One of the things I wanted to do as a remedy to my simplex algorithm (refer to my last blog entry) was to switch to another algorithm for LU factorization which is used in my matrix inverse algorithm. The original LU factorization algorithm obviously was not robust enough to inverse an initial matrix generated in solving Markus’ model. This time, instead of blindly looking for a new algorithm to use all over the net, I decided to dive into Calc’s code to see what algorithm Calc uses internally for matrix inversion since Calc was able to inverse the very matrix my own algorithm was not.
Of course, I can’t just copy and paste Calc’s matrix inverse code, but luckily there was a reference within the code from which it was derived, and I just happened to have a copy of that very same reference which one of my friends was kind enough to lend to me a few weeks ago. Lucky me!
Anyway, now my solver can at least solves Markus’ model, though my solution differs from the Excel Solver’s solution that he included because of simplex’s positive variable limitation (his Excel solution included negative numbers). Adding support for negative numbers shouldn’t be too complex, but requires a bit more work.
The new snapshot (revision 101) is up which includes this new LU factorization algorithm.