matrix manupulation and reading diagonally

Hello Team,

i have a matrix

Matrix_test = [13,10,5,2;7,14,11,6;3,8,15,12;1,4,9,16];

I want to read the matrix in the order mentioned in the matrix.

Starting from left bottom (1), then right top (2) and then again 2nd diagonal from left (3,4) and then 2nd right diagonal (5,6) and so on and so forth.

Please support in resolving it.

Edit : i there any way to create this kind of matrix for any n-by-n matrix automatically. i have created this Matrix_test manually but if i want 8x8 matrix in similar pattern . How to create it through generic code.

Thanks in advance.

Answer 1

[Stephan]

This function may help:

M = [13,10,5,2;7,14,11,6;3,8,15,12;1,4,9,16]
MyResult = readDiag(M)

function R = readDiag(M)
R = cell(2,numel(diag(M)));
for k = 1:numel(diag(M))-1
    R{1,k} = diag(M,-numel(diag(M))+k);
    R{2,k} = diag(M,numel(diag(M))-k);
end
R = reshape(R,[],1);
R = [R; {diag(M)}];
R = cell2mat(R);
end

result is:

M =

    13    10     5     2
     7    14    11     6
     3     8    15    12
     1     4     9    16


MyResult =

     1
     2
     3
     4
     5
     6
     7
     8
     9
    10
    11
    12
    13
    14
    15
    16

[NIKHIL]

Thank your for your solution.

[NIKHIL]

Hello Stephen, I have edited one additional question related to this query. How to create similar type of Matrix_test automatically with some code. can you please revert back to this query also ?

Answer 2

[Bruno Luong]

Matrix_test = [13,10,5,2;7,14,11,6;3,8,15,12;1,4,9,16]

[m,n]=size(Matrix_test);
[i,j]=ndgrid(1:m,1:n);
jmi = j(:)-i(:);
[~,is]=sortrows([-abs(jmi) jmi]);
Matrix_test(is)

[NIKHIL]

Thank you for your response. It is working well.

[NIKHIL]

Hello Bruno, I have edited one additional question related to this query. How to create similar type of Matrix_test automatically with some code. can you please revert back to this query also ?

[Bruno Luong]

Create matrix with dimension m x n.

m=8; n=8;
[i,j]=ndgrid(1:m,1:n);
jmi = j(:)-i(:);
[~,is]=sortrows([-abs(jmi) jmi]);

M=zeros(m,n);
M(is)=1:m*n

[NIKHIL]

Thank you so much Bruno for quick response.

It is working really good