288 lines
12 KiB
C++
288 lines
12 KiB
C++
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// 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: moll.markus@arcor.de (Markus Moll)
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#include <limits>
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#include "ceres/internal/eigen.h"
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#include "ceres/internal/scoped_ptr.h"
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#include "ceres/dense_qr_solver.h"
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#include "ceres/dogleg_strategy.h"
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#include "ceres/linear_solver.h"
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#include "ceres/trust_region_strategy.h"
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#include "glog/logging.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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namespace {
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class Fixture : public testing::Test {
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protected:
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scoped_ptr<DenseSparseMatrix> jacobian_;
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Vector residual_;
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Vector x_;
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TrustRegionStrategy::Options options_;
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};
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// A test problem where
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//
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// J^T J = Q diag([1 2 4 8 16 32]) Q^T
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//
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// where Q is a randomly chosen orthonormal basis of R^6.
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// The residual is chosen so that the minimum of the quadratic function is
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// at (1, 1, 1, 1, 1, 1). It is therefore at a distance of sqrt(6) ~ 2.45
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// from the origin.
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class DoglegStrategyFixtureEllipse : public Fixture {
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protected:
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virtual void SetUp() {
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Matrix basis(6, 6);
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// The following lines exceed 80 characters for better readability.
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basis << -0.1046920933796121, -0.7449367449921986, -0.4190744502875876, -0.4480450716142566, 0.2375351607929440, -0.0363053418882862, // NOLINT
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0.4064975684355914, 0.2681113508511354, -0.7463625494601520, -0.0803264850508117, -0.4463149623021321, 0.0130224954867195, // NOLINT
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-0.5514387729089798, 0.1026621026168657, -0.5008316122125011, 0.5738122212666414, 0.2974664724007106, 0.1296020877535158, // NOLINT
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0.5037835370947156, 0.2668479925183712, -0.1051754618492798, -0.0272739396578799, 0.7947481647088278, -0.1776623363955670, // NOLINT
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-0.4005458426625444, 0.2939330589634109, -0.0682629380550051, -0.2895448882503687, -0.0457239396341685, -0.8139899477847840, // NOLINT
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-0.3247764582762654, 0.4528151365941945, -0.0276683863102816, -0.6155994592510784, 0.1489240599972848, 0.5362574892189350; // NOLINT
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Vector Ddiag(6);
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Ddiag << 1.0, 2.0, 4.0, 8.0, 16.0, 32.0;
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Matrix sqrtD = Ddiag.array().sqrt().matrix().asDiagonal();
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Matrix jacobian = sqrtD * basis;
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jacobian_.reset(new DenseSparseMatrix(jacobian));
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Vector minimum(6);
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minimum << 1.0, 1.0, 1.0, 1.0, 1.0, 1.0;
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residual_ = -jacobian * minimum;
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x_.resize(6);
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x_.setZero();
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options_.min_lm_diagonal = 1.0;
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options_.max_lm_diagonal = 1.0;
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}
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};
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// A test problem where
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//
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// J^T J = diag([1 2 4 8 16 32]) .
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//
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// The residual is chosen so that the minimum of the quadratic function is
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// at (0, 0, 1, 0, 0, 0). It is therefore at a distance of 1 from the origin.
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// The gradient at the origin points towards the global minimum.
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class DoglegStrategyFixtureValley : public Fixture {
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protected:
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virtual void SetUp() {
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Vector Ddiag(6);
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Ddiag << 1.0, 2.0, 4.0, 8.0, 16.0, 32.0;
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Matrix jacobian = Ddiag.asDiagonal();
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jacobian_.reset(new DenseSparseMatrix(jacobian));
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Vector minimum(6);
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minimum << 0.0, 0.0, 1.0, 0.0, 0.0, 0.0;
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residual_ = -jacobian * minimum;
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x_.resize(6);
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x_.setZero();
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options_.min_lm_diagonal = 1.0;
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options_.max_lm_diagonal = 1.0;
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}
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};
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const double kTolerance = 1e-14;
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const double kToleranceLoose = 1e-5;
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const double kEpsilon = std::numeric_limits<double>::epsilon();
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} // namespace
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// The DoglegStrategy must never return a step that is longer than the current
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// trust region radius.
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TEST_F(DoglegStrategyFixtureEllipse, TrustRegionObeyedTraditional) {
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scoped_ptr<LinearSolver> linear_solver(
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new DenseQRSolver(LinearSolver::Options()));
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options_.linear_solver = linear_solver.get();
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// The global minimum is at (1, 1, ..., 1), so the distance to it is
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// sqrt(6.0). By restricting the trust region to a radius of 2.0,
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// we test if the trust region is actually obeyed.
