Matrix.hpp

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/*
 * Copyright(c):
 * Signal Image and Communications (SIC) Department 
 * http://www.sic.sp2mi.univ-poitiers.fr/ 
 *  - University of Poitiers, France http://www.univ-poitiers.fr 
 *  - XLIM  Institute UMR CNRS 7252  http://www.xlim.fr/ 
 * 
 * and 
 * 
 * D2 Fluid, Thermic and Combustion 
 *  - University of Poitiers, France http://www.univ-poitiers.fr 
 *  - PPRIME Institute -  UPR CNRS 3346  http://www.pprime.fr
 *  - ISAE-ENSMA http://www.ensma.fr
 *
 * Contributor(s):
 * The SLIP team,
 * Benoit Tremblais <tremblais_AT_sic.univ-poitiers.fr>,
 * Laurent David <laurent.david_AT_lea.univ-poitiers.fr>, 
 * Ludovic Chatellier <ludovic.chatellier_AT_univ-poitiers.fr>, 
 * Lionel Thomas <lionel.thomas_AT_univ-poitiers.fr>, 
 * Denis Arrivault <arrivault_AT_sic.univ-poitiers.fr>, 
 * Julien Dombre <julien.dombre_AT_univ-poitiers.fr>.
 *
 * Description:
 * The Simple Library of Image Processing (SLIP) is a new image processing 
 * library. It is written in the C++ language following as much as possible 
 * the ISO/ANSI C++ standard. It is consequently compatible with any system  
 * satisfying the ANSI C++ complience. It works on different Unix , Linux ,  
 * Mircrosoft Windows and Mac OS X plateforms. SLIP is a research library that  
 * was created by the Signal, Image and Communications (SIC) departement of  
 * the XLIM, UMR 7252 CNRS Institute in collaboration with the Fluids, Thermic  
 * and Combustion departement of the P', UPR 3346 CNRS Institute of the  
 * University of Poitiers.
 * 
 * The SLIP Library source code has been registered to the APP (French Agency 
 * for the Protection of Programs) by the University of Poitiers and CNRS, 
 * under  registration number IDDN.FR.001.300034.000.S.P.2010.000.21000.

 * http://www.sic.sp2mi.univ-poitiers.fr/slip/
 *
 * This software is governed by the CeCILL-C license under French law and
 * abiding by the rules of distribution of free software.  You can  use, 
 * modify and/ or redistribute the software under the terms of the CeCILL-C 
 * license as circulated by CEA, CNRS and INRIA at the following URL 
 * http://www.cecill.info.
 * As a counterpart to the access to the source code and  rights to copy,
 * modify and redistribute granted by the license, users are provided only
 * with a limited warranty  and the software's author,  the holder of the
 * economic rights,  and the successive licensors  have only  limited
 * liability.
 * 
 * In this respect, the user's attention is drawn to the risks associated
 * with loading,  using,  modifying and/or developing or reproducing the
 * software by the user in light of its specific status of free software,
 * that may mean  that it is complicated to manipulate,  and  that  also
 * therefore means  that it is reserved for developers  and  experienced
 * professionals having in-depth computer knowledge. Users are therefore
 * encouraged to load and test the software's suitability as regards their
 * requirements in conditions enabling the security of their systems and/or
 * data to be ensured and,  more generally, to use and operate it in the 
 * same conditions as regards security. 
 *
 * The fact that you are presently reading this means that you have had
 * knowledge of the CeCILL-C license and that you accept its terms.
 */



#ifndef SLIP_MATRIX_HPP
#define SLIP_MATRIX_HPP

#include <iostream>
#include <iterator>
#include <cassert>
#include <numeric>
#include <algorithm>
#include <cmath>
#include <string>
#include <cstddef>
#include "Array2d.hpp"
#include "Point2d.hpp"
#include "DPoint2d.hpp"
#include "stride_iterator.hpp"
#include "iterator2d_box.hpp"
#include "Range.hpp"
#include "iterator2d_range.hpp"
#include "apply.hpp"
#include "norms.hpp"
#include "linear_algebra.hpp"
#include "linear_algebra_traits.hpp"
#include "linear_algebra_eigen.hpp"
#include "linear_algebra_svd.hpp"
#include "complex_cast.hpp"


