Extracting columns from multidimensional list

Question

Perhaps a very easy question but I posted this on the Wolfram Community and didn't get any answer..

Suppose I have data like:

data = Table[{{Subscript[a, x, 1, 1], Subscript[a, x, 1, 2], 
    Subscript[a, x, 1, 3]}, {Subscript[b, x, 2, 1], Subscript[b, x, 2,
     2], Subscript[b, x, 2, 3]}}, {x, 1, 3}]

Now suppose I wan't to get from all rows the first item in the first list and the third item in the second list like:

It can be done by using:

{data[[All, 1, 1]], data[[All, 2, 3]]}\[Transpose]

or

{#[[1, 1]], #[[2, 3]]} & /@ data

But I'm wondering if there isn't an easier way by only using Part,Extract? It seems that going through the documentation the option only apply to one column (or more) but not to subparts in these columns.

Any thoughts?

Answer 1

I don't think there is any way to do it using just Part or Extract. With these functions you specify the elements you want at level 1, then at level 2, then level 3 etc. At each level you may specify a single element, a list of elements, All or a Span. There is no syntax for specifying different sub-parts for each of the elements selected at a certain level.

For an alternative, I suggest using the operator form of Extract along with Map:

Extract[{{1, 1}, {2, 3}}] /@ data

Answer 2

My favorite being a slight variation of @Lou's own solution

Transpose[{data[[;;, 1, 1]], data[[;;, -1, -1]]}]

you can also use

Transpose@Rest@Extract[data, {{}, {;; , 1, 1}, {;; , -1, -1}}]
(* version 9 only -- does not work in version 10 -- thanks: Simon Woods *)

or

ReplacePart[data, p_ :> {data[[p, 1, 1]], data[[p, -1, -1]]}]

or

{First@First@#, Last@Last@#} & /@ data

or

ClearAll[f];
f[{{a_, __}, {__, b_}}] := {a, b}
f /@ data

all give

Answer 3

My try

{#1[[1]], #2[[-1]]} & @@@ data

or

data /. {{f_, __}, {__, l_}} -> {f, l}