C++ for Scientists - Technische Universität Dresden

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