| 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223 | // 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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