// Copyright (c) 2006  GeometryFactory (France). All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.2-beta1/Surface_mesh_simplification/include/CGAL/Cartesian/MatrixC33.h $
// $Id: include/CGAL/Cartesian/MatrixC33.h 431cfb5357d $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Fernando Cacciola <fernando.cacciola@geometryfactory.com>
//
#ifndef CGAL_CARTESIAN_MATRIXC33_H
#define CGAL_CARTESIAN_MATRIXC33_H

#include <CGAL/license/Surface_mesh_simplification.h>

#include <CGAL/internal/robust_cross_product.h>

#include <CGAL/determinant.h>
#include <CGAL/Null_matrix.h>
#include <CGAL/number_utils.h>
#include <CGAL/Vector_3.h>

#include <optional>

namespace CGAL {

template <class R_>
class MatrixC33
{
public:
  typedef R_                                                R;

  typedef typename R::FT                                    RT;
  typedef typename R::Vector_3                              Vector_3;

  MatrixC33(Null_matrix)
   : mR0(NULL_VECTOR),
     mR1(NULL_VECTOR),
     mR2(NULL_VECTOR)
  {}

  MatrixC33(const RT& r0x, const RT& r0y, const RT& r0z,
            const RT& r1x, const RT& r1y, const RT& r1z,
            const RT& r2x, const RT& r2y, const RT& r2z)
    : mR0(r0x,r0y,r0z),
      mR1(r1x,r1y,r1z),
      mR2(r2x,r2y,r2z)
  {}

  MatrixC33(const Vector_3& r0, const Vector_3& r1, const Vector_3& r2)
    : mR0(r0),
      mR1(r1),
      mR2(r2)
  {}

  const Vector_3& r0() const { return mR0; }
  const Vector_3& r1() const { return mR1; }
  const Vector_3& r2() const { return mR2; }

  Vector_3& r0() { return mR0; }
  Vector_3& r1() { return mR1; }
  Vector_3& r2() { return mR2; }

  const Vector_3& operator[](int row) const { return row == 0 ? mR0 : (row == 1 ? mR1 : mR2); }
  Vector_3& operator[](int row) { return row == 0 ? mR0 : (row == 1 ? mR1 : mR2); }

  MatrixC33& operator+=(const MatrixC33& m)
  {
    mR0 = mR0 + m.r0();
    mR1 = mR1 + m.r1();
    mR2 = mR2 + m.r2();
    return *this;
  }

  MatrixC33& operator-=(const MatrixC33& m)
  {
    mR0 = mR0 - m.r0();
    mR1 = mR1 - m.r1();
    mR2 = mR2 - m.r2();
    return *this;
  }

  MatrixC33& operator*=(const RT& c)
  {
    mR0 = mR0 * c;
    mR1 = mR1 * c;
    mR2 = mR2 * c;
    return *this;
  }

  MatrixC33& operator/=(const RT& c)
  {
    mR0 = mR0 / c;
    mR1 = mR1 / c;
    mR2 = mR2 / c;
    return *this;
  }

  friend MatrixC33 operator+(const MatrixC33& a, const MatrixC33& b)
  {
    return MatrixC33(a.r0() + b.r0(),
                     a.r1() + b.r1(),
                     a.r2() + b.r2());
  }

  friend MatrixC33 operator-(const MatrixC33& a, const MatrixC33& b)
  {
    return MatrixC33(a.r0() - b.r0(),
                     a.r1() - b.r1(),
                     a.r2() - b.r2());
  }

  friend MatrixC33 operator*(const MatrixC33& m, const RT& c)
  {
    return MatrixC33(m.r0()*c, m.r1()*c, m.r2()*c);
  }
  friend MatrixC33 operator*(const RT& c, const MatrixC33& m)
  {
    return MatrixC33(m.r0()*c, m.r1()*c, m.r2()*c);
  }

  friend MatrixC33 operator/(const MatrixC33& m, const RT& c)
  {
    return MatrixC33(m.r0()/c, m.r1()/c, m.r2()/c);
  }

  friend Vector_3 operator*(const MatrixC33& m, const Vector_3& v)
  {
    return Vector_3(m.r0()*v, m.r1()*v, m.r2()*v);
  }
  friend Vector_3 operator*(const Vector_3& v, const MatrixC33& m)
  {
    return Vector_3(v*m.r0(), v*m.r1(), v*m.r2());
  }

  friend std::ostream& operator<<(std::ostream & os, const MatrixC33& m)
{
  return os << m.r0() << std::endl
            << m.r1() << std::endl
            << m.r2() << std::endl;
}

