Little problem with Through

Question

list = Partition[Range[20], 5, 5, 1, {}]

{{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}, {11, 12, 13, 14, 15}, {16, 17, 18, 19, 20}}

pos = Transpose[{Through[First, Last] /@ list, Through[Last, First] /@ list}]

{{1, 5}, {6, 10}, {11, 15}, {16, 20}}

As you see, I've used Through twice. I think once should be enough, but I haven't been able to see how to do it with one Through. Any ideas?

@b.gatessucks yes, me silly, haha, you can post that as one answer. — HyperGroups, Jun 12 '13 at 06:10
To properly use Through[]: Through[{First, Last}[#]] & /@ list. Slot-free version: Composition[Through, {First, Last}] /@ list. — J. M.'s missing motivation, Jun 12 '13 at 06:19
@0x4A4D nice+1, you've done it, I've tried Through[{First,Last}]/@list, you can answer my question too. — HyperGroups, Jun 12 '13 at 06:22
Through[{First, Last}] /@ list won't work, as you've seen. That's because the syntax is supposed to be Through[{f1, f2, f3, ...}[arg1, arg2, arg3, ...]]. You put in the functions, but forgot the arguments. — J. M.'s missing motivation, Jun 12 '13 at 06:24
Anyway, maybe you can answer your own question, if you understood what I was trying to point out to you. — J. M.'s missing motivation, Jun 12 '13 at 06:40
@0x4A4D Fine, seems people do not like this question. I'll delete it later, thanks. well, my output-style was edited,@@, — HyperGroups, Jun 12 '13 at 06:44
I didn't ask you to delete the question; I asked you if you could write an answer to your question (answering your own question is acceptable in this site, in case that wasn't made clear to you.) You can stand to gain rep from upvotes to your answer, and we can critique your understanding of the matter at hand. — J. M.'s missing motivation, Jun 12 '13 at 06:46
Are you aware that you can do this with Part? list[[All,{1,-1}]] — Simon Woods, Jun 12 '13 at 07:45
@SimonWoods en, that time my first thought is use through, I tried your method here by {First[#], Last[#]} &/@. Maybe you can also give me come comments about that question. http://mathematica.stackexchange.com/q/27114/6648 — HyperGroups, Jun 17 '13 at 04:06

score 7 · Accepted Answer · edited Jun 12 '13 at 10:35

7

I have tried this

list = Partition[Range[20], 5, 5, 1, {}];
Through[{First, Last}] /@ list
(* {Through[{First,Last}][{1,2,3,4,5}],Through[{First,Last}][{6,7,8,9,10}],
    Through[{First,Last}][{11,12,13,14,15}],Through[{First,Last}][{16,17,18,19,20}]} *)

Let's see the example in help page of Through

Through[{f, g, h}[x]]   
(* {f[x],g[x],h[x]} *)

as @0x4A4D metioned in the comment. We need one argument for

Through[{First, Last}[#]] & /@ list
(* {{1,5},{6,10},{11,15},{16,20}} *)

this is one error usage

Through[{f, g, h}][x]
(* Through[{f,g,h}][x] *)

Through[{f, g, h}[#]] &[x]
(* {f[x],g[x],h[x]} *)

edited Jun 12 '13 at 10:35

J. M.'s missing motivation

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answered Jun 12 '13 at 07:11

HyperGroups

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Well done. ${}$ – J. M.'s missing motivation Jun 12 '13 at 07:21
2

Please don't make this an orgy of different formatting styles... – rm -rf Jun 12 '13 at 08:34
@rm-rf hi,Do you mean the tag? I'm learning format in SE, Do you think the hint word Output is necessary? – HyperGroups Jun 12 '13 at 08:37
@HyperGroups nice answer (+1). The <kbd> tag stands for keyboard, which is usually used for indicating a key on the keyboard, e.g., Ctrl. So it may not be a best choice for "Output". In fact, on this site, people usually just put the output results in blockquotes without any "hint word". – Silvia Jun 12 '13 at 08:52
@Silvia Ok, I learned that. – HyperGroups Jun 12 '13 at 08:57
@HyperGroups Yes, that, but also several other things that I've noticed from other posts. 1) There is no need to repeat the question title in <h1> or to have a heading "My answer", because both are clear from the context. 2) Please do not use <pre> — when you asked me earlier, I was referring to its use in some tricky situations (very rare). You're indenting by 4 and using <pre>, which messes up the layout. Please learn how to indent using markdown instead (hundreds of thousands of users across the SE network have no problem with it...). [continued...] – rm -rf Jun 12 '13 at 10:11
<kbd> tags should be used for indicating keys on a keyboard. 4) The quote block is being heavily abused (not just by you). While sometimes it is justified, I disagree with its use for output (although I can't do much about it). I prefer the alternate convention of commenting out the output (like I did in my edit above), because then you can simply copy the block and run in Mathematica and you won't run into issues. Also, output in code within blockquote will mess with this API based code extractor, since is is inserted in an input cell.

rm -rf

Jun 12 '13 at 10:12

@rm-rf I agree that using (*...*) would be more convenient for copying the whole code block all at once. But about the extractor, please see my comment. :) – Silvia Jun 12 '13 at 11:37

@rm-rf fine, I'll take some suggestions. – HyperGroups Jun 12 '13 at 12:06

Little problem with Through

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