QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: PolterCuch, I can try comparing with Eigen -- regarding LU decompositions, it hasPartialPivLU (LU decomposition of a matrix with partial pivoting) and FullPivLU (LU decomposition of a matrix with complete pivoting) which offer different performance/accuracy/matrix-requirements trade-offs/characteristics (see below).As for Cholesky decompositions, those two are available:Standard Cholesky decomposition (LL^T)Robust Cholesky decomposition of a matrix with pivoting (LDL^T).http://eigen.tuxfamily.org/dox/Tutorial ... s.htmlThat
would be very good. I would look at my LU code again to fix size_t stuff and so on. I have not used pivoting (matices are positive definite) yet and I assume symmetric matrices for CGM.Having a sparse CGM solver is useful because I can use Rothe's method to discretise BS PDE to an elliptic PDE to solve at each time level. The matrix is typically O(1600X1600). Maybe we should use this triad for Thijs as well?Great! Yeah, we can try solving some kind of simple linear system, perhaps indeed something along the lines of your CGM example (will wait for your presentation of the cleaned up code, of course). As I've mentioned, I can look into porting into Eigen and benchmarking against its linear algebra decompositions' implementations. Just a simple benchmark, V1, solely dense algebra. Sparse matrices and/or PDEs are "interesting future research directions" / V2, no time to look at it right now. If the code-relevant-for-benchmarking doesn't fit on a single screen of a traditional 80x25 terminal, I'd say let's consider that a V3 and leave to future generations!