bandwidth

Matrix bandwidth

Usage

[low,up] = bandwidth(A)

• A should be a (non-character) numeric matrix (2D).
• It returns the lower (low) and upper (up) bandwidths of A.
• All elements lying strictly below the low-th lower-diagonal or strictly above the up-th upper-diagonal are equal to zero.
• The main diagonal is the 0th diagonal.
• low and up are zeros if A is empty.

bandwidth(A, type)

• A should be a (non-character) numeric matrix.
• type should be either 'upper' or 'lower'.
• If type is 'upper', it returns the upper bandwidth of A. If otherwise, it returns the lower bandwidth.
• It returns zero if A is empty.

Examples

• Using [l, u] = bandwidth(a) to find lower and upper bandwidths of a randomly generated matrix.

Input

% Creating a random complex matrix with 30% of its entries
% being non-zero.
a=zeros(5);
i=randi(numel(a),1,ceil(numel(a)*.3));
a(i)=7+7i
% Finding lower and upper bandwidths
[l,u]=bandwidth(a)

Output

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

l =
 3.000

u =
 2.000

• Finding lower and upper bandwidths of a randomly generated matrix.

Input

% Creating a random complex matrix with 30% of its entries
% being non-zero.
a=zeros(5);
i=randi(numel(a),1,ceil(numel(a)*.3));
a(i)=7+7i
% Finding lower and upper bandwidths
l=bandwidth(a,'lower')
u=bandwidth(a,'upper')

Output

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

l =
 2.000

u =
 2.000