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/
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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
44namespace ceres {
45namespace internal {
46
47DenseQRSolver::DenseQRSolver(const LinearSolver::Options& options)
48    : options_(options) {
49  work_.resize(1);
50}
51
52LinearSolver::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
64LinearSolver::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
122LinearSolver::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