Learning to build band matrices in MATLAB

Question

I am trying to build square band matrices using blkdiag or spdiags, but can\'t figure out how. I find the documentation for spdiags a bit confusing, and am not

Answer 1

A tricky one-line way to create a matrix like this is with convolution:

M = sign(conv2(eye(matrix_size),ones(band_width+1),'same'));

An identity matrix is created of the given size, then convolved in 2-D with a square matrix of ones, then converted to zeroes and ones by taking the sign.

The above is fine for making relatively small non-sparse matrices. For larger matrices the convolution may get expensive and you would probably want to represent the result as a sparse matrix instead. Here is how you can do this in a general way using SPDIAGS:

M = spdiags(ones(matrix_size,2*band_width+1),...
            -band_width:band_width,matrix_size,matrix_size);