Introduction to Julia for Bioinformatics

Transcription

1 Introduction to Juli for Bioinformtics This introduction ssumes tht you hve bsic knowledge of some scripting lnguge nd provides n exmple of the Juli syntx. Continuous Assessment Problems In this course problems for you to solve re presented on the ROSALIND website. You cn enroll here. ( Using Juli's REPL (Red, Evlute, Print Loop), you will solve most of these problems by writing nd executing short Juli scripts. Mny of the Juli detils for solving these problems will be covered in clss, some will not. Solve s mny or s few problems s you cn during the semester. Documenttion The min source of informtion is the Juli Documenttion ( You my need to use some externl resources: ( ( So let's just tret it like scripting lnguge, tke hed-first dive into Juli, nd see wht hppens. Firstly, the Juli REPL itself lso provides lots of built-in documenttion nd wys to find out wht's going on. For exmple, the? gets you to the documenttion for type, function, etc. In [1]:?split serch: split splitext splitdir splitdrive rsplit specilized_bitwise_unry Out[1]: split(string, [chrs]; limit=0, keep=true) Return n rry of substrings by splitting the given string on occurrences of the given chrcter delimiters, which my be specified in ny of the formts llowed by serch's second rgument (i.e. single chrcter, collection of chrcters, string, or regulr expression). If chrs is omitted, it defults to the set of ll spce chrcters, nd keep is tken to be flse. The two keyword rguments re optionl: they re mximum size for the result nd flg determining whether empty fields should be kept in the result. To find out wht methods re vilble, we cn use the methods function. For exmple, let's see how split is defined: In [2]: Out[2]: methods(split) 3 methods for generic function split: split{t<:substring{t<:abstrctstring}}(str::t, splitter; limit, keep) t strings/util.jl:126 ( split(str::abstrctstring) t strings/util.jl:151 ( split{t<:abstrctstring}(str::t, splitter; limit, keep) t strings/util.jl:127 ( We cn inspect type by finding its fields with fieldnmes In [3]:?linspce serch: linspce LinSpce Out[3]: linspce(strt, stop, n=50) Construct rnge of n linerly spced elements from strt to stop.

2 In [4]: Out[4]: fieldnmes(linspce) 4-element Arry{Symbol,1}: :strt :stop :len :divisor more bout itertors lter. We cn find out wht type vrible is with the typeof function: In [19]: = [1 2 3; 5 4 6; 9 8 7] typeof() Out[19]: Arry{Int64,2} In [22]: Out[22]: inv() * 3 3 Arry{Flot64,2}: e e e e Arry Syntx The rry syntx is similr to MATLAB's conventions. In [1]: = Vector{Flot64}(5) # Crete length 5 Vector (dimension 1 rry) of Flot64's = [1;2;3;4;5] # Crete the column vector [ ] = [ ] # Crete the row vector [ ] [3] = 2 # Chnge the third element of (using liner indexing) to 2 Out[1]: 1 4 Arry{Int64,2}: In [7]: b = Mtrix{Flot64}(4,2) # Define Mtrix of Flot64's of size (4,2) c = Arry{Flot64}(4,5,6,7) # Define (4,5,6,7) rry of Flot64's mt = [ ] #Define the mtrix inline mt[1,2] = 4 # Set element (1,2) (row 1, column 2) to 4 mt Out[7]: 4 4 Arry{Int64,2}: Note tht the "vlue" of n rry is its pointer to the memory loction. This mens tht rrys which re set equl ffect the sme vlues: In [8]: = [1;3;4] b = b[1] = 10 Out[8]: 3-element Arry{Int64,1}: To set n rry equl to the vlues to nother rry, use copy

