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1 NUMERICALRECIPESThe Art of Scientific ComputingThird Cambridge University PressCambridge University Press978-0-521-88068-8 - NUMERICAL RECIPES : The Art of Scientific Computing, Third EditionWilliam H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. FlanneryFrontmatterMore informationNUMERICALRECIPESThe Art of Scientific ComputingThird EditionWilliamH. PressRaymer Chairin ComputerSciences and Integrative BiologyThe University of Texas at AustinSaulA. TeukolskyHans A. Bethe Professor of Physics and AstrophysicsCornell UniversityWilliamT. VetterlingResearch Fellow and Director of ImageScienceZINKI maging,LLCB rianP. FlanneryScience, Strategyand ProgramsManagerExxon Cambridge University PressCambridge University Press978-0-521-88068-8 - NUMERICAL RECIPES : The Art of Scientific Computing, Third EditionWilliam H.

2 Press, Saul A. Teukolsky, William T. Vetterling and Brian P. FlanneryFrontmatterMore informationCAMBRIDGE UNIVERSITY PRESSC ambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S ao PauloCambridge University Press32 Avenue of the Americas, New York, NY 10013-2473, on this title: Cambridge University Press 1988, 1992, 2002, 2007except for , which is placed into the public domain,and except for all other computer programs and procedures, which arec NUMERICAL RECIPES Software 1986, 1988, 1992, 1997, 2002, 2007 All Rights book is in copyright. Subject to statutory exception and to the provisions of relevantcollective licensing agreements, no reproduction of any part may take place withoutthe written permission of Cambridge University sections of this book were originally published, in different form, inComputersin Physicsmagazinec American Institute of Physics 1988 of the code in Chapter 17 arec Ernst Hairer 2004.

3 Used by edition first published 1986 Second edition first published 1992 Third edition first published 2007 This printing is corrected to software version in Hong Kong by Golden CupAffiliations shown on title page are for purposes of identification only. No implicationthat the work contained herein was created in the course of employment is intended,nor is any knowledge or endorsement of these works by the listed institutions to be an additional license to use the contained software, this book is intended as atext and reference book, for reading and study purposes only. However, a restricted, limitedfree license for use of the software by the individual owner of a copy of this book who person-ally keyboards one or more routines into a single computer is granted under terms describedon p.

4 Xix. See the section License and Legal Information (pp. xix xxi) for information onobtaining more general media containing the software in this book, with included license foruse by a single individual, are available from Cambridge University software may also be downloaded, with immediate purchase of a license also pos-sible, from the NUMERICAL RECIPES Software Web site ( ). Unlicensedtransfer of NUMERICAL RECIPES programs to any other format, or to any computer except onethat is specifically licensed, is strictly prohibited. Technical questions, corrections, and re-quests for information should be addressed to NUMERICAL RECIPES Software, Box 380243,Cambridge, MA 02238-0243 (USA), email or fax catalog record for this book is available from the British of Congress Cataloging in Publication DataNumerical RECIPES : the art of scientific computing / William H.

5 Press .. [et al.].p. bibliographical references and 978-0-521-88068-8 (hardback)1. NUMERICAL analysis Computer programs. 2. Science Mathematics Computer FORTRAN (Computer program language).I. Press, William dc222007062003 ISBN978-0-521-88068-8hardbackISBN978-0-5 21-70685-8source code CD ROMISBN978-0-521-88407-5hardback with source code CD ROMC ambridge University Press has no responsibility for the persistence or accuracy of URLs forexternal or third-party Internet Web sites referred to in this book and does not guarantee thatany content on such Web sites is, or will remain, accurate or Cambridge University PressCambridge University Press978-0-521-88068-8 - NUMERICAL RECIPES : The Art of Scientific Computing, Third EditionWilliam H.

6 Press, Saul A. Teukolsky, William T. Vetterling and Brian P. FlanneryFrontmatterMore informationContentsPreface to the Third Edition (2007)xiPreface to the Second Edition (1992)xivPreface to the First Edition (1985)xviiLicense and Legal Informationxix1 .. , Accuracy, and Stability .. Objects,Classes,andInheritance .. Further Conventions and Capabilities .. 302 Solution of Linear Algebraic .. Gauss-JordanElimination .. Elimination with Backsubstitution .. and Its Applications .. and Band-Diagonal Systems of Equations .. IterativeImprovementofaSolutiontoLinearE quations .. Value Decomposition .. Matrices and Toeplitz Matrices .. Decomposition .. Is Matrix Inversion anN3 Process?

7 1063 Interpolation and .. Preliminaries:SearchinganOrderedTable .. Interpolation and Extrapolation .. RationalFunctionInterpolationandExtrapol ation .. Cambridge University PressCambridge University Press978-0-521-88068-8 - NUMERICAL RECIPES : The Art of Scientific Computing, Third EditionWilliam H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. FlanneryFrontmatterMore of the Interpolating on a Grid in Multidimensions .. on Scattered Data in LaplaceInterpolation .. 1504 Integration of .. Formulas for Equally Spaced Abscissas .. ElementaryAlgorithms .. ImproperIntegrals .. Quadratures and Orthogonal Integrals .. 1965 Evaluation of.

8 And Rational Functions .. Relations and Clenshaw s Recurrence Formula .. QuadraticandCubicEquations .. or Integrals of a Chebyshev-Approximated Function .. Polynomial Approximation from Chebyshev Coefficients .. Economization of Power Series .. Pad eApproximants .. 2516 Special .. Function, Beta Function, Factorials, Binomial Integrals .. IncompleteBetaFunction .. Functions of Fractional Order, Airy Functions, FresnelIntegrals, Dawson sIntegral .. Inverse of the Elliptic Integrals and Jacobian Elliptic Functions .. Cambridge University PressCambridge University Press978-0-521-88068-8 - NUMERICAL RECIPES : The Art of Scientific Computing, Third EditionWilliam H.

9 Press, Saul A. Teukolsky, William T. Vetterling and Brian P. FlanneryFrontmatterMore StatisticalFunctions .. 3207 Random .. UniformDeviates .. CompletelyHashingaLargeArray .. MultivariateNormalDeviates .. HashTablesandHashMemories .. (that is, Sub-) Random Sequences .. and Recursive Monte Carlo Methods .. 4108 Sorting and .. StraightInsertionandShell Heapsort .. IndexingandRanking .. 4399 Root Finding and Nonlinear Sets of .. BracketingandBisection .. Method, False Position Method, and Ridders Method .. VanWijngaarden-Dekker-BrentMethod .. of Polynomials .. Method for Nonlinear Systems of Equations .. Convergent Methods for Nonlinear Systems of Equations47710 Minimization or Maximization of Introduction.

10 Initially Bracketing a Parabolic Interpolation and Brent s Method in One Dimension .. Downhill Simplex Method in Multidimensions .. Line Methods in Multidimensions .. Direction Set (Powell s) Methods in Multidimensions .. Conjugate Gradient Methods in Multidimensions .. Quasi-Newton or Variable Metric Methods in Multidimensions .. Linear Programming: Interior-Point Methods .. Simulated Annealing Methods .. Cambridge University PressCambridge University Press978-0-521-88068-8 - NUMERICAL RECIPES : The Art of Scientific Computing, Third EditionWilliam H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. FlanneryFrontmatterMore informationviiiContents11 Introduction.