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Intro
duct
ionto
Julia
forR
User
s
Hans
Wer
nerB
orch
ers
Duale
Hoch
schu
leM
annh
eim
Köln
RUs
erGr
oup
Mee
tup
Dece
mbe
r201
4
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
121
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Ove
rview
New
prog
ram
min
glan
guag
essin
ce20
02
2002
IoSm
allt
alk,
LISP
;pr
otot
ype-
base
d20
03Ne
merl
eCL
I;C#
-lik
e,LI
SP20
03Sc
ala
JVM;
Java
,Sm
allt
alk;
stat
.-ty
ped
2004
Groo
vyJV
M;Ja
va,
Pyth
on,
Ruby
,Sm
allt
alk
2004
Nimr
odPy
thon
,Pa
scal
;st
atic
ally
-typ
ed20
05F#
(Mic
roso
ft)
CLI;
C#-l
ike,
OCam
l,Ha
skel
l20
07Cl
ojur
eJV
M,CL
R;LI
SP,
Hask
ell,
Erla
ng20
09Go
(Goo
gle)
C,Ob
eron
;st
atic
ally
type
d20
10Ru
st(M
ozil
la)
C++-
like
,Er
lang
,LI
SP;
LLVM
2012
Juli
aMA
TLAB
(,R)
;mu
lt.d
ispa
tch;
LLVM
2014
Swif
t(A
pple
)Ob
ject
ive-
C;LL
VM
See
also:
Pyth
on+
num
ba,L
uaJI
T,Ru
bini
us,R
LLVM
,Has
kell,
Mat
lab(?
),...
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
122
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Ove
rview
The
LLVM
com
piler
infra
struc
ture
proj
ect
“The
LLVM
proj
ectp
rovid
eslib
rarie
sfor
am
oder
n,in
dust
rials
treng
thop
timize
r,alo
ngwi
thco
dege
nera
tion
supp
ort[
and
inte
grat
edlin
ker]
form
any
CPUs
.The
libra
riesa
rebu
ildar
ound
awe
llsp
ecifi
edco
dere
pres
enta
tion,
calle
dLL
VMIn
term
ediat
eRe
pres
enta
tion
(IR).”
2012
ACM
Softw
are
Syst
emAw
ard
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
123
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Ove
rview
Wha
tisJ
ulia?
“Jul
iais
ahi
gh-le
vel,
high
-per
form
ance
dyna
mic
prog
ram
min
gla
ngua
gefo
rte
chni
calc
ompu
ting,
with
asy
ntax
that
isfa
milia
rto
user
sofo
ther
tech
nica
l[sc
ientifi
c]co
mpu
ting
envir
onm
ents
.
“Jul
ia’sL
LVM
-bas
edju
st-in
-tim
e(J
IT)c
ompi
lerco
mbi
ned
with
the
langu
age’s
desig
nall
owit
toap
proa
chan
dof
ten
mat
chth
epe
rform
ance
ofC.
“The
core
ofth
eJu
liaim
plem
enta
tion
islic
ense
dun
dert
heM
ITlic
ense
.Var
ious
libra
riesu
sed
byth
eJu
liaen
viron
men
tinc
lude
their
own
licen
sess
uch
asth
eGP
L,LG
PL,a
ndBS
D.”
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
124
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Ove
rview
40+
scien
tific
com
putin
gen
viron
men
ts
APL
Axio
mCh
Colt
[Jav
a]Eu
ler
Free
Mat
GAUS
SGD
L/PV
-WAV
EGe
nius
gret
lID
LIg
or_P
rojL
abLa
bVie
wMa
gma
Mapl
eMa
thca
dMa
them
atic
aMA
TLAB
Maxi
maMu
Pad
O-Ma
trix
Octa
veOr
igin
Lab
OxPA
RI/G
PPD
L[Pe
rl]
RRL
aBpl
usRO
OTS-
PLUS
SAGE
SAS
SCaV
iSSc
iLab
SciP
y[Py
thon
]Sc
iRub
ySp
eake
asy
Stat
aSc
iLua
[Lua
JIT]
Yori
ck
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
125
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Julia
synt
axan
dde
velo
pmen
t
REPL
:“He
llo,w
orld
.”ex
ampl
es
»h
="H
ello
";w
="w
orld
"»
prin
tln(
"$h,
$w."
)He
llo,
worl
d.