#include <boost/serialization/access.hpp>
#include <boost/serialization/split_member.hpp>
#include <boost/serialization/string.hpp>
#include <boost/serialization/complex.hpp>
#include <boost/serialization/version.hpp>

namespace slip
{

template<class T>
class stride_iterator;

template<class T>
class iterator2d_box;

template<class T>
class iterator2d_range;

template<class T>
class const_iterator2d_box;

template<class T>
class const_iterator2d_range;

template <class T>
class DPoint2d;

template <class T>
class Point2d;

template <class T>
class Box2d;

template <typename T>
class Matrix;

template <typename T>
class Array2d;

template <typename T>
std::ostream& operator<<(std::ostream & out, const slip::Matrix<T>& a);

template<typename T>
bool operator==(const slip::Matrix<T>& x, 
                                const slip::Matrix<T>& y);

template<typename T>
bool operator!=(const slip::Matrix<T>& x, 
                                const slip::Matrix<T>& y);

template<typename T>
bool operator<(const slip::Matrix<T>& x, 
                       const slip::Matrix<T>& y);

template<typename T>
bool operator>(const slip::Matrix<T>& x, 
                       const slip::Matrix<T>& y);

template<typename T>
bool operator<=(const slip::Matrix<T>& x, 
                                const slip::Matrix<T>& y);

template<typename T>
bool operator>=(const slip::Matrix<T>& x, 
                                const slip::Matrix<T>& y);

template <typename T>
class Matrix
{
public :

  typedef T value_type;
  typedef Matrix<T> self;
  typedef const Matrix<T> const_self;

  typedef value_type* pointer;
  typedef value_type const * const_pointer;
  typedef value_type& reference;
  typedef value_type const & const_reference;

  typedef ptrdiff_t difference_type;
  typedef std::size_t size_type;

  typedef pointer iterator;
  typedef const_pointer const_iterator;
  
  typedef std::reverse_iterator<iterator> reverse_iterator;
  typedef std::reverse_iterator<const_iterator> const_reverse_iterator;

  typedef pointer row_iterator;
  typedef const_pointer const_row_iterator;
  typedef slip::stride_iterator<pointer> col_iterator;
  typedef slip::stride_iterator<const_pointer> const_col_iterator;

  
  typedef typename slip::Array2d<T>::iterator2d iterator2d;
  typedef typename slip::Array2d<T>::const_iterator2d const_iterator2d;
  typedef slip::stride_iterator<pointer> row_range_iterator;
  typedef slip::stride_iterator<const_pointer> const_row_range_iterator;
  typedef slip::stride_iterator<col_iterator> col_range_iterator;
  typedef slip::stride_iterator<const_col_iterator> const_col_range_iterator;
  typedef typename slip::Array2d<T>::iterator2d_range iterator2d_range;
  typedef typename slip::Array2d<T>::const_iterator2d_range const_iterator2d_range;


  typedef std::reverse_iterator<iterator> reverse_row_iterator;
  typedef std::reverse_iterator<const_iterator> const_reverse_row_iterator;
  typedef std::reverse_iterator<col_iterator> reverse_col_iterator;
  typedef std::reverse_iterator<const_col_iterator> const_reverse_col_iterator;
  typedef std::reverse_iterator<iterator2d> reverse_iterator2d;
  typedef std::reverse_iterator<const_iterator2d> const_reverse_iterator2d;
  typedef std::reverse_iterator<row_range_iterator> reverse_row_range_iterator;
  typedef std::reverse_iterator<const_row_range_iterator> const_reverse_row_range_iterator;
  typedef std::reverse_iterator<col_range_iterator> reverse_col_range_iterator;
  typedef std::reverse_iterator<const_col_range_iterator> const_reverse_col_range_iterator;
  typedef std::reverse_iterator<iterator2d_range> reverse_iterator2d_range;
  typedef std::reverse_iterator<const_iterator2d_range> const_reverse_iterator2d_range;
  
  typedef typename slip::lin_alg_traits<value_type>::value_type norm_type;

  
  //default iterator of the container
  typedef iterator2d default_iterator;
  typedef const_iterator2d const_default_iterator;

  static const std::size_t DIM = 2;
public:
  
  Matrix();
 
  Matrix(const size_type d1,
                 const size_type d2);
  
  Matrix(const size_type d1,
                 const size_type d2, 
                 const T& val);
 
  Matrix(const size_type d1,
                 const size_type d2, 
                 const T* val);

  template<typename InputIterator>
  Matrix(const size_type d1,
                 const size_type d2, 
                 InputIterator first,
                 InputIterator last)
  {
    array_ = new slip::Array2d<T>(d1,d2,first,last);
  } 
  Matrix(const self& rhs);

