# LU Factorization (G Dataflow)

Last Modified: June 25, 2019

Performs the LU factorization of a matrix.  ## matrix A

A real matrix.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

What Does the Node Return if Matrix A Is a Singular Matrix?

For a singular matrix, the node completes the factorization and returns a warning, and there is at least one zero at the diagonal of U.

Default: Empty array ## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error ## matrix L

A lower triangular matrix with ones on the diagonal. ## matrix U

An upper triangular matrix. ## matrix P

A permutation matrix. ## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm for Calculating the LU Factorization of a Matrix

This node factors an m × n matrix A into the following types of matrices so that P A = L U:

• L is an m × min(m,n) matrix. When mn, L is a lower triangular matrix with ones on the diagonal. When m > n, L is a lower trapezoidal matrix with ones on the diagonal.
• U is a min(m,n) × n matrix. When mn, U is an upper triangular matrix. When m < n, U is an upper trapezoidal matrix.
• P is an m × n permutation matrix, which serves as the identity matrix with some rows exchanged.

## Calculating the LU Factorization of a Square Matrix

The following equation illustrates one useful property of LU factorization when A is a square matrix:

$\mathrm{det}\left(A\right)=\prod _{k=0}^{n-1}{u}_{kk}$

where det(A) is the determinant of A.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application