Numerical Recipes - The Art of Scientific Computing(3rd) 无水印pdf

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nr3”-2007/5/1—20:53— page I一#1 NUMERICAL RECIPES The Art of scientific computing Third edition nr3”-2007/5/1—20:53— page ll-#2 n3-2007/5/1-20:53- Page ill-#3 NUⅣ ERICAL RECIPES The Art of Scientific Computing Third edlition WIlliam h press Raymer Chair in Computer Sciences and Integrative Biology The University of Texas at Austin Saul A. Teukolsky s A. Bethe Professor of Physics and Astrophysics Cornell University William T Vetterling Research Fellow and Director of Image Science ZINK Imaging, LLC Brian p flanne Science, Strategy and Programs Manager Exxon Mobil Corporation CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNTVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Informationonthistitlewww.cambridge.org/9780521880688 o Cambridge University Press 1988, 1992, 2002, 2007 except for 13.10, which is placed into the public domain, and except for all other computer programs and procedures, which are This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2007 ISBN-13 978-0-511-33555-6 eBook(Netlibrary) ISBN-10 0-511-33555-5 eBook(NetLibrary ISBN-13978-0-521-88068-8 hardback ISBN-10 0-521-88068-8 hardback ambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate Without an additional license to use the contained software, this book is intended as a text and reference book, for reading and study purposes only. However, a restricted, limited free license for use of the software by the individual owner of a copy of this book who personally keyboards one or more routines into a single computer is granted under terms described on p. xix. See the section"License and Legal Information"(pp xix xxi)for information on obtaining more general licenses. Machine-readable media containing the g software in this book, with included license for use by a single individual, are available from Cambridge University Press. The software may also be downloaded, with immediate purchaseofalicensealsopossiblefromtheNumericalRecipesSoftwareWebsite(http //www.nr.com).UnlicensedtransferofnUmericalRecipesprogramstoanyotherformat or to any computer except one that is specifically licensed, is strictly prohibited. Technical questions, corrections, and requests for information should be addressed to Numerical Recipes Software, P O. Box 380243, Cambridge, MA 02238-0243 (USA), email info@nr com, or fax781-863-1739 2007/5/1 20:53 page v—#5 Contents Preface to the Third Edition(2007) Preface to the Second Edition(1992) Preface to the First Edition (1985) XV License and Legal Information XIX 1 Preliminaries 1.0 Introduction 1.1 Error, Accuracy, and stability 8 1.2 C Family Syntax 12 1.3 Objects, Classes, and Inheritance 17 1.4 Vector and Matrix Objects 24 1.5 Some Further Conventions and capabilities .30 2 Solution of Lincar Algcbraic Equations 37 2.0 Introduction 37 2.1 Gauss-Jordan elimination 41 2.2 Gaussian elimination with backsubstitution 46 2.3 LU Decomposition and Its Applications 48 2.4 Tridiagonal and Band-Diagonal Systems of equations 56 2.5 Iterative Improvement of a solution to linear equations 61 2.6 Singular value Decomposition 65 2.7 Sparse Linear systems 75 2.8 Vandermonde matrices and Toeplitz matrices 93 2.9 Cholesky Decomposition 2.10 OR Decomposition 102 2.11 Is Matrix Inversion an n3 Process? 106 3 Interpolation and Extrapolation 110 3.0 Introduction l10 3.1 Preliminaries: Scarching an Ordered Table 114 3.2 Polynomial Interpolation and Extrapolation............. 118 3.3 Cubic Spline Interpolation 120 3.4 Rational Function Interpolation and Extrapolation ........ 124 n3”-2007/5/1-20:53- Page vI一# Contents 3.5 Coefficients of the Interpolating Polynomial 129 3.6 Interpolation on a grid in Multidimensions .132 3.7 Interpolation on Scattered data in multidimensions 29 3.8 Laplace Interpolation 150 4 Intcgration of Functions 155 4.0 Introduction 155 4.1 Classical Formulas for Equally Spaced Abscissas 156 4.2 Elementary Algorithms 4.3 Romberg Integration .166 4.4 Improper Integrals 4.5 Quadrature by Variable Transformation 172 4.6 Gaussian Quadratures and Orthogonal Polynomials ....,179 4.7 Adaptive Quadrature ...194 4. 8 Multidimensional integrals 196 5 Evaluation of functions 201 5.0 Introduction 201 5.1 Polynomials and Rational Functions 201 5.2 Evaluation of Continued fractions 206 5.3 Series and Their Convergence 209 5.4 Recurrence relations and Clenshaws Recurrence formula 219 5.5 Complex arithmetic 225 5.6 Quadratic and Cubic equations .227 5.7 Numerical Derivatives .229 5.8 Chebyshev Approximation 233 5.9 Derivatives or Integrals of a Chebyshev-Approximated Function.. 