Linear Algebra Domain

The LinearAlgebra domain solves massive Systems of Equations.

While Vector and Matrix are for 3D graphics, this domain is for "hard" science and engineering. It answers questions like: "If 3x + 2y = 10 and x - y = 5, what are x and y?"... but for systems with thousands of variables.

Whether you're simulating heat flow across a computer chip, calculating structural loads on a bridge, or training a neural network, you are solving systems of linear equations. This domain wraps industrial-grade solvers (like LAPACK) to do the heavy lifting for you.

Overview

use aivi.linalg (solve, eigen)

// Matrix A and Vector b
// Solve for x in: Ax = b
// (Finds the inputs that produce the known output)
x = solve(A, b)

Features

Vec = { size: Int, data: List Float }
Mat = { rows: Int, cols: Int, data: List Float }

Domain Definition

domain LinearAlgebra over Vec = {
  (+) : Vec -> Vec -> Vec
  (+) a b = { size: a.size, data: zipWith (+) a.data b.data }
  
  (-) : Vec -> Vec -> Vec
  (-) a b = { size: a.size, data: zipWith (-) a.data b.data }
  
  (*) : Vec -> Float -> Vec
  (*) v s = { size: v.size, data: map (\x -> x * s) v.data }
}

Helper Functions

Function	Explanation
dot a b Vec -> Vec -> Float	Returns the dot product of two vectors.
matMul a b Mat -> Mat -> Mat	Multiplies matrices (rows of a by columns of b).
solve2x2 m v Mat -> Vec -> Vec	Solves the system m * x = v.

Usage Examples

use aivi.linear_algebra

v1 = { size: 3, data: [1.0, 2.0, 3.0] }
v2 = { size: 3, data: [4.0, 5.0, 6.0] }

prod = dot v1 v2