Julia

What is

Julia is an open-source, multi-platform, high-level, high-performance programming language for technical computing.

Julia has an LLVM Low-Level Virtual Machine (LLVM) is a compiler infrastructure to build intermediate and/or binary machine code. -based JIT Just-In-Time compilation occurs at run-time rather than prior to execution, which means it offers both the speed of compiled code and the flexibility of interpretation. The compiler parses the code and infers types, after which the LLVM code is generated, which in turn is compiled into native code. compiler that allows it to match the performance of languages such as C and FORTRAN without the hassle of low-level code. Because the code is compiled on the fly you can run (bits of) code in a shell or REPL Read-Eval-Print-Loop , which is part of the recommended workflow .

Julia is dynamically typed, provides multiple dispatch Because function argument types are determined at run-time, the compiler can choose the implementation that is optimized for the provided arguments and the processor architecture. , and is designed for parallelism and distributed computation.

Julia has a built-in package manager.

Julia has many built-in mathematical functions, including special functions (e.g. Gamma), and supports complex numbers right out of the box.

Julia allows you to generate code automagically thanks to Lisp-inspired macros.

Julia was born in 2012.

Basics

   
Assignment answer = 42
x, y, z = 1, [1:10; ], "A string"
x, y = y, x # swap x and y
Constant declaration const DATE_OF_BIRTH = 2012
End-of-line comment i = 1 # This is a comment
Delimited comment #= This is another comment =#
Chaining x = y = z = 1 # right-to-left
0 < x < 3 # true
5 < x != y < 5 # false
Function definition function add_one(i)
return i + 1
end
Insert LaTeX symbols \delta + [Tab]

Operators

   
Basic arithmetic +, -,*,/
Exponentiation 2^3 == 8
Division 3/12 == 0.25
Inverse division 7\3 == 3/7
Remainder x % y or rem(x,y)
Negation !true == false
Equality a == b
Inequality a != b or a ≠ b
Less and larger than < and >
Less than or equal to <= or ≤
Greater than or equal to >= or ≥
Element-wise operation [1, 2, 3] .+ [1, 2, 3] == [2, 4, 6]
[1, 2, 3] .* [1, 2, 3] == [1, 4, 9]
Not a number isnan(NaN) not(!) NaN == NaN
Ternary operator a == b ? "Equal" : "Not equal"
Short-circuited AND and OR a && b and a || b
Object equivalence a === b

The shell aka REPL

   
Recall last result ans
Interrupt execution [Ctrl] + [C]
Clear screen [Ctrl] + [L]
Run program include("filename.jl")
Get help for func is defined ?func
See all places where func is defined apropos("func")
Command line mode ;
Package Manager mode ] ([Ctrl] + [C] to exit)
Help mode ?
Exit special mode / Return to REPL [Backspace] on empty line
Exit REPL exit() or [Ctrl] + [D]

Standard libraries

To help Julia load faster, many core functionalities exist in standard libraries that come bundled with Julia. To make their functions available, use using PackageName. Here are some Standard Libraries and popular functions.

   
Random rand, randn, randsubseq
Statistics mean, std, cor, median, quantile
LinearAlgebra I, eigvals, eigvecs, det, cholesky
SparseArrays sparse, SparseVector, SparseMatrixCSC
Distributed @distributed, pmap, addprocs
Dates DateTime, Date

Package management

Packages must be registered before they are visible to the package manager. In Julia 1.0, there are two ways to work with the package manager: either with using Pkg and using Pkg functions, or by typing ] in the REPL to enter the special interactive package management mode. (To return to regular REPL, just hit BACKSPACE on an empty line in package management mode). Note that new tools arrive in interactive mode first, then usually also become available in regular Julia sessions through Pkg module.

Using Pkg in Julia session

   
List installed packages (human-readable) Pkg.status()
List installed packages (machine-readable) Pkg.installed()
Update all packages Pkg.update()
Install PackageName Pkg.add("PackageName")
Rebuild PackageName Pkg.build("PackageName")
Use PackageName (after install) using PackageName
Remove PackageName Pkg.rm("PackageName")

In Interactive Package Mode

   
Add PackageName add PackageName
Remove PackageName rm PackageName
Update PackageName update PackageName
Use development version dev PackageName or dev GitRepoUrl
Stop using development version, revert to public release free PackageName

Characters and strings

   
Character chr = 'C'
String str = "A string"
Character code Int('J') == 74
Character from code Char(74) == 'J'
Any UTF character chr = '\uXXXX' # 4-digit HEX
chr = '\UXXXXXXXX' # 8-digit HEX
Loop through characters for c in str
println(c)
end
Concatenation str = "Learn" * " " * "Julia"
String interpolation a = b = 2
println("a * b = $(a*b)")
First matching character or regular expression findfirst(isequal('i'), "Julia") == 4
Replace substring or regular expression replace("Julia", "a" => "us") == "Julius"
Last index (of collection) lastindex("Hello") == 5
Number of characters length("Hello") == 5
Regular expression pattern = r"l[aeiou]"
Subexpressions str = "+1 234 567 890"
pat = r"\+([0-9]) ([0-9]+)"
m = match(pat, str)
m.captures == ["1", "234"]
All occurrences [m.match for m = eachmatch(pat, str)]
All occurrences (as iterator) eachmatch(pat, str)

Beware of multi-byte Unicode encodings in UTF-8:
10 == lastindex("Ångström") != length("Ångström") == 8

Strings are immutable.

Numbers

   
Integer types IntN and UIntN, with N ∈ {8, 16, 32, 64, 128}, BigInt
Floating-point types FloatN with N ∈ {16, 32, 64}
BigFloat
Minimum and maximum values by type typemin(Int8)
typemax(Int64)
Complex types Complex{T}
Imaginary unit im
Machine precision eps() # same as eps(Float64)
Rounding round() # floating-point
round(Int, x) # integer
Type conversions convert(TypeName, val) # attempt/error
typename(val) # calls convert
Global constants pi # 3.1415...
π # 3.1415...
im # real(im * im) == -1
More constants using Base.MathConstants

Julia does not automatically check for numerical overflow. Use package SaferIntegers for ints with overflow checking.

Random Numbers

Many random number functions require using Random.

   
Set seed seed!(seed)
Random numbers rand() # uniform [0,1)
randn() # normal (-Inf, Inf)
Random from Other Distribution using Distributions
my_dist = Bernoulli(0.2) # For example
rand(my_dist)
Random subsample elements from A with inclusion probability p randsubseq(A, p)
Random permutation elements of A shuffle(A)

Arrays

   
Declaration arr = Float64[]
Pre-allocation sizehint!(arr, 10^4)
Access and assignment arr = Any[1,2]
arr[1] = "Some text"
Comparison a = [1:10;]
b = a # b points to a
a[1] = -99
a == b # true
Copy elements (not address) b = copy(a)
b = deepcopy(a)
Select subarray from m to n arr[m:n]
n-element array with 0.0s zeros(n)
n-element array with 1.0s ones(n)
n-element array with #undefs Vector{Type}(undef,n)
n equally spaced numbers from start to stop range(start,stop=stop,length=n)
Array with n random Int8 elements rand(Int8, n)
Fill array with val fill!(arr, val)
Pop last element pop!(arr)
Pop first element popfirst!(a)
Push val as last element push!(arr, val)
Push val as first element pushfirst!(arr, val)
Remove element at index idx deleteat!(arr, idx)
Sort sort!(arr)
Append a with b append!(a,b)
Check whether val is element in(val, arr) or val in arr
Scalar product dot(a, b) == sum(a .* b)
Change dimensions (if possible) reshape(1:6, 3, 2)' == [1 2 3; 4 5 6]
To string (with delimiter del between elements) join(arr, del)

Linear Algebra

For most linear algebra tools, use using LinearAlgebra.

