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Re: problem with Pick

  • To: mathgroup at
  • Subject: [mg78221] Re: [mg78194] problem with Pick
  • From: Oyvind Tafjord <tafjord at>
  • Date: Tue, 26 Jun 2007 04:30:10 -0400 (EDT)
  • References: <> <> <> <>

Chris Chiasson wrote:
> On 6/25/07, Oyvind Tafjord <tafjord at> wrote:
>> In this case, sel={{},{1}}. sel[[]] matches patt, and so list[[]] is 
>> picked out.
>> This behavior, in which all of list gets picked, does produce a fair 
>> amount
>> of confusion, unfortunately. It often shows up in connection with Except:
>> In[1]:= Pick[{a, b, c}, {1, 2, 3}, Except[2]]
>> Out[1]= {a, b, c}
>> In[2]:= Pick[{a, b, c}, {1, 2, 3}, Except[2, _Integer]]
>> Out[2]= {a, c}
> Thank you for the reply.
> You seem to be implying that the above behavior is intended, even
> though it violates the documentation. I believe it is unintended, due
> to the following output, which seems to indicate that the matches are
> supposed to be checked on the first level:
> In[1]:= Pick[{a,b,c},SparseArray@{1,2,3},Except[2]]
> Pick[{a,b,c},{1,2,3},Except[2]]
> Out[1]= {a,c}
> Out[2]= {a,b,c}
> If I am wrong, then this SparseArray behavior is a bug, the
> documentation is wrong, and I suggest that an optional level argument
> be added to Pick.

In what way does this behavior violate the documentation? It uses the 
statement you quoted:

Pick[list,sel,patt] picks out those list[[i1,i2,...]] for which
sel[[i1,i2,...]] matches patt.

with the 0-length version of i1,i2,... I agree this is often what you don't 
want though.

The SparseArray case is treated differently, in this case only the 
individual elements are treated as "selectors", for optimization and 
usefulness. This could be explained better in the documentation.

E.g., compare

In[20]:= Pick[{{a, b, c}, {d, e, f}},
  SparseArray@{{3, 4, 5}, {1, 2, 3}}, 4]

Out[20]= {{b}, {}}

In[21]:= Pick[{{a, b, c}, {d, e, f}},
  SparseArray@{{3, 4, 5}, {1, 2, 3}}, {3, 4, 5}]

Out[21]= {{}, {}}

In[22]:= Pick[{{a, b, c}, {d, e, f}}, {{3, 4, 5}, {1, 2, 3}}, {3, 4, 5}]

Out[22]= {{a, b, c}, {}}

Oyvind Tafjord
Wolfram Research

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