实验二MATLAB基础知识二.docx

实验二MATLAB基础知识二.docx

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实验二MATLAB基础知识二

Experiment1.FundamentalKnowledgeofMatlab（II>

【ExperimentalPurposes】

1、熟悉并掌握MATLAB的工作环境。

2、运行简单命令，实现数组及矩阵的输入输出，了解在MATLAB下如何绘图。

【ExperimentalPrinciple】

1.Vectors

Let'sstartoffbycreatingsomethingsimple,likeavector.Entereachelementofthevector（separatedbyaspace>betweenbrackets,andsetitequaltoavariable.Forexample,tocreatethevectora,enterintotheMATLABcommandwindow（youcan"copy"and"paste"fromyourbrowserintoMATLABtomakeiteasy>:

b5E2RGbCAP

a=[123456987]

MATLABshouldreturn:

a=

123456987

Togenerateaseriesthatdoesnotusethedefaultofincrementingby1,specifyanadditionalvaluewiththecolonoperator（first:

step:

last>.InbetweenthestartingandendingvalueisastepvaluethattellsMATLABhowmuchtoincrement（ordecrement,ifstepisnegative>betweeneachnumberitgenerates.Togenerateavectorwithelementsbetween0and20,incrementingby2（thismethodisfrequentlyusedtocreateatimevector>,usep1EanqFDPw

t=0:

2:

20

t=

02468101214161820

Manipulatingvectorsisalmostaseasyascreatingthem.First,supposeyouwouldliketoadd2toeachoftheelementsinvector'a'.Theequationforthatlookslike:

DXDiTa9E3d

b=a+2

b=

34567811109

Nowsuppose,youwouldliketoaddtwovectorstogether.Ifthetwovectorsarethesamelength,itiseasy.Simplyaddthetwoasshownbelow:

RTCrpUDGiT

c=a+b

c=

468101214201816

Subtractionofvectorsofthesamelengthworksexactlythesameway.5PCzVD7HxA

MATLABsometimesstoressuchalistinamatrixwithjustonerow,andothertimesinamatrixwithjustonecolumn.Inthefirstinstance,sucha1-rowmatrixiscalledarow-vector。

inthesecondinstance,sucha1-columnmatrixiscalledacolumn-vector.Eitherway,thesearemerelydifferentwaysforstoringvectors,notdifferentkindsofvectors.jLBHrnAILg

2.MatricesandArrays

ThemostbasicMATLABdatastructureisthematrix:

atwo-dimensional,rectangularlyshapeddatastructurecapableofstoringmultipleelementsofdatainaneasilyaccessibleformat.Thesedataelementscanbenumbers,characters,logicalstatesoftrueorfalse,orevenotherMATLABstructuretypes.MATLABusesthesetwo-dimensionalmatricestostoresinglenumbersandlinearseriesofnumbersaswell.Inthesecases,thedimensionsare1-by-1and1-by-nrespectively,wherenisthelengthofthenumericseries.MATLABalsosupportsdatastructuresthathavemorethantwodimensions.ThesedatastructuresarereferredtoasarraysintheMATLABdocumentation.xHAQX74J0X

MATLABisamatrix-basedcomputingenvironment.AllofthedatathatyouenterintoMATLABisstoredintheformofamatrixoramultidimensionalarray.Evenasinglenumericvaluelike100isstoredasamatrix（inthiscase,amatrixhavingdimensions1-by-1>:

LDAYtRyKfE

A=100。

NameSizeBytesClass

A1x18doublearray

EnteringmatricesintoMATLABisthesameasenteringavector,excepteachrowofelementsisseparatedbyasemicolon（。

>orareturn:

Zzz6ZB2Ltk

B=[1234。

5678。

9101112]

B=

1234

5678

9101112

B=[1234

5678

9101112]

B=

1234

5678

9101112

Thesquarebracketsoperatorconstructstwo-dimensionalmatricesonly,（including0-by-0,1-by-1,and1-by-nmatrices>.dvzfvkwMI1

MatricesinMATLABcanbemanipulatedinmanyways.Forone,youcanfindthetransposeofamatrixusingtheapostrophekey:

rqyn14ZNXI

C=B'

C=

159

2610

3711

4812

ItshouldbenotedthatifChadbeencomplex,theapostrophewouldhaveactuallygiventhecomplexconjugatetranspose.Togetthetranspose,use.'（thetwocommandsarethesameifthematixisnotcomplex>.EmxvxOtOco

NowyoucanmultiplythetwomatricesBandCtogether.Rememberthatordermatterswhenmultiplyingmatrices.SixE2yXPq5

D=B*C

D=

3070110

70174278

110278446

D=C*B

D=

107122137152

122140158176

137158179200

152176200224

Anotheroptionformatrixmanipulationisthatyoucanmultiplythecorrespondingelementsoftwomatricesusingthe.*operator（thematricesmustbethesamesizetodothis>.6ewMyirQFL

E=[12。

34]

F=[23。

45]

G=E.*F

E=

12

34

F=

23

45

G=

26

1220

Ifyouhaveasquarematrix,likeE,youcanalsomultiplyitbyitselfasmanytimesasyoulikebyraisingittoagivenpower.kavU42VRUs

E^3

ans=

3754

81118

Ifwantedtocubeeachelementinthematrix,justusetheelement-by-elementcubing.y6v3ALoS89

E.^3

ans=

18

2764

Youcanalsofindtheinverseofamatrix:

X=inv（E>

X=

-2.00001.0000

1.5000-0.5000

oritseigenvalues:

eig（E>

ans=

-0.3723

5.3723

Thereisevenafunctiontofindthecoefficientsofthecharacteristicpolynomialofamatrix.The"poly"functioncreatesavectorthatincludesthecoefficientsofthecharacteristicpolynomial.M2ub6vSTnP

p=poly（E>

p=

1.0000-5.0000-2.0000

Rememberthattheeigenvaluesofamatrixarethesameastherootsofitscharacteristicpolynomial:

