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Re: How to use Pick[]; Is this a bug?

What has been will be again, what has been done will be done again; there is nothing new under the sun.
(Ecclesiastes 1:9)

Andrzej Kozlowski

On 24 Aug 2012, at 02:50, awnl <awnl at> wrote:

> Hi,
>> Sigh... Yes, documentation can be improved. But it truly isn't
>> accurate to say "nothing in the documentation gives a hint...".
>> The key point is the syntax specified for Pick, i.e.,
>> Pick[list, sel, patt]
>> The important part is patt short for pattern, telling you Pick
>> is doing pattern matching. Other parts of the documentation
>> discussion pattern matching and how Mathematica goes about it
>> point out Mathematica tries to match the entire expression with
>> the specified pattern.
> I don't think that's the point and tried to make clear that I appreciate
> and understand the explanation of Peter about what happens.
> Pattern matching can very well be restricted to only work on certain
> levels of an expression and probably is more often used with such
> restrictions than without, ReplaceAll probably rather being an exception
> than the rule. There are several functions which do use pattern matching
> and *do* restrict levels, at least by default (c.f. Cases[{0, 1, 2, 0,
> 3, 4}, Except[0]]) because *that makes sense for their intended
> purpose*. There are even functions which basically do the same thing
> except for the (default) level specification, c.f. MemberQ[expr,pat,{0}]
> vs. MatchQ[expr,pat] (not that MatchQ always only works at level 0). I
> think it's not unreasonable to expect Pick to choose an appropriate
> level specification as well when reading this (from the documentation):
> Pick[list,sel,patt] picks out those list[[Subscript[i, 1],Subscript[i,
> 2],...]] for which sel[[Subscript[i, 1],Subscript[i, 2],...]] matches patt.
> especially when there is such an obvious match of the shapes of list and
> sel as in this case and.
> Thinking about it I agree that it might not be justified to call this a
> plain bug, as the documentation is indeed vague enough to allow the
> observed behavior (if you allow Subscript[i, 1],Subscript[i, 2],... to
> also mean All) -- just as it would allow something else. But I don't see
> the problem here is just that the documentation could be improved, but
> believe that the design decision to use all levels for the pattern
> matching in Pick without an alternative is not optimal. I say this
> because I found that making an explicit level specification in pattern
> matching functions has proven to be a much clearer and more robust
> approach for me than to try to tweak the patterns to perform the desired
> level specification "implicitly". Because of that I think a better
> solution would be to add a level specification argument to Pick, which
> could do something like:
> myPick[list_, sel_, pat_, levelspec_] :=
>  Pick[list, Replace[sel, {pat :> True, _ :> False}, levelspec]]
> and would allow to get the desired result like this:
> myPick[{1, 2, 3, 4, 5}, {9, 0, 7, 0, 6}, Except[0], {1}]
> Comparing to such an explicit level specification you'll find that Pick
> implicitly uses levelspec={0,Infinity}. An alternative would be to use
> levelspec={1,Infinity} for a default behavior which would make more
> sense IMHO, as making a function call to pick All of an expression seems
> a relatively odd corner case of how one would want to use Pick. Note
> that e.g. for Cases and many other functions such an admittedly somewhat
> arbitrary choice has been made. As it doesn't make a statement about
> which levelspec it uses for it's pattern matching, the documentation for
> Pick would perfectly well allow to use {1,Infinity} (or any other level
> specification) as the internal setting...
> Whatever we call it, I would certainly not blame the user here for
> having a wrong expectation of how Mathematica should work in this case.
> To make that clear was the only intention of my previous post...
> regards,
> albert

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