Introduction to Julia

Introduction to Julia

This is curated from lecture notes on quantecon.org.

Using Packages

using LinearAlgebra, Statistics, Compat

Plotting in Julia

using Plots
gr(fmt=:png) # setting for easier display in jupyter notebooks

n = 100
ϵ = randn(n)
plot(1:n, ϵ)

Arrays:

ϵ[1:5]

5-element Array{Float64,1}:
 -0.5563748011324748 
  1.0086062002662834 
 -0.25949551453379965
 -1.0171126481937203 
 -1.0206506194582479 

M = [1 2; 3.5 4];
typeof(M)

Array{Float64}

For Loops

Using the counter method:

n = 100
ϵ = zeros(n)
for i in 1:n
    ϵ[i] = randn()
end

Using the index of an array:

n = 100
ϵ = zeros(n)
for i in eachindex(ϵ)
    ϵ[i] = randn()
end

Looping directly over the array:

ϵ_sum = 0.0 # careful to use 0.0 here, instead of 0
m = 5
for ϵ_val in ϵ[1:m]
    ϵ_sum = ϵ_sum + ϵ_val
end
ϵ_mean = ϵ_sum / m

User defined Functions

function generatedata(n)
    ϵ = zeros(n)
    for i in eachindex(ϵ)
        ϵ[i] = (randn())^2 # squaring the result
    end
    return ϵ
end

data = generatedata(10)
plot(data)

One line function

# direct solution with broadcasting, and small user-defined function
n = 100
f(x) = x^2

x = randn(n)
plot(f.(x), label="x^2")
plot!(x, label="x") # layer on the same plot