Tutorial: First Steps

Tensor Properties

Tensors have the following properties:

• shape - the shape of the tensor. It is a sequence of a the tensor's dimensions along each axis.
• strides - the strides of the tensor. It is a sequence of numbers of steps to get the next item along a dimension.
• size - the total number of elements in the tensor.
• rank() - the number of dimensions in the tensor. It is 0 for scalars, 1 for vectors, 2 for matrices and N for tensors of rank N.

import vtl

t := vtl.from_2d([[1, 2, 3], [4, 5, 6]])!

println(t)
// [[1, 2, 3], [4, 5, 6]]

println(t.size) // 6
println(t.rank()) // 2
println(t.shape) // [2, 3]
println(t.strides) // [3, 1] => next row is 3 elements away in memory while the next column is 1 element away in memory

Tensor Creation

The canonical way to create a tensor is to use the vtl.from_* functions.

import vtl

t1d := vtl.from_1d([1, 2, 3])!

println(t1d)
// [1, 2, 3]

t2d := vtl.from_2d([[1, 2, 3], [4, 5, 6]])!

println(t2d)
// [[1, 2, 3], [4, 5, 6]]

t := vtl.from_array([1, 2, 3, 4, 5, 6, 7, 8], [2, 4])!

println(t)
// [[1, 2, 3, 4], [5, 6, 7, 8]]

println(t.size) // 8
println(t.rank()) // 2
println(t.shape) // [2, 4]
println(t.strides) // [4, 1] => next row is 4 elements away in memory while the next column is 1 element away in memory

Other ways to create a tensor are:

• tensor - creates a new tensor. This can be used to initialize a tensor of a specific shape with a default value. (0 for numbers, false for bool, ...)
• zeros - creates a tensor of zeros.
• ones - creates a tensor of ones.
• zeros_like - creates a tensor of zeros with the same shape as the given tensor.
• ones_like - creates a tensor of ones with the same shape as the given tensor.

import vtl

t := vtl.tensor(0.0, [2, 3])

println(t)
// [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]

booleans := vtl.tensor(false, [2, 3])

println(booleans)
// [[false, false, false], [false, false, false]]

z := vtl.zeros[f64]([2, 3])

println(z)
// [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]

o := vtl.ones[f64]([2, 3])

println(o)
// [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]

tmp := vtl.from_array([1, 2, 3, 4], [2, 2])!

h := vtl.zeros_like(tmp)

println(h)
// [[0.0, 0.0], [0.0, 0.0]]

i := vtl.ones_like(tmp)

println(i)
// [[1.0, 1.0], [1.0, 1.0]]

Accessing and modifying a value

import vtl

mut t := vtl.from_array([1, 2, 3, 4, 5, 6, 7, 8], [2, 4])!

println(t.get([1, 1]))
// 5

t.set([1, 1], 10)

println(t)
// [[1, 2, 3, 4], [10, 5, 6, 7]]

Copying a tensor

Warning: When you do the following, both tensors a and b will share the same data. Full copy must be explicitly requested via the copy() function.

import vtl

a := vtl.from_array([1, 2, 3, 4, 5, 6, 7, 8], [2, 4])!

println(a)
// [[1, 2, 3, 4], [5, 6, 7, 8]]

b := a.reshape([4, 2])!

println(b)
// [[1, 2], [3, 4], [5, 6], [7, 8]]

Here modifying b WILL modify a. This behaviour is the same as Numpy and Julia.