[R语言]Using R for Numerical Analysis in Science and Engineering

[Victor A. Bloomfield]Using R for Numerical Analysis in Science and Engineering R经典英文书籍Chapman Hall/crCTher seriesSeries editorsJohn m. chambersTorsten hothornDepartment of statisticsDivision of biostatisticsStanford UniversityUniversity of zurichStanford california, USASwitzerlandDuncan Temple LangHadley WickhamDepartment of statisticsSTudioUniversity of California, DavisBoston massachusetts USADavis California, USAAims and scopeThis book series reflects the recent rapid growth in the development and applicationof r, the programming language and software environment for statistical computingand graphics. R is now widely used in academic research, education, and industryIt is constantly growing, with new versions of the core software released regularlyand more than 5, 000 packages available. It is difficult for the documentation tokeep pace with the expansion of the software, and this vital book series provides aforum for the publication of books covering many aspects of the development andapplication of rThe scope of the series is wide, covering three main threads:Applications of R to specific disciplines such as biology, epidemiology,genetics, engineering, finance, and the social sciencesUsing r for the study of topics of statistical methodology, such as linear andmixed modeling, time series, Bayesian methods, and missing dataThe development of R, including programming, building packages, andgraphics.The books will appeal to programmers and developers of R software, as well asapplied statisticians and data analysts in many fields. The books will featuredetailed worked examples and r code fully integrated into the text, ensuring theirusefulness to researchers, practitioners and studentso 2014 by Taylor Francis Group, LLCK13976 FM indd3/24/1411:19AMPublished titlesUsing R for Numerical Analysis in Science and Engineering, victor A. bloomfieldEvent History Analysis with R, Goran BrostromComputational Actuarial Science with R, Arthur CharpentierStatistical Computing in C++ and R, Randall L. Eubank and Ana KupresaninReproducible Research with R and RStudio, Christopher GandrudDisplaying Time Series, Spatial, and Space-Time Data with ROscar Perpinan LamigueiroProgramming Graphical User Interfaces with R, Michael F Lawrenceand John verzanAnalyzing Baseball Data with R, Max Marchi and Jim albertGrowth Curve Analysis and visualization Using R, Danie/ MirmanR Graphics, Second Edition, Paul MurrellCustomer and Business Analytics: Applied Data Mining for Business DecisionMaking Using R, DanielS. Putler and robert E KriderImplementing Reproducible Research, Victoria Stodden, Friedrich Leischand Roger D PengDynamic Documents with R and knit, yihui Xieo 2014 by Taylor Francis Group, LLCK13976 FM indd 33/24/1411:19AMMATLAB is a trademark of The MathWorks, Inc. and is used with permission. The mathWorks does not warrantthe accuracy of the text or exercises in this book. This book's use or discussion of MATLAB software or relatedproducts does not constitute endorsement or sponsorship by The Math Works of a particular pedagogical approachor particular use of the MATlAB'softwareCRC PressTaylor Francis Group6000 Broken Sound Parkway NW, Suite 300Boca raton, Fl 33487-2742o 2014 by Taylor Francis Group, LLCCRC Press is an imprint of Taylor Francis Group, an Informa businessNo claim to original U.S. Government worksPrinted on acid-free paperVersion date: 2014.0220International Standard Book Number-13: 978-1-4398-8448-5(Hardback)This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have beenmade to publish reliable data and information, but the author and publisher cannot assume responsibility for thevalidity of all materials or the consequences of their use. The authors and publishers have attempted to trace thecopyright holders of all material reproduced in this publication and apologize to copyright holders if permission topublish in this form has not been obtained. If any copyright material has not been acknowledged please write and letus know so we may rectify in any future reprint.Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted,or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without writtenission from the publisheForpermissiontophotocopyorusematerialelectronicallyfromthisworkpleaseaccesswww.copyright.com(http://www.copyright.com/)orcontacttheCopyrightClearancecEnter,Inc.(ccc),222RosewoodDrive,Danvers,MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a varietyof users. For organizations that have been granted a photocopy license by the CCC, a separate system of paymenthas been arrangedTrademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only foridentification and explanation without intent to infringeLibrary of Congress Cataloging-in-Publication DataBloom field, Victor A, authorUsing R for numerical analysis in science and engineering/Victor A bloomfieldpages cm. -- Chapman Hall/CRC the R series)Summary: This book shows how the free and open-source R environment can be used as apowerful and comprehensive platform for the kinds of numerical analysis that are traditionallyemployed by MatlaB?. With R code fully integrated, the book offers brief descriptions ofbasic approaches and emphasizes detailed worked examples. It covers functions in the baseinstallation of R as well as those in contributed packages, which greatly enhance the numericalanalysis capabilities of R"--Provided by publisherIncludes bibliographical references and indexISBN978-1-4398-8448-5( hardback)1. Science--Data processing. 2. Engineering--Data processing 3. Numerical analysis. 4. R( Computer program language)I. TitleQ1839B56201518.02855133-dc232014003930Visit the taylor francis Web site athttp://www.taylorandfrancis.comand the crc press web site athttp://www.crcpress.como 2014 by Taylor Francis Group, LLCK13976 FM indd 43/24/1411:19AMContentsList of Figures1 Introduction1.1 Obtaining and installing r12LearningR1.3 Learning numerical methods1. 4 Finding help2g1.6 Learning more about r16.1 Books1.6.2 Online resources2 Calculating72. 1 Basic operators and functions2.2 Complex numbers82.3 Numerical display, round-off error, and rounding2.4 Assigning variables2.4.1 Listing and removing variables122.5 Relational operators122.6Ⅴ ectors2.6.1 Vector elements and indexes132.6.2 Operations with vectors2.6.3 Generating sequences2.6.3.1 Regular sequences152.6.3.2 Repeating values162.6.3.3 Sequences of random numbers162.6.4 Logical vect2.6.5 Speed of forming large vectors182.6.6 Vector dot product and crossproduct192.7 Matrices212.7.1 Forming matrices212.7.2 Operations on matrices242.7. 2.1 Arithmetic operations on matrices242.7.2.2 Matrix multiplicationo 2014 by Taylor Francis Group, LLCCONTENTS2.7.2.3 Transpose and determinant262.7. 2 4 Matrix crossproduct262.7.2.5 Matrix exponential2.7.2.6verse and solve272.7.2.7 Eigenvalues and eigenvectors292.7. 2.8 Singular value decomposition312.7.3 The Matrix pack332.7.4 Additional matrix functions and packages342.8 Time and date calculations343 Graphing3.1 Scatter plots373.2 Function plots393.3 Other common plots3.3.1 Bar charts403.3.2 Histograms423.3.3 Box-and-whisker plots433.4 Customizing plots443. 4.1 Points and lines443.4.2 Axes, ticks, and par()443.4.3 Overlaying plots with graphic elements463.5 Error bars483.6 Superimposing vectors in a plot493. 7 Modifying axes503.7.1 Logarithmic axes513.7.2 Supplementary axes3.7.3 Incomplete axis boxes3.7. 4 Broken523.8 Adding text and math expressions543.8.1 Making math annotations with expression(553.9 Placing several plots in a figure563.10 Two-and three-dimensional plots3. 11 The plotrix package3.11.1 radial plot and polar plot603. 11.2 Triangle plot613.11.3 Error bars in plotrix3.12 Animation3. 13 Additional plotting packages4 Programming and functions654.1 Conditional execution if and ifelse654.2 Loops6642.1 for loo4.2.2 Looping with while and repeat684.3 User-defined functionso 2014 by Taylor Francis Group, LLCCONTENTS4.4 Debugging4.5 Built-in mathematical functions4.5.1 Bessel funct4.5.2 Beta and gamma functions744.5.3 Binomial coefficients4.6 Special functions of mathematical physics4.6gsl4.6.2 Special functions in other packages4.7 Polynomial functions in packages784.7.1 PolynomF package74.7. 