  ~Matrix();
  

  void resize(const size_type d1,
                      const size_type d2,
                      const T& val = T());


 
  iterator begin();


  iterator end();

  const_iterator begin() const;

  
  const_iterator end() const;
  
  reverse_iterator rbegin();
  
  reverse_iterator rend();
  
  const_reverse_iterator rbegin() const;

  
  const_reverse_iterator rend() const;

 
  row_iterator row_begin(const size_type row);

  
  row_iterator row_end(const size_type row);


  const_row_iterator row_begin(const size_type row) const;


  const_row_iterator row_end(const size_type row) const;
  
  col_iterator col_begin(const size_type col);


  col_iterator col_end(const size_type col);

  const_col_iterator col_begin(const size_type col) const;



  const_col_iterator col_end(const size_type col) const;


  row_range_iterator row_begin(const size_type row,
                                                       const slip::Range<int>& range);



  row_range_iterator row_end(const size_type row,
                                                     const slip::Range<int>& range);


  const_row_range_iterator row_begin(const size_type row,
                                                                     const slip::Range<int>& range) const;


  const_row_range_iterator row_end(const size_type row,
                                                                   const slip::Range<int>& range) const;


  col_range_iterator col_begin(const size_type col,
                                                       const slip::Range<int>& range);

  col_range_iterator col_end(const size_type col,
                                                     const slip::Range<int>& range);




  const_col_range_iterator col_begin(const size_type col,
                                                                     const slip::Range<int>& range) const;

 
  const_col_range_iterator col_end(const size_type col,
                                                                   const slip::Range<int>& range) const;

  

  reverse_row_iterator row_rbegin(const size_type row);


  reverse_row_iterator row_rend(const size_type row);

  const_reverse_row_iterator row_rbegin(const size_type row) const;

  const_reverse_row_iterator row_rend(const size_type row) const;

  reverse_col_iterator col_rbegin(const size_type col);

  
  reverse_col_iterator col_rend(const size_type col);

  const_reverse_col_iterator col_rbegin(const size_type col) const;

    
  const_reverse_col_iterator col_rend(const size_type col) const;
 

  reverse_row_range_iterator row_rbegin(const size_type row,
                                                                                const slip::Range<int>& range);

 
  reverse_row_range_iterator row_rend(const size_type row,
                                                                      const slip::Range<int>& range);



  const_reverse_row_range_iterator row_rbegin(const size_type row,
                                                                                      const slip::Range<int>& range) const;


  const_reverse_row_range_iterator row_rend(const size_type row,
                                                                                    const slip::Range<int>& range) const;
 
 


  reverse_col_range_iterator col_rbegin(const size_type col,
                                                                                const slip::Range<int>& range);

  reverse_col_range_iterator col_rend(const size_type col,
                                                                      const slip::Range<int>& range);


  const_reverse_col_range_iterator 
  col_rbegin(const size_type col,
                     const slip::Range<int>& range) const;

 
  const_reverse_col_range_iterator col_rend(const size_type col,
                                                                                    const slip::Range<int>& range) const;


  iterator2d upper_left();
  
  
  iterator2d bottom_right();


  const_iterator2d upper_left() const;
  
 
  const_iterator2d bottom_right() const;

  iterator2d upper_left(const Box2d<int>& box);

 
  iterator2d bottom_right(const Box2d<int>& box);


  const_iterator2d upper_left(const Box2d<int>& box) const;

 
  const_iterator2d bottom_right(const Box2d<int>& box) const;


  iterator2d_range upper_left(const Range<int>& row_range,
                                                      const Range<int>& col_range);

  iterator2d_range bottom_right(const Range<int>& row_range,
                                                                const Range<int>& col_range);


  const_iterator2d_range upper_left(const Range<int>& row_range,
                                                                    const Range<int>& col_range) const;


  const_iterator2d_range bottom_right(const Range<int>& row_range,
                                                                      const Range<int>& col_range) const;


 


  iterator2d_range upper_left(const Range<int>& range);
 

  iterator2d_range bottom_right(const Range<int>& range);

 

  
  const_iterator2d_range upper_left(const Range<int>& range) const;

 

  const_iterator2d_range bottom_right(const Range<int>& range) const;

 
  reverse_iterator2d rupper_left();
  
  reverse_iterator2d rbottom_right();

  const_reverse_iterator2d rupper_left() const;
 
 
  const_reverse_iterator2d rbottom_right() const;
  

  reverse_iterator2d rupper_left(const Box2d<int>& box);

  reverse_iterator2d rbottom_right(const Box2d<int>& box);

  const_reverse_iterator2d rupper_left(const Box2d<int>& box) const;


  const_reverse_iterator2d rbottom_right(const Box2d<int>& box) const;

 
  reverse_iterator2d_range rupper_left(const Range<int>& row_range,
                                                                       const Range<int>& col_range);


 
  reverse_iterator2d_range rbottom_right(const Range<int>& row_range,
                                                                                 const Range<int>& col_range);


 
  const_reverse_iterator2d_range rupper_left(const Range<int>& row_range,
                                                                                     const Range<int>& col_range) const;

  const_reverse_iterator2d_range rbottom_right(const Range<int>& row_range,
                                                                                       const Range<int>& col_range) const;


 
  reverse_iterator2d_range rupper_left(const Range<int>& range);



  reverse_iterator2d_range rbottom_right(const Range<int>& range);
  

  const_reverse_iterator2d_range rupper_left(const Range<int>& range) const;


  const_reverse_iterator2d_range rbottom_right(const Range<int>& range) const;
  


  friend std::ostream& operator<< <>(std::ostream & out, 
                                                                     const self& a);

