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G&GMatlabTutorial
OriginalversionfromGeology392tutorialithasnowbeenheavilymodified.Seetheendforcurrentmaintainer.

PlotoftheMatlabpeaks()functionasamplefunctionfor3dgraphicsbuiltfromtranslatedandscaled
Gaussians.

GettingStarted
Ingeneral,Matlabisrunbyselectingtheapplicationfromamenu,ortypingmatlabatthecommandlineprompt
inaUNIXenvironment.Oncerunning,Matlabisitselfacommandlineprogram,whereinyouwillbegivena
prompttotypeinspecificcommands.

Youshouldseeagraphicswindowflashuponthescreenandthendisappear.Ifso,youareallsetotherwiseyou
needtocheckthatyouhavesetyourdisplayvariablesproperly.Ifyoucan'tgetthegraphicstoappearonthe
screen,Matlabshouldwork,butwithoutanyplotting.

Toseethegraphicswindow,youjustneedtoplotsomething.Trytyping

>>plot(1:0.5:5)

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whichwillplotthenumbers1to5(countingby0.5)bytheirindex(1to9).Asyou'llseelater,thecolon(:)isa
shorthandforcreatingavectorofnumbers.YouwilluseitalotinMatlab.

WhatisMatlab?
Matlabisaprogramfordoingscientificcalculationsusingmatrices.Thematrixisthebasicdatatypeofmatlab,
anditmayberealorcomplex.Matlabonlyusesdoubleprecisionfloatingpointnumberstherearenointeger
matrices.Youcanalsousescalars(1x1matrices)orvectors(nx1or1xnmatrices).WhatmakesMatlabvery
powerfulisthatyoucanperformoperationsonwholevectorsormatricesatonetime,withouthavingtoloop
througheachelement.Matlabisalsoquitegoodatplottingdata(in2and3d),whichmakesitusefulfor
plottingdatageneratedelsewhere.

Inthistutorial,we'llgooversomeofthebasiccommands,howtoreadindata,howtosavedata,howtoplot
data,andhowtocreatesimpleprograms,calledmfiles.

GettingHelpinMatlab
IfyougetstuckorjustneedmoreinformationaboutMatlab,thereareanumberofdifferentresources.The
easiestonetouseisbuiltintoMatlabitself.Bytypinghelporhelpcommand,youcangetadescriptionofa
commandorgroupofcommands.Trytyping

>>helpgraph2d

Thisgivesyoualistofallofthe2dimensionalplottingfunctionsavailable.Anotherhelpfulcommandisthe
lookforcommand.Bytypinglookforkeyword,youwillgetalistofallcommandsrelatedtokeyword,evenif
youaren'tsureoftheexactfunctionname.

Therearealsoanumberofbooks,includingtheMatlabmanualandGettingStartedinMatlabbyRudraPratap.

TheMathworks(developersofMatlab)WWWsite,http://www.mathworks.com,hasextensivedocumentation
available(underSupport).ThedocumentationforMatlab(butnotthetoolboxesorotherMathworksproducts)is
availablehere.Foruserswhowishtokillaforestoftreesforpapermanuals,theyareavailablefororderfrom
Mathworks,orasPDFfilesonthewebhere.

DealingWithVariables
Here'sashorttutorialonworkingwithvariables,takenfromthebook,GettingStartedinMatlab.Itishighly
recommendedthatyouobtainthisbookasitwillmakeyourlifeinMatlabeasier.VariablesinMatlabcanhave
anyname,butifthevariablehasthesamenameasafunction,thatfunctionwillbeunavailablewhilethe
variableexists.TrytypingthefollowingintoMatlab:

>>2+2 %Addtwonumbers
%
ans= %Matlabuses'ans'if
%thereisnovariable
4 %assignment(lvalue)

>>x=2+2 %Assignstheresult
%tovariable'x'
x= %anddisplaysthe
%valueof'x'
4 %

>>y=2^2+log(pi)*sin(x); %Thesemicolonat
>>y %theendsuppressesoutput
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%Toseethevalueofa
y= %variable,enterjustits'
%name
3.1337

>>theta=acos(1) %Assignarccos(1)totheta
%Matlabusesradianforall
theta= %trigfunctions

3.1416

>>thetapi %Notethatpiisbuiltinto
%Matlab,andmoreprecision
ans= %iskeptinternallythanis
%printedonthescreen
0

CreatingandWorkingWithMatrices
InMatlab,thereareanumberofwaystocreatematrices.First,let'slookathowtogeneratevectors(callthemx
andy),whichare1xNmatrices.Wewillmakexgofrom0to3*pi.