3 In [9]: = [1;4;5] b = copy() b[1] = 10 Out[9]: 3-element Arry{Int64,1}: We cn lso mke n rry of similr size nd shpe vi the function similr, or mke n rry of zeros/ones with zeros or ones respectively: In [23]: = [1 4 5] c = similr() d = zeros() e = ones() println(c); println(d); println(e) [ ] [0 0 0] [1 1 1] Note tht rrys cn be index'd by rrys: In [11]: Out[11]: [1:2] 2-element Arry{Int64,1}: 1 4 Arrys cn be of ny type, specified by the type prmeter. One interesting thing is tht this mens tht rrys cn be of rrys: In [12]: Out[12]: = Vector{Vector{Flot64}}(3) [1] = [1;2;3] [2] = [1;2] [3] = [3;4;5] 3-element Arry{Arry{Flot64,1},1}: [1.0,2.0,3.0] [1.0,2.0] [3.0,4.0,5.0] Agin ssignment sets rry ddresses equl: In [13]: Out[13]: b = b[1] = [1;4;5;9] 3-element Arry{Arry{Flot64,1},1}: [1.0,4.0,5.0,9.0] [1.0,2.0] [3.0,4.0,5.0] To solve this, there is recursive copy function: deepcopy In [14]: Out[14]: b = deepcopy() b[1] = [1;2;3] 3-element Arry{Arry{Flot64,1},1}: [1.0,4.0,5.0,9.0] [1.0,2.0] [3.0,4.0,5.0] Mutting functions For high performnce, Juli provides mutting functions. These functions chnge the input vlues tht re pssed in, insted of returning new vlue. By convention, mutting functions t to be defined with! t the nd t to mutte their first rgument. An exmple of mutting function in scle! which scles n rry by sclr (or rry)

4 In [15]: = [1;6;8] scle!(,2) # chnges Out[15]: 3-element Arry{Int64,1}: The purpose of mutting functions is tht they llow one to reduce the number of memory lloctions which is crucil for chiving high performnce. Control Flow Control flow in Juli is pretty stndrd. You hve your bsic for nd while loops, nd your if sttements. There's more in the documenttion. In [16]: for i=1:5 #for i goes from 1 to 5 print(i," ") println() t = 0 while t<5 print(t," ") t+=1 # t = t + 1 println() school = :UKZN if school==:ukzn println("yy!") else println("not even worth discussing.") yy! One interesting feture bout Juli control flow is tht we cn write multiple loops in one line: In [17]: for i=1:2,j=2:4 print(i*j," ") Function Syntx In [18]: Out[18]: f(x,y) = 2x+y # Crete n inline function f (generic function with 1 method) In [19]: f(1,2) # Cll the function Out[19]: 4 In [20]: Out[20]: function f(x) x+2 # Long form definition f (generic function with 2 methods) By defult, Juli functions return the lst vlue computed within them. In [21]: f(2) Out[21]: 4 Multiple Disptch A key feture of Juli is multiple disptch. Suppose tht there is "one function", f, with two methods. Methods re the ctionble prts of function. One method defined s f(::any,::any) nd nother s f(::any), mening tht if you give f two vlues then it will cll the first method, nd if you give it one vlue then it will cll the second method.

5 Multiple disptch works on types. To define disptch on type, use ::Type signifier: In [2]: Out[2]: f(x,y) = 2x+y f (generic function with 1 method) In [3]: Out[3]: f(x::int,y::int) = 3x+2y f (generic function with 2 methods) Juli will disptch onto the strictest cceptible type signture. In [24]: f(2,3) # 3x+2y Out[24]: 12 In [25]: f(2.0,3) # 2x+y since 2.0 is not n Int Out[25]: 7.0 Types in signtures cn be prmetric. For exmple, we cn define method for "two vlues re pssed in, both Numbers nd hving the sme type". Note tht <: mens " subtype of". In [26]: Out[26]: f{t<:number}(x::t,y::t) = 4x+10y f (generic function with 4 methods) In [27]: f(2,3) # 3x+2y since (::Int,::Int) is stricter Out[27]: 12 In [28]: f(2.0,3.0) # 4x+10y Out[28]: 38.0 In [29]: Out[29]: f(1+2im,1+2im) im We will go into more depth on multiple disptch lter since this is the core design feture of Juli. The key feture is tht Juli functions specilize on the types of their rguments. This mens tht f is seprtely compiled function for ech method (nd for prmetric types, ech possible method). The first time it is clled it will compile. Question Cn you explin these timings? In [30]: f(x,y,z,w) = f(1,1,1,1.0) Out[30]: seconds (385 lloctions: KB) seconds (4 lloctions: 160 bytes) seconds (3 lloctions: 144 bytes) seconds (1.33 k lloctions: KB) seconds (5 lloctions: 176 bytes) functions cn lso feture optionl rguments nd return multiple vlues: In [31]: Out[31]: function test_function(x,y;z=0) #z is n optionl rgument if z==0 return x+y,x*y #Return tuple else return x*y*z,x+y+z #Return different tuple test_function (generic function with 1 method)

