理研バイオインフォマティクスセミナー

1. Introduction to Julia
for Bioinformatics
Kenta Sato (佐藤建太)
@ Bioinformatics Research Unit, RIKEN ACCC
November 19, 2015
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2. Topics
About Me
Julia
BioJulia
Julia Updates '15
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3. About Me
Graduate school student at the University of Tokyo.
About 2-year experience of Julia programming.
Contributing to Julia and its ecosystem:
https://github.com/docopt/DocOpt.jl
https://github.com/bicycle1885/IntArrays.jl
https://github.com/BioJulia/IndexableBitVectors.jl
https://github.com/BioJulia/WaveletMatrices.jl
https://github.com/BioJulia/FMIndexes.jl
https://github.com/isagalaev/highlight.js (Julia support)
etc.
Core developer of BioJulia - https://github.com/BioJulia/Bio.jl
Julia Summer of Code 2015 Student -
http://julialang.org/blog/2015/10/biojulia-sequence-analysis/
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4. JuliaCon 2015 at MIT, Boston
https://twitter.com/acidflask/status/633349038226690048
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5. Julia is ...
Julia is a high­level, high­performance
dynamic programming language for technical
computing, with syntax that is familiar to users of
other technical computing environments. It provides
a sophisticated compiler, distributed parallel
execution, numerical accuracy, and an extensive
mathematical function library. Julia’s Base library,
largely written in Julia itself, also integrates mature,
best­of­breed open source C and Fortran libraries for
linear algebra, random number generation, signal
processing, and string processing.
— http://julialang.org/
“
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6. Two­Language Problem
In technical computing, users use easier and slower script languages,
while developers use harder and faster compiled languages.
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7. Two­Language Problem
Both users and developers can use a handy language without
sacrificing performance.
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8. Three Virtues of the Julia Language
Simple
Fast
Dynamic
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9. Simple
Syntax with least astonishment
no semicolons
no variable declarations
no argument types
Unicode support
1-based index
blocks end with end
No implicit type conversion
Quick sort with 24 lines
quicksort(xs)=quicksort!(copy(xs))
quicksort!(xs)=quicksort!(xs,1,endof(xs))
functionquicksort!(xs,lo,hi)
iflo<hi
p=partition(xs,lo,hi)
quicksort!(xs,lo,p-1)
quicksort!(xs,p+1,hi)
end
returnxs
end
functionpartition(xs,lo,hi)
pivot=div(lo+hi,2)
pvalue=xs[pivot]
xs[pivot],xs[hi]=xs[hi],xs[pivot]
j=lo
@inboundsforiinlo:hi-1
ifxs[i]≤pvalue
xs[i],xs[j]=xs[j],xs[i]
j+=1
end
end
xs[j],xs[hi]=xs[hi],xs[j]
returnj
end
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10. Fast
Comparable performance to compiled languages.
http://julialang.org/ 10 / 72

11. Fast
The LLVM-backed JIT compiler emits machine code at runtime.
julia>4>>1 #bitwiseright-shiftfunction
2
julia>@code_native4>>1
.section __TEXT,__text,regular,pure_instructions
Filename:int.jl
Sourceline:115
pushq %rbp
movq %rsp,%rbp
movl $63,%ecx
cmpq $63,%rsi
Sourceline:115
cmovbeq%rsi,%rcx
sarq %cl,%rdi
movq %rdi,%rax
popq %rbp
ret
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12. Dynamic
No need to precompile your program.
hello.jl:
println("hello,world")
Output:
$juliahello.jl
hello,world
In REPL:
julia>include("hello.jl")
hello,world
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13. Dynamic
High-level code generation at runtime (macros).
julia>x=5
5
julia>@assertx>0"xshouldbepositive"
julia>x=-2
-2
julia>@assertx>0"xshouldbepositive"
ERROR:AssertionError:xshouldbepositive
julia>macroexpand(:(@assertx>0"xshouldbepositive"))
:(ifx>0
nothing
else
Base.throw(Base.Main.Base.AssertionError("xshouldbepositive"
end)
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14. Who Created?
Jeff Bezanson, Stefan Karpinski, Viral B. Shah, and Alan Edelman
Soon the team was building their dream language.