240 5.10 Polynomial Approximation from Chebyshev Coefficients 241 5.11 Economization of power series .243 5.12 Pade Approximants 245 5.13 Rational Chebyshev Approximation .247 5.14 Evaluation of Functions by Path Integration 251 6 Special Functions 255 6.0 Introduction 255 6.1 Gamma Function. Beta Function Factorials. Binomial Coefficients 256 6.2 Incomplete Gamma Function and Error Function 59 6.3 Exponential Integral 266 6. 4 Incomplete beta Function 270 6.6 Bessel Functions of Fractional Order, Airy Functions, Spherical.274 6.5 Bessel Functions of Integer Order Bessel functions 283 6.7 Spherical harmonics 292 6.8 Fresnel Integrals, Cosine and sine integrals 297 6.9 Dawson’ s Integral 302 6. 10 Generalized Fermi-Dirac Integrals 304 6. 11 Inverse of the Function x log(x) 307 6. 12 Elliptic Integrals and Jacobian Elliptic Functions 309 nr3”-2007/5/1-20:53— page vil-#7 Contents 6.13 Hypergeometric Functions .318 6.14 Statistical functions 7 Random Numbers 340 7.0 Introductio 340 7.1 Uniform Deviates 341 7.2 Completely Hashing a Large array 358 7.3 Deviates from Other distributions 361 7. 4 Multivariate normal deviates .378 7.5 Linear Feedback Shift Registers ..380 7.6 Hash Tables and Hash memories 386 7. 8 Quasi-(that is. Sub-)Random Sequencer 7.7 Simple monte Carlo Integration 397 403 7.9 Adaptive and Recursive Monte Carlo Methods 410 8 Sorting and Selection 419 8. 0 Introduction 419 8.1 Straight Insertion and shell's method 420 8.2 Quicksort 423 8.3H 426 8.4 Indexing and Rankin 428 8.5 Selecting the M th 431 8.6 Determination of Equivalence Classes 439 9 Root Finding and Nonlinear sets of Equations 442 9.0 Introduction 442 9. 1 Bracketing and Bisection 445 9.2 Secant method. false position method. and ridders method 449 9.3 Van Wijngaarden-Dekker- Brent Method 454 9.4 Newton-Raphson Method Using Derivative 456 9.5 Roots of pc 463 9.6 Newton-Raphson Method for Nonlinear Systems of equations 473 9.7 Globally Convergent Methods for Nonlinear Systems of Equations 477 10 Minimization or maximization of functions 487 10.0 Introduction 487 10.1 Initially Bracketing a Minimum 490 10.2 Golden Section Search in One dimension 492 10.3 Parabolic Interpolation and Brents method in One dimension... 496 10.4 One-Dimensional search with first derivatives 4 10.5 Downhill Simplex Method in Multidimensions 502 10.6 Line methods in multidimensions 507 10.7 Direction Set(Powells) Methods in Multidimensions 509 10.8 Conjugate Gradient Methods in Multidimensions 515 10.9 Quasi-Newton or Variable Metric Methods in Multidimensions 521 10.10 Linear Programming: The Simplex Method 526 10.11 Linear Programming: Interior-Point Methods 537 10.12 Simulated Annealing methods 549 10.13 Dynamic Programming .555 nr3”-2007/5/1-20:53—pa Contents 11 Eigensystems 563 11. 0 Introduction ..563 11. 1 Jacobi Transformations of a Symmetric Matrix 570 11.2 Real s ymmetric matrices 576 11.3 Reduction of a Symmetric Matrix to Tridiagonal Form: Givens and householder reductions .,,..578 11. 4 Eigenvalues and Eigenvectors of a Tridiagonal matrix 583 11.5 Hermitian matrices .590 11.6 Real Nonsymmetric Matrices 590 11.7 The OR Algorithm for Real Hessenberg Matrices .596 11.8 Improving Eigenvalues and/or Finding Eigenvectors by Inverse Iteratio 597 12 Fast Fourier Transform 600 12. 0 Introducti 600 12.1 Fourier Transform of Discretely Sampled Data 605 12.2 Fast h 608 12. 3 FFT of Real Functions .617 12.4 Fast sine and cosine transforms 620 12.5 FFT in Two or more dimensions 6 7 12.6 Fourier Transforms of Real data in Two and Three dimensions . 631 12.7 External Storage or Memory-Local FFTs .637 13 Fourier and Spectral Applications 640 13.0 Introduction 640 13.1 Convolution and Deconvolution Using the FFt .641 13.2 Correlation and autocorrelation using the fft 648 13.3 Optimal (Wiener) Filtering with the FFT 649 13.4 Power Spectrum estimation Using the FFt 652 13.5 Digital filtering in the Time domain 667 13.6 Linear Prediction and Linear Predictive Coding .673 13.7 Power Spectrum Estimation by the Maximum Entropy(All-poles Method 681 13.8 Spectral analysis of Unevenly Sampled data 685 13.9 Computing Fourier Integrals Using the FFt .692 13.10 Wavelet Transforms 699 13.11 Numerical Use of the Sampling Theorem 717 14 Statistical Description of Data 720 14.0 Introduction 720 14.1 Moments of a distribution: Mean. Variance Skewness and so forth 721 14.2 Do Two Distributions have the same means or variances? 726 14.3 Are Two Distributions Different? 730 14.4 Contingency Table Analysis of Two Distributions 741 14.5 Linear correlation 745 14.6 Nonparametric or Rank Correlation 748 14.7 Information-Theoretic Properties of Distributions 754 14.8 Do Two-Dimensional Distributions Differ?......,......762 【实例截图】
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