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│
└ ┘
)
