Slides for a 20 minute presentation about Julia, with a brief introduction to multiple dispatch/multimethods and how it is used for numerical linear algebra

1. Technical computing in
Jiahao Chen
MIT CSAIL
Alan EdelmanJeff Bezanson Stefan Karpinski Viral B. Shah Andreas Noack Jake Bolewski

2. 720 contributors + package writers

3. https://github.com/jiahao/ijulia-notebooks
The world of
557 packages, 720 authors
345 contributors to julia repo
5,239 stargazers
436 watchers

4. What’s the big deal about Julia ?
A high level language
with C-like speed
julialang.org/benchmarks

5. It bridges the divide between computer science
and computational science
What’s the big deal about Julia ?

6. It bridges the divide between computer science
and computational science
What’s the big deal about Julia ?
data abstraction
performance

7. It bridges the divide between computer science
and computational science
What’s the big deal about Julia ?
data abstraction
performance
What if you didn’t have to choose between
data abstraction and performance?

8. Object-oriented programming with classes
What can I do with/to a thing?

9. methods objects
Object-oriented programming with classes
What can I do with/to a thing?

10. methods objects
Object-oriented programming with classes
What can I do with/to a thing?

11. methods objects
Object-oriented programming with classes
What can I do with/to a thing?
top up
pay fare
lose
buy

12. methods objects
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

13. methods objects
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

14. methods objects
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

15. methods objects
Object-oriented programming with classes
What can I do with/to a thing?
top up
pay fare
lose
buy
classes are more
fundamental
than methods
top up
pay fare
lose
buy
pay fare
lose
buy

16. OOP with classes 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

17. Multi-methods for linear algebra
What can I do with/to a thing?
compute spectral factorization
compute singular values
compute singular values and vectors
compute eigenvalues
generic
function
objectsmethods
Methods can take advantage of special matrix structures
eigvals
eigfact
svdvals
svdfact
Matrix
SymTridiagonal
Bidiagonal

24. easy to call external C
functions, e.g. CLAPACK
sstev, dstev…

25. So how does this help us with linear algebra?
Multi-method dispatch with generic fallbacks
Matrix operations on general rings

26. So how does this help us with linear algebra?
Multi-method dispatch with generic fallbacks
Matrix operations on general rings textbook algorithm

27. So how does this help us with linear algebra?
Multi-method dispatch with generic fallbacks
Matrix operations on general rings

28. Native parallelism constructs

29. Native parallelism constructs

30. Native parallelism constructs

31. JuMP: a domain specific language
Iain Dunning Miles Lubin
MIT
Operations Research

32. http://github.com/JuliaLang/IJulia.jl

33. Summary
Types allow users to express scientific computations
and the compiler to specialize code for performance
Other advanced features for performance: code generation,
native parallel computing, …
MS246: High-level Technical Computing with Julia
4:25 PM - 6:05 PM in Room 254 B

36. Pure-­‐Julia
FFT
performance2
4
8
16
32
64
128
256
512
1024
2048
4096
8192
16384
32768
65536
131072
2621440
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
speed(mflops)
intel-mkl-dfti in-place
intel-mkl-dfti out-of-place
fftw3 out-of-place
fftw3 in-place
fftw3-no-simd out-of-place
fftw3-no-simd in-place
dfftpack
emayer
julia
bloodworth
cross
cwplib
esrfft
double-precision complex, 1d transforms
powers of two
already
comparable
to
FFTPACK
[
actually
was
even
a
bit
better;
some
recent
inlining
regressions
in
Julia
snapshots
]
Steven Johnson, 2014-06
Presented at NAIS Codegen workshop