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1、GeographicalAnalysisISSN0016-7363ApplyingMeasuresofSpatialAutocorrelation:ComputationandSimulationRogerBivandDepartmentofEconomics,NorwegianSchoolofEconomicsandBusinessAdministration,Bergen,NorwayKnowingaboutthechallengesandopportunitiesofspatialautocorrelationisonething,butapplyingthemeasurestoo
2、ne’sowndataisanothermatterentirely.Whilemanualcomputationofthemeasuresfortoydatasetsispossible,applyingthemtosmalldatasetsrequiredtheuseofcomputersandthussoftware.Thisarticlewillshedsomelightonhowthemeasureswereandareimplementedinsoftwareandonimplementationissuesthatarestillnotfullyresolved.Backg
3、roundWhentheempiricalworkreportedinCliffandOrd(1969)wasbeingcarriedout,statisticalcomputingwasdonebypeopleinlaboratorycoatswhokeptresearchersawayfromcomputingmachinery.TheElliott503systemusedatthattimeattheUniversityofBristolhadlimitedRAM(afastsectionof8Kwordsof3911bitlength,andabackingsectionofu
4、pto816Kwordunits,maximum136Kwords,680Kbytes).Researchersinteractedwiththesystembysubmittingcode(inthiscaseinAlgol60)anddataforpunchingontopapertapeorcards.Whencomputingjobswerepreparedforexecuting,theywerescheduledwiththoseofotherre-searchers,andturnaroundtimesmightbefromhourstoovernight—thinkoft
5、hetimeinvolvedinorderingalibrarybookfromoff-sitestorage.Justgettingcodetoexecute,letalonecorrectlyrepresentformulae,wassome-thingthattookconsiderableresolve.Inadditiontothetimedelayofanexecutioncycle,memorywasverylimited,andveryoftenresearchersdidnothaveaccesstostandardlibraries.Onlyin1968didAppl
6、iedStatisticsbegintopublishalgorithms,mostoftenimplementedinFORTRANIVinitsFORTRAN66form,notinAlgol60,thelanguageavailableontheElliott503.Writingcodethatwasbothcorrectandparsimoniouswasanendeavorofhighorder.Offeringtosendprintedcopiesofcodelistingstoanyinterestedresearchersalsowasusual(CliffandOrd
7、1969,p.39).BecausebothAlgol60andFORTRAN66couldberunfairlyreadilyonCorrespondence:RogerBivand,DepartmentofEconomics,NorwegianSchoolofEconomicsandBusinessAdministration,Helleveien30,N-5045Bergen,Norwaye-mail:Roger.Bivand
