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// 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;
Minimizer::Options minimizer_options;
minimizer_options.evaluator.reset(
CHECK_NOTNULL(Evaluator::Create(evaluator_options_, program, &error)));
minimizer_options.jacobian.reset(
CHECK_NOTNULL(minimizer_options.evaluator->CreateJacobian()));
TrustRegionStrategy::Options trs_options;
trs_options.linear_solver = linear_solver;
minimizer_options.trust_region_strategy.reset(
CHECK_NOTNULL(TrustRegionStrategy::Create(trs_options)));
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