mirror of
https://github.com/ceres-solver/ceres-solver.git
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Keir Mierle
7492b0d8de
Since Ceres is moving to using GitHub for issues, and the Google Code URL in the current copyright header will soon become invalid, update all the headers. Change-Id: I1fce70375d1bcf098591f07b4d8f01a5c1e0789c
906 lines
29 KiB
C++
906 lines
29 KiB
C++
// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2015 Google Inc. All rights reserved.
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// http://ceres-solver.org/
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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//
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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#include "ceres/covariance.h"
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#include <algorithm>
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#include <cmath>
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#include <map>
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#include <utility>
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#include "ceres/compressed_row_sparse_matrix.h"
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#include "ceres/cost_function.h"
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#include "ceres/covariance_impl.h"
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#include "ceres/local_parameterization.h"
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#include "ceres/map_util.h"
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#include "ceres/problem_impl.h"
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#include "gtest/gtest.h"
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namespace ceres {
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namespace internal {
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using std::make_pair;
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using std::map;
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using std::pair;
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using std::vector;
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TEST(CovarianceImpl, ComputeCovarianceSparsity) {
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double parameters[10];
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double* block1 = parameters;
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double* block2 = block1 + 1;
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double* block3 = block2 + 2;
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double* block4 = block3 + 3;
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ProblemImpl problem;
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// Add in random order
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problem.AddParameterBlock(block1, 1);
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problem.AddParameterBlock(block4, 4);
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problem.AddParameterBlock(block3, 3);
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problem.AddParameterBlock(block2, 2);
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// Sparsity pattern
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//
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// x 0 0 0 0 0 x x x x
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// 0 x x x x x 0 0 0 0
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// 0 x x x x x 0 0 0 0
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// 0 0 0 x x x 0 0 0 0
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// 0 0 0 x x x 0 0 0 0
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// 0 0 0 x x x 0 0 0 0
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// 0 0 0 0 0 0 x x x x
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// 0 0 0 0 0 0 x x x x
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// 0 0 0 0 0 0 x x x x
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// 0 0 0 0 0 0 x x x x
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int expected_rows[] = {0, 5, 10, 15, 18, 21, 24, 28, 32, 36, 40};
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int expected_cols[] = {0, 6, 7, 8, 9,
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1, 2, 3, 4, 5,
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1, 2, 3, 4, 5,
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3, 4, 5,
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3, 4, 5,
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3, 4, 5,
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6, 7, 8, 9,
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6, 7, 8, 9,
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6, 7, 8, 9,
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6, 7, 8, 9};
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vector<pair<const double*, const double*> > covariance_blocks;
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covariance_blocks.push_back(make_pair(block1, block1));
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covariance_blocks.push_back(make_pair(block4, block4));
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covariance_blocks.push_back(make_pair(block2, block2));
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covariance_blocks.push_back(make_pair(block3, block3));
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covariance_blocks.push_back(make_pair(block2, block3));
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covariance_blocks.push_back(make_pair(block4, block1)); // reversed
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Covariance::Options options;
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CovarianceImpl covariance_impl(options);
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EXPECT_TRUE(covariance_impl
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.ComputeCovarianceSparsity(covariance_blocks, &problem));
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const CompressedRowSparseMatrix* crsm = covariance_impl.covariance_matrix();
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EXPECT_EQ(crsm->num_rows(), 10);
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EXPECT_EQ(crsm->num_cols(), 10);
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EXPECT_EQ(crsm->num_nonzeros(), 40);
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const int* rows = crsm->rows();
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for (int r = 0; r < crsm->num_rows() + 1; ++r) {
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EXPECT_EQ(rows[r], expected_rows[r])
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<< r << " "
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<< rows[r] << " "
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<< expected_rows[r];
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}
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const int* cols = crsm->cols();
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for (int c = 0; c < crsm->num_nonzeros(); ++c) {
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EXPECT_EQ(cols[c], expected_cols[c])
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<< c << " "
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<< cols[c] << " "
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<< expected_cols[c];
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}
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}
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class UnaryCostFunction: public CostFunction {
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public:
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UnaryCostFunction(const int num_residuals,
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const int32 parameter_block_size,
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const double* jacobian)
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: jacobian_(jacobian, jacobian + num_residuals * parameter_block_size) {
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set_num_residuals(num_residuals);
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mutable_parameter_block_sizes()->push_back(parameter_block_size);
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}
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virtual bool Evaluate(double const* const* parameters,
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double* residuals,
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double** jacobians) const {
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for (int i = 0; i < num_residuals(); ++i) {
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residuals[i] = 1;
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}
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if (jacobians == NULL) {
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return true;
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}
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if (jacobians[0] != NULL) {
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copy(jacobian_.begin(), jacobian_.end(), jacobians[0]);
