C++ for Scientists - Technische Universität Dresden

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4 CONTENTS 4.3 Generic classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.4 Concepts and Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.5 Inheritance or Generics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.6 Template Specialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.7 Non-Type Parameters for Templates . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.8 Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.9 STL — The Mother of All Generic Libraries . . . . . . . . . . . . . . . . . . . . . 121 4.10 Cursors and Property Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5 Meta-programming 133 5.1 Let the Compiler Compute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.2 Providing Type Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.3 Expression Templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 5.4 Meta-Tuning: Write Your Own Compiler Optimization . . . . . . . . . . . . . . . 156 5.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 6 Inheritance 187 6.1 Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 6.2 Dynamic Selection by Sub-typing . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 6.3 Remove Redundancy With Base Classes . . . . . . . . . . . . . . . . . . . . . . . 189 6.4 Casting Up and Down and Elsewhere . . . . . . . . . . . . . . . . . . . . . . . . . 189 6.5 Barton-Nackman Trick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 7 Effective Programming: The Polymorphic Way 199 7.1 Imperative Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 7.2 Generic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 7.3 Programming with Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 7.4 Functional Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 7.5 From Monomorphic to Polymorphic Behavior . . . . . . . . . . . . . . . . . . . . 212 7.6 Best of Both Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 II Using C++ 223 8 Finite World of Computers 225 8.1 Mathematical Objects inside the Computer . . . . . . . . . . . . . . . . . . . . . 225 8.2 More Numbers and Basic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 226 8.3 A Loop and More . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 8.4 The Other Way Around . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 9 How to Handle Physics on the Computer 233 9.1 Finite Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 9.2 Again, Integrators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 10 Programming tools 235 10.1 GCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10.2 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 10.3 Valgrind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 10.4 Gnuplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
CONTENTS 5 10.5 Unix and Linux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 11 C++ Libraries for Scientific Computing 243 11.1 GLAS: Generic Linear Algebra Software . . . . . . . . . . . . . . . . . . . . . . . 243 11.2 Boost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 11.3 Boost.Bindings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 11.4 Matrix Template Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 11.5 Blitz++ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 11.6 Graph Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 11.7 Geometric Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 12 Real-World Programming 253 12.1 Transcending Legacy Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 253 13 Parallelism 259 13.1 Multi-Threading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 13.2 Message Passing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 14 Numerical exercises 263 14.1 Computing an eigenfunction of the Poisson equation . . . . . . . . . . . . . . . . 263 14.2 The 2D Poisson equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 14.3 The solution of a system of differential equations . . . . . . . . . . . . . . . . . . 272 14.4 Google’s Page rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 14.5 The bisection method for finding the zero of a function in an interval . . . . . . . 276 14.6 The Newton-Raphson method for finding the minimum of a convex function . . . 278 14.7 Sequential noise reduction of real-time measurements by least squares . . . . . . 281 15 Programmierprojekte 285 15.1 Exponisation von Matrizen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 15.2 Exponisation von Matrizen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 15.3 LU-Zerlegung für m × n-Matrizen . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 15.4 Bunch-Kaufman Zerlegung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 15.5 Konditionszahl (reziprok) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 15.6 Matrix-Skalierung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 15.7 QR mit Überschreiben . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 15.8 Direkter Löser für schwach besetzte Matrizen . . . . . . . . . . . . . . . . . . . . 287 15.9 Anwendung MTL4 auf Typen der Intervallarithmetik . . . . . . . . . . . . . . . . 288 15.10Anwendung MTL4 auf Typen mit höherer Genauigkeit . . . . . . . . . . . . . . . 289 15.11Anwendung MTL4 auf AD-Typen . . . . . . . . . . . . . . . . . . . . . . . . . . 289 16 Acknowledgement 291
Page 1 and 2: Technische Universität Dresden Fak
Page 3: Contents I Understanding C++ 7 Intr
Page 7: Part I Understanding C ++ 7
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54 CHAPTER 2. C++ BASICS As a pract
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56 CHAPTER 2. C++ BASICS A function
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58 CHAPTER 2. C++ BASICS Now that t
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60 CHAPTER 2. C++ BASICS we need sm
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62 CHAPTER 2. C++ BASICS 2.12 Exerc
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64 CHAPTER 2. C++ BASICS 2.13 Opera
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66 CHAPTER 3. CLASSES apply symm bl
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68 CHAPTER 3. CLASSES int main() {
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70 CHAPTER 3. CLASSES class solver
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72 CHAPTER 3. CLASSES • Compilers
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74 CHAPTER 3. CLASSES a real number
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76 CHAPTER 3. CLASSES } return ∗t
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78 CHAPTER 3. CLASSES This mechanis
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80 CHAPTER 3. CLASSES One could not
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82 CHAPTER 3. CLASSES class matrix
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84 CHAPTER 3. CLASSES Approach 3: R
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86 CHAPTER 3. CLASSES of the decrem
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88 CHAPTER 3. CLASSES There are two
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90 CHAPTER 4. GENERIC PROGRAMMING }
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92 CHAPTER 4. GENERIC PROGRAMMING c
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94 CHAPTER 4. GENERIC PROGRAMMING A
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96 CHAPTER 4. GENERIC PROGRAMMING v
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100 CHAPTER 4. GENERIC PROGRAMMING
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150 CHAPTER 5. META-PROGRAMMING 5.3
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188 CHAPTER 6. INHERITANCE { } std:
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190 CHAPTER 6. INHERITANCE 6.4.1 Ca
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192 CHAPTER 6. INHERITANCE dbp= sta
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194 CHAPTER 6. INHERITANCE Our comp
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196 CHAPTER 6. INHERITANCE Another
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198 CHAPTER 6. INHERITANCE
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200 CHAPTER 7. EFFECTIVE PROGRAMMIN
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Finite World of Computers Chapter 8
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8.2. MORE NUMBERS AND BASIC STRUCTU
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8.2. MORE NUMBERS AND BASIC STRUCTU
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8.4. THE OTHER WAY AROUND 231 As ca
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How to Handle Physics on the Comput
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Programming tools Chapter 10 In thi
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10.2. DEBUGGING 237 T& glas::contin
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10.3. VALGRIND 239 Stepi and Nexti
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10.5. UNIX AND LINUX 241 • top: l
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C ++ Libraries for Scientific Compu
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11.3. BOOST.BINDINGS 245 • Math a
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11.3. BOOST.BINDINGS 247 #include
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11.4. MATRIX TEMPLATE LIBRARY 249 c
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11.7. GEOMETRIC LIBRARIES 251 11.7.
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Real-World Programming Chapter 12 1
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12.1. TRANSCENDING LEGACY APPLICATI
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Parallelism Chapter 13 13.1 Multi-T
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13.2. MESSAGE PASSING 261 int main
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15.6. MATRIX-SKALIERUNG 287 Siehe h
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15.10. ANWENDUNG MTL4 AUF TYPEN MIT
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Acknowledgement Chapter 16 Special
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Bibliography [AG04] David Abrahams
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