Re: Re: ListDimension function

• To: mathgroup at smc.vnet.net
• Subject: [mg72623] Re: [mg72578] Re: ListDimension function
• From: "Chris Chiasson" <chris at chiasson.name>
• Date: Fri, 12 Jan 2007 06:17:52 -0500 (EST)
• References: <eo25ue\$as5\$1@smc.vnet.net> <200701110728.CAA24289@smc.vnet.net>

```I just noticed those tests it had to pass...

here is a new version:

In[1]:= ListDimension[xpr_]:=With[{darg=xpr/.Except[_List|List]->Sequence[]},ListDimensionKernel@darg];
Attributes@ListDimensionKernel={HoldAllComplete};
ListDimensionKernel[Sequence[]]=0;
ListDimensionKernel[darg_]:=Depth@darg-1;

test1=a+b;
test2={1,2,x*y};
test3={1,2,{3,0,1}};
test4={{},{},{}};
test5={{},{{1,2}},a};
ListDimension/@{test1,test2,test3,test4,test5}

Out[10]= {0,1,2,2,3}

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

--
http://chris.chiasson.name/

```

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