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}
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return true;
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}
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private:
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vector<double> jacobian_;
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};
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class BinaryCostFunction: public CostFunction {
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public:
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BinaryCostFunction(const int num_residuals,
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const int32 parameter_block1_size,
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const int32 parameter_block2_size,
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const double* jacobian1,
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const double* jacobian2)
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: jacobian1_(jacobian1,
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jacobian1 + num_residuals * parameter_block1_size),
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jacobian2_(jacobian2,
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jacobian2 + num_residuals * parameter_block2_size) {
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set_num_residuals(num_residuals);
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mutable_parameter_block_sizes()->push_back(parameter_block1_size);
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mutable_parameter_block_sizes()->push_back(parameter_block2_size);
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}
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virtual bool Evaluate(double const* const* parameters,
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double* residuals,
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double** jacobians) const {
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for (int i = 0; i < num_residuals(); ++i) {
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residuals[i] = 2;
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}
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if (jacobians == NULL) {
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return true;
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}
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if (jacobians[0] != NULL) {
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copy(jacobian1_.begin(), jacobian1_.end(), jacobians[0]);
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}
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if (jacobians[1] != NULL) {
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copy(jacobian2_.begin(), jacobian2_.end(), jacobians[1]);
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}
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return true;
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}
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private:
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vector<double> jacobian1_;
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vector<double> jacobian2_;
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};
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// x_plus_delta = delta * x;
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class PolynomialParameterization : public LocalParameterization {
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public:
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virtual ~PolynomialParameterization() {}
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virtual bool Plus(const double* x,
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const double* delta,
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double* x_plus_delta) const {
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x_plus_delta[0] = delta[0] * x[0];
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x_plus_delta[1] = delta[0] * x[1];
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return true;
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}
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virtual bool ComputeJacobian(const double* x, double* jacobian) const {
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jacobian[0] = x[0];
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jacobian[1] = x[1];
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return true;
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}
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virtual int GlobalSize() const { return 2; }
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virtual int LocalSize() const { return 1; }
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};
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class CovarianceTest : public ::testing::Test {
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protected:
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typedef map<const double*, pair<int, int> > BoundsMap;
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virtual void SetUp() {
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double* x = parameters_;
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double* y = x + 2;
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double* z = y + 3;
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x[0] = 1;
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x[1] = 1;
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y[0] = 2;
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y[1] = 2;
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y[2] = 2;
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z[0] = 3;
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{
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double jacobian[] = { 1.0, 0.0, 0.0, 1.0};
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problem_.AddResidualBlock(new UnaryCostFunction(2, 2, jacobian), NULL, x);
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}
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{
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double jacobian[] = { 2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0 };
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problem_.AddResidualBlock(new UnaryCostFunction(3, 3, jacobian), NULL, y);
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}
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{
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double jacobian = 5.0;
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problem_.AddResidualBlock(new UnaryCostFunction(1, 1, &jacobian),
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NULL,
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z);
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}
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{
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double jacobian1[] = { 1.0, 2.0, 3.0 };
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double jacobian2[] = { -5.0, -6.0 };
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problem_.AddResidualBlock(
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new BinaryCostFunction(1, 3, 2, jacobian1, jacobian2),
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NULL,
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y,
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x);
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}
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{
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double jacobian1[] = {2.0 };
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double jacobian2[] = { 3.0, -2.0 };
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problem_.AddResidualBlock(
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new BinaryCostFunction(1, 1, 2, jacobian1, jacobian2),
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NULL,
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z,
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x);
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}
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all_covariance_blocks_.push_back(make_pair(x, x));
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all_covariance_blocks_.push_back(make_pair(y, y));
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all_covariance_blocks_.push_back(make_pair(z, z));
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all_covariance_blocks_.push_back(make_pair(x, y));
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all_covariance_blocks_.push_back(make_pair(x, z));
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all_covariance_blocks_.push_back(make_pair(y, z));
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column_bounds_[x] = make_pair(0, 2);
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column_bounds_[y] = make_pair(2, 5);
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column_bounds_[z] = make_pair(5, 6);
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}
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// Computes covariance in ambient space.
