isdiag

Determine if matrix is diagonal

Syntax

tf = isdiag(A)

Description

tf = isdiag(A) returns logical 1 (true) if A is a diagonal matrix; otherwise, it returns logical 0 (false).

Examples

Test Diagonal Matrix

Create a 4-by-4 identity matrix.

I = eye(4)

I = 4×4

     1     0     0     0
     0     1     0     0
     0     0     1     0
     0     0     0     1

Test to see if the matrix is diagonal.

isdiag(I)

ans = logical
   1

The result is logical 1 (true) because all of the nonzero elements in I are on the main diagonal.

Test Banded Matrix

Create a matrix with nonzero elements on the main and first diagonals.

A = 3*eye(4) + diag([2 2 2],1)

A = 4×4

     3     2     0     0
     0     3     2     0
     0     0     3     2
     0     0     0     3

Test to see if the matrix is diagonal.

isdiag(A)

ans = logical
   0

The matrix is not diagonal since there are nonzero elements above the main diagonal.

Create a new matrix, B, from the main diagonal elements of A.

B = diag(diag(A));

Test to see if B is a diagonal matrix.

isdiag(B)

ans = logical
   1

The result is logical 1 (true) because there are no nonzero elements above or below the main diagonal of B.

Input Arguments

A — Input array

numeric array

Input array, specified as a numeric array. isdiag returns logical 0 (false) if A has more than two dimensions.

Data Types: single | double
Complex Number Support: Yes

More About

Diagonal Matrix

A matrix is diagonal if all elements above and below the main diagonal are zero. Any number of the elements on the main diagonal can also be zero.

For example, the 4-by-4 identity matrix,

$$I_4=\left(\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right)$$

is a diagonal matrix. Diagonal matrices are typically, but not always, square.

Tips

• Use the diag function to produce diagonal matrices for which isdiag returns logical 1 (true).

• The functions isdiag, istriu, and istril are special cases of the function isbanded, which can perform all of the same tests with suitably defined upper and lower bandwidths. For example, isdiag(A) == isbanded(A,0,0).

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.

GPU Arrays

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

This function fully supports GPU arrays. 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).