Introduc)ontoJulia:Whyarewedoingthistoyou?

(Spring2017)

StevenG.Johnson,MITAppliedMath

MITclasses18.06,18.303,18.330,18.08[56],18.335,18.337,…

Whatlanguageforteachingscien)ficcompu)ng?

Forthemostpart,thesearenothard-coreprogrammingcourses,andweonlyneedliSle“throw-away”scriptsandtoynumericalexperiments.

Almostanyhigh-level,interac)ve(dynamic)languagewitheasyfacili)esforlinearalgebra(Ax=b,Ax=λx),ploZng,mathema)calfunc)ons,andworkingwithlargearraysofdatawouldbefine.

Andtherearelotsofchoices…

Lotsofchoicesforinterac)vemath…

[image:ViralShah]

Justpickthemostpopular?MatlaborPythonorR?

Wefeelguiltypushingalanguageonyouthatwe

arestar;ngtoabandonourselves.

Tradi)onalHLcompu)nglanguageshitaperformancewallin“real”work…eventuallyforceyoutoC,Cython,…

Anewprogramminglanguage?

julialang.org

[begun2009,“0.1”in2013,~35kcommits,“0.5”releaseinFall2016]

AlanEdelmanJeffBezanson

ViralShah

StefanKarpinski

[30+developerswith100+commits,1000+externalpackages,3rdJuliaConin2016]

[MIT]

Ashigh-levelandinterac)veasMatlaborPython+IPython,asgeneral-purposeasPython,

asproduc)vefortechnicalworkasMatlaborPython+SciPy,butasfastasC.

Performanceonsynthe)cbenchmarks[loops,recursion,etc.,implementedinmoststraighjorwardstyle]

(normalizedsothatCspeed=1)

SpecialFunc)onsinJuliaSpecialfunc)onss(x):classiccasethatcannotbevectorizedwell

…switchbetweenvariouspolynomialsdependingonx

ManyofJulia’sspecialfunc)onscomefromtheusualC/Fortranlibraries,butsomearewriSeninpureJuliacode.

PureJuliaerfinv(x)[=erf–1(x)] 3–4×fasterthanMatlab’sand2–3×fasterthanSciPy’s(FortranCephes).

PureJuliapolygamma(m,z)[=(m+1)thderiva)veofthelnΓfunc)on]

~2×fasterthanSciPy’s(C/Fortran)forrealz…andunlikeSciPy’s,samecodesupportscomplexargumentz

Juliacodecanactuallybefasterthantypical“op)mized”C/Fortrancode,byusingtechniques[metaprogramming/codegenera)on]thatarehardinalow-levellanguage.

Pure-JuliaFFTperformance

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spee

d (m

flops

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intel-mkl-dfti in-placeintel-mkl-dfti out-of-placefftw3 out-of-placefftw3 in-placefftw3-no-simd out-of-placefftw3-no-simd in-placedfftpackemayerjuliabloodworthcrosscwplibesrfft

double-precision complex, 1d transformspowers of two

alreadycomparabletoFFTPACK[probablysometweakstoinliningwillmakeitbeSer]

FFTW1.0-likecodegenera)on+recursioninJulia~1/3linesofcodecomparedtoFFTPACK,morefunc)onality

(FFTW,MKL:“unfair”factorof~2frommanualSIMD)

JuliaFFTWw/oSIMD

Genera)ngVandermondematricesgivenx=[α1,α2,…],generate: NumPy(numpy.vander):[followlinks]

Pythoncode…wrapsCcode…wrapsgeneratedCcodetype-genericathigh-level,butlowlevellimitedtosmallsetoftypes.

Wri)ngfastcode“in”PythonorMatlab=miningthestandardlibraryforpre-wriSenfunc)ons(implementedinCorFortran).Iftheproblemdoesn’t“vectorize”intobuilt-infunc)ons,ifyouhavetowriteyourowninnerloops…sucksforyou.

Genera)ngVandermondematricesgivenx=[α1,α2,…],generate: NumPy(numpy.vander):[followlinks]

Pythoncode…wrapsCcode…wrapsgeneratedCcodetype-genericathigh-level,butlowlevellimitedtosmallsetoftypes.

function vander{T}(x::AbstractVector{T}, n=length(x)) m = length(x) V = Array(T, m, n) for j = 1:m V[j,1] = one(x[j]) end for i = 2:n for j = 1:m V[j,i] = x[j] * V[j,i-1] end end return Vend

Julia(type-genericcode):

Genera)ngVandermondematricesfunction vander{T}(x::AbstractVector{T}, n=length(x)) m = length(x) V = Array(T, m, n) for j = 1:m V[j,1] = one(x[j]) end for i = 2:n for j = 1:m V[j,i] = x[j] * V[j,i-1] end end return Vend

note:worksforanycontainerofanytypewith“*”opera)on…performance≠inflexibility

ButIdon’t“need”performance!

Forlotsofproblems,especially“toy”problemsincourses,Matlab/Pythonperformanceisgoodenough.Butifusethoselanguagesforallofyour“easy”problems,thenyouwon’tbepreparedtoswitchwhenyouhitahardproblem.Whenyouneedperformance,itistoolate.Youdon’twanttolearnanewlanguageatthesame)methatyouaresolvingyourfirsttrulydifficultcomputa)onalproblem.

Justvectorizeyourcode?=relyonmatureexternallibraries,opera)ngonlargeblocksofdata,forperformance-cri)calcode

Goodadvice!But…

•Someonehastowritethoselibraries.

•Eventuallythatpersonwillbeyou. —someproblemsareimpossibleor justveryawkwardtovectorize.

ButeveryoneelseisusingMatlab/Python/R/…

Juliaiss)llayoung,nichelanguage.Thatimposesrealcosts—lackoffamiliarity,roughedges,con)nuallanguagechanges.Thesearerealobstacles.ButitalsogivesyouadvantagesthatMatlab/Pythonusersdon’thave.

ButIloseaccesstoallthelibrariesavailableforotherlanguages?

VeryeasytocallC/FortranlibrariesfromJulia,andalsotocallPython…

[ipython.org]

viaIPython/Jupyter:Modernmul)mediainterac)venotebooksmixingcode,results,graphics,richtext,equa)ons,interac)on

“IJulia”

JulialeveragesPython…DirectlycallPythonlibraries(PyCallpackage),

e.g.toplotwithMatplotlib(PyPlotpackage)

gotoliveIJulianotebookdemo…

Gotojuliabox.orgforinstall-freeIJuliaontheAmazoncloud

Seealsojulialang.orgformoretutorialmaterials…