Tensor word can have slightly different meaning depending upon the nature of study, like it’s defined differently in Physics, slightly different in computer science. In computer terms, it is basically a ndimensional array. A scalar (one value) is a tensor with 0 dimensions, a vector is a tensor with 1 dimension, a matrix is a tensor with 2 dimensions.
It’s possible to define a tensor in Ruby using the Array
class of Ruby but it gets tedious when defining multidimensional tensors. Also, the Array
object is designed to be heterogeneous which means that the elements of the array can be of different type or different classes which would seem as a plus point overall but it has a huge downside. Due to Array
being heterogeneous, the memory allocation has to be in such a way that any element of any size can be added or removed from the array, which causes a lot of reallocations. Also, the indexing and other array functions gets slower due to the heterogeneous nature.
What if there’s a scenario where there is only one type of tensor elements, which means that a homogeneous array would also do, and there are memory and speed constraints? NumRuby
is the solution for such requirements.
Tensors in NumRuby
A tensor can be defined using the NMatrix
object of NumRuby
.
1


shape
is the number of dimensions and size of each dimension of the tensor. For example, [2, 2, 2]
shape tensor is a tensor with 3 dimensions and each dimension of size 2, hence number of elements is 8. A sample value of elements array for this could be [1, 2, 3, 4, 5, 6, 7, 8]
. type
is the data type of each of the tensor element, it could be any of :nm_bool
, :nm_int
, :nm_float32
, :nm_float64
, :nm_complex32
or :nm_complex64
depending on the requirements.
An example usage is shown below:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 

Elementwise Operations
One can also perform elementwise operations using NumRuby
. Elementwise operations are broadly of 2 types, Unioperand and bioperand.
UniOperand Operations
Unioperand operators are those that apply to just one tensor. For example, sine, cos or tan of each of element of the tensor.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 

BiOperand Operations
Bioperand operators are those that apply to two tensor. For example, addition, subtraction or multiplication of each of the corresponding elements of the the 2 tensor.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 

Linear Algebra
NumRuby
also supports linear algebra capabilities for 2dimensional tensors. One can easily do operations such as matrix inverse, dot product, matrix decompositions.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 
