Synopsis for C++ for Scientific Computing

Special topic for M.Sc. in Mathematical Modelling and Scientific Computing

Overview

Producing almost any numerical software requires writing codes that manipulate matrices and vectors, making Matlab a natural choice as an introductory programming language for scientific computing. However, the ease of programming in Matlab comes at a cost: the codes take a relatively long time to execute; and the software is commercial. While the use of procedural languages such as Fortran and C will overcome these limitations, they do not allow the straightforward coding of operations between matrices and vectors permitted by Matlab. An alternative approach is to use an object-oriented language such as C++ , where vectors and matrices can be represented as classes. Writing subroutines for these classes that have the same syntax as employed by Matlab allows code developed in Matlab to be translated with minimal effort into C++ code. Such an approach combines the ease of development in the Matlab environment without the associated drawbacks.

Synopsis

C++ programming fundamentals:

1. Variables and expressions;
2. Input and output;
3. Flow of control: if, switch, while, for;
4. Pointers and references;
5. Arrays;
6. Functions.

Object orientation in C++:

1. Concept of a class;
2. Private, public and protected class members;
3. Constructors;
4. Operator overloading;
5. Function overloading - templates;
6. Defining functions that may take default values;
7. Exceptions;
8. Derived classes using the example of sparse matrices from Matlab, where a matrix is represented by three vectors.

Assessment

A class of vectors and matrices should be written. Code, similar to Matlab code, should then be written using the classes described above to solve one of the following problems:

1. The implementation of a numerical technique such as an implicit solver for the heat equation in one dimension;
2. The replication of a Matlab function such as cgs, the conjugate gradient solver.

The code will be assessed based on the following criteria:

1. The clarity of the code and documentation;
2. Whether the code achieves its objectives.

Advanced concepts from C++ will not be expected.