Julia cheatsheet

Ways to work in Julia

REPL (Read-Eval-Print Loop)

This is the default way to start and run Julia.

• Press ] to enter package management mode; press backspace to leave it.

• Press Ctrl-C to interrupt execution.

• Press Ctrl-D to exit.

• Press ? to enter help mode.

• Press Up/Down arrows to walk through the command history.

• There are other interactive utilities described [in the manual]](https://docs.julialang.org/en/v1/stdlib/InteractiveUtils/).

Jupyter notebook

Install the IJulia package, then import it and run IJulia.notebook() at the REPL to launch a session in a web browser.

• You can put multiple lines in a code cell. Press Shift-Enter to execute the cell.

• Click the Stop button (square icon) to interrupt execution.

• Use include Pkg and then Pkg.add, etc. for package management.

Pluto notebook

Unlike a Jupyter notebook, a Pluto notebook is reactive in the sense that a change anywhere affects all of the code cells immediately. To use it, install and import the \texttt{Pluto} package, then use \texttt{Pluto.run()} to launch it in a web browser.

Visual Studio Code

Install the Julia extension and run the REPL in a pane. This option is most like an IDE such as PyCharm or Spyder and has many features to assist with coding.

Basics

Item/Reference	Example
Help on a function	?func
Search help	apropos("topic")
Assign to variable	=
Comment	starts with #
Function definition	function foo(x,y) or foo = (x,y) ->
Other defined symbols	% ÷ ∘
Symbols using LaTeX nomenclature	\beta+Tab, \le+Tab, x\_0+Tab, z\hat+Tab

Input and output

	Example	Package
Integers	176, -1, 0
Floats	3.14, 1.0, 0., NaN, Inf
Scientific notation	1.234e-5
Complex numbers	3+4im, complex(3,4)
Constants	pi, π, exp(1)
Strings	"string"
Show result	@show
Print to screen	print, println
Formatted print	@sprintf, @printf	Printf
Interpolate into string	"x is $x"
Table	pretty_table	PrettyTables

Operators

	Example
Arithmetic	+ - * / ^
Broadcast over array	prefix with dot, or @. in front of all
Equality test	==
Comparison	< <= > >=
Logical AND / OR / NOT	& `
Short-circuit logic	&& `

Errors

Message/Symptom	Possible cause
BoundsError	Accessed a nonexistent array element
MethodError	Probably used the wrong number/type of function arguments
InexactError	Illegal type conversion, maybe by assigning to an array
“Cannot juxtapose string literal”	Invalid string construction
Unexpected array changes	Use copy instead of array reference
Wrong norm	Used norm when opnorm is needed

Iteration

	Example
Predetermined number	for i in 1:10
Based on condition	while abs(x) > 1
Comprehension	[i+j for i in 1:3, j in 1:3]
Generator	sum(k for k in 1:10)

Vectors, matrices, arrays

	Example	Package
All ones, all zeros	ones(4), zeros(2,5)
Random elements	rand(100), randn(3,3)
Concatenate	[1;2;3] vertically, [1 2 3] horizontally
Get dimensions	length, size
Extract diagonal	diag(A), diag(A,-1)	LinearAlgebra
Build by diagonal	diagm([1,2,3]), diagm(1=>[-1,-1])	LinearAlgebra
Access element	x[2], A[1,4]
Access block	x[1:end-1], A[1:4,2:3]
Access row/column	A[4,:], A[:,2:2:end]
Range by step size	0:4, 1:2:9, 5:-1:1
Range by length	range(a,b,length=10)
Make a copy	copy

Linear algebra

	Example	Package
Adjoint/transpose	A'
Inner (scalar) product	dot(x,y)	LinearAlgebra
Outer product	x*v'
Solve linear system	A\b
Solve overdetermined system	A\b
Identity	I, I(5)	LinearAlgebra
Factorizations	lu, qr, Cholesky	LinearAlgebra
Norm	norm, opnorm	LinearAlgebra
Condition number	cond	LinearAlgebra
Eigenvalues	eigen, eigvals, eigs	LinearAlgebra
Singular values	svd, svdvals	LinearAlgebra

Major problem types

	Example	Package
Linear system / least squares	A\b
Sparse matrix	A\b, gmres, minres, cg, eigs	SparseArrays, IterativeSolvers, Arpack
Polynomial interpolation/approximation	fit	Polynomials
Polynomial roots	roots(Polynomial(-1,1,1))	Polynomials
Rootfinding	nlsolve	NLsolve
Integration	quadgk(sin,0,pi)	QuadGK
Initial-value problem	ODEProblem, solve	DifferentialEquations
Boundary-value problem	BVProblem, solve	DifferentialEquations

Graphics

	Example	Package
One variable	plot, scatter, hline, vline	Plots
Two variables	surface, contour, contourf	Plots
Network	graphplot	GraphRecipes
Matrix values	spy	Plots
Modify existing plot	plot! etc., xlabel!, xlims!, title!	Plots
Layouts	layout=(2,1), subplot=2	Plots
Log scales	yscale=:log10	Plots
Colors and images	RGB(1,0,1), Gray.(img)	Images