internal/ceres/visibility_based_preconditioner_test.cc - ceres-solver - Git at Google


            
            // 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/visibility_based_preconditioner.h"


            #include <memory>


            #include "Eigen/Dense"

            
            #include "ceres/block_random_access_dense_matrix.h"

            
            #include "ceres/block_random_access_sparse_matrix.h"

            
            #include "ceres/block_sparse_matrix.h"

            
            #include "ceres/casts.h"

            
            #include "ceres/file.h"

            
            #include "ceres/internal/eigen.h"

            
            #include "ceres/linear_least_squares_problems.h"

            
            #include "ceres/schur_eliminator.h"

            
            #include "ceres/stringprintf.h"

            
            #include "ceres/test_util.h"

            
            #include "ceres/types.h"

            
            #include "glog/logging.h"

            
            #include "gtest/gtest.h"


            namespace ceres {

            
            namespace internal {


            // TODO(sameeragarwal): Re-enable this test once serialization is

            
            // working again.


            // using testing::AssertionResult;

            
            // using testing::AssertionSuccess;

            
            // using testing::AssertionFailure;


            // static const double kTolerance = 1e-12;


            // class VisibilityBasedPreconditionerTest : public ::testing::Test {

            
            //  public:

            
            //   static const int kCameraSize = 9;


            //  protected:

            
            //   void SetUp() {

            
            //     string input_file = TestFileAbsolutePath("problem-6-1384-000.lsqp");


            //     std::unique_ptr<LinearLeastSquaresProblem> problem =

            
            //     CreateLinearLeastSquaresProblemFromFile(input_file));

            
            //     A_.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));

            
            //     b_.reset(problem->b.release());

            
            //     D_.reset(problem->D.release());


            //     const CompressedRowBlockStructure* bs =

            
            //         CHECK_NOTNULL(A_->block_structure());

            
            //     const int num_col_blocks = bs->cols.size();


            //     num_cols_ = A_->num_cols();

            
            //     num_rows_ = A_->num_rows();

            
            //     num_eliminate_blocks_ = problem->num_eliminate_blocks;

            
            //     num_camera_blocks_ = num_col_blocks - num_eliminate_blocks_;

            
            //     options_.elimination_groups.push_back(num_eliminate_blocks_);

            
            //     options_.elimination_groups.push_back(

            
            //         A_->block_structure()->cols.size() - num_eliminate_blocks_);


            //     vector<int> blocks(num_col_blocks - num_eliminate_blocks_, 0);

            
            //     for (int i = num_eliminate_blocks_; i < num_col_blocks; ++i) {

            
            //       blocks[i - num_eliminate_blocks_] = bs->cols[i].size;

            
            //     }


            //     // The input matrix is a real jacobian and fairly poorly

            
            //     // conditioned. Setting D to a large constant makes the normal

            
            //     // equations better conditioned and makes the tests below better

            
            //     // conditioned.

            
            //     VectorRef(D_.get(), num_cols_).setConstant(10.0);


            //     schur_complement_ =

            
            //     std::make_unique<BlockRandomAccessDenseMatrix>(blocks);

            
            //     Vector rhs(schur_complement_->num_rows());


            //     std::unique_ptr<SchurEliminatorBase> eliminator;

            
            //     LinearSolver::Options eliminator_options;

            
            //     eliminator_options.elimination_groups = options_.elimination_groups;

            
            //     eliminator_options.num_threads = options_.num_threads;


            //     eliminator = SchurEliminatorBase::Create(eliminator_options);

            
            //     eliminator->Init(num_eliminate_blocks_, bs);

            
            //     eliminator->Eliminate(A_.get(), b_.get(), D_.get(),

            
            //                           schur_complement_.get(), rhs.data());

            
            //   }


            //   AssertionResult IsSparsityStructureValid() {

            
            //     preconditioner_->InitStorage(*A_->block_structure());

            
            //     const std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =

            
            //     get_cluster_pairs(); const vector<int>& cluster_membership =

            
            //     get_cluster_membership();


            //     for (int i = 0; i < num_camera_blocks_; ++i) {

            
            //       for (int j = i; j < num_camera_blocks_; ++j) {

            
            //         if (cluster_pairs.count(make_pair(cluster_membership[i],

            
            //                                           cluster_membership[j]))) {

            
            //           if (!IsBlockPairInPreconditioner(i, j)) {

            
            //             return AssertionFailure()