»v
=[1
,2]
;A
=[1
2;3
4];
»w
=A
*v;
»A
\w
2-el
emen
tAr
ray{
Floa
t64,
1}:
1.0
2.0
»f(
x)=
x*
exp(
x);
»ma
p(f,
[0:0
.1:1
])11
-ele
ment
Arra
y{Fl
oat6
4,1}
:..
.H
ans
WBo
rche
rsKö
lnR
User
Grou
pM
eetu
p20
14-1
2-12
6/
32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Julia
synt
axan
dde
velo
pmen
t
Nice
tieso
fJul
iaSy
ntax
a=
[1.0
,2]
;b
=a;
b[1]
=0;
a#
0,2,
3,..
.γ
=0.
5772
1_56
649_
0153
2_86
f(x,
y,z)
=2x
+3y
+4z
r=
1//3
+1/
/6+
1//1
2+
1//1
5#
13//
20fa
ctor
ial(
big(
100)
)H
=[1
/(i+
j-1)
for
i=1:
8,j=
1:8]
22<
pi^e
<e^
pi<
24#
true
prin
tln(
"The
resu
ltof
pi*e
is$(
pi*e
).")
func
tion
f(x.
..)
for
ain
xpr
intl
n(a)
end
end
�ti
meq,
err
=qu
adgk
(sin
,0,
pi)
[1:5
]|>
x->x
.^2
|>su
m|>
inv
s=
:bfg
s#
symb
ol
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
127
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Julia
synt
axan
dde
velo
pmen
t
Som
edi
ffere
nces
toR
Julia
uses
=fo
rvar
iable
assig
nmen
t.Ve
ctor
sand
mat
rices
defin
edth
roug
hbr
acke
ts[,
];m
atrix
mul
tiplic
atio
n:*,
oper
atio
ns:.
*./
.+;
elem
entw
iseco
mpa
rison
s:.=
=.<
=.<
etc.
Nopa
rent
hese
sreq
uire
din
if,
for,
whil
eco
nstru
cts.
Use
true
inst
ead
ofTR
UE;0
or1
are
notb
oolea
ns.
Julia
dist
ingu
ishes
scala
rs,ve
ctor
s,m
atric
es,o
rarra
ysby
type
;ut
ilize
type
decla
ratio
nsfo
rerro
rhan
dlin
g.Fu
nctio
nar
gum
ents
are
prov
ided
byre
fere
nce,
notb
yva
lue.
Cons
eque
nce:
Func
tions
can
mut
ate
their
argu
men
ts.
Mul
tiple
retu
rnva
lues
thro
ugh
tupl
es;n
olis
tsor
nam
edve
ctor
s.St
atist
icsfu
nctio
nalit
yis
prov
ided
inpa
ckag
es,n
otin
Julia
base
.
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
128
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
How
tosp
eed
upfu
nctio
ns
Trap
ezoid
alru
le—
vect
orize
d
func
tion
trap
z1(x
,y)
loca
ln
=le
ngth
(x)
ifle
ngth
(y)
!=n
erro
r("V
ecto
rsmu
stbe
ofsa
mele
ngth
")en
dsu
m((x
[2:e
nd]-
x[1:
end-
1]).
*(y[
2:en
d]+y
[1:e
nd-1
]))/
2en
d
»x
=li
nspa
ce(0
,pi
,10
0);
y=
sin(
x);
»pr
intl
n(tr
apz1
(x,
y));
gc()
1.99
9832
1638
9399
24»
@tim
e[t
rapz
1(x,
y)fo
ri
in1:
1000
];el
apse
dti
me:
0.02
0384
185
seco
nds
(692
1872
byte
sal
loca
ted)
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
129
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
How
tosp
eed
upfu
nctio
ns
Trap
ezoid
alru
le—
non-
vect
orize
d
func
tion
trap
z2(x
,y)
loca
ln
=le
ngth
(x)
ifle
ngth
(y)
!=n
erro
r("V
ecto
rs’x
’,’y
’mu
stbe
ofsa
mele
ngth
")en
dr
=0
ifn
==1
retu
rnr;
end
for
iin
2:n
r+=
(x[i
]-
x[i-
1])
*(y
[i]
+y[
i-1]
)en
dr
/2
end
»@t
ime
[tra
pz2(
x,y)
for
iin
1:10
00];
elap
sed
time
:0.
