Scientific and Engineering C++: Two Faces of Polymorphism

In this column we compare two forms of polymorphism side-by-side for a problem that either form can tackle. The template form uses common names in similar classes; the virtual function form uses common function prototypes in base classes. The problem requires neither accessing elements of collections through base class pointers-a forte of virtual functions-nor does it have many small objects that need efficient random access-a forte of templates. The choice between virtual function and template polymorphism being non-obvious, it is instructive to compare these two forms of polymorphism on the one problem. The problem is to generalize the LAPACK wrapper classes we've discussed in our last two columns [1,2]. From a software design point of view, our wrapper classes are usability coating on a high performance core provided by LAPACK's FORTRAN code. We won't discuss the core here; we want to focus on the software, not the math. Overall the problem we tacle has two input objects, a matrix of equation coefficients A and a matrix of equation results b. THe output is a matrix of solution values, x, where Ax = b. The method of solution is to factor A into matrices that are easily inverted, e.g., A = LU, then to solve the factored equations, e.g., x = U-(1)L-(1)b.