  Matrix& operator=(const self & rhs);

  self& operator=(const T& val);

  

  void fill(const T& value)
  {
    std::fill_n(this->begin(),this->size(),value);
  } 
  
  void fill(const T* value)
  {
    std::copy(value,value + this->size(), this->begin());
  } 

  template<typename InputIterator>
  void fill(InputIterator first,
                    InputIterator last)
  {
    std::copy(first,last, this->begin());
  }

  friend bool operator== <>(const Matrix<T>& x, 
                                                    const Matrix<T>& y);

  friend bool operator!= <>(const Matrix<T>& x, 
                                                    const Matrix<T>& y);

  friend bool operator< <>(const Matrix<T>& x, 
                                                   const Matrix<T>& y);

  friend bool operator> <>(const Matrix<T>& x, 
                                                   const Matrix<T>& y);

  friend bool operator<= <>(const Matrix<T>& x, 
                                                    const Matrix<T>& y);

  friend bool operator>= <>(const Matrix<T>& x, 
                                                    const Matrix<T>& y);


  pointer operator[](const size_type i);

  const_pointer operator[](const size_type i) const;


  reference operator()(const size_type i,
                                       const size_type j);
 
  const_reference operator()(const size_type i,
                                                     const size_type j) const;

  reference operator()(const Point2d<size_type>& point2d);
 
  const_reference operator()(const Point2d<size_type>& point2d) const;


  self operator()(const Range<int>& row_range,
                                  const Range<int>& col_range);
 

  std::string name() const;

  size_type dim1() const;

  size_type rows() const;
  
  size_type dim2() const;

  size_type columns() const;

  size_type cols() const;

  size_type size() const;

  size_type max_size() const;

  bool empty()const;

  void swap(self& M);

 
  self& operator+=(const T& val);
  self& operator-=(const T& val);
  self& operator*=(const T& val);
  self& operator/=(const T& val);
//   self& operator%=(const T& val);
//   self& operator^=(const T& val);
//   self& operator&=(const T& val);
//   self& operator|=(const T& val);
//   self& operator<<=(const T& val);
//   self& operator>>=(const T& val);


  self  operator-() const;
  //self  operator!() const;

  

  self& operator+=(const self& rhs);
  self& operator-=(const self& rhs);
  self& operator*=(const self& rhs);
  self& operator/=(const self& rhs);
    

  T& min() const;


  T& max() const;

  T sum() const;

  T trace() const;

  T det() const;

  norm_type cond() const;


  size_type rank() const;

  self inv() const;

  norm_type L1_norm() const
  {
    assert(this->size() != 0);
    return slip::row_norm(*this);
  }

  norm_type L2_norm() const
  {
    assert(this->size() != 0);
    slip::Array2d<T> U(this->rows(),this->cols());
    slip::Array2d<T> V(this->cols(),this->cols());
    slip::Array<T> W(this->cols());
    slip::svd(*this,U,W.begin(),W.end(),V);
    return std::abs(W[0]);
  }

  norm_type infinite_norm() const
  {
    return slip::col_norm(*this);
  }
  
  norm_type frobenius_norm() const
  {
    return slip::frobenius_norm(*this);
  }

  norm_type spectral_radius() const
  {
    return slip::spectral_radius(*this);
  }
    
  Matrix<T>& apply(T (*fun)(T));

  Matrix<T>& apply(T (*fun)(const T&));

 private:
  Array2d<T>* array_;

  private:
    friend class boost::serialization::access;
    template<class Archive>
    void save(Archive & ar, const unsigned int version) const
    {
      ar & this->array_;
    }
    template<class Archive>
    void load(Archive & ar, const unsigned int version)
    {
      ar & this->array_;
    }
    BOOST_SERIALIZATION_SPLIT_MEMBER();
};

  typedef slip::Matrix<double> Matrix_d;
  typedef slip::Matrix<float> Matrix_f;
  typedef slip::Matrix<long> Matrix_l;
  typedef slip::Matrix<unsigned long> Matrix_ul;
  typedef slip::Matrix<short> Matrix_s;
  typedef slip::Matrix<unsigned short> Matrix_us;
  typedef slip::Matrix<int> Matrix_i;
  typedef slip::Matrix<unsigned int> Matrix_ui;
  typedef slip::Matrix<char> Matrix_c;
  typedef slip::Matrix<unsigned char> Matrix_uc;

