« Julia, my new optimization friend » Intro to the Julia programming language, for MATLAB users Date: 14th of June 218 Who: Lilian Besson & Pierre Haessig (SCEE & AUT team @ IETR / CentraleSupélec campus Rennes)
«
Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Agenda for today [25 min] 1. What is Julia [3 min] 2. Comparison with MATLAB [3 min] 3. Examples of problems solved Julia [5 min] 4. Longer example on optimization with JuMP [1min] 5. Links for more information ? [2 min]
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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1. What is Julia ? Developed and popular from the last 7 years Open-source and free programming language (MIT license) Interpreted and compiled, very efficient But easy syntax, dynamic typing, inline documentation etc Multi-platform, imperative MATLAB-like syntax for linear algebra etc Designed and acknowledged as simple to learn and use Easy to run your code in parallel (multi-core & cluster) Used worldwide: research, data science, finance etc… « Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Ressources Website: JuliaLang.org for the language & Pkg.JuliaLang.org for packages Documentation : docs.JuliaLang.org
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Comparison with MATLAB Cost License Comes from Scope Performances
Julia Free Open-source A non-profit foundation, and the community Mainly numeric Very good performance
MATLAB Hundreds of euros / year 1 year user license (no longer after your PhD!) MathWorks company Numeric only Faster than Python, slower than Julia
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Comparison with MATLAB Julia Packaging Editor/IDE Parallel computations
Pkg manager included. Based on git
+ GitHub, very easy to use Jupyter
MATLAB Toolboxes already included but have to pay if you wat more!
is recommended (Juno is also good)
Very easy, low overhead cost
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
Good IDE already included Possible, high overhead
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Comparison with MATLAB Julia Usage Fame Support?
Generic, worldwide
MATLAB Research in academia and industry
Young but starts to be known
Old and known, in decline
Community1 (StackOverflow, mailing lists etc).
By MathWorks
Documentation OK and growing, inline/online Note1 : JuliaPro offer paid licenses, if professional support is needed.
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
OK, inline/online
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How to install Julia
(1/2)
You can try online for free on JuliaBox.com On Linux, Mac OS or Windows: You can use the default installer from the website julialang.org/downloads Takes about 4 minutes... and it's free ! You also need Python 3 to use Jupyter , I suggest to use Anaconda.com/download if you don't have Python yet.
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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How to install Julia
(2/2)
1. Select the binary of your platform
2. Run the binary 3. Wait 4. Done
…
!
! Test with julia in a terminal
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Different tools to use Julia Use julia for the command line for short experiments
Use the Juno IDE to edit large projects Demo time
!
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Different tools to use Julia Use Jupyter notebooks to write or share your experiments (examples: github.com/Naereen/notebooks )
Demo time
!
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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How to install modules in Julia ? Installing is easy ! julia> Pkd.add "IJulia"
# installs IJulia
Updating also! julia> Pkg.update
How to find the module you need ? First
… ask your colleagues
!
Complete list on pkg.JuliaLang.org
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Overview of famous Julia modules for easy plotting like MATLAB The JuliaDiffEq collection for differential equations The JuliaOpt collection for optimization The JuliaStats collection for statistics And many more! Find more specific packages on GitHub.com/svaksha/Julia.jl/ Winston.jl
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Many packages, and a quickly growing community
Julia is still in development, in version v.6 but version 1. is planned soon! « Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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2. Main differences in syntax between Julia and MATLAB Ref: cheatsheets.quantecon.org
File ext. Comment Indexing Slicing Operations Block
Julia
MATLAB
.jl
.m
# blabla
a[ ] to a[end] a[
] (view)
% blabla a a
to a end (
copy)
Linear algebra by default
Linear algebra by default
Use end to close all blocks
Use endif endfor etc
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Help And Or Datatype Array Size Nb Dim Last
Julia
MATLAB
?func
help func
a & b
a
b
a | b
a
b
Arra of any type [
;
]
multi-dim doubles array [
;
]
size a
size a
ndims a
ndims a
a[end]
a end
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Tranpose Conj. transpose Matrix x Element-wise x Element-wise / Element-wise ^ Zeros Ones Identity Range
Julia
MATLAB
a.'
a.'
a'
a'
a * b
a * b
a .* b
a .* b
a ./ b
a ./ b
a ^
a .^
zeros
,
,
zeros
,
,
ones
,
,
ones
,
,
e e range
,
,
or
e e
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Julia
MATLAB
ma a ma ma a ? Maximum Random matrix rand , rand , norm v norm v L2 Norm Inverse inv a inv a a \ b a \ b Solve syst. Eigen vals V, D = eig a [V,D]=eig a fft a , ifft a fft a , ifft a FFT/IFFT Very close to MATLAB for linear algebra!
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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3. Scientific problems solved with Julia Just to give examples of syntax and modules 1. 1D numerical integration and plot 2. Solving a 2nd order Ordinary Differential Equation
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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3.1. 1D numerical integration and plot Exercise : evaluate and plot this function on [-1, 1] :
Ei(x) := ∫
∞
−x
eu du u
How to? Use packages and everything is easy! QuadGK.jl for integration Winston.jl for 2D plotting
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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using QuadGK function Ei , f = t e if > return + else return end end
minfloat= e- , ma float= p t / t # inline function, with '- >' quadgk f, , minfloat [ ] quadgk f, minfloat, ma float [ ] quadgk f,
X = linspace - , Y = [ Ei for
, in X ]
, ma float [ ]
#
points
using Winston plot X, Y title "The function Ei " label " " ; label " " savefig "figures/Ei_integral.png"
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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3.2. Solving a 2nd order ODE Goal : solve and plot the differential equation of a pendulum:
θ′′ (t) + b θ′ (t) + c sin(θ(t)) = 0 For b
= 1/4, c = 5, θ(0) = π − 0.1, θ′ (0) = 0, t ∈ [0, 10]
How to? Use packages! DifferentialEquations.jl function for ODE integration Winston.jl for 2D plotting
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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using DifferentialEquations b, c =
.
,
.
# macro magic! pend = @ode_def Pendulum begin dθ = ω # es, this is UTF8 dω = b * ω - c * sin θ end prob = ODEProblem pend, sol = solve prob t, = sol.t, hcat sol.u
, . , . # ↑ solve on interval [ , '
]
using Winston plot t, [:, ], t, [:, ] title " D Differential Equation" savefig "figures/Pendulum_solution.png"
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Conclusion (1/2) Sum-up I hope you got a good introduction to Julia It's not hard to migrate from MATLAB to Julia Good start: docs.JuliaLang.org/en/stable/manual/getting started
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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Conclusion (2/2) Thanks for joining
!
Your mission, if you accept it... 1.
Train yourself a little bit on Julia ↪ JuliaBox.com ? Or install it on your laptop! And ead introduction in the Julia manual! 2. Jedi level: Try to solve a numerical system, from your research or teaching, in Julia instead of MATLAB 3. Master level: From now on, try to use open-source & free tools for your research (Julia, Python and others)… Padawan level:
« Julia, my new optimization friend » | 14 June 218 | By: Lilian Besson | IETR @ Vannes
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