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

Performs a fast Givens rotation on a set of two-element vectors.  ## y increment

An integer that determines whether and how this node skips elements in y for the calculation.

The following table explains how this node behaves depending on the value of y increment.

Value Behavior
y increment ≥ number of elements in y Uses only the first element in y.
1 < y increment < number of element in y Uses only the elements whose indexes are multiples of the value of y increment.
y increment = 1 Does not skip any elements in y.
y increment = 0 Returns an error.
y increment < 0 Reverses the order of the elements, and then uses elements that have indexes that are multiples of the value of y increment.

Default: 1 ## x increment

An integer that determines whether and how this node skips elements in x for the calculation.

The following table explains how this node behaves depending on the value of x increment.

Value Behavior
x increment ≥ number of elements in x Uses only the first element in x.
1 < x increment < number of element in x Uses only the elements whose indexes are multiples of the value of x increment.
x increment = 1 Does not skip any elements in x.
x increment = 0 Returns an error.
x increment < 0 Reverses the order of the elements, and then uses elements that have indexes that are multiples of the value of x increment.

Default: 1 ## x

Vector that contains the x-components of the set of two-element vectors. ## y

Vector that contains the y-components of the set of two-element vectors. ## rotation matrix flag

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

You can use Givens Rotation (Fast Givens Rotation Parameters) to obtain a value for this input.

Let H represent rotation matrix, and h 11, h 12, h 21, and h 22 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 $H=\left[\begin{array}{cc}{h}_{11}& 1\\ -1& {h}_{22}\end{array}\right]$

Default: -1 ## rotation matrix

2 × 2 fast Givens rotation matrix.

You can use Givens Rotation (Fast Givens Rotation Parameters) to obtain a value for this input. ## 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 ## drotm x

Vector that contains the x-components of the set of two-element vectors after the rotation. ## drotm y

Vector that contains the y-components of the set of two-element vectors after the rotation. ## 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 Performing Fast Givens Rotation

If you set both x increment and y increment to 1, this node performs fast Givens rotation according to the following equation:

$\left[\begin{array}{c}{\mathrm{drotm}\text{}x}_{i}\\ {\mathrm{drotm}\text{}y}_{i}\end{array}\right]=H*\left[\begin{array}{c}{x}_{i}\\ {y}_{i}\end{array}\right]$

where

• x i is the i th element of x
• y i is the i th element of y
• drotm x i is the i th element of drotm x
• drotm y i is the i th element of drotm y
• H is the 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