Program Listing for File solvers.h

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/*

Copyright (c) 2013, Markus Achtelik, ASL, ETH Zurich, Switzerland
You can contact the author at <markus dot achtelik at mavt dot ethz dot ch>

All rights reserved.

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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
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documentation and/or other materials provided with the distribution.
* Neither the name of ETHZ-ASL 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
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*/

#ifndef MAV_PLANNING_UTILS_SOLVERS_H_
#define MAV_PLANNING_UTILS_SOLVERS_H_

template <typename Derived>
Eigen::Matrix<typename Derived::Scalar, Derived::RowsAtCompileTime, 1> pseudoInverseSolver(
    const Eigen::MatrixBase<Derived>& A,
    const Eigen::Matrix<typename Derived::Scalar, Derived::RowsAtCompileTime, 1>& b,
    double tol = 1e-12) {
  // Eigen 3.2.9 changed the Jacobi SVD solver which lead to inaccurate
  // results in the trajectory generation. To fix this, directly use the
  // inverse if the matrix is square.
  if (A.rows() == A.cols()) {
    return A.inverse() * b;
  }
  typedef Derived A_type;
  typedef Eigen::Matrix<typename A_type::Scalar, A_type::RowsAtCompileTime, 1> X_type;

  Eigen::JacobiSVD<A_type> svd(A, Eigen::ComputeFullU | Eigen::ComputeFullV);

  A_type U, V;
  X_type S;

  U = svd.matrixU();
  V = svd.matrixV();
  S = svd.singularValues();

  for (int i = 0; i < A.rows(); i++) {
    if (S[i] < tol)
      S[i] = 0;
    else
      S[i] = 1.0 / S[i];
  }

  return V * S.asDiagonal() * U.transpose() * b;
}

#endif  // MAV_PLANNING_UTILS_SOLVERS_H_