C++ for Scientists - Technische Universität Dresden

Good and Bad Scientific Software
Chapter 1
This chapter will give you an idea what we consider good scientific software and what not. If
you have never programmed before in your life you might wish to skip the entire chapter. This
is o.k. because if you had no contact with the program sources of bad software you can learn
programming with a pure mind.
If you have some software knowledge, there might be still some details you will not understand
right now but this is no reason to worry. If you do not understand it after reading this script
then you can start worrying, or we as authors could. This chapter is only about getting a feeling
what distinguishes good from bad software in science.
As foundation of our discussion — and to not start the book with hello world — we consider an
iterative method to solve system of linear equations Ax = b where A is a symmetric positivedefinite
(SPD) matrix, x and b are vectors, and x is searched. The method is called ‘Conjugate
Gradients’ (CG) and was introduced by Magnus R. Hestenes and Eduard Stiefel [?].
The mathematical details do not matter here but the different styles of implementation. The
algorithm can be written in the following form: 1
Algorithm 1: Conjugate Gradient Method Algorithm.
Input: SPD matrix A, vector b, and left preconditioner L, termination criterion ε.
Output: Vector x such Ax ≈ b.
1 r = b − Ax
2 while |r| ≥ ε do
z = L−1 3
r
4 ρ = 〈r, z〉
5 if First iteration then
6 p = z
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else
p = z + ρ
ρ ′ p
q = Ap
α = ρ/〈p, q〉
x = x + αp
r = r − αq
ρ ′ = ρ
1 This is not precisely the original notation but a slightly adapted version that introduces some extra variables
to avoid redundant calculations.
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