# Polynomial Eigenvalues and Vectors (G Dataflow)

Solves the polynomial eigenvalue problem.

## matrices

Array of size n × n × p that contains square input matrices of the same size. The matrices are in ascending order of power for eigenvalues.

This input accepts a 3D array of double-precision, floating-point numbers or a 3D array of complex double-precision, floating-point numbers.

## output option

A value specifying whether this node computes eigenvalues and vectors.

Name Value Description
Eigenvalues 0

The node computes only the eigenvalues of the input matrix.

Eigenvalues and Vectors 1

The node computes both the eigenvalues and the eigenvectors of the input matrix.

Default: Eigenvalues and Vectors

## 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

## eigenvalues

Vector of n * p elements that contains the computed eigenvalues.

## eigenvectors

Matrix of size n × (n * p) that contains the computed eigenvectors in its columns.

## 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 Solving the Polynomial Eigenvalue Problem

The following equation defines the polynomial eigenvalue problem.

$\left({\lambda }_{j}^{p-1}{C}_{p-1}+{\lambda }_{j}^{p-2}{C}_{p-2}+...+{\lambda }_{j}{C}_{1}+{C}_{0}\right){x}_{j}=0$

where

• C 0, C 1, ..., C p-1 are square n × n matrices in matrices
• λ j is the j th element in eigenvalues
• x j has length n and is the j th column in eigenvectors with j = 0, 1, ..., n * p - 1

If p = 1, this node calculates eigenvalues and eigenvectors using the following equation:

C 0 x j = λ j x j

If p = 2, this node calculates generalized eigenvalues and eigenvectors using the following equation:

C 0 x j = -λ j C 1 x j

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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