            
            //                 << "block pair (" << i << "," << j << "missing";

            
            //           }

            
            //         } else {

            
            //           if (IsBlockPairInPreconditioner(i, j)) {

            
            //             return AssertionFailure()

            
            //                << "block pair (" << i << "," << j << "should not be present";

            
            //           }

            
            //         }

            
            //       }

            
            //     }

            
            //     return AssertionSuccess();

            
            //   }


            //   AssertionResult PreconditionerValuesMatch() {

            
            //     preconditioner_->Update(*A_, D_.get());

            
            //     const std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =

            
            //     get_cluster_pairs(); const BlockRandomAccessSparseMatrix* m = get_m();

            
            //     Matrix preconditioner_matrix;

            
            //     m->matrix()->ToDenseMatrix(&preconditioner_matrix);

            
            //     ConstMatrixRef full_schur_complement(schur_complement_->values(),

            
            //                                          m->num_rows(),

            
            //                                          m->num_rows());

            
            //     const int num_clusters = get_num_clusters();

            
            //     const int kDiagonalBlockSize =

            
            //         kCameraSize * num_camera_blocks_ / num_clusters;


            //     for (int i = 0; i < num_clusters; ++i) {

            
            //       for (int j = i; j < num_clusters; ++j) {

            
            //         double diff = 0.0;

            
            //         if (cluster_pairs.count(make_pair(i, j))) {

            
            //           diff =

            
            //               (preconditioner_matrix.block(kDiagonalBlockSize * i,

            
            //                                            kDiagonalBlockSize * j,

            
            //                                            kDiagonalBlockSize,

            
            //                                            kDiagonalBlockSize) -

            
            //                full_schur_complement.block(kDiagonalBlockSize * i,

            
            //                                            kDiagonalBlockSize * j,

            
            //                                            kDiagonalBlockSize,

            
            //                                            kDiagonalBlockSize)).norm();

            
            //         } else {

            
            //           diff = preconditioner_matrix.block(kDiagonalBlockSize * i,

            
            //                                              kDiagonalBlockSize * j,

            
            //                                              kDiagonalBlockSize,

            
            //                                              kDiagonalBlockSize).norm();

            
            //         }

            
            //         if (diff > kTolerance) {

            
            //           return AssertionFailure()

            
            //               << "Preconditioner block " << i << " " << j << " differs "

            
            //               << "from expected value by " << diff;

            
            //         }

            
            //       }

            
            //     }

            
            //     return AssertionSuccess();

            
            //   }


            //   // Accessors

            
            //   int get_num_blocks() { return preconditioner_->num_blocks_; }


            //   int get_num_clusters() { return preconditioner_->num_clusters_; }

            
            //   int* get_mutable_num_clusters() { return &preconditioner_->num_clusters_; }


            //   const vector<int>& get_block_size() {

            
            //     return preconditioner_->block_size_; }


            //   vector<int>* get_mutable_block_size() {

            
            //     return &preconditioner_->block_size_; }


            //   const vector<int>& get_cluster_membership() {

            
            //     return preconditioner_->cluster_membership_;

            
            //   }


            //   vector<int>* get_mutable_cluster_membership() {

            
            //     return &preconditioner_->cluster_membership_;

            
            //   }


            //   const set<pair<int, int>>& get_block_pairs() {

            
            //     return preconditioner_->block_pairs_;

            
            //   }


            //   set<pair<int, int>>* get_mutable_block_pairs() {

            
            //     return &preconditioner_->block_pairs_;

            
            //   }


            //   const std::unordered_set<pair<int, int>, pair_hash>& get_cluster_pairs() {

            
            //     return preconditioner_->cluster_pairs_;

            
            //   }


            //   std::unordered_set<pair<int, int>, pair_hash>* get_mutable_cluster_pairs()

            
            //   {

            
            //     return &preconditioner_->cluster_pairs_;

            
            //   }


            //   bool IsBlockPairInPreconditioner(const int block1, const int block2) {

            
            //     return preconditioner_->IsBlockPairInPreconditioner(block1, block2);

            
            //   }


            //   bool IsBlockPairOffDiagonal(const int block1, const int block2) {

            
            //     return preconditioner_->IsBlockPairOffDiagonal(block1, block2);

            
            //   }


            //   const BlockRandomAccessSparseMatrix* get_m() {

            
            //     return preconditioner_->m_.get();

            
            //   }


            //   int num_rows_;

