| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2013 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/covariance.h" |
| |
| #include <algorithm> |
| #include <cmath> |
| #include "ceres/compressed_row_sparse_matrix.h" |
| #include "ceres/cost_function.h" |
| #include "ceres/covariance_impl.h" |
| #include "ceres/local_parameterization.h" |
| #include "ceres/map_util.h" |
| #include "ceres/problem_impl.h" |
| #include "gtest/gtest.h" |
| |
| namespace ceres { |
| namespace internal { |
| |
| TEST(CovarianceImpl, ComputeCovarianceSparsity) { |
| double parameters[10]; |
| |
| double* block1 = parameters; |
| double* block2 = block1 + 1; |
| double* block3 = block2 + 2; |
| double* block4 = block3 + 3; |
| |
| ProblemImpl problem; |
| |
| // Add in random order |
| problem.AddParameterBlock(block1, 1); |
| problem.AddParameterBlock(block4, 4); |
| problem.AddParameterBlock(block3, 3); |
| problem.AddParameterBlock(block2, 2); |
| |
| // Sparsity pattern |
| // |
| // x 0 0 0 0 0 x x x x |
| // 0 x x x x x 0 0 0 0 |
| // 0 x x x x x 0 0 0 0 |
| // 0 0 0 x x x 0 0 0 0 |
| // 0 0 0 x x x 0 0 0 0 |
| // 0 0 0 x x x 0 0 0 0 |
| // 0 0 0 0 0 0 x x x x |
| // 0 0 0 0 0 0 x x x x |
| // 0 0 0 0 0 0 x x x x |
| // 0 0 0 0 0 0 x x x x |
| |
| int expected_rows[] = {0, 5, 10, 15, 18, 21, 24, 28, 32, 36, 40}; |
| int expected_cols[] = {0, 6, 7, 8, 9, |
| 1, 2, 3, 4, 5, |
| 1, 2, 3, 4, 5, |
| 3, 4, 5, |
| 3, 4, 5, |
| 3, 4, 5, |
| 6, 7, 8, 9, |
| 6, 7, 8, 9, |
| 6, 7, 8, 9, |
| 6, 7, 8, 9}; |
| |
| |
| vector<pair<const double*, const double*> > covariance_blocks; |
| covariance_blocks.push_back(make_pair(block1, block1)); |
| covariance_blocks.push_back(make_pair(block4, block4)); |
| covariance_blocks.push_back(make_pair(block2, block2)); |
| covariance_blocks.push_back(make_pair(block3, block3)); |
| covariance_blocks.push_back(make_pair(block2, block3)); |
| covariance_blocks.push_back(make_pair(block4, block1)); // reversed |
| |
| Covariance::Options options; |
| CovarianceImpl covariance_impl(options); |
| EXPECT_TRUE(covariance_impl |
| .ComputeCovarianceSparsity(covariance_blocks, &problem)); |
| |
| const CompressedRowSparseMatrix* crsm = covariance_impl.covariance_matrix(); |
| |
| EXPECT_EQ(crsm->num_rows(), 10); |
| EXPECT_EQ(crsm->num_cols(), 10); |
| EXPECT_EQ(crsm->num_nonzeros(), 40); |
| |
| const int* rows = crsm->rows(); |
| for (int r = 0; r < crsm->num_rows() + 1; ++r) { |
| EXPECT_EQ(rows[r], expected_rows[r]) |
| << r << " " |
| << rows[r] << " " |
| << expected_rows[r]; |
| } |
| |
| const int* cols = crsm->cols(); |
| for (int c = 0; c < crsm->num_nonzeros(); ++c) { |
| EXPECT_EQ(cols[c], expected_cols[c]) |
| << c << " " |
| << cols[c] << " " |
| << expected_cols[c]; |
| } |
| } |
| |
| |
| class UnaryCostFunction: public CostFunction { |
| public: |
| UnaryCostFunction(const int num_residuals, |
| const int32 parameter_block_size, |
| const double* jacobian) |
| : jacobian_(jacobian, jacobian + num_residuals * parameter_block_size) { |
| set_num_residuals(num_residuals); |
| mutable_parameter_block_sizes()->push_back(parameter_block_size); |
| } |
| |
| virtual bool Evaluate(double const* const* parameters, |
