1 // Ceres Solver - A fast non-linear least squares minimizer
2 // Copyright 2010, 2011, 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
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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
27 // POSSIBILITY OF SUCH DAMAGE.
28 //
29 // Author: sameeragarwal@google.com (Sameer Agarwal)
30
31 #include "ceres/dense_qr_solver.h"
32
33
34 #include <cstddef>
35 #include "Eigen/Dense"
36 #include "ceres/dense_sparse_matrix.h"
37 #include "ceres/internal/eigen.h"
38 #include "ceres/internal/scoped_ptr.h"
39 #include "ceres/lapack.h"
40 #include "ceres/linear_solver.h"
41 #include "ceres/types.h"
42 #include "ceres/wall_time.h"
43
44 namespace ceres {
45 namespace internal {
46
DenseQRSolver(const LinearSolver::Options & options)47 DenseQRSolver::DenseQRSolver(const LinearSolver::Options& options)
48 : options_(options) {
49 work_.resize(1);
50 }
51
SolveImpl(DenseSparseMatrix * A,const double * b,const LinearSolver::PerSolveOptions & per_solve_options,double * x)52 LinearSolver::Summary DenseQRSolver::SolveImpl(
53 DenseSparseMatrix* A,
54 const double* b,
55 const LinearSolver::PerSolveOptions& per_solve_options,
56 double* x) {
57 if (options_.dense_linear_algebra_library_type == EIGEN) {
58 return SolveUsingEigen(A, b, per_solve_options, x);
59 } else {
60 return SolveUsingLAPACK(A, b, per_solve_options, x);
61 }
62 }
63
SolveUsingLAPACK(DenseSparseMatrix * A,const double * b,const LinearSolver::PerSolveOptions & per_solve_options,double * x)64 LinearSolver::Summary DenseQRSolver::SolveUsingLAPACK(
65 DenseSparseMatrix* A,
66 const double* b,
67 const LinearSolver::PerSolveOptions& per_solve_options,
68 double* x) {
69 EventLogger event_logger("DenseQRSolver::Solve");
70
71 const int num_rows = A->num_rows();
72 const int num_cols = A->num_cols();
73
74 if (per_solve_options.D != NULL) {
75 // Temporarily append a diagonal block to the A matrix, but undo
76 // it before returning the matrix to the user.
77 A->AppendDiagonal(per_solve_options.D);
78 }
79
80 // TODO(sameeragarwal): Since we are copying anyways, the diagonal
81 // can be appended to the matrix instead of doing it on A.
82 lhs_ = A->matrix();
83
84 if (per_solve_options.D != NULL) {
85 // Undo the modifications to the matrix A.
86 A->RemoveDiagonal();
87 }
88
89 // rhs = [b;0] to account for the additional rows in the lhs.
90 if (rhs_.rows() != lhs_.rows()) {
91 rhs_.resize(lhs_.rows());
92 }
93 rhs_.setZero();
94 rhs_.head(num_rows) = ConstVectorRef(b, num_rows);
95
96 if (work_.rows() == 1) {
97 const int work_size =
98 LAPACK::EstimateWorkSizeForQR(lhs_.rows(), lhs_.cols());
99 VLOG(3) << "Working memory for Dense QR factorization: "
100 << work_size * sizeof(double);
101 work_.resize(work_size);
102 }
103
104 LinearSolver::Summary summary;
105 summary.num_iterations = 1;
106 summary.termination_type = LAPACK::SolveInPlaceUsingQR(lhs_.rows(),
107 lhs_.cols(),
108 lhs_.data(),
109 work_.rows(),
110 work_.data(),
111 rhs_.data(),
112 &summary.message);
113 event_logger.AddEvent("Solve");
114 if (summary.termination_type == LINEAR_SOLVER_SUCCESS) {
115 VectorRef(x, num_cols) = rhs_.head(num_cols);
116 }
117
118 event_logger.AddEvent("TearDown");
119 return summary;
120 }
121
SolveUsingEigen(DenseSparseMatrix * A,const double * b,const LinearSolver::PerSolveOptions & per_solve_options,double * x)122 LinearSolver::Summary DenseQRSolver::SolveUsingEigen(
123 DenseSparseMatrix* A,
124 const double* b,
125 const LinearSolver::PerSolveOptions& per_solve_options,
126 double* x) {
127 EventLogger event_logger("DenseQRSolver::Solve");
128
129 const int num_rows = A->num_rows();
130 const int num_cols = A->num_cols();
131
132 if (per_solve_options.D != NULL) {
133 // Temporarily append a diagonal block to the A matrix, but undo
134 // it before returning the matrix to the user.
135 A->AppendDiagonal(per_solve_options.D);
136 }
137
138 // rhs = [b;0] to account for the additional rows in the lhs.
139 const int augmented_num_rows =
140 num_rows + ((per_solve_options.D != NULL) ? num_cols : 0);
141 if (rhs_.rows() != augmented_num_rows) {
142 rhs_.resize(augmented_num_rows);
143 rhs_.setZero();
144 }
145 rhs_.head(num_rows) = ConstVectorRef(b, num_rows);
146 event_logger.AddEvent("Setup");
147
148 // Solve the system.
149 VectorRef(x, num_cols) = A->matrix().householderQr().solve(rhs_);
150 event_logger.AddEvent("Solve");
151
152 if (per_solve_options.D != NULL) {
153 // Undo the modifications to the matrix A.
154 A->RemoveDiagonal();
155 }
156
157 // We always succeed, since the QR solver returns the best solution
158 // it can. It is the job of the caller to determine if the solution
159 // is good enough or not.
160 LinearSolver::Summary summary;
161 summary.num_iterations = 1;
162 summary.termination_type = LINEAR_SOLVER_SUCCESS;
163 summary.message = "Success.";
164
165 event_logger.AddEvent("TearDown");
166 return summary;
167 }
168
169 } // namespace internal
170 } // namespace ceres
171