Create a 5-by-5 square matrix with nonzero diagonals above and below the main diagonal.

A = [2 3 0 0 0 ; 1 -2 -3 0 0; 0 -1 2 3 0 ; 0 0 1 -2 -3; 0 0 0 -1 2]

A = 5×5

     2     3     0     0     0
     1    -2    -3     0     0
     0    -1     2     3     0
     0     0     1    -2    -3
     0     0     0    -1     2

Specify both bandwidths, lower and upper, as 1 to test if A is tridiagonal.

isbanded(A,1,1)

ans = logical
   1

The result is logical 1 (true).

Test if A has nonzero elements below the main diagonal by specifying lower as 0.

isbanded(A,0,1)

ans = logical
   0

The result is logical 0 (false) because A has nonzero elements below the main diagonal.

Create a 3-by-5 matrix.

A = [1 0 0 0 0; 2 1 0 0 0; 3 2 1 0 0]

A = 3×5

     1     0     0     0     0
     2     1     0     0     0
     3     2     1     0     0

Test if A has nonzero elements above the main diagonal.

isbanded(A,2,0)

ans = logical
   1

The result is logical 1 (true) because the elements above the main diagonal are all zero.

Create a 100-by-100 sparse block matrix.

B = kron(speye(25),ones(4));

Test if B has a lower and upper bandwidth of 1.

isbanded(B,1,1)

ans = logical
   0

The result is logical 0 (false) because the nonzero blocks centered on the main diagonal are larger than 2-by-2.

Test if B has a lower and upper bandwidth of 3.

isbanded(B,3,3)

ans = logical
   1

The result is logical 1 (true). The matrix, B, has an upper and lower bandwidth of 3 since the nonzero diagonal blocks are 4-by-4.