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void ComputeAndCompareCovarianceBlocks(const Covariance::Options& options,
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const double* expected_covariance) {
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ComputeAndCompareCovarianceBlocksInTangentOrAmbientSpace(
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options,
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true, // ambient
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expected_covariance);
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}
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// Computes covariance in tangent space.
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void ComputeAndCompareCovarianceBlocksInTangentSpace(
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const Covariance::Options& options,
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const double* expected_covariance) {
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ComputeAndCompareCovarianceBlocksInTangentOrAmbientSpace(
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options,
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false, // tangent
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expected_covariance);
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}
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void ComputeAndCompareCovarianceBlocksInTangentOrAmbientSpace(
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const Covariance::Options& options,
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bool lift_covariance_to_ambient_space,
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const double* expected_covariance) {
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// Generate all possible combination of block pairs and check if the
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// covariance computation is correct.
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for (int i = 1; i <= 64; ++i) {
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vector<pair<const double*, const double*> > covariance_blocks;
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if (i & 1) {
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covariance_blocks.push_back(all_covariance_blocks_[0]);
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}
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if (i & 2) {
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covariance_blocks.push_back(all_covariance_blocks_[1]);
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}
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if (i & 4) {
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covariance_blocks.push_back(all_covariance_blocks_[2]);
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}
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if (i & 8) {
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covariance_blocks.push_back(all_covariance_blocks_[3]);
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}
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if (i & 16) {
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covariance_blocks.push_back(all_covariance_blocks_[4]);
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}
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if (i & 32) {
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covariance_blocks.push_back(all_covariance_blocks_[5]);
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}
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Covariance covariance(options);
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EXPECT_TRUE(covariance.Compute(covariance_blocks, &problem_));
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for (int i = 0; i < covariance_blocks.size(); ++i) {
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const double* block1 = covariance_blocks[i].first;
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const double* block2 = covariance_blocks[i].second;
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// block1, block2
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GetCovarianceBlockAndCompare(block1,
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block2,
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lift_covariance_to_ambient_space,
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covariance,
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expected_covariance);
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// block2, block1
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GetCovarianceBlockAndCompare(block2,
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block1,
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lift_covariance_to_ambient_space,
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covariance,
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expected_covariance);
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}
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}
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}
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void GetCovarianceBlockAndCompare(const double* block1,
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const double* block2,
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bool lift_covariance_to_ambient_space,
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const Covariance& covariance,
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const double* expected_covariance) {
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const BoundsMap& column_bounds = lift_covariance_to_ambient_space ?
