matlab - caltech astronomygeorge/aybi199/oldlectures/donalek_matlab1.pdf · • applicaon...

MatlabCiroDonalek

Ay/Bi199ab:MethodsofComputa=onalSciences‐hAp://esci101.blogspot.com

[email protected]

Summary•  Introduc=ontoMatlab•  ProgramminginMatlab–  datatypes,variables–  loopsvsBuilt‐InFunc=ons

•  MatrixandArrayOpera=ons–  SubmatricesandColumnNota=on

•  M‐Files–  script,func=ons

•  Visualiza=on•  Performanceevalua=onandimproving•  AdvancedUse–  Compiler,Databaseconnec=on,HowtobuildaGUI...

•  ThirdPartytoolboxesAy/Bi199ab:MethodsofComputa=onalSciences‐hAp://esci101.blogspot.com

WhatisMatlab?•  MATLABisaninterac=ve,matrix‐basedsystemforscien=ficand

technicalcompu=ng.


•  Itismatrixoriented,thatmeansthatallthematrixopera=onsarehighlyop=mized.

•  Itintegratescomputa=on,visualiza=onandprogramminginaneasy‐to‐useenvironment.

TypicalUsesMatlabisusedinmanyfieldsfor:

•  MathandComputa=on•  AlgorithmDevelopment•  DataAcquisi=on•  Modeling,Simula=on,andPrototyping•  DataAnalysis,Explora=on,andVisualiza=on•  Scien=ficandEngineeringGraphics•  Applica=onDevelopment,includingGraphicalUserInterfacebuilding


Ge[ngMatlab


Proprietaryso\ware:distributedbyMathWorks:hAp://www.mathworks.comLatestversion:2009a(releasedMarch6th,2009)

Mul=plaaorm:availableforLinux,Mac,Solaris,Windows.

Supportfor64bitsarchitectures.

*Caltechpersonnelcandownloaditforfreeat:

hAp://so\ware.caltech.edu/

MatlabFamilyProducts•  Availablemanytoolboxesforspecificapplica=ons.


ProgramminginMatlab•  TheLanguage

–  TheMATLABlanguageisahigh‐levelmatrixorientedlanguagewith:•  controlflowstatements(loops,condi=onals)•  func=ons,datastructures,input/output,andobject‐orientedprogrammingfeatures

•  ithashigh‐levelfunc=onsfortwo‐dimensionalandthree‐dimensionaldatavisualiza=on,imageprocessing,anima=on...

•  Mathema=calFunc=onLibrary–  Thislibraryisavastcollec=onofcomputa=onalalgorithmsrangingfromelementaryfunc=ons,likesum,sine,cosine,andcomplexarithme=c,tomoresophis=catedfunc=onslikematrixinverse,matrixeigenvalues,andfastFouriertransforms.

•  Itcanbeusedforbothsmallandlargeapplica=ons.


Variables•  MATLABdoesnotrequireanytypedeclara=onsordimensionstatements.–  newvariablename:automa=callycreatesthevariableandallocatestheappropriateamountofstorage

>>num=3;%createsadouble"num"bydefault–  ifthevariablealreadyexists:MATLABchangesitscontents(andallocatesnewstorageifneeded)

>>num=[13];%numbecomesanarray

•  Variablename(casesensi=ve)–  anylengthbutusesonlythefirstN(namelengthmax)–  leAer,followedbyanynumberofleAers,digits,orunderscores


SpecialVariables•  ans(answer)– whenyoudonotspecifyanoutputvariable,MATLABusesthevariableanstostoretheresultsofacalcula=on


>>2+3>>ans=5

•  inf(infinite)•  NaN•  returnstheIEEEarithme=crepresenta=onforNot‐a‐Number

•  markerformissingobserva=on•  pi,eps,realmin,realmax,etc.

NumericalandLogicalTypes•  Numerical

–  integer,floa=ngpoint,complex(x=2+3i;)–  short,long–  allnumbersareinternallystoredaslong–  format:changethewayhowthenumbersaredisplayed

•  Logical(boolean)–  true:1,false:0

•  Char–  integervalueconvertedtoitsUnicodeequivalent–  astringisavectorofcharacters–  theactualcharactersdisplayeddependonthecharactersetencoding

foragivenfont

AllMATLABdatatypesareimplementedasobject‐orientedclasses.


