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Sample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X) Copyright (C) 1986-1992 by Cambridge University Press.Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin g of machine- readable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes booksor CDROMs, v isit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to [email protected] (outside North Amer ica).License Information Read this section if you want to use the programs in this book on a computer. You’llneedtoreadthefollowingDisclaimerofWarranty,gettheprogramsontoyour computer,and acquire a Numerical Recipes software license. (Without this license, whichcan bethe free“immediatelicense” underterms describedbelow,the bookis intended as a text and reference book, for reading purposes only.) Disclaimer ofWarranty We make no warranties, express or implied, that the programs contained in this volume are free of error, or are consistent with any particular standard of merchantability,or that theywill meet yourrequirements forany particular application. Theyshouldnotbereliedonforsolvingaproblemwhoseincorrect solution could result in injury to a person or loss of property. If you do use the programs in such a manner, it is at your own risk. The authors and publisherdisclaim all liability for direct or consequential damages resulting from your use of the programs. HowtoGet the Code ontoYour Computer Pick one of the following methods: Youcan typetheprogramsfromthis bookdirectlyintoyourcomputer. In this case, the onlykind of license available to you is the free “immediate license” (see below). You are not authorized to transfer or distribute a machine-readablecopy to any other person, nor to have any other person typetheprogramsintoacomputeronyourbehalf. Wedonotwanttohear bug reports from you if you choose this option, because experience has shown that virtually all reportedbugs in such cases are typingerrors! You can download the Numerical Recipes programs electronically from the Numerical Recipes On-Line Software Store, located at our Web site(http://www.nr.com ). They are packaged as a password-protected file, and you’ll need to purchase a license to unpack them. You can get a single-screen license and password immediately, on-line, from theOn-Line Store, with fees ranging from $50 (PC, Macintosh, educational institutions’ UNIX) to $140 (general UNIX). Downloading the packaged software from the On-Line Store is also the way to start if you want to acquire a more general (multiscreen, site, or corporate) license. xx LicenseInformation xxiSample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X) Copyright (C) 1986-1992 by Cambridge University Press.Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin g of machine- readable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes booksor CDROMs, v isit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to [email protected] (outside North Amer ica).You can purchase media containing the programs from Cambridge Uni- versity Press. Diskette versions are available in IBM-compatible formatfor machines runningWindows 3.1, 95, or NT. CDROM versions in ISO- 9660 format for PC, Macintosh, and UNIX systems are also available; these include both Fortran and C versions (as well as versions in Pascaland BASIC from the first edition) on a single CDROM. Diskettes pur- chased from Cambridge University Press include a single-screen license for PC or Macintosh only. The CDROM is available with a single- screen license for PC or Macintosh (order ISBN 0 521 576083), or (at a slightly higher price) with a single-screen license for UNIX workstations(order ISBN 0 521 576075). Orders for media from Cambridge Univer- sity Press can be placed at 800 872-7423 (North America only) or by email to [email protected] (North America) or [email protected] (restofworld). Or,visittheWebsites http://www.cup.org (NorthAmerica) orhttp://www.cup.cam.ac.uk (rest of world). Types ofLicense Offered Here are the types of licenses that we offer. Note that some types are automatically acquired with the purchase of media from Cambridge University Press, or of an unlocking password from the Numerical Recipes On-Line SoftwareStore, while other types of licenses require that you communicate specifically with Numerical Recipes Software (email: [email protected] or fax: 781 863-1739). Our Web site http://www.nr.com has additional information. [“Immediate License”] If you are the individual owner of a copy of this book and you type one or more of its routines into your computer, weauthorize you to use them on that computer for your own personal and noncommercialpurposes. You are not authorized to transfer or distribute machine-readable copies to any other person, or to use the routines on more than one machine, or to distribute executable programs containing our routines. This is the only free license. [“Single-Screen License”] This is the most common type of low-cost license, with terms governed by our Single Screen (Shrinkwrap) License document(completetermsavailablethroughourWebsite). Basically,thislicense lets you use Numerical Recipes routines on any one screen (PC, workstation, X-terminal, etc.). You may also, under this license, transfer pre-compiled, executable programs incorporating our routines to other, unlicensed, screens or computers, providing that (i) your application is noncommercial (i.e., does not involve the selling of your program for afee), (ii) the programs were first developed, compiled, and successfully runonalicensedscreen,and(iii)ourroutinesareboundintotheprograms in such a manner that they cannot be accessed as individual routines andcannotpracticablybeunboundandusedinotherprograms. Thatis,under this license, your program user must not be able to use our programs as part of a programlibrary or “mix-and-match”workbench. Conditionsfor other types of commercial or noncommercial distribution may be found on our Web site ( http://www.nr.com ). xxii LicenseInformationSample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X) Copyright (C) 1986-1992 by Cambridge University Press.Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin g of machine- readable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes booksor CDROMs, v isit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to [email protected] (outside North Amer ica).[“Multi-Screen, Server, Site, and Corporate Licenses”] The terms of the Single Screen License can be extended to designated groups ofmachines, defined by number of screens, number of machines, locations, or ownership. Significant discounts fromthe correspondingsingle-screen prices are available when the estimated number of screens exceeds 40.Contact Numerical Recipes Software (email: [email protected] or fax: 781 863-1739) for details. [“Course Right-to-Copy License”] Instructors at accredited educational institutionswhohaveadoptedthisbookforacourse,andwhohavealready purchased a Single Screen License (either acquired with the purchase of media, or from the Numerical Recipes On-Line Software Store), maylicensetheprogramsforuseinthatcourseasfollows: Mailyourname,title, and address; the course name, number, dates, and estimated enrollment; and advancepayment of $5 per (estimated) student to Numerical Recipes Software, at this address: P.O. Box 243, Cambridge, MA 02238 (USA). You will receive by return mail a license authorizing you to make copies of the programs for use by your students, and/or to transfer the programs to a machine accessible to your students (but only for the duration of the course). AboutCopyrightson ComputerPrograms Like artistic or literary compositions, computer programs are protected by copyright. Generally it is an infringement for you to copy into your computer a program from a copyrighted source. (It is also not a friendly thing to do, since it deprivesthe program’sauthorofcompensationforhis orhercreativeeffort.) Undercopyrightlaw,all“derivativeworks”(modifiedversions,ortranslationsintoanother computerlanguage)also come under the same copyrightas the original work. Copyright does not protect ideas, but only the expression of those ideas in a particular form. In the case of a computer program, the ideas consist of the program’s methodology and algorithm, including the necessary sequence of steps adopted by the programmer. The expression of those ideas is the program source code(particularlyanyarbitraryorstylisticchoicesembodiedinit),itsderivedobject code, and any other derivative works. If you analyze the ideas contained in a program, and then express those ideas in your own completely different implementation, then that new program implementation belongs to you. That is what we have done for those programs inthis bookthat are not entirelyofour owndevising. When programsin this bookare said to be “based” on programs published in copyright sources, we mean that the ideas are the same. The expression of these ideas as source code is our own. We believe that no material in this book infringes on an existing copyright. Trademarks Several registered trademarks appear within the text of this book: Sun is a trademark of Sun Microsystems, Inc. SPARC and SPARCstation are trademarks of SPARC International, Inc. Microsoft, Windows 95, Windows NT, PowerStation, and MS are trademarks of Microsoft Corporation. DEC, VMS, Alpha AXP, and LicenseInformation xxiiiSample page from NUMERICAL RECIPES IN FORTRAN 77: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43064-X) Copyright (C) 1986-1992 by Cambridge University Press.Programs Copyright (C) 1986-1992 by Numerical Recipes Software. Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copyin g of machine- readable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes booksor CDROMs, v isit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to [email protected] (outside North Amer ica).ULTRIX are trademarks of Digital Equipment Corporation. IBM is a trademark of InternationalBusiness MachinesCorporation. Apple andMacintoshare trademarksofAppleComputer,Inc. UNIXis a trademarklicensedexclusivelythroughX/Open Co. Ltd. IMSL is a trademark of Visual Numerics, Inc. NAG refers to proprietary computer software of Numerical Algorithms Group (USA) Inc. PostScript andAdobeIllustratoraretrademarksofAdobeSystemsIncorporated. Last,andnodoubt least, Numerical Recipes (when identifying products) is a trademark of Numerical Recipes Software. Attributions The fact that ideas are legally “free as air” in no way supersedes the ethical requirement that ideas be credited to their known originators. When programs inthisbookarebasedonknownsources,whethercopyrightedorinthepublicdomain, published or “handed-down,” we have attempted to give proper attribution. Unfor- tunately, the lineage of many programs in common circulation is often unclear. Wewouldbegratefultoreadersforneworcorrectedinformationregardingattributions, which we will attempt to incorporate in subsequent printings.