istriu

Determine if matrix is upper triangular

Syntax

tf = istriu(A)

Description

tf = istriu(A) returns logical 1 (true) if A is an upper triangular matrix. Otherwise, it returns logical 0 (false).

Examples

Test Upper Triangular Matrix

Create a 5-by-5 matrix.

A = triu(magic(5))

A = 5×5

    17    24     1     8    15
     0     5     7    14    16
     0     0    13    20    22
     0     0     0    21     3
     0     0     0     0     9

Test if the matrix is upper triangular.

istriu(A)

ans = logical
   1

The matrix is upper triangular because all elements below the main diagonal are zero.

Test Matrix of Zeros

Create a 5-by-5 matrix of zeros. Test if the matrix is upper triangular.

Z = zeros(5);
istriu(Z)

ans = logical
   1

The result is logical 1 (true) because an upper triangular matrix can have any number of zeros on the main diagonal.

Input Arguments

A — Input array

array

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

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

More About

Upper Triangular Matrix

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

For example, this matrix is upper triangular.

$$A=\left(\begin{array}{cccc}1& -1& -1& -1\\ 0& 1& -2& -2\\ 0& 0& 1& -3\\ 0& 0& 0& 1\end{array}\right)$$

A diagonal matrix is both upper and lower triangular.

Tips

• Use the triu function to produce upper triangular matrices for which istriu 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, istriu(A) == isbanded(A,0,size(A,2)).

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 Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU 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 istriu 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