Julia Foundations - UCF CAP-6318

Computational Analysis of Social Complexity
Fall 2025, Spencer Lyon

Prerequisites

Laptop or personal computer with internet connection

Outcomes

Understand the main benefits and features of Julia
See how to define variables, functions, and types in Julia
Install commonly used packages for Graphs, DataFrames, Plotting and more

References

Packages and Software Engineering sections of QuantEcon julia lectures
Julia documentation
Documentation for packages: Graphs, DataFrames, Plots

What is Julia?¶

Julia is a relatively new programming language (first public release in 2012, 1.0 release in 2018)
General purpose, but specializes in numerical computation
Leverages advanced compiler technology to generate very efficient code
It can be as clear to read and write as Python, and as quick to evaluate as C!

Core Types¶

We’ll start by learning about the core datatypes built in to Julia
Along the way we’ll pick up some of the key syntax elements
We will move quickly, so some prior programming experience would be helpful

Numbers¶

Let’s start with numbers
To work with a number, just type it!

42

We can also do basic arithmetic in the way you would expect

10 * 3

30

1 + 2

3

So far we’ve worked with integers (whole numbers)
Julia can also work with numbers containing a decimal
In Julia these are called floating point numbers

1.234 ^ 2.2  # use `^` for exponentiation, not `**` like in python

1.5881567008330448

553.34 / 12.9

42.89457364341085

We can mix and match integers and floats

25 / 2.5

10.0

25 / 2  # dividing integers returns a float (notice the `.`)

12.5

notice we used # to define a comment

Text Data¶

Not all data is numerical
Some is textual
To represent text in Julia we use a String
To define a String we use quotation marks (") as below

"My name is Spencer"

"My name is Spencer"

"1"  # an integer in a string

"1"

You cannot use single quotes for strings as in other languages (like Python or Javascript)
Go ahead... try it by removing the # and excuting the cell below

# 'hello'

"""
This

is

also

a

string
"""

"This\n\nis\n\nalso\n\na\n\nstring\n"

Arrays¶

When doing numerical work, we often need to deal with multiple pieces of data at the same time
In Julia the default way of doing this is to use an array
Arrays are defined with [ and ] as below

[1, 2, 3.14]  # a 3 element array

3-element Vector{Float64}:
 1.0
 2.0
 3.14

[1 2 3]  # a 1x3 matrix

1×3 Matrix{Int64}:
 1  2  3

[1 2; 3 4]  # a 2x2 matrix

2×2 Matrix{Int64}:
 1  2
 3  4

[1 2
 3 4]  # another way to write a 2x2 matrix

2×2 Matrix{Int64}:
 1  2
 3  4

[1 "hello"; 2 "world"]  # a 2x2 matrix with int and string

2×2 Matrix{Any}:
 1  "hello"
 2  "world"

Accessing array items¶

We can use [N] to access the Nth element
We can also use [i:j] to access items i through j
Finally we can use [[n1, n2]] to access the n1th and n2th elements

[100, 101, 102, 103][2]

101

[100, 101, 102, 103][2:4]

3-element Vector{Int64}:
 101
 102
 103

[100, 101, 102, 103][[1, 3]]

2-element Vector{Int64}:
 100
 102

Note that unlike Python, Julia starts counting at 1
Also note that end can be used to refer to the last element, end-1 to second to last, and so on

[1, 2, 3, 4][end]

4

[1, 2, 3, 4][end-2]

2

Tuples¶

There is another data type for holding “lists” of data called a tuple
Tuples are create using parenthesis instead of square brackets as follows

(1, 2, 3, "hello")

(1, 2, 3, "hello")

("hello", 5)

("hello", 5)

("hello", 5)[2]

5

The main differences between tuples and arrays are
1. Tuples are meant to hold immutable or non-changing data
2. Tuples aren’t usually meant for computation or linear algebra

Dictionary¶

Very often in programming we want to be able to associate a key or name to a specific value
One data type for doing that is a Dict
Dicts are created with the somewhat inconvenient syntax Dict(name => value, ...) where the ... means we can repeat the pattern multiple times
They keys and values can be of any type

