       Re: comparing two lists

• To: mathgroup at smc.vnet.net
• Subject: [mg54330] Re: comparing two lists
• From: Peter Pein <petsie at arcor.de>
• Date: Thu, 17 Feb 2005 10:30:48 -0500 (EST)
• References: <cv086r\$j2k\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Curt Fischer wrote:
> Dear Group:
>
> I want to write a function that accepts a n-vector and an n x m matrix.
> It should return a list of positions in the matrix where mat[[i,j]] >
> vec[[i]].  For example,
>
> In:=
> vec=Table[Random[],{2}]
>
> Out=
> {0.482259,0.314393}
>
> In:=
> mat=Table[Table[Random[],{4}],{2}]
>
> Out=
> {{0.183706,0.758693,0.462242,0.170041},{0.457054,0.349658,0.805455,0.127763}}
>
> I would like myFunc[] to return {{2},{1,2,3}}.
>
> How could I write this as a pure function?  Ideally I would like to be
> able to Map or Apply my function to the list {mat, vec} and get my result.
>
> Something like
>
> Position[#1,_?(#>#2&)]&@@{mat,vec}
>
> is doomed to fail because the PatternTest required in Position[] messes
> up the slotting of the other arguments.
>
> Ideas?  How do you nest pure functions?
>
You can use Function:

In:=
(vec = Table[Random[], {2}]) // ColumnForm
(mat = Table[Random[], {2}, {4}]) // TableForm
Out=
0.360588
0.689747

Out=
0.948523   0.688799    0.265442    0.953434
0.956405   0.416535    0.205109    0.272335

In:=
Function[{v, m},
(Cases[
Position[Inner[#1 > #2 &, Transpose[m], v, List], True],
{#1, x_} -> x] &) /@ Range[Length[First[m]]]
] [vec, mat]

Out=
{{1, 2}, {1}, {}, {1}}

--
Peter Pein
Berlin

```

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