MATLAB Guide

486 Pages·32.049 MB·English

by  Desmond J. Higham, Nicholas J. Higham

OT150_Higham-Higham_FM.indd 1 11/1/2016 10:43:36 AM
T E
hird diTion
d J. h
Esmond igham
University of Strathclyde
Glasgow, Scotland

n J. h
icholas igham
University of Manchester
Manchester, England
Society for Industrial and Applied Mathematics
Philadelphia
OT150_Higham-Higham_FM.indd 3 11/1/2016 10:43:37 AM
Copyright © 2017 by the Society for Industrial and Applied Mathematics
10 9 8 7 6 5 4 3 2 1
All rights reserved. Printed in the United States of America. No part of this book may be reproduced,
stored, or transmitted in any manner without the written permission of the publisher. For information,
write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia,
PA 19104-2688 USA.
MATLAB is a registered trademark of The MathWorks, Inc. For MATLAB product information,
please contact The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098 USA, 508-647-7000,
Fax: [phone], [email protected], www.mathworks.com.
No warranties, express or implied, are made by the publisher, authors, and their employers that the
programs contained in this volume are free of error. They should not be relied on as the sole basis to
solve a problem whose incorrect solution could result in injury to person or property. If the programs
are employed in such a manner, it is at the user’s own risk and the publisher, authors, and their
employers disclaim all liability for such misuse.
Publisher David Marshall
Acquisitions Editor Elizabeth Greenspan
Developmental Editor Gina Rinelli Harris
Managing Editor Kelly Thomas
Production Editor David Riegelhaupt
Copy Editor Sam Clark, T&T Productions Ltd, London
Production Manager Donna Witzleben
Production Coordinator Cally Shrader
Graphic Designer Lois Sellers
Library of Congress Cataloging-in-Publication Data
Names: Higham, Desmond J., 1964- | Higham, Nicholas J., 1961-
Title: MATLAB guide / Desmond J. Higham, University of Strathclyde, Glasgow,
Scotland, United Kingdom, Nicholas J. Higham, University of Manchester,
Manchester, United Kingdom.
Description: Third edition. | Philadelphia : Society for Industrial and
Applied Mathematics, [2016] | Series: Other titles in applied mathematics
; 150 | Includes bibliographical references and index.
Identifiers: LCCN 2016039121 (print) | LCCN 2016039323 (ebook) | ISBN
9781611974652 (print) | ISBN 9781611974669 (e-book)
Subjects: LCSH: MATLAB. | Numerical analysis--Data processing.
Classification: LCC QA297 .H5217 2016 (print) | LCC QA297 (ebook) | DDC
518.0285/53--dc23
LC record available at https://lccn.loc.gov/2016039121

