How can I assign a value to the diagonals of a 4-D matrix using linear indexing in MATLAB?

Question

I have a 4-D matrix A of size NxNxPxQ. How can I easily change the diagonal values to 1 for each NxN 2-D submatrix in a vectorized way?

Answer 1

Incorporating gnovice's suggestion, an easy way to index the elements is:

[N,~,P,Q]=size(A);%# get dimensions of your matrix

diagIndex=repmat(logical(eye(N)),[1 1 P Q]);%# get logical indices of the diagonals    
A(diagIndex)=1;%# now index your matrix and set the diagonals to 1.

Answer 2

You can actually do this very simply by directly computing the linear indices for every diagonal element, then setting them to 1:

[N,N,P,Q] = size(A);
diagIndex = cumsum([1:(N+1):N^2; N^2.*ones(P*Q-1,N)]);
A(diagIndex) = 1;

The above example finds the N diagonal indices for the first N-by-N matrix (1:(N+1):N^2). Each subsequent N-by-N matrix (P*Q-1 of them) is offset by N^2 elements from the last, so a matrix of size PQ-1-by-N containing only the value N^2 is appended to the linear indices for the diagonal of the first matrix. When a cumulative sum is performed over each column using the function CUMSUM, the resulting matrix contains the linear indices for all diagonal elements of the 4-D matrix.

Answer 3

You can use direct indexing, and some faffing about with repmat, to add the indexes for a single 50x50 diagonal to the offsets within the larger matrix of each 50x50 block:

Here's an example for a smaller problem:

A = NaN(10,10,5,3);
inner = repmat(sub2ind([10 10], [1:10],[1:10]), 5*3, 10); % diagonals
outer = repmat([10*10 * [0:5*3-1]]', 1, 10*10); % offsets to blocks
diags = inner + outer;
A(diags(:)) = 1;