0096
1744
5se
cond
s(3
2159
04by
tes
allo
cate
d)
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1210
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
How
tosp
eed
upfu
nctio
ns
Trap
ezoid
alru
le—
type
-stab
le
func
tion
trap
z3(x
,y)
loca
ln
=le
ngth
(x)
ifle
ngth
(y)
!=n
erro
r("V
ecto
rs’x
’,’y
’mu
stbe
ofsa
mele
ngth
")en
dr
=0.
0if
n==
1re
turn
r;en
dfo
ri
in2:
nr
+=(x
[i]
-x[
i-1]
)*
(y[i
]+
y[i-
1])
end
r/
2en
d
@tim
e[t
rapz
3(x,
y)fo
ri
in1:
1000
];el
apse
dti
me:
0.00
1451
867
seco
nds
(479
04by
tes
allo
cate
d)
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1211
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
How
tosp
eed
upfu
nctio
ns
Trap
ezoid
alru
le—
w/o
boun
dsch
eckin
g
func
tion
trap
z{T<
:Num
ber}
(x::
Arra
yT,1
,y:
:Arr
ayT,
1)lo
cal
n=
leng
th(x
)if
leng
th(y
)!=
ner
ror(
"Vec
tors
’x’,
’y’
must
beof
same
leng
th")
end
r=
zero
(T)
ifn
==1
retu
rnr
end
for
iin
2:n
@inb
ound
sr
+=(x
[i]
-x[
i-1]
)*
(y[i
]+
y[i-
1])
end
r/
2en
d
»@t
ime
[tra
pz(x
,y)
for
iin
1:10
00];
elap
sed
time
:0.
0007
3023
3se
cond
s(4
7904
byte
sal
loca
ted)
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1212
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
How
tosp
eed
upfu
nctio
ns
Trap
ezoid
alru
le—
com
paris
ons
Resu
ltsan
dco
mpa
rison
with
Ran
dPy
thon
Timi
ngs
Resu
ltµ
s/lo
optr
apz1
0.02
0384
185
1.99
9832
1638
9399
2420
.4tr
apz2
0.00
9617
445
1.99
9832
1638
9399
299.
6tr
apz3
0.00
1451
867
1.99
9832
1638
9399
291.
5tr
apz
0.00
0740
450
1.99
9832
1638
9399
290.
75
R:un
vect
.28
5µ
s,ve
ct.
19µ
sco
mp:
78µ
s,15
µs
(=Re
njin
?)Rc
pp:
unve
ct.
3.5
µs
(inl
ine)
Pyth
on:
unve
ct.
119
µs,
vect
.39
µs
numb
a:un
vect
.0.
72µ
s,ve
ct.
54µ
s
MATL
AB:
unve
ct.
12µ
s,ve
ct.
35µ
sOc
tave
:un
vect
.20
00µ
s,ve
ct.
200
µs
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1213
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
How
tosp
eed
upfu
nctio
ns
Perfo
rman
cetip
s
Avoi
dgl
obal
varia
bles
(orm
ake
them
cons
t).
Forb
estp
erfo
rman
ce,u
seno
n-ve
ctor
ized
code
;de
vect
orize
arra
yas
signm
ents
,writ
eex
plici
telo
ops,
etc.
Brea
kfu
nctio
nsin
tom
ultip
lede
finiti
ons,
base
don
type
s.Ty
pest
abili
ty:A
void
chan
ging
the
type
ofa
varia
ble.
Acce
ssar
rays
inm
emor
yor
der,
i.e.,
along
colu
mns
.Av
oid
arra
yswi
thab
stra
ctty
pepa
ram
eter
s:Ve
ctor
{Rea
l}Pa
yat
tent
ion
tom
emor
yal
loca
tions
(see
mac
ro@t
ime)
:pr
eallo
cate
large
rdat
ast
ruct
ures
(arra
ys);
avoi
dth
ene
edto
copy
data
stru
ctur
es.