>>x=0:0.1:3*pi; %Createvectorxfrom0to3*piin
%incrementsof0.1
%But,couldalsouse:
>>x=linspace(0,3*pi,100); %Createvectorxfrom0to3*piwith
%100stepsexactly
>>beta=0.5; %Createconstantbetaforerrorfunction
>>y=beta*erf(x/5); %Computeerf()foreachxvalue,and
%assigntoayvalue
%Notethatthereisnoloophere,but
%ynowhasasmanyentriesasx!
>>plot(x,y) %Plotxvs.ywithaline

Theplotshouldlooksomethinglikethis.

Now,let'strymakingtruetwodimensionalmatrices(MxN)startwitha3x3matrixtypedonthecommandline:

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>>x=[147;258;369]; %semicolonsdenotechangesof
%row

>>x=[1,4,7 %Matlab'scommandlineknows
2,5,8 %thematrixisnotfinished
3,6,9]; %untiltheclosing']'

Inanycase,theresultisthesame,thefollowing3x3matrixstoredasthevariablex:
>>x %Displaythecurrentvalueofx

x=

147
258
369

Youshouldnoticethatsquarebrackets([])enclosethematrix,spacesorcommas(,)denoteelementswithina
row,andeitherasemicolon(;)orahardreturndenoterows.

Matlabalsohasfunctionstoproducematricesofzerosandonesofaspecifiedsize:

>>zeros([33]) %Producematrixofallzeros,
%sizeof3x3
ans=

000
000
000

>>zeros(3,3) %Alternatesizeformatofabove

ans=

000
000
000

>>zeros(2) %Matrixofzeros,size2x2

ans=

00
00

>>zeros([12]) %Rowvectorofzeros,2long

ans=

00

>>zeros([21]) %Columnvectorofzeros,2long

ans=

0
0

>>ones(2,2) %Sameaszeros(),butmatrixfilledwith1

ans=

11

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11

Toaccessmatrixelements,specifytherowsandcolumnsweareinterestedin.Rememberhowweusedthe
colon(:)tofillinnumberswhenweplottednumbersfrom1to5inthefirstsection?Wewillusethatagain.The
syntaxisx(row,col)so,forexample,ifwewantthetoassigntheelementinthethirdrow,firstcolumntothe
variabley,wetype:

>>y=x(3,1); %Assignrow3,col1elementofxtoy

Tospecifyanentireroworcolumn,useacolon(:)inplaceoftheroworcolumnnumber.So,ifwewantthe
entiresecondcolumn,wewouldtype:
>>y=x(:,2); %Assignallrows,col2elementstoy

Nowlet'stryashortexercisetousematricesandmatrixoperations.

1.Createavectoroftheintegersfrom1to5andnameita.
2.Add1toalltheelementsofa,andstoreina.
3.Createavectoroftheintegersfrom5to1andnameitb.
4.Addatobandstoretheresultinc.

Hereisatranscript(diary)ofamatlabsessionimplementingtheexercise:

>>a=1:5; %vectorof1to5,increment1
>>a=a+1 %add1toallelementsofa

a=

23456

>>b=5:1:1 %vectorof5to1,increment1

b=

54321

>>c=a+b %addaandb,storeinc

c=

77777

Notethatallvectorsusedsofarhavebeenrowvectorsthevectorisarowfromamatrix(onerow,many
columns).Therearealsocolumnvectors,whicharedisplayedvertically(manyrows,onecolumn).Totransform
arowvectortoacolumnvector(orback),usethetransposeoperationinMatlab,thisisdenotedby'afterthe
vector(ormatrix)name.
>>a'

ans=

2
3
4
5
6

Matlab,beingfocusedonmatrixoperations,alwaysassumesoperationsarematrixoperationsunlesstold
otherwise.Intheexerciseabove,weaddedascalartoamatrix,whichisthesameasaddingascalartoevery

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elementofthematrix.Ingeneral,though,Matlabwilldomatrixaddition,multiplication,division,etc.