6 In [32]: x,y = test_function(1,2) Out[32]: (3,2) In [33]: x,y = test_function(1,2;z=3) Out[33]: (6,6) The return type for multiple return vlues is Tuple. The syntx for tuple is (x,y,z,...) or inside of functions you cn use the shorthnd x,y,z,... Note tht functions in Juli re "first-clss". This mens tht functions re just type themselves. Therefore functions cn mke functions, you cn store functions s vribles, pss them s vribles nd return them. For exmple: In [34]: Out[34]: function plytime(x) y = 2+x function test(z=1) 2y + z # y is defined in the previous scope, so it's vilble here z = test() * test() return z,test #End function definition plytime (generic function with 1 method) In [35]: Out[35]: z,t = plytime(2) (81,test) In [36]: t(3) Out[36]: 11 Notice tht test() does not get pssed in y but knows wht y is. This is due to the function scoping rules: n inner function cn know the vribles defined in the sme scope s the function. This rule is recursive, leding us to the conclusion tht the top level scope is globl. Tht mens: In [37]: = 2 Out[37]: 2 defines globl vrible. We will go into more detil on this. Lstly we show the nonymous function syntx. This llows you to define function inline. In [38]: Out[38]: g = (x,y) -> 2x+y (::#3) (generic function with 1 method) In [3]: ((x,y) -> 4x+2y)(4,5) Out[3]: 26 Unlike nmed functions, g is simply function in vrible nd cn be overwritten t ny time: In [40]: Out[40]: g = (x) -> 2x (::#5) (generic function with 1 method) In [41]: g(3) Out[41]: 6 An nonymous function cnnot hve more thn 1 disptch. However, s of v0.5, they re compiled nd thus do not hve ny performnce disdvntges from nmed functions. In [42]: g(4,5) MethodError: no method mtching (::##5#6)(::Int64, ::Int64) Closest cndidtes re: #5(::Any) t In[40]:1

7 Type Declrtion Syntx A type is wht in mny other lnguges is n "object" thing which hs nmed components. An instntition of the type is specific one. For exmple, you cn think of cr s hving n mke nd model. So tht mens Toyot RAV4 is n instntition of the cr type. In Juli, we would define the cr type s follows: In [43]: type Cr mke model We could then mke the instnce of cr s follows: In [44]: Out[44]: mycr = Cr("Toyot","Rv4") Cr("Toyot","Rv4") In [45]: Out[45]: mycr.mke "Toyot" To "enhnce Juli's performnce", one usully likes to mke the typing stricter. For exmple, we cn define WorkshopPrticipnt (notice the convention for types is cpitl letters, CmelCse) s hving nme nd field. The nme will be string nd the field will be Symbol type, (defined by :Symbol, which we will go into plenty more detil lter). In [46]: Out[46]: type WorkshopPrticipnt nme::string field::symbol tony = WorkshopPrticipnt("Tony",:physics) WorkshopPrticipnt("Tony",:physics) As with functions, types cn be set "prmetriclly". For exmple, we cn hve n StffMember hve nme nd field, but lso n ge. We cn llow this ge to be ny Number type s follows: In [47]: Out[47]: type StffMember{T<:Number} nme::string field::symbol ge::t ter = StffMember("Terry",:footbll,17) StffMember{Int64}("Terry",:footbll,17) Most of Juli's types, like Flot64 nd Int, re ntively defined in Juli in this mnner. This mens tht there's no limit for user defined types, only your imgintion. Juli lso hs bstrct types. These types cnnot be instntited but re used to build the type hierrchy. You've lredy seen one bstrct type, Number. You cn define type heirrchies on bstrct types. See the beutiful explntion t: ( Another "version" of type is immutble. When one uses immutble, the fields of the type cnnot be chnged. Mny things like Juli's built-in Number types re defined s immutble in order to give good performnce. One importnt detil in Juli is tht everything is type (nd every piece of code is n Expression type). Thus functions re lso types, which we cn ccess the fields of.

