An overview of the software package

The software developed can generate unrolled Fortran code which performs the sparse QR factorization and back-substitution in a ``hopefully close to optimal'' way, on some system of linear equations, given the structure of the system.

Clearly, if one has run an optimization of some system for days, and then decides to change something in the way the resulting Fortran code is generated, it would be rather inconvenient and somewhat redundant to have to re-run the entire optimization. Thus, the software package was split into several programs:

• One program for optimizing the system, the optimizer
• And one program for generating Fortran code from the more abstract description generated by the optimizer.

To give some assurance that the solver generated is correct, a regression test tool was developed. It's a very simple program that solves a large number of random systems (obeying the given structure), keeping track of the maximal relative error, eg. $\vert\vert Ax-b\vert\vert/\vert\vert b\vert\vert$. This tool should be run whenever a solver has been generated.