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Sameer Agarwal
b44cfdef25
Up till now ITERATIVE_SCHUR evaluates matrix-vector products between the Schur complement and a vector implicitly by exploiting the algebraic expression for the Schur complement. This cost of this evaluation scales with the number of non-zeros in the Jacobian. For small to medium sized problems there is a sweet spot where computing the Schur complement is cheap enough that it is much more efficient to explicitly compute it and use it for evaluating the matrix-vector products. This changes implements support for an explicit Schur complement in ITERATIVE_SCHUR in combination with the SCHUR_JACOBI preconditioner. API wise a new bool Solver::Options::use_explicit_schur_complement has been added. The implementation extends the SparseSchurComplementSolver to use Conjugate Gradients. Example speedup: use_explicit_schur_complement = false Time (in seconds): Preprocessor 0.585 Residual evaluation 0.319 Jacobian evaluation 1.590 Linear solver 25.685 Minimizer 27.990 Postprocessor 0.010 Total 28.585 use_explicit_schur_complement = true Time (in seconds): Preprocessor 0.638 Residual evaluation 0.318 Jacobian evaluation 1.507 Linear solver 5.930 Minimizer 8.144 Postprocessor 0.010 Total 8.791 Which indicates an end-to-end speedup of more than 3x, with the linear solver being sped up by > 4x. The idea to explore this optimization was inspired by the recent paper: Mining structure fragments for smart bundle adjustment L. Carlone, P. Alcantarilla, H. Chiu, K. Zsolt, F. Dellaert British Machine Vision Conference, 2014 which uses a more complicated algorithm to compute parts of the Schur complement to speed up the matrix-vector product. Change-Id: I95324af0ab351faa1600f5204039a1d2a64ae61d