Everythingisa...Matrix

•  IntheMATLABamatrixisarectangulararrayofnumbers.– scalarscanbeseenas1‐by‐1matrices;– array(vectors)arematriceswithjustoneroworonecolumn.

•  MATLABallowsyoutoworkwithen=rematricesquicklyandeasily.

•  Itisusuallybesttothinkofeverythingasamatrix.


EnteringMatricesMatricescanbeintroducedinseveraldifferentways:

•  Enteredbyanexplicitlistofelements>>A=[123;456;789]

•  Generatedbybuilt‐instatementsandfunc=ons>>A=rand(3)

•  CreatedinM‐filesusingbuilt‐infunc=ons

•  Loadedfromexternaldatafiles


EnteringMatrices

Basicconven=ons:

•  Separatetheelementsofarowwithblanksorcommas.

•  Useasemicolon;toindicatetheendofeachrow.

•  Surroundtheen=relistofelementswithsquarebrackets[].

>>A=[1,2,3;4,5,6]


MatrixandArrayOpera=ons•  Matrixopera=onsapplyalsotoscalars(1‐by‐1matrices).

•  Ifthesizesofthematricesareincompa=bleforthematrixopera=on,anerrormessagewillresult.Forexample,*istheusualmatrixproduct,while.*istheelementbyelementproduct.


The“matrixdivision”.IfAisaninver=blesquarematrixandbisacompa=blecolumn:

>>x=A\b%leftdivision,solutionofA*x=b>>x=b/A%rightdivision,solutionofx*A=b

MatrixBuildingFunc=ons

•  Usedtobuildmatriceswithspecificproper=es


>>MB1=zeros(3)%builda3x3matrixwithall0>>MB2=[ones(3),zeros(3,2);zeros(2,3),eye(2)]%5x5matrix‐concatenation

MatrixandVectorsfunc=ons


%findthemaximumvalueina%matrix>>A=[723;452];>>max_vec=max(A)[753]>>max2=max(max_vec)7>>max2=max(max(A))7

%whenanarrayoperationis%appliedtoamatrix,itis%appliedtoeachcolumn,%theresultisanarray!

SubmatricesandColumnnota=on•  Powerfulwaytoaccessdatastoredinmatrices.•  TheelementinrowiandcolumnjofAisdenotedbyA(i,j).

•  Thecolonoperator:isoneofthemostimportantMATLABoperators.

•  Thesefeaturespermittominimizetheuseofloops(whichslowsMATLAB)andtomakecodesimple.


>>a=[2:2:10];%createanarray>>A(1:3,3)%accesspartofamatrix>>A([24],:)%access2ndand4throw,allthecolumns>>A(:,2:end)%allrows,column2tothelast>>A(:,[245])=B(:,1:3)

Example:MagicMatrix•  Knownforover4000years(foundinancientEgyptandIndia)wasseenfor

thefirst=meinEuropeanartintherenaissanceengravingMelencoliaIbytheGermanar=standamateurmathema=cianAlbrechtDürer.

•  Knownasamagicsquare,wasbelievedhavingmagicalproper=es.Itdoesturnouttohavesomefascina=ngcharacteris=csworthexploring.


OtherDataStructuresMatricescanbeusedtostorehomogenousdata,otherusefulstructuresare:

• Mul=dimensionalArrays•  Structures•  CellArrays•  Func=onHandlers


Mul=dimensionalArrays

•  Mul=dimensionalArrays– arrayswithmorethantwosubscripts;

>>B=rand(2,3,2);– usedtorepresentasequenceofmatrices,A(k),orsamplesofa=me‐dependentmatrix,A(t)•  the(i,j)thelementofthekthmatrix

isdenotedbyA(i,j,k)


Ifwehaveamagicmatrixthatchangeover=me,wecanaccessthevaluesatacertain=mekusingaA(i,j,k)

StructuresStructuresandcellarrays,provideawaytostoredissimilartypesofdatainthesamearray.

