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Evaluating
Derivatives
Evaluating
Derivatives
Principles and Techniques of
Algorithmic Differentiation
Second Edition
Andreas Griewank
Institut für Mathematik
Humboldt–Universität zu Berlin
Berlin, Germany
Andrea Walther
Institut für Wissenschaftliches Rechnen
Technische Universität Dresden
Dresden, Germany
Society for Industrial and Applied Mathematics • Philadelphia
Copyright © 2008 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.
Trademarked names may be used in this book without the inclusion of a trademark symbol.
These names are used in an editorial context only; no infringement of trademark is intended.
Maple is a registered trademark of Waterloo Maple, Inc.
Mathematica is a registered trademark of Wolfram Research, Inc.
MATLAB is a registered trademark of The MathWorks, Inc. For MATLAB product informa-
tion, please contact The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098 USA,
508-647-7000, Fax: 508-647-7101, info@mathworks.com, www.mathworks.com.
Library of Congress Cataloging-in-Publication Data
Griewank, Andreas.
Evaluating derivatives : principles and techniques of algorithmic differentiation. – 2nd ed. /
Andreas Griewank, Andrea Walther.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-898716-59-7 (alk. paper)
1. Differential calculus–Data processing. I. Walther, Andrea. II. Title.
QA304.G76 2008
515'.33--dc22
2008021064
is a registered trademark.
Contents
Rules ix
Preface xi
Prologue xv
Mathematical Symbols xix
1 Introduction 1
I Tangents and Gradients 13
2 A Framework for Evaluating Functions 15
2.1 TheLighthouseExample ...................... 16
2.2 Three-PartEvaluationProcedures ................. 18
2.3 Elemental Differentiability . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Generalizations and Connections . . . . . . . . . . . . . . . . . . 25
2.5 ExamplesandExercises ....................... 29
3 Fundamentals of Forward and Reverse 31
3.1 Forward Propagation of Tangents . . . . . . . . . . . . . . . . . . 32
3.2 Reverse Propagation of Gradients . . . . . . . . . . . . . . . . . . 37
3.3 Cheap Gradient Principle with Examples . . . . . . . . . . . . . 44
3.4 ApproximateErrorAnalysis..................... 50
3.5 SummaryandDiscussion ...................... 52
3.6 ExamplesandExercises ....................... 56
4 Memory Issues and Complexity Bounds 61
4.1 MemoryAllocationandOverwrites................. 61
4.2 RecordingPrevaluesontheTape.................. 64
4.3 SelectiveSavesandRestores..................... 70
4.4 ATemporalComplexityModel ................... 73
4.5 Complexity of Tangent Propagation . . . . . . . . . . . . . . . . 80
4.6 Complexity of Gradient Propagation . . . . . . . . . . . . . . . . 83
4.7 ExamplesandExercises ....................... 88
v
剩余459页未读,继续阅读
资源评论
- zengjing19872019-07-09原版书,体积小,清晰。
- junzeng06032018-08-02找了很久,非常好的资源,完整且清晰。
- chenxing2632020-08-24thanks for sharing
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