            
            //   int num_cols_;

            
            //   int num_eliminate_blocks_;

            
            //   int num_camera_blocks_;


            //   std::unique_ptr<BlockSparseMatrix> A_;

            
            //   std::unique_ptr<double[]> b_;

            
            //   std::unique_ptr<double[]> D_;


            //   Preconditioner::Options options_;

            
            //   std::unique_ptr<VisibilityBasedPreconditioner> preconditioner_;

            
            //   std::unique_ptr<BlockRandomAccessDenseMatrix> schur_complement_;

            
            // };


            // TEST_F(VisibilityBasedPreconditionerTest, OneClusterClusterJacobi) {

            
            //   options_.type = CLUSTER_JACOBI;

            
            //   preconditioner_ =

            
            //       std::make_unique<VisibilityBasedPreconditioner>(

            
            //          *A_->block_structure(), options_);


            //   // Override the clustering to be a single clustering containing all

            
            //   // the cameras.

            
            //   vector<int>& cluster_membership = *get_mutable_cluster_membership();

            
            //   for (int i = 0; i < num_camera_blocks_; ++i) {

            
            //     cluster_membership[i] = 0;

            
            //   }


            //   *get_mutable_num_clusters() = 1;


            //   std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =

            
            //   *get_mutable_cluster_pairs(); cluster_pairs.clear();

            
            //   cluster_pairs.insert(make_pair(0, 0));


            //   EXPECT_TRUE(IsSparsityStructureValid());

            
            //   EXPECT_TRUE(PreconditionerValuesMatch());


            //   // Multiplication by the inverse of the preconditioner.

            
            //   const int num_rows = schur_complement_->num_rows();

            
            //   ConstMatrixRef full_schur_complement(schur_complement_->values(),

            
            //                                        num_rows,

            
            //                                        num_rows);

            
            //   Vector x(num_rows);

            
            //   Vector y(num_rows);

            
            //   Vector z(num_rows);


            //   for (int i = 0; i < num_rows; ++i) {

            
            //     x.setZero();

            
            //     y.setZero();

            
            //     z.setZero();

            
            //     x[i] = 1.0;

            
            //     preconditioner_->RightMultiply(x.data(), y.data());

            
            //     z = full_schur_complement

            
            //         .selfadjointView<Eigen::Upper>()

            
            //         .llt().solve(x);

            
            //     double max_relative_difference =

            
            //         ((y - z).array() / z.array()).matrix().lpNorm<Eigen::Infinity>();

            
            //     EXPECT_NEAR(max_relative_difference, 0.0, kTolerance);

            
            //   }

            
            // }


            // TEST_F(VisibilityBasedPreconditionerTest, ClusterJacobi) {

            
            //   options_.type = CLUSTER_JACOBI;

            
            //   preconditioner_ =

            
            //   std::make_unique<VisibilityBasedPreconditioner>(*A_->block_structure(),

            
            //   options_);


            //   // Override the clustering to be equal number of cameras.

            
            //   vector<int>& cluster_membership = *get_mutable_cluster_membership();

            
            //   cluster_membership.resize(num_camera_blocks_);

            
            //   static const int kNumClusters = 3;


            //   for (int i = 0; i < num_camera_blocks_; ++i) {

            
            //     cluster_membership[i] = (i * kNumClusters) / num_camera_blocks_;

            
            //   }

            
            //   *get_mutable_num_clusters() = kNumClusters;


            //   std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =

            
            //   *get_mutable_cluster_pairs(); cluster_pairs.clear(); for (int i = 0; i <

            
            //   kNumClusters; ++i) {

            
            //     cluster_pairs.insert(make_pair(i, i));

            
            //   }


            //   EXPECT_TRUE(IsSparsityStructureValid());

            
            //   EXPECT_TRUE(PreconditionerValuesMatch());

            
            // }


            // TEST_F(VisibilityBasedPreconditionerTest, ClusterTridiagonal) {

            
            //   options_.type = CLUSTER_TRIDIAGONAL;

            
            //   preconditioner_ =

            
            //     std::make_unique<VisibilityBasedPreconditioner>(*A_->block_structure(),

            
            //     options_);

            
            //   static const int kNumClusters = 3;


            //   // Override the clustering to be 3 clusters.

