Table Of Contents

LU Factorization (G Dataflow)

Version:
    Last Modified: March 15, 2017

    Performs the LU factorization of a matrix.

    connector_pane_image
    datatype_icon

    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.

    Default: Empty array

    datatype_icon

    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

    datatype_icon

    matrix L

    A lower triangular matrix with ones on the diagonal.

    datatype_icon

    matrix U

    An upper triangular matrix.

    datatype_icon

    matrix P

    A permutation matrix.

    datatype_icon

    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 PA = LU:

    • 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.

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

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

    det ( A ) = k = 0 n 1 u k k

    where det(A) is the determinant of A.

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: This product does not support FPGA devices


    Recently Viewed Topics