// This file is part of libigl, a simple c++ geometry processing library.
// 
// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
// 
// This Source Code Form is subject to the terms of the Mozilla Public License 
// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
// obtain one at http://mozilla.org/MPL/2.0/.
#ifndef IGL_POLAR_SVD
#define IGL_POLAR_SVD
#include "igl_inline.h"
#include <Eigen/Core>

namespace igl
{
  /// Computes the polar decomposition (R,T) of a matrix A using SVD singular
  /// value decomposition
  ///
  /// @param[in] A  3 by 3 matrix to be decomposed
  /// @param[in] includeReflections  Whether to force R to be a rotation, or allow it to be a reflection
  /// @param[out] R  3 by 3 rotation matrix part of decomposition (**always rotataion**)
  /// @param[out] T  3 by 3 stretch matrix part of decomposition
  /// @param[out] U  3 by 3 left-singular vectors
  /// @param[out] S  3 by 1 singular values
  /// @param[out] V  3 by 3 right-singular vectors
  ///
  ///
  template <
    typename DerivedA,
    typename DerivedR,
    typename DerivedT,
    typename DerivedU,
    typename DerivedS,
    typename DerivedV>
  IGL_INLINE void polar_svd(
    const Eigen::MatrixBase<DerivedA> & A,
    bool includeReflections,
    Eigen::PlainObjectBase<DerivedR> & R,
    Eigen::PlainObjectBase<DerivedT> & T,
    Eigen::PlainObjectBase<DerivedU> & U,
    Eigen::PlainObjectBase<DerivedS> & S,
    Eigen::PlainObjectBase<DerivedV> & V);
  /// \overload
  template <
    typename DerivedA,
    typename DerivedR,
    typename DerivedT>
  IGL_INLINE void polar_svd(
    const Eigen::MatrixBase<DerivedA> & A,
    const bool includeReflections,
    Eigen::PlainObjectBase<DerivedR> & R,
    Eigen::PlainObjectBase<DerivedT> & T);
  /// \overload
  /// \brief For backward compatibility, these set includeReflections = false.
  template <
    typename DerivedA,
    typename DerivedR,
    typename DerivedT,
    typename DerivedU,
    typename DerivedS,
    typename DerivedV>
  IGL_INLINE void polar_svd(
    const Eigen::MatrixBase<DerivedA> & A,
    Eigen::PlainObjectBase<DerivedR> & R,
    Eigen::PlainObjectBase<DerivedT> & T,
    Eigen::PlainObjectBase<DerivedU> & U,
    Eigen::PlainObjectBase<DerivedS> & S,
    Eigen::PlainObjectBase<DerivedV> & V);
  /// \overload
  template <
    typename DerivedA,
    typename DerivedR,
    typename DerivedT>
  IGL_INLINE void polar_svd(
    const Eigen::MatrixBase<DerivedA> & A,
    Eigen::PlainObjectBase<DerivedR> & R,
    Eigen::PlainObjectBase<DerivedT> & T);
}
#ifndef IGL_STATIC_LIBRARY
#  include "polar_svd.cpp"
#endif
#endif