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Re: selecting from lists
*To*: mathgroup at smc.vnet.net
*Subject*: [mg6137] Re: [mg6120] selecting from lists
*From*: support (Tom Zeller)
*Date*: Sun, 23 Feb 1997 00:10:50 -0500
*Sender*: owner-wri-mathgroup at wolfram.com
>The problem: given an arbitrary list v and a list b of the same
>length, whose entries are all Boolean (True or False), construct a
>function s[v, b] whose result is a list consisting only of those
>entries of v for which the corresponding entries in b are True. For
>example,
>
> v = {3, 82, 7, -12, 5};
> b = {False, True, True, False};
> s[v, b]
>{82, 7}
>
>Of course, a looping solution is obvious. But I want something that
>works on the entire list at once (as in the APL or J programming
>languages, where this sort of thing is utterly trivial). The best
>I've come up with so far is the following:
>
> bpick[x_, b_] := If[b, {x}, {}]
> SetAttributes[bpick, Listable]
> s[v_, b_] := Flatten[bpick[v, b]]
>
>Is there some nicer, more direct way? No Table's, Do's, or For's,
>please!
>
Like the passengers of the Titanic, I will attend to the tip of the iceberg
only ......
Here is a combination of Mathematica list handling functions and a pure
function that will do what you ask above.
In[16]:=
v = {3, 82, 7, -12, 5};
b = {False, True, True, False, True};
(* list b was added to to make the lists the same length *)
Here it is in steps:
In[21]:=
pairs=Transpose[{v, b}]
Out[21]=
{{3, False}, {82, True}, {7, True}, {-12, False}, {5, True}}
In[22]:=
Select[pairs, #[[2]]&]
Out[22]=
{{82, True}, {7, True}, {5, True}}
In[23]:=
Map[First, %]
Out[23]=
{82, 7, 5}
Here are the steps rolled into a function.
In[24]:=
f[x_List, y_List] := Map[First, Select[Transpose[{x,y}], #[[2]]&]]
In[25]:=
f[v, b]
Out[25]=
{82, 7, 5}
Tom Zeller
Wait! what is that under the water?!
>Actually, the general problem as I formulated it above is just the tip
>of the iceberg of things that are giving me trouble in Mathematica
>that are so easy for me in APL or J. For example, construct a
>function firstnonzero that returns the index of the first nonzero
>entry in a list (or, more generally, the first entry in a list
>satisfying a given property). Here the best I've come up with that
>avoids explicit looping is:
>
> nonzero[x_] != 0; SetAttributes[nonzero, Listable]
> firstnonzero[v_] := First[s[Range[Length[v]], nonzero[v]]]
>
>In these and similar problems, I have the feeling that there ought to
>be some slick approach using patterns, but I don't see how to do it.
>
>Any help in putting me onto the right track in "Mathematica thinking"
>about such problems would be appreciated.
>
>--
> Murray Eisenberg Internet: murray at math.umass.edu
> Mathematics & Statistics Dept. Voice: 413-545-2859 (W)
> University of Massachusetts 413-549-1020 (H)
> Amherst, MA 01003 Fax: 413-545-1801
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