| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2015 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are met: |
| // |
| // * Redistributions of source code must retain the above copyright notice, |
| // this list of conditions and the following disclaimer. |
| // * Redistributions in binary form must reproduce the above copyright notice, |
| // this list of conditions and the following disclaimer in the documentation |
| // and/or other materials provided with the distribution. |
| // * Neither the name of Google Inc. nor the names of its contributors may be |
| // used to endorse or promote products derived from this software without |
| // specific prior written permission. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| // POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| |
| #include "ceres/autodiff_local_parameterization.h" |
| |
| #include <cmath> |
| |
| #include "ceres/local_parameterization.h" |
| #include "ceres/rotation.h" |
| #include "gtest/gtest.h" |
| |
| namespace ceres { |
| namespace internal { |
| |
| struct IdentityPlus { |
| template <typename T> |
| bool operator()(const T* x, const T* delta, T* x_plus_delta) const { |
| for (int i = 0; i < 3; ++i) { |
| x_plus_delta[i] = x[i] + delta[i]; |
| } |
| return true; |
| } |
| }; |
| |
| TEST(AutoDiffLocalParameterizationTest, IdentityParameterization) { |
| AutoDiffLocalParameterization<IdentityPlus, 3, 3> parameterization; |
| |
| double x[3] = {1.0, 2.0, 3.0}; |
| double delta[3] = {0.0, 1.0, 2.0}; |
| double x_plus_delta[3] = {0.0, 0.0, 0.0}; |
| parameterization.Plus(x, delta, x_plus_delta); |
| |
| EXPECT_EQ(x_plus_delta[0], 1.0); |
| EXPECT_EQ(x_plus_delta[1], 3.0); |
| EXPECT_EQ(x_plus_delta[2], 5.0); |
| |
| double jacobian[9]; |
| parameterization.ComputeJacobian(x, jacobian); |
| int k = 0; |
| for (int i = 0; i < 3; ++i) { |
| for (int j = 0; j < 3; ++j, ++k) { |
| EXPECT_EQ(jacobian[k], (i == j) ? 1.0 : 0.0); |
| } |
| } |
| } |
| |
| struct ScaledPlus { |
| explicit ScaledPlus(const double& scale_factor) |
| : scale_factor_(scale_factor) {} |
| |
| template <typename T> |
| bool operator()(const T* x, const T* delta, T* x_plus_delta) const { |
| for (int i = 0; i < 3; ++i) { |
| x_plus_delta[i] = x[i] + T(scale_factor_) * delta[i]; |
| } |
| return true; |
| } |
| |
| const double scale_factor_; |
| }; |
| |
| TEST(AutoDiffLocalParameterizationTest, ScaledParameterization) { |
| const double kTolerance = 1e-14; |
| |
| AutoDiffLocalParameterization<ScaledPlus, 3, 3> parameterization( |
| new ScaledPlus(1.2345)); |
| |
| double x[3] = {1.0, 2.0, 3.0}; |
| double delta[3] = {0.0, 1.0, 2.0}; |
| double x_plus_delta[3] = {0.0, 0.0, 0.0}; |
| parameterization.Plus(x, delta, x_plus_delta); |
| |
| EXPECT_NEAR(x_plus_delta[0], 1.0, kTolerance); |
| EXPECT_NEAR(x_plus_delta[1], 3.2345, kTolerance); |
| EXPECT_NEAR(x_plus_delta[2], 5.469, kTolerance); |
| |
| double jacobian[9]; |
| parameterization.ComputeJacobian(x, jacobian); |
| int k = 0; |
| for (int i = 0; i < 3; ++i) { |
| for (int j = 0; j < 3; ++j, ++k) { |
| EXPECT_NEAR(jacobian[k], (i == j) ? 1.2345 : 0.0, kTolerance); |
| } |
| } |
| } |
| |
| struct QuaternionPlus { |
| template <typename T> |
| bool operator()(const T* x, const T* delta, T* x_plus_delta) const { |
| const T squared_norm_delta = |
| delta[0] * delta[0] + delta[1] * delta[1] + delta[2] * delta[2]; |
| |
| T q_delta[4]; |
