tril

Lower triangular part of matrix

Syntax

L = tril(A)

L = tril(A,k)

Description

L = tril(A) returns the lower triangular portion of matrix A.

L = tril(A,k) returns the elements on and below the kth diagonal of A.

Examples

Extract Lower Triangular Portions of Matrix

Create a 4-by-4 matrix of ones. Extract the lower triangular portion.

A = ones(4)

A = 4×4

     1     1     1     1
     1     1     1     1
     1     1     1     1
     1     1     1     1

B = tril(A)

B = 4×4

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

Extract only the elements below the main diagonal.

C = tril(A,-1)

C = 4×4

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

Input Arguments

A — Input matrix

matrix

Input matrix.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

k — Diagonals to include

0 (default) | scalar

Diagonals to include, specified as a scalar. k = 0 is the main diagonal, k > 0 is above the main diagonal, and k < 0 is below the main diagonal.

Example: tril(A,3)

More About

Lower Triangular

The lower triangular portion of a matrix includes the main diagonal and all elements below it. The shaded elements in this graphic depict the lower triangular portion of a 6-by-6 matrix.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• If you supply the argument that represents the order of the diagonal matrix, then it must be a real and scalar integer value.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• If you supply the argument that represents the order of the diagonal matrix, then it must be a real and scalar integer value.

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 tril 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 before R2006a