MIT, where Bezanson is a graduate student, became
an anchor for the project, with much of the work
being done within computer scientist and
mathematician Alan Edelman’s research group. But
development of the language remained completely
distributed. “Jeff and I didn’t actually meet until we’d
been working on it for over a year, and Viral was in
India the entire time,” Karpinski says. “So the whole
language was designed over email.”
— "Out in the Open: Man Creates One Programming Language to Rule Them All" ­
http://www.wired.com/2014/02/julia/
“
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15. Why Created?
In short, because we are greedy.
— "Why We Created Julia" ­ http://julialang.org/blog/2012/02/why­we­created­julia/
“
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16. Why Created?
The creators wanted a language that satisfies:
the speed of C
with the dynamism of Ruby
macros like Lisp
mathematical notations like Matlab
as usable for general programming as Python
as easy for statistics as R
as natural for string processing as Perl
as powerful for linear algebra as Matlab
as good at gluing programs together as the shell
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17. Batteries Included
You can start technical computing without installing lots of libraries.
Numeric types
{8, 16, 32, 64, 128}-bit {signed, unsigned} integers,
16, 32, 64-bit floating point numbers,
and arbitrary-precision numbers.
Numerical linear algebra
matrix multiplication, matrix decomposition/factorization, solver for
system of linear equations, and more!
sparse matrices
Random number generator
Mersenne-Twister method accelerated by SIMD
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18. Batteries Included
You can start technical computing without installing lots of libraries.
Unicode support
Perl-compatible regular expressions (PCRE)
Parallel computing
Dates and times
Unit tests
Profiler
Package manager
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19. Language Design
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20. Literals
#Int64
42
10_000_000
#UInt8
0x1f
#Float64
3.14
6.022e23
#Bool
true
false
#UnitRange{Int64}
1:100
#ASCIIString
"asciistring"
#UTF8String
"UTF8文字列"
#Regex
r"^>[^n]+n[ACGTN]+"
#Array{Float64,1}
#(Vector{Float64})
[1.0,1.1,1.2]
#Array{Float64,2}
#(Matrix{Float64})
[1.0 1.1;
2.0 2.2]
#Tuple{Int,Float64,ASCIIString}
(42,3.14,"asciistring")
#Dict{ASCIIString,Int64}
Dict("one"=>1,"two",=>2)
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21. Functions
All function definitions below are equivalent:
functionfunc(x,y)
returnx+y
end
functionfunc(x,y)
x+y
end
func(x,y)=returnx+y
func(x,y)=x+y
Force inlining:
@inlinefunc(x,y)=x+y
This simple function will be automatically inlined by the compiler.❏
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22. Functions ­ Arguments
Optional arguments:
functionincrement(x,by=1)
returnx+by
end
increment(3) #4
increment(3,2) #5
Keyword arguments:
functionincrement(x;by=1)
returnx+by
end
increment(3) #4
increment(3,by=2)#5
Variable number of arguments:
functionpushback!(list,vals...)
forvalinvals
push!(list,val)
end
returnlist
end
pushback!([]) #[]
pushback!([],1) #[1]
pushback!([],1,2) #[1,2]
Notice semicolon (;) in the argument list above.❏
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23. Functions ­ Return Values
You can return multiple values from a function as a tuple:
functiondivrem64(n)
returnn>>6,n&0b111111
end
And you can receive returned values with multiple assignments:
julia>divrem64(1025)
(16,1)
julia>d,r=divrem64(1025)
(16,1)
julia>d
16
julia>r
1
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24. Functions ­ Document
A document string can be attached to a function definition:
"""
Thisfunctioncomputesquotientandremainder
dividedby64foranon-negativeinteger.
"""
functiondivrem64(n)
returnn>>6,n&0b111111
end
In REPL, you can read the attached document with the ?command:
help?>divrem64
search:divrem64divrem
Thisfunctioncomputesquotientandremainder
dividedby64foranon-negativeinteger.
