Version:

Last Modified: March 15, 2017

Solves the polynomial eigenvalue problem.

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.

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 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.

**Default: **No error

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

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

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**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.

The following equation defines the polynomial eigenvalue problem.

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

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: This product does not support FPGA devices