Dict("x" => 1, 2 => "y", ["w", "z"] => [1, 2, 3])

Dict{Any, Any} with 3 entries:
  2          => "y"
  ["w", "z"] => [1, 2, 3]
  "x"        => 1

# use `[name]` to access element with `name`
Dict("x" => 1, 2 => "y", ["w", "z"] => [1, 2, 3])[2]

"y"

Dict("x" => 1, "y" =>2)

Dict{String, Int64} with 2 entries:
  "x" => 1
  "y" => 2

Dictionaries are often used for passing around groups of parameters
We’ll see examples later on

Named Tuples¶

The final “collection” we’ll talk about is the named tuple
It is a hybrid between a tuple and a dictionary
To create them we use the synax (name = value, ...)
They names or keys need to be just names (not numbers or arrays). The values can be anything

(x = 1, y = 2, z="hello")

(x = 1, y = 2, z = "hello")

(x = 1, y = 2, z="hello").z # use `.name` to access item

"hello"

Named tuples are a newer feature of Julia
They are often used for the same purpsoes as dictionaries because the syntax is much cleaner

Variables¶

Often when programming, we need to refer to the same piece of data more than once
To do this we use a variable
Variables are defined using an =, as in name = value

x = 1

1

y = 42

42

x + y  # 'use' or 'refer to' x and y

43

m1 = [1 0; 0 1]

2×2 Matrix{Int64}:
 1  0
 0  1

m2 = [1 2; 3 4]

2×2 Matrix{Int64}:
 1  2
 3  4

m1 * m2  # matrix multiplication

2×2 Matrix{Int64}:
 1  2
 3  4

m2 * m2  # again -- but with something besides identity matrix!

2×2 Matrix{Int64}:
  7  10
 15  22

d = Dict("X" => 1, "Y" => 2)

Dict{String, Int64} with 2 entries:
  "Y" => 2
  "X" => 1

d["X"]

1

Functions¶

Most Julia programs do more than basic arithmetic operations on data
To apply an operation to a piece of data, we call a function
To call a function we use the function_name(data1, data2)
A very handy function is the typeof function

typeof(1)

Int64

typeof(2.0)

Float64

typeof([1,2,3])

Vector{Int64} (alias for Array{Int64, 1})

typeof([1 2; 3 4.0])

Matrix{Float64} (alias for Array{Float64, 2})

Many standard operations are built in to Julia as functions

sum([1, 2, 3])  # compute sum of array of numbers

6

inv([1 2; 3 4])  # matrix inverse

2×2 Matrix{Float64}:
 -2.0   1.0
  1.5  -0.5

size([1 2; 3 4])  # number of (rows, columns)  in matrix

(2, 2)

length([1, 2, 3])  # number of elements in array

3

length([1 2; 3 4])  # returns total number of elements in a Matrix

4

rand(2, 2, 2)  # a 2x2x2 array of random numbers, sampled from uniform[0,1] dist

2×2×2 Array{Float64, 3}:
[:, :, 1] =
 0.362076  0.860015
 0.297667  0.572139

[:, :, 2] =
 0.775214  0.145788
 0.815195  0.820176

Julia has 1000s of functions
We’ll learn more as we go along...
Just watch for the pattern with parentisis: name(args)

Defining Functions¶

Functions are used to execute a predefined set of operations
Defining our own funcitons allows us to break programs into small, easily written an understood components
We define functions using the syntax

function name(arg1, arg2)
    # steps
end

function mean(x)
    total = sum(x)
    N = length(x)
    total / N
end

mean (generic function with 1 method)

mean([1, 2, 3])

2.0

# mean of 1000 random samples from U[0,1] -- should be ~ 0.5
mean(rand(1000))

0.48944092617754337

If a function only contains one line of code, you can also use a shorthand notation:

function_name(arg1, arg2) = # step

add_two(x) = x + 2

add_two (generic function with 1 method)

add_two(40)

