Alan Edelman Mathematics Computer Science & AI Laboratories June 9, 2014 Jeff Bezanson, Stefan Karpinski, Viral Shah and may collaborators worldwide Try.

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Presentation transcript:

Alan Edelman Mathematics Computer Science & AI Laboratories June 9, 2014 Jeff Bezanson, Stefan Karpinski, Viral Shah and may collaborators worldwide Try Julia/Ijulia today google: julia  downloads 8pm room 4

2/30 Stereotypes Computer Scientists don’t take derivatives but computer scientists are great at abstractions Computational Scientists can’t declare types but computational scientists are great at engineering simulations and numerical algorithms

methodsobjects Object-oriented programming with classes What can I do with/to a thing? top up pay fare lose buy top up pay fare lose buy pay fare lose buy class-based OO classes are more fundamental than methods 3

Object-oriented programming with multi-methods What can I do with/to a thing? top up pay fare lose buy generic function objectsmethods multimethods relationships between objects and functions 4

Multi-methods with type hierarchy top up pay fare lose buy generic function objectsmethods rechargeable subway pass single-use subway ticket is a subtype of subway ticket abstract object 5

6 Poincaré quipped: “Mathematics is the art of giving the same name to different things.” Technical computing is the art of applying operations to objects with the same name that represent different things. -- The Julia Team Abstractions

Multi-methods for linear algebra What can I do with/to a thing? find eigenvalues and eigenvectors find singular values find singular values and vectors find eigenvalues generic function objectsmethods general matrix symmetric tridiagonal matrix bidiagonal matrix Methods can take advantage of special matrix structures eigvals eigfact svdvals svdfact Matrix SymTridiagonal Bidiagonal 7

8/30 The “Two Language” Problem As long as the developers’ language is harder than the users language, technical computing will always be hindered

9/30 What might you ask from your language? A whole laundry list of easy to call functions: elist/ elist/ Performance Can develop libraries Flexibility Parallelism Abstractions Easy to call other languages/unnecessary to call …

10/30 Notebooks to demo What is multiple dispatch? iterators Inspired today Parallel Tracy widom Web server Block SVD Fractals Linear Algebra Tutorial The Colors of Chemistry