istril

Determine if matrix is lower triangular

Syntax

tf = istril(A)

Description

tf = istril(A) returns logical 1 (true) if A is a lower triangular matrix. Otherwise, it returns logical 0 (false).

Examples

Test Lower Triangular Matrix

Create a 5-by-5 matrix.

A = tril(magic(5))

A = 5×5

    17     0     0     0     0
    23     5     0     0     0
     4     6    13     0     0
    10    12    19    21     0
    11    18    25     2     9

Test if the matrix is lower triangular.

istril(A)

ans = logical
   1

The matrix is lower triangular because all elements above the main diagonal are zero.

Test Matrix of Zeros

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

Z = zeros(5);
istril(Z)

ans = logical
   1

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

Input Arguments

A — Input array

array

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

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

More About

Lower Triangular Matrix

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

For example, this matrix is lower triangular.

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

A diagonal matrix is both upper and lower triangular.

Tips

• Use the tril function to produce lower triangular matrices for which istril 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, istril(A) == isbanded(A,size(A,1),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 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 istril 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