Linear Algebra Library

From the same group that brought to you the Lua Statistics library, my open-source organization, Bytebit (Roblox group) has just made the new Lua Linear Algebra library!

This library is far from complete, but it currently features a wealth of matrix and vector functions. For those of you who have used Python before, the syntax in this library often resembles that of numpy. It uses its own immutable matrix data structure which works similarly to a 2D array of size (m x n). Vectors are implemented by just using (n x 1) matrix objects. All functions are annotated with RoDocs comments.

Matrices store things in A[row][column] orientation.

To access the dimensions of a matrix, use A.Shape, which will be a table like so: { [1] = m, [2] = n }.

All the arithmetic operators (+, - including the unary operator, *, /, %, and ^) are implemented for matrices and individual rows as expected (at least when using scalars).

This library is open-source! Please send in pull requests, I will gladly review them and hopefully add them in!

Upcoming goals

I am hoping to implement a sparse matrix data structure so as to increase performance. I also want to implement an SVD function (that would take advantage of the sparse matrix data structure when available). I would also like to implement a way to easily sync this into a Roblox game so that people don’t have to copy-paste the script into their games, which I’d like to accomplish using @Osyris’s RbxRefresh or a similar syncing tool.

Examples

matrix transpose

local mat = linalg.matrix.new({

{ 1, 2 },

{ 3, 4 }

})

print(mat.T)

Output:

1 3

2 4

vector + vector

local v1 = linalg.vector.new({ 1, 2 })

local v2 = linalg.vector.new({ 2, 1 })

print(v1 + v2)

Output:

3

3

vector * scalar

local v = linalg.vector.new({ 1, 2 })

print(v * 3)

Output:

3

6

vector norms

local v = linalg.vector.new({ 1, 2 })

print("L1 norm: " .. tostring(linalg.vector.norm.l1(v)))

print("L2 norm: " .. tostring(linalg.vector.norm.l2(v)))

print("L-infinity norm: " .. tostring(linalg.vector.norm.linf(v)))

Output:

L1 norm: 3

L2 norm: 51/2 (it’ll actually say a decimal number of the same value)

L-infinity norm: 2

inner products

local v1 = linalg.vector.new({ 1, 2 })

local v2 = linalg.vector.new({ 2, 1 })

print(linalg.vector.ip.dot(v1, v2))

Output:

4

vector projection

local v = linalg.vector.new({ 1, 2 })

local e1 = linalg.vector.e(1, 2)

print(v.project(e1))

Output:

1

0

Gram-Schmidt vector space creation

local e1 = linalg.vector.e(1, 2)

print(unpack(linalg.gramSchmidt(e1)))

Output:

1

0

0

1

33 Likes

This seems pretty cool! How are some of your functions different from the regular built-in functions provided with Vector2?

For functions that overlap, the main difference is that this library allows for vectors of any length - not just 2 or 3. It also allows for matrices of any dimension.

1 Like

Ooh! That’s pretty cool. What kind of use cases are there for applying this to gameplay?

The Gram-Schmidt function can be very useful for vectors of 2, 3, and up dimensions. For gameplay, it can be used for a wide variety of things such as adding a random spread to bullets being shot.

As for higher dimensions, those are likely going to be more useful for algorithms that would benefit from being able to carry out mathematical operations quicker by utilizing matrices and vectors, and this would then move into gameplay. An example of this could be for matchmaking, you could put every factor into that decision into a large vector and then create a matrix that could be used to multiply against that vector to produce a scalar that is your score for that particular matchup.

4 Likes

This looks pretty cool! , But how exactly can I import this library to roblox studio?!