   
Identity matrix I # just use variable I. Will automatically conform to dimensions required.
Define matrix M = [1 0; 0 1]
Matrix dimensions size(M)
Select i th row M[i, :]
Select i th column M[:, i]
Concatenate horizontally M = [a b] or M = hcat(a, b)
Concatenate vertically M = [a ; b] or M = vcat(a, b)
Matrix transposition transpose(M)
Conjugate matrix transposition M' or adjoint(M)
Matrix trace tr(M)
Matrix determinant det(M)
Matrix rank rank(M)
Matrix eigenvalues eigvals(M)
Matrix eigenvectors eigvecs(M)
Matrix inverse inv(M)
Solve M*x == v M\v is better Numerically more stable and typically also faster. than inv(M)*v
Moore-Penrose pseudo-inverse pinv(M)

Julia has built-in support for matrix decompositions.

Julia tries to infer whether matrices are of a special type (symmetric, hermitian, etc.), but sometimes fails. To aid Julia in dispatching the optimal algorithms, special matrices can be declared to have a structure with functions like Symmetric , Hermitian , UpperTriangular, LowerTriangular, Diagonal , and more.

Control flow and loops

   
Conditional if-elseif-else-end
Simple for loop for i in 1:10
println(i)
end
Unnested for loop for i in 1:10, j = 1:5
println(i*j)
end
Enumeration for (idx, val) in enumerate(arr)
println("the $idx-th element is $val")
end
while loop while bool_expr
# do stuff
end
Exit loop break
Exit iteration continue

Functions

All arguments to functions are passed by reference.

Functions with ! appended change at least one argument, typically the first: sort!(arr).

Required arguments are separated with a comma and use the positional notation.

Optional arguments need a default value in the signature, defined with =.

Keyword arguments use the named notation and are listed in the function’s signature after the semicolon:

function func(req1, req2; key1=dflt1, key2=dflt2)
    # do stuff
end

The semicolon is not required in the call to a function that accepts keyword arguments.

The return statement is optional but highly recommended.

Multiple data structures can be returned as a tuple in a single return statement.

Command line arguments julia script.jl arg1 arg2... can be processed from global constant ARGS:

for arg in ARGS
    println(arg)
end

Anonymous functions can best be used in collection functions or list comprehensions: x -> x^2.

Functions can accept a variable number of arguments:

function func(a...)
    println(a)
end

func(1, 2, [3:5]) # tuple: (1, 2, UnitRange{Int64}[3:5])

Functions can be nested:

function outerfunction()
    # do some outer stuff
    function innerfunction()
        # do inner stuff
        # can access prior outer definitions
    end
    # do more outer stuff
end

Functions can have explicit return types

# take any Number subtype and return it as a String
function stringifynumber(num::T)::String where T <: Number
    return "$num"
end

Functions can be vectorized by using the Dot Syntax

# here we broadcast the subtraction of each mean value
# by using the dot operator
julia> using Statistics
julia> A = rand(3, 4);
julia> B = A .- mean(A, dims=1)
3×4 Array{Float64,2}:
  0.0387438     0.112224  -0.0541478   0.455245
  0.000773337   0.250006   0.0140011  -0.289532
 -0.0395171    -0.36223    0.0401467  -0.165713
julia> mean(B, dims=1)
1×4 Array{Float64,2}:
 -7.40149e-17  7.40149e-17  1.85037e-17  3.70074e-17

Julia generates specialized versions Multiple dispatch a type of polymorphism that dynamically determines which version of a function to call. In this context, dynamic means that it is resolved at run-time, whereas method overloading is resolved at compile time. Julia manages multiple dispatch completely in the background. Of course, you can provide custom function overloadings with type annotations. of functions based on data types. When a function is called with the same argument types again, Julia can look up the native machine code and skip the compilation process.

Since Julia 0.5 the existence of potential ambiguities is still acceptable, but actually calling an ambiguous method is an immediate error.

