1 // Ceres Solver - A fast non-linear least squares minimizer
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3 // http://code.google.com/p/ceres-solver/
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29 // Author: sameeragarwal@google.com (Sameer Agarwal)
30 
31 #include "ceres/iterative_schur_complement_solver.h"
32 
33 #include <algorithm>
34 #include <cstring>
35 #include <vector>
36 
37 #include "Eigen/Dense"
38 #include "ceres/block_sparse_matrix.h"
39 #include "ceres/block_structure.h"
40 #include "ceres/conjugate_gradients_solver.h"
41 #include "ceres/detect_structure.h"
42 #include "ceres/implicit_schur_complement.h"
43 #include "ceres/internal/eigen.h"
44 #include "ceres/internal/scoped_ptr.h"
45 #include "ceres/linear_solver.h"
46 #include "ceres/preconditioner.h"
47 #include "ceres/schur_jacobi_preconditioner.h"
48 #include "ceres/triplet_sparse_matrix.h"
49 #include "ceres/types.h"
50 #include "ceres/visibility_based_preconditioner.h"
51 #include "ceres/wall_time.h"
52 #include "glog/logging.h"
53 
54 namespace ceres {
55 namespace internal {
56 
IterativeSchurComplementSolver(const LinearSolver::Options & options)57 IterativeSchurComplementSolver::IterativeSchurComplementSolver(
58     const LinearSolver::Options& options)
59     : options_(options) {
60 }
61 
~IterativeSchurComplementSolver()62 IterativeSchurComplementSolver::~IterativeSchurComplementSolver() {
63 }
64 
SolveImpl(BlockSparseMatrix * A,const double * b,const LinearSolver::PerSolveOptions & per_solve_options,double * x)65 LinearSolver::Summary IterativeSchurComplementSolver::SolveImpl(
66     BlockSparseMatrix* A,
67     const double* b,
68     const LinearSolver::PerSolveOptions& per_solve_options,
69     double* x) {
70   EventLogger event_logger("IterativeSchurComplementSolver::Solve");
71 
72   CHECK_NOTNULL(A->block_structure());
73   const int num_eliminate_blocks = options_.elimination_groups[0];
74   // Initialize a ImplicitSchurComplement object.
75   if (schur_complement_ == NULL) {
76     DetectStructure(*(A->block_structure()),
77                     num_eliminate_blocks,
78                     &options_.row_block_size,
79                     &options_.e_block_size,
80                     &options_.f_block_size);
81     schur_complement_.reset(new ImplicitSchurComplement(options_));
82   }
83   schur_complement_->Init(*A, per_solve_options.D, b);
84 
85   const int num_schur_complement_blocks =
86       A->block_structure()->cols.size() - num_eliminate_blocks;
87   if (num_schur_complement_blocks == 0) {
88     VLOG(2) << "No parameter blocks left in the schur complement.";
89     LinearSolver::Summary cg_summary;
90     cg_summary.num_iterations = 0;
91     cg_summary.termination_type = LINEAR_SOLVER_SUCCESS;
92     schur_complement_->BackSubstitute(NULL, x);
93     return cg_summary;
94   }
95 
96   // Initialize the solution to the Schur complement system to zero.
97   reduced_linear_system_solution_.resize(schur_complement_->num_rows());
98   reduced_linear_system_solution_.setZero();
99 
100   // Instantiate a conjugate gradient solver that runs on the Schur
101   // complement matrix with the block diagonal of the matrix F'F as
102   // the preconditioner.
103   LinearSolver::Options cg_options;
104   cg_options.max_num_iterations = options_.max_num_iterations;
105   ConjugateGradientsSolver cg_solver(cg_options);
106   LinearSolver::PerSolveOptions cg_per_solve_options;
107 
108   cg_per_solve_options.r_tolerance = per_solve_options.r_tolerance;
109   cg_per_solve_options.q_tolerance = per_solve_options.q_tolerance;
110 
111   Preconditioner::Options preconditioner_options;
112   preconditioner_options.type = options_.preconditioner_type;
113   preconditioner_options.visibility_clustering_type =
114       options_.visibility_clustering_type;
115   preconditioner_options.sparse_linear_algebra_library_type =
116       options_.sparse_linear_algebra_library_type;
117   preconditioner_options.num_threads = options_.num_threads;
118   preconditioner_options.row_block_size = options_.row_block_size;
119   preconditioner_options.e_block_size = options_.e_block_size;
120   preconditioner_options.f_block_size = options_.f_block_size;
121   preconditioner_options.elimination_groups = options_.elimination_groups;
122 
123   switch (options_.preconditioner_type) {
124     case IDENTITY:
125       break;
126     case JACOBI:
127       preconditioner_.reset(
128           new SparseMatrixPreconditionerWrapper(
129               schur_complement_->block_diagonal_FtF_inverse()));
130       break;
131     case SCHUR_JACOBI:
132       if (preconditioner_.get() == NULL) {
133         preconditioner_.reset(
134             new SchurJacobiPreconditioner(*A->block_structure(),
135                                           preconditioner_options));
136       }
137       break;
138     case CLUSTER_JACOBI:
139     case CLUSTER_TRIDIAGONAL:
140       if (preconditioner_.get() == NULL) {
141         preconditioner_.reset(
142             new VisibilityBasedPreconditioner(*A->block_structure(),
143                                               preconditioner_options));
144       }
145       break;
146     default:
147       LOG(FATAL) << "Unknown Preconditioner Type";
148   }
149 
150   bool preconditioner_update_was_successful = true;
151   if (preconditioner_.get() != NULL) {
152     preconditioner_update_was_successful =
153         preconditioner_->Update(*A, per_solve_options.D);
154     cg_per_solve_options.preconditioner = preconditioner_.get();
155   }
156   event_logger.AddEvent("Setup");
157 
158   LinearSolver::Summary cg_summary;
159   cg_summary.num_iterations = 0;
160   cg_summary.termination_type = LINEAR_SOLVER_FAILURE;
161 
162   // TODO(sameeragarwal): Refactor preconditioners to return a more
163   // sane message.
164   cg_summary.message = "Preconditioner update failed.";
165   if (preconditioner_update_was_successful) {
166     cg_summary = cg_solver.Solve(schur_complement_.get(),
167                                  schur_complement_->rhs().data(),
168                                  cg_per_solve_options,
169                                  reduced_linear_system_solution_.data());
170     if (cg_summary.termination_type != LINEAR_SOLVER_FAILURE &&
171         cg_summary.termination_type != LINEAR_SOLVER_FATAL_ERROR) {
172       schur_complement_->BackSubstitute(
173           reduced_linear_system_solution_.data(), x);
174     }
175   }
176   event_logger.AddEvent("Solve");
177   return cg_summary;
178 }
179 
180 }  // namespace internal
181 }  // namespace ceres
182