Array Operations

Get started handling multidimensional arrays in Julia with this simple guide.

Now that we know several ways of inputting arrays, we should take a look at how we can operate with them.

Getting the Size of an Array

The size of an array can be obtained with the ‘size’ function. Importantly, the elements of s=size(A) are treated as an array of integers, one for each dimension, even in the one-dimensional case. That is, we should always employ a syntax of the form s[dim].

A = rand(6)
s = size(A)
print(s)        # returns (6,)
print(s[1])     # returns 6

Matrix multiplication

Two dimensional arrays (or matrices) are a fundamental part of Julia. For example, you can resort to a Matlab-style syntax for matrix-matrix multiplication:

A * B

A Matrix and a Vector can be also multiplied with the * operator.

A * v

Element-wise multiplication

In case you need to multiply the elements of an n-dimensional array on an element-wise fashion, you can resort to the dot operator, which will broadcast the scalar multiplication operator on an element-wise fashion, just as we discussed in the previous post of this tutorial series:

A .* B

Dot product

You can do dot products by calling the dot function

v = rand(1000)
w = rand(1000)
z = dot(v,w)

Alternatively, you can resort to a typical linear algebra notation:

z = v'w

Array slicing

Array slicing is a very useful operation in Linear Algebra, which consists in extracting a subset of elements from an array and packaging them as another array. In Julia, we can resort to a very straightforward syntax for this operation.

For example, the code below will extract the odd indices in both dimensions from a 6x6 matrix, and store the results in a new 3x3 matrix.

A = rand(6,6)           # 6×6 Matrix{Float64}
B = A[1:2:5,1:2:5]      # 3×3 Matrix{Float64}

Logical Indexing

A very useful way of selecting array elements is to resort to a boolean array, in a process which is often referred to as logical indexing. This can be easily done in Julia by resorting to broadcasting the logical operations of interest.

For example, let’s generate a matrix of random numbers and set to zero all numbers in the array which are below 0.5:

A = rand(6,6)
A[ A .< 0.5 ] .= 0

Note that in this example we also needed to broadcast the assignment operator as well.

Backslash operator

Just like in Matlab, Julia has a built-in operator to solve matrices. For square matrices, it will try to solve the linear system, while for rectangular matrices, it will seek for the least squares solution.

One ‘gotcha’ that you will probably encounter sooner or later is that, as 1xN matrices are not the same as N-element vectors. We have to be careful and always employ vectors in the right-hand side of an equation.

b1 = [4.0, 5, 6]                # 3-element Vector{Float64}
b2 = [4.0; 5; 6]                # 3-element Vector{Float64}
m1 = [4.0 5 6]                  # 1×3 Matrix{Float64}

x=A\b1                          # Solves A*x=b
x=A\b2                          # Solves A*x=b  
x=A\m1                          # Error!!