| double* residuals, |
| double** jacobians) const { |
| for (int i = 0; i < num_residuals(); ++i) { |
| residuals[i] = 1; |
| } |
| |
| if (jacobians == NULL) { |
| return true; |
| } |
| |
| if (jacobians[0] != NULL) { |
| copy(jacobian_.begin(), jacobian_.end(), jacobians[0]); |
| } |
| |
| return true; |
| } |
| |
| private: |
| vector<double> jacobian_; |
| }; |
| |
| |
| class BinaryCostFunction: public CostFunction { |
| public: |
| BinaryCostFunction(const int num_residuals, |
| const int32 parameter_block1_size, |
| const int32 parameter_block2_size, |
| const double* jacobian1, |
| const double* jacobian2) |
| : jacobian1_(jacobian1, |
| jacobian1 + num_residuals * parameter_block1_size), |
| jacobian2_(jacobian2, |
| jacobian2 + num_residuals * parameter_block2_size) { |
| set_num_residuals(num_residuals); |
| mutable_parameter_block_sizes()->push_back(parameter_block1_size); |
| mutable_parameter_block_sizes()->push_back(parameter_block2_size); |
| } |
| |
| virtual bool Evaluate(double const* const* parameters, |
| double* residuals, |
| double** jacobians) const { |
| for (int i = 0; i < num_residuals(); ++i) { |
| residuals[i] = 2; |
| } |
| |
| if (jacobians == NULL) { |
| return true; |
| } |
| |
| if (jacobians[0] != NULL) { |
| copy(jacobian1_.begin(), jacobian1_.end(), jacobians[0]); |
| } |
| |
| if (jacobians[1] != NULL) { |
| copy(jacobian2_.begin(), jacobian2_.end(), jacobians[1]); |
| } |
| |
| return true; |
| } |
| |
| private: |
| vector<double> jacobian1_; |
| vector<double> jacobian2_; |
| }; |
| |
| // x_plus_delta = delta * x; |
| class PolynomialParameterization : public LocalParameterization { |
| public: |
| virtual ~PolynomialParameterization() {} |
| |
| virtual bool Plus(const double* x, |
| const double* delta, |
| double* x_plus_delta) const { |
| x_plus_delta[0] = delta[0] * x[0]; |
| x_plus_delta[1] = delta[0] * x[1]; |
| return true; |
| } |
| |
| virtual bool ComputeJacobian(const double* x, double* jacobian) const { |
| jacobian[0] = x[0]; |
| jacobian[1] = x[1]; |
| return true; |
| } |
| |
| virtual int GlobalSize() const { return 2; } |
| virtual int LocalSize() const { return 1; } |
| }; |
| |
| class CovarianceTest : public ::testing::Test { |
| protected: |
| virtual void SetUp() { |
| double* x = parameters_; |
| double* y = x + 2; |
| double* z = y + 3; |
| |
| x[0] = 1; |
| x[1] = 1; |
| y[0] = 2; |
| y[1] = 2; |
| y[2] = 2; |
| z[0] = 3; |
| |
| { |
| double jacobian[] = { 1.0, 0.0, 0.0, 1.0}; |
| problem_.AddResidualBlock(new UnaryCostFunction(2, 2, jacobian), NULL, x); |
| } |
| |
| { |
| double jacobian[] = { 2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0 }; |
| problem_.AddResidualBlock(new UnaryCostFunction(3, 3, jacobian), NULL, y); |
| } |
| |
| { |
| double jacobian = 5.0; |
| problem_.AddResidualBlock(new UnaryCostFunction(1, 1, &jacobian), NULL, z); |
| } |
| |
| { |
| double jacobian1[] = { 1.0, 2.0, 3.0 }; |
| double jacobian2[] = { -5.0, -6.0 }; |
| problem_.AddResidualBlock( |
| new BinaryCostFunction(1, 3, 2, jacobian1, jacobian2), |
| NULL, |
| y, |
| x); |
| } |
| |
| { |
| double jacobian1[] = {2.0 }; |