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column_bounds_ : local_column_bounds_;
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const int row_begin = FindOrDie(column_bounds, block1).first;
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const int row_end = FindOrDie(column_bounds, block1).second;
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const int col_begin = FindOrDie(column_bounds, block2).first;
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const int col_end = FindOrDie(column_bounds, block2).second;
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Matrix actual(row_end - row_begin, col_end - col_begin);
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if (lift_covariance_to_ambient_space) {
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EXPECT_TRUE(covariance.GetCovarianceBlock(block1,
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block2,
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actual.data()));
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} else {
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EXPECT_TRUE(covariance.GetCovarianceBlockInTangentSpace(block1,
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block2,
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actual.data()));
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}
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int dof = 0; // degrees of freedom = sum of LocalSize()s
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for (BoundsMap::const_iterator iter = column_bounds.begin();
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iter != column_bounds.end(); ++iter) {
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dof = std::max(dof, iter->second.second);
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}
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ConstMatrixRef expected(expected_covariance, dof, dof);
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double diff_norm = (expected.block(row_begin,
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col_begin,
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row_end - row_begin,
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col_end - col_begin) - actual).norm();
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diff_norm /= (row_end - row_begin) * (col_end - col_begin);
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const double kTolerance = 1e-5;
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EXPECT_NEAR(diff_norm, 0.0, kTolerance)
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<< "rows: " << row_begin << " " << row_end << " "
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<< "cols: " << col_begin << " " << col_end << " "
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<< "\n\n expected: \n " << expected.block(row_begin,
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col_begin,
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row_end - row_begin,
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col_end - col_begin)
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<< "\n\n actual: \n " << actual
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<< "\n\n full expected: \n" << expected;
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}
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double parameters_[6];
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Problem problem_;
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vector<pair<const double*, const double*> > all_covariance_blocks_;
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BoundsMap column_bounds_;
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BoundsMap local_column_bounds_;
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};
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TEST_F(CovarianceTest, NormalBehavior) {
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// J
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//
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// 1 0 0 0 0 0
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// 0 1 0 0 0 0
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// 0 0 2 0 0 0
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// 0 0 0 2 0 0
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// 0 0 0 0 2 0
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// 0 0 0 0 0 5
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// -5 -6 1 2 3 0
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// 3 -2 0 0 0 2
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// J'J
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//
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// 35 24 -5 -10 -15 6
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// 24 41 -6 -12 -18 -4
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// -5 -6 5 2 3 0
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// -10 -12 2 8 6 0
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// -15 -18 3 6 13 0
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// 6 -4 0 0 0 29
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// inv(J'J) computed using octave.
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double expected_covariance[] = {
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7.0747e-02, -8.4923e-03, 1.6821e-02, 3.3643e-02, 5.0464e-02, -1.5809e-02, // NOLINT
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-8.4923e-03, 8.1352e-02, 2.4758e-02, 4.9517e-02, 7.4275e-02, 1.2978e-02, // NOLINT
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1.6821e-02, 2.4758e-02, 2.4904e-01, -1.9271e-03, -2.8906e-03, -6.5325e-05, // NOLINT
