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//
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16//
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28//
29// Author: sameeragarwal@google.com (Sameer Agarwal)
30
31#include "ceres/dense_normal_cholesky_solver.h"
32
33#include <cstddef>
34
35#include "Eigen/Dense"
36#include "ceres/blas.h"
37#include "ceres/dense_sparse_matrix.h"
38#include "ceres/internal/eigen.h"
39#include "ceres/internal/scoped_ptr.h"
40#include "ceres/lapack.h"
41#include "ceres/linear_solver.h"
42#include "ceres/types.h"
43#include "ceres/wall_time.h"
44
45namespace ceres {
46namespace internal {
47
48DenseNormalCholeskySolver::DenseNormalCholeskySolver(
49    const LinearSolver::Options& options)
50    : options_(options) {}
51
52LinearSolver::Summary DenseNormalCholeskySolver::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 DenseNormalCholeskySolver::SolveUsingEigen(
65    DenseSparseMatrix* A,
66    const double* b,
67    const LinearSolver::PerSolveOptions& per_solve_options,
68    double* x) {
69  EventLogger event_logger("DenseNormalCholeskySolver::Solve");
70
71  const int num_rows = A->num_rows();
72  const int num_cols = A->num_cols();
73
74  ConstColMajorMatrixRef Aref = A->matrix();
75  Matrix lhs(num_cols, num_cols);
76  lhs.setZero();
77
78  event_logger.AddEvent("Setup");
79
80  //   lhs += A'A
81  //
82  // Using rankUpdate instead of GEMM, exposes the fact that its the
83  // same matrix being multiplied with itself and that the product is
84  // symmetric.
85  lhs.selfadjointView<Eigen::Upper>().rankUpdate(Aref.transpose());
86
87  //   rhs = A'b
88  Vector rhs = Aref.transpose() * ConstVectorRef(b, num_rows);
89
90  if (per_solve_options.D != NULL) {
91    ConstVectorRef D(per_solve_options.D, num_cols);
92    lhs += D.array().square().matrix().asDiagonal();
93  }
94  event_logger.AddEvent("Product");
95
96  LinearSolver::Summary summary;
97  summary.num_iterations = 1;
98  summary.termination_type = LINEAR_SOLVER_SUCCESS;
99  Eigen::LLT<Matrix, Eigen::Upper> llt =
100      lhs.selfadjointView<Eigen::Upper>().llt();
101
102  if (llt.info() != Eigen::Success) {
103    summary.termination_type = LINEAR_SOLVER_FAILURE;
104    summary.message = "Eigen LLT decomposition failed.";
105  } else {
106    summary.termination_type = LINEAR_SOLVER_SUCCESS;
107    summary.message = "Success.";
108  }
109
110  VectorRef(x, num_cols) = llt.solve(rhs);
111  event_logger.AddEvent("Solve");
112  return summary;
113}
114
115LinearSolver::Summary DenseNormalCholeskySolver::SolveUsingLAPACK(
116    DenseSparseMatrix* A,
117    const double* b,
118    const LinearSolver::PerSolveOptions& per_solve_options,
119    double* x) {
120  EventLogger event_logger("DenseNormalCholeskySolver::Solve");
121
122  if (per_solve_options.D != NULL) {
123    // Temporarily append a diagonal block to the A matrix, but undo
124    // it before returning the matrix to the user.
125    A->AppendDiagonal(per_solve_options.D);
126  }
127
128  const int num_cols = A->num_cols();
129  Matrix lhs(num_cols, num_cols);
130  event_logger.AddEvent("Setup");
131
132  // lhs = A'A
133  //
134  // Note: This is a bit delicate, it assumes that the stride on this
135  // matrix is the same as the number of rows.
136  BLAS::SymmetricRankKUpdate(A->num_rows(),
137                             num_cols,
138                             A->values(),
139                             true,
140                             1.0,
141                             0.0,
142                             lhs.data());
143
144  if (per_solve_options.D != NULL) {
145    // Undo the modifications to the matrix A.
146    A->RemoveDiagonal();
147  }
148
149  // TODO(sameeragarwal): Replace this with a gemv call for true blasness.
150  //   rhs = A'b
151  VectorRef(x, num_cols) =
152      A->matrix().transpose() * ConstVectorRef(b, A->num_rows());
153  event_logger.AddEvent("Product");
154
155  LinearSolver::Summary summary;
156  summary.num_iterations = 1;
157  summary.termination_type =
158      LAPACK::SolveInPlaceUsingCholesky(num_cols,
159                                        lhs.data(),
160                                        x,
161                                        &summary.message);
162  event_logger.AddEvent("Solve");
163  return summary;
164}
165}   // namespace internal
166}   // namespace ceres
167