}//slip::
namespace slip{
template<typename T>
Matrix<T> operator+(const Matrix<T>& M1, 
                                    const Matrix<T>& M2);

template<typename T>
Matrix<T> operator+(const Matrix<T>& M1, 
                                    const T& val);

  template<typename T>
  Matrix<T> operator+(const T& val, 
                                      const Matrix<T>& M1);
  
template<typename T>
Matrix<T> operator-(const Matrix<T>& M1, 
                                    const Matrix<T>& M2);

template<typename T>
Matrix<T> operator-(const Matrix<T>& M1, 
                                    const T& val);

  template<typename T>
  Matrix<T> operator-(const T& val, 
                                      const Matrix<T>& M1);
  
  template<typename T>
  Matrix<T> operator*(const Matrix<T>& M1, 
                                      const Matrix<T>& M2);

  template<typename T>
  Matrix<T> operator*(const Matrix<T>& M1, 
                                      const T& val);

  template<typename T>
  Matrix<T> operator*(const T& val, 
                                      const Matrix<T>& M1);
  
  template<typename T>
  Matrix<T> operator/(const Matrix<T>& M1, 
                                      const Matrix<T>& M2);

  template<typename T>
  Matrix<T> operator/(const Matrix<T>& M1, 
                                      const T& val);
/* @} */

  template<typename T>
  T& min(const Matrix<T>& M1);
  
  template<typename T>
  T& max(const Matrix<T>& M1);

  template<typename T>
  Matrix<typename slip::lin_alg_traits<T>::value_type> abs(const Matrix<T>& V);

  template<typename T>
  Matrix<T> sqrt(const Matrix<T>& V);

  template<typename T>
  Matrix<T> cos(const Matrix<T>& V);

  Matrix<float> acos(const Matrix<float>& V);
  Matrix<double> acos(const Matrix<double>& V);
  Matrix<long double> acos(const Matrix<long double>& V);
  

  template<typename T>
  Matrix<T> sin(const Matrix<T>& V);

 
  Matrix<float> asin(const Matrix<float>& V);
  Matrix<double> asin(const Matrix<double>& V);
  Matrix<long double> asin(const Matrix<long double>& V);
  

  template<typename T>
  Matrix<T> tan(const Matrix<T>& V);

 
  Matrix<float> atan(const Matrix<float>& V);
  Matrix<double> atan(const Matrix<double>& V);
  Matrix<long double> atan(const Matrix<long double>& V);
  

  template<typename T>
  Matrix<T> exp(const Matrix<T>& V);

  template<typename T>
  Matrix<T> log(const Matrix<T>& V);

  template<typename T>
  Matrix<T> cosh(const Matrix<T>& V);

  template<typename T>
  Matrix<T> sinh(const Matrix<T>& V);

  template<typename T>
  Matrix<T> tanh(const Matrix<T>& V);

  template<typename T>
  Matrix<T> log10(const Matrix<T>& V);
  

}//slip::

namespace slip
{
  template<typename T>
  inline
  Matrix<T>::Matrix():
    array_(new slip::Array2d<T>())
  {}

  template<typename T>
  inline
  Matrix<T>::Matrix(const typename Matrix<T>::size_type d1,
                                    const typename Matrix<T>::size_type d2):
    array_(new slip::Array2d<T>(d1,d2))
  {}
  
  template<typename T>
  inline
  Matrix<T>::Matrix(const typename Matrix<T>::size_type d1,
                                    const typename Matrix<T>::size_type d2, 
                                    const T& val):
    array_(new slip::Array2d<T>(d1,d2,val))
  {}

  template<typename T>
  inline
  Matrix<T>::Matrix(const typename Matrix<T>::size_type d1,
                                    const typename Matrix<T>::size_type d2, 
                                    const T* val):
    array_(new slip::Array2d<T>(d1,d2,val))   
  {}
  
  template<typename T>
  inline
  Matrix<T>::Matrix(const Matrix<T>& rhs):
    array_(new slip::Array2d<T>((*rhs.array_)))
  {}

  template<typename T>
  inline
  Matrix<T>::~Matrix()
  {
    delete array_;
  }
  
  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator=(const Matrix<T> & rhs)
  {
    if(this != &rhs)
      {
                *array_ = *(rhs.array_);
      }
    return *this;
  }

  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator=(const T& val)
  {
    std::fill_n((*array_)[0],array_->size(),val);
    return *this;
  }
  
  template<typename T>
  inline
  void Matrix<T>::resize(const typename Matrix<T>::size_type d1,
                                                 const typename Matrix<T>::size_type d2,
                                                 const T& val)
  {
    array_->resize(d1,d2,val);
  }


  template<typename T>
  inline
  typename Matrix<T>::iterator Matrix<T>::begin()
  {
    return array_->begin();
  }

  template<typename T>
  inline
  typename Matrix<T>::iterator Matrix<T>::end()
  {
    return array_->end();
  }
  
  template<typename T>
  inline
  typename Matrix<T>::const_iterator Matrix<T>::begin() const
  {
    Array2d<T> const * tp(array_);
    return tp->begin();
  }

  template<typename T>
  inline
  typename Matrix<T>::const_iterator Matrix<T>::end() const
  {
    Array2d<T> const * tp(array_);
    return tp->end();
  }
  

