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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@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