Re: Re: problem with Pick

*To*: mathgroup at smc.vnet.net*Subject*: [mg78254] Re: [mg78222] Re: [mg78194] problem with Pick*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 27 Jun 2007 05:21:00 -0400 (EDT)*References*: <acbec1a40706230431p4f1db9a9i4320680dda027396@mail.gmail.com> <200706260830.EAA05573@smc.vnet.net> <76C6BC8F-C94E-4574-BEFB-9903EFEDAA86@mimuw.edu.pl> <acbec1a40706260631y785868bcnadd36c795d0c557e@mail.gmail.com>

On 26 Jun 2007, at 22:31, Chris Chiasson wrote: > On 6/26/07, Andrzej Kozlowski <akoz at mimuw.edu.pl> plays Devil's > advocate (;-)): >> It is not actually the case that in this respect we have "one way >> for SparseArray and another way for lists" because "the way for >> lists" is in fact the way for most other selectors except >> SparseArrays. For example, using an arbitrary head f, we have: >> >> Pick[{a, b}, f[2, 3], Except[2]] >> {a, b} >> >> which behaves the same way as List. The fact that SparseArray behaves >> in a special way becoems clear if you examine its FullForm: > > You have sufficiently demonstrated that, when used as the selector in > Pick, SparseArray is not matched at level zero like List and general > expressions of other heads. However, you haven't provided a reason why > the situation should be that way. Also, not to be pedantic, but > >> It is not actually the case that in this respect we have "one way >> for SparseArray and another way for lists" > > is false. > >> FullForm[SparseArray[{1, 2}]] >> FullForm[SparseArray[Automatic, {2}, 0, {1, {{0, 2}, {{1}, {2}}}, >> {1, 2}}]] >> >> Normally, it is the FullForm of the expression that is used in Pick >> (or for pattern matching) but of course it would be extremly >> inconvenient if this were the case with SparseArrays. >> >> Actually, not only SparseArray but also other atomic expressions are >> also treated in "special ways", for example: >> >> Pick[{a, b}, Complex[2, 3], 2] >> Sequence[] >> >> Pick[{a, b}, complex[2, 3], 2] >> {a} >> >> Note that List[a,b] is not an atom and there is no reason to treat it >> in any way different from the way one treats an expression with an >> arbitrary head f. On the other hand, >> >> AtomQ[SparseArray@{1, 2}] >> True >> >> and Atoms in Mathematica are generally treated in special ways as far >> as pattern matching or Part extraction are concerned. > > I agree with these statements, but they are somewhat peripheral to > determining the intended behavior of Pick and making the documentation > consistent. It seems you are not actually taking a position, but are > illuminating certain concepts. > > > -- > http://chris.chiasson.name/ Well, I think the the behaviour of Pick is logically consistent and I am sure it does what was intended. I am not sure that it is the optimal behaviour: in fact I once suggested that a level specification be added to Pick, see the last line of the post: http://forums.wolfram.com/mathgroup/archive/2005/Dec/msg00221.html and the reply by Oyvind Tafjord. My own current feeling is that having a level secification in Pick would be less elegant and less aesthetically satisfying than the present situation to a "purist" (the kind of person who frowns on procedural constructs in functional languages) but could be convenient in some situations. Andrzej Kozlowski

**References**:**Re: problem with Pick***From:*"Chris Chiasson" <chris@chiasson.name>