is a registered trademark.
OT150_Higham-Higham_FM.indd 4 11/1/2016 10:43:37 AM
In memory of our mother and father, Doris and Ken.
Contents
List of Figures xiii
List of Tables xvii
List of Program Files xix
Preface xxi
1 A Brief Tutorial 1
2 Basics 23
2.1 MATLAB Desktop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Interaction and Script Files. . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 More Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Variables and the Workspace . . . . . . . . . . . . . . . . . . . . . . . 30
3 Distinctive Features of MATLAB 35
3.1 Automatic Storage Allocation . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Variable Arguments Lists . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Complex Arrays and Arithmetic . . . . . . . . . . . . . . . . . . . . . 37
4 Arithmetic 39
4.1 IEEE Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Precedence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Mathematical Functions . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Other Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5 Matrices 47
5.1 Matrix Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Subscripting and the Colon Notation . . . . . . . . . . . . . . . . . . 54
5.3 Matrix and Array Operations . . . . . . . . . . . . . . . . . . . . . . 57
5.3.1 Implicit Expansion . . . . . . . . . . . . . . . . . . . . . . . . 61
5.4 Empty Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.5 Matrix Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.6 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6 Operators and Flow Control 71
6.1 Relational and Logical Operators . . . . . . . . . . . . . . . . . . . . 71
6.2 Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
vii
viii Contents
7 Program Files 83
7.1 Scripts and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.2 Naming and Editing Program Files . . . . . . . . . . . . . . . . . . . 90
7.3 Working with Program Files and the MATLAB Path . . . . . . . . . 91
7.4 Startup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.5 Command/Function Duality . . . . . . . . . . . . . . . . . . . . . . . 93
8 Graphics 97
8.1 Two-Dimensional Graphics . . . . . . . . . . . . . . . . . . . . . . . . 97
8.1.1 Basic Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
8.1.2 Axes and Annotation . . . . . . . . . . . . . . . . . . . . . . . 102
8.1.3 Multiple Plots in a Figure . . . . . . . . . . . . . . . . . . . . 109
8.2 Three-Dimensional Graphics . . . . . . . . . . . . . . . . . . . . . . . 113
8.3 Specialized Graphs for Displaying Data . . . . . . . . . . . . . . . . . 125
8.4 Saving and Printing Figures . . . . . . . . . . . . . . . . . . . . . . . 129
8.5 On Things Not Treated . . . . . . . . . . . . . . . . . . . . . . . . . . 131
9 Linear Algebra 135
9.1 Matrix Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.2 Norms and Condition Numbers . . . . . . . . . . . . . . . . . . . . . 136
9.3 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
9.3.1 Square System . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
9.3.2 Overdetermined System . . . . . . . . . . . . . . . . . . . . . 140
9.3.3 Underdetermined System . . . . . . . . . . . . . . . . . . . . . 141
9.4 Inverse, Pseudoinverse, and Determinant . . . . . . . . . . . . . . . . 142
9.5 LU, LDL∗, and Cholesky Factorizations . . . . . . . . . . . . . . . . . 143
9.6 QR Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
9.7 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . 146
9.8 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
9.8.1 Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
9.8.2 More about Eigenvalue Computations. . . . . . . . . . . . . . 150
9.8.3 Generalized Eigenvalues . . . . . . . . . . . . . . . . . . . . . 151
9.9 Iterative Linear Equation and Eigenproblem Solvers . . . . . . . . . . 153
9.10 Functions of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
10 More on Functions 159
10.1 Function Handles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
10.2 Anonymous Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . 160
10.3 Local Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10.4 Default Input Arguments . . . . . . . . . . . . . . . . . . . . . . . . . 163
10.5 Variable Numbers of Arguments . . . . . . . . . . . . . . . . . . . . . 165
10.6 Argument Checking and Parsing . . . . . . . . . . . . . . . . . . . . . 167
10.7 Nested Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
10.8 Private Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
10.9 Recursive Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
10.10 Global and Persistent Variables . . . . . . . . . . . . . . . . . . . . . 173
10.11 Exemplary Functions in MATLAB . . . . . . . . . . . . . . . . . . . 174
Contents ix
11 Numerical Methods: Part I 175
11.1 Polynomials and Data Fitting . . . . . . . . . . . . . . . . . . . . . . 175
11.2 Nonlinear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
11.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
11.4 The Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . 185
12 Numerical Methods: Part II 189
12.1 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
12.2 Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . 193
12.2.1 Examples with Ode45 . . . . . . . . . . . . . . . . . . . . . . . 193
12.2.2 Case Study: Pursuit Problem with Event Location . . . . . . 201
12.2.3 StiffProblems,Differential-AlgebraicEquations,andtheChoice
of Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
12.3 Boundary-Value Problems . . . . . . . . . . . . . . . . . . . . . . . . 213
12.4 Delay-Differential Equations . . . . . . . . . . . . . . . . . . . . . . . 221
12.5 Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . 225
13 Input and Output 233
13.1 User Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
13.2 Output to the Screen . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
13.3 File Input and Output . . . . . . . . . . . . . . . . . . . . . . . . . . 236
13.4 Fine Tuning the Display of Arrays . . . . . . . . . . . . . . . . . . . . 238
