Re: Using Select within Map
- To: mathgroup at smc.vnet.net
- Subject: [mg71803] Re: Using Select within Map
- From: "Ray Koopman" <koopman at sfu.ca>
- Date: Wed, 29 Nov 2006 02:56:54 -0500 (EST)
- References: <ekh70s$s7p$1@smc.vnet.net>
Mark Teagarden wrote:
> Hi,
>
> I have a data set which comprises several paired lists, like so (I apologize
> if the tabs do not come out correctly in your mail client):
>
> x =
> {
> {
> { , },
> { , },
> { , }
> },
> {
> { , },
> { , },
> { , }
> },
> {
> { , },
> { , },
> { , }
> }
> }
>
> What I would like to do is to select from each of those paired lists, only
> those pairs where the first value in the pair falls within some specified
> range, and then obtain a mean. This would be simple enough if I was
> operating on a single paired list, for example:
>
> Select[x[[1]],a < #[[1]] < b&]
>
> However, I would like to Map over x so that I would end up with means for
> each of the level 1 lists within x; therein lies the problem. Both Map and
> Select use the Slot operator (#), and I don't know how to distinguish
> between the slot operator used by Map, and the slot operator used by Select:
>
> Select[#,a < #[[1]] < b&]/@x
>
> Or if you prefer:
>
> Map[Select[#, a < #[[1]] < b&,x]
>
> This problem has been plaguing me for some time, and if I could punch
> through it I would be very happy indeed. Any ideas? I have had no luck
> looking through the archives or the Help Browser. On a similar note, I
> would eventually like to modify this solution so that the criteria, a and b,
> could vary with each level 1 list in x, but one thing at a time...
>
> Thanks in advance,
> Mark
>
> --
> Mark A. Teagarden, Ph.D.
> University of Texas at San Antonio
> Department of Biology
> One UTSA Circle
> San Antonio, TX 78249
In[1]:= x = {{{1,2},{3,4},{5,6}},
{{7,8},{9,0},{0,9}},
{{8,7},{6,5},{4,3}}};
Your code for the first list in x works nicely:
In[2]:= With[{a = 2, b = 6}, Select[x[[1]], a < #[[1]] < b &]]
Out[2]= {{3,4},{5,6}}
Your code for the whole x needs another ampersand, after the Select:
In[3]:= With[{a = 2, b = 6}, Select[#, a < #[[1]] < b &]& /@ x]
Out[3]= {{{3,4},{5,6}},{},{{4,3}}}
If a and b are not constant, but have values specified in a list ab,
write one of the functions in the form that uses named parameters:
In[4]:= With[{ab = {{2,5},{3,6},{4,7}}},
MapThread[Function[{x,ab}, Select[x, ab[[1]] < #[[1]] < ab[[2]] &]],
{x,ab}]]
Out[4]= {{{3,4}},{},{{6,5}}}