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?

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Why not using ArrayFlatten ? – b.gatessucks Nov 13 '12 at 10:10
Related (possible dupe): mathematica.stackexchange.com/questions/189/… – R. M. Nov 13 '12 at 15:08

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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..or, as the Wizard reminds, you could use the replacement rule v_?VectorQ :> Transpose[{v}]. – J. M. Nov 13 '12 at 15:20

This appears to be faster than J. M.'s funcions in all cases on my system:

columnAttach2[ak__List] :=
Replace[Unevaluated@Join[ak, 2], v_?VectorQ :> {v}\[Transpose], 1]


Timings, using J. M.'s Join function (which tested faster):

SetAttributes[timeAvg, HoldFirst]

timeAvg[func_] :=
Do[If[# > 0.3, Return[#/5^i]] & @@ Timing@Do[func, {5^i}], {i, 0, 15}]

m1 = RandomInteger[999, {50, 100}];
m2 = RandomInteger[999, 50];

columnAttach[m1, m2, m2, m1, m2, m1] // timeAvg

columnAttach2[m1, m2, m2, m1, m2, m1] // timeAvg


0.00019968

0.0000141696

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Correction: it is no faster but also no slower than J. M.'s code for non-packed arrays but apparently always faster with packed arrays. – Mr.Wizard Nov 13 '12 at 15:28