0YujCfmUCw

roots（p>

ans=

5.3723

-0.3723

3.Functions

Tomakelifeeasier,MATLABincludesmanystandardfunctions.Eachfunctionisablockofcodethataccomplishesaspecifictask.MATLABcontainsallofthestandardfunctionssuchassin,cos,log,exp,sqrt,aswellasmanyothers.Commonlyusedconstantssuchaspi,andiorjforthesquarerootof-1,arealsoincorporatedintoMATLAB.eUts8ZQVRd

sin（pi/4>

ans=

0.7071

Todeterminetheusageofanyfunction,typehelp[functionname]attheMATLABcommandwindow.MATLABevenallowsyoutowriteyourownfunctionswiththefunctioncommand。

followthelinktolearnhowtowriteyourownfunctionsandseealistingofthefunctionswecreatedforthistutorial.sQsAEJkW5T

4.Plotting

ItisalsoeasytocreateplotsinMATLAB.Supposeyouwantedtoplotasinewaveasafunctionoftime.Firstmakeatimevector（thesemicolonaftereachstatementtellsMATLABwedon'twanttoseeallthevalues>andthencomputethesinvalueateachtime.GMsIasNXkA

t=0:

0.25:

7。

y=sin（t>。

plot（t,y>

Theplotcontainsapproximatelyoneperiodofasinewave.BasicplottingisveryeasyinMATLAB,andtheplotcommandhasextensiveadd-oncapabilities.Iwouldrecommendyouvisittheplottingpagetolearnmoreaboutit.TIrRGchYzg

5.Polynomials

InMATLAB,apolynomialisrepresentedbyavector.TocreateapolynomialinMATLAB,simplyentereachcoefficientofthepolynomialintothevectorindescendingorder.Forinstance,let'ssayyouhavethefollowingpolynomial:

7EqZcWLZNX

ToenterthisintoMATLAB,justenteritasavectorinthefollowingmannerlzq7IGf02E

x=[13-15-29]

x=

13-15-29

MATLABcaninterpretavectoroflengthn+1asannthorderpolynomial.Thus,ifyourpolynomialismissinganycoefficients,youmustenterzerosintheappropriateplaceinthevector.Forexample,zvpgeqJ1hk

wouldberepresentedinMATLABas:

y=[10001]

Youcanfindthevalueofapolynomialusingthepolyvalfunction.Forexample,tofindthevalueoftheabovepolynomialats=2,NrpoJac3v1

z=polyval（[10001],2>

z=

17

Youcanalsoextracttherootsofapolynomial.Thisisusefulwhenyouhaveahigh-orderpolynomialsuchas1nowfTG4KI

Findingtherootswouldbeaseasyasenteringthefollowingcommand。

fjnFLDa5Zo

roots（[13-15-29]>

ans=

-5.5745

2.5836

-0.7951

0.7860

Let'ssayyouwanttomultiplytwopolynomialstogether.Theproductoftwopolynomialsisfoundbytakingtheconvolutionoftheircoefficients.MATLAB'sfunctionconvthatwilldothisforyou.tfnNhnE6e5

x=[12]。

y=[148]。

z=conv（x,y>

z=

161616

Dividingtwopolynomialsisjustaseasy.Thedeconvfunctionwillreturntheremainderaswellastheresult.Let'sdividezbyyandseeifwegetx.HbmVN777sL

[xx,R]=deconv（z,y>

xx=

12

R=

0000

Asyoucansee,thisisjustthepolynomial/vectorxfrombefore.Ifyhadnotgoneintozevenly,theremaindervectorwouldhavebeensomethingotherthanzero.V7l4jRB8Hs

Ifyouwanttoaddtwopolynomialstogetherwhichhavethesameorder,asimplez=x+ywillwork（thevectorsxandymusthavethesamelength>.Inthegeneralcase,theuser-definedfunction,polyaddcanbeused.Tousepolyadd,copythefunctionintoanm-file,andthenuseitjustasyouwouldanyotherfunctionintheMATLABtoolbox.Assumingyouhadthepolyaddfunctionstoredasam-file,andyouwantedtoaddthetwounevenpolynomials,xandy,youcouldaccomplishthisbyenteringthecommand:

83lcPA59W9

z=polyadd（x,y>

x=

12

y=

148

z=

1510

【Experimentcontentsandprocedure】

1、运行简单命令，实现数组及矩阵的输入输出；

2、运行特殊矩阵的输入及输出；

MATLABhasanumberoffunctionsthatcreatedifferentkindsofmatrices.SomecreatespecializedmatricesliketheHankelorVandermondematrix.Thefunctionsshowninthetablebelowcreatematricesformoregeneraluse.mZkklkzaaP

Function

Description

ones

Createamatrixorarrayofallones.

zeros

Createamatrixorarrayofallzeros.

eye

Createamatrixwithonesonthediagonalandzeroselsewhere.

accumarray

Distributeelementsofaninputmatrixtospecifiedlocationsinanoutputmatrix,alsoallowingforaccumulation.

diag

Createadiagonalmatrixfromavector.

magic

Createasquarematrixwithrows,columns,anddiagonalsthatadduptothesamenumber.

rand

Createamatrixorarrayofuniformlydistributedrandomnumbers.

randn

Createamatrixorarrayofnormallydistributedrandomnumbersandarrays.

randperm

Createavector（1-by-nmatrix>containingarandompermutationofthespecifiedintegers.

Mostofthesefunctionsreturnmatricesoftypedouble（double-precisionfloatingpoint>.However,you