isbanded

Determine if a matrix is banded

Usage

isbanded(A, l, u)

• A should be a numeric array.
• l and u should be non-negative real integer scalars not equal to Inf nor NaN.
• It returns logical 1 if elements lying strictly above the u-th diagonal and elements lying strictly below the l-th diagonal are all zeros. It returns logical 0 if otherwise.
• The main diagonal is the 0th diagonal.
• It returns logical 1 if A is empty.

Example

• Test if a randomly generated matrix (30% of its entries are non-zero) has lower and upper bandwidths equal to 3 and 1, respectively.

Input

a = zeros([5 4]);
% 30% of the elements are non-zero (randomly generated)
i = randi(numel(a),1, ceil(numel(a)*.3));
a(i) = 7+7i
isbanded(a,3,1)

Output

a =
 0.000 + 0.000i   7.000 + 7.000i   0.000 + 0.000i   0.000 + 0.000i
 0.000 + 0.000i   7.000 + 7.000i   0.000 + 0.000i   0.000 + 0.000i
 0.000 + 0.000i   7.000 + 7.000i   0.000 + 0.000i   0.000 + 0.000i
 7.000 + 7.000i   0.000 + 0.000i   0.000 + 0.000i   7.000 + 7.000i
 0.000 + 0.000i   0.000 + 0.000i   0.000 + 0.000i   0.000 + 0.000i

ans =
 1