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25. Types
Two kinds of types:
concrete types: instantiatable
abstract types: not instantiatable
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26. Defining Types
Abstract type:
abstractAbstractFloat<:Real
Composite type:
#mutable
typePoint
x::Float64
y::Float64
end
#immutable
immutablePoint
x::Float64
y::Float64
end
Bits type:
bitstype64Int64<:Signed
Type alias:
typealiasUIntUInt64
Enum:
@enumVotepositivenegative
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27. Parametric Types
Types can take type parameters:
typePoint{T}
x::T
y::T
end
Point: abstract type
Point{Int64}: concrete type
subtype of Point(Point{Int64}<:Point)
all of the members (i.e. xand y) are Int64s
typeNucleotideSequence{T<:Nucleotide}<:Sequence
data::Vector{UInt64}
...
end
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28. Constructors
Julia automatically generates default constructors.
Point(1,2)creates an object of Point{Int}type.
Point(1.0,2.0)creates an object of Point{Float64}type.
Point{Float64}(1,2)creates an object of Point{Float64}type.
Users can create custom constructors.
typePoint{T}
x::T
y::T
end
#outerconstructor
functionPoint(x)
returnPoint(x,x)
end
p=Point(1) #>Point{Int64}(1,1)
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29. Memory Layout
Compact memory layout like C's structs
C compatible memory layout
You can pass Julia objects to C functions without copy.
This is especially important in bioinformatics
when defining data structures for efficient algorithms
when handling lots of small objects
julia>@enumStrandforwardreversebothunknown
julia>immutableExon
chrom::Int
start::Int
stop::Int
strand::Strand
end
julia>sizeof(Exon(1,12345,12446,forward))
32
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30. Multiple Dispatch
Combination of all argument types determines a called method.
Single dispatch (e.g. Python)
The first argument is special and
determines a method.
Multiple dispatch (e.g. Julia)
All arguments are equally
responsible to determine a
method.
classSerializer:
defwrite(self,val):
ifisinstance(val,int)
#...
elifisinstance(val,float)
#...
#...
functionwrite(dst::Serializer,
val::Int64)
#...
end
functionwrite(dst::Serializer,
val::Float64)
#...
end
#...
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31. Multiple Dispatch ­ Example (1)
base/char.jl:
-(x::Char,y::Char) =Int(x)-Int(y)
-(x::Char,y::Integer)=Char(Int32(x)-Int32(y))
+(x::Char,y::Integer)=Char(Int32(x)+Int32(y))
+(x::Integer,y::Char)=y+x
julia>'c'-'a'
2
julia>'c'-1
'b'
julia>'a'+0x01
'b'
julia>0x01+'a'
'b'
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32. Multiple Dispatch ­ Example (2)
functionhas{T<:Integer}(range::UnitRange{Int},target::T)
returnfirst(range)≤target≤last(range)
end
functionhas(iter,target) #sameashas(iter::Any,target::Any)
forelminiter
ifelm==target
returntrue
end
end
returnfalse
end
julia>has(1:10,4)
true
julia>has(1:10,-2)
false
julia>has([1,2,3],2)
true
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33. Metaprogramming
Julia can represent its own program code as a data structure (Expr).
Three metaprogramming components in Julia:
Macros
generate an expression from expressions.
Expr↦ Expr
Generated functions
generate an expression from types.
Types↦ Expr
Non-standard string literals
generate an expression from a string.
String↦ Expr
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34. Metaprogramming ­ Macros
Generate an expression from expressions.
Expr↦ Expr
Denoted as @<macroname>.
Distinguishable from function calls
We've already seen some macros.
macroassert(ex)
msg=string(ex)
:($ex?nothing:throw(AssertionError($msg)))
end
julia>x=-1
-1
julia>@assertx>1
ERROR:AssertionError:x>1
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35. Metaprogramming ­ Useful Macros (1)
@show: print variables, useful for debug:
julia>x=-1
-1
julia>@showx
x=-1
@inbounds: omit to check bounds:
@inboundsh[i,j]=h[i-1,j-1]+submat[a[i],b[j]]
@which: return which function will be called:
julia>@whichmax(1,2)
max{T<:Real}(x::T<:Real,y::T<:Real)atpromotion.jl:239
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36. Metaprogramming ­ Useful Macros (2)
@time: measure elapsed time to evaluate the expression:
julia>xs=rand(1_000_000);
julia>@timesum(xs)
0.022633seconds(27.24kallocations:1.155MB)
499795.2805424741
julia>@timesum(xs)
0.000574seconds(5allocations:176bytes)
499795.2805424741
@profile: profile the expression:
julia>sort(xs);@profilesort(xs);
julia>Profile.print()
69REPL.jl;anonymous;line:92
68REPL.jl;eval_user_input;line:62
...