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator Matrix<T>::rbegin()
  {
    return typename Matrix<T>::reverse_iterator(this->end());
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator Matrix<T>::rend()
  {
    return typename Matrix<T>::reverse_iterator(this->begin());
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator Matrix<T>::rbegin() const
  {
    return typename Matrix<T>::const_reverse_iterator(this->end());
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator Matrix<T>::rend() const
  {
    return typename Matrix<T>::const_reverse_iterator(this->begin());
  }

  template<typename T>
  inline
  typename Matrix<T>::row_iterator 
  Matrix<T>::row_begin(const typename Matrix<T>::size_type row)
  {
    return array_->row_begin(row);
  }

 template<typename T>
 inline
 typename Matrix<T>::row_iterator 
 Matrix<T>::row_end(const typename Matrix<T>::size_type row)
  {
    return array_->row_end(row);
  }

  template<typename T>
  inline
  typename Matrix<T>::col_iterator 
  Matrix<T>::col_begin(const typename Matrix<T>::size_type col)
  {
    return array_->col_begin(col);
  }


  template<typename T>
  inline
  typename Matrix<T>::col_iterator
  Matrix<T>::col_end(const typename Matrix<T>::size_type col)
  {
    return array_->col_end(col);
  }


 template<typename T>
 inline
 typename Matrix<T>::const_row_iterator
 Matrix<T>::row_begin(const typename Matrix<T>::size_type row) const
  {
    Array2d<T> const * tp(array_);
    return tp->row_begin(row);
  }

 template<typename T>
 inline
 typename Matrix<T>::const_row_iterator 
 Matrix<T>::row_end(const typename Matrix<T>::size_type row) const
  {
    Array2d<T> const * tp(array_);
    return tp->row_end(row);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_col_iterator Matrix<T>::col_begin(const typename Matrix<T>::size_type col) const
  {
    Array2d<T> const * tp(array_);
    return tp->col_begin(col);
  }
  
  template<typename T>
  inline
  typename Matrix<T>::const_col_iterator Matrix<T>::col_end(const typename Matrix<T>::size_type col) const
  {
    Array2d<T> const * tp(array_);
    return tp->col_end(col);
  }


  template<typename T>
  inline
  typename Matrix<T>::reverse_row_iterator
  Matrix<T>::row_rbegin(const typename Matrix<T>::size_type row)
  {
    return array_->row_rbegin(row);
  }
 
  template<typename T>
  inline
  typename Matrix<T>::const_reverse_row_iterator 
  Matrix<T>::row_rbegin(const typename Matrix<T>::size_type row) const
  {
    Array2d<T> const * tp(array_);
    return tp->row_rbegin(row);
  }
  
  template<typename T>
  inline
  typename Matrix<T>::reverse_row_iterator Matrix<T>::row_rend(const typename Matrix<T>::size_type row)
  {
    return array_->row_rend(row);
  }
 
  template<typename T>
  inline
  typename Matrix<T>::const_reverse_row_iterator
  Matrix<T>::row_rend(const typename Matrix<T>::size_type row) const
  {
    Array2d<T> const * tp(array_);
    return tp->row_rend(row);
  }

  
  template<typename T>
  inline
  typename Matrix<T>::reverse_col_iterator Matrix<T>::col_rbegin(const typename Matrix<T>::size_type col)
  {
    return array_->col_rbegin(col);
  }
 
  template<typename T>
  inline
  typename Matrix<T>::const_reverse_col_iterator 
  Matrix<T>::col_rbegin(const typename Matrix<T>::size_type col) const
  {
    Array2d<T> const * tp(array_);
    return tp->col_rbegin(col);
  }
  
  template<typename T>
  inline
  typename Matrix<T>::reverse_col_iterator 
  Matrix<T>::col_rend(const typename Matrix<T>::size_type col)
  {
    return array_->col_rend(col);
  }
 
  template<typename T>
  inline
  typename Matrix<T>::const_reverse_col_iterator
  Matrix<T>::col_rend(const typename Matrix<T>::size_type col) const
  {
    Array2d<T> const * tp(array_);
    return tp->col_rend(col);
  }

  template<typename T>
  inline
  typename Matrix<T>::row_range_iterator 
  Matrix<T>::row_begin(const typename Matrix<T>::size_type row,
                                       const slip::Range<int>& range)
  {
    return array_->row_begin(row,range);
  }

   template<typename T>
  inline
   typename Matrix<T>::const_row_range_iterator 
   Matrix<T>::row_begin(const typename Matrix<T>::size_type row,
                                                const slip::Range<int>& range) const
   {
     Array2d<T> const * tp(array_);
     return tp->row_begin(row,range);
   }

