Version:

Last Modified: January 9, 2017

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

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.

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 |
$\Vert x\Vert =\left|{x}_{0}\right|+\left|{x}_{1}\right|+\dots +\left|{x}_{n-1}\right|$ |

2-norm |
$\Vert x\Vert =\surd ({\left|{x}_{0}\right|}^{2}+{\left|{x}_{1}\right|}^{2}+\dots +{\left|{x}_{n-1}\right|}^{2})$ |

Inf-norm |
$\Vert x\Vert ={\mathrm{max}}_{i}\left(\left|{x}_{i}\right|\right)$ |

-Inf-norm |
$\Vert x\Vert ={\mathrm{min}}_{i}\left(\left|{x}_{i}\right|\right)$ |

User Defined |
$\Vert x\Vert ={({\left|{x}_{0}\right|}^{y}+{\left|{x}_{1}\right|}^{y}+\dots +{\left|{x}_{n-1}\right|}^{y})}^{\frac{1}{y}}$ |

where

*x*is**input vector***y*is**user defined norm**- ||
*x*|| is**norm**

**Default: **2-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 conditions that occur before this node runs. The node responds to this input according to standard error behavior.

**Default: **No error

Output normalized vector.

Norm of the input vector.

This node calculates **unit vector** using the following equation:

$U=\frac{X}{\Vert X\Vert}$

where *U* is **unit vector**.

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported