# Find Norm¶

## Group (Subgroup)¶

DREAM3D Review (Statistics)

## Description¶

This Filter computes the pth norm of an Attribute Array. Specifically, for each tuple of the array, the following is computed:

\f[ \left| \mathbf{x} \right| p := \bigg( \sum{i=1}^n \left| x_i \right| ^p \bigg) ^{1/p} \f]

where \f$n \f$ is the number of components for the Attribute Array. When \f$p = 2 \f$, this results in the Euclidean norm; when \f$p = 1 \f$, this results in the Manhattan norm (also called the taxicab norm). The p-space value may be any real number greater than or equal to zero. When \f$0 \leq p < 1 \f$, the result may not strictly be a norm in the exact sense. Additionally, when \f$p = 0 \f$, the result is simply the number of components for the Attribute Array.

Note: If the input array is a scalar array, the output array will contain the same values as the input array, but in 32-bit floating point precision.

## Parameters¶

Name Type Description
p-Space Value float p-Value used for computing the norm

Any

## Required Objects¶

Kind Default Name Type Component Dimensions Description
Any Attribute Array None Any Any Input Attribute Array for computing the norm

## Created Objects¶

Kind Default Name Type Component Dimensions Description
Attribute Array Norm float (1) Norm of the input Attribute Array

## Example Pipelines¶

Please see the description file distributed with this plugin.