1 // Ceres Solver - A fast non-linear least squares minimizer 2 // Copyright 2012 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 // Solve dense rectangular systems Ax = b by forming the normal 32 // equations and solving them using the Cholesky factorization. 33 34 #ifndef CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_ 35 #define CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_ 36 37 #include "ceres/linear_solver.h" 38 #include "ceres/internal/macros.h" 39 40 namespace ceres { 41 namespace internal { 42 43 class DenseSparseMatrix; 44 45 // This class implements the LinearSolver interface for solving 46 // rectangular/unsymmetric (well constrained) linear systems of the 47 // form 48 // 49 // Ax = b 50 // 51 // Since there does not usually exist a solution that satisfies these 52 // equations, the solver instead solves the linear least squares 53 // problem 54 // 55 // min_x |Ax - b|^2 56 // 57 // Setting the gradient of the above optimization problem to zero 58 // gives us the normal equations 59 // 60 // A'Ax = A'b 61 // 62 // A'A is a positive definite matrix (hopefully), and the resulting 63 // linear system can be solved using Cholesky factorization. 64 // 65 // If the PerSolveOptions struct has a non-null array D, then the 66 // augmented/regularized linear system 67 // 68 // [ A ]x = [b] 69 // [ diag(D) ] [0] 70 // 71 // is solved. 72 // 73 // This class uses the LDLT factorization routines from the Eigen 74 // library. This solver always returns a solution, it is the user's 75 // responsibility to judge if the solution is good enough for their 76 // purposes. 77 class DenseNormalCholeskySolver: public DenseSparseMatrixSolver { 78 public: 79 explicit DenseNormalCholeskySolver(const LinearSolver::Options& options); 80 81 private: 82 virtual LinearSolver::Summary SolveImpl( 83 DenseSparseMatrix* A, 84 const double* b, 85 const LinearSolver::PerSolveOptions& per_solve_options, 86 double* x); 87 88 LinearSolver::Summary SolveUsingLAPACK( 89 DenseSparseMatrix* A, 90 const double* b, 91 const LinearSolver::PerSolveOptions& per_solve_options, 92 double* x); 93 94 LinearSolver::Summary SolveUsingEigen( 95 DenseSparseMatrix* A, 96 const double* b, 97 const LinearSolver::PerSolveOptions& per_solve_options, 98 double* x); 99 100 const LinearSolver::Options options_; 101 CERES_DISALLOW_COPY_AND_ASSIGN(DenseNormalCholeskySolver); 102 }; 103 104 } // namespace internal 105 } // namespace ceres 106 107 #endif // CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_ 108
