Documentation

dsp.LUFactor

Factor square matrix into lower and upper triangular matrices

Description

The LUFactor object factors a square matrix into lower and upper triangular matrices.

To factor a square matrix into lower and upper triangular matrices:

1. Define and set up your System object™. See Construction.

2. Call step to factor the square matrix according to the properties of dsp.LUFactor. The behavior of step is specific to each object in the toolbox.

Note

Starting in R2016b, instead of using the step method to perform the operation defined by the System object, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

Construction

lu = dsp.LUFactor returns an LUFactor System object, lu, which factors a row permutation of a square input matrix A as , where L is the unit-lower triangular matrix, and U is the upper triangular matrix. The row-pivoted matrix Ap contains the rows of A permuted as indicated by the permutation index vector P. The equivalent MATLAB® code is Ap = A(P,:).

lu = dsp.LUFactor('PropertyName',PropertyValue,...) returns an LUFactor object, lu, with each specified property set to the specified value.

Properties

 ExceptionOutputPort Set to true to output singularity of input Set this property to true to output the singularity of the input as logical data type values of true or false. An output of true indicates that the current input is singular, and an output of false indicates the current input is nonsingular.

Methods

 step Decompose matrix into lower and upper triangular matrices
Common to All System Objects
release

Allow System object property value changes

Examples

expand all

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent step syntax. For example, myObject(x) becomes step(myObject,x).

Decompose a square matrix into the lower and upper components.

lu = dsp.LUFactor;
x = rand(4)
x = 4×4

0.8147    0.6324    0.9575    0.9572
0.9058    0.0975    0.9649    0.4854
0.1270    0.2785    0.1576    0.8003
0.9134    0.5469    0.9706    0.1419

[LU, P] = lu(x);
L = tril(LU,-1)+diag(ones(size(LU,1),1));
U = triu(LU);
y = L*U
y = 4×4

0.9134    0.5469    0.9706    0.1419
0.9058    0.0975    0.9649    0.4854
0.8147    0.6324    0.9575    0.9572
0.1270    0.2785    0.1576    0.8003

Check back whether y equals the permuted x

xp = x(P,:)
xp = 4×4

0.9134    0.5469    0.9706    0.1419
0.9058    0.0975    0.9649    0.4854
0.8147    0.6324    0.9575    0.9572
0.1270    0.2785    0.1576    0.8003

Algorithms

This object implements the algorithm, inputs, and outputs described on the LU Factorization block reference page. The object properties correspond to the block parameters.