purescript-linalg

A linear algebra library written in Purescript

currently supports

• vectors and matrices over any field
• vector: addition, dot product, product by scalar, ...
• matrix: addition, difference, product, transpose, inverse, determinant, kernel, image, ...
• Gauss Jordan elimination
• solves systems of linear equations (returns a solution and a basis if there is an infinite number of solutions)

Documentation is published on Pursuit

Install

spago install linalg

Consider the following linear system in $\mathbb{Q}$

• x + 2y = 7
• 3y + 4z = 8
• 5z + 6t = 9

This is equivalent to solve

$$\begin{bmatrix} 1 & 2 & 0 & 0\\ 0 & 3 & 4 & 0\\ 0 & 0 & 5 & 6 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \\ t \end{bmatrix} = \begin{bmatrix} 7 \\ 8 \\ 9 \end{bmatrix}$$

You can solve with LinAlg in that way.

module Main where
import Prelude
import Effect.Console (logShow)
import Data.Rational ((%))
import LinearAlgebra.Vector as V
import LinearAlgebra.Matrix as M

main = do
  let m = M.fromArray 3 4 [ [1, 2, 0, 0]
                          , [0, 3, 4, 0]
                          , [0, 0, 5, 6]
                          ] <#> (_ % 1)
  let b = V.fromArray [7, 8, 9] <#> (_ % 1)
  logShow $ M.solveLinearSystem m b

and obtain Just { basis: [(Vector [1 % 1,-1 % 2,3 % 8,-5 % 16])], sol: (Vector [97 % 15,4 % 15,9 % 5,0 % 1]) }

That means the solutions are

$$\begin{bmatrix} \frac{97}{15} \\ \frac{4}{15} \\ \frac{9}{5} \\ 0 \end{bmatrix} + q \begin{bmatrix} 1 \\ -\frac{1}{2} \\ \frac{3}{8} \\ -\frac{5}{16} \end{bmatrix}$$

for any $q \in \mathbb{Q}$