Tensor, the Vector/Matrix/Tensor library has reached v1.0!

With the recent addition of Numbers and some improvements of the documentation, Tensor now has reached version 1.0.0!

For people that do not yet know about it:

Tensor is a library that allows you to work with sparse Vectors, Matrices and higher-order Tensors, with the following nice features:

• An implementation of the Access protocol, so you can do mymatrix[42][3].
• It supports the arithmetic functions you would expect from vectors, matrices and tensors. These are implemented using Numbers, which means that they work on any numeric type.
• What is even more, Tensor itself implements Numbers’ Numeric behaviour, which means that anything that does number arithmetic can now do (elementwise) vector/matrix/tensor arithmetic! It also means that you can nest matrices ad infinitum!
• A sparse implementation: Only elements deviating from the default element of a data structure are stored. This means that e.g. a nearly-empty 10000x10000 element matrix takes up only a neglegible amount of memory.
• While you can work with numbers, you can store anything inside: Using it as a representation of a game board (a matrix for chess, or a 3-dimensional tensor for a Rubik’s Cube), for instance, is something that is very possible.
• Functions to rotate, transpose, transform, combine, separate, map over and reduce vectors/matrices/tensors.

Here are some examples from the Readme:

Vectors

iex> vec = Vector.new([1,2,3,4,5])
#Vector-(5)[1, 2, 3, 4, 5]
iex> vec2 = Vector.new(~w{foo bar baz qux})
#Vector-(4)["foo", "bar", "baz", "qux"]
iex> vec2[2]
"baz"
iex> Vector.add(vec, 3)
#Vector-(5)[4, 5, 6, 7, 8]
iex> Vector.add(vec, vec)
#Vector-(5)[2, 4, 6, 8, 10]

Matrices

iex> mat = Matrix.new([[1,2,3],[4,5,6],[7,8,9]],3,3)
#Matrix-(3×3)
┌                          ┐
│       1,       2,       3│
│       4,       5,       6│
│       7,       8,       9│
└                          ┘
iex> Matrix.rotate_clockwise(mat)
#Matrix-(3×3)
┌                          ┐
│       7,       4,       1│
│       8,       5,       2│
│       9,       6,       3│
└                          ┘
iex> mat[0]
#Vector-(3)[1, 2, 3]
iex> mat[2][2]
9
iex> Matrix.diag([1,2,3])
#Matrix-(3×3)
┌                          ┐
│       1,       0,       0│
│       0,       2,       0│
│       0,       0,       3│
└                          ┘

iex> Matrix.add(mat, 2)
#Matrix-(3×3)
┌                          ┐
│       3,       4,       5│
│       6,       7,       8│
│       9,      10,      11│
└                          ┘
iex> Matrix.add(mat, mat)
#Matrix-(3×3)
┌                          ┐
│       2,       4,       6│
│       8,      10,      12│
│      14,      16,      18│
└                          ┘

Tensors

  iex> tensor = Tensor.new([[[1,2],[3,4],[5,6]],[[7,8],[9,10],[11,12]]], [3,3,2])
  #Tensor(3×3×2)
        1,       2
          3,       4
            5,       6
        7,       8
          9,      10
            11,      12
        0,       0
          0,       0
            0,       0
  iex> tensor[1]
  #Matrix-(3×2)
  ┌                 ┐
  │       7,       8│
  │       9,      10│
  │      11,      12│
  └                 ┘

You can find it on Hex.pm and on GitHub.