TomakeMatlabapplyanoperationtoeachelementindividually(ratherthanusematrixoperations),usea.
(period)beforetheoperatorforexample,tosquareeachelementofavector,weuse:
>>a=1:5;
>>a.*a %the.makesMatlabapplythe*
%toeachelementasasetofscalar
ans= %operations,NOTmatrixmultiplication

1491625

Ifthereisno.,Matlabassumestheintentisamatrixoperation,whichwon'tworkfortworowvectors:

>>a*a
???Errorusing==>*
Innermatrixdimensionsmustagree.

Iftheintentreallyistodoamatrixmultiplicationofabya,weneedtotakethetransposeofthesecondvector:
>>a*a'

ans=

55

Sinceaisa1x5vector,a'(transposeofa)isa5x1vector.Whenmultiplied,theresultisa1x1vector,whichisa
scalar,asseenhere.

Keepingtrackofmatrixdimensionscanbedifficult,butisextremelyimportant.Fortunately,Matlabwill
normallyproduceerrorswhenyourcodetriestodosomethingmathematicallyincorrect.

AdvancedMatrixIndexingskipandcomebackifdesired
Matlabhasaverygeneralindexingability,whichcanmakecodethatiscompactandefficient,butless
transparent.Ingeneral,anywhereyoucanindexamatrixwithasinglenumber(orsetofnumbers),youcanalso
indexwithavectorormatrix.Someexamples:

EDU>>a=[1:3;4:6;7:9]%Create3x3matrix

a=

123
456
789

EDU>>a(:)%Accessmatrixasavector.
%Notethattheelementsaretaken
ans=%fromeachcolumnfirst,theneach
%row.Thisformatallowsthetreatment
1%ofanymultidimensionalarrayasa
4%vector,whichcanbeusefulforsome
7%functioncalls.
2%3+dimensionalarrayswilltakeelements
5%firstfromthelastdimension,working
8%backtothefirstdimension!
3
6
9

EDU>>b=[1:10].^2
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b=

149162536496481100

EDU>>b(a)%Accesselementsofbusingvaluesofa.
%Notethattheresultisamatrixwiththe
ans=%sameshapeasa,butwithvaluestakenfrom
%b;theentriesofaareusedasindexes
149%intothevectorb.Matlabwillproducean
162536%errorifanyindexfromaisoutsidethe
496481%boundsofb.

EDU>>a%Reminderofentriesofmatrixa

a=

123
456
789

EDU>>b=flipud(a)

b=

789
456
123

EDU>>b(a)%Accesselementsofbusingvaluesofa.
%Notethattheelementsweretakenin
ans=%columnorder(elements13arethefirst
%column).ThiscomesfromMatlabtreating
741%basavectorfortheindexingoperation,
852%withtheresultingvectorreshapedtothe
963%sizeofa.

TheseexamplesarealldesignedtoshowhowMatlabstoresandretrievesinformationinarrays.Matlabstores
allarraysasalongvectorinmemory,regardlessofthenumberofdimensions.Amultidimensionalarray(a
matrix)isstoredasavector,withadditionalinformationonhowmanyrowsandcolumnsareinthematrix,so
Matlabcanquicklyaccessanyelementusing(row,column)indexing.Thetranslationfora2Dmatrix(nrxnc
elements)issimple:
A(i,j)==A(j*nr+i)

wherenristhenumberofrowsinthematrix.A3Darray(n1xn2xn3elements)issimilar:
A(i,j,k)==A((k*n1*n2)+(j*n2)+i)

wheren1isthestrideforthelastdimension,andn2isthestridefortheseconddimension.

Giventhismemorylayoutforamultidimensionalmatrix,itisclearwhyaccessingthematrixasavector(using
theA(:)notation)resultsinavectorwithcolumnsattachedendtoendMatlabisstartingatthefirstelement
andreadingstraightthroughuntiltheend.Thissortofindexing,onceunderstood,canmakesomeveryefficient
algorithms.Forexample,translatinggrayscalevaluesinanimagefromonescaletoanother:

EDU>>A=floor(rand(10)*255)%Createrandom10x10matrix
%of8bitgrayscalevalues
A=%[0255].

36713717318211192118466
731921581849233169233127221
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208168174189628225581076
2515417237020769219168132
41532235719623110616717149
2081543131803954227244182
158168791161623191244863
142461981792511942025328238
62162781481281842169514434
2094323612924116686135247133

EDU>>B=[0:2:100linspace(101,199,25680)200:2:256];size(B)
%Createnewgrayscalemapping
ans=%thatcompressestheendsand
%expandsthemiddleofthe
1256%spectrum;mustbe256entries!

EDU>>floor(B(A+1))%RemapAbychoosingentriesof
%thenewmap(B)accodingtovalues
ans=%inA.Notetheadditionof1,to
%shift[0255]to[1256].
4109148168341901791379010
1121791603496210166210143195
188165169341255419710413110
2461021684111187110194165145
615719610318120613116516796
188158414511676102199232173
160165116136162601614194107
151901821722461803825054220
10616211515414317419212515266
18884216144226164120147238146

Thisefficient,butlesstransparent,implementationofaremappingcouldalsobedoneviaforloops(oneortwo,
dependingonimplementation),butthatwouldbemuch,muchslowerforlargematrices.

LoadingandSavingData
ThekeytoloadingdataintoMatlabistorememberthatMatlabonlyusesmatrices.Thatmeansthatifyouwant
toeasilyreadadatasetintoMatlab,alloftherowsmusthavethesamenumberofelements,andtheymustall
benumbers.

Mostcommonly,you'llbedealingwithatext(ASCII)file.Ifyouhaveasetofdataondiskinafilecalled
points.dat,thentoloadit,youwouldtype:
>>loadpoints.dat

ThiswillloadyourdataintotheMatlabvariablepoints.Let'sassumethatthefilepoints.datcontainstwo
columns,wherecolumn1isheightandcolumn2isdistance.Tobreakapartpointsintosomethingmore
meaningful,weuse:
>>height=points(:,1);
>>distance=points(:,2);

Thiscreatesavectorheightfromthefirstcolumn(allrows),anddistancefromthesecondcolumn.

TosavethesamedataintoanASCIIfilecalledmydata.dat,weuseeither:
>>savemydata.datheightdistanceascii %commonformfor
%commandline

or

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>>save('mydata.dat','height','distance','ascii');
%commonformfor
%useinscriptsand
%functions

TheasciiflagisimportanthereittellsMatlabtomakethefileinASCIItext,notaplatformindependant
binaryfile.Withouttheflag,thefilewouldbeunreadablewithstandardeditors.Textisthemostportableand
editableformat,butislargerondisk.Matlab'sbinaryformatiscompatibleacrossallplatformsofMatlab
(Windows,UNIX,Mac,etc.),andismorecompactthantext,butcannotbeeditedoutsideofMatlab.

YouwillnotethatwhenMatlabsavesfilesinASCIIformat,itusesscientificnotationwhetheritneedsitornot.

MorepowerfulandflexiblesaveandloadschemesexistinMatlabtheyusethefprintf()andfscanf()functions
alongwithfopen()tocontrolfileoutput.Adiscussionoftheintricaciesofusingfscanf/fprintfisbeyondthis
tutorialseethehelppagesorsomeonewithfirsthandexperience.

Plotting
Nowthatwecansave,load,andcreatedata,weneedawaytoplotit.Themainfunctionformaking2
dimensionalplotsiscalledplot.Tocreateaplotoftwovectorsxandy,typeplot(x,y).Withonlyoneargument
(plot(x))plotwillplottheargumentxasafunctionofitsindex.Ifxisamatrix,plotwillproduceaplotofthe
columnsofxeachinadifferentcolororlinestyle.Moredetailonthebasicuseofplotisavailableviathehelp
plotcommandinMatlab.

Thatbringsustothethirdpossibleargumentforplot,thelinestyle.plot(x,y,s)willplotyasafunctionofx
usinglinestyles,wheresisa1to3characterstring(enclosedbysinglequotes)madeupofthefollowing
characters.
yyellow .point
mmagenta ocircle
ccyan xxmark
rred +plus
ggreen solid
bblue *star
wwhite :dotted
kblack .dashdot
dashed

Forexample,tocreateaplotofxversusy,usingmagentacircles,typethecommandplot(x,y,'mo');.Toplot
morethanoneline,youcancombineplotsbytypingplot(x1,y1,s1,x2,y2,s2,...);.

Asanexample,plotarandomvector(10x1)andanintegervectorfrom1to10usingtwodifferentlinetypes:

>>y1=rand(10,1);
>>y2=linspace(1,0,10);
>>x=1:10;
>>plot(x,y1,'g+',x,y2,'r');
>>title('Testoflinetypestrings');
>>xlabel('XAxis');
>>ylabel('YAxis');

Theplotshouldlooksomethinglikethis:

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Anotherusefulplottingcommandiscallederrorbar.Thefollowingexamplewillgenerateaplotoftherandom
vectory1usinganerrorof0.1aboveandbelowtheline:
>>errorbar(x,y1,ones(size(y1)).*0.1,'r')
>>title('Testoferrorbar');
>>xlabel('XAxis');ylabel('YAxis');

Theplotshouldnowlooksomethinglikethis:

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LabellingthePlot
title,xlabel,andylabelcreatelabelsforthetopandsidesoftheplot.Theyeachtakeastringvariable,which
mustbeinsinglequotes.Oneotherlabellingfunctionthatmightbeusefulisthetextfunction.Thecommand
text(1,10,'Hereissometext');willwritethetextstring'Hereissometext'atthe(x,y)position(1,10)in
dataunits.

ChangingtheAxes

Onethingyoumightwanttodowithyourplotistochangetheaxes.Normally,Matlabautomaticallychooses
appropriateaxesforyou,butthey'reeasytochange.Theaxiscommandwillallowyoutofindoutthecurrent
axesandchangethem.
>>axis %Getthecurrentaxis
%settings
ans=

012.00000.20001.4000

>>axis([2100.21.0]) %Resetaxesextentsto
%[xminxmaxyminymax]

Sometimesyouwillwanttoswitchthepositionoftheplotorigin(normallyusedforplottingimagesof
matrices).Typing

>>axis('ij')

willswitchtheYaxisdirectionsothat(0,0)istotheupperright.
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AppendingDatatoPlots

Sometimesit'susefultobeabletoaddsomethingtoaplotwindowwithouthavingtodrawtwolineswiththe
sameplotstatement(aswedidabove).SoMatlabhasacommand,holdwhichwillcausetheplottoremain(it
doesn'tredrawit).Typingholdonwillholdthecurrentplot,andholdoffwillreleasetheplot.Also,holdby
itselfwilltoggletheholdstate.Youmightalsowanttouseclftoclearthegraphicswindowandreleasethe
window.

UsingGraphicsHandlesinMatlab

ForthoseofyouthatwilluseMatlabtomakeplotsforpublicationsandpresentationswillgreatlybenefitfroma
fewusefulbutpoorlydocumentedMatlabfunctions.Thecommandsgetandsetallowtheusertocheckor
tweakaplotintomorepleasingform.Forexamplebyusingthesecommands,onecanchangefontsizes,colors,
linewidthsandaxeslabelsaswellasmanyotherplotattributes.

Wewillstartbygeneratingasimpleplot:

>>x=[0:100]*pi/50;
>>y=sin(x);

Alltheattributesofaplotarestoredinadatastructurewhichmaybeobtainedbytyping:
>>p=plot(x,y)

Bygivingaplotanoutputvarible,youhaveobtainedtheobjecthandles.Inordertofindoutwhathandlesexist
weusethegetcommand.

>>get(p)

Alistwillbeprintedoutwhichispartiallylistedbelow:

Color=[001]
EraseMode=normal
LineStyle=
LineWidth=[0.5]
...

Ifyouwishtoobtainthevaluetojustoneaxishandle,forexamplethelinestyle,thiscanbedonebytyping:

>>get(p,'LineStyle')
ans=

Eachoftheseisagraphichandlesthatmaybechangedbyusingthecommandset.Forexample,supposethat
wenowwishtomaketheplotredinsteadofblueandincreasethelinewidthfrom0.5to1.

>>set(p,'Color',[100],'LineWidth',1);

Anygraphichandlemaybechangedusingthismethod.AsyoubegintouseMatlab,thesecommandsmaynot
beusedoften,butasyoubecomemoreproficient,youmayfindthesecommandstobeinvaluable.Other
attributesofaplotcanbechangedbyusinggca(foraxesproperties)andgcf(forfigurewindowproperties).
Typeget(gca)andget(gcf)toseewhatotherattributesmaybechanged.AndlikeanyotherpartofMatlab,
thesecommandsmaybeaddedtoscriptstocreatedcustomplots.

Creatingmfiles

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InMatlab,youcancreateafileusingMatlabcommands,calledanmfile.Thefileneedstohavea.mextension
(hencethenamemfile).Therearetwotypesofmfiles:(1)scriptsand(2)functions.Wewillstartwith
scripts,astheyareeasiertowrite.

MatlabScripts
RunningaMatlabscriptisthesameastypingthecommandsintheworkspace.Anyvariablescreatedorchanged
inthescriptarechangedintheworkspace.Ascriptfileisexecutedbytypingthenameofthescript(withoutthe
.mextension).Scriptfilesdonottakeorreturnanyarguments,theyonlyoperateonthevariablesinthe
workspace.Ifyouneedtobeabletospecifyanargument,thenyouneedtouseafunction.Hereisanexampleof
asimplescripttoplotafunction:

%makefunction.m
%scripttoploterfcindomain[0,pi]

x=linspace(0,pi,25); %Createxfrom0topiwith25values
y=erfc(x); %Calc.erfcofx
scl=0.25; %Plottingscalingfactor
y=y*scl;
plot(x,y,'r'); %Plotxandy
title('MyScript'); %Createatitle
xlabel('X'); %Labelthexandyaxes
ylabel('Y');

Notetheuseof'%'characterstointroducecomments,justasintheexamplesthroughoutthistutorial.Ingeneral,
Matlabtreatsanythingaftera'%'asifitwasn'ttherecommentsaresilentlyignored.Thiscanbeveryuseful
whenwritingmfiles,asdebuggingcommandscanbecommentedoutafterthemfileistested.

Runningthismfileproducesthefollowingvariablesintheworkspaceandplot(inaseparatewindow):
>>whos %Emptyworkspace;novariablesdefined
>>makefunction %Createvars,plot
>>whos %Listvarsinworkspace
NameSizeBytesClass

scl1x18doublearray
x1x25200doublearray
y1x25200doublearray

Grandtotalis51elementsusing408bytes

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Youshouldnoticethatallofthevariablesusedinthescriptarenowsittingintheworkspace,sothattheycanbe
usedagain.Thisisexactlythesameasiftheyhadbeentypedinseparately.Anytimeacomputationisgoingto
takemorethanasingleline,itisworthwhiletocreateathrowawaymfilethefilecanbesaved,edited,and
revisedmucheasierthanusingjustthecommandline.

MatlabFunctions
Matlabfunctionsareverysimilartoscripts,buttheycanacceptandreturnvaluesasarguments.Mostofthe
commandsavailableinMatlabareactuallyprewrittenMatlabfunctionsonlyasmallnumberofimportant
functionsarecompiledintotheprogram(e.g.matrixmultiply).

Towriteafunction,createanmfilewithafunctiondeclarationasthefirstline(seetheexample,below).The
returnvaluesinthedeclarationwillneedtobesetsomewhereinthefunctionbodywhatevervaluethese
variableshaveattheendofthefunctionwillbereturned.

Commentsimmediatelyafterthefunctiondeclarationwillbeusedasthehelppageforthefunctionitshould
haveusefulinformationonfunctionargumentsandreturnvalues.Ifthefunctionusesaspecial(named)
algorithm,thatisusefultoputinthehelpaswell.

Functionskeepvariableslocalvariablesdefinedinthefunctionarenotpartoftheworkspace,andthefunction
cannotaccessvariablesintheworkspaceunlesstheyarepassedasarguments.Hence,functionscandefinea
variablewithoutworryingifitalreadyexists.Allvariablesinafunctionarelostoncethefunctioncompletes.

Anexamplefunctiondefinition(fromafilenamedllsqErr.m):
function[mean,sigma]=llsqErr(x,y,N,dx,dy);
%function[mean,sigma]=llsqErr(x,y,N,dx,dy);
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%
%Generatemeanands.d.ofslopeandintercept
%forlinearleastsquaresfittox,ydataset,usingMC
%techniquewithrandomerrorsofscaledx,dy.Randomerrors
%areuniformlydistributed,andsymmetric(withscaledx,dy)
%aboutxandyvalues.
%
%x,yarevectorsofdata,oflength>2
%dx,dyarescalars
%Nisscalar(#oftrials);typicallyshouldbe>1e3
%
%UsesNtrialswithrandomperturbationscomputedforeachtrial
%
%Returnsvaluesas[slopeintercept]formeansands.d.s

%%Notes%%
%Thiscodereallyoughttoguaranteethattherandomlygenerated
%pertrubationsareunique.Thisisassumedfromtheuseofa
%pseudorandomnumbergenerator,andthelikelyeventthatNis
%lessthantherecurrenceintervalofthePRNG.
%
%Itappearsnecessarytocomputethepredictederrorsforeach
%datasetindividually;attemptstogenerateageneralcorrelation
%plotdidn'tpanout.

m=zeros(N,2);
fori=1:N
xh=x+dx*(2*rand(size(x))1);%generateperturbedx,yvecs
yh=y+dy*(2*rand(size(y))1);

p=polyfit(xh,yh,1);%getslope,intercept
m(i,:)=p;%store
end

mean=[mean(m(:,1))mean(m(:,2))];
sigma=[std(m(:,1))std(m(:,2))];

Thisfunctionaccepts5arguments:x,y,N,dx,anddy.Itreturnstwovectors:meanandsigma.Notethatthe
commentsafterthefunctiondeclarationindicatewhattheargumentsandreturnvaluesare,aswellashowthe
functiondoesits'work.Alsonotethattherearecommentsaboutpossibleproblemswiththisalgorithmand
implementation.Auserlookingatthesourcecodeforthisfunctioncandeterminewhatishappening,andwhat
mightneedtobechanged.Alsonotethatthefunctionusessimplevariablenames,whichcouldexistinthe
workspace(x,y,etc.)becausethisisafunction,thevariablesusedarenotpartoftheworkspace,sothereareno
concerns.

Whenausergetshelpforthisfunction,thefirstsetofcomments(uptotheblankline)isreturnedasthehelp
page:
>>helpllsqErr

function[mean,sigma]=llsqErr(x,y,N,dx,dy);

Generatemeanands.d.ofslopeandintercept
forlinearleastsquaresfittox,ydataset,usingMC
techniquewithrandomerrorsofscaledx,dy.Randomerrors
areuniformlydistributed,andsymmetric(withscaledx,dy)
aboutxandyvalues.

x,yarevectorsofdata,oflength>2
dx,dyarescalars
Nisscalar(#oftrials);typicallyshouldbe>1e3

UsesNtrialswithrandomperturbationscomputedforeachtrial
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Returnsvaluesas[slopeintercept]formeansands.d.s

SavingYourSession
Oneotherusefulcommandisthediarycommand.Typing
>>diaryfilename.txt

willcreateafilewithallthecommandsyou'vetyped.Whenyou'redone,typing
>>diaryoff

willclosethefile.Thismightbeusefultocreatearecordofyourworktohandinwithalabortocreatethe
beginningsofanmfile.

EndoftheTutorial
Atthispoint,youshouldknowenoughtomaneuveraroundinMatlabandfindwhateverelseyouneed.Helpis
availablefromthebuiltinhelpcommand,theonlinehelpsystematwww.mathworks.com,orfellowstudents
andfaculty.

Questions?Comments?Suggestions?
Contactgettings@mines.utah.edu

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