Stack overflow is possible when recursive functions nest many levels deep. Trampolining can be used to do tail-call optimization, as Julia does not do that automatically yet. Alternatively, you can rewrite the tail recursion as an iteration.

Dictionaries

   
Dictionary d = Dict(key1 => val1, key2 => val2, ...)
d = Dict(:key1 => val1, :key2 => val2, ...)
All keys (iterator) keys(d)
All values (iterator) values(d)
Loop through key-value pairs for (k,v) in d
println("key: $k, value: $v")
end
Check for key :k haskey(d, :k)
Copy keys (or values) to array arr = collect(keys(d))
arr = [k for (k,v) in d]

Dictionaries are mutable; when symbols are used as keys, the keys are immutable.

Sets

   
Declaration s = Set([1, 2, 3, "Some text"])
Union s1 ∪ s2 union(s1, s2)
Intersection s1 ∩ s2 intersect(s1, s2)
Difference s1 \\ s2 setdiff(s1, s2)
Difference s1 △ s2 symdiff(s1, s2)
Subset s1 ⊆ s2 issubset(s1, s2)

Checking whether an element is contained in a set is done in O(1).

Collection functions

   
Apply f to all elements of collection coll map(f, coll) or
map(coll) do elem
# do stuff with elem
# must contain return
end
Filter coll for true values of f filter(f, coll)
List comprehension arr = [f(elem) for elem in coll]

Types

Julia has no classes and thus no class-specific methods.

Types are like classes without methods.

Abstract types can be subtyped but not instantiated.

Concrete types cannot be subtyped.

By default, struct s are immutable.

Immutable types enhance performance and are thread safe, as they can be shared among threads without the need for synchronization.

Objects that may be one of a set of types are called Union types.

   
Type annotation var::TypeName
Type declaration struct Programmer
name::String
birth_year::UInt16
fave_language::AbstractString
end
Mutable type declaration replace struct with mutable struct
Type alias const Nerd = Programmer
Type constructors methods(TypeName)
Type instantiation me = Programmer("Ian", 1984, "Julia")
me = Nerd("Ian", 1984, "Julia")
Subtype declaration abstract type Bird end
struct Duck <: Bird
pond::String
end
Parametric type struct Point{T <: Real}
x::T
y::T
end

p =Point{Float64}(1,2)
Union types Union{Int, String}
Traverse type hierarchy supertype(TypeName) and subtypes(TypeName)
Default supertype Any
All fields fieldnames(TypeName)
All field types TypeName.types

When a type is defined with an inner constructor, the default outer constructors are not available and have to be defined manually if need be. An inner constructor is best used to check whether the parameters conform to certain (invariance) conditions. Obviously, these invariants can be violated by accessing and modifying the fields directly, unless the type is defined as immutable. The new keyword may be used to create an object of the same type.

Type parameters are invariant, which means that Point{Float64} <: Point{Real} is false, even though Float64 <: Real. Tuple types, on the other hand, are covariant: Tuple{Float64} <: Tuple{Real}.

The type-inferred form of Julia’s internal representation can be found with code_typed(). This is useful to identify where Any rather than type-specific native code is generated.

Missing and Nothing

   
Programmers Null nothing
Missing Data missing
Not a Number in Float NaN
Filter missings collect(skipmissing([1, 2, missing])) == [1,2]
Replace missings collect((df[:col], 1))
Check if missing ismissing(x) not x == missing

Exceptions

   
Throw SomeExcep throw(SomeExcep())
Rethrow current exception rethrow()
Define NewExcep struct NewExcep <: Exception
v::String
end

Base.showerror(io::IO, e::NewExcep) = print(io, "A problem with $(e.v)!")

throw(NewExcep("x"))
Throw error with msg text error(msg)
Handler try
# do something potentially iffy
catch ex
if isa(ex, SomeExcep)
# handle SomeExcep
elseif isa(ex, AnotherExcep)
# handle AnotherExcep
else
# handle all others
end
finally
# do this in any case
end

Modules

Modules are separate global variable workspaces that group together similar functionality.

