C++ for Scientists - Technische Universität Dresden

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16 CHAPTER 1. GOOD AND BAD SCIENTIFIC SOFTWARE than C ++. Yes, C ++ can look like this if one puts enough effort in good software. Evidently, it is also much easier to write algorithms at this abstraction level than expressing it with low-level operations. The Purpose of Scienfic Software Scientists shall do science. Excellent scientific software is expressed only in mathematical and domainspecific operations without any technical detail exposed. At this abstraction level, scientists can focus on models and algorithms, being much more productive and progress scientific discovery. Nobody knows how many scientists wasting how much time every year dwelling on small technical details of bad software like in Listing 1.1. Of course, the technical details have to be realized in some place but not in a scientific application. This is the worst possible location. Use a two-level approach: write your applications in terms of expressive mathematical operations and if they do not exist, implement them separately. These mathematical operations must be carefully implemented for maximal performance or use other operations with maximal performance. Investing time in the performance of these fundamental operations is highly rentable because the functions will be reused very often. Advise Use the right abstractions! If they do not exist, implement them. Speaking of abstractions, the CG implementation in Listing 1.2 does not commit to any technical detail. In no place, the function is restricted to a numerical type like double. It works as well for float, GNU’s multiprecision, complex, interval arithmetic, quaternions, . . . The matrix A can have any internal format, as long as it can be multiplied with a vector it can be used in the function. In fact, it does not even need to be matrix but can be any linear operator. For instance, an object that performs a Fast Fourier Transformation (FFT) on a vector can be used as A when the FFT is expressed by a product of A with the vector. Similarly, the vectors do not need to be represented by finite-dimensional arrays but can be elements of any vector space that is somehow computer-representable as long as all operations in the algorithm can be performed. We are also open to other computer architectures. If the matrix and the vectors are distributed over the nodes of a parallel supercomputer and according parallel operations are available, the functions runs in parallel without changing any single line. (GP)GPU acceleration can be also realized within the data structures and their operations without changing the algorithm. In
general, any existing or new platform that is supported in the operations of the matrix and vector types is also supported by our ‘Generic’ conjugate gradient function. As mentioned before, we do not even need to change it. If we have a sophisticated scientific application of several thousand lines (not 100,000s) written with appropriate abstractions, we need to modify it either. Starting with the next chapter, we will explain you how to write good scientific software. 17
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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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100 CHAPTER 4. GENERIC PROGRAMMING
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150 CHAPTER 5. META-PROGRAMMING 5.3
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162 CHAPTER 5. META-PROGRAMMING num
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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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Numerical exercises Chapter 14 In t
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14.1. COMPUTING AN EIGENFUNCTION OF
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14.4. GOOGLE’S PAGE RANK 275 Taki
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Programmierprojekte Kapitel 15 Die
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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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