Julia

1. Syntax
2. Unicode Input
3. Packages
4. REPL
5. References

High-Level, Speed of C, Dynamism of Ruby, General Purpose Skills of Python, Meta Programming of Lisp, String Processing Power of Pearl, Linear Algebra Support of Matlab, Statistics Support of R; in a massively parallel situations.

1. Syntax

Rank Polymorphism is available.
; Equivalent to the newline.

1.1. Definition

1.1.1. Type Hierarchy

Number
- Real
  - Float
  - Integer
    - Int
      - Int8
      - Int16
      - Int32
      - Int64
    - BigInt

1.1.2. Variables

x::Integer = 1
x::Char = 'a'
x::String = "hello!"
- String interpolation with "...$var..." or "...$(myfunc())..."
- Regular Expression Literal r"..."
  - Postfix with flags i, m, s and x to modify the behavior.
- Byte Array Literal b"..."
- Version Number Literal v"..."
  - It allows comparison between version numbers.
- Raw String Literal raw"..."
  - Quotation marks still must be escaped.
- Python Literal py"..."
x::Vector = [1, 2, 3]
x::Matrix = [1 2; 3 4]
- Array Interpolation is possible with for loop within the brackets.
x::Rational = 1//2
x::Complex = 1 + 2im

Subtype can be defined with

<:: Subtype Of

1.1.3. Function

function my_function(x::Number, y::Number)
x+y
end
# or
function my_func(x::Number, y::Number)::Number; x+y; end
# or
f(x::Number, y::Number)::Number = x + y

Anonymous Function with

(x, y) -> x+y

Composition ∘ and Pipe |> is available.

1.1.3.1. Multiple Dispatch

Function can have multiple methods via multiple dispatch based on the argument types.

1.1.3.2. Parametric Method

Generic type can be used:

myappend(v::Vector{T}, x::T) where {T<:Number} ...

1.1.3.3. Mutating Function

Function ending with ! means that it might mutate the arguments.

1.1.3.4. Broadcasting

. after the function name (or before for binary functions) vectorizes the function—broadcast it. For example, f.(vector) is equivalent to broadcast(f, vector).

broadcast is a generalization of map. It expands the unary dimensions—dimension of length 1—to match the size.

.= is special. X .= sin.(Y) is equivalent to broadcast!(f, X, Y). Note that X needs to be pre-allocated, which can be done by X = similar(Y).

@. in the beginning of a statement vectorizes every functions within it.

1.2. Operation

a + b + c is the shorthand for +(a, b, c).
^: Exponentiation
Juxtaposition of a number and a variable is multiplication.
÷: Integer Division
%: Remainder

1.3. Control Flow

1.3.1. Ternary Operation

... ? ... : ...

1.3.2. If Statement

if x > n; ... ;elseif x == n; ...; else; ...; end

1.3.3. Short-Circuiting

... && ... and ... || ...

Note that with a single & or |, which is also the binary operation, the second expression will be evaluated regardless of the value of the first expression.

1.3.4. While Loop

while x < n; ...; end

1.3.5. For Loop

for i = 1:n; ...; end
for i in 1:n; ...; end, for i ∈ 1:n; ...; end
for i = 1:n, j=1:n; ...; end

1.4. Struct

struct MyStruct{T<:Real} x::T y::T end

1.4.1. Constructor

Inner constructor method: struct MyStruct ... MyStruct(x, y) = ... end
Outer constructor method: MyStruct(x, y, z) = ... MyStruct(x, y) ...

1.5. Symbol

Starts with :.

1.6. Macro

Starts with @.
@benchmark: Benchmark the function after it.
@show: Show the value of the expression after it.
@which: Similar to the $which in the shell.

1.7. Command

Enclosed by ` which can be piped, or executed with run, read, write.
String interpolation also works.

2. Unicode Input

Use the TeX notations.
The comprehensive list of available symbols

3. Packages

3.1. LinearAlgebra

lu::Matrix -> LU: The LU Decomposition
qr::Matrix -> QRCompact: The QR decomposition
eigen::Matrix -> Eigen: The Spectral Decomposition

3.1.1. Special Matrix Structures

Julia defines special strut for the special matrices to save memory and computation power.
Diagonal, Triangular, Symmetric, Hermitian, …

3.2. Plots

For plotting
plot, scatter, histogram, surface, plot3d

3.3. Symbolics

@variables x to define symbols.

4. REPL

]: Enter Package Environment
?: Enter Help Environment
;: Enter Shell Environment