# bandwidth

Matrix bandwidth

### low = bandwidth(A)

• A should be a matrix.
• It returns the lower bandwidth of A.
• It returns, say, low==3, if elements of A lying below the 3rd lower-diagonal are all equal to zero.
• It returns 0 if A is empty.

### [low,up] = bandwidth(A)

• A should be a matrix.
• It returns the lower and upper bandwidths of A.
• It returns, say, low==3 and upper==4, if elements of A lying below the 3rd lower-diagonal or above the 4th upper-diagonal are all equal to zero.
• It returns 0 if A is empty.

Example 1: Finding lower and upper bandwidths of a randomly generated matrix.

% 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)
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

### bandwidth(A, type)

• A should be a 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 0 if A is empty.

Example 2: Finding lower and upper bandwidths of a randomly generated matrix.

% 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')
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