// Ceres Solver - A fast non-linear least squares minimizer // Copyright 2012 Google Inc. All rights reserved. // http://code.google.com/p/ceres-solver/ // // Redistribution and use in source and binary forms, with or without // modification, are permitted provided that the following conditions are met: // // * Redistributions of source code must retain the above copyright notice, // this list of conditions and the following disclaimer. // * Redistributions in binary form must reproduce the above copyright notice, // this list of conditions and the following disclaimer in the documentation // and/or other materials provided with the distribution. // * Neither the name of Google Inc. nor the names of its contributors may be // used to endorse or promote products derived from this software without // specific prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE // POSSIBILITY OF SUCH DAMAGE. // // Author: sameeragarwal@google.com (Sameer Agarwal) // // Solve dense rectangular systems Ax = b by forming the normal // equations and solving them using the Cholesky factorization. #ifndef CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_ #define CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_ #include "ceres/linear_solver.h" #include "ceres/internal/macros.h" namespace ceres { namespace internal { class DenseSparseMatrix; // This class implements the LinearSolver interface for solving // rectangular/unsymmetric (well constrained) linear systems of the // form // // Ax = b // // Since there does not usually exist a solution that satisfies these // equations, the solver instead solves the linear least squares // problem // // min_x |Ax - b|^2 // // Setting the gradient of the above optimization problem to zero // gives us the normal equations // // A'Ax = A'b // // A'A is a positive definite matrix (hopefully), and the resulting // linear system can be solved using Cholesky factorization. // // If the PerSolveOptions struct has a non-null array D, then the // augmented/regularized linear system // // [ A ]x = [b] // [ diag(D) ] [0] // // is solved. // // This class uses the LDLT factorization routines from the Eigen // library. This solver always returns a solution, it is the user's // responsibility to judge if the solution is good enough for their // purposes. class DenseNormalCholeskySolver: public DenseSparseMatrixSolver { public: explicit DenseNormalCholeskySolver(const LinearSolver::Options& options); private: virtual LinearSolver::Summary SolveImpl( DenseSparseMatrix* A, const double* b, const LinearSolver::PerSolveOptions& per_solve_options, double* x); const LinearSolver::Options options_; CERES_DISALLOW_COPY_AND_ASSIGN(DenseNormalCholeskySolver); }; } // namespace internal } // namespace ceres #endif // CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_