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      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 //
      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
     23 // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
     24 // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
     25 // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
     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 (at) google.com (Sameer Agarwal)
     30 
     31 #include "ceres/coordinate_descent_minimizer.h"
     32 
     33 #ifdef CERES_USE_OPENMP
     34 #include <omp.h>
     35 #endif
     36 
     37 #include <iterator>
     38 #include <numeric>
     39 #include <vector>
     40 #include "ceres/evaluator.h"
     41 #include "ceres/linear_solver.h"
     42 #include "ceres/minimizer.h"
     43 #include "ceres/ordered_groups.h"
     44 #include "ceres/parameter_block.h"
     45 #include "ceres/problem_impl.h"
     46 #include "ceres/program.h"
     47 #include "ceres/residual_block.h"
     48 #include "ceres/solver.h"
     49 #include "ceres/solver_impl.h"
     50 #include "ceres/trust_region_minimizer.h"
     51 #include "ceres/trust_region_strategy.h"
     52 
     53 namespace ceres {
     54 namespace internal {
     55 
     56 CoordinateDescentMinimizer::~CoordinateDescentMinimizer() {
     57 }
     58 
     59 bool CoordinateDescentMinimizer::Init(
     60     const Program& program,
     61     const ProblemImpl::ParameterMap& parameter_map,
     62     const ParameterBlockOrdering& ordering,
     63     string* error) {
     64   parameter_blocks_.clear();
     65   independent_set_offsets_.clear();
     66   independent_set_offsets_.push_back(0);
     67 
     68   // Serialize the OrderedGroups into a vector of parameter block
     69   // offsets for parallel access.
     70   map<ParameterBlock*, int> parameter_block_index;
     71   map<int, set<double*> > group_to_elements = ordering.group_to_elements();
     72   for (map<int, set<double*> >::const_iterator it = group_to_elements.begin();
     73        it != group_to_elements.end();
     74        ++it) {
     75     for (set<double*>::const_iterator ptr_it = it->second.begin();
     76          ptr_it != it->second.end();
     77          ++ptr_it) {
     78       parameter_blocks_.push_back(parameter_map.find(*ptr_it)->second);
     79       parameter_block_index[parameter_blocks_.back()] =
     80           parameter_blocks_.size() - 1;
     81     }
     82     independent_set_offsets_.push_back(
     83         independent_set_offsets_.back() + it->second.size());
     84   }
     85 
     86   // The ordering does not have to contain all parameter blocks, so
     87   // assign zero offsets/empty independent sets to these parameter
     88   // blocks.
     89   const vector<ParameterBlock*>& parameter_blocks = program.parameter_blocks();
     90   for (int i = 0; i < parameter_blocks.size(); ++i) {
     91     if (!ordering.IsMember(parameter_blocks[i]->mutable_user_state())) {
     92       parameter_blocks_.push_back(parameter_blocks[i]);
     93       independent_set_offsets_.push_back(independent_set_offsets_.back());
     94     }
     95   }
     96 
     97   // Compute the set of residual blocks that depend on each parameter
     98   // block.
     99   residual_blocks_.resize(parameter_block_index.size());
    100   const vector<ResidualBlock*>& residual_blocks = program.residual_blocks();
    101   for (int i = 0; i < residual_blocks.size(); ++i) {
    102     ResidualBlock* residual_block = residual_blocks[i];
    103     const int num_parameter_blocks = residual_block->NumParameterBlocks();
    104     for (int j = 0; j < num_parameter_blocks; ++j) {
    105       ParameterBlock* parameter_block = residual_block->parameter_blocks()[j];
    106       const map<ParameterBlock*, int>::const_iterator it =
    107           parameter_block_index.find(parameter_block);
    108       if (it != parameter_block_index.end()) {
    109         residual_blocks_[it->second].push_back(residual_block);
    110       }
    111     }
    112   }
    113 
    114   evaluator_options_.linear_solver_type = DENSE_QR;
    115   evaluator_options_.num_eliminate_blocks = 0;
    116   evaluator_options_.num_threads = 1;
    117 
    118   return true;
    119 }
    120 
    121 void CoordinateDescentMinimizer::Minimize(
    122     const Minimizer::Options& options,
    123     double* parameters,
    124     Solver::Summary* summary) {
    125   // Set the state and mark all parameter blocks constant.
