Combine two matrices (every other column)

I have two matrices A and B which are for example

A=[1 2 3;4 5 6; 7 8 9] and B=[10 11 12; 13 14 15; 16 17 18]

And I would like to combine these matrices so that every other column is from A and every other is from B. So the answer should be matrix:

[1 10 2 11 3 12; 4 13 5 14 6 15; 7 16 8 17 9 18]

Of course my matrices are not only 3x3 matrices but n x n matrices.

My history with Matlab is so short that I don't figure out if that is even possible to do?

Answer 1

[Walter Roberson]

Provided that A and B have the same number of rows and columns,

AB = reshape([A;B], size(A,1), []);

[Ke Xu]

this really helps me a lot. Thank you very much!! But I still do not understand why 'reshape' can automatically combine them every other column. That's perfect!

[Walter Roberson]

Suppose you have

A11 A12  and   B11 B12
A21 A22        B21 B22
A31 A32        B31 B32

then [A;B] would be

A11 A12
A21 A22
A31 A32
B11 B12
B21 B22
B31 B32

MATLAB stores numbers "down" columns, so for example A21 is the entry immediately after A21, and B32 is the entry immediately after B22 . That applies for the [A;B] as well: the B11 is immediately after the A31. The order in memory for [A;B] is

A11 A21 A31 B11 B21 B31 A12 A22 A32 B12 B22 B32

Now reshape that to have 3 rows, knowing that it stores down columns:

A11 B11 A12 B12
A21 B21 A22 B22
A31 B31 A32 B32

this has exactly the same in-memory order: you have just changed the information about how to organize it into rows and columns.

[Jan Siegmund]

should be the top answer

[Ehsan Asadi]

@Walter Roberson

This is amazing. Can you please explain why and how it works? I am trying to understand it.

[Walter Roberson]

@Ehsan Asadi I already explained. It is a natural consequence of the fact that MATLAB stores values "down" columns, that for any matrix, the next item in memory after the first row first column is the second row first column then the third row first column, and so on, then then first row second column, second row second column, and so on. That, and the fact that reshape() does not change the order of items in memory and just changes how you refer to them.

A11 A12 A13
A21 A22 A23

is stored in memory as A11 A21 A12 A22 A13 A23 . You can reshape() it to be 3 x 2 and the order in memory would continue to be A11 A21 A12 A22 A13 A23 even though it would now appear to the user as

A11 A22
A21 A13
A12 A23

MATLAB stores (numeric) arrays as blocks of consecutive memory, and indexing is used to compute where to find where in the linear list to look. B(J,K) is found at linear location J + (K-1)*NumberOfRows

If you have used C or C++ you might be wanting to compare how they work. C and C++ store data "across the columns", so in the case of

A11 A12 A13
A21 A22 A23

the order in memory would be A11 A12 A13 A21 A22 A23. But in C or C++ it gets more complicated than that: it does have that way of storing memory but it has another more common way that can be difficult to tell apart.

Answer 2

[Snowfall]

Thank you for you both. These worked perfectly in my case.

Answer 3

[Dillen.A]

I wanted to "weave" some colourmaps, then I came across this topic. In the end I solved it like this, since I wanted to do it a couple of times.

function out = weave(varargin)
% Example: weave(jet,cool,autumn,spring);
N = numel(varargin);
out = nan(N * max(cellfun(@(s) (size(s, 1)), varargin)), size(varargin{1}, 2));
for ii = 1:N
  out(ii:N:size(varargin{ii}, 1) * N - (N - ii), :) = varargin{ii};
end
while all(isnan(out(end, :)))
  out(end, :) = [];
end
end

[Stephen23]

>> C = {[0,1,2;3,4,5],[6,7,8;9,10,11],[12,13,14;15,16,17]};
>> M = reshape(permute(cat(3,C{:}),[3,1,2]),[],3); % in one line
>> isequal(weave(C{:}),M)
ans = 1

[Dillen.A]

Nice!

Only difference is when you have C={jet(8),cool(7)}; doesn't like it. but appending with nans would solve that.

[RAJA SEKHAR BATTU]

Can we do the same for rows with three matrices to form in to one matrix with alternate rows of the three matrices?

[Walter Roberson]

Yes, this user weave function would be happy with any 2D matrices passed in, as long as the matrices all have the same number of columns.