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
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26// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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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
40namespace ceres {
41namespace internal {
42
43class 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.
77class 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