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options_.dogleg_type = TRADITIONAL_DOGLEG;
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options_.initial_radius = 2.0;
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options_.max_radius = 2.0;
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DoglegStrategy strategy(options_);
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TrustRegionStrategy::PerSolveOptions pso;
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TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,
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jacobian_.get(),
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residual_.data(),
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x_.data());
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EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);
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EXPECT_LE(x_.norm(), options_.initial_radius * (1.0 + 4.0 * kEpsilon));
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}
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TEST_F(DoglegStrategyFixtureEllipse, TrustRegionObeyedSubspace) {
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scoped_ptr<LinearSolver> linear_solver(
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new DenseQRSolver(LinearSolver::Options()));
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options_.linear_solver = linear_solver.get();
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options_.dogleg_type = SUBSPACE_DOGLEG;
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options_.initial_radius = 2.0;
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options_.max_radius = 2.0;
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DoglegStrategy strategy(options_);
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TrustRegionStrategy::PerSolveOptions pso;
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TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,
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jacobian_.get(),
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residual_.data(),
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x_.data());
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EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);
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EXPECT_LE(x_.norm(), options_.initial_radius * (1.0 + 4.0 * kEpsilon));
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}
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TEST_F(DoglegStrategyFixtureEllipse, CorrectGaussNewtonStep) {
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scoped_ptr<LinearSolver> linear_solver(
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new DenseQRSolver(LinearSolver::Options()));
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options_.linear_solver = linear_solver.get();
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options_.dogleg_type = SUBSPACE_DOGLEG;
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options_.initial_radius = 10.0;
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options_.max_radius = 10.0;
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DoglegStrategy strategy(options_);
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TrustRegionStrategy::PerSolveOptions pso;
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TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,
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jacobian_.get(),
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residual_.data(),
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x_.data());
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EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);
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EXPECT_NEAR(x_(0), 1.0, kToleranceLoose);
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EXPECT_NEAR(x_(1), 1.0, kToleranceLoose);
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EXPECT_NEAR(x_(2), 1.0, kToleranceLoose);
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EXPECT_NEAR(x_(3), 1.0, kToleranceLoose);
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EXPECT_NEAR(x_(4), 1.0, kToleranceLoose);
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EXPECT_NEAR(x_(5), 1.0, kToleranceLoose);
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}
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// Test if the subspace basis is a valid orthonormal basis of the space spanned
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// by the gradient and the Gauss-Newton point.
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TEST_F(DoglegStrategyFixtureEllipse, ValidSubspaceBasis) {
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scoped_ptr<LinearSolver> linear_solver(
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new DenseQRSolver(LinearSolver::Options()));
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options_.linear_solver = linear_solver.get();
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options_.dogleg_type = SUBSPACE_DOGLEG;
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options_.initial_radius = 2.0;
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options_.max_radius = 2.0;
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DoglegStrategy strategy(options_);
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TrustRegionStrategy::PerSolveOptions pso;
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strategy.ComputeStep(pso, jacobian_.get(), residual_.data(), x_.data());
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// Check if the basis is orthonormal.
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const Matrix basis = strategy.subspace_basis();
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EXPECT_NEAR(basis.col(0).norm(), 1.0, kTolerance);
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EXPECT_NEAR(basis.col(1).norm(), 1.0, kTolerance);
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EXPECT_NEAR(basis.col(0).dot(basis.col(1)), 0.0, kTolerance);
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// Check if the gradient projects onto itself.
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const Vector gradient = strategy.gradient();
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EXPECT_NEAR((gradient - basis*(basis.transpose()*gradient)).norm(),
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0.0,
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kTolerance);
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// Check if the Gauss-Newton point projects onto itself.
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const Vector gn = strategy.gauss_newton_step();
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EXPECT_NEAR((gn - basis*(basis.transpose()*gn)).norm(),
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0.0,
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kTolerance);
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}
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// Test if the step is correct if the gradient and the Gauss-Newton step point
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// in the same direction and the Gauss-Newton step is outside the trust region,
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// i.e. the trust region is active.
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TEST_F(DoglegStrategyFixtureValley, CorrectStepLocalOptimumAlongGradient) {
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scoped_ptr<LinearSolver> linear_solver(
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new DenseQRSolver(LinearSolver::Options()));
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options_.linear_solver = linear_solver.get();
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options_.dogleg_type = SUBSPACE_DOGLEG;
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options_.initial_radius = 0.25;
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options_.max_radius = 0.25;
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DoglegStrategy strategy(options_);
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TrustRegionStrategy::PerSolveOptions pso;
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TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,
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jacobian_.get(),
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residual_.data(),
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x_.data());
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EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);
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EXPECT_NEAR(x_(0), 0.0, kToleranceLoose);
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EXPECT_NEAR(x_(1), 0.0, kToleranceLoose);
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EXPECT_NEAR(x_(2), options_.initial_radius, kToleranceLoose);
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EXPECT_NEAR(x_(3), 0.0, kToleranceLoose);
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EXPECT_NEAR(x_(4), 0.0, kToleranceLoose);
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EXPECT_NEAR(x_(5), 0.0, kToleranceLoose);
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}
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// Test if the step is correct if the gradient and the Gauss-Newton step point
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// in the same direction and the Gauss-Newton step is inside the trust region,
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// i.e. the trust region is inactive.
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TEST_F(DoglegStrategyFixtureValley, CorrectStepGlobalOptimumAlongGradient) {
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scoped_ptr<LinearSolver> linear_solver(
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new DenseQRSolver(LinearSolver::Options()));
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options_.linear_solver = linear_solver.get();
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options_.dogleg_type = SUBSPACE_DOGLEG;
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options_.initial_radius = 2.0;
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options_.max_radius = 2.0;
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DoglegStrategy strategy(options_);
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TrustRegionStrategy::PerSolveOptions pso;
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TrustRegionStrategy::Summary summary = strategy.ComputeStep(pso,
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jacobian_.get(),
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residual_.data(),
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x_.data());
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EXPECT_NE(summary.termination_type, LINEAR_SOLVER_FAILURE);
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EXPECT_NEAR(x_(0), 0.0, kToleranceLoose);
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EXPECT_NEAR(x_(1), 0.0, kToleranceLoose);
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EXPECT_NEAR(x_(2), 1.0, kToleranceLoose);
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EXPECT_NEAR(x_(3), 0.0, kToleranceLoose);
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EXPECT_NEAR(x_(4), 0.0, kToleranceLoose);
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EXPECT_NEAR(x_(5), 0.0, kToleranceLoose);
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}
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} // namespace internal
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} // namespace ceres
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