In my script I generate a matrix where each column is coupled with at least another one. For example, column 1 is coupled with column 2, column 3 is coupled with column 4, etc... But I could also couple columns 3 by 3 or 4 by 4 or any other number.
This is for the moment just an image in mind, but then I would like to move coupled columns on their own line, so that I can easily mix them up using any() or sum().
This will become clearer with this example:
A = reshape(1:12, 3, []) % A is the matrix I start with, this reshape is OK
A =
1 4 7 10
2 5 8 11
3 6 9 12
reshape(A, [], 2) % this reshape is not OK
ans =
1 7
2 8
3 9
4 10
5 11
6 12
However, I would like the answer to be:
ans =
1 4
2 5
3 6
7 10
8 11
9 12
As I said, this example is just for 2 columns, but in my use case I also need to support any number of columns couples. Here for 3 columns:
B = reshape(1:18, 3, [])
B =
1 4 7 10 13 16
2 5 8 11 14 17
3 6 9 12 15 18
reshape(B, [], 3)
ans =
1 7 13
2 8 14
3 9 15
4 10 16
5 11 17
6 12 18
What I would like:
ans =
1 4 7
2 5 8
3 6 9
10 13 16
11 14 17
12 15 18
Is there any way to do that in a vectorized manner?
Assuming M to be the input matrix, see if this works for you -
ncols = 2; %// number of columns (needs to be edited)
[m,n] = size(M) %// get size of input matrix for later usage
r = numel(M)/(m*ncols);
out = reshape(permute(reshape(M,m,ncols,[]),[1 3 2]),m*r,[])
Sample runs -
M =
1 4 7 10
2 5 8 11
3 6 9 12
ncols =
2
out =
1 4
2 5
3 6
7 10
8 11
9 12
and
M =
1 4 7 10 13 16
2 5 8 11 14 17
3 6 9 12 15 18
ncols =
3
out =
1 4 7
2 5 8
3 6 9
10 13 16
11 14 17
12 15 18
Going by your words - "column 1 is coupled with column 2, column 3 is coupled with column 4, etc... But I could also couple columns 3 by 3 or 4 by 4 or any other number", I am sensing you might actually be looking to form all possible combinations of the columns of the input matrix and vertically concatenate them to form a slenderish matrix as the output. This section of the solution would cover that base. The code to achieve such a goal (if that's what you meant hopefully)
would be something like this -
ncols = 2; %// number of columns (needs to be edited)
[m,n] = size(M) %// get size of input matrix for later usage
combs = dec2base(0:n^2-1,n,ncols)-'0'+1 %// find combinations
combsp = permute(combs,[3 2 1]) %// make a 3D array of those combinations
idx = bsxfun(@plus,[1:m]',(combsp-1)*m) %//'# Indices as a 3D array
idx1 = reshape(permute(idx,[1 3 2]),m*size(idx,3),[]) %// vertically concatenate
%// 3D indices array into a 2D array
out = M(idx1) %// desired output
One sample run -
M =
6 7 3 6
3 1 6 3
5 1 4 2
ncols = 2
out =
6 6
3 3
5 5
6 7
3 1
5 1
6 3
3 6
5 4
6 6
3 3 ....