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HuazhongUniversityofScien__andTechnologySchoolofManagement《__the__ticalProgramming》管理学院财政1001U201015883姚小晋YukunBao2012/5ExperimentalrequirementsTheexperimentalreportsshouldinclude:aProblemstatement;bModelingpro__ss:includingbutnotlimitedtovariabledefinitionalgorithmdesigndatadescriptionkeytechniquesdescriptionetc.c____ysisanddiscussion.ExperimentalContents
1.Programtheequation1-3andsolvethemultistepdecisionproblemofMerchantsCrossingRiverandtheprogrammingcanbeusedtocarryNservantsbyNmerchants.Requirements:aChooseanyprogramminglanguageasyoulike.bProgrammingflowchartsandalgorithmdesigningpro__ssareneeded.cCommentsshouldbeincludedinthesour__code.Problemstatement:Threemerchantswanttocrosstheriveralongwiththreeservants.Thereisonlyoneboatandthecapacityoftheboatistwopeople.Theyh__etocrosstheriverbythemselves.Howevertheservantsplotthatifthenumberofservantsismorethanthemerchantstheywillkillthemerchantswhatweh__etoistoletthemcrosstheriversafely.Modelingpro__ss:Inorderto__kethemerchantssafewemustensurethatthenumberofmerchantsisnotlessthanthenumberofservantsinbothsidesoftheriver.Thenwecandefinethestateoftheonesideofriver:thenumberofthemerchantsisxkthenumberoftheservantsisykthevectorsk=xkyk.Sointhesafeconditionthesetofthestatecanbewrittenas:S={xy|x=0y=0123;x=3y=0123;x=y=12}Thendefinethatinthekthcrossingtheriverthenumberofthemerchantsintheboatisukthenumberoftheservantsisvkthevectordk=ukvkwhichisthedecision.ItisdenotedbyDD={uv|0u+v3uv=012}Whenkisanoddnumberitmeansthattheboatisfromonesideoftheothersidewhenkisaevennumberitmeansthattheboatisfromtheothersidetooneside.Thenweget:Sk+1=Sk+-1^k*dkPro__dure:functionjueche=guohen=inputPleaseinputthenumberofmerchants:;nn=inputPleaseinputthenumberofservants:;nnn=inputPleaseinputthecapacityoftheboats:;%generatethedecisionjc=1;%putthedecisionvectorintothe__trixdjcistherowlabeloftheinsertsofnewelements.fori=0:nnnforj=0:nnnifi+j=nnni+j0%meettherequirement{uv|1=u+v=nnnuv=012}djc1:3=[ij1];%expandintothreedimensionswhilegeneratingadecisionvectordjc+11:3=[-i-j-1];%generatereciprocalvectorjc=jc+2;%duetogeneratetwovectorsweneedtomovetwostepsendj=0;endend%generatestatearraykx=1;%putthestatevectorintothe__trixAwhichissimilartothe__trixdfori=n:-1:0forj=nn:-1:0ifi=jn-i=nn-j||i==0|i==n%i=jn-i=nn-j|i==0|i==nistheconstrainofthestateAkx1:3=[ij1];%generatethesetofthestatearrayAkx+11:3=[ij0];kx=kx+2;endendj=nn;end;%letthestatevectorgenerateabstract__trixk=1/2*sizeA1;CX=zeros2*k2*k;a=sized1;fori=1:2*kforj=1:ac=Ai:+dj:;x=findA:1==c1A:2==c2A:3==c3vix=1;%whilexisnullvwillnotchangeitsvalueendend%dijstraalgorithmx=1;y=sizeA1;m=sizev1;T=zerosm1;T=T.^-1;lmd=T;P=T;S=zerosm1;Sx=1;Px=0;lmdx=0;k=x;while1a=findS==0;aa=findS==1;ifsizeaa1==mbreak;endforj=1:sizea1pp=aj1;ifvkpp~=0ifTppPk+vkppTpp=Pk+vkpp;lmdpp=k;endendendmi=minTa;ifmi==infbreak;elsed=findT==mi;d=d1;Pd=mi;Td=inf;k=d;Sd=1;endendiflmdy==infjueche=cannotreach;return;endjueche1=y;g=2;h=y;while1ifh==xbreak;endjuecheg=lmdh;g=g+1;h=lmdh;endjueche=Ajueche:;jueche:3=[];FlowchartsandalgorithmdesigingThetransferpro__ssisasfollows:Intherectanglethefirstnumberstandsforthenumberofthemerchantsandthesecondnumberstandforthenumberofservants.leftsideoftheriverrightsideoftheriverontheboatWhenitcomestonmerchantsandnservantswejustneedtoinputthenumbernatthefirstofthepro__dure.Itisveryconvenientforustosolven-thcoupleproblem.
