Numerical recipes in FORTRAN

1724 Pages·1992·18.871 MB·English

by  William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling

Numerical Recipes
ThFeoHAaDrrevtrpaWrtarSadrBioWt-SimSnnalrfmleeuViiiniPNlaatStchFlloooismnluocfAaaoolPrnoiummnPi.heaiTdrynm.dTsn.CetiCFHceoVrtsereErlu,in.piaaeCftocdekP1iorntnracaritofntrontieooelerilCnle7rsolAfRsUlsrkoin7tnseyrnioyvmpceghrsiypipstyicuestsing visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
EXXONResearchandEngineeringCompany rth AmericaDROMsg of machin
). e-
PublishedbythePressSyndicateoftheUniversityofCambridge
ThePitt Building,TrumpingtonStreet, CambridgeCB21RP
40West 20thStreet, NewYork, NY10011-4211,USA
10StamfordRoad,Oakleigh,Melbourne3166,Australia
Copyright(cid:13)c CambridgeUniversityPress 1986,1992
exceptforx13.10,whichisplacedintothepublicdomain,
andexceptforallothercomputerprogramsandprocedures,whichare
NASiCFNRRSTPTnUecS7lfo“Maasr“coiryhoueeoulooorlxotLir8oi:lmPpppintssrnpmwmeudrifcrse1:faitoedrrlthtynrRcteteexeiwde:iiII1esiuewlEyrrccternnpnnSra8tdieperi.ceisssaoengdittfiitagenc[Bt6@MTWoeeatpcieefcrnNssehiircslchido3ncesdadrtohaNtueoeinsttsiiaict.suontr-idsllCene,oAdnntbinmwIi1cuwnmah(cid:13)omdtbrsRnneteyortvch07PhpRleTio,nioselsif.tneem.atei-3Eeeac.t]ooutroOsafehnct5rchggh.naaa,ib9XeNhprfttrisapei2oUn.aenscuitrmic.epafusam-giwcuebei1fzdatsreosrtirBennin–thosinaomlfni-lvne,ita.rnsinigee4nahrtoccmrgiaoaePtiradriaresre2leenc3igLeieoexonddlgdeeionlsr,dcebon.qv0lrinaa.cirdurbtFy(bstCracfd2buimah6tlbF”tsciiVkepodoySricaotNp4ocee4ooClpoc”Oi(aeoauorskleetnrsho3o-ppmuttanucyhirkeladtNXerRsRmin,ks(.yptbsyismecale,o,.rdpe–fiaT,r.uel1Cenansoaefwf1souiCilfecRcxotmslslgtd1,woa9fetralso7eotihoxrtoeAhi9irimprro9Chlearnac7fceem–r,lfrt9eoNesr6reyeeafodebxNciiiFeo3(cid:13)s:fbep,Ansnrl:coacnorxf,o1rbYe1uRaisfdlStrogntgawmieTdir9oheiowl91tiicfoverntrtAgeihgn8rde1ooar9e9ae)eRtcfaaacrmieaego6o0imrrktnsn7n9fiiarenpwne,liplsco;w5e,taa,s4dAcrspuaiecreoetreM7StlnaCaa,)oNbunsrrideilv(spd,rp3isogeioyetglrpla1mneceuAyp,eoucepfnrNo.ot(t9tafrpmrsoaaahnaohUos1osrfn9iouufmdni0liedcssesr9ferSl5oSSgombeehmdi2oIwer8sstcoe.gcrnAnlsdiosrht2meo.ia6onEcraifoists,)uoriet3)nifmt2r,2atnttshedtw,itiinlini8gel.wcw.tCoc1rd“fiteisf0abtalumatatooRdin9yicSniaita8(oilfirtntltoobnr.ryU,9omercsedehoocdcRneeei2fiPcaASkndoneeobudWieCC,piniiuoneAmrnpnfrrawmcordys1fsobasitrdceedoirb)dPh@optiic9hmpmlmebeose,hgfdhitgehrfu9of)e–xceatiiritpibcreeeeyhtsn7sbwSbaieM.iupurrdmlniesnaesiitibiineUapetititiicrdnsladgicenaaeoonfrrl.enefgtnooyesdtsitnogFoho/dnelge,o(i,rr.kfrenpvhoWsgmmD1nto“m,methueprtU”i9paroawaotirnibuamtflarTl8.ssnttr(lfoltlriiaaptiexy8NNei,iiot,ocibtrasvhn:ccxyo–h@gnitohuomelshny/ir1ai7ie.oemr.–rnmnPpnt/9stn7sCdkoChHcSeireeri9we:ic.teloe1istroacr2y.wuasesiAomTaen9mo.coldPwsdlfihy9maPm.ptnenr.plhqeu2leriudectanu”eceeuessotAaR,rltorSesseeneiesmilsrs.nrcrecsideoerot,csetsecamcpcerpifeeon)iootdu1rnpsioftftsonmot1hahsaeoerea)gsnx0eeeesssrr.t,rams. visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
Q531A.92.F49O070R.2NT88R560A563N–1d(C9c29o02mputerprogramlanguage) I.Press, WilliamH. 92-8876 rth AmericaDROMsg of machin
AcatalogrecordforthisbookisavailablefromtheBritishLibrary. ). e-
ISBN 052143064X Volume1(thisbook)
ISBN 0521574390 Volume2
ISBN 0521437210 ExamplebookinFORTRAN
ISBN 0521574404 FORTRANdiskette(IBM3.500)
ISBN 0521576083 CDROM(IBMPC/Macintosh)
ISBN 0521576075 CDROM(UNIX)
Contents
12 PCLPSPP111222222222222...............ilrror171004589123612ocaeee10lPSIITIVCELSGGmenunntflfIQrpirarUehiaaaanttsnoirtnmraprruuodRoogagiccooMrdsDssliorutsureddafsse,iieeDeaeealvsg-inuurntAamacJtktmeeLoeccrrttonaohIyccittniooInoorVrmxiiOconremEaoodDnuamiffelrIPpnnalttderlpoeagniaTnuohhpaLmecrrravsnrcesoowonoeEeiSeMdiiymsvnmtnDirl,yigizoesBiaFtSaoeasmepaaiimttrntoa-onctioireaeatiiVonneroindsonamiccrnndsmmiononaaeSttsoitwtdnsDAptnolaiosaouonaniEInNifbltantnsdghmsdaibgdid3ltCAioeBSiyitTPeoEnytoobaponrianclCpodoeErluktlcpartSiisnhedoictluyoiisailactibssnotzSt?tispietonttMEoorimtntuequnasLscttrtiuriounoifacareneeaEntssriqdoEuqanStuisaoetnicostnison xxvxxxx2iii9284182935364v1xi2vi511297872514332ii visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
3 I3n.0teInrtproodulacttiioonnandExtrapolation 9999 rth AmericaDROMsg of machin
). e-
3.1PolynomialInterpolationandExtrapolation 102
3.2RationalFunctionInterpolationandExtrapolation 104
3.3CubicSplineInterpolation 107
3.4HowtoSearchanOrderedTable 110
3.5CoefficientsoftheInterpolatingPolynomial 113
3.6InterpolationinTwoorMoreDimensions 116
v
vi Contents
4 IntegrationofFunctions 123
4.0Introduction 123
4.1ClassicalFormulasforEquallySpacedAbscissas 124
4.2ElementaryAlgorithms 130
4.3RombergIntegration 134
4.4ImproperIntegrals 135
56 ES4455555555555555566666666.........................vp557101246891111023456763120134aeGGRNISECQCDIIEIBMBMPnnnnPCBPPEREeolvxceoheeaauuettccouurraolcacvpssrrmureuamemaooiiyodloodissulolestaboaasdtmvmmuyneeibimpiddese´ssrlnynrofidalltlaunoerariuluuapposeanAataeieeiitlbaoFFmtlFccihmcillmnonnndxaiatvoeeFiFmpttuuaceitldlictuiitteneinoiupliBAuQannviooeeezCaiatsnvnlTnanrnccDynnaloensruAGBseohRoolttcchtisoIfdiciiaFeaixtetrAtnBsepoooaeeohffdriCinubiettCmtioplIonnninmmpiraFderailnyvnoFnnranassoupgtmucsaotFoCnaeFtloi,sRuooebrrhuttnontxnftuIBmuoaiiaogiffiiaerncnovnticncPnnlxnersestmvIFtiFstsenaiccusioaintecvEorsuoma,ltaAtalegwteaasiqintnnCentdoDoFrrcnapiiuaeogcsgadontunotudpFliratifleiebnssm,ionsoCtrFrnrSnoOatyiSoanocnrouulcOnescixttCreafPennrblifu,ttnliraoirIhihsacumEddeonotsOnttoeitesehrhimtnavi,bgronreroatsFedoyoIgntiwnCn’oaersnePsscrth’nrhFao,esDteleOuogiARvsbPinrrrss-iiayeocdrtaoatcrsytlpeliniiyuhsorbopF,nreFnunrrBuvoouet,nmiinxnCConccicinohtomaeti,eiimolo-aFFsfnSfitino-easqDcrd,luimSCieFasnpurotutrehlesniaebfcfirutiicctoiiaoenlnnt,s 211121211222111121111221112056805077130594981965228790590319581544950749297399216 visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
666...1890SFDprehasewnreiscloaInln’HtseIagnrrmtaelgos,rnaCilcossineandSineIntegrals 222544268 rth AmericaDROMsg of machin
6.11EllipticIntegralsandJacobianEllipticFunctions 254 ). e-
6.12HypergeometricFunctions 263
7 RandomNumbers 266
7.0Introduction 266
7.1UniformDeviates 267
Contents vii
7.2TransformationMethod: ExponentialandNormalDeviates 277
7.3RejectionMethod: Gamma, Poisson,BinomialDeviates 281
7.4GenerationofRandomBits 287
7.5RandomSequencesBasedonDataEncryption 290
7.6SimpleMonteCarloIntegration 295
7.7Quasi-(thatis,Sub-)RandomSequences 299
8910 SRM99999788888889991111111111......0.......0000...00000o3342526780140561oi..........3018924567nrHVNQSSNGAISIIDBRonnntiOIGLSPDDCVeetaoreeudeletirmtdtnlcoaniaiarrawwtnaooinaooiemetnaecoorcbFrrpirptncelwxWaenttrikigegkddosadsutoo-atjmzibicatehisilnouuduDennoblnnitnvlrotoaatMnhjrccuigiygfli--igennlodtrtPenItticatRmRietPiiSCnlgaanecgiartttooildMaaietnotoeoshaennonnoihSSIppaecandlgeoAdGnnnenoyeinrghhtrsrnmtvittMdRtdnnrdRiasseorioeaeoooo,onimo(rpaanecBrdnPnpntnFfnemnlgcrhmina–eoSoaMiaEkueeaMMsilxlDlwelLMnidnairneqiasSnenanslttMceeaedteeustriggeigtattrMkhMlNvcioihhaPgSlevkaoohe’MxnrooeothesaeonendchsdM)dtiisltaerdhesnhtehonmi–nlMttUfnloodiothwBdiOol’nhcoddsniiesoririeeBnznnsitstnMdteMnNheheaSnCrfsieMMgoneouCoetiDFtladnmrltDnaeMiauMithsitosrrNtilrm’lpeohdisslisteunnrltooniedoSieteidlMmeshnDvdntxMMiaeioolam,sedeeriMdtitanneurtifioSeshmintvselvnnehytoiFdaeiteoasosorddhinutRntdoiSioefissmvsninnmdyideoEsescdOssntnqeetsonsrmiifuesoo’sEDannMoqstisfumieoaEtethqninooussdniaostinons 333333333334333433443343334332845224823020462145970133729907053007736972122068366372395 visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
11 E11i.g0eInntrsoydusctteiomn s 444499 rth AmericaDROMsg of machin
). e-
11.1JacobiTransformationsofaSymmetricMatrix 456
11.2ReductionofaSymmetricMatrixtoTridiagonalForm:
GivensandHouseholderReductions 462
11.3EigenvaluesandEigenvectorsofaTridiagonalMatrix 469
11.4HermitianMatrices 475
11.5ReductionofaGeneralMatrixtoHessenbergForm 476
viii Contents
11.6TheQRAlgorithmforRealHessenbergMatrices 480
11.7ImprovingEigenvaluesand/orFindingEigenvectorsby
InverseIteration 487
12 FastFourierTransform 490
12.0Introduction 490
1143 SF1111111111111111111111111122233342223333344443344433ot..........................a25681121340147903672614535u01t(aFFESDFFFICPPCIANDCLMCLODriAnnnWNaopoFFoosixiioooooroopittnnoedsgueuwweltTTrrnmrnnuttlateeemTooTcriirrriSvtpmTeevmtraaPeiiFtpddoiicwwaneeeorrroannrrwleaououufelaaanrraarloolgSSPClrtuucclTFtolaeFRnltTeT-ieiilppsttrmtrtDA(nwoocDoiSsiineeDrirdiWeelDooTa)ogrorneaatatdceinoccirtleoinnsfrnnnrmMlythiettFaisearStarUrcorressTaFtlrlianioaneuuTtrfafynsenricnprusigdioonubDsmmtatseogabeMcidnhfoerrsrubieronnAiuommsiicior)ostrlEEoDensoontcriettaudoifRfFirosimrnrrsspooneootttfeiAtnttiIaaMoohcbhnfrdiirslnntUslnmmtDcfomenauessDieteLkHDonaeno,RtrDTiaalSmiirlmgii(veSttiaCoseyirnnnFaiAiisrvomvoceinafooesemgtaonFeflrlerrlin:nnalpueaoreeeynisTwspDrrsbMtrttt-lUbpDeoif)lhaieieUyiuPLoioaoylntlfnenesolathDrtynnsonSdiitiaaTgettmSion?sccihnaUntSdUwaoCianahgTmea,ganiamnlsssetcooihVmtiMipntatFtThDnsneeFhiaDilpiwFveogogearFeinMliefiTrdxFoeeTsatfntFeshihedtCFnemDmTFarsreeacTionD?TrabnueFFaddtu,samnaFiFttSnTosaiTTgfokEhronernVrewstmaernrosiDepasniysmc,eesn?sions 656566565655555655556655456403130060336138734501235490293040349910554873209580179424 visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
15 M14o.8dSeavliintzgky-oGfoDlayaStamoothingFilters 665404 rth AmericaDROMsg of machin
). e-
15.0Introduction 650
15.1LeastSquaresasaMaximumLikelihoodEstimator 651
15.2FittingDatatoaStraightLine 655
15.3Straight-LineDatawithErrorsinBothCoordinates 660
15.4GeneralLinearLeastSquares 665
15.5NonlinearModels 675
Contents ix
15.6ConfidenceLimitsonEstimatedModelParameters 684
15.7RobustEstimation 694
16 IntegrationofOrdinaryDifferentialEquations 701
16.0Introduction 701
16.1Runge-KuttaMethod 704
111789 TIP1111111111111111111111111n6788866667777788888996799wat.........................5434623460135601257017223reotSAIIBAMRSITRAHIFVLMIFMSDIginnnnnnetrlhhoiaPaieduairiutvtttinoauecWcfocellefrrrtnatalfxdexhetdalioofooookgoupdetarSoaixh-ainDlidddSmurtrmslistlfiCsrrraohiadriiuuuneeisEtVnkdvnetaailvloRoue--tcccimfgdesPttegasOGoepEnomqtttEefeodliiirnt,stoSMedBIuqgoooIriqnouEoielnMndEEfntueunnnuMbbrArqetiEoieaagxalEnvaeeedltPpuuareitxleattrtrauFqpMaisrrllnairmtCntmtitootiooiuoloihtrionizMzattincovebanvsaiVppotaoelinatpsnidnetlsayltdaaaehnnBietteCiolswoinlItssaoosmgulMI:eouholnnodmndaeirorneoPuEiSstsnvta,etyfhtdMniaoiptoPhiaatoqangrtnhdihStnferhonlneVieoauoeddiMvMelVttUrnadrbhaReayfoPaSnglsuoeoIleleEidtrueeCsnldurudsemitchlqsteioaotoRdavoeodhuslfrnPiPnunreieacHdKmoAadnPrttrsBitiooiagetioensKrPbrioruernn-otmonlernl-siCsseniinKeiboromosodlsTunrsrlconsiitrehhrsctIea-nmsecSSftioootnsorrgremMyuralMeatitrohePntohodoisndts 787787777777877778787887777771482297747912850154304061849858557455998666163998844820 visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
1199..54VRFoaeluluarexieaPrtiraoonnbdlMeCmeytschloicdsRfeodruBctoiounndMareythVoadlsuefoPrrBoboluenmdsary 885448 rth AmericaDROMsg of machin
19.6MultigridMethodsforBoundaryValueProblems 862 ). e-
20 Less-NumericalAlgorithms 881
20.0Introduction 881
20.1DiagnosingMachineParameters 881
20.2GrayCodes 886
x Contents
20.3CyclicRedundancyandOtherChecksums 888
20.4HuffmanCodingandCompressionofData 896
20.5ArithmeticCoding 902
20.6ArithmeticatArbitraryPrecision 906
ReferencesforVolume1 916
22BB2BBBB321654213CoIGnneNLIFFIPSEISPIdnnnntniooeepvroructttteeerrxnarreeelmeuetfoolrlgrtciranaouswtpmddeairicslfaaoarouunooieIieltPtnnlccncrifai9FotdraottIadVotnooii0unrilnooeoboffignVRCexnnoolynoLrcuosreoafftitttmMmlaoncoomdiFuFonieaeiuempVuFPsncdatnenoChosia2eraocEsclarr:hAunntta2xteUairNmidllotaloglprtuennMeniDaetllmsesispbee9tPriorept01seraclreosaiLiaanccgtnlafiadfrooEndalerngqmRn2Fuucemoaaicregtitiinsperogaen(FnVsseo9ianl0.tuF1r)oerstran11111119x000000099990vv48750118263ixi3i0390427125ii visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
BB78 RSoarntdinogmNumbers 11114617 rth AmericaDROMsg of machin
B9 RootFindingandNonlinearSetsofEquations 1182 ). e-
B10 MinimizationorMaximizationofFunctions 1201
B11 Eigensystems 1225
B12 FastFourierTransform 1235
Contents xi
B13 FourierandSpectralApplications 1253
B14 StatisticalDescriptionofData 1269
B15 ModelingofData 1285
B16 IntegrationofOrdinaryDifferentialEquations 1297
BBBBCCC11213127098 RATGLPLIILnnweiiapeestdssrefponttetesiigeiexnnrPa-rnreNggalooadnDlulfiooicnEmcIiPffnefteqfrUEesdeBsuorxetrfoagiieopxclturinrlaitationytcloVmindAaiMotVsaslllIogrouEnaaydolmqtnuneurVudmdeirltaaefhIeD2altsnumisceove(epsnen1sPersrastrnynoedpdbeTeln2ehacmenioesdrsyn(rVuotli.l)2) 111111111333334343168534342414294735 visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
rth AmericaDROMsg of machin
). e-
visit website http://www.nr.com or call 1-800-872-7423 (North America only),(cid:10)or send email to [email protected] (outside Noreadable files (including this one) to any server(cid:10)computer, is strictly prohibited. To order Numerical Recipes books,(cid:10)diskettes, or CPermission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyinCopyright (C) 1986-1992 by Cambridge University Press.(cid:10)Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X)
rth AmericaDROMsg of machin
). e-
xii