  template<typename T>
  inline
  typename Matrix<T>::col_range_iterator 
  Matrix<T>::col_begin(const typename Matrix<T>::size_type col,
                                       const slip::Range<int>& range)
  {
    return array_->col_begin(col,range);
  }

   template<typename T>
  inline
   typename Matrix<T>::const_col_range_iterator 
   Matrix<T>::col_begin(const typename Matrix<T>::size_type col,
                                                const slip::Range<int>& range) const
   {
     Array2d<T> const * tp(array_);
     return tp->col_begin(col,range);
   }
  

  template<typename T>
  inline
  typename Matrix<T>::row_range_iterator 
  Matrix<T>::row_end(const typename Matrix<T>::size_type row,
                                       const slip::Range<int>& range)
  {
    return array_->row_end(row,range);
  }

   template<typename T>
  inline
   typename Matrix<T>::const_row_range_iterator 
   Matrix<T>::row_end(const typename Matrix<T>::size_type row,
                                                const slip::Range<int>& range) const
   {
     Array2d<T> const * tp(array_);
     return tp->row_end(row,range);
   }

  template<typename T>
  inline
  typename Matrix<T>::col_range_iterator 
  Matrix<T>::col_end(const typename Matrix<T>::size_type col,
                                     const slip::Range<int>& range)
  {
    return array_->col_end(col,range);
  }

   template<typename T>
  inline
   typename Matrix<T>::const_col_range_iterator 
   Matrix<T>::col_end(const typename Matrix<T>::size_type col,
                                      const slip::Range<int>& range) const
   {
     Array2d<T> const * tp(array_);
     return tp->col_end(col,range);
   }

  template<typename T>
  inline
  typename Matrix<T>::reverse_row_range_iterator 
  Matrix<T>::row_rbegin(const typename Matrix<T>::size_type row,
                                                const slip::Range<int>& range)
  {
     return typename Matrix<T>::reverse_row_range_iterator(this->row_end(row,range));
  }

 template<typename T>
  inline
  typename Matrix<T>::const_reverse_row_range_iterator 
  Matrix<T>::row_rbegin(const typename Matrix<T>::size_type row,
                                                 const slip::Range<int>& range) const
  {
    return typename Matrix<T>::const_reverse_row_range_iterator(this->row_end(row,range));
  }


  template<typename T>
  inline
  typename Matrix<T>::reverse_col_range_iterator 
  Matrix<T>::col_rbegin(const typename Matrix<T>::size_type col,
                                                 const slip::Range<int>& range)
  {
    return typename Matrix<T>::reverse_col_range_iterator(this->col_end(col,range));
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_col_range_iterator 
  Matrix<T>::col_rbegin(const typename Matrix<T>::size_type col,
                                                 const slip::Range<int>& range) const
  {
    return typename Matrix<T>::const_reverse_col_range_iterator(this->col_end(col,range));
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_row_range_iterator 
  Matrix<T>::row_rend(const typename Matrix<T>::size_type row,
                                       const slip::Range<int>& range)
  {
    return typename Matrix<T>::reverse_row_range_iterator(this->row_begin(row,range));
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_row_range_iterator 
  Matrix<T>::row_rend(const typename Matrix<T>::size_type row,
                                                 const slip::Range<int>& range) const
  {
    return typename Matrix<T>::const_reverse_row_range_iterator(this->row_begin(row,range));
  }


  template<typename T>
  inline
  typename Matrix<T>::reverse_col_range_iterator 
  Matrix<T>::col_rend(const typename Matrix<T>::size_type col,
                                       const slip::Range<int>& range)
  {
    return typename Matrix<T>::reverse_col_range_iterator(this->col_begin(col,range));
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_col_range_iterator 
  Matrix<T>::col_rend(const typename Matrix<T>::size_type col,
                                       const slip::Range<int>& range) const
  {
    return typename Matrix<T>::const_reverse_col_range_iterator(this->col_begin(col,range));
  }

  template<typename T>
  inline
  typename Matrix<T>::iterator2d Matrix<T>::upper_left()
  {
    return array_->upper_left();
  }

  template<typename T>
  inline
  typename Matrix<T>::const_iterator2d Matrix<T>::upper_left() const
  {
    Array2d<T> const * tp(array_);
    return tp->upper_left();
  }


  template<typename T>
  inline
  typename Matrix<T>::iterator2d Matrix<T>::bottom_right()
  {
    return array_->bottom_right();
  }

  template<typename T>
  inline
  typename Matrix<T>::const_iterator2d Matrix<T>::bottom_right() const
  {
    Array2d<T> const * tp(array_);
    return tp->bottom_right();
  }

  template<typename T>
  inline
  typename Matrix<T>::iterator2d Matrix<T>::upper_left(const Box2d<int>& box)
  {
    return array_->upper_left(box);
  }


