Immediately after PLU factorization, the average solve time will be rather high because PLU factorization is slow. For some number of factor updates, the average solve time is expected to decrease because the updates and solves are fast. However, updates increase the compexity of the factorization, so solve times are expected to increase with each update. When the average solve time stops decreasing and begins increasing, we perform PLU factorization from scratch rather than updating. PLU factorization is also performed after the maximum permitted number of updates is reached to prevent further accumulation of roundoff error.
This decorator records the time spent in the major BGLU routines - refactor, update, and solve - in order to calculate the average time required to solve a system. It also forces PLU factorization of the basis matrix from scratch to minimize the average solve time and to accumulation of roundoff error.
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