Elixir-Linear-Algebra

Vector and matrix-operations implemented in Elixir. The goal of Elixir-Linear-Algebra (ELA for short) is to provide a complete and consistent set of functions for basic linear algebra operations. Should you want to contribute you are more than welcome to!

Installation

Simply add ELA to your list of dependencies in your mix.exs file, then run mix deps.get.

def deps do
    [{:elixir_linear_algebra, "~> 0.9.5", hex: :ela}]
end

Implemented and planned features

• Vector

  • Addition
  • Subtraction
  • Scalar multiplication
  • Dot product
  • Cross product
  • Hadmard product
  • Euclidian norm

• Matrix

  • Addition
  • Subtraction
  • Scalar multiplication
  • Vector multiplication
  • Matrix multiplication
  • Hadmard product
  • Pivoting
  • Reduced row echelon form
  • LU decomposition
  • Determinants

Vector operations

Creation

iex> Vector.new(3)
[0, 0, 0]

Addition

iex> Vector.add([1, 2, 1], [2, 2, 2])
[3, 4, 3]

Subtraction

iex> Vector.sub([1, 2, 1], [2, 2, 2])
[-1, 0, -1]

Multiplication with scalar

iex> Vector.scalar([2, 2, 2], 2)
[4, 4, 4]

Dot product

iex> Vector.dot([1, 2, 1], [2, 2, 2])
8

Cross product

iex> Vector.cross([1, 2, 1], [2, 2, 2])
[2, 0, -2]

Hadmard product

iax> Vector.hadmard([1, 2], [2, 2])
[2, 4]

Euclidian norm

iex> Vector.norm([3, 4])
0.5

Transpose

iex> Vector.transp([1, 1, 1])
[[1],
 [1],
 [1]]

Matrix operations

Creation

iex> Matrix.new(3, 2)
[[0, 0],
 [0, 0],
 [0, 0]]

Identity matrix

iex> Matrix.identity(3)
[[1, 0, 0],
 [0, 1, 0],
 [0, 0, 1]]

Addition

iex> Matrix.add([[1, 2, 3],
                 [1, 1, 1]],
                [[1, 2, 2],
                 [1, 2, 1]])
[[2, 4, 5],
 [2, 3, 2]]

Subtraction

iex> Matrix.sub([[1, 2, 3],
                 [1, 2, 2]],
                [[1, 2, 3],
                 [2, 2, 2]])
[[0, 0, 0],
 [-1, 0, 0]]

Multiplication with scalar

iex> Matrix.scalar([[2, 2, 2],
                    [1, 1, 1]], 2)
[[4, 4, 4],
 [2, 2, 2]]

Multiplication with vector

iex> Matrix.mult([1, 1], [[1, 0, 1],
                          [1, 1, 1]])
[[2, 1, 2]]

iex> Matrix.mult([[1, 0, 1],
                  [1, 1, 1]],
                 [[1],
                  [1],
                  [1]])
[[2],
 [3]]

Multiplication with matrix

iex> Matrix.mult([[1, 2],
                  [1, 1]],
                 [[1, 2],
                  [0, 2]])
[[1, 6],
 [1, 4]]

Hadmard product

iex> Matrix.hadmard([[1, 2],
                     [1, 1]],
                    [[1, 2],
                     [0, 2]])
[[1, 4],
 [0, 2]]

Transpose

iex> Matrix.transp([[1, 2, 3],
                    [4, 5, 6]])
[[1, 4],
 [2, 5],
 [3, 6]]

Dimensions

iex> Matrix.dim([[1, 1, 1],
                 [2, 2, 2]])
{2, 3}

Pivoting

iex> Matrix.pivot([[2.0, 3.0],
                   [2.0, 3.0],
                   [3.0, 6.0]], 1, 0)
[[0.0, 0.0],
 [1.0, 1.5],
 [0.0, 1.5]]

Reduced row echelon form

iex> Matrix.reduce([[1.0, 1.0, 2.0, 1.0],
                    [2.0, 1.0, 6.0, 4.0],
                    [1.0, 2.0, 2.0, 3.0]])
[[1.0, 0.0, 0.0, -5.0],
 [0.0, 1.0, 0.0, 2.0],
 [0.0, 0.0, 1.0, 2.0]]

LU decomposition Returns a LUP decomposed matrix as a tuple.

iex> Matrix.lu([[1, 3, 5],
                [2, 4, 7],
                [1, 1, 0]])
{[[1,    0,  0],
  [0.5,  1,  0],
  [0.5, -1,  1]],
 [[2,  4,    7],
  [0,  1.0,  1.5],
  [0,  0,   -2.0]]
 [[0, 1, 0],
  [1, 0, 0],
  [0, 0, 1]]}

Determinant

iex> Matrix.det([[1, 3, 5],
                 [2, 4, 7],
                 [1, 1, 0]])
4