            
            //   vector<int>& cluster_membership = *get_mutable_cluster_membership();

            
            //   cluster_membership.resize(num_camera_blocks_);

            
            //   for (int i = 0; i < num_camera_blocks_; ++i) {

            
            //     cluster_membership[i] = (i * kNumClusters) / num_camera_blocks_;

            
            //   }

            
            //   *get_mutable_num_clusters() = kNumClusters;


            //   // Spanning forest has structure 0-1 2

            
            //   std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =

            
            //   *get_mutable_cluster_pairs(); cluster_pairs.clear(); for (int i = 0; i <

            
            //   kNumClusters; ++i) {

            
            //     cluster_pairs.insert(make_pair(i, i));

            
            //   }

            
            //   cluster_pairs.insert(make_pair(0, 1));


            //   EXPECT_TRUE(IsSparsityStructureValid());

            
            //   EXPECT_TRUE(PreconditionerValuesMatch());

            
            // }


            }  // namespace internal

            
            }  // namespace ceres
	// 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/visibility_based_preconditioner.h"

	#include <memory>

	#include "Eigen/Dense"
	#include "ceres/block_random_access_dense_matrix.h"
	#include "ceres/block_random_access_sparse_matrix.h"
	#include "ceres/block_sparse_matrix.h"
	#include "ceres/casts.h"
	#include "ceres/file.h"
	#include "ceres/internal/eigen.h"
	#include "ceres/linear_least_squares_problems.h"
	#include "ceres/schur_eliminator.h"
	#include "ceres/stringprintf.h"
	#include "ceres/test_util.h"
	#include "ceres/types.h"
	#include "glog/logging.h"
	#include "gtest/gtest.h"

	namespace ceres {
	namespace internal {

	// TODO(sameeragarwal): Re-enable this test once serialization is
	// working again.

	// using testing::AssertionResult;
	// using testing::AssertionSuccess;
	// using testing::AssertionFailure;

	// static const double kTolerance = 1e-12;

	// class VisibilityBasedPreconditionerTest : public ::testing::Test {
	// public:
	// static const int kCameraSize = 9;

	// protected:
	// void SetUp() {
	// string input_file = TestFileAbsolutePath("problem-6-1384-000.lsqp");

	// std::unique_ptr<LinearLeastSquaresProblem> problem =
	// CreateLinearLeastSquaresProblemFromFile(input_file));
	// A_.reset(down_cast<BlockSparseMatrix*>(problem->A.release()));
	// b_.reset(problem->b.release());
	// D_.reset(problem->D.release());

	// const CompressedRowBlockStructure* bs =
	// CHECK_NOTNULL(A_->block_structure());
	// const int num_col_blocks = bs->cols.size();

	// num_cols_ = A_->num_cols();
	// num_rows_ = A_->num_rows();
	// num_eliminate_blocks_ = problem->num_eliminate_blocks;
	// num_camera_blocks_ = num_col_blocks - num_eliminate_blocks_;
	// options_.elimination_groups.push_back(num_eliminate_blocks_);
	// options_.elimination_groups.push_back(
	// A_->block_structure()->cols.size() - num_eliminate_blocks_);

	// vector<int> blocks(num_col_blocks - num_eliminate_blocks_, 0);
	// for (int i = num_eliminate_blocks_; i < num_col_blocks; ++i) {
	// blocks[i - num_eliminate_blocks_] = bs->cols[i].size;
	// }

	// // The input matrix is a real jacobian and fairly poorly
	// // conditioned. Setting D to a large constant makes the normal
	// // equations better conditioned and makes the tests below better
	// // conditioned.
	// VectorRef(D_.get(), num_cols_).setConstant(10.0);

	// schur_complement_ =
	// std::make_unique<BlockRandomAccessDenseMatrix>(blocks);
	// Vector rhs(schur_complement_->num_rows());

	// std::unique_ptr<SchurEliminatorBase> eliminator;
	// LinearSolver::Options eliminator_options;
	// eliminator_options.elimination_groups = options_.elimination_groups;
	// eliminator_options.num_threads = options_.num_threads;

	// eliminator = SchurEliminatorBase::Create(eliminator_options);
	// eliminator->Init(num_eliminate_blocks_, bs);
	// eliminator->Eliminate(A_.get(), b_.get(), D_.get(),
	// schur_complement_.get(), rhs.data());
	// }

	// AssertionResult IsSparsityStructureValid() {
	// preconditioner_->InitStorage(*A_->block_structure());
	// const std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =
	// get_cluster_pairs(); const vector<int>& cluster_membership =
	// get_cluster_membership();

