1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
|
// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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 <memory>
#include "ceres/dense_cholesky.h"
#include "ceres/internal/disable_warnings.h"
#include "ceres/internal/export.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 CERES_NO_EXPORT DenseNormalCholeskySolver
: public DenseSparseMatrixSolver {
public:
explicit DenseNormalCholeskySolver(LinearSolver::Options options);
private:
LinearSolver::Summary SolveImpl(
DenseSparseMatrix* A,
const double* b,
const LinearSolver::PerSolveOptions& per_solve_options,
double* x) final;
const LinearSolver::Options options_;
std::unique_ptr<DenseCholesky> cholesky_;
};
} // namespace internal
} // namespace ceres
#include "ceres/internal/reenable_warnings.h"
#endif // CERES_INTERNAL_DENSE_NORMAL_CHOLESKY_SOLVER_H_
|