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37. Generated Functions
Generate a specialized program code for argument types.
Type(s)↦ Expr
Same as function call.
indistinguishable syntax from a calling site
@generatedfunction_sub2ind{N,M}(dims::NTuple{N,Integer},
subs::NTuple{M,Integer})
meta=Expr(:meta,:inline)
ex=:(subs[$M]-1)
fori=M-1:-1:1
ifi>N
ex=:(subs[$i]-1+$ex)
else
ex=:(subs[$i]-1+dims[$i]*$ex)
end
end
Expr(:block,meta,:($ex+1))
end
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38. Non­standard String Literals
Generate an expression from a string.
String↦ Expr
Denoted as <literalname>"..."
Regular expression literal (e.g. r"^>[^n]+n[ACGTN]+") is an
example.
In Bio.jl, dna"ACGT"is converted to a DNASequenceobject.
macror_str(s)
Regex(s)
end
#Regexobject
r"^>[^n]+n[ACGTN]+"
#DNASequenceobject
dna"ACGT"
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39. Modules
Modules are namespace.
Names right under a module are considered as global names.
Import/export system enables to exchange names between
modules.
moduleFoo
exportfoo,gvar
#function
foo()=println("hello,foo")
bar()=println("hello,bar")
#globalvariable
constgvar=42
end
Foo.foo()
Foo.bar()
Foo.gvar
importFoo:foo
foo()
importFoo:bar
bar()
usingFoo
foo()
gvar
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40. Packages
A package manager is bundled with Julia.
No other package manager; this is the standard.
The package manager can build, install, and create packages.
Almost all packages are hosted on GitHub.
Registered packages
Registered packages are public packages that can be installed by
name.
List: http://pkg.julialang.org/
Repository: https://github.com/JuliaLang/METADATA.jl
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41. Packages ­ Management
The package manager is accessible from REPL.
Pkg.update(): update registered package data and upgrade
packages
The way to install a package depends on whether the package is
registered or not.
Pkg.add(<package>): install a registered package
Pkg.clone(<url>): install a package from the git URL
julia>Pkg.update()
julia>Pkg.add("DocOpt")
julia>Pkg.clone("git@github.com:docopt/DocOpt.jl.git")
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42. Packages ­ Create a Package
Package template can be generated with Pkg.generate(<package>).
This generates a disciplined scaffold to develop a new package.
Generated packages will be located in ~/.julia/v0.4/.
Pkg.tag(<package>,<version>)tags the version to the current
commit of the package.
This tag is considered as a release of the package.
Developers should follow Semantic Versioning.
major: incompatible API changes
minor: backwards-compatible functionality addition
patch: backwards-compatible bug fixes
julia>Pkg.generate("DocOpt")
julia>Pkg.tag("DocOpt",:patch) #patchupdate
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43. BioJulia
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44. BioJulia
Collaborative project to build bioinformatics infrastructure for Julia.
Packages:
Bio.jl - https://github.com/BioJulia/Bio.jl
Other packages - https://github.com/BioJulia
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45. BioJulia ­ Basic Principles
BioJulia will be fast.
All contributions undergo code review.
We'll design it to suit modern bioinformatics and Julia, not just copy
other Bio-projects.
https://github.com/BioJulia/Bio.jl/wiki/roadmap
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46. Bio.jl
Major modules:
Bio.Seq: biological sequences
Bio.Intervals: genomic intervals
Bio.Align: sequence alignments (coming soon!)
Bio.Phylo: phylogenetics (common soon!)
Under (active!) development.
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47. Bio.jl
Major modules:
Bio.Seq: biological sequences
Bio.Intervals: genomic intervals
Bio.Align: sequence alignments (coming soon!)
Bio.Phylo: phylogenetics (common soon!)
Under (active!) development.
