numLuau

numluau (numerical luau) is a math library for luau.

features:

• a N dimensional array object

  • broadcasting
  • sophisicated slice indexing
  • element wise operations

• linear algebra

  • linear equation solvers
  • eigen value/vectors
  • QR and LU decompositions
  • determinants
  • dot/cross products
  • matrix multiplications

and alot more

installation

its reccomended to install using pesde

pesde add chocolate_bar2410/numluau

quick start

require it from your packages

local numluau = require("path.to.library")

the main feature of numluau are its N-Dimensional arrays
the code below provides a example of how you could create and handle these arrays

-- create a ndarray using a table
local array1 : numluau.ndArray<number> = numluau.array({1,2,3,4,5})
local array2 : numluau.ndArray<number> = numluau.array({5,4,3,2,1})

print(array1 + array2) -- [6 6 6 6 6]
print(array1 * array2) -- [5 8 9 8 5]
print(array1 / array2) -- [0.2 0.5 1 2 5]
print(array1 % array2) -- [1 2 0 0 0]
print(array1 * 20)     -- [20 40 60 80 100]

print(array1[1])       -- 1
print(array1["1:3"])   -- [1 2 3]

-- numluau allows you to also convert nested tables
local array3 : numluau.ndArray<number> = numluau.array({{2,4},{6,8},{10,12}})
print(array3[1][1])          -- 2
print(array3[":,2"])         -- [4 8 12]

print(array3:reshape(2,3))   -- [[2  4  6] [8 10 12]]
print(numluau.sum(array3))   -- [42]
print(numluau.sum(array3,1)) -- [(2 + 6 + 10) (4 + 8 + 12)] -> [18 24]

example code

circuit voltage problem

--[[
After examining a circuit full of resistors, you find that the voltage at 4 specified points is given by:

3v₁ + 2v₂ + 3v₃ + 10v₄ = 4
2v₁ - 2v₂ + 5v₃ + 8v₄  = 1
3v₁ + 3v₂ + 4v₃ + 9v₄  = 3
3v₁ + 4v₂ - 3v₃ - 7v₄  = 2

where v₁ - v₄ are voltages
find v₁,v₂,v₃,v₄
]]
local numluau = require("../numluau/numluau")
local A : numluau.ndArray<number> = numluau.array({
    {3, 2, 3, 10},
    {2,-2, 5,  8},
    {3, 3, 4,  9},
    {3, 4,-3, -7},
})

local C : numluau.ndArray<number> = numluau.array({4,1,3,2})
local voltages = numluau.linalg.solve(A, C)

print(string.format("voltage results: \nv₁ : %g \nv₂ : %g \nv₃ : %g  \nv₄ : %g",voltages[1],voltages[2],voltages[3],voltages[4]))
--[[
voltage results:
v₁ : 0.783784
v₂ : 0.036036
v₃ : -0.675676 
v₄ : 0.36036
]]

integration problem

--[[
let f(x,y) = exp(-(x² + y²)) ∙ sin(x) for -2 ≤ x ≤ 2 and -2 ≤ y ≤ 2

find:
1. Find the volume |f(x,y)| in the specified x and y range
2. Find the volume |f(x,y)| only in the region where √(x² + y^²) > 0.5
]]
local numluau = require("../numluau/numluau")

local grid_x,grid_y = 1000,1000

local x = numluau.linspace(-2, 2, grid_x)
local y = numluau.linspace(-2, 2, grid_y)

local xv,yv = numluau.meshgrid(x,y)

local Z = numluau.exp(-(xv^2 + yv^2)) * numluau.sin(xv)

local dx = numluau.diff(x)[1]
local dy = numluau.diff(y)[1]

local volume = numluau.sum(numluau.abs(Z:flatten())) * dx * dy

local f = Z[numluau.greater(xv^2 + yv^2,0.5 ^ 2)]
local volume_contained = numluau.sum(numluau.abs(f:flatten())) * dx * dy
print("volume of |f(x,y)|:\n" .. volume:item() .. "\n")
print("volume of |f(x,y)| inside √(x² + y^²) > 0.5:\n" .. volume_contained:item())
--[[
volume of f(x,y):
1.4861858145125453

volume of f(x,y) inside √(x² + y^²) > 0.5:
1.344765293020408
]]