2 orthopolynom pack834.8 Case studies864.8.1 Two-dimensional random wal4.8.2 Eigenvalues of a polymer chain875 Solving systems of algebraic equations915.1 Finding the zeros of a polynomial915.2 Finding the zeros of a function5.2.1 Bisection method5.2.2 Newton's method5.2. 3 uniroot and uniroot. all5.3 Systems of linear equations: matrix solve965.4 Matrix inverse975.5 Singular matrix975.6 Overdetermined systems and generalized inverse5. 7 Sparse matrices995.7.1 Tridiagonal matrix995.7.2 Banded matrix1015.7.3 Block matrix5.8 Matrix decomposition5.8. 1 QR decomposition1055.8.2 Singular value decomposition5.8.3 Eigendecomposition1075.8.4 Lu decomposition1075.8.5 Cholesky decomposition1085.8.6 Schur decomposition5.8. 7 backsolve and forwardsolve1095.9 Systems of nonlinear equations1095.9.1 multiroot in the root solve package10959.2gslv5.9.3 BBsolve) in the BB package1125.10 Case studies5.10.1 Spectroscopic analysis of a mixture1175.10.2 van der Waals equation1205.10.3 Chemical equilibriumc 2014 by Taylor &FtGroup LLCCONTENTS6 Numerical differentiation and integration1256.1 Numerical differentiation1256. 1. 1 Numerical differentiation using base R6. I Using the fundamental definition1256.1.1.2diff(1266. 1. 2 Numerical differentiation using the numDeriv package1276.1.2.1grad(6.1.2.2bian1286.1.2.3 hessian1296.1.3 Numerical differentiation using the pracma package1296.1.3deriv6. 1.3.2 numderivo and numdiffo1306.1.3.3gradO and gradient o1316.1.3. 4 jacobian()13l6.1.3.5 hessian136.1.3.6 laplacianO)6.2 Numerical integration1336.2.1 integrate: Basic integration in R1346.2.2 Integrating discretized functions1366.2. 3 Gaussian quadrature1376. 2.5 Functions with singularities acma6.2.4 More integration routines in pracma1401426.2.6 Infinite integration domains1446.2.7 Integrals in higher dimensions1466.2.8 Monte Carlo and sparse grid integration1486.2.9 Complex line integrals1506.3 Symbolic manipulations in R15263.1D06.3.2 derive1526.3.3 Polynomial functions1546.3.4 Interfaces to symbolic packages1556.4 Case studies1556.4.1 Circumference of an ellipse6.4.2 Integration of a lorentzian derivative spectrum1566.4.3 Volume of an ellipsoid1577 Optimization1597.1 One-dimensional oplimization1597. 2 Multi-dimensional optimization with opt im()1627.2.1 optim)with"Nelcdefault7.2.2 optim( with"BFGS "method1657.2.3 optith“CCethod7. 2. 4 optim() with"L-BFGS-B method to find a local minimum 1677.3 Other optimization packages7.31n1m()c 2014 by Taylor &FtGroup LLCCONTENTS7.3.2 ucminf package7.3.3 BB package1717.3.4imxo wrapper7.3.5 Derivative-free optimization algorithms1727.4 Optimization with constraints1737.4.1 constrOptim to optimize functions with linear constraints 1737.4.2 External packages alabama and Rsolnp1757. 5 Global optimization with many local minima1777.5.1 Simulated annealing1787.5.2 Genetic algorithms1817.5.2.1 DEopt im1817.5.2.2 rgenoud1837.5.2.3GA1837.6 Linear and quadratic programming7.6.1 Linear programming1837.6.2 Quadratic programming1867.7 Mixed-integer linear programming1897.7.1 Mixed-int e1897.7.2 Integer programming problems7. 7.2.1 Knapsack problems1917.7.2.2 Transportation problems1917.7.2.3 Assignment problems7.7. 2.4 Subsetsum problems1937.8 Case stud1947. 8.1 Monte Carlo simulation of the 2d ising model1948 Ordinary differential equations1998.1 Euler method2008.1. Projectile motion2018.1.2 Orbital motion2038.2 Improved Euler method2058.3 desolve pa2088.3.1 Isoda( and isode2108.3.2“ adams” and related methods2l18.3.3 Stiff syste2138.4 Matrix exponential solution for sets of linear ODEs2148.5 Events and roots2158.6 Difference equations2208.7 Delay differential equations2218.8 Differential algebraic equations2248.9 root Solve for steady state solutions of systems of odes2278.10 bvpSolve package for boundary value OdE problems2308.10.1 bvpshooto2308.10.2bwpO2318.10.3 bvpco1(232c 2014 by Taylor &FtGroup LLC