| if (squared_norm_delta > T(0.0)) { |
| T norm_delta = sqrt(squared_norm_delta); |
| const T sin_delta_by_delta = sin(norm_delta) / norm_delta; |
| q_delta[0] = cos(norm_delta); |
| q_delta[1] = sin_delta_by_delta * delta[0]; |
| q_delta[2] = sin_delta_by_delta * delta[1]; |
| q_delta[3] = sin_delta_by_delta * delta[2]; |
| } else { |
| // We do not just use q_delta = [1,0,0,0] here because that is a |
| // constant and when used for automatic differentiation will |
| // lead to a zero derivative. Instead we take a first order |
| // approximation and evaluate it at zero. |
| q_delta[0] = T(1.0); |
| q_delta[1] = delta[0]; |
| q_delta[2] = delta[1]; |
| q_delta[3] = delta[2]; |
| } |
| |
| QuaternionProduct(q_delta, x, x_plus_delta); |
| return true; |
| } |
| }; |
| |
| static void QuaternionParameterizationTestHelper(const double* x, |
| const double* delta) { |
| const double kTolerance = 1e-14; |
| double x_plus_delta_ref[4] = {0.0, 0.0, 0.0, 0.0}; |
| double jacobian_ref[12]; |
| |
| QuaternionParameterization ref_parameterization; |
| ref_parameterization.Plus(x, delta, x_plus_delta_ref); |
| ref_parameterization.ComputeJacobian(x, jacobian_ref); |
| |
| double x_plus_delta[4] = {0.0, 0.0, 0.0, 0.0}; |
| double jacobian[12]; |
| AutoDiffLocalParameterization<QuaternionPlus, 4, 3> parameterization; |
| parameterization.Plus(x, delta, x_plus_delta); |
| parameterization.ComputeJacobian(x, jacobian); |
| |
| for (int i = 0; i < 4; ++i) { |
| EXPECT_NEAR(x_plus_delta[i], x_plus_delta_ref[i], kTolerance); |
| } |
| |
| // clang-format off |
| const double x_plus_delta_norm = |
| sqrt(x_plus_delta[0] * x_plus_delta[0] + |
| x_plus_delta[1] * x_plus_delta[1] + |
| x_plus_delta[2] * x_plus_delta[2] + |
| x_plus_delta[3] * x_plus_delta[3]); |
| // clang-format on |
| |
| EXPECT_NEAR(x_plus_delta_norm, 1.0, kTolerance); |
| |
| for (int i = 0; i < 12; ++i) { |
| EXPECT_TRUE(std::isfinite(jacobian[i])); |
| EXPECT_NEAR(jacobian[i], jacobian_ref[i], kTolerance) |
| << "Jacobian mismatch: i = " << i << "\n Expected \n" |
| << ConstMatrixRef(jacobian_ref, 4, 3) << "\n Actual \n" |
| << ConstMatrixRef(jacobian, 4, 3); |
| } |
| } |
| |
| TEST(AutoDiffLocalParameterization, QuaternionParameterizationZeroTest) { |
| double x[4] = {0.5, 0.5, 0.5, 0.5}; |
| double delta[3] = {0.0, 0.0, 0.0}; |
| QuaternionParameterizationTestHelper(x, delta); |
| } |
| |
| TEST(AutoDiffLocalParameterization, QuaternionParameterizationNearZeroTest) { |
| double x[4] = {0.52, 0.25, 0.15, 0.45}; |
| // clang-format off |
| double norm_x = sqrt(x[0] * x[0] + |
| x[1] * x[1] + |
| x[2] * x[2] + |
| x[3] * x[3]); |
| // clang-format on |
| for (int i = 0; i < 4; ++i) { |
| x[i] = x[i] / norm_x; |
| } |
| |
| double delta[3] = {0.24, 0.15, 0.10}; |
| for (int i = 0; i < 3; ++i) { |
| delta[i] = delta[i] * 1e-14; |
| } |
| |
| QuaternionParameterizationTestHelper(x, delta); |
| } |
| |
| TEST(AutoDiffLocalParameterization, QuaternionParameterizationNonZeroTest) { |
| double x[4] = {0.52, 0.25, 0.15, 0.45}; |
| // clang-format off |
| double norm_x = sqrt(x[0] * x[0] + |
| x[1] * x[1] + |
| x[2] * x[2] + |
| x[3] * x[3]); |
| // clang-format on |
| |
| for (int i = 0; i < 4; ++i) { |
| x[i] = x[i] / norm_x; |
| } |
| |
| double delta[3] = {0.24, 0.15, 0.10}; |
| QuaternionParameterizationTestHelper(x, delta); |
| } |
| |
| } // namespace internal |
| } // namespace ceres |