   
Definition module PackageName
# add module definitions
# use export to make definitions accessible
end
Include filename.jl include("filename.jl")
Load using ModuleName # all exported names
using ModuleName: x, y # only x, y
import ModuleName # only ModuleName
import ModuleName: x, y # only x, y
import ModuleName.x, ModuleName.y # only x, y
Exports # Get an array of names exported by Module
names(ModuleName)

# include non-exports, deprecateds
# and compiler-generated names
names(ModuleName, all::Bool)

#also show names explicitly imported from other modules
names(ModuleName, all::Bool, imported::Bool)

With using Foo you need to say function Foo.bar(... to extend module Foo’s function bar with a new method, but with import Foo.bar, you only need to say function bar(... and it automatically extends module Foo’s function bar .

Expressions

Julia is homoiconic: programs are represented as data structures of the language itself. In fact, everything is an expression Expr.

Symbols are interned strings Only one copy of each distinct (immutable) string value is stored. prefixed with a colon. Symbols are more efficient and they are typically used as identifiers, keys (in dictionaries), or columns in data frames. Symbols cannot be concatenated.

Quoting :( ... ) or quote ... end creates an expression, just like Meta.parse(str) This form is probably most familiar to people with knowledge of dynamic SQL. The Meta.parse function is similar to Oracle”s and PostgreSQL”s EXECUTE IMMEDIATE statement or SQL Server’s sp_executesql() procedure. , and Expr(:call, ...).

x = 1
line = "1 + $x"         # some code
expr = Meta.parse(line) # make an Expr object
typeof(expr) == Expr    # true
dump(expr)              # generate abstract syntax tree
eval(expr) == 2         # evaluate Expr object: true

Macros

Macros allow generated code (i.e. expressions) to be included in a program.

   
Definition macro macroname(expr)
# do stuff
end
Usage macroname(ex1, ex2, ...) or @macroname ex1, ex2, ...
Built-in macros @test # equal (exact)
@test x ≈ y # isapprox(x, y)
@assert # assert (unit test)
@which # types used
@time # time and memory statistics
@elapsed # time elapsed
@allocated # memory allocated
@profile # profile
@spawn # run at some worker
@spawnat # run at specified worker
@async # asynchronous task
@distributed # parallel for loop
@everywhere # make available to workers

Rules for creating hygienic macros:

  • Declare variables inside macro with local .
  • Do not call eval inside macro.
  • Escape interpolated expressions to avoid expansion: $(esc(expr))

Parallel Computing

Parallel computing tools are available in the Distributed standard library.

   
Launch REPL with N workers julia -p N
Number of available workers nprocs()
Add N workers addprocs(N)
See all worker ids for pid in workers()
println(pid)
end
Get id of executing worker myid()
Remove worker rmprocs(pid)
Run f with arguments args on pid r = remotecall(f, pid, args...)
# or:
r = @spawnat pid f(args)
...
fetch(r)
Run f with arguments args on pid (more efficient) remotecall_fetch(f, pid, args...)
Run f with arguments args on any worker r = @spawn f(args) ... fetch(r)
Run f with arguments args on all workers r = [@spawnat w f(args) for w in workers()] ... fetch(r)
Make expr available to all workers @everywhere expr
Parallel for loop with reducerA reducer combines the results from different (independent) workers. function red sum = @distributed (red) for i in 1:10^6
# do parallelstuff
end
Apply f to all elements in collection coll pmap(f, coll)

Workers are also known as concurrent/parallel processes.

Modules with parallel processing capabilities are best split into a functions file that contains all the functions and variables needed by all workers, and a driver file that handles the processing of data. The driver file obviously has to import the functions file.

A non-trivial (word count) example of a reducer function is provided by Adam DeConinck.

