I think Mathematica is biased towards rows not columns.
Given a matrix, to insert a row seems to be easy, just use Insert[]
(a = {{1, 2, 3}, {4, 0, 8}, {7 , 8, 0}}) // MatrixForm
1 2 3
4 0 8
7 8 0
row = {97, 98, 99};
(newa = Insert[a, row, 2]) // MatrixForm
1 2 3
97 98 99
4 0 8
7 8 0
But to insert a column, after some struggle, I found 2 ways, I show below, and would like to ask the experts here if they see a shorter and more direct way (Mathematica has so many commands, and I could have overlooked one that does this sort of thing in much direct way), as I think the methods I have now are still too complex for such a basic operation.
Have to do double transpose:
a = {{1, 2, 3}, {4, 0, 8}, {7 , 8, 0}}
column = {97, 98, 99}
newa = Transpose[Insert[Transpose[a], column, 2]]
1 97 2 3
4 98 0 8
7 99 8 0
Use SparseArray, but need to watch out for index locations. Kinda awkward for doing this:
(SparseArray[{{i_, j_} :> column[[i]] /; j == 2, {i_, j_} :> a[[i, j]] /; j == 1,
{i_, j_} :> a[[i, j - 1]] /; j > 1}, {3, 4}]) // Normal
1 97 2 3
4 98 0 8
7 99 8 0
The question is: Is there a more functional way, that is little shorter than the above? I could ofcourse use one of the above, and wrap the whole thing with a function, say insertColumn[...]
to make it easy to use. But wanted to see if there is an easier way to do this than what I have.
For reference, this is how I do this in Matlab:
EDU>> A=[1 2 3;4 0 8;7 8 0]
A =
1 2 3
4 0 8
7 8 0
EDU>> column=[97 98 99]';
EDU>> B=[A(:,1) column A(:,2:end)]
B =
1 97 2 3
4 98 0 8
7 99 8 0
Your double Transpose
method seems fine. For very large matrices, this will be 2-3 times faster:
MapThread[Insert, {a, column, Table[2, {Length[column]}]}]
If you want to mimic your Matlab way, the closest is probably this:
ArrayFlatten[{{a[[All, ;; 1]], Transpose[{column}], a[[All, 2 ;;]]}}]
Keep in mind that insertions require making an entire copy of the matrix. So, if you plan to build a matrix this way, it is more efficient to preallocate the matrix (if you know its size) and do in-place modifications through Part
instead.