  RT determinant() const
  {
    return CGAL::determinant(r0().x(), r0().y(), r0().z(),
                             r1().x(), r1().y(), r1().z(),
                             r2().x(), r2().y(), r2().z());
  }

  MatrixC33& transpose()
  {
    mR0 = Vector_3(r0().x(),r1().x(),r2().x());
    mR1 = Vector_3(r0().y(),r1().y(),r2().y());
    mR2 = Vector_3(r0().z(),r1().z(),r2().z());
    return *this;
  }

private:

  Vector_3 mR0;
  Vector_3 mR1;
  Vector_3 mR2;
};

template<class R>
inline
MatrixC33<R> direct_product(const Vector_3<R>& u,
                            const Vector_3<R>& v)
{
  return MatrixC33<R>(v * u.x(),
                      v * u.y(),
                      v * u.z());
}

template<class R>
MatrixC33<R> transposed_matrix(const MatrixC33<R>& m)
{
  MatrixC33<R> copy = m;
  copy.Transpose();
  return copy;
}

template<class R>
MatrixC33<R> cofactors_matrix(const MatrixC33<R>& m)
{
  typedef typename R::RT RT;

  using ::CGAL::Surface_mesh_simplification::internal::diff_of_products;

  RT c00 =  diff_of_products(m.r1().y(), m.r2().z(), m.r2().y(), m.r1().z());
  RT c01 = -diff_of_products(m.r1().x(), m.r2().z(), m.r2().x(), m.r1().z());
  RT c02 =  diff_of_products(m.r1().x(), m.r2().y(), m.r2().x(), m.r1().y());

  RT c10 = -diff_of_products(m.r0().y(), m.r2().z(), m.r2().y(), m.r0().z());
  RT c11 =  diff_of_products(m.r0().x(), m.r2().z(), m.r2().x(), m.r0().z());
  RT c12 = -diff_of_products(m.r0().x(), m.r2().y(), m.r2().x(), m.r0().y());

  RT c20 =  diff_of_products(m.r0().y(), m.r1().z(), m.r1().y(), m.r0().z());
  RT c21 = -diff_of_products(m.r0().x(), m.r1().z(), m.r1().x(), m.r0().z());
  RT c22 =  diff_of_products(m.r0().x(), m.r1().y(), m.r1().x(), m.r0().y());

  return MatrixC33<R>(c00,c01,c02,
                      c10,c11,c12,
                      c20,c21,c22);
}

template<class R>
MatrixC33<R> adjoint_matrix(const MatrixC33<R>& m)
{
  return cofactors_matrix(m).transpose();
}

template<class R>
std::optional< MatrixC33<R> > inverse_matrix(const MatrixC33<R>& m)
{
  typedef typename R::RT                                        RT;
  typedef MatrixC33<R>                                          Matrix;
  typedef std::optional<Matrix>                                 result_type;

  using ::CGAL::Surface_mesh_simplification::internal::diff_of_products;

  result_type rInverse;

  RT det = m.determinant();

  if(! CGAL_NTS is_zero(det))
  {
    RT c00 = diff_of_products(m.r1().y(),m.r2().z(),m.r2().y(),m.r1().z()) / det;
    RT c01 = diff_of_products(m.r2().y(),m.r0().z(),m.r0().y(),m.r2().z()) / det;
    RT c02 = diff_of_products(m.r0().y(),m.r1().z(),m.r1().y(),m.r0().z()) / det;

    RT c10 = diff_of_products(m.r2().x(),m.r1().z(),m.r1().x(),m.r2().z()) / det;
    RT c11 = diff_of_products(m.r0().x(),m.r2().z(),m.r2().x(),m.r0().z()) / det;
    RT c12 = diff_of_products(m.r1().x(),m.r0().z(),m.r0().x(),m.r1().z()) / det;

    RT c20 = diff_of_products(m.r1().x(),m.r2().y(),m.r2().x(),m.r1().y()) / det;
    RT c21 = diff_of_products(m.r2().x(),m.r0().y(),m.r0().x(),m.r2().y()) / det;
    RT c22 = diff_of_products(m.r0().x(),m.r1().y(),m.r1().x(),m.r0().y()) / det;

    rInverse = result_type(Matrix(c00,c01,c02,
                                  c10,c11,c12,
                                  c20,c21,c22));
  }

  return rInverse;
}

} // namespace CGAL

#endif // CGAL_CARTESIAN_MATRIXC33_H //
// EOF //