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48. Sequences
Sequence types are defined in Bio.Seqmodule:
DNASequence, RNASequence, AminoAcidSequence, Kmer
julia>usingBio.Seq
julia>dna"ACGTN" #non-standardstringliteral
5ntDNASequence
ACGTN
julia>rna"ACGUN"
5ntRNASequence
ACGUN
julia>aa"ARNDCWYV"
8aaSequence:
ARNDCWYV
julia>kmer(dna"ACGT")
DNA4-mer:
ACGT
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49. Sequences ­ Packed Nucleotides
A/C/G/Tare packed into an array with 2-bit encoding (+1 bit for N).
typeNucleotideSequence{T<:Nucleotide}<:Sequence
data::Vector{UInt64}#2-bitencodedsequence
ns::BitVector #'N'mask
...
end
In Kmer, nucleotides are packed into a 64-bit type.
bitstype64Kmer{T<:Nucleotide,K}
typealiasDNAKmer{K}Kmer{DNANucleotide,K}
typealiasRNAKmer{K}Kmer{RNANucleotide,K}
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50. Sequences ­ Immutable by Convention
Sequences are immutable by convention.
No copy when creating a subsequence from an existing sequence.
julia>seq=dna"ACGTATG"
7ntDNASequence
ACGTATG
julia>seq[2:4]
3ntDNASequence
CGT
#internaldataissharedbetween
#theoriginalanditssubsequences
julia>seq.data===seq[2:4].data
true
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51. Intervals
Genomic interval types are defined in Bio.Intervalsmodule:
Interval{T}: Tis the type of metadata attached to the interval.
typeInterval{T}<:AbstractInterval{Int64}
seqname::StringField
first::Int64
last::Int64
strand::Strand
metadata::T
end
This is useful when annotating a genomic range:
julia>usingBio.Intervals
julia>Interval("chr2",5692667,5701385,'+',"SOX11")
chr2:5692667-5701385 + SOX11
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52. Intervals ­ Indexed Collections
Set of intervals can be indexed by IntervalCollection:
immutableCDS;gene::ASCIIString;index::Int;end
ivals=IntervalCollection{CDS}()
push!(ivals,Interval("chr6",156777930,156779471,'+',
CDS("ARID1B",1)))
push!(ivals,Interval("chr6",156829227,156829421,'+',
CDS("ARID1B",2)))
push!(ivals,Interval("chr6",156901376,156901525,'+',
CDS("ARID1B",3)))
intersectiterates over intersecting intervals:
julia>query=Interval("chr6",156829200,156829300);
julia>foriinintersect(ivals,query)
println(i)
end
chr6:156829227-156829421 + CDS("ARID1B",2)
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53. Parsers
Parsers are generated from the Ragel state machine compiler.
Finite state machines are described in regular language.
The Ragel compiler generates pure Julia programs.
Actions can be injected into the state transition.
The next Ragel release (v7) will be shipped with the Julia generator.
http://www.colm.net/open-source/ragel/
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54. Parsers ­ FASTA
<name>=<expression>><enteringaction>%<leavingaction>;
FASTA parser:
newline ='r'?'n' >count_line;
hspace =[tv];
whitespace =space|newline;
identifier =(any-space)+ >mark %identifier;
description=((any-hspace)[^rn]*)>mark %description;
letters =(any-space-'>')+ >mark %letters;
sequence =whitespace*letters?(whitespace+letters)*;
fasta_entry='>'identifier(hspace+description)?newline
sequencewhitespace*;
main:=whitespace*(fasta_entry%finish_match)**;
https://github.com/BioJulia/Bio.jl/blob/master/src/seq/fasta.rl
https://github.com/BioJulia/Bio.jl/blob/master/src/seq/fasta.jl
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55. Parsers ­ Fast
Ragel can generate fast parsers.
julia>@timeforrecinopen("hg38.fa",FASTA)
println(rec)
end
>chr1
248956422ntMutableDNASequence
NNNNNNNNNNNNNNNNNNNNNNN…NNNNNNNNNNNNNNNNNNNNNNNN
>chr10
133797422ntMutableDNASequence
NNNNNNNNNNNNNNNNNNNNNNN…NNNNNNNNNNNNNNNNNNNNNNNN
#...
>chrY_KI270740v1_random
37240ntMutableDNASequence
TAATAAATTTTGAAGAAAATGAA…GAATGAAGCTGCAGACATTTACGG
32.198314seconds(174.92kallocations:1.464GB,1.14%gctime)
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56. Alignments
The Bio.Alignmodule supports various pairwise alignment types.
