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diff --git a/internal/ceres/coordinate_descent_minimizer.cc b/internal/ceres/coordinate_descent_minimizer.cc
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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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"
+
+#include <algorithm>
+#include <iterator>
+#include <memory>
+#include <numeric>
+#include <vector>
+
+#include "ceres/evaluator.h"
+#include "ceres/linear_solver.h"
+#include "ceres/minimizer.h"
+#include "ceres/parallel_for.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"
+
+namespace ceres {
+namespace internal {
+
+using std::map;
+using std::max;
+using std::min;
+using std::set;
+using std::string;
+using std::vector;
+
+CoordinateDescentMinimizer::CoordinateDescentMinimizer(ContextImpl* context)
+ : context_(context) {
+ CHECK(context_ != nullptr);
+}
+
+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 (const auto& g_t_e : group_to_elements) {
+ const auto& elements = g_t_e.second;
+ for (double* parameter_block: elements) {
+ parameter_blocks_.push_back(parameter_map.find(parameter_block)->second);
+ parameter_block_index[parameter_blocks_.back()] =
+ parameter_blocks_.size() - 1;
+ }
+ independent_set_offsets_.push_back(
+ independent_set_offsets_.back() + elements.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 auto 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;
+ evaluator_options_.context = context_;
+
+ 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();
+ }
+
+ std::unique_ptr<LinearSolver*[]> linear_solvers(
+ new LinearSolver*[options.num_threads]);
+
+ LinearSolver::Options linear_solver_options;
+ linear_solver_options.type = DENSE_QR;
+ linear_solver_options.context = context_;
+
+ 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) {
+ const int num_problems =
+ independent_set_offsets_[i + 1] - independent_set_offsets_[i];
+ // Avoid parallelization overhead call if the set is empty.
+ if (num_problems == 0) {
+ continue;
+ }
+
+ const int num_inner_iteration_threads =
+ min(options.num_threads, num_problems);
+ evaluator_options_.num_threads =
+ max(1, options.num_threads / num_inner_iteration_threads);
+
+ // The parameter blocks in each independent set can be optimized
+ // in parallel, since they do not co-occur in any residual block.
+ ParallelFor(
+ context_,
+ independent_set_offsets_[i],
+ independent_set_offsets_[i + 1],
+ num_inner_iteration_threads,
+ [&](int thread_id, int j) {
+ 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(
+ Evaluator::Create(evaluator_options_, program, &error));
+ CHECK(minimizer_options.evaluator != nullptr);
+ minimizer_options.jacobian.reset(
+ minimizer_options.evaluator->CreateJacobian());
+ CHECK(minimizer_options.jacobian != nullptr);
+
+ TrustRegionStrategy::Options trs_options;
+ trs_options.linear_solver = linear_solver;
+ minimizer_options.trust_region_strategy.reset(
+ TrustRegionStrategy::Create(trs_options));
+ CHECK(minimizer_options.trust_region_strategy != nullptr);
+ 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
+ for (const auto& g_t_e : group_to_elements) {
+ if (!program.IsParameterBlockSetIndependent(g_t_e.second)) {
+ *message =
+ StringPrintf("The user-provided "
+ "parameter_blocks_for_inner_iterations does not "
+ "form an independent set. Group Id: %d", g_t_e.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) {
+ std::unique_ptr<ParameterBlockOrdering> ordering(new ParameterBlockOrdering);
+ ComputeRecursiveIndependentSetOrdering(program, ordering.get());
+ ordering->Reverse();
+ return ordering.release();
+}
+
+} // namespace internal
+} // namespace ceres