42

Getting help for functions¶

Given that there are so many functions, sometimes it is hard to remember exactly what a function does
Thankfully we can get help from Julia
If we type ?function_name, Julia will present us with documentation about the function

?map

ParseError:

# Error @ /Users/sglyon/Teaching/UCF/CAP-6318/book-myst/week01/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_Y145sZmlsZQ==.jl:1:1

?map

╙ ── not a unary operator



Stacktrace:

 [1] top-level scope

   @ ~/Teaching/UCF/CAP-6318/book-myst/week01/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_Y145sZmlsZQ==.jl:1

?extrema

Control Flow¶

Julia has the basic elements of control flow:
- if-else statements
- for loops

if 1 > 2 # no parenthesis needed
    println("what???")
else     # else is optional
    return mean([1, 2, 3])
    print("phew")
end      # all "blocks" terminate with word `end`

2.0

for i in 1:5 # range of numbers 1 to 5
    println(i, " ", i^2)
end

We will see many more examples as we go forward

Packages¶

Julia comes ready to go with many powerful functions and data types
However, there is a very active community of Julia programmers who are experts in different subfields of science and engineering
This has led to the development of vibrant and exciting ecosystem of packages or toolboxes for performing specific tasks
We can access these routines by using Julia packages

Loading packages¶

By default Julia ships with a “standard library”
These are packages that come bundled with Julia itself and are pre-installed
To load a package and all of its types/functions use the using keyword
For example, we can load the Dates package and start using it

using Dates

t1 = Dates.now()

2024-08-19T20:39:10.885

Dates.format(t1, "yyyy-mm-dd")

"2024-08-19"

t2 = Dates.now()

2024-08-19T20:39:11.197

t2 > t1

true

t3 = DateTime(1776, 7, 4)

1776-07-04T00:00:00

"America is $(t1 - t3) ($(floor(t1 - t3, Dates.Day))) old"

"America is 7830160750885 milliseconds (90626 days) old"

Installing Packages¶

In addition to the standard library, we can also use packages created by other Julia users
To use a 3rd party package, we first need to install it
There are two ways to do this

]add PackageName

using Pkg  # a standard library package
Pkg.add("PackageName")

Let’s try them both

]add Plots

   Resolving package versions...
  No Changes to `~/.julia/environments/v1.10/Project.toml`
  No Changes to `~/.julia/environments/v1.10/Manifest.toml`

using Pkg
Pkg.add("DataFrames")

   Resolving package versions...
  No Changes to `~/.julia/environments/v1.10/Project.toml`
  No Changes to `~/.julia/environments/v1.10/Manifest.toml`

After installing packages, we can load and use them just as we did the standard library packages

using Plots  # Python: from Plots import *

plot([sin, cos], -2pi, 2pi)

using DataFrames
df = DataFrame(c1=1:10, c2=(1:10).^2)

Package Composability¶

One unique feature sof Julia is that most of the language itself, in addition to packages, are written in Julia
For other languages like Python or R the “built in” part of the language is often written in another language like C
This difference has a large impact for Julia users
- Built in code and user code (including packages) are given the same “treatment”
- Anything the language creators can do, so can you
A practical implication of this is that packages can operate on built in types (like we saw in our examples above) as well as types from other packages
Let’s see what this looks like by plotting a DataFrame

# install "StatsPlots", which links Plots and DataFrames
Pkg.add("StatsPlots")

using StatsPlots

   Resolving package versions...
  No Changes to `~/.julia/environments/v1.10/Project.toml`
  No Changes to `~/.julia/environments/v1.10/Manifest.toml`

@df df scatter(:c1, :c2)

Pkg.add("RDatasets") # common datasets from R programming language
using RDatasets
school = RDatasets.dataset("mlmRev","Hsb82")
@df school density(:MAch, group = :Sx)

@df school density(:MAch, group = (:Sx, :Sector))

Julia 1

Julia Setup

Julia 2

Julia Types and Methods