Score maximization:
GlobalAlignment
SemiGlobalAlignment
OverlapAlignment
LocalAlignment
Cost minimization:
EditDistance
LevenshteinDistance
HammingDistance
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57. Alignments ­ Simple Interfaces (1)
julia>affinegap=AffineGapScoreModel(match=5,
mismatch=-4,
gap_open=-3,
gap_extend=-2);
julia>pairalign(GlobalAlignment(),
dna"ATGGTGACT",
dna"ACGTGCCCT",
affinegap)
PairwiseAlignment{Int64,Bio.Seq.NucleotideSequence{Bio.Seq.DNANucleotide},B
score:12
seq:ATGGTGAC-T
||||||
ref:ACG-TGCCCT
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58. Alignments ­ Simple Interfaces (2)
pairalign(<type>,<seq1>,<seq2>,<score/costmodel>)
pairalign(GlobalAlignment(),a,b,model)
pairalign(SemiGlobalAlignment(),a,b,model)
pairalign(OverlapAlignment(),a,b,model)
pairalign(LocalAlignment(),a,b,model)
pairalign(EditDistance(),a,b,model)
pairalign(LevenshteinDistance(),a,b)
pairalign(HammingDistance(),a,b)
Alignment options:
pairalign(GlobalAlignment(),a,b,model,banded=true)
pairalign(GlobalAlignment(),a,b,model,score_only=true)
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59. Alignments ­ Speed (1)
Global alignment of titin sequences (human and mouse):
affinegap=AffineGapScoreModel(BLOSUM62,-10,-1)
a=first(open("Q8WZ42.fasta",FASTA)).seq
b=first(open("A2ASS6.fasta",FASTA)).seq
@timealn=pairalign(
GlobalAlignment(),
Vector{AminoAcid}(a),
Vector{AminoAcid}(b),
affinegap,
)
println(score(aln))
8.012499seconds(601.99kallocations:1.155GB,0.09%gctime)
165611
vs. R (Biostrings):
user systemelapsed
14.042 1.233 15.475
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60. Alignments ­ Speed (2)
vs. R (Biostrings):
user systemelapsed
14.042 1.233 15.475
library(Biostrings,quietly=T)
a=readAAStringSet("Q8WZ42.fasta")[[1]]
b=readAAStringSet("A2ASS6.fasta")[[1]]
t0=proc.time()
aln=pairwiseAlignment(a,b,type="global",
substitutionMatrix="BLOSUM62",
gapOpening=10,gapExtension=1)
t1=proc.time()
print(t1-t0)
print(score(aln))
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61. Indexable Bit Vectors
Bit vectors that supports bit counting in constant time.
rank1(bv,i): Count the number of 1 bits within bv[1:i].
rank0(bv,i): Count the number of 0 bits within bv[1:i].
A fundamental data structure when defining other data structures.
WaveletMatrix, a generalization of the indexable bit vector,
depends on this data structure.
'N'nucleotides in a reference sequence can be compressed
using this data structure.
julia>bv=SucVector(bitrand(10_000_000));
julia>rank1(bv,9_000_000); #precompile
julia>@timerank1(bv,9_000_000)
0.000006seconds(149allocations:10.167KB)
4502258
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62. Indexable Bit Vectors ­ Internals
A bit vector is divided into 256-bit large blocks and each large block is
divided into 64-bit small blocks:
immutableBlock
#largeblock
large::UInt32
#smallblocks
smalls::NTuple{4,UInt8}
#bitchunks(64bits×4=256bits)
chunks::NTuple{4,UInt64}
end
Each block has a cache that counts the number of 1s.
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63. FM­Indexes
Index for full-text search.
Fast, compact, and often used in short-read sequence mappers
(Bowtie2, BWA, etc.).
Product of Julia Summer of Code 2015
https://github.com/BioJulia/FMIndexes.jl
This package is not specialized for biological sequences.
FMIndexes.jl does not depend on Bio.jl.
