I have a list as follows:


and would like to delete certain elements from it resp. pick certain elements to get a list as follows

lis2= {{{a1,c1,e1},{a2,c2,e2}},

My problem is that the data I would like to select are not in an consecutive order (otherwise I could use the Part function). Does anyone have an hint?


5 Answers 5


You actually can still use the Part function!

If you know the positions explicitly you can try:

lis1[[All, All, {1, 3, 5}]]

Or, if they follow a regular pattern:

lis1[[All, All, 1 ;; 5 ;; 2]]

Just learned from this answer by ciao that Downsample is made for this kind of task:

Downsample[#, {1, 2}] & /@ lis1
(* {{{a1, c1, e1}, {a2, c2, e2}}, {{a3, c3, e3}, {a4, c4, e4}}} *)

You can also use Take, Drop and Extract to get the same result:

Take[#, All, {1, -1, 2}] & /@ lis1
Drop[#, {}, {2, -1, 2}] & /@ lis1
First@Rest@Extract[lis1, {{0}, {;; , ;; , ;; ;; 2}}]

You can use arbitrary lists for Part specifications with Part and Extract. For example

#[[All, ;; , {1, 4, 5}]] &@lis1  (* or *)
First@Rest@Extract[lis1, {{0}, {All, ;; , {1, 4, 5}}}]

both give all rows and columns 1, 4 and 5 in all matrices in lis1:

(* {{{a1, d1, e1}, {a2, d2, e2}}, {{a3, d3, e3}, {a4, d4, e4}}} *)
  • $\begingroup$ That only works for the specific example. OP said: "My problem is that the data I would like to select are not in an consecutive order (otherwise I could use the Part function)." $\endgroup$
    – rm -rf
    May 2, 2015 at 17:57
  • $\begingroup$ @TheToad, i may be wrong, but i thought the quote meant the OP was not aware of the part specifications other than from;;to (since Part specs can be any list). $\endgroup$
    – kglr
    May 2, 2015 at 18:08
  • $\begingroup$ @TheToad Even though the origins of the name change are clear, it will take (me) some time to get used to. Is it planned as permanent? $\endgroup$ May 2, 2015 at 19:34
  • 1
    $\begingroup$ @LeonidShifrin It was just for fun, mostly. I came across an image that I really liked and just went along with it :) How long I'll keep it, I don't know, lol. I've always treated online personas as ephemeral and have fun changing things around but I can see how it might be confusing for others, especially when there are some artifacts and other bread crumbs lying around :) I can revert if you'd like me to/find it confusing. $\endgroup$
    – rm -rf
    May 4, 2015 at 4:34
  • $\begingroup$ @TheToad Oh no, by all means keep it as long as you want :). It's fun to everyone. I wasn't really serious. $\endgroup$ May 4, 2015 at 9:00
lis1 /. b1|d1|b2|d2|b3|d3|b4|d4->Sequence[]
lis1 = {{{a1, b1, c1, d1, e1}, {a2, b2, c2, d2, e2}}, {{a3, b3, c3, 
    d3, e3}, {a4, b4, c4, d4, e4}}};

MapAt[Nothing, {All, All, {2, 4}}] @ lis1

ReplaceAt[_ :> Nothing, {All, All, {2, 4}}] @ lis1

Both give the expected result:

{{{a1, c1, e1}, {a2, c2, e2}}, {{a3, c3, e3}, {a4, c4, e4}}}

ReplaceAt was introduced in V 13.1 and has the advantage that we can use the usual Condition syntax. Example:

ReplaceAt[lis1, x_ /; SymbolName[x] != "b1" :> Nothing, {All, All, {2, 4}}]

{{{a1, b1, c1, e1}, {a2, c2, e2}}, {{a3, c3, e3}, {a4, c4, e4}}}


Another way using ReplaceAll and Span:

(lis1 /. x_?VectorQ :> x[[1 ;; 5 ;; 2]]) === lis2


Or using ReplaceAll and Select:

(lis1 /. x_?VectorQ :> Select[x, OddQ[Det@Position[x, #]] &]) === lis2


Thanks to @eldo for showing me the following shorter way:

  (lis1 /. x_?VectorQ :> x[[;; ;; 2]]) === lis2

  • 1
    $\begingroup$ Or, even shorter, lis1 /. x_?VectorQ :> x[[;; ;; 2]] +1 $\endgroup$
    – eldo
    Sep 15 at 6:20
  • $\begingroup$ Thanks, mate! :-) $\endgroup$ Sep 15 at 6:27

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