2.GivenTable1andequation3inpage10completethefollowingworkwithne__ssarydescriptionand____ysisaFitEq.3withdatafrom1790to1900inTable1Calculaterandx0anddrawthefittingcurve;t1=0:11;%from1790to1900onedifferen__representonedecadex1=[
3.
95.
37.
29.
612.
917.
123.
231.
438.
650.
262.976];%thepopulationfrom1790to1900y1=logx1;%takethelogformofthepopulationthuscan__keitlineartoacquiretheparameters.p1=polyfitt1y11;%linearfittingtogettheparametersY1=exppolyvalp1t1;%accordingtothelinearmodeltogetitsoutputplott1x1+t1Y1;%drawthepictureoftheoriginaldataandtheoutputofthedataP1=[
0.
27431.1580]r=
0.2743/10=
0.02743x0=e
1.158=
4.1884bFitEq.3withdatafrom1790to2000inTable1calculaterandx0anddrawthefittingcurvet2=0:21;%from1790to2000onedifferen__representonedecadex2=[
3.
95.
37.
29.
612.
917.
123.
231.
438.
650.
262.
97692106.
5123.
2131.
7150.
7179.
3204226.
5251.
4281.4];%thepopulationfrom1790to2000y2=logx2;%takethelogformofthepopulationthuscan__keitlineartoacquiretheparameters.p2=polyfitt2y21;%linearfittingtogettheparametersY2=exppolyvalp2t2;%accordingtothelinearmodeltogetitsoutputplott2x2+t2Y2;%drawthepictureoftheoriginaldataandtheoutputofthedataP2=[
0.
20221.5970];sor=
0.0202x0=
6.0450____ysis:fromtheabovetwofigureswecanseethatthismodelissuitableforthegrowthofpopulationin19th__nturybutin20ththegrowthofpopulationbecomeslowly.Inthiscasethismodelisnotsuitable.Duetothespa__andresour__sarelimited.Sothismodelisridiculouspredictthefuturepopulation.Weregardthepopulationasafunctionoftimeneglectingtheinfluen__ofdifferen__betweenindividualstothegrowthofpopulation.Thegrowthrateofpopulationisaconstantwhichmeansthatpeopleliveinanenviro__entthatdoesnotchangeastimegoesby.Howeverthismodelissuitableforpeoplethatlivein__rtainclosespa__.Andamongthetimeintheresearchtherearenopeoplemovinginorout.Theseassumptionsareharshandunrealistic.Sothismodelisfitintothepast.Itisnotsuitabletopredictthefuture.
