| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2015 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
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| // modification, are permitted provided that the following conditions are met: |
| // |
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| // this list of conditions and the following disclaimer. |
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| // this list of conditions and the following disclaimer in the documentation |
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| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
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| // |
| // 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" |
| |
| 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: |
| LinearSolver::Summary SolveImpl( |
| DenseSparseMatrix* A, |
| const double* b, |
| const LinearSolver::PerSolveOptions& per_solve_options, |
| double* x) final; |
| |
| LinearSolver::Summary SolveUsingLAPACK( |
| DenseSparseMatrix* A, |
| const double* b, |
| const LinearSolver::PerSolveOptions& per_solve_options, |
| double* x); |
| |
| LinearSolver::Summary SolveUsingEigen( |
| DenseSparseMatrix* A, |
| const double* b, |
| const LinearSolver::PerSolveOptions& per_solve_options, |
| double* x); |
| |
| const LinearSolver::Options options_; |
| }; |
| |
| } // namespace internal |
| } // namespace ceres |
| |
| #endif // CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_ |