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							- // 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 <cmath>
 
- #include "ceres/autodiff_local_parameterization.h"
 
- #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);
 
-   }
 
-   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]);
 
-   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};
 
-   double norm_x = sqrt(x[0] * x[0] +
 
-                        x[1] * x[1] +
 
-                        x[2] * x[2] +
 
-                        x[3] * x[3]);
 
-   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};
 
-   double norm_x = sqrt(x[0] * x[0] +
 
-                        x[1] * x[1] +
 
-                        x[2] * x[2] +
 
-                        x[3] * x[3]);
 
-   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
 
 
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