Appl
ype
rform
ance
anno
tatio
nsif
appr
opria
te(e
.g.,
@inb
ound
s)
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1214
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Type
Syst
em
Julia
’snu
mer
icalt
ypes
Numb
er Real
Floa
ting
Poin
tBi
gFlo
atFl
oat6
4Fl
oat3
2Fl
oat1
6In
tege
rBi
gInt
Sign
ed Int1
28In
t64
[=In
t=]
Int3
2In
t16
Int8
Unsi
gned
Uint
128
Uint
64Ui
nt32
Uint
16Ui
nt8
Bool
Char
Rati
onal
Comp
lex
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1215
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Type
Syst
em
Oper
ator
over
loadi
ng
»me
thod
s(+)
#14
6me
thod
sfo
rge
neri
cfu
ncti
on+
+(x:
:Boo
l)at
bool
.jl:
34+(
x::B
ool,
y::B
ool)
atbo
ol.j
l:37
+(y:
:Flo
atin
gPoi
nt,x
::Bo
ol)
atbo
ol.j
l:47
...
»+(
s,t)
=s
*t
#wo
uld
bewr
ong
»++
(s,
t)=
s*
t#
isno
tpo
ssib
le»
⊕(s
,t)
=s
*t
#is
not
advi
sabl
e
»+(
s::S
trin
g,t:
:Str
ing)
=s
*t
»"1
23"
+".
.."
+"x
yz"
#=>
"123
...x
yz"
»+(
"123
",".
..",
"xyz
")»
+(["
123"
,".
..",
"xyz
"]..
.)
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1216
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Type
Syst
em
User
-defi
ned
(or:
com
posit
e)ty
pes
immu
tabl
eGa
ussI
nt<:
Numb
er#
or:
type
Gaus
sInt
a::I
ntb:
:Int
#Ga
ussI
nt(n
::In
t,m:
:Int
)=
new(
n,m)
end
Gaus
sInt
(1,
1)#=
>Ga
ussI
nt(1
,1)
impo
rtBa
se.s
how,
Base
.nor
m,Ba
se.i
spri
mesh
ow(i
o::I
O,x:
:Gau
ssIn
t)=
show
(io,
comp
lex(
x.a,
x.b)
)Ga
ussI
nt(1
,1)
#=>
1+
1im
*(x:
:Gau
ssIn
t,y:
:Gau
ssIn
t)=
Gaus
sInt
(x.a
*y.a
-x.
b*y.
b,x.
a*y.
b+
x.b*
y.a)
;no
rm(x
::Ga
ussI
nt)
=x.
a^2
+x.
b^2;
ispr
ime(
x::G
auss
Int)
=is
prim
e(no
rm(x
));
#wr
ong!
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1217
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Opt
imiza
tion
Mod
eling
Optim
izatio
npa
ckag
esin
Julia
Opt
im–
BFGS
,CG,
simul
ated
anne
aling
GLP
K,C
bc,C
lp–
mixe
d-in
tege
rlin
earp
rogr
amm
ing
CPLE
X,G
urob
i,M
osek
–in
terfa
cing
com
mer
cials
yste
ms
Ipop
t–
inte
rface
toth
eIP
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vex
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ase
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Find
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least
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res,
allm
inim
a
Han
sW
Borc
hers
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erGr
oup
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tup
2014
-12-
1218
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Opt
imiza
tion
Mod
eling
JuM
P–
Julia
forM
athe
mat
icalP
rogr
amm
ing
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ain-sp
ecifi
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atica
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athe
mat
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class
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P,M
ILP,
SOCP
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linea
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min
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ppor
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eed:
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lemcr
eatio
nfa
ster
than
com
mer
cialm
odeli
ngto
ols
(AM
PL,G
AMS,
etc.)
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1219
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Opt
imiza
tion
Mod
eling
Mod
eling
exam
ple:
Knap
sack
prob
lem
»p
=[9
2,57
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ri
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[1,1
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]#
1,2,
3,10
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1220
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Opt
imiza
tion
Mod
eling
Auto
mat
icDi
ffere
ntiat
ion(A
D)Au
tom
atic
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rent
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ase
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ique
sto
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erica
llyev
aluat
eth
ede
rivat
iveof
afu
nctio
nsp
ecifi
edby
aco
mpu
terp
rogr
am.”
