Eigen/src/Core/Redux.h - platform/external/eigen - Git at Google

 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra. Eigen itself is part of the KDE project.
 //
 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
 // Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
 //
 // Eigen is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
 // License as published by the Free Software Foundation; either
 // version 3 of the License, or (at your option) any later version.
 //
 // Alternatively, you can redistribute it and/or
 // modify it under the terms of the GNU General Public License as
 // published by the Free Software Foundation; either version 2 of
 // the License, or (at your option) any later version.
 //
 // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
 // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
 // GNU General Public License for more details.
 //
 // You should have received a copy of the GNU Lesser General Public
 // License and a copy of the GNU General Public License along with
 // Eigen. If not, see <http://www.gnu.org/licenses/>.

 #ifndef EIGEN_REDUX_H
 #define EIGEN_REDUX_H

 template<typename BinaryOp, typename Derived, int Start, int Length>
 struct ei_redux_unroller
 {
   enum {
     HalfLength = Length/2
   };

   typedef typename ei_result_of<BinaryOp(typename Derived::Scalar)>::type Scalar;

   static Scalar run(const Derived &mat, const BinaryOp& func)
   {
     return func(
       ei_redux_unroller<BinaryOp, Derived, Start, HalfLength>::run(mat, func),
       ei_redux_unroller<BinaryOp, Derived, Start+HalfLength, Length - HalfLength>::run(mat, func));
   }
 };

 template<typename BinaryOp, typename Derived, int Start>
 struct ei_redux_unroller<BinaryOp, Derived, Start, 1>
 {
   enum {
     col = Start / Derived::RowsAtCompileTime,
     row = Start % Derived::RowsAtCompileTime
   };

   typedef typename ei_result_of<BinaryOp(typename Derived::Scalar)>::type Scalar;

   static Scalar run(const Derived &mat, const BinaryOp &func)
   {
     return mat.coeff(row, col);
   }
 };

 template<typename BinaryOp, typename Derived, int Start>
 struct ei_redux_unroller<BinaryOp, Derived, Start, Dynamic>
 {
   typedef typename ei_result_of<BinaryOp(typename Derived::Scalar)>::type Scalar;
   static Scalar run(const Derived&, const BinaryOp&) { return Scalar(); }
 };


 /** \class PartialRedux
   *
   * \brief Generic expression of a partially reduxed matrix
   *
   * \param Direction indicates the direction of the redux (Vertical or Horizontal)
   * \param BinaryOp type of the binary functor implementing the operator (must be associative)
   * \param MatrixType the type of the matrix we are applying the redux operation
   *
   * This class represents an expression of a partial redux operator of a matrix.
   * It is the return type of MatrixBase::verticalRedux(), MatrixBase::horizontalRedux(),
   * and most of the time this is the only way it is used.
   *
   * \sa class CwiseBinaryOp
   */
 template<int Direction, typename BinaryOp, typename MatrixType>
 struct ei_traits<PartialRedux<Direction, BinaryOp, MatrixType> >
 {
   typedef typename ei_result_of<
                      BinaryOp(typename MatrixType::Scalar)
                    >::type Scalar;
   typedef typename ei_xpr_copy<MatrixType>::type MatrixTypeXprCopy;
   typedef typename ei_unref<MatrixTypeXprCopy>::type _MatrixTypeXprCopy;
   enum {
     RowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::RowsAtCompileTime,
     ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
     MaxRowsAtCompileTime = Direction==Vertical   ? 1 : MatrixType::MaxRowsAtCompileTime,
     MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
     Flags = (RowsAtCompileTime == Dynamic || ColsAtCompileTime == Dynamic)
           ? (unsigned int)_MatrixTypeXprCopy::Flags
           : (unsigned int)_MatrixTypeXprCopy::Flags & ~LargeBit,
     TraversalSize = Direction==Vertical ? RowsAtCompileTime : ColsAtCompileTime,
     CoeffReadCost = TraversalSize * _MatrixTypeXprCopy::CoeffReadCost
                   + (TraversalSize - 1) * ei_functor_traits<BinaryOp>::Cost
   };
 };

 template<int Direction, typename BinaryOp, typename MatrixType>
 class PartialRedux : ei_no_assignment_operator,
   public MatrixBase<PartialRedux<Direction, BinaryOp, MatrixType> >
 {
   public:

     EIGEN_GENERIC_PUBLIC_INTERFACE(PartialRedux)
     typedef typename ei_traits<PartialRedux>::MatrixTypeXprCopy MatrixTypeXprCopy;
     typedef typename ei_traits<PartialRedux>::_MatrixTypeXprCopy _MatrixTypeXprCopy;

     PartialRedux(const MatrixType& mat, const BinaryOp& func = BinaryOp())
       : m_matrix(mat), m_functor(func) {}

   private:

     int _rows() const { return (Direction==Vertical   ? 1 : m_matrix.rows()); }
     int _cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }

     const Scalar _coeff(int i, int j) const
     {
       if (Direction==Vertical)
         return this->col(j).redux(m_functor);
       else
         return this->row(i).redux(m_functor);
     }

   protected:
     const MatrixTypeXprCopy m_matrix;
     const BinaryOp m_functor;
 };

 /** \returns a row vector expression of *this vertically reduxed by \a func
   *
   * The template parameter \a BinaryOp is the type of the functor
   * of the custom redux operator. Note that func must be an associative operator.
   *
   * \sa class PartialRedux, MatrixBase::horizontalRedux()
   */
 template<typename Derived>
 template<typename BinaryOp>
 const PartialRedux<Vertical, BinaryOp, Derived>
 MatrixBase<Derived>::verticalRedux(const BinaryOp& func) const
 {
   return PartialRedux<Vertical, BinaryOp, Derived>(derived(), func);
 }

 /** \returns a row vector expression of *this horizontally reduxed by \a func
   *
   * The template parameter \a BinaryOp is the type of the functor
   * of the custom redux operator. Note that func must be an associative operator.
   *
   * \sa class PartialRedux, MatrixBase::verticalRedux()
   */
 template<typename Derived>
 template<typename BinaryOp>
 const PartialRedux<Horizontal, BinaryOp, Derived>
 MatrixBase<Derived>::horizontalRedux(const BinaryOp& func) const
 {
   return PartialRedux<Horizontal, BinaryOp, Derived>(derived(), func);
 }


 /** \returns the result of a full redux operation on the whole matrix or vector using \a func
   *
   * The template parameter \a BinaryOp is the type of the functor \a func which must be
   * an assiociative operator. Both current STL and TR1 functor styles are handled.
   *
   * \sa MatrixBase::sum(), MatrixBase::minCoeff(), MatrixBase::maxCoeff(), MatrixBase::verticalRedux(), MatrixBase::horizontalRedux()
   */
 template<typename Derived>
 template<typename BinaryOp>
 typename ei_result_of<BinaryOp(typename ei_traits<Derived>::Scalar)>::type
 MatrixBase<Derived>::redux(const BinaryOp& func) const
 {
   const bool unroll = SizeAtCompileTime * CoeffReadCost
                     + (SizeAtCompileTime-1) * ei_functor_traits<BinaryOp>::Cost
                     <= EIGEN_UNROLLING_LIMIT;
   if(unroll)
     return ei_redux_unroller<BinaryOp, Derived, 0,
                              unroll ? SizeAtCompileTime : Dynamic>
            ::run(derived(), func);
   else
   {
     Scalar res;
     res = coeff(0,0);
     for(int i = 1; i < rows(); i++)
       res = func(res, coeff(i, 0));
     for(int j = 1; j < cols(); j++)
       for(int i = 0; i < rows(); i++)
         res = func(res, coeff(i, j));
     return res;
   }
 }

