isbanded

Determine if matrix is within specified bandwidth

Syntax

tf = isbanded(A,lower,upper)

Description

tf = isbanded(A,lower,upper) returns logical 1 (true) if A is a matrix within the specified lower and upper bandwidths. Otherwise, it returns logical 0 (false).

Examples

Test Square Matrix

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

Test if the matrix is tridiagonal by specifying both the lower and upper bandwidths as 1.

isbanded(A,1,1)

ans = logical
   1

The matrix is tridiagonal because it has nonzero elements only on the main diagonal and the diagonals above and below the main diagonal.

Test if the matrix has only elements with a value of 0 below the main diagonal by specifying the lower bandwidth as 0.

isbanded(A,0,1)

ans = logical
   0

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

Test Nonsquare Matrix

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 the matrix has only elements with a value of 0 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.

Test Sparse Block Matrix

Create a 100-by-100 sparse block matrix. Test if the matrix is within a lower and upper bandwidth of 1.

B = kron(speye(25),ones(4));
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 the matrix is within a lower and upper bandwidth of 3.

isbanded(B,3,3)

ans = logical
   1

The matrix has an upper and lower bandwidth of 3 because the nonzero diagonal blocks are 4-by-4.

Input Arguments

A — Input array

array

Input array. isbanded returns logical 0 (false) if A has more than two dimensions.

Data Types: single | double | logical
Complex Number Support: Yes

lower — Lower bandwidth

nonnegative integer scalar

Lower bandwidth, specified as a nonnegative integer scalar. The lower bandwidth is the number of nonzero diagonals below the main diagonal. isbanded returns logical 0 (false) if there are nonzero elements below the boundary diagonal, diag(A,-lower).

upper — Upper bandwidth

nonnegative integer scalar

Upper bandwidth, specified as a nonnegative integer scalar. The upper bandwidth is the number of nonzero diagonals above the main diagonal. isbanded returns logical 0 (false) if there are nonzero elements above the boundary diagonal, diag(A,upper).

Tips

• Use the bandwidth function to find the upper and lower bandwidths of a given matrix.

• Use isbanded to test for several different matrix structures by specifying appropriate upper and lower bandwidths. This table lists some common tests.

  Lower Bandwidth	Upper Bandwidth	Function Call	Matrix Structure
  0	0	isbanded(A,0,0)	Diagonal matrix
  1	1	isbanded(A,1,1)	Tridiagonal matrix
  0	size(A,2)	isbanded(A,0,size(A,2))	Upper triangular matrix
  size(A,1)	0	isbanded(A,size(A,1),0)	Lower triangular matrix
  1	size(A,2)	isbanded(A,1,size(A,2))	Upper Hessenberg matrix
  size(A,1)	1	isbanded(A,size(A,1),1)	Lower Hessenberg matrix

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Code generation does not support sparse matrix inputs for this function.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The isbanded 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).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using 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 R2014a