Specifying the system structure

The optimqr program only needs one input file. A file that describes the dimensions and the structure of the system for which we wish to generate a solver.

Although it is possible to specify different numbers of equations and unknowns, the OPTIMQR package only supports square systems.

The system need not have a non-zero diagonal in the specification, but it must be possible to re-order it in a way that it gets one.

A sample input file describing a 15 x 15 system could look like:

15 15
x 0 x 0 x x x 0 0 0 0 0 0 0 0
x x x 0 0 x 0 0 0 x 0 0 0 0 0
0 0 x x 0 0 0 0 0 0 0 x 0 x x
0 0 0 x 0 0 0 0 0 0 0 0 0 0 0
x 0 0 x 0 x 0 0 0 0 0 0 x 0 0
0 0 x 0 0 0 x 0 0 0 0 x 0 0 0
x x 0 0 0 0 0 x 0 0 x 0 0 0 0
0 x 0 0 0 0 0 0 x 0 0 0 0 0 0
0 0 x 0 0 0 0 0 0 0 0 0 0 x 0
0 0 0 x 0 0 0 0 x 0 0 x 0 0 0
0 0 0 0 x 0 0 0 0 0 x 0 0 0 0
0 0 0 0 x 0 0 0 0 0 0 x 0 0 0
0 0 0 0 0 x 0 0 0 0 0 0 x 0 0
0 0 0 0 0 0 x 0 0 0 0 0 0 x 0
0 0 0 x 0 0 0 0 0 x 0 0 0 0 x

The x's specify non-zeros, and the 0's specify the zeros.

In the rest of this document, we assume the above data can be found in a file named system.size15. The file is found in the OPTIMQR distribution.