    126   for (int i = 0; i < parameter_blocks_.size(); ++i) {
    127     ParameterBlock* parameter_block = parameter_blocks_[i];
    128     parameter_block->SetState(parameters + parameter_block->state_offset());
    129     parameter_block->SetConstant();
    130   }
    131 
    132   scoped_array<LinearSolver*> linear_solvers(new LinearSolver*[options.num_threads]);
    133 
    134   LinearSolver::Options linear_solver_options;
    135   linear_solver_options.type = DENSE_QR;
    136 
    137   for (int i = 0; i < options.num_threads; ++i) {
    138     linear_solvers[i] = LinearSolver::Create(linear_solver_options);
    139   }
    140 
    141   for (int i = 0; i < independent_set_offsets_.size() - 1; ++i) {
    142     // No point paying the price for an OpemMP call if the set if of
    143     // size zero.
    144     if (independent_set_offsets_[i] ==  independent_set_offsets_[i + 1]) {
    145       continue;
    146     }
    147 
    148     // The parameter blocks in each independent set can be optimized
    149     // in parallel, since they do not co-occur in any residual block.
    150 #pragma omp parallel for num_threads(options.num_threads)
    151     for (int j = independent_set_offsets_[i];
    152          j < independent_set_offsets_[i + 1];
    153          ++j) {
    154 #ifdef CERES_USE_OPENMP
    155       int thread_id = omp_get_thread_num();
    156 #else
    157       int thread_id = 0;
    158 #endif
    159 
    160       ParameterBlock* parameter_block = parameter_blocks_[j];
    161       const int old_index = parameter_block->index();
    162       const int old_delta_offset = parameter_block->delta_offset();
    163       parameter_block->SetVarying();
    164       parameter_block->set_index(0);
    165       parameter_block->set_delta_offset(0);
    166 
    167       Program inner_program;
    168       inner_program.mutable_parameter_blocks()->push_back(parameter_block);
    169       *inner_program.mutable_residual_blocks() = residual_blocks_[j];
    170 
    171       // TODO(sameeragarwal): Better error handling. Right now we
    172       // assume that this is not going to lead to problems of any
    173       // sort. Basically we should be checking for numerical failure
    174       // of some sort.
    175       //
    176       // On the other hand, if the optimization is a failure, that in
    177       // some ways is fine, since it won't change the parameters and
    178       // we are fine.
    179       Solver::Summary inner_summary;
    180       Solve(&inner_program,
    181             linear_solvers[thread_id],
    182             parameters + parameter_block->state_offset(),
    183             &inner_summary);
    184 
    185       parameter_block->set_index(old_index);
    186       parameter_block->set_delta_offset(old_delta_offset);
    187       parameter_block->SetState(parameters + parameter_block->state_offset());
    188       parameter_block->SetConstant();
    189     }
    190   }
    191 
    192   for (int i =  0; i < parameter_blocks_.size(); ++i) {
    193     parameter_blocks_[i]->SetVarying();
    194   }
    195 
    196   for (int i = 0; i < options.num_threads; ++i) {
    197     delete linear_solvers[i];
    198   }
    199 }
    200 
    201 // Solve the optimization problem for one parameter block.
    202 void CoordinateDescentMinimizer::Solve(Program* program,
    203                                        LinearSolver* linear_solver,
    204                                        double* parameter,
    205                                        Solver::Summary* summary) {
    206   *summary = Solver::Summary();
    207   summary->initial_cost = 0.0;
    208   summary->fixed_cost = 0.0;
    209   summary->final_cost = 0.0;
    210   string error;
    211 
    212   scoped_ptr<Evaluator> evaluator(
    213       Evaluator::Create(evaluator_options_, program,  &error));
    214   CHECK_NOTNULL(evaluator.get());
    215 
    216   scoped_ptr<SparseMatrix> jacobian(evaluator->CreateJacobian());
    217   CHECK_NOTNULL(jacobian.get());
    218 
    219   TrustRegionStrategy::Options trs_options;
    220   trs_options.linear_solver = linear_solver;
    221 
    222   scoped_ptr<TrustRegionStrategy>trust_region_strategy(
    223       CHECK_NOTNULL(TrustRegionStrategy::Create(trs_options)));
    224 
    225   Minimizer::Options minimizer_options;
    226   minimizer_options.evaluator = evaluator.get();
    227   minimizer_options.jacobian = jacobian.get();
    228   minimizer_options.trust_region_strategy = trust_region_strategy.get();
    229 
    230   TrustRegionMinimizer minimizer;
    231   minimizer.Minimize(minimizer_options, parameter, summary);
    232 }
    233 
    234 }  // namespace internal
    235 }  // namespace ceres
    236