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
>
> --
> *******************
> Oorganisk miljökemi
> CTH
> 412 96 Göteborg
>
> Tel. 031-772 8072
> Tel. Lab. 031-55 38 67
> Fax  031-772 28 53
>
>
>

```

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