// Ceres Solver - A fast non-linear least squares minimizer // Copyright 2012 Google Inc. All rights reserved. // http://code.google.com/p/ceres-solver/ // // 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) #include "ceres/coordinate_descent_minimizer.h" #ifdef CERES_USE_OPENMP #include <omp.h> #endif #include <iterator> #include <numeric> #include <vector> #include "ceres/evaluator.h" #include "ceres/linear_solver.h" #include "ceres/minimizer.h" #include "ceres/parameter_block.h" #include "ceres/parameter_block_ordering.h" #include "ceres/problem_impl.h" #include "ceres/program.h" #include "ceres/residual_block.h" #include "ceres/solver.h" #include "ceres/trust_region_minimizer.h" #include "ceres/trust_region_strategy.h" #include "ceres/parameter_block_ordering.h" namespace ceres { namespace internal { CoordinateDescentMinimizer::~CoordinateDescentMinimizer() { } bool CoordinateDescentMinimizer::Init( const Program& program, const ProblemImpl::ParameterMap& parameter_map, const ParameterBlockOrdering& ordering, string* error) { parameter_blocks_.clear(); independent_set_offsets_.clear(); independent_set_offsets_.push_back(0); // Serialize the OrderedGroups into a vector of parameter block // offsets for parallel access. map<ParameterBlock*, int> parameter_block_index; map<int, set<double*> > group_to_elements = ordering.group_to_elements(); for (map<int, set<double*> >::const_iterator it = group_to_elements.begin(); it != group_to_elements.end(); ++it) { for (set<double*>::const_iterator ptr_it = it->second.begin(); ptr_it != it->second.end(); ++ptr_it) { parameter_blocks_.push_back(parameter_map.find(*ptr_it)->second); parameter_block_index[parameter_blocks_.back()] = parameter_blocks_.size() - 1; } independent_set_offsets_.push_back( independent_set_offsets_.back() + it->second.size()); } // The ordering does not have to contain all parameter blocks, so // assign zero offsets/empty independent sets to these parameter // blocks. const vector<ParameterBlock*>& parameter_blocks = program.parameter_blocks(); for (int i = 0; i < parameter_blocks.size(); ++i) { if (!ordering.IsMember(parameter_blocks[i]->mutable_user_state())) { parameter_blocks_.push_back(parameter_blocks[i]); independent_set_offsets_.push_back(independent_set_offsets_.back()); } } // Compute the set of residual blocks that depend on each parameter // block. residual_blocks_.resize(parameter_block_index.size()); const vector<ResidualBlock*>& residual_blocks = program.residual_blocks(); for (int i = 0; i < residual_blocks.size(); ++i) { ResidualBlock* residual_block = residual_blocks[i]; const int num_parameter_blocks = residual_block->NumParameterBlocks(); for (int j = 0; j < num_parameter_blocks; ++j) { ParameterBlock* parameter_block = residual_block->parameter_blocks()[j]; const map<ParameterBlock*, int>::const_iterator it = parameter_block_index.find(parameter_block); if (it != parameter_block_index.end()) { residual_blocks_[it->second].push_back(residual_block); } } } evaluator_options_.linear_solver_type = DENSE_QR; evaluator_options_.num_eliminate_blocks = 0; evaluator_options_.num_threads = 1; return true; } void CoordinateDescentMinimizer::Minimize( const Minimizer::Options& options, double* parameters, Solver::Summary* summary) { // Set the state and mark all parameter blocks constant. for (int i = 0; i < parameter_blocks_.size(); ++i) { ParameterBlock* parameter_block = parameter_blocks_[i]; parameter_block->SetState(parameters + parameter_block->state_offset()); parameter_block->SetConstant(); } scoped_array<LinearSolver*> linear_solvers( new LinearSolver*[options.num_threads]); LinearSolver::Options linear_solver_options; linear_solver_options.type = DENSE_QR; for (int i = 0; i < options.num_threads; ++i) { linear_solvers[i] = LinearSolver::Create(linear_solver_options); } for (int i = 0; i < independent_set_offsets_.size() - 1; ++i) { // No point paying the price for an OpemMP call if the set if