Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing, 2nd ed. (Fortran Numerical Recipes 2) PDF
Preview Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing, 2nd ed. (Fortran Numerical Recipes 2)
NumSieencrFoiconrdatrlEaRdniet9ico0nipes visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR FortranVNoulummereic2aol fRecipes (North America only),or send email to [email protected] (outside Northter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDaper copy for their own personal use. Further reproduction, or any copying oss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) AmROf m erica).Msachine- visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR (North America only),or send email to [email protected] (outside Northter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDaper copy for their own personal use. Further reproduction, or any copying oss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) AmROf m erica).Msachine- Numerical Recipes The ArFt oorftPraaiSnnreaVNcFloluoeolumnlrmdSetrcreEiaicde2nanitolti9oifRfni0eccCipoemsputing visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR EHXaDrXevOpaWarNSdrBtW-iRmMSalermelusiiiniiPelaatcthllaoosimnrhlfaAacoFPrhnaomoPih.aairTdeyenn.Tsw.dCliCFHceooEVseMrrnl,udnp.aeCgtobeekiPornntyrarettofntroneiceoeerrlnliaerlsAnsUglslrkitnfsCrynioyvopegmhrsypisatyincys (North America only),or send email to [email protected] (outside North Amter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROaper copy for their own personal use. Further reproduction, or any copying of mss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) CERN,Geneva,Switzerland erica).Msachine- PublishedbythePressSyndicateoftheUniversityofCambridge ThePitt Building,TrumpingtonStreet, CambridgeCB21RP 40West 20thStreet, NewYork, NY10011-4211,USA 10StamfordRoad,Oakleigh,Melbourne3166,Australia Copyright(cid:1)c CambridgeUniversityPress1986,1996, exceptforallcomputerprogramsandprocedures,whichare Copyright(cid:1)c NumericalRecipesSoftware1986,1996, aANVRTPTasr“lnyroheoluooLidlplpetnwmufueierttetcRxmcwieseixcennotedironaecgtietdWaecresshsie2nedateipnt.inidlstibtnoIwnhtRnyrftfhTRooeofieteEFttoufrehhahceXortsiiUAermsserpaecitrinpennrnaovnvasiptgcrodteainreeeliolddieennudvnN.dbcdmci”FtiodSuioitxeoooiu(mmtopakrnaiCntptep,lssrear.1aufosilc1oxn,twcole9rvaoiw9rrnc9lirfri0eiehe7eR–srAn:ai.cxcgedsotmxThceerifna)idheptiangfoseretoticoepscpuArod,ualsispraSrneuotycpfenfteooothocddwfsroefemePnaitrcsnhrdaatoeotietronsiEanrovtmllbdtanleyheoiisr.tneolosideoAinkSpoedncuosnw,fsicbbreohfir2eltnifoiaer.bctt0siwiepnlt8fidideiacpconrreousmgeCnnob,smanoltpeiihams.oniflhxr.slopeeyvrubdigttoilyieii1on.mpn9kgeSe9i,strie6esaeo.dlintnlhueitceseoeensrndeosmcefetdsoitohraaenest visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR QNI.fo“MaUccS7Auotloor8o.Prsn7mrdimr1.afodrlr6etdie.II1seeulwprc.nS8acsepr7c.seuisnaci6[@BtMToe3fcnet,eiFrld3oes.oahunNsetFcOaso-rrlWneA,edc1miuc2neadrsbepRe7vh0p5Pxel,i)ls.s.Tl3ei.