IO

   
Read stream stream = stdin
for line in eachline(stream)
# do stuff
end
Read file open(filename) do file
for line in eachline(file)
# do stuff
end
end
Read CSV file using CSV
data = CSV.read(filename)
Write CSV file using CSV
CSV.write(filename, data)
Save Julia Object using JLD
save(filename, "object_key", object, ...)
Load Julia Object using JLD
d = load(filename) # Returns a dict of objects
Save HDF5 using HDF5
h5write(filename, "key", object)
Load HDF5 using HDF5
h5read(filename, "key")

DataFrames

For dplyr-like tools, see DataFramesMeta.jl.

   
Read Stata, SPSS, etc. StatFiles Package
DescribeSimilar to summary(df) in R. data frame describe(df)
Make vector of column col v = df[:col]
Sort by col sort!(df, [:col])
CategoricalSimilar to df$col = as.factor(df$col) in R. col categorical!(df, [:col])
List col levels levels(df[:col])
All observations with col==val df[df[:col] .== val, :]
Reshape from wide to long format stack(df, [1:n; ])
stack(df, [:col1, :col2, ...])
melt(df, [:col1, :col2])
Reshape from long to wide format unstack(df, :id, :val)
Make Nullable allowmissing!(df) or allowmissing!(df, :col)
Loop over Rows for r in eachrow(df)
# do stuff.
# r is Struct with fields of col names.
end
Loop over Columns for c in eachcol(df)
# do stuff.
# c is tuple with name, then vector
end
Apply func to groups by(df, :group_col, func)
Query using Query
query = @from r in df begin
@where r.col1 > 40
@select {new_name=r.col1, r.col2}
@collect DataFrame # Default: iterator
end

Introspection and reflection

   
Type typeof(name)
Type check isa(name, TypeName)
List subtypes subtypes(TypeName)
List supertype supertype(TypeName)
Function methods methods(func)
JIT bytecode code_llvm(expr)
Assembly code code_native(expr)

Noteworthy packages and projects

Many core packages are managed by communities with names of the form Julia[Topic].

   
Statistics JuliaStats
Differential Equations JuliaDiffEq (DifferentialEquations.jl)
Automatic differentiation JuliaDiff
Numerical optimization JuliaOpt
Plotting JuliaPlots
Network (Graph) Analysis JuliaGraphs
Web JuliaWeb
Geo-Spatial JuliaGeo
Machine Learning JuliaML
Super-used Packages DataFrames # linear/logistic regression
Distributions # Statistical distributions
Flux # Machine learning
Gadfly # ggplot2-likeplotting
LightGraphs # Network analysis
TextAnalysis # NLP

Naming Conventions

The main convention in Julia is to avoid underscores unless they are required for legibility.

Variable names are in lower (or snake) case: somevariable.

Constants are in upper case: SOMECONSTANT.

Functions are in lower (or snake) case: somefunction.

Macros are in lower (or snake) case: @somemacro.

Type names are in initial-capital camel case: SomeType.

Julia files have the jl extension.

For more information on Julia code style visit the manual: style guide .

Performance tips

  • Avoid global variables.
  • Write type-stable code.
  • Use immutable types where possible.
  • Use sizehint! for large arrays.
  • Free up memory for large arrays with arr = nothing.
  • Access arrays along columns, because multi-dimensional arrays are stored in column-major order.
  • Pre-allocate resultant data structures.
  • Disable the garbage collector in real-time applications: disable_gc().
  • Avoid the splat (...) operator for keyword arguments.
  • Use mutating APIs (i.e. functions with ! to avoid copying data structures.
  • Use array (element-wise) operations instead of list comprehensions.
  • Avoid try-catch in (computation-intensive) loops.
  • Avoid Any in collections.
  • Avoid abstract types in collections.
  • Avoid string interpolation in I/O.
  • Vectorizing does not improve speed (unlike R, MATLAB or Python).
  • Avoid eval at run-time.

IDEs Editors and Plugins

Source

See Also

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