Re: pure functions
- To: mathgroup at smc.vnet.net
- Subject: [mg23287] Re: pure functions
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Sun, 30 Apr 2000 21:13:37 -0400 (EDT)
- References: <8eg4bn$g5i@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Helge,
(1) Some ideas
data = {{1, 2}, {3, 4}, {5, 6}, {7, 8}};
The first five below work even when the subsequences are of different
lengths.
The symbol ## (SlotSequence[1]) is useful since it will receive any number
of inputs.
Plus[##] &[Sequence @@ Transpose[data]]
{3, 7, 11, 15}
Apply[Plus, data, {1}]
{3, 7, 11, 15}
Plus @@@ data (*in version 4.0x*)
{3, 7, 11, 15}
Plus @@ Transpose[data]
{3, 7, 11, 15}
The following only works when the subsequences are of the same length.
data.Table[1, {Dimensions[data][[2]]}]
{3, 7, 11, 15}
(2)
Select[{1, 2, 3, 4, 5, 6}, # > 3 &]
{4, 5, 6}
Works by tresting the successive entries in [{1, 2, 3, 4, 5, 6}, with the
function
# > 3 &. An entry is selected if an only if this gives True. Thus
# > 3 &[2]
False
# > 3 &[4]
True
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565
"Helge Andersson" <helgea at inoc.chalmers.se> wrote in message
news:8eg4bn$g5i at smc.vnet.net...
> Hello,
>
>
> Of all the nice functions such as Map, Mapall, Thread, Apply .... I have
> not been able to write a simple code to generate the following
> procedure.
>
> I have a two dimensional list like
>
> li={{11,12,13,..},{21,22,23,...},{31,32,33,..},...}
>
> Since i like to use the pure function command I would like to map my
> pure function with arguments #1,#2,#3,.... on all the sublists in li.
>
> Let me exemplify with a simple pure function that add to numbers.
> (#1+#2)&
>
> if exli={{1,2},{3,4},{5,6},{7,8}}
>
> then I want to get the result
> {3,7,11,15}
>
> One solution, but not allways suitable for me, is the following
>
> (#1+#2)&[Sequence @@ Transpose[exli]].
>
> I want to get rid of the Transpose command and if possible also making
> use of the /@ notation for Map. Since I have seen so many elegant
> examples in the mailing lists I hope I can get something out of this.
>
> Finally, When using pure functions inside Mathematica defined functions
> such as Select for instance,
> Select[{1,2,3,4,5,6},#>3&]
> why don't we need to specify the argument list after the &sign. I can
> figure out that in this case the list sent to the Select command will be
> used as argument list for the pure function but how does this work in
> general. Which are the functions where this feature is possible?
>
> /Helge
>
> --
> *******************
> Helge Andersson
> Oorganisk miljökemi
> CTH
> 412 96 Göteborg
>
> Tel. 031-772 8072
> Tel. Lab. 031-55 38 67
> Fax 031-772 28 53
>
>
>