Exam
ple:
lam
bert
Wis
anite
rativ
elyde
fined
func
tion
com
putin
gth
eLa
mbe
rtW
spec
ialfu
nctio
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mber
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Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1221
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Stat
istics
with
Julia
Stat
istics
pack
ages
inJu
lia
Stat
sBas
e,Di
strib
utio
nsDi
stan
ces,
Clus
terin
gHy
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men
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ram
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oug
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CMC
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ase
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RegE
RMs
SVM
,Neu
ralN
ets
Han
sW
Borc
hers
Köln
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erGr
oup
Mee
tup
2014
-12-
1222
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Stat
istics
with
Julia
Data
Arra
ysan
dDa
taFr
ames
»us
ing
RDat
aset
s#
700+
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tase
ts»
plan
ets
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tase
t("H
SAUR
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anet
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ass]
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ing
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ys#
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ppor
t»
usin
gDa
taFr
ames
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scri
be(p
lane
ts)
#su
mmar
y
The
Dat
aFra
mes
pack
age
supp
orts
func
tiona
lity
like
the
follo
wing
:jo
in,s
plit-
appl
y-co
mbi
neso
rting
,res
hapi
ngfa
ctor
s,m
odel
fram
es(fo
rmul
ae)
Han
sW
Borc
hers
Köln
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erGr
oup
Mee
tup
2014
-12-
1223
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Calli
ngO
ther
Lang
uage
s
Callin
gC
and
Fortr
an
Shar
edlib
rary
spec
fun.
soha
sbee
nge
nera
ted
with
the
Rco
mm
and
“RCM
DSH
LIB
spec
fun.
f”
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=0.
5»
y=
ccal
l((:
gamm
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ecfu
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unct
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libr
ary)
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put
type
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tupl
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);#
inpu
t(s)
»y
1.77
2453
8509
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sqrt
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But:
The
Julia
Core
team
inte
ndst
om
ake
poss
ible
the
com
pilat
ion
ofJu
liafu
nctio
nsan
dpa
ckag
esin
tosh
ared
libra
ries!
BUT:
... Han
sW
Borc
hers
Köln
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erGr
oup
Mee
tup
2014
-12-
1224
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Calli
ngO
ther
Lang
uage
s
Rca
lling
Julia
?
“Jul
iaha
sani
cean
dsim
ple
Cin
terfa
ce.S
oth
atge
tsus
som
ethi
nglik
e.C
().
Buta
srec
ently
disc
usse
don
r-dev
el,yo
ure
ally
dono
twan
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mos
tca
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ther
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esre
pres
entin
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objec
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orig
htno
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ulia
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eof
this
limita
tion.
May
bean
indi
rect
inte
rface
usin
gtc
p/ip
toRs
erve
coul
dbe
afir
stst
art
befo
reJu
liam
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esa
little
and
wege
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oper
C++
inte
rface
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dth
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dof
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day,
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epa
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anno
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erlim
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ities
then
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the
full
prom
iseof
the
Sla
ngua
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fcou
rse,
sowe
knew
weha
da
win
ner)
.[...
]Ju
liam
aywe
llge
tthe
re.B
utfo
rnow
Isus
pect
man
yof
uswi
llge
twor
kdo
nein
R,an
dha
veju
sta
few
curio
usgl
imps
esat
Julia
.”Di
rkEd
delb
ütte
l,St
acko
verfl
ow,A
pril
1,20
12H
ans
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rche
rsKö
lnR
User
Grou
pM
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p20
14-1
2-12
25/
32In
trod
uctio
nto
Julia
forR
User
sCa
lling
Oth
erLa
ngua
ges
Para
lleliz
ation
“Jul
iapr
ovid
esa
mul
tipro
cess
ing
envir
onm
entb
ased
onm
essa
gepa
ssin
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allow
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ram
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run
onm
ultip
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sepa
rate
mem
ory
dom
ainsa
tonc
e.”
$ju
lia
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...
»r
=re
mote
call
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2)»
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pawn
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2)»
s=
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nd(2
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ef(
x)=
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remo
teca
ll_f
etch
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f,1)
»r2
=re
mote
call
_fet
ch(2
,f,
2)
Han
sW
Borc
hers
Köln
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erGr
oup
Mee
tup
2014
-12-
1226
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Plot
ting
and
Pyth
on
Gram
mar
ofGr
aphi
csin
Julia
»us
ing
Gadf
ly»
xs=
lins
pace
(-0.
3,5.
0);
ys=
map(
lamb
ertW
,xs
);»
fig
=pl
ot(x
=xs,
y=ys
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om.l
ine,
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e.ti
tle=
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bert
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g)
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0.0
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1.0
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Lam
bert
W f
unct
ion
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1227
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Plot
ting
and
Pyth
on
Callin
gPy
thon
Exam
ple:
Func
tion
inte
rpol
atio
n,sy
mbo
licin
tegr
atio
n
»us
ing
PyCa
ll»
xs=
[1.0
:10]
;ys
=sq
rt(x
s);
»@p
yimp
ort
scip
y.in
terp
olat
eas
spi
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y=
spi.
inte
rp1d
(xs,
ys,
kind
="cu
bic"
)»
pyca
ll(f
py,
Floa
t64,
pi)
#1.
