# Vector Norm (G Dataflow)

Last Modified: January 9, 2017

Computes the norm of a vector.  ## vector

The input vector.

This input accepts a 1D array of double-precision, floating point numbers or 1D array of complex double-precision, floating point numbers.

If this input is an empty array, this node returns NaN. ## norm type

Type of norm this node computes.

If norm type is User Defined, this node uses user defined norm as the norm type.

Name Value Description
1-norm 0 Uses 1-norm.
2-norm 1 Uses 2-norm.
Inf-norm 2 Uses infinity-norm.
-Inf-norm 3 Uses -infinity-norm.
User Defined 4 Uses the user defined norm as the norm type.

Algorithms for Calculating the Norm

This node calculates the norm according to the following equations.

Norm type Algorithm
1-norm $‖x‖=|{x}_{0}|+|{x}_{1}|+...+|{x}_{n-1}|$
2-norm $‖x‖=\sqrt{\left({|{x}_{0}|}^{2}+{|{x}_{1}|}^{2}+...+{|{x}_{n-1}|}^{2}\right)}$
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 the input vector
• y is the input user defined norm
• ||x|| is the norm

Default: 2-norm ## user defined norm

Norm type that you specify.

If norm type is User Defined, this node uses user defined norm as the norm type.

This input 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 ## norm

The norm of the input vector. ## error out

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

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported