InteractiveComputingwithMatlabGeraldW.RecktenwaldDepartmentofMechanicalEngineeringThese slides are a supplement to the book Numerical Methods withMatlab: Implementations and Applications, by Gerald W. Recktenwald,c 2000, Prentice-Hall, Upper Saddle River, NJ. These slides are c 2000GeraldW.Recktenwald.My intention is that the slides will be helpful for instructors usingNumerical MethodswithMatlabasatextbookfortheircourse. Theslidesmaybedownloadedorstoredorprintedonlyfornoncommercial,educationaluse.The repackaging and sale of these slides in any formis expresslyprohibited.The latest version of this PDF le, along with other supplemental materialforthebookVersion1.0 August16,2000Overview BasicMatlabOperations StartingMatlab UsingMatlabasacalculator Introductiontovariablesandfunctions MatricesandVectors: Allvariablesarematrices. Creatingmatricesandvectors Subscriptnotation Colonnotation AdditionalTypesofVariables Complexnumbers Strings Polynomials WorkingwithMatricesandVectors Linearalgebra Vectorizedoperations Arrayoperators ManagingtheInteractiveEnvironment PlottingNMM:InteractiveComputingwithMatlab page1StartingMatlab DoubleclickontheMatlabicon,oronunixsystemstypematlabatthecommandline. AfterstartupMatlabdisplaysacommandwindowthatisusedtoentercommandsanddisplaytext-onlyresults. EnterCommandsatthecommandprompt:>> forfullversionEDU> foreducationalversion Matlabrespondstocommandsbyprintingtextinthecommandwindow,orbyopeningagurewindowforgraphicaloutput. Togglebetweenwindowsbyclickingonthemwiththemouse.NMM:InteractiveComputingwithMatlab page2MatlabWindows(version5)Command WindowHelpwin WindowPlot WindowNMM:InteractiveComputingwithMatlab page3MatlabasaCalculatorWorkdirectlywithnumbers>> 2 + 6 - 4 (pressreturn after 4)ans =4>> ans/2ans =2Or,deneandusevariables>> a = 5a =5>> b = 6b =6>> c = b/ac =1.2000NMM:InteractiveComputingwithMatlab page4Built-inVariablespi(=)andansareabuilt-invariables>> pians =3.1416>> sin(ans/4)ans =0.7071Note: Thereisnodegreesmode. Allanglesaremeasuredinradians.NMM:InteractiveComputingwithMatlab page5Built-inFunctionsManystandardmathematicalfunctions,suchassin,cos,log,andlog10,arebuilt-in>> log(256)ans =5.5452>> log10(256)ans =2.4082>> log2(256)ans =8NMM:InteractiveComputingwithMatlab page6LookingforFunctionsSyntax:lookfor stringsearchesrstlineoffunctiondescriptionsforstring.Example:>> lookfor cosineproducesACOS Inverse cosine.ACOSH Inverse hyperbolic cosine.COS Cosine.COSH Hyperbolic cosine.NMM:InteractiveComputingwithMatlab page7WaystoGetHelp Useon-linehelptorequestinfoonaspecicfunction>> help sqrt Thehelpwinfunctionopensaseparatewindowforthehelpbrowser>> helpwin(sqrt) Uselookfortondfunctionsbykeywords>> lookfor functionNameNMM:InteractiveComputingwithMatlab page8On-lineHelpSyntax:help functionNameExample:>> help logproducesLOG Natural logarithm.LOG(X) is the natural logarithm of the elements of X.Complex results are produced if X is not positive.See also LOG2, LOG10, EXP, LOGM.NMM:InteractiveComputingwithMatlab page9SuppressOutputwithSemicolonResultsofintermediatestepscanbesuppressedwithsemicolons.Example: Assignvaluestox,y,andz,butonlydisplaythevalueof zinthecommandwindow:>> x = 5;>> y = sqrt(59);>> z = log(y) + x^0.25z =3.5341Typevariablenameandomitthesemicolontoprintthevalueofavariable(thatisalreadydened)>> yy =7.6811 ( = log(sqrt(59)) + 5^0.25 )NMM:InteractiveComputingwithMatlab page10MultipleStatementsperLineUsecommasorsemicolonstoentermorethanonestatementatonce. Commasallowmultiplestatementsperlinewithoutsuppressingoutput.>> a = 5; b = sin(a), c = cosh(a)b =-0.9589c =74.2099NMM:InteractiveComputingwithMatlab page11MatlabVariablesNamesLegal variablenames: BeginwithoneofazorAZ Haveremainingcharacterschosenfromaz,AZ,09,or Haveamaximumlengthof31characters Shouldnotbethenameofabuilt-invariable,built-infunction,oruser-denedfunctionExamples:xxxxxxxxxpipeRadiuswidgets_per_baubblemySummysumNote: mySumandmysumaredierentvariables. Matlabiscasesensitive.NMM:InteractiveComputingwithMatlab page12Built-inMatlabVariablesName Meaningans valueofanexpressionwhenthatexpressionisnotassignedtoavariableeps oatingpointprecisionpi , (3.141492 . . . )realmax largestpositiveoatingpointnumberrealmin smallestpositiveoatingpointnumberInf ,anumberlargerthanrealmax,theresultofevaluating1/0.NaN notanumber,theresultofevaluating0/0Rule: Onlyusebuilt-invariablesontherighthandsideofanexpression. Reassigningthevalueofabuilt-invariablecancreateproblemswithbuilt-infunctions.Exception: iand jarepreassignedto1. Oneorbothofiorjareoftenreassignedasloopindices. MoreonthislaterNMM:InteractiveComputingwithMatlab page13MatricesandVectorsAllMatlabvariablesarematricesAMatlabvectorisamatrixwithoneroworonecolumnAMatlabscalarisamatrixwithonerowandonecolumnOverviewofWorkingwithmatricesandvectors Creatingvectors:linspaceandlogspace Creatingmatrices:ones,zeros,eye,diag. . . Subscriptnotation Colonnotation VectorizationNMM:InteractiveComputingwithMatlab page14CreatingMatlabVariablesMatlabvariablesarecreatedwithanassignmentstatement>> x = expressionwhereexpressionisavalidMatlabexpressionthatevaluatestoamatrix,vectororscalar.Theexpressioncaninvolve: Manualentry Built-infunctionsthatreturnmatrices Custom(user-written)functionsthatreturnmatrices LoadingmatricesfromtextlesormatlesNMM:InteractiveComputingwithMatlab page15Manual EntryFormanualentry,theelementsinavectorareenclosedinsquarebrackets. Whencreatingarowvector,separateelementswithaspace.>> v = [7 3 9]v =7 3 9Separatecolumnswithasemicolon>> w = [2; 6; 1]w =261Inamatrix,rowelementsareseparatedbyspaces,andcolumnsareseparatedbysemicolons>> A = [1 2 3; 5 7 11; 13 17 19]A =1 2 35 7 1113 17 19NMM:InteractiveComputingwithMatlab page16TransposeOperatorOnceitiscreated,avariablecanbetransformedwithotheroperators. Thetransposeoperator convertsarowvectortoacolumnvector(andviceversa),anditchangestherowsofamatrixtocolumns.>> v = [2 4 1 7]v =2 4 1 7>> vans =2417>> A = [1 2 3; 4 5 6; 7 8 9 ]A =1 2 34 5 67 8 9>> Aans =1 4 72 5 83 6 9NMM:InteractiveComputingwithMatlab page17OverwritingVariablesOnceavariablehasbeencreated,itcanbereassigned>> x = 2;>> x = x + 2x =4>> y = [1 2 3 4]y =1 2 3 4>> y = yy =1234NMM:InteractiveComputingwithMatlab page18CreatingvectorswithlinspaceThelinspacefunctioncreatesvectorswithelementshavinguniformlinearspacing.Syntax:x = linspace(startValue,endValue)x = linspace(startValue,endValue,nelements)Examples:>> u = linspace(0.0,0.25,5)u =0 0.0625 0.1250 0.1875 0.2500>> u = linspace(0.0,0.25);>> v = linspace(0,9,4)v =0369Note: ColumnvectorsarecreatedbyappendingthetransposeoperatortolinspaceNMM:InteractiveComputingwithMatlab page19Example: ATableofTrigFunctions>> x = linspace(0,2*pi,6); (note transpose)>> y = sin(x);>> z = cos(x);>> [x y z]ans =0 0 1.00001.2566 0.9511 0.30902.5133 0.5878 -0.80903.7699 -0.5878 -0.80905.0265 -0.9511 0.30906.2832 0 1.0000Theexpressionsy = sin(x)andz = cos(x)takeadvantageofvectorization. Iftheinputtoavectorizedfunctionisavectorormatrix,theoutputisoftenavectorormatrixhavingthesameshape. Moreonthislater.NMM:InteractiveComputingwithMatlab page20CreatingvectorswithlogspaceThelogspacefunctioncreatesvectorswithelementshavinguniformlogarithmicspacing.Syntax:x = logspace(startValue,endValue)x = logspace(startValue,endValue,nelements)createsnelementselementsbetween10startValueand10endValue.Thedefaultvalueofnelementsis100.Example:>> w = logspace(1,4,4)w =10 100 1000 10000NMM:InteractiveComputingwithMatlab page21FunctionstoCreateMatrices(1)Name Operation(s)Performeddiag create a matrix with a specied diagonal entries,orextractdiagonalentriesofamatrixeye createanidentitymatrixones createamatrixlledwithonesrand createamatrixlledwithrandomnumberszeros createamatrixlledwithzeroslinspace createarowvectoroflinearlyspacedelementslogspace create a rowvector of logarithmically spacedelementsNMM:InteractiveComputingwithMatlab page22FunctionstoCreateMatrices(2)Useonesandzerostosetintialvaluesofamatrixorvector.Syntax:A = ones(nrows,ncols)A = zeros(nrows,ncols)Examples:>> D = ones(3,3)D =1 1 11 1 11 1 1>> E = ones(2,4)E =0 0 0 00 0 0 0NMM:InteractiveComputingwithMatlab page23FunctionstoCreateMatrices(3)onesandzerosarealsousedtocreatevectors. Todoso,seteithernrowsorncolsto1.>> s = ones(1,4)s =1 1 1 1>> t = zeros(3,1)t =000NMM:InteractiveComputingwithMatlab page24FunctionstoCreateMatrices(4)Theeyefunctioncreatesidentitymatricesofaspeciedsize. Itcanalsocreatenon-squarematriceswithonesonthemaindiagonal.Syntax:A = eye(n)A = eye(nrows,ncols)Examples:>> C = eye(5)C =1 0 0 0 00 1 0 0 00 0 1 0 00 0 0 1 00 0 0 0 1>> D = eye(3,5)D =1 0 0 0 00 1 0 0 00 0 1 0 0NMM:InteractiveComputingwithMatlab page25FunctionstoCreateMatrices(5)Thediagfunctioncaneither createamatrixwithspecieddiagonalelements,or extractthediagonalelementsfromamatrixSyntax:A = diag(v)v = diag(A)Example: Usediagtocreateamatrix>> v = [1 2 3];>> A = diag(v)A =1 0 00 2 00 0 3NMM:InteractiveComputingwithMatlab page26FunctionstoCreateMatrices(6)Example: Usediagtoextractthediagonalofamatrix>> B = [1:4; 5:8; 9:12]B =1 2 3 45 6 7 89 10 11 12>> w = diag(B)w =1611Note: Theactionofthediagfunctiondependsonthecharacteristicsandnumberoftheinput(s). ThispolymorphicbehaviorofMatlabfunctionsiscommon. Theon-linedocumentation(help diag)explainsthepossiblevariations.NMM:InteractiveComputingwithMatlab page27SubscriptNotation(1)If Aisamatrix,A(i,j)selectstheelementintheithrowandjthcolumn. Subscriptnotationcanbeusedontherighthandsideofanexpressiontorefertoamatrixelement.>> A = [1 2 3; 4 5 6; 7 8 9];>> b = A(3,2)b =8>> c = A(1,1)c =1Subscriptnotationisalsousedtoassignmatrixelements>> A(1,1) = c/bA =0.2500 2.0000 3.00004.0000 5.0000 6.00007.0000 8.0000 9.0000NMM:InteractiveComputingwithMatlab page28SubscriptNotation(2)Referringtoelementsoutsideofcurrentmatrixdimensionsresultsinanerror>> A = [1 2 3; 4 5 6; 7 8 9];>> A(1,4)??? Index exceeds matrix dimensions.Assigninganelementsoutsideofcurrentmatrixdimensionscausesthematrixtoberesized!>> A = [1 2 3; 4 5 6; 7 8 9];A =1 2 34 5 67 8 9>> A(4,4) = 11A =1 2 3 04 5 6 07 8 9 00 0 0 11Matlabautomaticallyresizesmatricesonthey.NMM:InteractiveComputingwithMatlab page29ColonNotation(1)ColonnotationisverypowerfulandveryimportantintheeectiveuseofMatlab. Thecolonisusedasbothanoperatorandasawildcard.Usecolonnotationto: createvectors refertoorextractrangesofmatrixelementsSyntax:startValue:endValuestartValue:increment:endValueNote: startValue,increment,andendValuedonotneedtobeintegersNMM:InteractiveComputingwithMatlab page30ColonNotation(2)Creatingrowvectors:>> s = 1:4s =1 2 3 4>> t = 0:0.1:0.4t =0 0.1000 0.2000 0.3000 0.4000Creatingcolumnvectors:>> u = (1:5)u =12345>> v = 1:5v =1 2 3 4 5visarowvectorbecause1:5createsavectorbetween1andthetransposeof5.NMM:InteractiveComputingwithMatlab page31ColonNotation(3)Usecolonasawildcardtorefertoanentirecolumnorrow>> A = [1 2 3; 4 5 6; 7 8 9];>> A(:,1)ans =147>> A(2,:)ans =4 5 6Orusecolonnotationtorefertosubsetsofcolumnsorrows>> A(2:3,1)ans =47>> A(1:2,2:3)ans =ans =2 35 6NMM:InteractiveComputingwithMatlab page32ColonNotation(4)Colonnotationisoftenusedincompactexpressionstoobtainresultsthatwouldotherwiserequireseveralsteps.Example:>> A = ones(8,8);>> A(3:6,3:6) = zeros(4,4)A =1 1 1 1 1 1 1 11 1 1 1 1 1 1 11 1 0 0 0 0 1 11 1 0 0 0 0 1 11 1 0 0 0 0 1 11 1 0 0 0 0 1 11 1 1 1 1 1 1 11 1 1 1 1 1 1 1NMM:InteractiveComputingwithMatlab page33ColonNotation(5)Finally,colonnotationisusedtoconvertanyvectorormatrixtoacolumnvector.Examples:>> x = 1:4;>> y = x(:)y =1234>> A = rand(2,3);>> v = A(:)v =0.95010.23110.60680.48600.89130.76210.4565Note: Therandfunctiongeneratesrandomelementsbetweenzeroandone. Repeatingtheprecedingstatementswill,inalllikelihood,producedierentnumericalvaluesfortheelementsof v.NMM:InteractiveComputingwithMatlab page34Additional TypesofVariablesThebasicMatlabvariableisamatrixatwodimensionalarrayofvalues. Theelementsofamatrixvariablecaneitherbenumericvaluesorcharacters. Iftheelementsarenumericvaluestheycaneitherberealorcomplex(imaginary).Moregeneralvariabletypesareavailable: n-dimensionalarrays(wheren>2),structs,cellarrays,andobjects. Numeric(realandcomplex)andstringarraysofdimensiontwoorlesswillbesucientforourpurposes.Wenowconsidersomesimplevariationsonnumericandstringmatrices: ComplexNumbers Strings PolynomialsNMM:InteractiveComputingwithMatlab page35ComplexNumbersMatlabautomaticallyperformscomplexarithmetic>> sqrt(-4)ans =0 + 2.0000i>> x = 1 + 2*i (or, x = 1 + 2*j)x =1.0000 + 2.0000i>> y = 1 - 2*iy =1.0000 - 2.0000i>> z = x*yz =5NMM:InteractiveComputingwithMatlab page36UnitImaginaryNumbersiandjareordinaryMatlabvariablesthathavebepreassignedthevalue1.>> i^2ans =-1Bothoreitheriandjcanbereassigned>> i = 5;>> t = 8;>> u = sqrt(i-t) (i-t = -3, not -8+i)u =0 + 1.7321i>> u*uans =-3.0000>> A = [1 2; 3 4];>> i = 2;>> A(i,i) = 1A =1 23 1NMM:InteractiveComputingwithMatlab page37EulerNotation(1)Eulernotationrepresentsacomplexnumberbyaphaserz=eix=Re(z)= |z| cos()= cos()y=iIm(z)=i|z| sin()=i sin()realimaginaryxiy z = eiNMM:InteractiveComputingwithMatlab page38FunctionsforComplexArithmetic(1)Function Operationabs Computethemagnitudeofanumberabs(z)isequivalenttotosqrt( real(z)^2 + imag(z)^2 )angle AngleofcomplexnumberinEulernotationexp If xisreal,exp(x)=exIf ziscomplex,exp(z)=eRe(z)(cos(Im(z) + i sin(Im(z))conj Complexconjugateofanumberimag Extracttheimaginarypartofacomplexnumberreal ExtracttherealpartofacomplexnumberNote: Whenworkingwithcomplexnumbers,itisagoodideatoreserveeitheriorjfortheunitimaginaryvalue1.NMM:InteractiveComputingwithMatlab page39FunctionsforComplexArithmetic(2)Examples:>> zeta = 5; theta = pi/3;>> z = zeta*exp(i*theta)z =2.5000 + 4.3301i>> abs(z)ans =5>> sqrt(z*conj(z))ans =5>> x = real(z)x =2.5000>> y = imag(z)y =4.3301>> angle(z)*180/pians =60.0000Remember: ThereisnodegreesmodeinMatlab. Allanglesaremeasuredinradians.NMM:InteractiveComputingwithMatlab page40Strings Stringsarematriceswithcharacterelements. Stringconstantsareenclosedinsinglequotes ColonnotationandsubscriptoperationsapplyExamples:>> first = John;>> last = Coltrane;>> name = [first, ,last]name =John Coltrane>> length(name)ans =13>> name(9:13)ans =traneNMM:InteractiveComputingwithMatlab page41FunctionsforStringManipulation(1)Function Operationchar convertanintegertothecharacterusingASCIIcodes,orcombinecharactersintoacharactermatrixfindstr ndsonestringinanotherstringlength returnsthenumberofcharactersinastringnum2str convertsanumbertostringstr2num convertsastringtoanumberstrcmp comparestwostringsstrmatch identiesrowsofacharacterarraythatbeginwithastringstrncmp comparestherstnelementsoftwostringssprintf convertsstringsandnumericvaluestoastringNMM:InteractiveComputingwithMatlab page42FunctionsforStringManipulation(2)Examples:>> msg1 = [There are ,num2str(100/2.54), inches in a meter]message1 =There are 39.3701 inches in a meter>> msg2 = sprintf(There are %5.2f cubic inches in a liter,1000/2.54^3)message2 =There are 61.02 cubic inches in a liter>> both = char(msg1,msg2)both =There are 39.3701 inches in a meterThere are 61.02 cubic inches in a liter>> strcmp(msg1,msg2)ans =0>> strncmp(msg1,msg2,9)ans =1>> findstr(in,msg1)ans =19 26NMM:InteractiveComputingwithMatlab page43PolynomialsMatlabpolynomialsarestoredasvectorsofcoecients. ThepolynomialcoecientsarestoredindecreasingpowersofxPn(x)=c1xn+ c2xn1+. . . + cnx + cn+1Example: Evaluatex32x + 12atx= 1.5>> c = [1 0 -2 12];>> polyval(c,1.5)ans =12.3750NMM:InteractiveComputingwithMatlab page44FunctionsforManipulatingPolynomialsFunction Operationsperformedconv product(convolution)oftwopolynomialsdeconv division(deconvolution)oftwopolynomialspoly Createapolynomialhavingspeciedrootspolyder Dierentiateapolynomialpolyval Evaluateapolynomialpolyfit Polynomialcurvetroots FindrootsofapolynomialNMM:InteractiveComputingwithMatlab page45ManipulationofMatricesandVectorsThenameMatlabevolvedasanabbreviationofMATrixLABoratory. ThedatatypesandsyntaxusedbyMatlabmakeiteasytoperformthestandardoperationsoflinearalgebraincludingadditionandsubtraction,multiplicationofvectorsandmatrices,andsolvinglinearsystemsofequations.Chapter7providesadetailedreviewoflinearalgebra. Hereweprovideasimpleintroductiontosomeoperationsthatarenecessaryforroutinecalculation. Vectoradditionandsubtraction Innerandouterproducts Vectorization ArrayoperatorsNMM:InteractiveComputingwithMatlab page46VectorAdditionandSubtractionVectorandadditionandsubtractionareelement-by-elementoperations.Example:>> u = [10 9 8]; (u andv are row vectors)>> v = [1 2 3];>> u+vans =11 11 11>> u-vans =9 7 5NMM:InteractiveComputingwithMatlab page47VectorInnerandOuterProductsTheinnerproductcombinestwovectorstoformascalar=u v=uvT=

uiviTheouterproductcombinestwovectorstoformamatrixA=uTv ai,j=uivjNMM:InteractiveComputingwithMatlab page48InnerandOuterProductsinMatlabInnerandouterproductsaresupportedinMatlabasnaturalextensionsofthemultiplicationoperator>> u = [10 9 8]; (u andv are row vectors)>> v = [1 2 3];>> u*v (inner product)ans =52>> u*v (outer product)ans =10 20 309 18 278 16 24NMM:InteractiveComputingwithMatlab page49Vectorization Vectorizationistheuseofsingle,compactexpressionsthatoperateonallelementsofavectorwithoutexplicitlyexecutingaloop. TheloopisexecutedbytheMatlabkernel,whichismuchmoreecientatloopingthaninterpretedMatlabcode. Vectorizationallowscalculationstobeexpressedsuccintlysothatprogrammersgetahighlevel(asopposedtodetailed)viewoftheoperationsbeingperformed. VectorizationisimportanttomakeMatlaboperateeciently.NMM:InteractiveComputingwithMatlab page50VectorizationofBuilt-inFunctionsMostbuilt-infunctionsupportvectorizedoperations. Iftheinputisascalartheresultisascalar. Iftheinputisavectorormatrix,theoutputisavectorormatrixwiththesamenumberofrowsandcolumnsastheinput.Example:>> x = 0:pi/4:pi (dene a row vector)x =0 0.7854 1.5708 2.3562 3.1416>> y = cos(x) (evaluate cosine of eachx(i)y =1.0000 0.7071 0 -0.7071 -1.0000ContrastwithFortranimplementation:real x(5),y(5)pi = 3.14159624dx = pi/4.0do 10 i=1,5x(i) = (i-1)*dxy(i) = sin(x(i))10 continueNoexplicitloopisnecessaryinMatlab.NMM:InteractiveComputingwithMatlab page51VectorCalculations(3)Moreexamples>> A = pi*[ 1 2; 3 4]A =3.1416 6.28329.4248 12.5664>> S = sin(A)S =0 00 0>> B = A/2B =1.5708 3.14164.7124 6.2832>> T = sin(B)T =1 0-1 0NMM:InteractiveComputingwithMatlab page52ArrayOperatorsArrayoperatorssupportelement-by-elementoperationsthatarenotdenedbytherulesoflinearalgebraArrayoperatorsaredesignatedbyaperiodprependedtothestandardoperatorSymbol Operation.* element-by-elementmultiplication./ element-by-elementrightdivision.\ element-by-elementleftdivision.^ element-by-elementexponentiationArrayoperatorsareaveryimportanttoolforwritingvectorizedcode.NMM:InteractiveComputingwithMatlab page53UsingArrayOperators(1)Examples: Element-by-elementmultiplicationanddivision>> u = [1 2 3];>> v = [4 5 6];>> w = u.*v (element-by-element product)w =4 10 18>> x = u./v (element-by-element division)x =0.2500 0.4000 0.5000>> y = sin(pi*u/2) .* cos(pi*v/2)y =1 0 1>> z = sin(pi*u/2) ./ cos(pi*v/2)Warning: Divide by zero.z =1 NaN 1NMM:InteractiveComputingwithMatlab page54UsingArrayOperators(2)Examples: Applicationtomatrices>> A = [1 2 3 4; 5 6 7 8];>> B = [8 7 6 5; 4 3 2 1];>> A.*Bans =8 14 18 2020 18 14 8>> A*B??? Error using ==> *Inner matrix dimensions must agree.>> A*Bans =60 20164 60>> A.^2ans =1 4 9 1625 36 49 64NMM:InteractiveComputingwithMatlab page55TheMatlabWorkspace(1)Allvariablesdenedastheresultofenteringstatementsinthecommandwindow,existintheMatlabworkspace.AtthebeginningofaMatlabsession,theworkspaceisempty.Beingawareoftheworkspaceallowsyouto Create,assign,anddeletevariables Loaddatafromexternalles ManipulatetheMatlabpathNMM:InteractiveComputingwithMatlab page56TheMatlabWorkspace(2)Theclearcommanddeletesvariablesfromtheworkspace. Thewhocommandliststhenamesofvariablesintheworkspace>> clear (Delete all variables from the workspace)>> who(No response, no variables are dened after clear)>> a = 5; b = 2; c = 1;>> d(1) = sqrt(b^2 - 4*a*c);>> d(2) = -d(1);>> whoYour variables are:a b c dNMM:InteractiveComputingwithMatlab page57TheMatlabWorkspace(3)Thewhoscommandliststhename,size,memoryallocation,andtheclassofeachvariablesdenedintheworkspace.>> whosName Size Bytes Classa 1x1 8 double arrayb 1x1 8 double arrayc 1x1 8 double arrayd 1x2 32 double array (complex)Grand total is 5 elements using 56 bytesBuilt-invariableclassesaredouble,char,sparse,struct,andcell. Theclassofavariabledeterminesthetypeofdatathatcanbestoredinit. Wewillbedealingprimarilywithnumericdata,whichisthedoubleclass,andoccasionallywithstringdata,whichisinthecharclass.NMM:InteractiveComputingwithMatlab page58WorkingwithExternal DataFilesWritedatatoalesave fileNamesave fileName variable1 variable2 . . .save fileName variable1 variable2 . . . -asciiReadindatastoredinmatricesload fileNameload fileName matrixVariableNMM:InteractiveComputingwithMatlab page59LoadingDatafromExternal FileExample: Loaddatafromaleandplotthedata>> load wolfSun.dat;>> xdata = wolfSun(:,1);>> ydata = wolfSun(:,2);>> plot(xdata,ydata)NMM:InteractiveComputingwithMatlab page60TheMatlabPathMatlabwillonlyusethosefunctionsanddatalesthatareinitspath.ToaddN:\IMAUSER\ME352\PS2tothepath,type>> p = path;>> path(p,N:\IMAUSER\ME352\PS2);Matlabversion5hasaninteractivepatheditorthatmakesiteasytoadjustthepathThepathspecicationstringdependsontheoperatingsystem.OnaUnix/Linuxcomputerapathsettingoperationmightlooklike:>> p = path;>> path(p,~/matlab/ME352\ps2);NMM:InteractiveComputingwithMatlab page61Plotting Plotting(x, y)data Axisscalingandannotation 2D(contour)and3D(surface)plottingNMM:InteractiveComputingwithMatlab page62Plotting (x, y)Data(1)TwodimensionalplotsarecreatedwiththeplotfunctionSyntax:plot(x,y)plot(xdata,ydata,symbol)plot(x1,y1,x2,y2, . . . )plot(x1,y1,symbol1,x2,y2,symbol2, . . . )Note: xandymusthavethesameshape,x1andy1musthavethesameshape,x2andy2musthavethesameshape,etc.NMM:InteractiveComputingwithMatlab page63Plotting (x, y)Data(2)Example: Asimplelineplot>> x = linspace(0,2*pi);>> y = sin(x);>> plot(x,y);0 2 4 6 8-1-0.500.51NMM:InteractiveComputingwithMatlab page64LineandSymbol Types(1)Thecurvesforadatasetaredrawnfromcombinationsofthecolor,symbol,andlinetypesinthefollowingtable.Color Symbol Liney yellow . point - solidm magenta o circle : dottedc cyan x x-mark -. dashdotr red + plus -- dashedg green * starb blue s squarew white d diamondk black v triangle(down)^ triangle(up)< triangle(left)> triangle(right)p pentagramh hexagramTochooseacolor/symbol/linestyle,choseoneentryfromeachcolumn.NMM:InteractiveComputingwithMatlab page65LineandSymbol Types(2)Examples:Putyellowcirclesatthedatapoints:plot(x,y,yo)Plotareddashedlinewithnosymbols:plot(x,y,r--)Putblackdiamondsateachdatapointandconnectthediamondswithblackdashedlines:plot(x,y,kd--)NMM:InteractiveComputingwithMatlab page66AlternativeAxisScaling(1)Combinationsoflinearandlogarithmicscalingareobtainedwithfunctionsthat,otherthantheirname,havethesamesyntaxastheplotfunction.Name Axisscalingloglog log10(y)versuslog10(x)plot linearyversusxsemilogx linearyversuslog10(x)semilogy log10(y)versuslinearxNote: Asexpected,useoflogarithmicaxisscalingfordatasetswithnegativeorzerovaluesresultsinaerror.Matlabwillcomplainandthenplotonlythepositive(nonzero)data.NMM:InteractiveComputingwithMatlab page67AlternativeAxisScaling(2)Example:>> x = linspace(0,3);>> y = 10*exp(-2*x);>> plot(x,y);0 1 2 30246810>> semilogy(x,y);0 1 2 310-210-1100101NMM:InteractiveComputingwithMatlab page68Multipleplotspergurewindow(1)Thesubplotfunctionisusedtocreateamatrixofplotsinasinglegurewindow.Syntax:subplot(nrows,ncols,thisPlot)Repeatthevaluesofnrowsandncolsforallplotsinasinglegurewindow. IncrementthisPlotforeachplotExample:>> x = linspace(0,2*pi);>> subplot(2,2,1);>> plot(x,sin(x)); axis([0 2*pi -1.5 1.5]); title(sin(x));>> subplot(2,2,2);>> plot(x,sin(2*x)); axis([0 2*pi -1.5 1.5]); title(sin(2x));>> subplot(2,2,3);>> plot(x,sin(3*x)); axis([0 2*pi -1.5 1.5]); title(sin(3x));>> subplot(2,2,4);>> plot(x,sin(4*x)); axis([0 2*pi -1.5 1.5]); title(sin(4x));(Seenextslidefortheplot.)NMM:InteractiveComputingwithMatlab page69Multipleplotspergurewindow(2)0 2 4 6-1.5-1-0.500.511.5sin(x)0 2 4 6-1.5-1-0.500.511.5sin(2x)0 2 4 6-1.5-1-0.500.511.5sin(3x)0 2 4 6-1.5-1-0.500.511.5sin(4x)NMM:InteractiveComputingwithMatlab page70PlotAnnotationName Operation(s)performedaxis Resetaxislimitsgrid Drawgridlinescorrespondingtothemajormajorticksonthexandyaxesgtext Addtexttoalocationdeterminedbyamouseclicklegend Createalegendtoidentifysymbolsandlinetypeswhenmultiplecurvesaredrawnonthesameplottext Addtexttoaspecied(x, y)locationxlabel Labelthex-axisylabel Labelthey-axistitle AddatitleabovetheplotNMM:InteractiveComputingwithMatlab page71PlotAnnotationExample>> D = load(pdxTemp.dat); m = D(:,1); T = D(:,2:4);>> plot(m,t(:,1),ro,m,T(:,2),k+,m,T(:,3),b-);>> xlabel(Month);>> ylabel(Temperature ({}^\circ F));>> title(Monthly average temperature at PDX);>> axis([1 12 20 100]);>> legend(High,Low,Average,2);2 4 6 8 10 122030405060708090100MonthTemperature ( F)Monthly average temperatures at PDXHigh LowAverageNote: ThepdxTemp.datleisinthedatadirectoryoftheNMMtoolbox. MakesurethetoolboxisinstalledandisincludedintheMatlabpath.NMM:InteractiveComputingwithMatlab page72