3.ProgramtheEq.2inP64anddrawFigure3-4inpage
65.Thentryto____ysistheproblem.Problemstatement:Afarminvest4yuanwhichcan__kea80kgpig’sweightincrease2kg.Atpresenttheunitpri__inthe__rketis8yuan/kgbutitforecaststhatthepri__willdecreaseby
0.1yuaneveryday.Investmentcan__ketheweightofthepigsincreaseastimegoesonbutthesellingpri__unitpri__decreases.Sotheremustbeanopti__ltimetosellthepigswhichcan__ketheprofit__ximize.Soweneedto____yzethefactorsofthisissueandfindtheopti__ltime.Modelingpro__ss:Firstdefinesomevariablesasfollows:t~timedayw~weightofpigkgp~unitpri__yuan/kgR~revenueyuanC~theinvestmentoftdaysyuanQ~pureprofityuanr~theincrementalweightofthepigg~thedes__ndentofthedaily__rketpri__ofthepig;ThenR=p*wC=4*tQ=R-C-80*8O__ectivefunction:Q=8-g*t*80+r*t-4*t-640Fromtheproblemstatementwecanknowthatg=
0.1r=2Thenweget:t=4*r-40*g-2/r*g;Sensitivity____ysis:1assumethatg=
0.1findhowthechangeofrcaninfluen__tt=40*r-60/rr
1.5;pro__dure:r=
1.5:
0.001:3;%definethescopeoftheincrementalweightofthepigfori=1:1501;t:i=40*r:i-60/r:i;%thefunctionrelationshipbetweentimeandtheincrementalweightofthepigendplotrt;%drawgraphforrandtgridon%drawgridlines2assumethatr=2findhowthechangeofgcaninfluen__t;t=3-20*g/g0=g=
0.15Pro__dure:g=
0.06:
0.0001:
0.15;%definethescopeofthedes__ndentofthedaily__rketpri__ofthepigfori=1:901;T:i=3-20*g:i/g:i;%thefunctionrelationshipbetweentimeandthedes__ndentofthedaily__rketpri__ofthepigendplotgT;%drawthegraphforgandTgridon____ysis:Wecanuserelativevariabletomeasurethesensitivitytotheparameters.ThesensitivityfromttoraredenotedbyStrWhenr=2wecancalculatethatStr=3Whichmeansthatthepig’sweightrincrease1%everydaythesaletimedelay3%.SimilarlydefineStgasthesensitivityfromttogthenwheng=
0.1Stg=-3Namelythepig’spri__gdecrease1%everydaythesaletimeshouldbeadvan__d3%.Inthemodelingpro__ssweassumethattheincreaseinthepig’sweightandthedecreaseofthepri__bothareconstantsthenwandparelinearfunctions.Thissimplifytherealsituation.Amorepracticalmodelshouldconsiderthenonlinearityandun__rtainty.Forexamplew=wtp=ptthenQt=pt*wt-4*t-
640.usethedifferentialmethodwecangettheoptimumsolution:p’twt+pt*w’t=4sotheopti__lsaletimeiswhentheincreaseoftheprofitequaltotheinvestmenteveryday.Inadditionfromthesensitivity____ysiswegetStr=3sowhen
1.8=w’=
2.2lessthan10%theresultshouldbe7=t=13lessthan30%.Ifp’=-
0.1istheworstconditionorit__ybe__allertshouldbelarger.Sothebestsolutionistoesti__tepp’ww’againafteraweek.
4.ProgramtheEq.14inP139andcompletethefollowingProblemstatement:ThetotalnumberofpeopleisN.thereisthreekindsofpeople:healthypeople、patientsandremovedpeople.Thesethreekindsofpeopletakeaper__ntageofNwhicharedenotedbystitandrt.therateofthepatientdailycontactisdenotedbydenotedbyλtherateofdailycureisμandsig__=λ/μtherateofdailycureisμasthecontactnumberandst+it+rt=1aCalculatethenumericalresultssimilartoTable1inpage140;Pro__dure:functiony=illtxa=1;b=
0.3;y=[a*x1*x2-b*x1-a*x1*x2];ts=0:50;%thescopeofthetimex0=[
0.
020.98];%theoriginalvalueofthetwodifferentialequations[tx]=ode45illtsx0;[tx]%getthesolutionofthetwodifferentialequationsplottx:1tx:2gridfigure%drawthegraphoftheabovetwosolutionsinthesamefigureplotx:2x:1grid%drawthegraphbetweenthesetwosolution
00.
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0731680.
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091729120.
159950.
076718130.
127240.
066474140.
100360.
059332150.
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054268160.
0613930.
05065170.
0477790.
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0370780.
046005190.
0287310.
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0222570.
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30.
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000161150.
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03986419.567e-
0050.
039856427.___6e-
0050.
039853435.6953e-
0050.
03985444.3812e-
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039848453.376e-
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039847462.6113e-
0050.
039845472.018e-
0050.
039844481.555e-
0050.
039844491.199e-
0050.
039843509.2499e-
0060.039843bDrawFigure7-8inP140;c____ysistheinfluen__ofλandμtoiandsλistherateofdailycontact.Itreflectsthelevelofthe__nagementofpatients.Effective__nagementisthekeytohinderthespreadoftheinfectiousdiseases.μistherateofdailycure.Itreflectsthemedicalstandards.Sowhentheyincreaseitmeansthatthesanitationandthelevelofmedicalimprovealot.λincreaseswhichwill__kelesspeopleinfected.Thustheinfectiouspeoplewilldecrease.Sotheitwilldecreaseandstincrease.μincreasewhichwill__kemorepatientcuredsotheremovedpeoplewillincrease.Thusrtwillincreaseanditwilldecrease.Fromtheabovefigurewecanseehealthypeoplewilldecreaseastimegoesby.Thisisbecausethenumberofpatientsincreases;healthypeoplebecomepatientsorremovedpeople.Sothehealthypeopledecreasegradually.Whilethenumberofpatients’firstincreaseandthendecrease.Thisisbecausethenumberofpatients’increasesmoreandmorepeoplewillbeinfectious.Afterwardsduetothegover__ents’policyandpeople’spreventionawarenessstrengtheningpatients’conditionisundercontrol.Sothenumberofpatientsfirstincreaseandthendecrease.
5.aAccordingtotheequation5orequation6inpage136ofthetextbookdrawfigure1andfigure2inP
137.SImodelModelingpro__ss:duringthetimeoftheepidemicspreadweassumethatthetotalnumberofpeopleisN.anditcanbedividedintoSus__ptibleandInfective.Attimetthistwokindsofpeopletakingaccountofthetotalpeoplearedenotedbystandit.alsoweassumethattherateofdailycontactislemtawhichmeanswhenpatientscontactwithhealthypeopleit__kesthehealthypeoplebecomepatients.Pro__dure:symsititi0lemta%definesymbolicvariables[it]=dsolveDi-lemta*i*1-ii0=i0%acquirethesolutionofthedifferentialequationit=1/1-exp-lemta*t*-1+i0/i0lemta=4;i0=
0.1;it=1/1-exp-lemta*t*-1+i0/i0%givetheparametersvaluesit=1/1+9*exp-4*tfplot1/1+9*exp-4*t
[02];%drawthegraphezplot4*x*1-x
[01];____ysis:Fromtheabovefigurewecanseethatwheni=1/2di/dtgetsits__xvalue.Andatthismomenttheimpatiensincreasesthequickest.Sothehospitalwillbeverybusy.Itisthecli__xoftheepidemicandthekeytothemedicaldepartment.Thismomentisinverselyproportionaltodailycontactwhichstandsforthestandardofhealthlevel.Soimprovinghealth-carefacilitiesandraisingthelevelofhealthcandelaythecomingoftheepidemiccli__x.Inadditionwhentconvergetoinfinityiwillbecloseto1whichmeansthatallpeoplewillbeinfectious.Obviouslythisisinconsistentwiththereality.Becauseinthismodelitisnotconsideredthatthepatientscanbecure.Peopleonlycanbecomepatientwhilepatientscannotbecomehealthy.bAccordingtotheequation11inP138drawfigure3-6inP
138.SISmodelModelingpro__ss:Inthismodelweh__esimilarassumptionintheabovemodel----modelSI.Weonlyaddaassumptionintoit.Weassumethattheproportionofthenumberofpatientswhohasbeencuredeverydaytothetotalnumberofpeoplewhicharedenotebymuandsig__=lemta/muwhichdemotesthenumberofeverypatientcontactwithhealthypeopleand__kethemill.symslemtaxsig__di%definesymbolicvariableslemta=4;sig__=5;%givethevaluesoftheparametersdi=-lemta*x*x-1-1/sig__di=-4*x*x-4/5ezplot-4*x*x-4/5
[02];%drawthegraphsymsitilemtatsig__i0di%definesymbolicvariables[it]=dsolveDi+lemta*i*i-1-1/sig__i0=i0;%acquirethesolutionofthedifferentialequationlemta=4;sig__=5;i0=
0.1;it=sig__-1/sig__-exp-lemta*sig__-1*t/sig__*-sig__+1+i0*sig__/i0/sig__-1*sig__+exp-lemta*sig__-1*t/sig__*-sig__+1+i0*sig__/i0/sig__-1%givetheparametersvaluesit=4/5+35*exp-16/5*tlemta=4;sig__=5;i0=
0.9;it=sig__-1/sig__-exp-lemta*sig__-1*t/sig__*-sig__+1+i0*sig__/i0/sig__-1*sig__+exp-lemta*sig__-1*t/sig__*-sig__+1+i0*sig__/i0/sig__-1%changetheparametersvaluesit=4/5-5/9*exp-16/5*tezplot4/5-5/9*exp-16/5*t
[02];%drawthegraphholdon;%drawgraphinthesamefugureezplot4/5+35*exp-16/5*t
[02];ezplot-4*x*x+1
[02];symsitilemtatsig__i0%definethesymbolicparameters[it]=dsolveDi+lemta*i*i-1-1/sig__i0=i0%solvethedifferentialequationit=sig__-1/sig__-exp-lemta*sig__-1*t/sig__*-sig__+1+i0*sig__/i0/sig__-1*sig__+exp-lemta*sig__-1*t/sig__*-sig__+1+i0*sig__/i0/sig__-1lemta=4;sig__=
0.5;i0=
0.1;it=sig__-1/sig__-exp-lemta*sig__-1*t/sig__*-sig__+1+i0*sig__/i0/sig__-1*sig__+exp-lemta*sig__-1*t/sig__*-sig__+1+i0*sig__/i0/sig__-1%givethevaluestheoftheparametersit=-1/2/1/2-11/2*exp4*tezplot-1/2/1/2-11/2*exp4*t
[03];____ysis:Fromtheabovefigureswecanseethatsig__=1isathreshold.Whensig__1theincreaseordecreaseofitdependsoni0theoriginalvaluebutitslimitvalueis1-1/sig__whichwillincreaseasthesig__increases.Whensig__=1itwilldecreaseastimegoesby.Atlastitwilltendtobezero.Thisisbecausethateffectivecontact__kesthenumberofpeoplewhoarehealthybecomingpatientslessthantheoriginalpatients.AlsowecanfindthatSImodelisaspecialofSISmodel.
6、FinancialTimeSeriesPredictionTheEx__lspreadsheetDatasets.xlscontainstwosheetsnamed“Nikkei255”and“ShanghaiB-Sharestockindex”.WewilluseNeuralNetworkToolboxtomodelandpredictthesetwofinancialtimeseriesrespectively.Foradetailedintroductionthistaskpleasereferto[Daietal.2012].aForeachtimeseriesthefirst80%ofthetotalsamplepointsareusedasthetrainingsamplewhilethere__ining20%ofthetotalsamplepointsareusedasthetestingsample.bSelectnetworktypeandtrainingfunctionetc.cThetimedelayembeddingorthenumberofinputnodestobetestedwassetto5and10;thenumberofhiddennodestobetestwassetto789and
10.Andthenetworkhasonlyoneoutputnode.dComparethepredictionperfor__n__intermsofmeansquareerror.pro__dure:a=Nikkei.;%__ketheoriginaldataNikkeitransposeb=shanghaiB.;%%__ketheoriginaldatashanghaiBtranspose%generateNikkei’sneeddataX11:=a11:1000;%get80%traindataY11:=a11001:1249;%get20%testdata[TrainX1PS]=__pmin__xX101;%nor__lizethetraindata[TrainY1PS]=__pmin__xY101;%nor__lizethetestdata%generatethe994*5__trixastraindatafori=1:994x1i1:5=TrainX11i:i+4;%generateinput__trixy1i1=TrainX11i+5;%generatetarget__trixend%generatethe224*5__trixastestdatafori=1:244tX1i1:5=TrainY11i:i+4;%generateinputtest__trixtY1i1=TrainY11i+5;%generatetargettest__trixend%__ketheabovegenerated__trixtransposetrainX1=x
1.;trainY1=y
1.;testX1=tX
1.;testY1=tY
1.;%generateshanghaiB’sneeddataX21:=b11:792;%get80%traindataY21:=b1793:990;%get20%testdata[TrainX2PS]=__pmin__xX201;%nor__lizethetraindata[TrainY2PS]=__pmin__xY201;%nor__lizethetestdata%generatethe787*5__trixastraindatafori=1:787x2i1:5=TrainX21i:i+4;y2i1=TrainX21i+5;end%generatethe193*5__trixastestdatafori=1:193tX2i1:5=TrainY21i:i+4;%generateinputtest__trixtY2i1=TrainY21i+5;%generatetargettest__trixend%__ketheabovegenerated__trixtransposetrainX2=x
2.;trainY2=y
2.;testX2=tX
2.;testY2=tY
2.;Nikkei:msenetwork1_errorsans=
3.9995e-004msenetwork1_errors_simans=
0.0015____ysis Ifoundthatthemeansquareerrorswilldecreaseasthenumberoftrainingincrease.Thenetwork1_errorsorderof__gnitudeisalwayse-004whilethenetwork1_errors_simmeansquareerroratfirstis
0.
0016.Itrytochangeparametersto__ketheerror__all.Howevertheresultsdonotseemtosatisfy.Ichanged__nytimesbutitstillis
0.
0016.ThenIclosednntoolandstartedagainalsochangesomeparametersthenitbecome
0.
0015.Justastheaboveresult.AlsoIfoundthatitisnotthatthemeansquareerrorwill__allerwhentheepochsincreases.Sometimesit__ybecomelarger.IalsotrieddifferenttrainfunctionssuchasTRAINGDMTRAINGDATRAINOSSandsoon.Butthemeansquareerroristhe__allestwhenIchooseTRAINLM.
0.0015istrainedthroughthistrainfunction.ShanghaiB:msenetwork1_errorsans=
3.3575e-004msenetwork1_errors_simans=
8.4081e-004____ysis:Intheshanghai_B_sharethemeansquareerrorsseemnotlarge.Theorderof__gnitudeise-
004.Ithinkit__ybethatwhenIdotheNikkeitrainandtestIh__efoundhowto__kethemeansquareerrors__allasitcanbesuchasthefunction’ssetandtrainingmoretimes.Sotheresultsseemtobeac__ptable.Referen__DaiWSWuJYLuCJ.Combiningnonlinearindependentcomponent____ysisandneuralnetworkforthepredictionofAsianstock__rketindexes.ExpertSystemswithApplications3920124444–
4452.InputvariableGeneratedecisionGeneratestatearrayGenerateabstract__trixGettheresults330011221110320102013003river20310211221122112001023102033001013202310200338。