| double jacobian2[] = { 3.0, -2.0 }; |
| problem_.AddResidualBlock( |
| new BinaryCostFunction(1, 1, 2, jacobian1, jacobian2), |
| NULL, |
| z, |
| x); |
| } |
| |
| all_covariance_blocks_.push_back(make_pair(x, x)); |
| all_covariance_blocks_.push_back(make_pair(y, y)); |
| all_covariance_blocks_.push_back(make_pair(z, z)); |
| all_covariance_blocks_.push_back(make_pair(x, y)); |
| all_covariance_blocks_.push_back(make_pair(x, z)); |
| all_covariance_blocks_.push_back(make_pair(y, z)); |
| |
| column_bounds_[x] = make_pair(0, 2); |
| column_bounds_[y] = make_pair(2, 5); |
| column_bounds_[z] = make_pair(5, 6); |
| } |
| |
| void ComputeAndCompareCovarianceBlocks(const Covariance::Options& options, |
| const double* expected_covariance) { |
| // Generate all possible combination of block pairs and check if the |
| // covariance computation is correct. |
| for (int i = 1; i <= 64; ++i) { |
| vector<pair<const double*, const double*> > covariance_blocks; |
| if (i & 1) { |
| covariance_blocks.push_back(all_covariance_blocks_[0]); |
| } |
| |
| if (i & 2) { |
| covariance_blocks.push_back(all_covariance_blocks_[1]); |
| } |
| |
| if (i & 4) { |
| covariance_blocks.push_back(all_covariance_blocks_[2]); |
| } |
| |
| if (i & 8) { |
| covariance_blocks.push_back(all_covariance_blocks_[3]); |
| } |
| |
| if (i & 16) { |
| covariance_blocks.push_back(all_covariance_blocks_[4]); |
| } |
| |
| if (i & 32) { |
| covariance_blocks.push_back(all_covariance_blocks_[5]); |
| } |
| |
| Covariance covariance(options); |
| EXPECT_TRUE(covariance.Compute(covariance_blocks, &problem_)); |
| |
| for (int i = 0; i < covariance_blocks.size(); ++i) { |
| const double* block1 = covariance_blocks[i].first; |
| const double* block2 = covariance_blocks[i].second; |
| // block1, block2 |
| GetCovarianceBlockAndCompare(block1, block2, covariance, expected_covariance); |
| // block2, block1 |
| GetCovarianceBlockAndCompare(block2, block1, covariance, expected_covariance); |
| } |
| } |
| } |
| |
| void GetCovarianceBlockAndCompare(const double* block1, |
| const double* block2, |
| const Covariance& covariance, |
| const double* expected_covariance) { |
| const int row_begin = FindOrDie(column_bounds_, block1).first; |
| const int row_end = FindOrDie(column_bounds_, block1).second; |
| const int col_begin = FindOrDie(column_bounds_, block2).first; |
| const int col_end = FindOrDie(column_bounds_, block2).second; |
| |
| Matrix actual(row_end - row_begin, col_end - col_begin); |
| EXPECT_TRUE(covariance.GetCovarianceBlock(block1, |
| block2, |
| actual.data())); |
| |
| ConstMatrixRef expected(expected_covariance, 6, 6); |
| double diff_norm = (expected.block(row_begin, |
| col_begin, |
| row_end - row_begin, |
| col_end - col_begin) - actual).norm(); |
| diff_norm /= (row_end - row_begin) * (col_end - col_begin); |
| |
| const double kTolerance = 1e-5; |
| EXPECT_NEAR(diff_norm, 0.0, kTolerance) |
| << "rows: " << row_begin << " " << row_end << " " |
| << "cols: " << col_begin << " " << col_end << " " |
| << "\n\n expected: \n " << expected.block(row_begin, |
| col_begin, |
| row_end - row_begin, |
| col_end - col_begin) |
