| commit | cab853fd5fa17d37c55e6340a192da202dd10579 | [log] [tgz] |
|---|---|---|
| author | Sameer Agarwal <sameeragarwal@google.com> | Wed Jan 26 11:00:48 2022 -0800 |
| committer | Sameer Agarwal <sameeragarwal@google.com> | Mon Feb 07 11:54:01 2022 -0800 |
| tree | fdfed2355ac5cd51e0437aaf7fc6cda7ff086c16 | |
| parent | 8ae054ad91ae402af94f82e4d4ef24957188233b [diff] |
Add DenseQR Interface 1. Add EigenDenseQR & tests. This implementation now uses an in place decomposition, which means that we are not allocating, deallocating memory every call. 2. Add LAPACKDenseQR and tests. The LAPACK implementation instead of using dgels which is a routine which does the factorization and solve in one call, now uses dgeqrf for factorization and then dormqr and dtrtrs for solving. This allows us to have a factorize and solve interface like DenseCholesky. And opens the door to iterative refinement and mixed precision solves. 3. The refactor also allows us to simplify the interface to DenseSparseMatrix considerably. The internals of this class were complicated because we had the AppendDiagonal and RemoveDiagonal methods and we did not want to allocate deallocate memory every call. But since we pay the cost of the copy anyways, we can just hold that buffer in DenseQRSolver. 4. Delete lapack.cc/h 5. The net result is that everything seems to be a bit faster. For LAPACK we are not doing some of the scaling work that dgels was doing. For Eigen I think it maybe the inplace decomposition. Benchmark Time CPU Time Old Time New CPU Old CPU New ---------------------------------------------------------------------------------------------------------------------------------------------------------- BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/1/1 -0.1154 -0.1159 692 612 691 611 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/2/1 -0.1601 -0.1553 717 603 712 601 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/3/1 -0.1673 -0.1575 733 610 724 610 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/6/2 -0.1008 -0.1003 886 797 884 796 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/10/3 -0.1489 -0.1514 1283 1092 1281 1087 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/12/4 -0.1040 -0.1104 1556 1394 1553 1381 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/20/5 -0.0007 -0.0097 1911 1910 1908 1890 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/40/5 -0.1033 -0.1022 2981 2673 2957 2655 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/100/10 -0.0147 +0.0015 9275 9138 9026 9040 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/200/10 -0.1408 -0.1284 15093 12968 14778 12880 BM_DenseSolver<ceres::EIGEN, ceres::DENSE_QR>/200/20 -0.0310 -0.0355 38973 37765 38837 37460 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/1/1 -0.1228 -0.1256 736 646 731 640 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/2/1 -0.1401 -0.1396 740 636 735 633 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/3/1 -0.1731 -0.1695 744 615 738 613 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/6/2 -0.1399 -0.1408 1121 965 1113 956 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/10/3 -0.1110 -0.1145 1571 1397 1560 1382 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/12/4 -0.1411 -0.1417 2006 1722 1993 1710 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/20/5 -0.1740 -0.1729 2741 2264 2724 2253 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/40/5 -0.0966 -0.1123 3462 3128 3425 3040 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/100/10 -0.0387 -0.0998 10365 9964 10339 9307 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/200/10 -0.2044 -0.2049 16031 12754 15998 12720 BM_DenseSolver<ceres::LAPACK, ceres::DENSE_QR>/200/20 -0.2391 -0.2386 35777 27223 35716 27193 Change-Id: I782f0d7664efe1435eebda92ddf47a0fe66c9c72
Ceres Solver is an open source C++ library for modeling and solving large, complicated optimization problems. It is a feature rich, mature and performant library which has been used in production at Google since 2010. Ceres Solver can solve two kinds of problems.
Please see ceres-solver.org for more information.