text: // This code comes from the Theia-SfM library:
  //    https://github.com/sweeneychris/TheiaSfM
  //
  // Copyright (C) 2018 The Regents of the University of California (Regents).
  // All rights reserved.
  //
  // 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 The Regents or University of California 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 HOLDERS 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.
  //
  // Please contact the author of this library if you have any questions.
  // Author: Victor Fragoso (victor.fragoso@mail.wvu.edu)
  
  #ifndef THEIA_SFM_POSE_BUILD_UPNP_ACTION_MATRIX_USING_SYMMETRY_H_
  #define THEIA_SFM_POSE_BUILD_UPNP_ACTION_MATRIX_USING_SYMMETRY_H_
  
  #include <Eigen/Core>
  
  namespace theia {
  
  using Matrix10d = Eigen::Matrix<double, 10, 10>;
  using Vector10d = Eigen::Matrix<double, 10, 1>;
  using RowMajorMatrixXd =
      Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
  
  // Builds an action matrix for estimating rotations given Upnp cost parameters.
  // The function returns the 8x8 action matrix since exploits symmetry in the
  // underlying polynomial system of Upnp.
  //
  // Params:
  //   a_matrix:  The quadratic penalty matrix.
  //   b_vector:  The linear penalty vector.
  //   template_matrix:  The template matrix buffer.
  Eigen::Matrix<double, 8, 8> BuildActionMatrixUsingSymmetry(
      const Matrix10d& a_matrix,
      const Vector10d& b_vector,
      RowMajorMatrixXd* template_matrix);
  
  inline Eigen::Matrix<double, 8, 8> BuildActionMatrixUsingSymmetry(
      const Matrix10d& a_matrix,
      const Vector10d& b_vector) {
    RowMajorMatrixXd template_matrix;
    return BuildActionMatrixUsingSymmetry(a_matrix, b_vector, &template_matrix);
  }
  
  }  // namespace theia
  
  #endif  // THEIA_SFM_POSE_BUILD_UPNP_ACTION_MATRIX_USING_SYMMETRY_H_
  