 /** \returns the sum of all coefficients of *this
   *
   * \sa trace()
   */
 template<typename Derived>
 typename ei_traits<Derived>::Scalar
 MatrixBase<Derived>::sum() const
 {
   return this->redux(Eigen::ei_scalar_sum_op<Scalar>());
 }

 /** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
   *
   * \c *this can be any matrix, not necessarily square.
   *
   * \sa diagonal(), sum()
   */
 template<typename Derived>
 typename ei_traits<Derived>::Scalar
 MatrixBase<Derived>::trace() const
 {
   return diagonal().sum();
 }

 /** \returns the minimum of all coefficients of *this
   */
 template<typename Derived>
 typename ei_traits<Derived>::Scalar
 MatrixBase<Derived>::minCoeff() const
 {
   return this->redux(Eigen::ei_scalar_min_op<Scalar>());
 }

 /** \returns the maximum of all coefficients of *this
   */
 template<typename Derived>
 typename ei_traits<Derived>::Scalar
 MatrixBase<Derived>::maxCoeff() const
 {
   return this->redux(Eigen::ei_scalar_max_op<Scalar>());
 }


 template<typename Derived, int UnrollCount>
 struct ei_all_unroller
 {
   enum {
     col = (UnrollCount-1) / Derived::RowsAtCompileTime,
     row = (UnrollCount-1) % Derived::RowsAtCompileTime
   };

   static bool run(const Derived &mat)
   {
     return ei_all_unroller<Derived, UnrollCount-1>::run(mat) && mat.coeff(row, col);
   }
 };

 template<typename Derived>
 struct ei_all_unroller<Derived, 1>
 {
   static bool run(const Derived &mat) { return mat.coeff(0, 0); }
 };

 template<typename Derived>
 struct ei_all_unroller<Derived, Dynamic>
 {
   static bool run(const Derived &) { return false; }
 };

 template<typename Derived, int UnrollCount>
 struct ei_any_unroller
 {
   enum {
     col = (UnrollCount-1) / Derived::RowsAtCompileTime,
     row = (UnrollCount-1) % Derived::RowsAtCompileTime
   };

   static bool run(const Derived &mat)
   {
     return ei_any_unroller<Derived, UnrollCount-1>::run(mat) || mat.coeff(row, col);
   }
 };

 template<typename Derived>
 struct ei_any_unroller<Derived, 1>
 {
   static bool run(const Derived &mat) { return mat.coeff(0, 0); }
 };

 template<typename Derived>
 struct ei_any_unroller<Derived, Dynamic>
 {
   static bool run(const Derived &) { return false; }
 };

 /** \returns true if all coefficients are true
   *
   * \sa MatrixBase::any()
   */
 template<typename Derived>
 bool MatrixBase<Derived>::all(void) const
 {
   const bool unroll = SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost)
                       <= EIGEN_UNROLLING_LIMIT;
   if(unroll)
     return ei_all_unroller<Derived,
                            unroll ? SizeAtCompileTime : Dynamic
      >::run(derived());
   else
   {
     for(int j = 0; j < cols(); j++)
       for(int i = 0; i < rows(); i++)
         if (!coeff(i, j)) return false;
     return true;
   }
 }

 /** \returns true if at least one coefficient is true
   *
   * \sa MatrixBase::any()
   */
 template<typename Derived>
 bool MatrixBase<Derived>::any(void) const
 {
   const bool unroll = SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost)
                       <= EIGEN_UNROLLING_LIMIT;
   if(unroll)
     return ei_any_unroller<Derived,
                            unroll ? SizeAtCompileTime : Dynamic
            >::run(derived());
   else
   {
     for(int j = 0; j < cols(); j++)
       for(int i = 0; i < rows(); i++)
         if (coeff(i, j)) return true;
     return false;
   }
 }