| << "\n\n actual: \n " << actual |
| << "\n\n full expected: \n" << expected; |
| } |
| |
| double parameters_[10]; |
| Problem problem_; |
| vector<pair<const double*, const double*> > all_covariance_blocks_; |
| map<const double*, pair<int, int> > column_bounds_; |
| }; |
| |
| |
| TEST_F(CovarianceTest, NormalBehavior) { |
| // J |
| // |
| // 1 0 0 0 0 0 |
| // 0 1 0 0 0 0 |
| // 0 0 2 0 0 0 |
| // 0 0 0 2 0 0 |
| // 0 0 0 0 2 0 |
| // 0 0 0 0 0 5 |
| // -5 -6 1 2 3 0 |
| // 3 -2 0 0 0 2 |
| |
| // J'J |
| // |
| // 35 24 -5 -10 -15 6 |
| // 24 41 -6 -12 -18 -4 |
| // -5 -6 5 2 3 0 |
| // -10 -12 2 8 6 0 |
| // -15 -18 3 6 13 0 |
| // 6 -4 0 0 0 29 |
| |
| // inv(J'J) computed using octave. |
| double expected_covariance[] = { |
| 7.0747e-02, -8.4923e-03, 1.6821e-02, 3.3643e-02, 5.0464e-02, -1.5809e-02, // NOLINT |
| -8.4923e-03, 8.1352e-02, 2.4758e-02, 4.9517e-02, 7.4275e-02, 1.2978e-02, // NOLINT |
| 1.6821e-02, 2.4758e-02, 2.4904e-01, -1.9271e-03, -2.8906e-03, -6.5325e-05, // NOLINT |
| 3.3643e-02, 4.9517e-02, -1.9271e-03, 2.4615e-01, -5.7813e-03, -1.3065e-04, // NOLINT |
| 5.0464e-02, 7.4275e-02, -2.8906e-03, -5.7813e-03, 2.4133e-01, -1.9598e-04, // NOLINT |
| -1.5809e-02, 1.2978e-02, -6.5325e-05, -1.3065e-04, -1.9598e-04, 3.9544e-02, // NOLINT |
| }; |
| |
| Covariance::Options options; |
| |
| #ifndef CERES_NO_SUITESPARSE |
| options.algorithm_type = SPARSE_CHOLESKY; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| |
| options.algorithm_type = SPARSE_QR; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| #endif |
| |
| options.algorithm_type = DENSE_SVD; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| } |
| |
| #ifdef CERES_USE_OPENMP |
| |
| TEST_F(CovarianceTest, ThreadedNormalBehavior) { |
| // J |
| // |
| // 1 0 0 0 0 0 |
| // 0 1 0 0 0 0 |
| // 0 0 2 0 0 0 |
| // 0 0 0 2 0 0 |
| // 0 0 0 0 2 0 |
| // 0 0 0 0 0 5 |
| // -5 -6 1 2 3 0 |
| // 3 -2 0 0 0 2 |
| |
| // J'J |
| // |
| // 35 24 -5 -10 -15 6 |
| // 24 41 -6 -12 -18 -4 |
| // -5 -6 5 2 3 0 |
| // -10 -12 2 8 6 0 |
| // -15 -18 3 6 13 0 |
| // 6 -4 0 0 0 29 |
| |
| // inv(J'J) computed using octave. |
| double expected_covariance[] = { |
| 7.0747e-02, -8.4923e-03, 1.6821e-02, 3.3643e-02, 5.0464e-02, -1.5809e-02, // NOLINT |
| -8.4923e-03, 8.1352e-02, 2.4758e-02, 4.9517e-02, 7.4275e-02, 1.2978e-02, // NOLINT |
| 1.6821e-02, 2.4758e-02, 2.4904e-01, -1.9271e-03, -2.8906e-03, -6.5325e-05, // NOLINT |
| 3.3643e-02, 4.9517e-02, -1.9271e-03, 2.4615e-01, -5.7813e-03, -1.3065e-04, // NOLINT |
| 5.0464e-02, 7.4275e-02, -2.8906e-03, -5.7813e-03, 2.4133e-01, -1.9598e-04, // NOLINT |
| -1.5809e-02, 1.2978e-02, -6.5325e-05, -1.3065e-04, -1.9598e-04, 3.9544e-02, // NOLINT |
| }; |
| |
| Covariance::Options options; |
| options.num_threads = 4; |
| |
| #ifndef CERES_NO_SUITESPARSE |
| options.algorithm_type = SPARSE_CHOLESKY; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| |
| options.algorithm_type = SPARSE_QR; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| #endif |
| |
| options.algorithm_type = DENSE_SVD; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| } |
| |
| #endif // CERES_USE_OPENMP |
| |
