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FW: comparing two lists

• To: mathgroup at smc.vnet.net
• Subject: [mg54363] FW: [mg54284] comparing two lists
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Sat, 19 Feb 2005 02:32:10 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

 

-----Original Message-----
From: Wolf, Hartmut 
To: mathgroup at smc.vnet.net
Subject: [mg54363] Re: [mg54284] comparing two lists

 
>-----Original Message-----
>From: Curt Fischer [mailto:tentrillion at gmail.NOSPAM.com] 
To: mathgroup at smc.vnet.net
>Sent: Wednesday, February 16, 2005 8:36 PM
>To: mathgroup at smc.vnet.net
>Subject: [mg54363] [mg54284] comparing two lists
>
>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[287]:=
>vec=Table[Random[],{2}]
>
>Out[287]=
>{0.482259,0.314393}
>
>In[288]:=
>mat=Table[Table[Random[],{4}],{2}]
>
>Out[288]=
>{{0.183706,0.758693,0.462242,0.170041},{0.457054,0.349658,0.805
>455,0.127763}}
>
>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?
>
>--
>Curt Fischer
>
>

Curt,

you can easily avoid the problems of entangled function definitions by
resorting to Condition and named pattern:

In[3]:=
MapThread[Flatten@Position[#1, x_ /; x > #2] &, {mat, vec}]

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

For your question of nesting: at least one function definition must be
made by supplying explicit argument names to Function.  You can do that
one way or the other:

In[4]:=
MapThread[Function[{m, v}, Flatten[Position[m, _?(# > v &)]]], {mat,
vec}]

Out[4]=
{{2}, {1, 2, 3}}

or

In[5]:=
MapThread[Flatten[Position[#1, _?(Function[x, x > #2])]] &, {mat, vec}]

Out[5]=
{{2}, {1, 2, 3}}

The parentheses around Function[x,..] are neccessary because ?
(PatternTest) has such a strong precedence.



To your original problem, you might consider:

In[6]:=
Position[mat - vec, _?Positive, {2}]
Out[6]=
{{1, 2}, {2, 1}, {2, 2}, {2, 3}}

which is not quite of the form specified, but perhaps better. 
You might convert one form to the other, e.g

In[7]:=
Split[%, First[#1] === First[#2] &][[All, All, 2]]
Out[7]=
{{2}, {1, 2, 3}}

In[8]:=
Flatten[MapIndexed[Outer[List, #2, #1] &, %], 2]
Out[8]=
{{1, 2}, {2, 1}, {2, 2}, {2, 3}}



--
Hartmut Wolf