tril

Lower triangular part of matrix

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Syntax

L = tril(A)

L = tril(A,k)

Description

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

example

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

Examples

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Extract Lower Triangular Portions of Matrix

Open Live Script

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

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`A` — Input matrix
matrix

Input matrix.

`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.

Matrix with the main diagonal labeled as k=0. Values of k greater than zero are for diagonals above the main diagonal, and values of k less than zero are for diagonals below the main diagonal.

Example: tril(A,3)

More About

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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.

6-by-6 matrix with shaded elements on and below the main diagonal

Extended Capabilities

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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

tril

Syntax

Description

Examples

Extract Lower Triangular Portions of Matrix

Input Arguments

A — Input matrix matrix

k — Diagonals to include 0 (default) | scalar

More About

Lower Triangular

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

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

Thread-Based Environment Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

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

Distributed Arrays Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Version History

See Also

`A` — Input matrix
matrix

`k` — Diagonals to include
`0` (default) | scalar

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

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

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

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

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.