1 // Ceres Solver - A fast non-linear least squares minimizer 2 // Copyright 2013 Google Inc. All rights reserved. 3 // http://code.google.com/p/ceres-solver/ 4 // 5 // Redistribution and use in source and binary forms, with or without 6 // modification, are permitted provided that the following conditions are met: 7 // 8 // * Redistributions of source code must retain the above copyright notice, 9 // this list of conditions and the following disclaimer. 10 // * Redistributions in binary form must reproduce the above copyright notice, 11 // this list of conditions and the following disclaimer in the documentation 12 // and/or other materials provided with the distribution. 13 // * Neither the name of Google Inc. nor the names of its contributors may be 14 // used to endorse or promote products derived from this software without 15 // specific prior written permission. 16 // 17 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 18 // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19 // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20 // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 21 // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 22 // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 26 // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 27 // POSSIBILITY OF SUCH DAMAGE. 28 // 29 // Author: sameeragarwal (at) google.com (Sameer Agarwal) 30 31 #ifndef CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_ 32 #define CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_ 33 34 #include <vector> 35 #include <utility> 36 #include "ceres/compressed_row_sparse_matrix.h" 37 38 namespace ceres { 39 namespace internal { 40 41 // Incomplete LQ factorization as described in 42 // 43 // Preconditioning techniques for indefinite and nonsymmetric linear 44 // systems. Yousef Saad, Preprint RIACS-ILQ-TR, RIACS, NASA Ames 45 // Research Center, Moffett Field, CA, 1987. 46 // 47 // An incomplete LQ factorization of a matrix A is a decomposition 48 // 49 // A = LQ + E 50 // 51 // Where L is a lower triangular matrix, and Q is a near orthonormal 52 // matrix. The extent of orthonormality depends on E. E is the "drop" 53 // matrix. Each row of L has a maximum of l_level_of_fill entries, and 54 // all non-zero entries are within l_drop_tolerance of the largest 55 // entry. Each row of Q has a maximum of q_level_of_fill entries and 56 // all non-zero entries are within q_drop_tolerance of the largest 57 // entry. 58 // 59 // E is the error of the incomplete factorization. 60 // 61 // The purpose of incomplete factorizations is preconditioning and 62 // there one only needs the L matrix, therefore this function just 63 // returns L. 64 // 65 // Caller owns the result. 66 CompressedRowSparseMatrix* IncompleteLQFactorization( 67 const CompressedRowSparseMatrix& matrix, 68 const int l_level_of_fill, 69 const double l_drop_tolerance, 70 const int q_level_of_fill, 71 const double q_drop_tolerance); 72 73 // In the row vector dense_row(0:num_cols), drop values smaller than 74 // the max_value * drop_tolerance. Of the remaining non-zero values, 75 // choose at most level_of_fill values and then add the resulting row 76 // vector to matrix. 77 // 78 // scratch is used to prevent allocations inside this function. It is 79 // assumed that scratch is of size matrix->num_cols(). 80 void DropEntriesAndAddRow(const Vector& dense_row, 81 const int num_entries, 82 const int level_of_fill, 83 const double drop_tolerance, 84 vector<pair<int, double> >* scratch, 85 CompressedRowSparseMatrix* matrix); 86 87 } // namespace internal 88 } // namespace ceres 89 90 #endif // CERES_INTERNAL_INCOMPLETE_LQ_FACTORIZATION_H_ 91
