bandwidth
Lower and upper matrix bandwidth
Description
Examples
Create a 6-by-6 lower triangular matrix.
A = tril(magic(6))
A = 6×6
35 0 0 0 0 0
3 32 0 0 0 0
31 9 2 0 0 0
8 28 33 17 0 0
30 5 34 12 14 0
4 36 29 13 18 11
Find the lower bandwidth of A
by specifying type
as 'lower'
. The result is 5 since every diagonal below the main diagonal has nonzero elements.
B = bandwidth(A,'lower')
B = 5
Find the upper bandwidth of A
by specifying type
as 'upper'
. The result is 0 since there are no nonzero elements above the main diagonal.
B = bandwidth(A,'upper')
B = 0
Create a 100-by-100 sparse block matrix.
B = kron(speye(25),ones(4));
View a 10-by-10 section of elements from the top left of B
.
full(B(1:10,1:10))
ans = 10×10
1 1 1 1 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0
1 1 1 1 0 0 0 0 0 0
0 0 0 0 1 1 1 1 0 0
0 0 0 0 1 1 1 1 0 0
0 0 0 0 1 1 1 1 0 0
0 0 0 0 1 1 1 1 0 0
0 0 0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 0 1 1
B
has 4-by-4 blocks of ones centered on the main diagonal.
Find both the lower and upper bandwidths of B
by specifying two output arguments.
[lower,upper] = bandwidth(B)
lower = 3
upper = 3
Input Arguments
Input matrix, specified as a 2-D numeric matrix. A
can
be either full or sparse.
Data Types: single
| double
Complex Number Support: Yes
Bandwidth type, specified as 'lower'
or 'upper'
.
Specify
'lower'
for the lower bandwidth (below the main diagonal).Specify
'upper'
for the upper bandwidth (above the main diagonal).
Output Arguments
Lower or upper bandwidth, returned as a nonnegative integer scalar.
If
type
is'lower'
, then0
≤B
≤size(A,1)-1
.If
type
is'upper'
, then0
≤B
≤size(A,2)-1
.
Lower bandwidth, returned as a nonnegative integer scalar. lower
is
in the range 0
≤ lower
≤ size(A,1)-1
.
Upper bandwidth, returned as a nonnegative integer scalar. upper
is
in the range 0
≤ upper
≤ size(A,2)-1
.
More About
The upper and lower bandwidths of a matrix are measured by finding the last diagonal (above or below the main diagonal, respectively) that contains nonzero values.
That is, for a matrix A with elements Aij:
The upper bandwidth B1 is the smallest number such that whenever .
The lower bandwidth B2 is the smallest number such that whenever .
Note that this measurement does not disallow intermediate diagonals in a band from being all zero, but instead focuses on the location of the last diagonal containing nonzeros. By convention, the upper and lower bandwidths of an empty matrix are both zero.
Tips
Use the
isbanded
function to test if a matrix is within a specific lower and upper bandwidth.
Extended Capabilities
Usage notes and limitations:
The input
type
argument must be a constant for sparse matrices.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
The bandwidth
function
fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray
(Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced in R2014aThe bandwidth
supports C/C++ code generation for sparse matrix
inputs.
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Sélectionner un site web
Choisissez un site web pour accéder au contenu traduit dans votre langue (lorsqu'il est disponible) et voir les événements et les offres locales. D’après votre position, nous vous recommandons de sélectionner la région suivante : .
Vous pouvez également sélectionner un site web dans la liste suivante :
Comment optimiser les performances du site
Pour optimiser les performances du site, sélectionnez la région Chine (en chinois ou en anglais). Les sites de MathWorks pour les autres pays ne sont pas optimisés pour les visites provenant de votre région.
Amériques
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)