•  Structures– mul=dimensionalMATLABarrayswithelementsaccessedbytextualfielddesignators

>>my=[];>>my.age=35;>>my.country='Italy';my=age:35country:'Italy'


CellArrays•  CellArray–  acellarrayisacollec=onofcontainerscalledcellsinwhichyoucanstoredifferenttypesofdata

>>my={35,'Italy',[79111315]}my=[35]'Italy'[1x5double]


FlowControl


Matlabhasloopsandcondi=onals:for,while,if‐else(if),con=nue,break,try,catch.

Whenappliedtoscalars,arela=onisactually1or0dependingonwhethertherela=onistrueorfalse.

Whenappliedtomatricesofthesamesize,arela=onisamatrixof0'sand1'sdependingonthevalueoftherela=onbetweencorrespondingentries.

>>a=[2:2:10]246810>>a>600011

LoopsandCondi=onals

•  Forloop:thesyntaxishighlightedintheboxes.


x=[];n=5;fori=1:nx=[x,i^2];end

x=[];n=5;fori=1:nx(i)=i^2;end

x=[];n=5;fori=n:‐1:1x(i)=i^2;end

•  If...else(elseif)...ifRELATIONstatementend

ifa==bstatementend

ifA~=Bstatementend

ifany(any(A~=B))statementend

aretheydifferent?why2“any”inthesecondone?

if(isequal(A,B))statementend

Loopsvs.Built‐inFunc=ons•  WhenprogrammingwithMatlabyoushouldalwaystrytoavoidloopsandcondi=onalsandusebuilt‐infunc=ons.

•  LoopsslowdownMatlabwhileBuilt‐infunc=onsarehighlyop=mized

•  Eg.“for”vs“find”


random=rand(1,100000);%goal:createanewarraywithonlyelements>0.5

%solu=on1:forloopreal1=[];j=1;n=size(random,2)fori=1:nif(random(i)>0.5)real1(j)=random(i);j=j+1;endend

%solu=on2:built‐infunc=on(find)real2=[];real2=random(find(random(:)>0.5));

MUCHFASTER!

LogicalSubscrip=ng

•  Anotherusefulnota=onisthelogicalsubscrip=ng.•  Thelogicalvectorscreatedfromlogicalandrela=onalopera=onscanbeusedtoreferencesubarrays.

%extractasubarrayfromxwithnoNANsx=[2.11.71.61.5NaN1.9];y=x(isfinite(x))y=[2.11.71.61.51.9]


M‐files•  WhenyouwriteaMATLABfunc=onorscript,yousaveittoafilecalledanM‐file(nameda\erits.mfileextension).

•  TherearetwotypesofM‐files:scriptfilesandfunc=onfiles.

•  M‐Filescanbeexecutedcallingtheirfilename.•  Don’tforgettoaddthepathtoyourcodestotellMatlabwheretheyare!

•  Alwaysusecomments(%)andgivemeaningful(notonlyforyou!)namestofunc=onsandvariables.


M‐files:script•  AscriptfileconsistsofasequenceofMATLABstatements.

•  Ifthefilenameismyfile.mtheMATLABcommandmyfilewillcausethestatementsinthefiletobeexecuted.

•  VariablesinascriptfileareglobalandwillchangethevalueofvariablesofthesamenameintheenvironmentofthecurrentMATLABsession.

•  AnM‐filecanreferenceotherM‐files,includingreferencingitselfrecursively.


M‐files:Func=ons•  Func=onfilesactuallyprovideawaytoaddnewfunc=onalitytoMatlab.

•  Youcancreatenewfunc=onsspecifictoyourproblemwhichwillthenhavethesamestatusasotherMATLABfunc=ons.

•  VariablesinafuncNonfilearebydefaultlocal;itispossibletodeclarevariablesasglobal.

•  Whenthefunc=onendsthelocalvariablesarenotavailableanymore.


Beorganized...•  SaveyourWork–  save–  diary

•  DIARYFILENAMEcausesacopyofallsubsequentcommandwindowinputandmostoftheresul=ngcommandwindowoutputtobeappendedtoit

•  WriteDocumenta=on–  help

•  CleanyourSpace–  clc–  clearall,clearname_var–  closeall


matlab - caltech astronomygeorge/aybi199/oldlectures/donalek_matlab1.pdf · • applicaon...

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