8 In [48]: Out[48]: foo(x) = 2x foo (generic function with 1 method) In [49]: Out[49]: methods(foo) 1 method for generic function foo: foo(x) t In[48]:1 In [50]: Out[50]: fieldnmes(first(methods(foo))) 15-element Arry{Symbol,1}: :nme :module :file :line :sig :tvrs :mbig :speciliztions :lmbd_templte :roots :invokes :clled :isstged :needs_sprm_vls_ducttpe Symbol("") In [51]: Out[51]: first(methods(foo)).nme :foo Some Bsic Types Juli provides mny bsic types. Indeed, you will come to know Juli s system of multiple disptch on types, mening tht the interction of types with functions is core to the design. Lzy Itertor Types While MATLAB or Python hs esy functions for building rrys, Juli ts to side-step the ctul "rry" prt with specilly mde types. One such exmple re rnges. To define rnge, use the strt:stepsize: syntx. For exmple: In [52]: = 1:5 println() b = 1:2:10 println(b) 1:5 1:2:9 We cn use them like ny rry. For exmple: In [53]: println([2]); println(b[3]) 2 5 But wht is b? In [54]: println(typeof(b)) StepRnge{Int64,Int64} b isn't n rry, it's StepRnge. A StepRnge hs the bility to ct like n rry using its fields: In [55]: Out[55]: fieldnmes(steprnge) 3-element Arry{Symbol,1}: :strt :step :stop Note tht t ny time we cn get the rry from these kinds of type vi the collect function:

9 In [56]: Out[56]: c = collect() 5-element Arry{Int64,1}: The reson why lzy itertor types re preferred is tht they do not do the computtions until it's bsolutely necessry, nd they tke up much less spce. We cn check this In = = b = collect(1:100000); seconds (5 lloctions: 192 bytes) seconds (5 lloctions: 192 bytes) seconds (8 lloctions: KB) Notice tht the mount of time the rnge tkes is much shorter. This is mostly becuse there is lot less memory lloction needed: only StepRnge is built, nd ll tht holds is the three numbers. However, b hs to hold numbers, leding to the huge difference. Dictionries Another common type is the Dictionry. It llows you to ccess (key,vlue) pirs in nmed mnner. For exmple: In [5]: d = Dict(:=>2,:b=>:24) println(d[:]) println(d[:b]) 2 24 Tuples Tuples re immutble rrys. Tht mens they cn't be chnged. However, they re super fst. They re mde with the (x,y,z,...) syntx nd re the stndrd return type of functions which return more thn one object. In [7]: tup = (2.,3) # Don't hve to mtch types x,y = (3.0,"hi") # Cn seprte tuple to multiple vribles println(y) hi Metprogrmming Metprogrmming is huge feture of Juli. The key ide is tht every sttement in Juli is of the type Expression. Juli builds n Abstrct Syntx Tree (AST) from the Expressions. You've lredy been exposed to this little bit: Symbol is not string becuse it is prt of the AST. One interesting thing is tht symbol comprisons re O(1) while string comprisons, like lwys, re O(n). Thus you cn think of metprogrmming s "code which tkes in code nd outputs code". One bsic exmple is mcro: In [60]: Out[60]: mcro my_time(ex) return quote locl t0 = time() locl vl = $ex locl t1 = time() println("elpsed time: ", t1-t0, " seconds") (mcro with 1 method) This tkes in n expression ex, gets the time before nd fter evlution, nd prints the elpsed time. Note tht $ex "interpoltes" the expression into the mcro.

10 Tril Problem Here s full whisky bottle. It hs height of 27cm nd dimeter of 7cm, nd contins 750 cubic centimetres of whisky. It hs dome-like indenttion t the bottom like mny bottles hve. <img src="imges/full.jpg" width=600> You were hoping for dry Jnury but spectculrly fell off the wgon lst night. You cn t remember wht hppened but now bottle only hs 14cm of whisky left in it. When you turn the bottle over, it hs 19cm of whisky. <img src="imges/not_full.jpg" width=600> Exercise: Write Juli script tht tkes two numbers s input nd then prints out how mny cubic centermeters of whiskey is left in the bottle. Homework Attempt the follwing problems from the COMP710-Bioinformtics-2018 course on the Roslind website, ( DNA Counting DNA neucleotides FIB Rbbits nd Recurrence Reltions In ech cse you must write Juli script to solve the problem. When you re stisfied with your script tell the Roslind system you re redy. Roslind will generte new input dt for your script. Run your script nd pste your output into the Roslind system. Uplod your script. Press submit. The Roslind will inform you if you re successful. If not, the Roslind system will llow you further ttempts.