Help talk:Julia

Presentation or workshop ideas

This is a brainstorm of a potential outline for a julia presentation (15m) or workshop (1h) on julia.

• Overview
  • replaces MatLab, R, python
    • matlab to julia translator
    • includes libraries from python, R
  • interpreted and compiled (LLVM)
  • direct integration of external code (C shared libs, R, python) is possible
  • hierarchical types (number, etc.)
    • number: Abstract(Integer, Real, Rational, Complex, Irrational) Int64 Float64 BigInt BigFloat Rational
  • symbolics (\pi π etc.) Base.MathConstants
• REPL user interface
  • \pi tab
  • built in help via ? followed by search word
    • ?int
    • ?big
  • [ add package...
• Examples to cover
  • typeof()
  • subtypes(Number) // real type tree
  • julia types and rational Pi (2-3m)
    • 1/3 vs 1//3
    • rationalize(Int8, pi) // also Int64 BigInt
    • rationalize(Int, pi, tol=0.2) [1]
    • rationalize(BigInt,setprecision(BigFloat,1024) do; BigFloat(pi) end, tol=BigFloat("1e-1024"))
    • eps(1.5)
    • eps(1500.0)
    • eps(BigFloat(1500))
    • using IrrationalConstants; names(IrrationalConstants)
  • matrixes
    • literal
    • matrix fuctions
  • using (and finding?) packages
  • ODE example (see below)
  • simple plot demo (with matricies, below)
  • surface plot demo [2]

future topics to research

• Examples
  • complex numbers
  • benchmark? vs. other languages
  • parallel or distributed computing example
  • gpu / linear algebra example
  • machine learning example
  • example translating matlab to julia (10-15m)
  • example with jupyter notebook
  • example with pluto
  • (advanced) example calling external C / python / R
  • julia + slurm
  • pandas or polars(julia/rust) example

Short presentation might include one or two examples from this list.

Types tree

using AbstractTrees
AbstractTrees.children(d::DataType) = subtypes(d)
print_tree(Number)

Simple plots example

using Plots
x=range(-10,10,length=100)
y=sin.(x)
plot(x,y)

Surface plot example

using Plots
x = y = -10:0.1:10
d(x,y) = sqrt(x*x+y*y)
f(x,y) = sin(d(x,y))/(d(x,y)+1)
z = f.(x', y)
surface(x, y, z)

Points of interest:

• range definition
• short form function definition
• matrix application of linear function
  • permute variable in matrix function call (x')

ODE example

Install

using Pkg
Pkg.add("OrdinaryDiffEq")

using Plots
using OrdinaryDiffEq
function lorenz!(du,u,p,t)
 du[1] = 10.0(u[2]-u[1])
 du[2] = u[1]*(28.0-u[3]) - u[2]
 du[3] = u[1]*u[2] - (8/3)*u[3]
end
u0 = [1.0;0.0;0.0]
tspan = (0.0,100.0)
prob = ODEProblem(lorenz!,u0,tspan)
sol = solve(prob,Tsit5())
plot(sol,idxs=(1,2,3))

References: OrdinaryDiffEq DifferentialEquations Plots tutorial

tweaks

env vars

• JULIA_DEPOT_PATH (defaults to ~/.julia ??)
• JULIA_NUM_THREADS defaults to 1 (alt: auto)

External links

• MIT: Introduction to Computational Thinking with julia