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 A to see if it is upper triangular.

istriu(A)

ans = logical
   1

The result is logical 1 (true) because all elements below the main diagonal are zero.

Test Matrix of Zeros

Create a 5-by-5 matrix of zeros.

Z = zeros(5);

Test Z to see if it is upper triangular.

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

numeric array

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

Data Types: single | double
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, the matrix

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

is upper triangular. 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.

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).