How to check a matrix is multibanded?

I have a sparse matrix which I need to verify whether it is multibanded or not?

Answer 1

[Chunru]

% Create a banded sparse matrix
B = bucky;
r = symrcm(B)

r = 1×60

1 6 2 5 7 26 30 10 11 12 3 4 8 27 29 9 15 13 16 17 21 25 42 28 43 38 37 14 20 18

a=B(r,r);
imagesc(a);

% Check if it is banded
m = size(a,1);      % assuming square matrix

lb = m; 
ub = m;
for i=-m+1:0
    % check the diagonal  
    if all(diag(a, i)==0)
        lb = i;
    else
        break
    end
end

for i=m-1:-1:0
    % check the diagonal  
    if all(diag(a, i)==0)
        ub = i;
    else
        break
    end
end

[lb, ub]

ans = 1×2

-12 12