Introduction to julia language

Introduction to Julia Language

Kou Qiang

Sun Yat-sen University

December 6, 2012

Kou Qiang (Sun Yat-sen University) Introduction to Julia Language December 6, 2012 1 / 33

Outline

Outline

1 Overview

2 FeaturesPerformanceParallelismCloud Computing

3 LLVM and Clang

4 Comparison between R and JuliaAdvantages and DisadvantagesThe State of Statistics in Julia

5 Installation and Usage

6 An Example

7 Other Projects


Overview

The blog of Douglas Bates

http://dmbates.blogspot.com/2012/04/r-programmer-looks-at-julia.html


Overview

The Homepage

http://julialang.org/


http://julialang.org/

Overview

Syntax

function mandel(z)

c = z

maxiter = 80

for n = 1: maxiter

if abs(z) > 2

return n-1

end

z = z^2 + c

end

return maxiter

end


Features Performance

Features

1 Overview


3 LLVM and Clang



6 An Example

7 Other Projects



Performance

benchmark times relative to C++ (smaller is better)



R

> fun1r = function () {

+ m = matrix(0, 1000, 1000)

+ s = 0

+ for(i in 1:1000)

+ {

+ for(j in 1:1000)

+ {

+ m[i, j] = runif (1)

+ s = s + m[i, j]

+ }

+ }

+ }

> system.time(fun1r())

user system elapsed

8.113 0.006 8.120



Julia

julia > function fun1j()

m = zeros (1000 , 1000)

s = 0

for i = 1:1000

for j = 1:1000

m[i, j] = rand()

s = s + m[i, j]

end

end

end

julia > @elapsed fun1j()

0.22739791870117188



R

> fun1optr = function () {

+ m = matrix(runif (1000 * 1000) , 1000, 1000)

+ sum(m)

+ }

> system.time(fun1optr ())

user system elapsed

0.132 0.003 0.136



Julia

julia > function fun1optj ()

m = rand (1000 , 1000)

sum(m)

end

julia > @elapsed fun1optj ()

0.010874032974243164



Julia

julia > 1//2

1//2

julia > 11//22

1//2

julia > 987//654 + 12//34 * 56//78

84917//48178


Features Parallelism

Features

1 Overview


3 LLVM and Clang



6 An Example

7 Other Projects


Features Parallelism

Parallelism

$ ./ julia -p 2

M = {rand (1000 ,1000) | i=1:10}

pmap(svd , M)

nheads = @parallel (+) for i=1:100000000

randbit ()

end


Features Cloud Computing

Features

1 Overview


3 LLVM and Clang



6 An Example

7 Other Projects


Features Cloud Computing

Cloud Computing

http://julia.forio.com/


http://julia.forio.com/

LLVM and Clang

LLVM and Clang

LLVM: Low Level Virtual Machine

Clang: an “LLVM native” C/C++/Objective-C compiler

JIT compilation: Just-in-time compilation


LLVM and Clang

LLVM and Clang





LLVM and Clang

LLVM and Clang





Comparison between R and Julia Advantages and Disadvantages

Comparison between R and Julia

1 Overview


3 LLVM and Clang



6 An Example

7 Other Projects



Advantages

A JIT

A richer type system

Multiple dispatch

Parallelism

A cleaner model for accessing libraries of compiled code

Memory-mapped I/O



Advantages

A JIT


Multiple dispatch

Parallelism


Memory-mapped I/O



Advantages

A JIT


Multiple dispatch

Parallelism


Memory-mapped I/O



Advantages

A JIT


Multiple dispatch

Parallelism


Memory-mapped I/O



Advantages

A JIT


Multiple dispatch

Parallelism


Memory-mapped I/O



Advantages

A JIT


Multiple dispatch

Parallelism


Memory-mapped I/O



Disadvantages

Default arguments of functions and named actual arguments infunction calls

The R package system and CRAN

Graphics



Disadvantages



Graphics



Disadvantages



Graphics


Comparison between R and Julia The State of Statistics in Julia

Comparison between R and Julia

1 Overview


3 LLVM and Clang



6 An Example

7 Other Projects



The State of Statistics in Julia

DataFrames

Distributions

Optim

MCMC

NHST: null hypothesis significance testing

Clustering: k-means clustering




DataFrames

Distributions

Optim

MCMC






DataFrames

Distributions

Optim

MCMC






DataFrames

Distributions

Optim

MCMC






DataFrames

Distributions

Optim

MCMC






DataFrames

Distributions

Optim

MCMC




Installation and Usage

Installation and Usage


An Example

Rosenbrock Function Optimization

f (x , y) = (1 − x)2 + 100(y − x2)2

A global minimum at (x , y) = (1, 1) where f (x , y) = 0


An Example


load("src/Optim.jl")

using Optim

function rosenbrock(x:: Vector)

(1.0-x[1]) ^2+100.0*(x[2]-x[1]^2) ^2

end

function rosenbrock_gradient(x:: Vector)

[ -2.0*(1.0 -x[1]) -400.0*(x[2]-x[1]^2)*x[1] ,200.0*(x[2]-x[1]^2)]

end

function rosenbrock_hessian(x:: Vector)

h = zeros(2, 2)

h[1 ,1]=2.0 -400.0*x[2]+1200.0*x[1]^2

h[1 ,2]= -400.0*x[1]

h[2 ,1]= -400.0*x[1]

h[2 ,2]=200.0

h

end


An Example


problem = Dict()

problem [:f] = rosenbrock

problem [:g] = rosenbrock_gradient

problem [:h] = rosenbrock_hessian

problem [: initial_x] = [0.0, 0.0]

problem [: solution] = [1.0, 1.0]

algorithms = [" naive_gradient_descent",

"gradient_descent",

"newton",

"bfgs",

"l-bfgs",

"nelder -mead",

"sa"]


An Example


for algorithm = algorithms

results = optimize(problem [:f],

problem [:g],

problem [:h],

problem [: initial_x],

algorithm ,

10e-8,

true)

print(results)

end


Other Projects

GraphChi: Disk-based large-scale graph computation

“Big Data - small machine”

Implemented in plain C++ and open-source

Support: ALS, SGD, bias-SGD, SVD, NMF, SVD++


Other Projects






Other Projects






Other Projects


A Mac Mini with 8 GB of RAM and 256 GB SSD drivehttp://code.google.com/p/graphchi/


http://code.google.com/p/graphchi/

Other Projects

CUDA

Device FLOPS Price(RMB)

Intel Core i7-980 XE 107.6G 2500∼3500nVIDIA Geforce GTX 690 about 6T 6500∼8000nVIDIA Geforce GT 430 91.564G 250∼450nVIDIA Tesla C2050 1.03T 6000∼8500


Other Projects

PyCUDA

http://documen.tician.de/pycuda/


http://documen.tician.de/pycuda/

Other Projects

PyCUDA

import pycuda.autoinit

import pycuda.driver as drv

import numpy

from pycuda.compiler import SourceModule

mod = SourceModule("""

__global__ void multiply_them (float *dest , float *a, float *b)

{

const int i = threadIdx.x;

dest[i] = a[i] * b[i];

}

""")

multiply_them = mod.get_function("multiply_them")

a = numpy.random.randn (400).astype(numpy.float32)

b = numpy.random.randn (400).astype(numpy.float32)

dest = numpy.zeros_like(a)

multiply_them(

drv.Out(dest), drv.In(a), drv.In(b),

block =(400 ,1 ,1), grid =(1 ,1))

print dest -a*b


Thanks

Thanks

Thank you for your time!


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Introduction to julia language

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