	// for (int i = 0; i < num_camera_blocks_; ++i) {
	// for (int j = i; j < num_camera_blocks_; ++j) {
	// if (cluster_pairs.count(make_pair(cluster_membership[i],
	// cluster_membership[j]))) {
	// if (!IsBlockPairInPreconditioner(i, j)) {
	// return AssertionFailure()
	// << "block pair (" << i << "," << j << "missing";
	// }
	// } else {
	// if (IsBlockPairInPreconditioner(i, j)) {
	// return AssertionFailure()
	// << "block pair (" << i << "," << j << "should not be present";
	// }
	// }
	// }
	// }
	// return AssertionSuccess();
	// }

	// AssertionResult PreconditionerValuesMatch() {
	// preconditioner_->Update(*A_, D_.get());
	// const std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =
	// get_cluster_pairs(); const BlockRandomAccessSparseMatrix* m = get_m();
	// Matrix preconditioner_matrix;
	// m->matrix()->ToDenseMatrix(&preconditioner_matrix);
	// ConstMatrixRef full_schur_complement(schur_complement_->values(),
	// m->num_rows(),
	// m->num_rows());
	// const int num_clusters = get_num_clusters();
	// const int kDiagonalBlockSize =
	// kCameraSize * num_camera_blocks_ / num_clusters;

	// for (int i = 0; i < num_clusters; ++i) {
	// for (int j = i; j < num_clusters; ++j) {
	// double diff = 0.0;
	// if (cluster_pairs.count(make_pair(i, j))) {
	// diff =
	// (preconditioner_matrix.block(kDiagonalBlockSize * i,
	// kDiagonalBlockSize * j,
	// kDiagonalBlockSize,
	// kDiagonalBlockSize) -
	// full_schur_complement.block(kDiagonalBlockSize * i,
	// kDiagonalBlockSize * j,
	// kDiagonalBlockSize,
	// kDiagonalBlockSize)).norm();
	// } else {
	// diff = preconditioner_matrix.block(kDiagonalBlockSize * i,
	// kDiagonalBlockSize * j,
	// kDiagonalBlockSize,
	// kDiagonalBlockSize).norm();
	// }
	// if (diff > kTolerance) {
	// return AssertionFailure()
	// << "Preconditioner block " << i << " " << j << " differs "
	// << "from expected value by " << diff;
	// }
	// }
	// }
	// return AssertionSuccess();
	// }

	// // Accessors
	// int get_num_blocks() { return preconditioner_->num_blocks_; }

	// int get_num_clusters() { return preconditioner_->num_clusters_; }
	// int* get_mutable_num_clusters() { return &preconditioner_->num_clusters_; }

	// const vector<int>& get_block_size() {
	// return preconditioner_->block_size_; }

	// vector<int>* get_mutable_block_size() {
	// return &preconditioner_->block_size_; }

	// const vector<int>& get_cluster_membership() {
	// return preconditioner_->cluster_membership_;
	// }

	// vector<int>* get_mutable_cluster_membership() {
	// return &preconditioner_->cluster_membership_;
	// }

	// const set<pair<int, int>>& get_block_pairs() {
	// return preconditioner_->block_pairs_;
	// }

	// set<pair<int, int>>* get_mutable_block_pairs() {
	// return &preconditioner_->block_pairs_;
	// }

	// const std::unordered_set<pair<int, int>, pair_hash>& get_cluster_pairs() {
	// return preconditioner_->cluster_pairs_;
	// }

	// std::unordered_set<pair<int, int>, pair_hash>* get_mutable_cluster_pairs()
	// {
	// return &preconditioner_->cluster_pairs_;
	// }

	// bool IsBlockPairInPreconditioner(const int block1, const int block2) {
	// return preconditioner_->IsBlockPairInPreconditioner(block1, block2);
	// }

	// bool IsBlockPairOffDiagonal(const int block1, const int block2) {
	// return preconditioner_->IsBlockPairOffDiagonal(block1, block2);
	// }

	// const BlockRandomAccessSparseMatrix* get_m() {
	// return preconditioner_->m_.get();
	// }

	// int num_rows_;
	// int num_cols_;
	// int num_eliminate_blocks_;
	// int num_camera_blocks_;

	// std::unique_ptr<BlockSparseMatrix> A_;
	// std::unique_ptr<double[]> b_;
	// std::unique_ptr<double[]> D_;

