# Unit Vector (G Dataflow)

Version:

Finds the norm of a vector and normalizes the vector with the norm.

## input vector

Input vector.

This input can be an array of double-precision floating-point numbers or an array of complex double-precision floating-point numbers.

If input vector is an empty array, unit vector is also an empty array, and norm is NaN.

## norm type

Type of norm this node uses to compute the norm.

Name Value Description
1-norm 1 Uses 1-norm.
2-norm 2 Uses 2-norm.
Inf-norm 3 Uses infinity-norm.
-Inf-norm 4 Uses -infinity-norm.
User Defined 5 Uses user defined norm as the norm type.

Algorithm for Calculating norm with Each norm type

This node calculates norm using the following equations:

 1-norm $‖x‖=|{x}_{0}|+|{x}_{1}|+\dots +|{x}_{n-1}|$ 2-norm $‖x‖=\surd \left({|{x}_{0}|}^{2}+{|{x}_{1}|}^{2}+\dots +{|{x}_{n-1}|}^{2}\right)$ Inf-norm $‖x‖={\mathrm{max}}_{i}\left(|{x}_{i}|\right)$ -Inf-norm $‖x‖={\mathrm{min}}_{i}\left(|{x}_{i}|\right)$ User Defined $‖x‖={\left({|{x}_{0}|}^{y}+{|{x}_{1}|}^{y}+\dots +{|{x}_{n-1}|}^{y}\right)}^{\frac{1}{y}}$

where

• x is input vector
• y is user defined norm
• ||x|| is norm

Default: 2-norm

## user defined norm

User-defined norm type.

This node uses user defined norm as the norm type only if you set norm type to User Defined. user defined norm must be nonzero.

Default: -1

## error in

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

Default: No error

## unit vector

Output normalized vector.

## norm

Norm of the input vector.

## error out

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

## Algorithm for Calculating unit vector

This node calculates unit vector using the following equation:

$U=\frac{X}{‖X‖}$

where U is unit vector.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported