c0-1 (Numerical Recipes in C)

License InformationDisclaimer of WarrantyWe make no warranties, express or implied, that the programs containedin this volume are free of error, or are consistent with any particular standardof merchantability, or that they will meet your requirements for any particularapplication. They should not be relied on for solving a problem whose incorrectsolution could result in injury to a person or loss of property. If you do use theprograms in such a manner, it is at your own risk. The authors and publisherdisclaim all liability for direct or consequential damages resulting from youruse of the programs.How to Get the Code onto Your ComputerPick one of the following methods:• You can type the programs from this book directly into your computer.

In thiscase, the only kind 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 type the programs into acomputer on your behalf.

We do not want to hear bug reports from you if youchoose this option, because experience has shown that virtually all reported bugsin such cases are typing errors!• You can download the Numerical Recipes programs electronically from theNumerical Recipes On-Line Software Store, located at http://www.nr.com, ourWeb site.

They are packaged as a password-protected file, and you’ll need topurchase a license to unpack them. You can get a single-screen license andpassword immediately, on-line, from the On-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 tostart if you want to acquire a more general (multiscreen, site, or corporate) license.• You can purchase media containing the programs from Cambridge UniversityPress.

Diskette versions are available in IBM-compatible format for machinesrunning Windows 3.1, 95, or NT. CDROM versions in ISO-9660 format for PC,Macintosh, and UNIX systems are also available; these include both C and Fortranversions on a single CDROM (as well as versions in Pascal and BASIC from thefirst edition). Diskettes purchased from Cambridge University Press include asingle-screen license for PC or Macintosh only. The CDROM is available witha single-screen license for PC or Macintosh (order ISBN 0 521 576083), or (at aslightly higher price) with a single-screen license for UNIX workstations (orderISBN 0 521 576075).

Orders for media from Cambridge University Press canbe placed at 800 872-7423 (North America only) or by email to orders@cup.org(North America) or trade@cup.cam.ac.uk (rest of world). Or, visit the Web siteshttp://www.cup.org (North America) or http://www.cup.cam.ac.uk (restof world).xviSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machinereadable files (including this one) to any servercomputer, is strictly prohibited.

To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).Read this section if you want to use the programs in this book on a computer.You’ll need to read the following Disclaimer of Warranty, get the programs onto yourcomputer, and acquire a Numerical Recipes software license. (Without this license,which can be the free “immediate license” under terms described below, the book isintended as a text and reference book, for reading purposes only.)License InformationxviiTypes of License Offered• [“Immediate License”] If you are the individual owner of a copy of this book andyou type one or more of its routines into your computer, we authorize you to usethem on that computer for your own personal and noncommercial purposes.

Youare not authorized to transfer or distribute machine-readable copies to any otherperson, or to use the routines on more than one machine, or to distribute executableprograms containing our routines. This is the only free license.• [“Single-Screen License”] This is the most common type of low-cost license, withterms governed by our Single Screen (Shrinkwrap) License document (completeterms available through our Web site). Basically, this license lets you use NumericalRecipes routines on any one screen (PC, workstation, X-terminal, etc.).

You mayalso, under this license, transfer pre-compiled, executable programs incorporatingour routines to other, unlicensed, screens or computers, providing that (i) yourapplication is noncommercial (i.e., does not involve the selling of your programfor a fee), (ii) the programs were first developed, compiled, and successfully runon a licensed screen, and (iii) our routines are bound into the programs in such amanner that they cannot be accessed as individual routines and cannot practicablybe unbound and used in other programs. That is, under this license, your programuser must not be able to use our programs as part of a program library or “mix-andmatch” workbench.

Conditions for other types of commercial or noncommercialdistribution may be found on our Web site (http://www.nr.com).• [“Multi-Screen, Server, Site, and Corporate Licenses”] The terms of the SingleScreen License can be extended to designated groups of machines, defined bynumber of screens, number of machines, locations, or ownership. Significantdiscounts from the corresponding single-screen prices are available when theestimated number of screens exceeds 40. Contact Numerical Recipes Software(email: orders@nr.com or fax: 781 863-1739) for details.• [“Course Right-to-Copy License”] Instructors at accredited educational institutionswho have adopted this book for a course, and who have already purchased a SingleScreen License (either acquired with the purchase of media, or from the NumericalRecipes On-Line Software Store), may license the programs for use in that courseas follows: Mail your name, title, and address; the course name, number, dates,and estimated enrollment; and advance payment of $5 per (estimated) studentto Numerical Recipes Software, at this address: P.O.

Box 243, Cambridge, MA02238 (USA). You will receive by return mail a license authorizing you to makecopies of the programs for use by your students, and/or to transfer the programs toa machine accessible to your students (but only for the duration of the course).About Copyrights on Computer ProgramsLike artistic or literary compositions, computer programs are protected bycopyright. Generally it is an infringement for you to copy into your computer aprogram from a copyrighted source.

(It is also not a friendly thing to do, since itdeprives the program’s author of compensation for his or her creative effort.) UnderSample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machinereadable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).Here are the types of licenses that we offer.

Note that some types areautomatically acquired with the purchase of media from Cambridge UniversityPress, or of an unlocking password from the Numerical Recipes On-Line SoftwareStore, while other types of licenses require that you communicate specifically withNumerical Recipes Software (email: orders@nr.com or fax: 781 863-1739). OurWeb site http://www.nr.com has additional information.xviiiLicense InformationTrademarksSeveral registered trademarks appear within the text of this book: Sun is atrademark of Sun Microsystems, Inc.

SPARC and SPARCstation are trademarks ofSPARC International, Inc. Microsoft, Windows 95, Windows NT, PowerStation,and MS are trademarks of Microsoft Corporation. DEC, VMS, Alpha AXP, andULTRIX are trademarks of Digital Equipment Corporation. IBM is a trademark ofInternational Business Machines Corporation. Apple and Macintosh are trademarksof Apple Computer, Inc. UNIX is a trademark licensed exclusively through X/OpenCo.

Ltd. IMSL is a trademark of Visual Numerics, Inc. NAG refers to proprietarycomputer software of Numerical Algorithms Group (USA) Inc. PostScript andAdobe Illustrator are trademarks of Adobe Systems Incorporated. Last, and no doubtleast, Numerical Recipes (when identifying products) is a trademark of NumericalRecipes Software.AttributionsThe fact that ideas are legally “free as air” in no way supersedes the ethicalrequirement that ideas be credited to their known originators. When programs inthis book are based on known sources, whether copyrighted or in the public domain,published or “handed-down,” we have attempted to give proper attribution. Unfortunately, the lineage of many programs in common circulation is often unclear.

Wewould be grateful to readers for new or corrected information regarding attributions,which we will attempt to incorporate in subsequent printings.Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software.Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machinereadable files (including this one) to any servercomputer, is strictly prohibited. To order Numerical Recipes books,diskettes, or CDROMsvisit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).copyright law, all “derivative works” (modified versions, or translations into anothercomputer language) also come under the same copyright as the original work.Copyright does not protect ideas, but only the expression of those ideas ina particular form.