C++ for Scientists - Technische Universität Dresden

Classes
Chapter 3
“Computer science is no more about computers than astronomy is about telescopes.”
— Edsger W. Dijkstra.
“Accordingly, computer science is more than programming language details.”
Good programming is more then drilling on small language details and more then cleverly
manipulating specific bits on the latest and greatest computer hardware. Focusing primarily
on technical details can lead to clever codes that perform a certain task in a certain context
extremely efficiently. If one is good at this one might even create the fastest solution for this
task and gain the admiration of the geeks.
3.1 Program for universal meaning not for technical details
Writing leading-edge scientific software with such an attitude is very painful and likely to fail.
The most important tasks in scientific programming are:
• Identifying the mathematical abstractions that are important in the domain; and
• Representing this abstractions comprehensively and efficiently in software.
Common abstractions that appear in almost every scientific application are vector spaces and
linear operators. A linear operator projects from one vector space to another one.
First we should decide how to represent this abstraction in a program. Be v an element of a
vector space and L a linear operator. Then C ++ allows us to represent the application of L on
v as
or
L(v)
L ∗ v
Which one is better suited is not so easy to say. What is easy to say is that both are better
then
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