| TEST_F(CovarianceTest, ConstantParameterBlock) { |
| problem_.SetParameterBlockConstant(parameters_); |
| |
| // J |
| // |
| // 0 0 0 0 0 0 |
| // 0 0 0 0 0 0 |
| // 0 0 2 0 0 0 |
| // 0 0 0 2 0 0 |
| // 0 0 0 0 2 0 |
| // 0 0 0 0 0 5 |
| // 0 0 1 2 3 0 |
| // 0 0 0 0 0 2 |
| |
| // J'J |
| // |
| // 0 0 0 0 0 0 |
| // 0 0 0 0 0 0 |
| // 0 0 5 2 3 0 |
| // 0 0 2 8 6 0 |
| // 0 0 3 6 13 0 |
| // 0 0 0 0 0 29 |
| |
| // pinv(J'J) computed using octave. |
| double expected_covariance[] = { |
| 0, 0, 0, 0, 0, 0, // NOLINT |
| 0, 0, 0, 0, 0, 0, // NOLINT |
| 0, 0, 0.23611, -0.02778, -0.04167, -0.00000, // NOLINT |
| 0, 0, -0.02778, 0.19444, -0.08333, -0.00000, // NOLINT |
| 0, 0, -0.04167, -0.08333, 0.12500, -0.00000, // NOLINT |
| 0, 0, -0.00000, -0.00000, -0.00000, 0.03448 // NOLINT |
| }; |
| |
| Covariance::Options options; |
| |
| #ifndef CERES_NO_SUITESPARSE |
| options.algorithm_type = SPARSE_CHOLESKY; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| |
| options.algorithm_type = SPARSE_QR; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| #endif |
| |
| options.algorithm_type = DENSE_SVD; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| } |
| |
| TEST_F(CovarianceTest, LocalParameterization) { |
| double* x = parameters_; |
| double* y = x + 2; |
| |
| problem_.SetParameterization(x, new PolynomialParameterization); |
| |
| vector<int> subset; |
| subset.push_back(2); |
| problem_.SetParameterization(y, new SubsetParameterization(3, subset)); |
| |
| // Raw Jacobian: J |
| // |
| // 1 0 0 0 0 0 |
| // 0 1 0 0 0 0 |
| // 0 0 2 0 0 0 |
| // 0 0 0 2 0 0 |
| // 0 0 0 0 0 0 |
| // 0 0 0 0 0 5 |
| // -5 -6 1 2 0 0 |
| // 3 -2 0 0 0 2 |
| |
| // Global to local jacobian: A |
| // |
| // |
| // 1 0 0 0 0 |
| // 1 0 0 0 0 |
| // 0 1 0 0 0 |
| // 0 0 1 0 0 |
| // 0 0 0 1 0 |
| // 0 0 0 0 1 |
| |
| // A * pinv((J*A)'*(J*A)) * A' |
| // Computed using octave. |
| double expected_covariance[] = { |
| 0.01766, 0.01766, 0.02158, 0.04316, 0.00000, -0.00122, |
| 0.01766, 0.01766, 0.02158, 0.04316, 0.00000, -0.00122, |
| 0.02158, 0.02158, 0.24860, -0.00281, 0.00000, -0.00149, |
| 0.04316, 0.04316, -0.00281, 0.24439, 0.00000, -0.00298, |
| 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, |
| -0.00122, -0.00122, -0.00149, -0.00298, 0.00000, 0.03457 |
| }; |
| |
| Covariance::Options options; |
| |
| #ifndef CERES_NO_SUITESPARSE |
| options.algorithm_type = SPARSE_CHOLESKY; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| |
| options.algorithm_type = SPARSE_QR; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| #endif |
| |
| options.algorithm_type = DENSE_SVD; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| } |
| |
| |
| TEST_F(CovarianceTest, TruncatedRank) { |
| // J |
| // |
| // 1 0 0 0 0 0 |
| // 0 1 0 0 0 0 |
| // 0 0 2 0 0 0 |
| // 0 0 0 2 0 0 |
| // 0 0 0 0 2 0 |
| // 0 0 0 0 0 5 |
| // -5 -6 1 2 3 0 |
| // 3 -2 0 0 0 2 |
| |
| // J'J |
| // |
| // 35 24 -5 -10 -15 6 |
| // 24 41 -6 -12 -18 -4 |
| // -5 -6 5 2 3 0 |
| // -10 -12 2 8 6 0 |
| // -15 -18 3 6 13 0 |
| // 6 -4 0 0 0 29 |
| |
| // 3.4142 is the smallest eigen value of J'J. The following matrix |
| // was obtained by dropping the eigenvector corresponding to this |
| // eigenvalue. |
| double expected_covariance[] = { |
| 5.4135e-02, -3.5121e-02, 1.7257e-04, 3.4514e-04, 5.1771e-04, -1.6076e-02, |
| -3.5121e-02, 3.8667e-02, -1.9288e-03, -3.8576e-03, -5.7864e-03, 1.2549e-02, |
| 1.7257e-04, -1.9288e-03, 2.3235e-01, -3.5297e-02, -5.2946e-02, -3.3329e-04, |
| 3.4514e-04, -3.8576e-03, -3.5297e-02, 1.7941e-01, -1.0589e-01, -6.6659e-04, |
| 5.1771e-04, -5.7864e-03, -5.2946e-02, -1.0589e-01, 9.1162e-02, -9.9988e-04, |
| -1.6076e-02, 1.2549e-02, -3.3329e-04, -6.6659e-04, -9.9988e-04, 3.9539e-02 |
| }; |
| |
| |
| { |
| Covariance::Options options; |
| options.algorithm_type = DENSE_SVD; |
| // Force dropping of the smallest eigenvector. |
| options.null_space_rank = 1; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| } |
| |
| { |
| Covariance::Options options; |
| options.algorithm_type = DENSE_SVD; |
| // Force dropping of the smallest eigenvector via the ratio but |
| // automatic truncation. |
| options.min_reciprocal_condition_number = 0.044494; |
| options.null_space_rank = -1; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| } |
| } |
| |
| class RankDeficientCovarianceTest : public CovarianceTest { |
| protected: |
| virtual void SetUp() { |
| double* x = parameters_; |
| double* y = x + 2; |
| double* z = y + 3; |
| |
| { |
| double jacobian[] = { 1.0, 0.0, 0.0, 1.0}; |
| problem_.AddResidualBlock(new UnaryCostFunction(2, 2, jacobian), NULL, x); |
| } |
| |
| { |
| double jacobian[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }; |
| problem_.AddResidualBlock(new UnaryCostFunction(3, 3, jacobian), NULL, y); |
| } |
| |
| { |
| double jacobian = 5.0; |
| problem_.AddResidualBlock(new UnaryCostFunction(1, 1, &jacobian), NULL, z); |
| } |
| |
| { |
| double jacobian1[] = { 0.0, 0.0, 0.0 }; |
| double jacobian2[] = { -5.0, -6.0 }; |
| problem_.AddResidualBlock( |
| new BinaryCostFunction(1, 3, 2, jacobian1, jacobian2), |
| NULL, |
| y, |
| x); |
| } |
| |
| { |
| double jacobian1[] = {2.0 }; |
| double jacobian2[] = { 3.0, -2.0 }; |
| problem_.AddResidualBlock( |
| new BinaryCostFunction(1, 1, 2, jacobian1, jacobian2), |
| NULL, |
| z, |
| x); |
| } |
| |
| all_covariance_blocks_.push_back(make_pair(x, x)); |
| all_covariance_blocks_.push_back(make_pair(y, y)); |
| all_covariance_blocks_.push_back(make_pair(z, z)); |
| all_covariance_blocks_.push_back(make_pair(x, y)); |
| all_covariance_blocks_.push_back(make_pair(x, z)); |
| all_covariance_blocks_.push_back(make_pair(y, z)); |
| |
| column_bounds_[x] = make_pair(0, 2); |
| column_bounds_[y] = make_pair(2, 5); |
| column_bounds_[z] = make_pair(5, 6); |
| } |
| }; |
| |
| TEST_F(RankDeficientCovarianceTest, AutomaticTruncation) { |
| // J |
| // |
| // 1 0 0 0 0 0 |
| // 0 1 0 0 0 0 |
| // 0 0 0 0 0 0 |
| // 0 0 0 0 0 0 |
| // 0 0 0 0 0 0 |
| // 0 0 0 0 0 5 |
| // -5 -6 0 0 0 0 |
| // 3 -2 0 0 0 2 |
| |
| // J'J |
| // |
| // 35 24 0 0 0 6 |
| // 24 41 0 0 0 -4 |
| // 0 0 0 0 0 0 |
| // 0 0 0 0 0 0 |
| // 0 0 0 0 0 0 |
| // 6 -4 0 0 0 29 |
| |
| // pinv(J'J) computed using octave. |
| double expected_covariance[] = { |
| 0.053998, -0.033145, 0.000000, 0.000000, 0.000000, -0.015744, |
| -0.033145, 0.045067, 0.000000, 0.000000, 0.000000, 0.013074, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, 0.000000, |
| -0.015744, 0.013074, 0.000000, 0.000000, 0.000000, 0.039543 |
| }; |
| |
| Covariance::Options options; |
| options.algorithm_type = DENSE_SVD; |
| options.null_space_rank = -1; |
| ComputeAndCompareCovarianceBlocks(options, expected_covariance); |
| } |
| |
| class LargeScaleCovarianceTest : public ::testing::Test { |
| protected: |
| virtual void SetUp() { |
| num_parameter_blocks_ = 2000; |
| parameter_block_size_ = 5; |
| parameters_.reset(new double[parameter_block_size_ * num_parameter_blocks_]); |
| |
| Matrix jacobian(parameter_block_size_, parameter_block_size_); |
| for (int i = 0; i < num_parameter_blocks_; ++i) { |
| jacobian.setIdentity(); |
| jacobian *= (i + 1); |
| |
| double* block_i = parameters_.get() + i * parameter_block_size_; |
| problem_.AddResidualBlock(new UnaryCostFunction(parameter_block_size_, |
| parameter_block_size_, |
| jacobian.data()), |
| NULL, |
| block_i); |
| for (int j = i; j < num_parameter_blocks_; ++j) { |
| double* block_j = parameters_.get() + j * parameter_block_size_; |
| all_covariance_blocks_.push_back(make_pair(block_i, block_j)); |
| } |
| } |
| } |
| |
| void ComputeAndCompare(CovarianceAlgorithmType algorithm_type, |
| int num_threads) { |
| Covariance::Options options; |
| options.algorithm_type = algorithm_type; |
| options.num_threads = num_threads; |
| Covariance covariance(options); |
| EXPECT_TRUE(covariance.Compute(all_covariance_blocks_, &problem_)); |
| |
| Matrix expected(parameter_block_size_, parameter_block_size_); |
| Matrix actual(parameter_block_size_, parameter_block_size_); |
| const double kTolerance = 1e-16; |
| |
| for (int i = 0; i < num_parameter_blocks_; ++i) { |
| expected.setIdentity(); |
| expected /= (i + 1.0) * (i + 1.0); |
| |
| double* block_i = parameters_.get() + i * parameter_block_size_; |
| covariance.GetCovarianceBlock(block_i, block_i, actual.data()); |
| EXPECT_NEAR((expected - actual).norm(), 0.0, kTolerance) |
| << "block: " << i << ", " << i << "\n" |
| << "expected: \n" << expected << "\n" |
| << "actual: \n" << actual; |
| |
| expected.setZero(); |
| for (int j = i + 1; j < num_parameter_blocks_; ++j) { |
| double* block_j = parameters_.get() + j * parameter_block_size_; |
| covariance.GetCovarianceBlock(block_i, block_j, actual.data()); |
| EXPECT_NEAR((expected - actual).norm(), 0.0, kTolerance) |
| << "block: " << i << ", " << j << "\n" |
| << "expected: \n" << expected << "\n" |
| << "actual: \n" << actual; |
| } |
| } |
| } |
| |
| scoped_array<double> parameters_; |
| int parameter_block_size_; |
| int num_parameter_blocks_; |
| |
| Problem problem_; |
| vector<pair<const double*, const double*> > all_covariance_blocks_; |
| }; |
| |
| #if !defined(CERES_NO_SUITESPARSE) && defined(CERES_USE_OPENMP) |
| |
| TEST_F(LargeScaleCovarianceTest, Parallel) { |
| ComputeAndCompare(SPARSE_CHOLESKY, 4); |
| ComputeAndCompare(SPARSE_QR, 4); |
| } |
| |
| #endif // !defined(CERES_NO_SUITESPARSE) && defined(CERES_USE_OPENMP) |
| |
| } // namespace internal |
| } // namespace ceres |