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3.3643e-02, 4.9517e-02, -1.9271e-03, 2.4615e-01, -5.7813e-03, -1.3065e-04, // NOLINT
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5.0464e-02, 7.4275e-02, -2.8906e-03, -5.7813e-03, 2.4133e-01, -1.9598e-04, // NOLINT
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-1.5809e-02, 1.2978e-02, -6.5325e-05, -1.3065e-04, -1.9598e-04, 3.9544e-02, // NOLINT
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};
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Covariance::Options options;
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#ifndef CERES_NO_SUITESPARSE
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options.algorithm_type = SUITE_SPARSE_QR;
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ComputeAndCompareCovarianceBlocks(options, expected_covariance);
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#endif
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options.algorithm_type = DENSE_SVD;
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ComputeAndCompareCovarianceBlocks(options, expected_covariance);
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options.algorithm_type = EIGEN_SPARSE_QR;
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ComputeAndCompareCovarianceBlocks(options, expected_covariance);
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}
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#ifdef CERES_USE_OPENMP
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TEST_F(CovarianceTest, ThreadedNormalBehavior) {
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// J
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//
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// 1 0 0 0 0 0
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// 0 1 0 0 0 0
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// 0 0 2 0 0 0
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// 0 0 0 2 0 0
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// 0 0 0 0 2 0
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// 0 0 0 0 0 5
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// -5 -6 1 2 3 0
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// 3 -2 0 0 0 2
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// 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 = SUITE_SPARSE_QR;
|
|
ComputeAndCompareCovarianceBlocks(options, expected_covariance);
|
|
#endif
|
|
|
|
options.algorithm_type = DENSE_SVD;
|
|
ComputeAndCompareCovarianceBlocks(options, expected_covariance);
|
|
|
|
options.algorithm_type = EIGEN_SPARSE_QR;
|
|
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 = SUITE_SPARSE_QR;
|
|
ComputeAndCompareCovarianceBlocks(options, expected_covariance);
|
|
#endif
|
|
|
|
options.algorithm_type = DENSE_SVD;
|
|
ComputeAndCompareCovarianceBlocks(options, expected_covariance);
|
|
|
|
options.algorithm_type = EIGEN_SPARSE_QR;
|
|
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 2 0
|
|
// 0 0 0 0 0 5
|
|
// -5 -6 1 2 3 0
|
|
// 3 -2 0 0 0 2
|
|
|
|
// Local to global jacobian: A
|
|
//
|
|
// 1 0 0 0
|
|
// 1 0 0 0
|
|
// 0 1 0 0
|
|
// 0 0 1 0
|
|
// 0 0 0 0
|
|
// 0 0 0 1
|
|
|
|
// A * inv((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 = SUITE_SPARSE_QR;
|
|
ComputeAndCompareCovarianceBlocks(options, expected_covariance);
|
|
#endif
|
|
|
|
options.algorithm_type = DENSE_SVD;
|
|
ComputeAndCompareCovarianceBlocks(options, expected_covariance);
|
|
|
|
options.algorithm_type = EIGEN_SPARSE_QR;
|
|
ComputeAndCompareCovarianceBlocks(options, expected_covariance);
|
|
}
|
|
|
|
TEST_F(CovarianceTest, LocalParameterizationInTangentSpace) {
|
|
double* x = parameters_;
|
|
double* y = x + 2;
|
|
double* z = y + 3;
|
|
|
|
problem_.SetParameterization(x, new PolynomialParameterization);
|
|
|
|
vector<int> subset;
|
|
subset.push_back(2);
|
|
problem_.SetParameterization(y, new SubsetParameterization(3, subset));
|
|
|
|
local_column_bounds_[x] = make_pair(0, 1);
|
|
local_column_bounds_[y] = make_pair(1, 3);
|
|
local_column_bounds_[z] = make_pair(3, 4);
|
|
|
|
// 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 2 0
|
|
// 0 0 0 0 0 5
|
|
// -5 -6 1 2 3 0
|
|
// 3 -2 0 0 0 2
|
|
|
|
// Local to global jacobian: A
|
|
//
|
|
// 1 0 0 0
|
|
// 1 0 0 0
|
|
// 0 1 0 0
|
|
// 0 0 1 0
|
|
// 0 0 0 0
|
|
// 0 0 0 1
|
|
|
|
// inv((J*A)'*(J*A))
|
|
// Computed using octave.
|
|
double expected_covariance[] = {
|
|
0.01766, 0.02158, 0.04316, -0.00122,
|
|
0.02158, 0.24860, -0.00281, -0.00149,
|
|
0.04316, -0.00281, 0.24439, -0.00298,
|
|
-0.00122, -0.00149, -0.00298, 0.03457 // NOLINT
|
|
};
|
|
|
|
Covariance::Options options;
|
|
|
|
#ifndef CERES_NO_SUITESPARSE
|
|
options.algorithm_type = SUITE_SPARSE_QR;
|
|
ComputeAndCompareCovarianceBlocksInTangentSpace(options, expected_covariance);
|
|
#endif
|
|
|
|
options.algorithm_type = DENSE_SVD;
|
|
ComputeAndCompareCovarianceBlocksInTangentSpace(options, expected_covariance);
|
|
|
|
options.algorithm_type = EIGEN_SPARSE_QR;
|
|
ComputeAndCompareCovarianceBlocksInTangentSpace(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, // NOLINT
|
|
-3.5121e-02, 3.8667e-02, -1.9288e-03, -3.8576e-03, -5.7864e-03, 1.2549e-02, // NOLINT
|
|
1.7257e-04, -1.9288e-03, 2.3235e-01, -3.5297e-02, -5.2946e-02, -3.3329e-04, // NOLINT
|
|
3.4514e-04, -3.8576e-03, -3.5297e-02, 1.7941e-01, -1.0589e-01, -6.6659e-04, // NOLINT
|
|
5.1771e-04, -5.7864e-03, -5.2946e-02, -1.0589e-01, 9.1162e-02, -9.9988e-04, // NOLINT
|
|
-1.6076e-02, 1.2549e-02, -3.3329e-04, -6.6659e-04, -9.9988e-04, 3.9539e-02 // NOLINT
|
|
};
|
|
|
|
|
|
{
|
|
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(SUITE_SPARSE_QR, 4);
|
|
}
|
|
|
|
#endif // !defined(CERES_NO_SUITESPARSE) && defined(CERES_USE_OPENMP)
|
|
|
|
} // namespace internal
|
|
} // namespace ceres
|