14 Troubleshooting 241
14.1 Errors and Assertions . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
14.2 Warnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
14.3 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
14.4 Pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
15 Sparse Matrices 249
15.1 Sparse Matrix Generation . . . . . . . . . . . . . . . . . . . . . . . . 249
15.2 Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
16 More on Coding 257
16.1 Elements of Coding Style . . . . . . . . . . . . . . . . . . . . . . . . . 257
16.2 Cleaning Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
16.3 Checking and Comparing Code Files . . . . . . . . . . . . . . . . . . 259
16.4 Profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
16.5 P-Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
16.6 Source Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
16.7 Live Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
16.8 Creating a Toolbox . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
16.9 Distributing Code Files . . . . . . . . . . . . . . . . . . . . . . . . . . 268
16.10 Unit Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
17 Advanced Graphics 273
17.1 Objects, Handles, and Properties . . . . . . . . . . . . . . . . . . . . 273
17.2 Root and Default Properties . . . . . . . . . . . . . . . . . . . . . . . 278
17.3 Animation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
17.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
x Contents
18 Other Data Types and Multidimensional Arrays 291
18.1 Character Vectors and Arrays . . . . . . . . . . . . . . . . . . . . . . 292
18.2 String Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
18.3 Multidimensional Arrays . . . . . . . . . . . . . . . . . . . . . . . . . 297
18.4 Categorical Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
18.5 Datetime and Duration Arrays . . . . . . . . . . . . . . . . . . . . . . 300
18.6 Tables and Timetables . . . . . . . . . . . . . . . . . . . . . . . . . . 304
18.7 Structures and Cell Arrays . . . . . . . . . . . . . . . . . . . . . . . . 308
19 Object-Oriented Programming 315
19.1 Max-Plus Algebra Class . . . . . . . . . . . . . . . . . . . . . . . . . 315
19.2 Circulant Matrix Class . . . . . . . . . . . . . . . . . . . . . . . . . . 321
19.3 On Things Not Treated . . . . . . . . . . . . . . . . . . . . . . . . . . 324
20 The Symbolic Math Toolbox 325
20.1 Creating Symbolic Variables and Expressions. . . . . . . . . . . . . . 325
20.2 Equation Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
20.3 Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
20.3.1 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
20.3.2 Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
20.3.3 Solving Differentiation Equations . . . . . . . . . . . . . . . . 335
20.3.4 Taylor Expansions. . . . . . . . . . . . . . . . . . . . . . . . . 336
20.4 Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
20.5 Polynomials and Rationals . . . . . . . . . . . . . . . . . . . . . . . . 339
20.6 Variable-Precision Arithmetic . . . . . . . . . . . . . . . . . . . . . . 343
20.7 Other Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
21 Graphs 349
21.1 Undirected Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
21.2 Directed Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
22 Large Data Sets 361
22.1 Datastores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
22.2 MapReduce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
22.3 Tall Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
23 Optimizing Codes 369
23.1 Timing Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
23.2 Vectorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
23.3 Accessing Matrices by Column . . . . . . . . . . . . . . . . . . . . . . 372
23.4 Preallocating Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
23.5 Miscellaneous Optimizations . . . . . . . . . . . . . . . . . . . . . . . 374
23.6 Illustration: Bifurcation Diagram . . . . . . . . . . . . . . . . . . . . 375
23.7 External Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
24 Tricks and Tips 379
24.1 Empty Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
24.2 Exploiting Infinities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
24.3 Permutations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
24.4 Rank-1 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
Contents xi
24.5 Set Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
24.6 Subscripting Matrices as Vectors . . . . . . . . . . . . . . . . . . . . . 384
24.7 Avoiding If Statements . . . . . . . . . . . . . . . . . . . . . . . . . . 385
25 The Parallel Computing Toolbox 387
25.1 The Parfor Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
25.2 Asynchronous Computing with Parfeval . . . . . . . . . . . . . . . . . 392
25.3 Batch Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
25.4 Single Program, Multiple Data . . . . . . . . . . . . . . . . . . . . . . 395
25.5 Distributed and Codistributed Arrays . . . . . . . . . . . . . . . . . . 397
25.6 GPU Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
25.7 On Things Not Treated . . . . . . . . . . . . . . . . . . . . . . . . . . 401
26 Case Studies 403
26.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
26.2 Brachistochrone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
26.3 Small-World Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 404
26.4 Performance Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
26.5 Multidimensional Calculus . . . . . . . . . . . . . . . . . . . . . . . . 416
26.6 L-Systems and Turtle Graphics . . . . . . . . . . . . . . . . . . . . . 420
26.7 Black–Scholes Delta Surface . . . . . . . . . . . . . . . . . . . . . . . 422
26.8 Chutes and Ladders . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
26.9 Pythagorean Sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
26.10 Fisher’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
A The Top 111 MATLAB Functions 439
Glossary 445
Bibliography 447
Index 459