Create Real Matrix from Eigenvalues (G Dataflow)

Generates a real matrix from a specified set of eigenvalues.

eigenvalues

Eigenvalues from which to create the real matrix. Eigenvalues must be real or conjugate pairs.

error in

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

Default: No error

matrix

Real matrix whose eigenvalues you specified.

error out

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

Algorithm for Calculating the Eigenvalues

This node generates the output matrix in the following form:

${\left[\begin{array}{cccccc}0& 1& 0& \cdots & \cdots & 0\\ 0& 0& 1& 0& \cdots & 0\\ ⋮& \ddots & \ddots & \ddots & \ddots & ⋮\\ 0& \cdots & \cdots & 0& 1& 0\\ 0& \cdots & \cdots & \cdots & 0& 1\\ -{a}_{0}& -{a}_{1}& -{a}_{2}& \cdots & -{a}_{n-2}& -{a}_{n-1}\end{array}\right]}_{n×n}$

where n is the length of the input eigenvalues and a0, a1, ..., an-1 are the coefficients of the polynomial P(x).

The following equation defines P(x):

$P\left(x\right)=\left(x-{\lambda }_{0}\right)\left(x-{\lambda }_{1}\right)\dots \left(x-{\lambda }_{n-1}\right)={a}_{0}+{a}_{1}x+{a}_{2}{x}^{2}+\dots +{a}_{n-1}{x}^{n-1}+{x}^{n}$

where λ0, λ1, ..., λn - 1 are the elements in eigenvalues.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported