How to reshape a square matrix diagonally to a vector?

Hello,

Suppose that we have the following 3x3 matrix:

A=[
0  1  0
1  1  1
1  1  0];

I need to reshape it to (010111101) where we read the matrix diagonaly from the extreme left of the top row (010) then we repeat this with the upper part (11) then the lower (11) and again from the left diagonal and the upper part is before the lower part (0) then (1) ==> 010111101. please see the attached figure.

So, How can I do that"

Regards,

[Walter Roberson]

Are you working on DCT ? If so then https://www.mathworks.com/matlabcentral/fileexchange/15317-zigzag-scan

Answer 1

[Stephen23]

>> A = [0,1,0;1,1,1;1,1,0]
A =
     0     1     0
     1     1     1
     1     1     0
>> V = 1:sum(size(A))-1;
>> W = fix(V/2).*(-1).^V;
>> C = arrayfun(@(x)diag(A,x),W, 'uni',0);
>> Z = cat(1,C{:})
Z =
     0
     1
     0
     1
     1
     1
     1
     0
     1

[Sarah A]

Thank you. It works with any NxN matrix.

Answer 2

[Johannes Fischer]

I would start with writing down the subscripts in the order you want to select the elements of the matrix.

A=[0  1  0;
1  1  1;
1  1  0];

row = [1 2 3 1 2 2 3 1 3];
col = [1 2 3 2 3 1 2 3 1];

If you need this for larger matrices I'm sure you'll be able to find an algorithm for NxN matrices

Having these coordinates, you can access the elements via their linear indices.

ind = sub2ind(size(A), row, col);
A(ind)

For a little more on the subject of matrix indexing, read here

[Sarah A]

Thank you.