 #endif // EIGEN_REDUX_H
	// This file is part of Eigen, a lightweight C++ template library
	// for linear algebra. Eigen itself is part of the KDE project.
	//
	// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
	// Copyright (C) 2006-2008 Benoit Jacob <jacob@math.jussieu.fr>
	//
	// Eigen is free software; you can redistribute it and/or
	// modify it under the terms of the GNU Lesser General Public
	// License as published by the Free Software Foundation; either
	// version 3 of the License, or (at your option) any later version.
	//
	// Alternatively, you can redistribute it and/or
	// modify it under the terms of the GNU General Public License as
	// published by the Free Software Foundation; either version 2 of
	// the License, or (at your option) any later version.
	//
	// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
	// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
	// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
	// GNU General Public License for more details.
	//
	// You should have received a copy of the GNU Lesser General Public
	// License and a copy of the GNU General Public License along with
	// Eigen. If not, see <http://www.gnu.org/licenses/>.

	#ifndef EIGEN_REDUX_H
	#define EIGEN_REDUX_H

	template<typename BinaryOp, typename Derived, int Start, int Length>
	struct ei_redux_unroller
	{
	enum {
	HalfLength = Length/2
	};

	typedef typename ei_result_of<BinaryOp(typename Derived::Scalar)>::type Scalar;

	static Scalar run(const Derived &mat, const BinaryOp& func)
	{
	return func(
	ei_redux_unroller<BinaryOp, Derived, Start, HalfLength>::run(mat, func),
	ei_redux_unroller<BinaryOp, Derived, Start+HalfLength, Length - HalfLength>::run(mat, func));
	}
	};

	template<typename BinaryOp, typename Derived, int Start>
	struct ei_redux_unroller<BinaryOp, Derived, Start, 1>
	{
	enum {
	col = Start / Derived::RowsAtCompileTime,
	row = Start % Derived::RowsAtCompileTime
	};

	typedef typename ei_result_of<BinaryOp(typename Derived::Scalar)>::type Scalar;

	static Scalar run(const Derived &mat, const BinaryOp &func)
	{
	return mat.coeff(row, col);
	}
	};

	template<typename BinaryOp, typename Derived, int Start>
	struct ei_redux_unroller<BinaryOp, Derived, Start, Dynamic>
	{
	typedef typename ei_result_of<BinaryOp(typename Derived::Scalar)>::type Scalar;
	static Scalar run(const Derived&, const BinaryOp&) { return Scalar(); }
	};


	/** \class PartialRedux
	*
	* \brief Generic expression of a partially reduxed matrix
	*
	* \param Direction indicates the direction of the redux (Vertical or Horizontal)
	* \param BinaryOp type of the binary functor implementing the operator (must be associative)
	* \param MatrixType the type of the matrix we are applying the redux operation
	*
	* This class represents an expression of a partial redux operator of a matrix.
	* It is the return type of MatrixBase::verticalRedux(), MatrixBase::horizontalRedux(),
	* and most of the time this is the only way it is used.
	*
	* \sa class CwiseBinaryOp
	*/
	template<int Direction, typename BinaryOp, typename MatrixType>
	struct ei_traits<PartialRedux<Direction, BinaryOp, MatrixType> >
	{
	typedef typename ei_result_of<
	BinaryOp(typename MatrixType::Scalar)
	>::type Scalar;
	typedef typename ei_xpr_copy<MatrixType>::type MatrixTypeXprCopy;
	typedef typename ei_unref<MatrixTypeXprCopy>::type _MatrixTypeXprCopy;
	enum {
	RowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::RowsAtCompileTime,
	ColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::ColsAtCompileTime,
	MaxRowsAtCompileTime = Direction==Vertical ? 1 : MatrixType::MaxRowsAtCompileTime,
	MaxColsAtCompileTime = Direction==Horizontal ? 1 : MatrixType::MaxColsAtCompileTime,
	Flags = (RowsAtCompileTime == Dynamic \|\| ColsAtCompileTime == Dynamic)
	? (unsigned int)_MatrixTypeXprCopy::Flags
	: (unsigned int)_MatrixTypeXprCopy::Flags & ~LargeBit,
	TraversalSize = Direction==Vertical ? RowsAtCompileTime : ColsAtCompileTime,
	CoeffReadCost = TraversalSize * _MatrixTypeXprCopy::CoeffReadCost
	+ (TraversalSize - 1) * ei_functor_traits<BinaryOp>::Cost
	};
	};

	template<int Direction, typename BinaryOp, typename MatrixType>
	class PartialRedux : ei_no_assignment_operator,
	public MatrixBase<PartialRedux<Direction, BinaryOp, MatrixType> >
	{
	public:

	EIGEN_GENERIC_PUBLIC_INTERFACE(PartialRedux)
	typedef typename ei_traits<PartialRedux>::MatrixTypeXprCopy MatrixTypeXprCopy;
	typedef typename ei_traits<PartialRedux>::_MatrixTypeXprCopy _MatrixTypeXprCopy;

	PartialRedux(const MatrixType& mat, const BinaryOp& func = BinaryOp())
	: m_matrix(mat), m_functor(func) {}

	private:

	int _rows() const { return (Direction==Vertical ? 1 : m_matrix.rows()); }
	int _cols() const { return (Direction==Horizontal ? 1 : m_matrix.cols()); }

	const Scalar _coeff(int i, int j) const
	{
	if (Direction==Vertical)
	return this->col(j).redux(m_functor);
	else
	return this->row(i).redux(m_functor);
	}

	protected:
	const MatrixTypeXprCopy m_matrix;
	const BinaryOp m_functor;
	};

	/** \returns a row vector expression of *this vertically reduxed by \a func
	*
	* The template parameter \a BinaryOp is the type of the functor
	* of the custom redux operator. Note that func must be an associative operator.
	*
	* \sa class PartialRedux, MatrixBase::horizontalRedux()
	*/
	template<typename Derived>
	template<typename BinaryOp>
	const PartialRedux<Vertical, BinaryOp, Derived>
	MatrixBase<Derived>::verticalRedux(const BinaryOp& func) const
	{
	return PartialRedux<Vertical, BinaryOp, Derived>(derived(), func);
	}

	/** \returns a row vector expression of *this horizontally reduxed by \a func
	*
	* The template parameter \a BinaryOp is the type of the functor
	* of the custom redux operator. Note that func must be an associative operator.
	*
	* \sa class PartialRedux, MatrixBase::verticalRedux()
	*/
	template<typename Derived>
	template<typename BinaryOp>
	const PartialRedux<Horizontal, BinaryOp, Derived>
	MatrixBase<Derived>::horizontalRedux(const BinaryOp& func) const
	{
	return PartialRedux<Horizontal, BinaryOp, Derived>(derived(), func);
	}


	/** \returns the result of a full redux operation on the whole matrix or vector using \a func
	*
	* The template parameter \a BinaryOp is the type of the functor \a func which must be
	* an assiociative operator. Both current STL and TR1 functor styles are handled.
	*
	* \sa MatrixBase::sum(), MatrixBase::minCoeff(), MatrixBase::maxCoeff(), MatrixBase::verticalRedux(), MatrixBase::horizontalRedux()
	*/
	template<typename Derived>
	template<typename BinaryOp>
	typename ei_result_of<BinaryOp(typename ei_traits<Derived>::Scalar)>::type
	MatrixBase<Derived>::redux(const BinaryOp& func) const
	{
	const bool unroll = SizeAtCompileTime * CoeffReadCost
	+ (SizeAtCompileTime-1) * ei_functor_traits<BinaryOp>::Cost
	<= EIGEN_UNROLLING_LIMIT;
	if(unroll)
	return ei_redux_unroller<BinaryOp, Derived, 0,
	unroll ? SizeAtCompileTime : Dynamic>
	::run(derived(), func);
	else
	{
	Scalar res;
	res = coeff(0,0);
	for(int i = 1; i < rows(); i++)
	res = func(res, coeff(i, 0));
	for(int j = 1; j < cols(); j++)
	for(int i = 0; i < rows(); i++)
	res = func(res, coeff(i, j));
	return res;
	}
	}

