Vector

Vectors in PowerShell

Vector

Numbers are great!

When we measure things with one number, it's technically called a scalar.

When we measure things with more than one number, it's called a vector

We can do lots of things with vectors. We can add or substract them, multiply and divide them.

Vectors are very useful.

This module helps you use Vectors in PowerShell

Vectors in PowerShell

Vectors are actually built into PowerShell.

Because PowerShell is built atop of the .NET Framework, and the .NET Framework has had vector support for over a decade, PowerShell has had vectors for over a decade.

# Create a 2D vector
[Numerics.Vector2]::new(1,2)
# Create a 3D vector
[Numerics.Vector3]::new(1,2,3)
# Create a 4D vector
[Numerics.Vector4]::new(1,2,3,4)

This module exists to make vectors a bit more useful by providing commands to construct them.

Getting Vectors

There are a few commands in this module:

• Get-Vector
• Get-Vector2
• Get-Vector3
• Get-Vector4

Each command constructs a vector of the corresponding dimension.

A Vector with one dimension is just a list.

We can also drop the Get and just refer to them by vector number

Vector2 1 2 
Vector3 1 2 3
Vector4 1 2 3 4

We can be even shorter, and use V2, V3, and V4

v2 1 2
v3 1 2 3
v4 1 2 3 4

We can turn anything into a series of vectors.

v2 1
v3 1
v4 1

Strings can become vectors, too! (after all, each byte is already a number)

v2 "hi"
v3 "hi"
v4 "hi"

Vector Operators

.NET vectors are very powerful, and overload many operators.

For example, we can add, subtract, multiply, or divide by a scalar.

# Let's start with addition.  
# We can add a scalar to a vector.
(v2 1 2) + 1 
(v3 1 2 3) + 1 
(v4 1 2 3 4) + 1

# Let's try substraction:
(v2 1 2) - 1 
(v3 1 2 3) - 1 
(v4 1 2 3 4) - 1

# How about multiplication?
(v2 1 2) * 2
(v3 1 2 3) * 2
(v4 1 2 3 4) * 2

# What about division?
(v2 1 2) / 2
(v3 1 2 3) / 2
(v4 1 2 3 4) / 2

We can also work with other vectors:

# Adding vectors:
(v2 1 2) + (v2 1 2)
(v3 1 2 3) + (v3 1 2 3)
(v4 1 2 3 4) + (v4 1 2 3 4)

# Subtracting vectors:
(v2 1 2) - (v2 1 2)
(v3 1 2 3) - (v3 1 2 3)
(v4 1 2 3 4) - (v4 1 2 3 4)

# Multiplying vectors:
(v2 1 2) * (v2 1 2)
(v3 1 2 3) * (v3 1 2 3)
(v4 1 2 3 4) * (v4 1 2 3 4)

# Dividing vectors:
(v2 1 2) / (v2 1 2)
(v3 1 2 3) / (v3 1 2 3)
(v4 1 2 3 4) / (v4 1 2 3 4)

Vector Methods

Vectors have a large number of methods to work with.

Let's start simple, by calculating the length of a given vector.

(v2 1 1).Length()
(v3 1 1 1).Length()
(v4 1 1 1 1).Length()

Many of the most useful things we can do with a vector are exposed as a static methods:

(v2 1 1) | Get-Member -Static
(v3 1 1 1) | Get-Member -Static
(v4 1 1 1 1) | Get-Member -Static

We can access static method with ::

For a small example, let's find the distance between vectors:

$vector1 = v2 1 2
$vector2 = v2 2 1
$vector1::Distance($vector1, $vector2)

For another simple example, let's find a few point between two points, using Linear Interpolation lerp

$vector1 = v2 1 5
$vector2 = v2 1 -5
$vector1::Lerp($vector1, $vector2, 0.25)
$vector1::Lerp($vector1, $vector2, 0.5)
$vector1::Lerp($vector1, $vector2, 0.75)

All of this would not be possible without the great work of the .NET team to build such incredibly useful data structures.

Hopefully this module helps us all work with vectors!

Installing and Importing

You can install Vector from the PowerShell gallery

Install-Module Vector -Scope CurrentUser -Force

Once installed, you can import the module with:

Import-Module Vector -PassThru

You can also clone the repo and import the module locally:

git clone https://github.com/PowerShellWeb/Vector
cd ./Vector
Import-Module ./ -PassThru

Functions

Vector has 1 function

Get-Vector

Gets vectors

Gets a vector in one, two, three, or four dimensions.

This will convert a variety of types into numbers.

• Vector1 will return a list of numbers
• Vector2 will return a list of [Numerics.Vector2]
• Vector3 will return a list of [Numerics.Vector3]
• Vector4 will return a list of [Numerics.Vector4]

Notes

This attempts to convert any type into a number.

Some types are special:

• Primitive types will be casted to float
• [Numerics.Vector2],[Numerics.Vector3],[Numerics.Vector4] output each component
• [string]s that match a range ($start..$end) will output that range
• [Version]s will output each numeric component
• [semver]s will output each numeric component, followed by the bytes of a release type
• [Numerics.Matrix3x2] and [Numerics.Matrix4x4] will return the numbers in the matrix
• [DateTime] and [DateTimeOffset] will become a series of 12 numbers
  • year,month,day
  • hour, minute, second
  • millisecond, microsecond, nanosecond
  • offset.hours, offset.minutes, offset.seconds
• [string]s will return their bytes in the current $outputEncoding
• Anything unknown will be stringified and the bytes will be returned

Examples

Example 1

Create a vector out of two numbers

Vector2 1 2

Example 2

(Vector2 1 2) + (Vector2 2 1)

Example 3

(Vector2 1 2) - (Vector2 2 1)

Example 4

Create a thousand vectors

$vectors = Vector2 1..2kb

Example 5

Create a thousand vectors in random order, using the pipeline

$vectors = 1..2kb | Get-Random -Count 2kb | Vector2

Example 6

Create a vector from a string

$vector = Vector2 "hi"

Example 7

Create a vector out of two numbers

Vector3 1 2 3

Example 8

(Vector3 1 2 3 ) + (Vector3 3 2 1)

Example 9

(Vector3 1 2 3 ) - (Vector3 3 2 1)

Example 10

Create a thousand vectors

$vectors = Vector3 1..3kb

Example 11

Create a thousand vectors in random order, using the pipeline

$vectors = 1..3kb | Get-Random -Count 3kb | Vector3

Example 12

Create a vector from a string

$vector = Vector3 "hi"

Example 13

Create a vector out of four numbers

Vector4 1 2 3 4

Example 14

(Vector4 1 2 3 4 ) + (Vector4 4 3 2 1 )

Example 15

(Vector4 1 2 3 4 ) - (Vector4 4 3 2 1)

Example 16

Create a thousand vectors

$vectors = Vector4 1..4kb

Example 17

Create a thousand vectors in random order, using the pipeline

$vectors = 1..4kb | Get-Random -Count 4kb | Vector4

Example 18

Create vectors from a string

Vector4 "hi"

Links

• system.numerics.vector2 (Learn DotNet)
• system.numerics.vector3 (Learn DotNet)
• system.numerics.vector4 (Learn DotNet)