# Givens Rotation (Fast Givens Rotation Parameters) (G Dataflow)

Creates a rotation matrix for performing a fast Givens rotation.

## x

x-component for a two-element vector.

Default: 0

## y

y-component for a two-element vector.

Default: 0

## d1 in

Scale factor for x.

Default: 0

## d2 in

Scale factor for y.

Default: 0

## 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

## r

x-component after the Givens rotation.

## rotation matrix flag

Value that determines the structure and values of elements in rotation matrix.

Let H represent the output rotation matrix, and h11, h12, h21, and h22 represent elements in rotation matrix.

Name Value Description
-2 -2 $H=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
-1 -1 $H=\left[\begin{array}{cc}{h}_{11}& {h}_{12}\\ {h}_{21}& {h}_{22}\end{array}\right]$
0 0 $H=\left[\begin{array}{cc}1& {h}_{12}\\ {h}_{21}& 1\end{array}\right]$
1 1 $H=\left[\begin{array}{cc}{h}_{11}& 1\\ -1& {h}_{22}\end{array}\right]$

## rotation matrix

2 × 2 fast Givens rotation matrix.

## d1 out

Updated scale factor for the x-component.

Algorithm for Updating Scale Factors

The fast Givens rotation matrix and scale factors must satisfy the following equation:

$\left[\begin{array}{cc}d1\text{\hspace{0.17em}}\mathrm{in}& 0\\ 0& d2\text{\hspace{0.17em}}\mathrm{in}\end{array}\right]={H}^{T}*\left[\begin{array}{cc}d1\text{\hspace{0.17em}}\mathrm{out}& 0\\ 0& d2\text{\hspace{0.17em}}\mathrm{out}\end{array}\right]*H$

where H represents rotation matrix.

## d2 out

Updated scale factor for the y-component.

Algorithm for Updating Scale Factors

The fast Givens rotation matrix and scale factors must satisfy the following equation:

$\left[\begin{array}{cc}d1\text{\hspace{0.17em}}\mathrm{in}& 0\\ 0& d2\text{\hspace{0.17em}}\mathrm{in}\end{array}\right]={H}^{T}*\left[\begin{array}{cc}d1\text{\hspace{0.17em}}\mathrm{out}& 0\\ 0& d2\text{\hspace{0.17em}}\mathrm{out}\end{array}\right]*H$

where H represents rotation matrix.

## 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 Fast Givens Rotation Matrix

This node calculates the fast Givens rotation matrix using the following equation:

$H*\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}r\\ 0\end{array}\right]$

where

• x is the x-component for the two-element vector
• y is the y-component for the two-element vector
• r is the x-component after the Givens rotation
• H is the 2 × 2 fast Givens rotation matrix

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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