	// Preconditioner::Options options_;
	// std::unique_ptr<VisibilityBasedPreconditioner> preconditioner_;
	// std::unique_ptr<BlockRandomAccessDenseMatrix> schur_complement_;
	// };

	// TEST_F(VisibilityBasedPreconditionerTest, OneClusterClusterJacobi) {
	// options_.type = CLUSTER_JACOBI;
	// preconditioner_ =
	// std::make_unique<VisibilityBasedPreconditioner>(
	// *A_->block_structure(), options_);

	// // Override the clustering to be a single clustering containing all
	// // the cameras.
	// vector<int>& cluster_membership = *get_mutable_cluster_membership();
	// for (int i = 0; i < num_camera_blocks_; ++i) {
	// cluster_membership[i] = 0;
	// }

	// *get_mutable_num_clusters() = 1;

	// std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =
	// *get_mutable_cluster_pairs(); cluster_pairs.clear();
	// cluster_pairs.insert(make_pair(0, 0));

	// EXPECT_TRUE(IsSparsityStructureValid());
	// EXPECT_TRUE(PreconditionerValuesMatch());

	// // Multiplication by the inverse of the preconditioner.
	// const int num_rows = schur_complement_->num_rows();
	// ConstMatrixRef full_schur_complement(schur_complement_->values(),
	// num_rows,
	// num_rows);
	// Vector x(num_rows);
	// Vector y(num_rows);
	// Vector z(num_rows);

	// for (int i = 0; i < num_rows; ++i) {
	// x.setZero();
	// y.setZero();
	// z.setZero();
	// x[i] = 1.0;
	// preconditioner_->RightMultiply(x.data(), y.data());
	// z = full_schur_complement
	// .selfadjointView<Eigen::Upper>()
	// .llt().solve(x);
	// double max_relative_difference =
	// ((y - z).array() / z.array()).matrix().lpNorm<Eigen::Infinity>();
	// EXPECT_NEAR(max_relative_difference, 0.0, kTolerance);
	// }
	// }

	// TEST_F(VisibilityBasedPreconditionerTest, ClusterJacobi) {
	// options_.type = CLUSTER_JACOBI;
	// preconditioner_ =
	// std::make_unique<VisibilityBasedPreconditioner>(*A_->block_structure(),
	// options_);

	// // Override the clustering to be equal number of cameras.
	// vector<int>& cluster_membership = *get_mutable_cluster_membership();
	// cluster_membership.resize(num_camera_blocks_);
	// static const int kNumClusters = 3;

	// for (int i = 0; i < num_camera_blocks_; ++i) {
	// cluster_membership[i] = (i * kNumClusters) / num_camera_blocks_;
	// }
	// *get_mutable_num_clusters() = kNumClusters;

	// std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =
	// *get_mutable_cluster_pairs(); cluster_pairs.clear(); for (int i = 0; i <
	// kNumClusters; ++i) {
	// cluster_pairs.insert(make_pair(i, i));
	// }

	// EXPECT_TRUE(IsSparsityStructureValid());
	// EXPECT_TRUE(PreconditionerValuesMatch());
	// }

	// TEST_F(VisibilityBasedPreconditionerTest, ClusterTridiagonal) {
	// options_.type = CLUSTER_TRIDIAGONAL;
	// preconditioner_ =
	// std::make_unique<VisibilityBasedPreconditioner>(*A_->block_structure(),
	// options_);
	// static const int kNumClusters = 3;

	// // Override the clustering to be 3 clusters.
	// vector<int>& cluster_membership = *get_mutable_cluster_membership();
	// cluster_membership.resize(num_camera_blocks_);
	// for (int i = 0; i < num_camera_blocks_; ++i) {
	// cluster_membership[i] = (i * kNumClusters) / num_camera_blocks_;
	// }
	// *get_mutable_num_clusters() = kNumClusters;

	// // Spanning forest has structure 0-1 2
	// std::unordered_set<pair<int, int>, pair_hash>& cluster_pairs =
	// *get_mutable_cluster_pairs(); cluster_pairs.clear(); for (int i = 0; i <
	// kNumClusters; ++i) {
	// cluster_pairs.insert(make_pair(i, i));
	// }
	// cluster_pairs.insert(make_pair(0, 1));

	// EXPECT_TRUE(IsSparsityStructureValid());
	// EXPECT_TRUE(PreconditionerValuesMatch());
	// }

	} // namespace internal
	} // namespace ceres