Matlab : Sliding window using a matrix - arrays

Question

I need some information on how to program the sliding window of matrix.
I have a diagonal matrix B defined below by:
I would like to deduce from the given matrix B and the size of the window W the different matrix for t ranging from 1 to the size L of the matrix.
Note: Each window has the same width and height. And the window moves on the diagonal.
Example: We have a matrix with size 5 by 8 and the size of the window is 3 by 4 and moves on the diagonal. The matrix B of the example is:
My code:
% Sliding window matrix
B = [ 1 1 0 0 0 0 0 0
2 2 1 1 0 0 0 0
0 0 2 2 1 1 0 0
0 0 0 0 2 2 1 1
0 0 0 0 0 0 2 2]; % Matrix B
W = 4; % Size of the window wanted here is 4
n = size(B,2) - W + 1;
X = zeros(size(B,1),W*n);
k = W-1:-1:0;
for i = 1:n
window = B(:,i:i+W-1)';
X(:,i*W - k) = B(:,i:i+W-1);
end
window;
With W = 4 and n of the for loop set to 1 I get:
window = [1 2 0 0 0
1 2 0 0 0
0 1 2 0 0
0 1 2 0 0];
Whereas I should get:
window = [1 1 0 0
2 2 1 1
0 0 2 2];
With my code I don't get exactly the different sub-matrix obtained by sliding window.
I would like my program to be able, depending on the matrix B and the choice of dimensions of my window, to return the diagonal matrix representing the window and shift one step to also recover the next diagonal matrix which is identical to the previous one, and so on until the end.
Any suggestions?

Answer 1

You need to specify window dimensions separately. Try this:
B = [ 1 1 0 0 0 0 0 0
2 2 1 1 0 0 0 0
0 0 2 2 1 1 0 0
0 0 0 0 2 2 1 1
0 0 0 0 0 0 2 2];
[bh, bw] = size(B); % matrix size
wh = 3; % window height
ww = 4; % window width
sx = 2; % sliding step length along 2nd dim
sy = 1; % sliding step length along 1st dim
wx = 1:sx:(bw-ww+1); % window left
wy = 1:sy:(bh-wh+1); % window top
n = min(numel(wx), numel(wy)); % number of windows which fit in matrix
for ii = 1:n
X = B((1:wh)+wy(ii)-1, (1:ww)+wx(ii)-1)
end
Note that the sliding window, as it is described in your question, does not necessarily visit the entire matrix diagonal. Unless you calculate the sx and sy based on the dimensions of the matrix.
B = randi(3, [8 13])
[bh, bw] = size(B); % matrix size
wh = 3; % window height
ww = 4; % window width
sx = 3; % slideing step length along 2nd dim
sy = 1; % slideing step length along 1st dim