7723
4955
2838
2518
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ing
SymP
y»
x,y,
z=
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"xy
z")
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mit(
sin(
x)/x
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1)#
1»
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inte
grat
e(si
n(x)
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6247
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Han
sW
Borc
hers
Köln
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erGr
oup
Mee
tup
2014
-12-
1228
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Refe
renc
esan
dO
utlo
ok
Web
Reso
urce
s
Julia
hom
epa
ge:j
ulial
ang.
org
Sour
ceCo
de:g
ithub
.com
/Jul
iaLan
g/ju
liaPe
rsona
lPac
kage
Arch
ives:
/jul
iarele
ases
[0.3
],/j
ulian
ight
lies[
0.4]
Avai
labl
epa
ckag
es:h
ttp:/
/iain
nz.g
ithub
.io/p
acka
ges.j
ulial
ang.
org/
Julia
Man
ual:
http
://d
ocs.j
ulial
ang.
org/
en/r
eleas
e-0.
3/m
anua
l/M
ailin
gLi
st:
http
s://g
roup
s.goo
gle.c
om/f
orum
/?fro
mgr
oups
=#
!foru
m/j
ulia-
user
sJu
liaB
logr
oll:
http
://w
ww.ju
liabl
ogge
rs.co
m/
The
Julia
Man
uali
saqu
itere
ason
able
intro
duct
ion
toth
eJu
lialan
guag
e.
David
Sand
ers:
Julia
tuto
rial,
SciP
y20
14St
even
John
son:
Keyn
ote
talk,
Euro
SciP
y20
14
Han
sW
Borc
hers
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oup
Mee
tup
2014
-12-
1229
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Intr
oduc
tion
toJu
liafo
rRUs
ers
Refe
renc
esan
dO
utlo
ok
Edito
rsfo
rJul
iade
velop
men
t
Julia
Stud
io[o
utda
ted,
com
m.?
]Li
ght
Tabl
e(w
/Je
wel/
Juno
plug
in)
IPyt
hon
note
book
(w/
IJul
ia)se
eth
eJu
pyte
rpr
ojec
tEd
itors
with
synt
axhi
ghlig
htin
g(a
ndau
to-c
ompl
etio
n):
Subl
ime
Text
3(w
/Su
blim
e-Ju
lia)[
Linu
x]Te
xtM
ate
[Mac
],ge
dito
rKat
e[L
inux
]No
tepa
d++
[Win
dows
]Ec
lipse
(w/
LiCl
ipse
)Em
acs(
w/ju
lia-m
ode.e
l)vim
(w/
julia
-vim
)
Han
sW
Borc
hers
Köln
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erGr
oup
Mee
tup
2014
-12-
1230
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Refe
renc
esan
dO
utlo
ok
Julia
Spec
ialIn
tere
stGr
oups
Spec
ialIn
tere
stGr
oups
(SIG
s)in
Julia
have
afu
nctio
nsim
ilart
oth
e‘T
ask
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s’in
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tthe
yals
okin
dof
orga
nize
the
task
area
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liaO
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mat
hem
atica
lopt
imiza
tion
Julia
Stat
–st
atist
icsan
dm
achi
nelea
rnin
gJu
liaQ
uant
–qu
antit
ative
finan
ceJu
liaD
iff–
diffe
rent
iatio
nto
ols
Julia
DB
–da
taba
sein
tegr
atio
n
BioJ
ulia,
Julia
Astro
,Jul
iaQua
ntum
Julia
Spar
se,J
uliaG
PU,J
uliaW
eb
Han
sW
Borc
hers
Köln
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erGr
oup
Mee
tup
2014
-12-
1231
/32
Intr
oduc
tion
toJu
liafo
rRUs
ers
Refe
renc
esan
dO
utlo
ok
Conc
lusio
ns/
Ques
tions
1W
illJu
liasu
rvive
and
beco
me
am
ayor
play
er?
2..
.3 4 5 6 7 8 9 10
Han
sW
Borc
hers
Köln
RUs
erGr
oup
Mee
tup
2014
-12-
1232
/32
