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@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 38namespace ceres { 39namespace 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. 66CompressedRowSparseMatrix* 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(). 80void 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