDim1,v],0],0]; (* Don
Taylor *)
ListDim2[lst_]:=Max[Length/@Position[lst,List]]; (* János *)
ListDim3[expr_]:=Max[Length/@Position[{expr},{___}]]; (* David Park *)
ListDim4[l_]:=Depth[DeleteCases[l,_?(!ListQ[#1]&)]]-1; (* Jean-Marc
Gulliet *)
ListDim5[e_]:=Max[Length/@Position[e,List]]; (* Carl Woll *)
ListDim6[list_List]:=Depth[list/.x_List/;(!MemberQ[x,{___}])->{}]-1;ListDim6[_]=0;
(* dh *)
ListDim7[expr_]:=Depth[0*expr]-1; (* Andrzej Kozlowski *)

(I excluded a solution by Adriano Pascoletti, who uses 2 functions)
Here is a quick test:

ListDimTest[e_]:={ListDim1[e],ListDim2[e],ListDim3[e],ListDim4[e],ListDim5[e],
                  ListDim6[e],ListDim7[e]};

t={1,Null,{},{1,2,3,4},{"s"+1},{{},{},{}}, {Infinity,Indefinite,{}},
{1,{{{{{{x,y*z}}}}}},{6}}, {{{{Sqrt[1+x*y]}}}},
{1,{2,Null+5,3},{{{4,Infinity,-4}}}},
   {0,{1,{2,{3^{1,2,3}}}}}, {c*{{1,2},{3+{x,y},4}}} } ;
Print[Table[ListDimTest[t[[i]]],{i,1,Length[t]}]//TableForm];

and the results are

Infinity::indet: Indeterminate expression 0 Infinity encountered.

Infinity::indet: Indeterminate expression 0 Infinity encountered.

 0  -Infinity  0  0  -Infinity  0  0
 0  -Infinity  0  0  -Infinity  0  0
 1          1  1  1          1  1  1
 1          1  1  1          1  1  1
 1          1  1  1          1  1  1
 2          2  2  2          2  2  2
 2          2  2  2          2  2  2
 7          7  7  8          7  7  7
 4          4  4  7          4  4  4
 4          4  4  5          4  4  4
 5          5  5  5          5  5  5
 4          4  4  6          4  4  4

Summary: #1, #3, #6 and #7 returned the correct value across the
board. However #7 produced a warning message when an entry
contained Infinity due to the 0*Infinite operation.  It seems that the
most compact solution that works, and produces no messages, is #3.
Congratulations to David.

BTW I found surprising that this is not provided as built-in function,
since it is such a basic operation in list preprocessing.


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