-.caeNc]otalOnc5na.9ri,ibeRtfape8aa2nus..pt3imfA-mne5wbi1dtetr.rnBhs–slo-,eNo.aigf5eaaPimoorNnreHclnc271eLdexgeorem9.bqun49.aiurFr0ttbaumd3am9bt2.oshhkorcpec96l4C(fea”eraaekeCsrh-3ttrhyret0drmNN(ii,iosyaeecorcs.me(nunuseaCaafofshtsdlm,mllofpepa9tsatirraremhoCuaar0eee,ondcretrrfocNibe:eifiiacebnoccfinrrlobrYtefaaiyngawcehpvodollsvtarnerergoda1oielaocmRsrRilero0kasi)ney–gl,lsew5,readsaiDrtlccn7tCMa)bineiioai,cag3moplapmlnfeteAonetatoe(ndhpaaaUslsrfsapideals0rileoSnSrrehnowp2sdagogAdootdmor2,lriocu,ofulefn)i3ieetatts,gxlwg8wewslCd“grf.s-soaosaeaitaii(tcnrtmbrr)nrUrmohideie-egcfesPSebut.iCnWir2lnAurarmysttia.tdibo@deth)fimmphdl,bgPeicrircacbreeasoeeusnacrdrimhsbiinpyaoUtistdiioaelfa.mbeolgnootoiodeineleirprt(kltvgemhhDu,“tedp”pUtoetwiara.ruinrtsnnto(tirTfiiNNpatgigcootfhevy:hronu@o/ceaia/r.mrhrnWmPmtsn/snhceerirmwaiilte.rcluyctwiAsoli,acdoisnwfalam.Pemgo.mqldraern”ue(lRr,SCrHseiiltcscesei.ooo.ce,tacecrmienP)ioao1pnsftrpnn1mheeoaseusye)ss0xesr,t.ser (North America only),or send email to [email protected] (outside Northter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDaper copy for their own personal use. Further reproduction, or any copying oss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) 519.4(cid:1)0285(cid:1)52–dc20 96-5567 AmROf m AcatalogrecordforthisbookisavailablefromtheBritishLibrary. CIP erica).Msachine- ISBN 0521574390 Volume2(thisbook) ISBN 052143064X Volume1 ISBN 0521437210 ExamplebookinFORTRAN ISBN 0521574404 FORTRANdiskette(IBM3.5(cid:1)(cid:1)) ISBN 0521576083 CDROM(IBMPC/Macintosh) ISBN 0521576075 CDROM(UNIX) Contents Preface to Volume 2 viii 222231 INIFL2222222222222222222222nn1111111222222333333333oiu......................ttc0123456012345012345678rrrmeooeIQFMFAAWFLPFMIRRARRRROnnnoooaawidedooooooudnrtttonihrshgrrrrrssuuuuuuivdraetrtttuuyooceuosttttttrrrealieaFdkdriiiiiiiCaaamlcccnTnnnnnnnrreounnnuoRocSgeeeeeedlIttaheRnccuenmssssss999oiitniSttLlraooednAii000utTRffffiyfbioorcakeooooRtnonnCtFnrhLIDuenninr:yrrrrgrnnPtoatrhrgeaaThaauPOSSUetrtttarSemynurnteMercrstockooriaMcusosgranantdanaleiakiitgnouiyacPnlitcaspewonnSPFiltcesnaeningnareetvgDcfueg:9orodilhgraOFoaOet?maoePa0imshFnrwevrrAalappDrmeloCdamnLTtaniioeeeierUsatrratFodosorlcrurRlaithlitaalaaorplecsnorrsatEeatetyeyCdanimncrMiiailncrostltouelanoSriarLsi:npntroa9oetdm9nPeeeistAsnyn5rscddsts0RbrtootcHr9iiRiFoCrennnon0aLaaceganugeMyVnuNllalssadfcrnreauntrulcaaeeitcmltnnrgdnmaoitdgecctruAiirseeooImisslancngntasgiorlsnirenRigtsfheiFoccmsierpsaeFstouRrortuertsainnes90 11119x9999900999909990999999998v3673500899603490439567887xi765902724244556717032113i visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to [email protected] (outside North Amreadable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of mCopyright (C) 1986-1996 by Cambridge University Press.