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Hessenberg Decomposition (G Dataflow)

Version:
    Last Modified: January 9, 2017

    Performs the Hessenberg decomposition of a matrix.

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    matrix A

    An n x n real matrix.

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

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    index low

    The form of the balanced matrix.

    You can obtain this input from the Matrix Balance node. If you do not wire this input, this node sets index low to 0.

    Default: -1

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    index high

    The form of the balanced matrix.

    You can obtain this input from the Matrix Balance node. If you do not wire this input, this node sets index low to n - 1.

    Default: -1

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    error in

    Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

    Default: No error

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    Hessenberg form H

    An n x n matrix in Hessenberg form.

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    orthogonal matrix Q

    An n x n orthogonal matrix.

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    error out

    Error information. The node produces this output according to standard error behavior.

    Algorithm for Calculating Hessenberg Decomposition

    The following expression defines the Hessenberg decomposition of an n × n matrix A:

    A = QHQH

    where

    • Q is an orthogonal matrix when matrix A is a real matrix and a unitary matrix when matrix A is a complex matrix
    • QH is the conjugate transpose of matrix Q
    • H is a Hessenberg matrix

    By definition, a Hessenberg matrix is a matrix with zeros under the main subdiagonal, as shown by the following matrix.

    H = [ h 11 h 12 h 1 n h 21 h 22 0 h 32 0 0 h n , ( n 1 ) h n , n ]

    Where This Node Can Run:

    Desktop OS: Windows

    FPGA: Not supported


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