of // size zero. if (independent_set_offsets_[i] == independent_set_offsets_[i + 1]) { continue; } // The parameter blocks in each independent set can be optimized // in parallel, since they do not co-occur in any residual block. #pragma omp parallel for num_threads(options.num_threads) for (int j = independent_set_offsets_[i]; j < independent_set_offsets_[i + 1]; ++j) { #ifdef CERES_USE_OPENMP int thread_id = omp_get_thread_num(); #else int thread_id = 0; #endif ParameterBlock* parameter_block = parameter_blocks_[j]; const int old_index = parameter_block->index(); const int old_delta_offset = parameter_block->delta_offset(); parameter_block->SetVarying(); parameter_block->set_index(0); parameter_block->set_delta_offset(0); Program inner_program; inner_program.mutable_parameter_blocks()->push_back(parameter_block); *inner_program.mutable_residual_blocks() = residual_blocks_[j]; // TODO(sameeragarwal): Better error handling. Right now we // assume that this is not going to lead to problems of any // sort. Basically we should be checking for numerical failure // of some sort. // // On the other hand, if the optimization is a failure, that in // some ways is fine, since it won't change the parameters and // we are fine. Solver::Summary inner_summary; Solve(&inner_program, linear_solvers[thread_id], parameters + parameter_block->state_offset(), &inner_summary); parameter_block->set_index(old_index); parameter_block->set_delta_offset(old_delta_offset); parameter_block->SetState(parameters + parameter_block->state_offset()); parameter_block->SetConstant(); } } for (int i = 0; i < parameter_blocks_.size(); ++i) { parameter_blocks_[i]->SetVarying(); } for (int i = 0; i < options.num_threads; ++i) { delete linear_solvers[i]; } } // Solve the optimization problem for one parameter block. void CoordinateDescentMinimizer::Solve(Program* program, LinearSolver* linear_solver, double* parameter, Solver::Summary* summary) { *summary = Solver::Summary(); summary->initial_cost = 0.0; summary->fixed_cost = 0.0; summary->final_cost = 0.0; string error; scoped_ptr<Evaluator> evaluator( Evaluator::Create(evaluator_options_, program, &error)); CHECK_NOTNULL(evaluator.get()); scoped_ptr<SparseMatrix> jacobian(evaluator->CreateJacobian()); CHECK_NOTNULL(jacobian.get()); TrustRegionStrategy::Options trs_options; trs_options.linear_solver = linear_solver; scoped_ptr<TrustRegionStrategy>trust_region_strategy( CHECK_NOTNULL(TrustRegionStrategy::Create(trs_options))); Minimizer::Options minimizer_options; minimizer_options.evaluator = evaluator.get(); minimizer_options.jacobian = jacobian.get(); minimizer_options.trust_region_strategy = trust_region_strategy.get(); minimizer_options.is_silent = true; TrustRegionMinimizer minimizer; minimizer.Minimize(minimizer_options, parameter, summary); } bool CoordinateDescentMinimizer::IsOrderingValid( const Program& program, const ParameterBlockOrdering& ordering, string* message) { const map<int, set<double*> >& group_to_elements = ordering.group_to_elements(); // Verify that each group is an independent set map<int, set<double*> >::const_iterator it = group_to_elements.begin(); for ( ; it != group_to_elements.end(); ++it) { if (!program.IsParameterBlockSetIndependent(it->second)) { *message = StringPrintf("The user-provided " "parameter_blocks_for_inner_iterations does not " "form an independent set. Group Id: %d", it->first); return false; } } return true; } // Find a recursive decomposition of the Hessian matrix as a set // of independent sets of decreasing size and invert it. This // seems to work better in practice, i.e., Cameras before // points. ParameterBlockOrdering* CoordinateDescentMinimizer::CreateOrdering( const Program& program) { scoped_ptr<ParameterBlockOrdering> ordering(new ParameterBlockOrdering); ComputeRecursiveIndependentSetOrdering(program, ordering.get()); ordering->Reverse(); return ordering.release(); } } // namespace internal } // namespace ceres