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list manipulation - Building matrices by attaching vectors (columns) and matrices



Having the need to attach a column to a matrix or to join matrices to make longer rows is an operation that I use very frequently and I find the Join function ideal for these cases.


m1 = {{10, 11, 12}, {21, 22, 23}};
m2 = {100, 101};

(* Join matrices to make longer rows: *)
Join[m1, m1, 2]
(* --> {{10, 11, 12, 10, 11, 12}, {21, 22, 23, 21, 22, 23}} *)

(* Attach a column to a matrix *)
Join[m1, List /@ m2, 2]

(* --> {{10, 11, 12, 100}, {21, 22, 23, 101}} *)

(* Join two columns to make a matrix *)
Join[List /@ m2, List /@ m2, 2]
(* --> {{100, 100}, {101, 101}} *)

However, I wanted to define my own function that would simplify the notation needed to reach my goal:


columnAttach[a1_List, a2_List] := 
  Join[If[VectorQ[a1], List /@ a1, a1], 
  If[VectorQ[a2], List /@ a2, a2], 2]


columnAttach[m1, m1]
(* --> {{10, 11, 12, 10, 11, 12}, {21, 22, 23, 21, 22, 23}} *)
columnAttach[m1, m2]
(* --> {{10, 11, 12, 100}, {21, 22, 23, 101}} *)
columnAttach[m2, m2]
(* --> {{100, 100}, {101, 101}} *)

This works as expected, but I would like to generalize it a bit. For instance, Join can take a list of vectors/matrices of any length:


Join[m1, m1, List /@ m2, List /@ m2, 2]

(* --> {{10, 11, 12, 10, 11, 12, 100, 100},
  {21, 22, 23, 21, 22, 23, 101, 101}} *)

How can I adapt my columnAttach function to achieve the same flexibility?



Answer



One possibility:


columnAttach[ak__List] := Join[##, 2] & @@ Replace[{ak}, v_?VectorQ :> List /@ v, 1]

columnAttach[{{10, 11, 12}, {21, 22, 23}}, {100, 101}, {{10, 11, 12}, {21, 22, 23}},
             {100, 101}, {100, 101}]

   {{10, 11, 12, 100, 10, 11, 12, 100, 100},
    {21, 22, 23, 101, 21, 22, 23, 101, 101}}


Alternatively:


columnAttach[ak__List] := ArrayFlatten[{Replace[{ak}, v_?VectorQ :> List /@ v, 1]}]

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