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) Fortran 90 Code Chapters 1009 erica).Msachine- B1 Preliminaries 1010 B2 Solution of Linear Algebraic Equations 1014 B3 Interpolation and Extrapolation 1043 v vi Contents B4 Integration of Functions 1052 B5 Evaluation of Functions 1070 B6 Special Functions 1083 B7 Random Numbers 1141 BBBBBBBBB8911111110123456 MEFFSMISRnaoitooiotgansuerodettitgritmiensinFreFlstaiigorizniyctnuaiagsaodrtntliinioeeodDnmfrnogeSDfTssopaarOcranetrranMcdidptsiarNtnfaixoooalirnmnrAmyloipiznDfpaeiDltfaiifcaoeratnrSateieoontfntsiFsaoulfEnEqcqtuiuoaatnitosionnss 111111111222212221629865038957573152 visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR BBBBCCC11121237890GeTIPLLAIRAnnnweialeptsdpeserfpotethersgiieanxraaP-rneNlgalboodnIDluenfioicnEmtcidPfieftqceferUeseBasuoxrtrlaogiietclLtuorinaitaionytslVmindtaAMoisaslnllogErugaaydomqnnourVuddeifltaaeshEIDltsnumix1oeve(psnpnealPsernircstrndyioedtpb2IeTenlnhetacmeeniroesfdrasycnerustil) 111111111333334343835464231429317544 (North America only),or send email to [email protected] (outside Northter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDaper copy for their own personal use. Further reproduction, or any copying oss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) AmROf m erica).Msachine- Contents vii Contents of Volume 1: Numerical Recipesin Fortran 77 Plan of the Two-Volume Edition xiii Prefaceto the Second Edition xv 123456 PSIIESPLCnnirovprottceeeealemeulfrglcianutpmpriicsaaooauieelttnlntiaiFeotoaIotnorunrinofifnPteoohnoLcrsrfefoitmaniFFgoFneauurnidatarnnsirsmocEctAnttxsiEilotogrdbnnaeiystspbiCooranlhaiactipoEtneqruaantidonSsection xx211vxx09522ii1ix59932vi visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR 11111111110123456789789 MEFFSMITIPRSRnnwaoitaoaoiottgansueernroodetttitggriditmiensiaPnFrreoFlstaaliigoorimzniyDctlniuaiagnsEaoidrtnNfttliqinfioeeodDneuBumfrnorgmeaoSeDfTsstounpabairOcornanteetrirandnMcdaridpsstasliarNtnErfaiaxoyooaqlnirnmnrVAumdylaaoipiznIDltfnpuaieoiDvletfaiinfecaoerPsratnrsSarteoieeoonbtfTntsliFhesaoumlefEnosEqcryqtuiuoaatnitosionnss 684763573427301405237896443891000970650 (North America only),or send email to [email protected] (outside Northter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDaper copy for their own personal use. Further reproduction, or any copying oss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) AmROf m 20 LReesfesr-eNnucmeesricalAlgorithms 981861 erica).Msachine- Index of Programs and Dependencies 921 Preface to Volume 2 Fortran 90 is not just the long-awaited updating of the Fortran language to moderncomputingpractices. Itisalsothevanguardofa muchlargerrevolutionin computing,thatofmultiprocessorcomputersandwidespreadparallelprogramming. Parallelcomputinghasbeen afeature ofthelargestsupercomputersforquitesome tCMmrtwchfFoiiaooatmoooetohrimdhnrmcmeeRtehhgrpr.fmrAFaSeaaeoaenneovn/Ntrsixt6ilttrehebtcWo90twreMfariew0a0otalenelieil0rn”le,ntlseycytwdlmhatnc9oa(eonofiaaat0atmdowednlwtncvfccrdppe,oss.teihoharnimviepemom9tingexidsec5pbpriprteN,liihfcitbalesllhoeioeuisrerrtterriimmrymsmeFnisi,sgnngpeoaataebctrsoirrcnerliseeaoheecrcttswptahaeraiehninwtsalo.diotetvtaorRhliiswdaynvItfino.henrgarritcm,wNaimloehtilyDnhtpauaoiA’yddebtegEsvdeGslhfiCUeobeulnoly’sffiny’glsNarcrsldaotnorFUIhtFoevimdowXobnnNoaowresioirtfFIawld)toarnaXr,boaFruaobildnbrtnroterlhtspyelr9rbed9ca.mlt0taer,o0nhawaMtcadcweffna7raooleoikmee7dycmrr9ea.merae0hAttdopsnoiFasiknsicldbn.vlpootgFleygoeehfrrofttpafaoiT’rrsaocr.tsatuiAlsohrrmnstFncameooXgendoir9olmeubPr0at9vtisrorrit0aiealiatntysntrPrnehewgnedxCcatesiPeaoctnInesosBemdmgtotxhwleesMlpce“esdeoedelmXkn,o’errolstStiltn3baougeextenJepibnlahln3ryrd;-tftt,, visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR byetEcgtpsaohpromfaouaqsircmruispu,ioadkrnrablpnrewolTWAkleluugel9velgfahytltegoiiesaretadtc0didarprhrhrlmoedcsetweehlmthy,ecasphp“iha(caharnaielaopetrororiyaaegcrrendnirumulvFifnsontehttwdctthgae”inndocsi)ispkninnnh.apiopeerasabspglttrtgoer,pteAo”tsrleeleavicuycapelghoeblfioa,ittnaastl,ntoorfilfihoinetlin,neca9whutcacrkgpdd(arCb0wtemieulrcystb“uesetoheclhaitoeolpFofatatvipheagi’tuhparnofntis,vaew“oetostgrarFpwpesto.cgiatupeehnunartotbaraasreaiafumrtarisonrdrreoatngtsnrmeiesrvkraretplcectaqhndene-9omhmeuinpauiea)py0fcelncsa.yaateeaa7iFidoltrnanrpraolt7cseaoesmilutrAnoho,pxt:tlprevfeolaaampbtstesleaxrReonlrp,siyecnlca”dretlol.ospinhtends”,twgtutclataihrwaweisho9rhlpacnenasceaotiTn0earathdnttarrwneensphhbswcoyatdfr.gotteioaorruseealta.awdFfyf,adihnrrnnumlt,O,besoye,eFdaydttsdao,rio.nute.uot(rothgiuchuwgrCrrrntereaTattioyuhttemrhosrlnrewoaharlecepareveroginueodk9opanngodiuesm0stitdafhleufmgneoo,udtooitnpprhtitubrmiaernioswosuosontyrnpe’ntptneue2agbtieetlaacanftn1fythrrbeloronfcosat–atmiayosant,ohuslsvb2ltrlttelpaistaogeete3rvempnhalrro)alpelytcaeds,aaspnoteracooptcsauryllb,vrpodugitihyyrpaahuziermdereigsleloetnrtcdlscoreoespdg“dcicaonbtwlcpsueruhbgoorimoeocasaztecaremaruliaudroaoippnlgatanwspait-wptitlleneilsohgoleeoularssoeesiueertnantyno.aededsfrlt-.l (North America only),or send email to [email protected] (outside North Amter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROaper copy for their own personal use. Further reproduction, or any copying of mss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) pstaarbailllietly.veWrsieonthoinfkC, tthhearteifsorceo,mthpaatraCbleprtoogFraomrtrmaners90wiinllmbaetuwrietlyl,saecrcveepdtabnyceu,sainngd erica).Msachine- thisvolumeforan educational excursionintoFortran90, itsparallel programming constructions, and the numerical algorithms that capitalize on them. C and C++ programming have not been far from our minds as we have written this volume, and we think that you will find that time spent in absorbing its principal lessons (in Chapters 21–23) will be amply repaid in the future, as C and C++ eventually develop standard parallel extensions. viii PrefacetoVolume2 ix A final word of truth in packaging: Don’t buy this volumeunless you also buy(or alreadyhave) Volume1 (now retitledNumericalRecipes inFortran77). Volume2doesnotrepeatanyofthediscussionofwhatindividualprogramsactually do, or of the mathematical methods they utilize, or how to use them. While our Fortran 90 code is thoroughly commented, and includes a header comment for each routinethatdescribes its inputand outputquantities, these comments are not sati“1ttlnAoshhiurV.os”eeecptwNooieprklTiouduunoWcnrnhmnmbseeueVpeyereoermdtrorleanecw2ail!eicvtaoubn”oraminlm(eilooeDlcytlbeuieneaRdeniasdlfiiu1edfngtaarecse,“dentrimVtchawpetdiGoodoetnehlemeeclscepbiurooecnrppesimrmshen:algtfeiebgspeanwFtIeeeucf1OMet)tetwh,dyat”RrteahteoeoeiTresuoeafsdcntRenrnaheraerAgatibetelapllhrNtnmkisteeeaicoeeaoxi,ec(pfdnnapwworyomfeemnohrhrrv.odeafiio)aiceqwnosrethnuykheudnceiesidneicntadoir.ogptoeeellrSynppalsoMe.e,snergaicni’anrhgnoBtantaaunimViuynvnend,todesgsdlth;Esiwuhwgcedtamorarhrheniuietteeotaedi’geost1chlgteinyoh.naiintvmeTvihtmoneheoneptflerroeultsauewhnwsi“lteoaeleVeotn,ntyhsrocdlo-tediwelsefsusradbstehmtv“cewphooVirnerensuieioepsegnr1lfiemttuint”hitoimaunetinoorlnsgweeesftrt, visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR dnooFtpbopASFctbFheoiufrrefauoaoomssaioernmkgrrugtttctagnttiihsoagnuirrnmFlbrunimlWWWasaydsagisoeela,nnnesamtYlrorlbeoiai,Hadttot9tiioapno9frmnhioionPn0aohsfrnto0da,nsopnitniSkp’lanp(ohlsgelsaac,if;e9negifionnnrletorsoKt0dwhhsamashrdrpgutvmieaaateSchasieletbFonbgiGooeyhriAmtntldlifisaohnucselueneTewioeuiracli.nomfkrnKcsdrrmsthaoaaretigheGseglronicresal.altsmee,sekexneyrsty)lgs,tharwpsn,lpuWbeaeveeniSoieorminiaasnaennenesnvccewlrnveglsbl,Bthemcatat,dsrsoliahewrhnhstoenh.Mlurlrieuidouiugeoahtwsssonhrgonms,anoatenbhaieleklorssenatrycleooeheitavscctoonaosfhtcpeoroekacehlosfgklaerhlmmnyoirgossmoiost(cocntocrvhpauvhrofowCaetvlioegurerepnentdpoiolnfaterlltFbbteearaspflahiifgiouddounentoirnufyeeioamamgurtsuruolenasinlttueliaoentddlr,tensteMmoadnacviB)otbglanf(eloisuutoGuicCacrporukmavlr7oalmrerrtrhdperine7bkia,oAeetyapsvpsnadoMggetpwpldpiohlodCtxrecothrrorLoaeieteipeoiuatcttnmtdaarithebipcgoronhodtrstreaBlmrfimlhtd.etnegicayhlintrh7nfoarsimphecoa,,ano)relcvoieut.wotlgLs,lergeidaegsUlTtarorhetrirutahasanagnr,sro.ndtnoiStiuedegaCseinadedung.trtesntuaeh/thNtitsFtocdMnddhmeaotctlroad)e.rehoeiueeltrnpecdaepiattdsiorrh(orssineseoaaspnasenoldvcVnngoreavgmuteolcerfaldhoir9lasjtrnneSeepooetu,s0mtcabcapcirria.MLeototmirtemmbeadnodustThoineloieateglonuauhscsonenahan-gsusetefltl, (North America only),or send email to [email protected] (outside Northter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDaper copy for their own personal use. Further reproduction, or any copying oss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) AmROf m February1996 SaWuillAlia.mTeHuk.oPlrseksys erica).Msachine- WilliamT.Vetterling BrianP.Flannery Foreword by Michael Metcalf fcbNt“if9daththoooNpe0eoeeuriuevp.uswnnoleaTNmdd,lrtBSaThuoehe,eeniehxmnpuetrprdeooieprtmtipenescrrwftgrtilegaeneeehniirthl,ngsucadiagescdathatmRtaeuiatitcolttdedtrelioefhRetacsrrofPieistdiieaftFnhcphsecvtoaaaeoeiyeiasfdolslpsrsnengstrnaeoiarritiieocssnaanivsnrwrsatngiiacialcFnateilouah9hFnygof,uttsmo0osrhabuflTtr?itrdroorssemnhtrrarrrHibeabfcrnsace,yaoeeenoosafibkc9rstmlwnriesraea0rewfisdt,sdnmt"apdtthnIhgnIlifiitut.aiadiuneadnwcrnlcarlalsihiyreFyagettrta,dydroebNccsneh,reotecbehuteeagenrowyamenacaicuodrnnadcaeelnm,nhdirrimst7wvrinooabclb7teaeulhoy,aeedddcmaalua.eteotnsanuRxeupdnsTssrripehruedimuihpncltcrac,rohearigappcppaisietleoestriefeaneoiisdratstsndestnaniiagfitr.nnlshathungl,gTtlayeltaCohyaldhnyrcrnscIp,uiedn,oiodtrbPsesihtnonetaeahmawcdtycsrbsronlunsoeciasuewdibcaamascgshtutr,lianiIits,eaotavohm’midonafeonert,genn?.enaeeiehdnlnrsdqFsOitCoenuttBtsohaawonei,eratceeantoinaskrtrorthfntiealolenocyyeddnafr.,, visit website http://www.nr.com or call 1-800-872-7423readable files (including this one) to any servercompuPermission is granted for internet users to make one pCopyright (C) 1986-1996 by Cambridge University PreSample page from NUMERICAL RECIPES IN FORTR lSdpwfeusIoPtdpTahatunerppiotasnhhvrdoabvggtswodgionigsceiecrCmuounerderaalhDBegoarmaeqdlaidBd,mhzgpeaBurueoridircoeedreBnaAniamfsiksdunrwaecngaFlttitsnwvkgIgsbinlcohttnnicyeiuorhyhgonrcaesruslteeom,c1tlorJtcfiillnrhoao91ontatPpeafduuntah69nrbhaipLaotdrln68gae7iseielpe/rtsl,0iu17sassrsrBn(fisaseSetl,ttAgpaswihaagcdecrmoarntcneiNeelsaaeanadbdkdmeumhsctSvdsyaiu,nepianeasIrpessodpXdo)dtlrideofa.anosNootil3FahintizasyernfIneoJoetcedotdthrrt3IenrridofareBwadetxrtt,rnArhkrrotnnopdMsbahuaaemdtfd.riysAnteeipze)iafiF’io.ettsmmtassnchoosdnacnfEeiaerpauaNtibFbttervrnplrnarrlkoieynaeadearblccewrgletnnctaot-tistnidmhttrfiA..doyueuanYeecinnaAdmanmcoeotiAtMlp.ewsilnalreetctsyrkhNOxgharraos,,i,ienk,ooncSgnbcheiadnduryaarrleIovnyoaegnolgbwtedomvwEhfceatynwaeoeocntuinnmhfltvIwhmnrnfoeSteeowneaaoawpapOrpripaistr,aircsuduedenrd.satFertierahwgshinlasftonnleeFhetleachtrsGgrh,hrenonotoemereegstrgtmpnadothtnAaerurtrnysomeasteenaatulmhm,wdhfvnde6giceeeat.se6eicdmrtoahn,crseresisfiaieaw,SsIeacscedncdnntp,stiwanahieooteaXncstan1fiiAvwrrsiittfiNtt93arczetii,lvshdn7iJcerscgatehee3teersu8otsnrilduc,bil,lgsawofitaaasaeiinhttnr(eonrdfinhehhdlilsrandenyncydeoets.l (North America only),or send email to [email protected] (outside North Amter, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROaper copy for their own personal use. Further reproduction, or any copying of mss.Programs Copyright (C) 1986-1996 by Numerical Recipes Software. AN 90: The Art of PARALLEL Scientific Computing (ISBN 0-521-57439-0) tloateFo1r9tr7a0ns,7w7.erIetwmaasintolybteoaadddectaodeFoorftrsatnrif7e7afnedatcuornetsenthtiaotnh.aTdhheadeatrolybpelalenfst,oinutthoef erica).Msachine- thatstandard. Amongthesewere dynamicstorageandanarraylanguage, enabling it to map directly onto the architecture of supercomputers, then coming onto the market. Theintentionwastohavethisnewversionreadywithinfiveyears,in1982. Buttwonewfactorsbecame significantatthattime. Thefirstwasthedecisionthat the next standard should not just codify existing practice, as had largely been the case in 1966 and 1978, but also extend the functionalityof the language through x
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