JIT compiler can optimize code for a specific type at runtime.
julia>fmindex=FMIndex(dna"ACGTATTGACTGTA");
julia>count(dna"TA",fmindex)
2
julia>count(dna"TATT",fmindex)
1
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64. FM­Indexed ­ Queries
Create an FM-Index for chromosome 22:
julia>fmindex=FMIndex(first(open("chr22.fa",FASTA)).seq);
count(pattern,index): count the number of occurrences of pattern:
julia>count(dna"ACGT",fmindex)
37672
julia>count(dna"ACGTACGT",fmindex)
42
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65. FM­Indexed ­ Queries
Create an FM-Index for chromosome 22:
julia>fmindex=FMIndex(first(open("chr22.fa",FASTA)).seq);
locate(pattern,index): locate positions of pattern:
#locatereturnsaniterator
julia>locate(dna"ACGTACGT",fmindex)|>collect
42-elementArray{Any,1}:
20774876
⋮
22729149
#locateallreturnsanarray
julia>locateall(dna"ACGTACGT",fmindex)
42-elementArray{Int64,1}:
20774876
⋮
22729149
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66. Other Julia Orgs You Should Know
Statistics - JuliaStats https://github.com/JuliaStats
https://github.com/JuliaStats/StatsBase.jl
https://github.com/JuliaStats/DataFrames.jl
https://github.com/JuliaStats/Clustering.jl
https://github.com/JuliaStats/Distributions.jl
https://github.com/JuliaStats/MultivariateStats.jl
https://github.com/JuliaStats/NullableArrays.jl
https://github.com/JuliaStats/GLM.jl
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67. Other Julia Orgs You Should Know
Optimization - JuliaOpt https://github.com/JuliaOpt
https://github.com/JuliaOpt/JuMP.jl
https://github.com/JuliaOpt/Optim.jl
https://github.com/JuliaOpt/Convex.jl
Graphs - JuliaGraphs https://github.com/JuliaGraphs
https://github.com/JuliaGraphs/LightGraphs.jl
Database - JuliaDB https://github.com/JuliaDB
https://github.com/JuliaDB/SQLite.jl
https://github.com/JuliaDB/PostgreSQL.jl
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68. Julia Updates '15
68 / 72

69. Julia Updates '15
Julia Computing Inc. was founded.
"Why the creators of the Julia programming language just
launched a startup" - http://venturebeat.com/2015/05/18/why-the-
creators-of-the-julia-programming-language-just-launched-a-
startup/
69 / 72

70. Julia Updates '15
Julia Computing Inc. was founded.
"Why the creators of the Julia programming language just
launched a startup" - http://venturebeat.com/2015/05/18/why-the-
creators-of-the-julia-programming-language-just-launched-a-
startup/
Moore foundation granted Julia Computing $600,000.
"Bringing Julia from beta to 1.0 to support data-intensive, scientific
computing" - https://www.moore.org/newsroom/in-the-
news/2015/11/10/bringing-julia-from-beta-to-1.0-to-support-data-
intensive-scientific-computing
70 / 72

71. Julia Updates '15
Julia Computing Inc. was founded.
"Why the creators of the Julia programming language just
launched a startup" - http://venturebeat.com/2015/05/18/why-the-
creators-of-the-julia-programming-language-just-launched-a-
startup/
Moore foundation granted Julia Computing $600,000.
"Bringing Julia from beta to 1.0 to support data-intensive, scientific
computing" - https://www.moore.org/newsroom/in-the-
news/2015/11/10/bringing-julia-from-beta-to-1.0-to-support-data-
intensive-scientific-computing
Multi-threading Support
https://github.com/JuliaLang/julia/pull/13410
71 / 72

72. Julia Updates '15
Julia Computing Inc. was founded.
"Why the creators of the Julia programming language just
launched a startup" - http://venturebeat.com/2015/05/18/why-the-
creators-of-the-julia-programming-language-just-launched-a-
startup/
Moore foundation granted Julia Computing $600,000.
"Bringing Julia from beta to 1.0 to support data-intensive, scientific
computing" - https://www.moore.org/newsroom/in-the-
news/2015/11/10/bringing-julia-from-beta-to-1.0-to-support-data-
intensive-scientific-computing
Multi-threading Support
https://github.com/JuliaLang/julia/pull/13410
Intel released ParallelAccelerator.jl
https://github.com/IntelLabs/ParallelAccelerator.jl
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