	/** \returns the sum of all coefficients of *this
	*
	* \sa trace()
	*/
	template<typename Derived>
	typename ei_traits<Derived>::Scalar
	MatrixBase<Derived>::sum() const
	{
	return this->redux(Eigen::ei_scalar_sum_op<Scalar>());
	}

	/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
	*
	* \c *this can be any matrix, not necessarily square.
	*
	* \sa diagonal(), sum()
	*/
	template<typename Derived>
	typename ei_traits<Derived>::Scalar
	MatrixBase<Derived>::trace() const
	{
	return diagonal().sum();
	}

	/** \returns the minimum of all coefficients of *this
	*/
	template<typename Derived>
	typename ei_traits<Derived>::Scalar
	MatrixBase<Derived>::minCoeff() const
	{
	return this->redux(Eigen::ei_scalar_min_op<Scalar>());
	}

	/** \returns the maximum of all coefficients of *this
	*/
	template<typename Derived>
	typename ei_traits<Derived>::Scalar
	MatrixBase<Derived>::maxCoeff() const
	{
	return this->redux(Eigen::ei_scalar_max_op<Scalar>());
	}



	template<typename Derived, int UnrollCount>
	struct ei_all_unroller
	{
	enum {
	col = (UnrollCount-1) / Derived::RowsAtCompileTime,
	row = (UnrollCount-1) % Derived::RowsAtCompileTime
	};

	static bool run(const Derived &mat)
	{
	return ei_all_unroller<Derived, UnrollCount-1>::run(mat) && mat.coeff(row, col);
	}
	};

	template<typename Derived>
	struct ei_all_unroller<Derived, 1>
	{
	static bool run(const Derived &mat) { return mat.coeff(0, 0); }
	};

	template<typename Derived>
	struct ei_all_unroller<Derived, Dynamic>
	{
	static bool run(const Derived &) { return false; }
	};

	template<typename Derived, int UnrollCount>
	struct ei_any_unroller
	{
	enum {
	col = (UnrollCount-1) / Derived::RowsAtCompileTime,
	row = (UnrollCount-1) % Derived::RowsAtCompileTime
	};

	static bool run(const Derived &mat)
	{
	return ei_any_unroller<Derived, UnrollCount-1>::run(mat) \|\| mat.coeff(row, col);
	}
	};

	template<typename Derived>
	struct ei_any_unroller<Derived, 1>
	{
	static bool run(const Derived &mat) { return mat.coeff(0, 0); }
	};

	template<typename Derived>
	struct ei_any_unroller<Derived, Dynamic>
	{
	static bool run(const Derived &) { return false; }
	};

	/** \returns true if all coefficients are true
	*
	* \sa MatrixBase::any()
	*/
	template<typename Derived>
	bool MatrixBase<Derived>::all(void) const
	{
	const bool unroll = SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost)
	<= EIGEN_UNROLLING_LIMIT;
	if(unroll)
	return ei_all_unroller<Derived,
	unroll ? SizeAtCompileTime : Dynamic
	>::run(derived());
	else
	{
	for(int j = 0; j < cols(); j++)
	for(int i = 0; i < rows(); i++)
	if (!coeff(i, j)) return false;
	return true;
	}
	}

	/** \returns true if at least one coefficient is true
	*
	* \sa MatrixBase::any()
	*/
	template<typename Derived>
	bool MatrixBase<Derived>::any(void) const
	{
	const bool unroll = SizeAtCompileTime * (CoeffReadCost + NumTraits<Scalar>::AddCost)
	<= EIGEN_UNROLLING_LIMIT;
	if(unroll)
	return ei_any_unroller<Derived,
	unroll ? SizeAtCompileTime : Dynamic
	>::run(derived());
	else
	{
	for(int j = 0; j < cols(); j++)
	for(int i = 0; i < rows(); i++)
	if (coeff(i, j)) return true;
	return false;
	}
	}

	#endif // EIGEN_REDUX_H