  template<typename T>
  inline
  typename Matrix<T>::const_iterator2d Matrix<T>::upper_left(const Box2d<int>& box) const
  {
    Array2d<T> const * tp(array_);
    return tp->upper_left(box);
  }

  template<typename T>
  inline
  typename Matrix<T>::iterator2d Matrix<T>::bottom_right(const Box2d<int>& box)
  {
    return array_->bottom_right(box);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_iterator2d Matrix<T>::bottom_right(const Box2d<int>& box) const
  {
    Array2d<T> const * tp(array_);
    return tp->bottom_right(box);
  }


  template<typename T>
  inline
  typename Matrix<T>::iterator2d_range 
  Matrix<T>::upper_left(const Range<int>& row_range,
                                                 const Range<int>& col_range)
  {
    return array_->upper_left(row_range,col_range);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_iterator2d_range 
  Matrix<T>::upper_left(const Range<int>& row_range,
                                                const Range<int>& col_range) const
  {
    Array2d<T> const * tp(array_);
    return tp->upper_left(row_range,col_range);
  }

  template<typename T>
  inline
  typename Matrix<T>::iterator2d_range 
  Matrix<T>::bottom_right(const Range<int>& row_range,
                                                  const Range<int>& col_range)
  {
    return array_->bottom_right(row_range,col_range);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_iterator2d_range 
  Matrix<T>::bottom_right(const Range<int>& row_range,
                                                  const Range<int>& col_range) const
  {
    Array2d<T> const * tp(array_);
    return tp->bottom_right(row_range,col_range);
  }

   template<typename T>
  inline
  typename Matrix<T>::iterator2d_range 
  Matrix<T>::upper_left(const Range<int>& range)
  {
    return array_->upper_left(range);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_iterator2d_range 
  Matrix<T>::upper_left(const Range<int>& range) const
  {
    Array2d<T> const * tp(array_);
    return tp->upper_left(range);
  }

  template<typename T>
  inline
  typename Matrix<T>::iterator2d_range 
  Matrix<T>::bottom_right(const Range<int>& range)
  {
    return array_->bottom_right(range);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_iterator2d_range 
  Matrix<T>::bottom_right(const Range<int>& range) const
  {
    Array2d<T> const * tp(array_);
    return tp->bottom_right(range);
  }

  
   template<typename T>
  inline
  typename Matrix<T>::reverse_iterator2d 
  Matrix<T>::rbottom_right()
  {
    return array_->rbottom_right();
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator2d 
  Matrix<T>::rbottom_right() const
  {
    Array2d<T> const * tp(array_);
    return tp->rbottom_right();
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator2d 
  Matrix<T>::rupper_left()
  {
    return array_->rupper_left();
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator2d 
  Matrix<T>::rupper_left() const
  {
    Array2d<T> const * tp(array_);
    return tp->rupper_left();
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator2d 
  Matrix<T>::rbottom_right(const Box2d<int>& box)
  {
    return array_->rbottom_right(box);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator2d 
  Matrix<T>::rbottom_right(const Box2d<int>& box) const
  {
    Array2d<T> const * tp(array_);
    return tp->rbottom_right(box);
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator2d 
  Matrix<T>::rupper_left(const Box2d<int>& box)
  {
    return array_->rupper_left(box);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator2d 
  Matrix<T>::rupper_left(const Box2d<int>& box) const
  {
    Array2d<T> const * tp(array_);
    return tp->rupper_left(box);
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator2d_range 
  Matrix<T>::rupper_left(const Range<int>& row_range,
                                                  const Range<int>& col_range)
  {
    return array_->rupper_left(row_range,col_range);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator2d_range 
  Matrix<T>::rupper_left(const Range<int>& row_range,
                                                 const Range<int>& col_range) const
  {
    Array2d<T> const * tp(array_);
    return tp->rupper_left(row_range,col_range);
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator2d_range 
  Matrix<T>::rbottom_right(const Range<int>& row_range,
                                                    const Range<int>& col_range)
  {
    return array_->rbottom_right(row_range,col_range); 
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator2d_range 
  Matrix<T>::rbottom_right(const Range<int>& row_range,
                                                    const Range<int>& col_range) const
  {
    Array2d<T> const * tp(array_);
    return tp->rbottom_right(row_range,col_range); 
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator2d_range 
  Matrix<T>::rupper_left(const Range<int>& range)
  {
    return this->rupper_left(range,range);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator2d_range 
  Matrix<T>::rupper_left(const Range<int>& range) const
  {
    return this->rupper_left(range,range);
  }

  template<typename T>
  inline
  typename Matrix<T>::reverse_iterator2d_range 
  Matrix<T>::rbottom_right(const Range<int>& range)
  {
    return this->rbottom_right(range,range);
  }

  template<typename T>
  inline
  typename Matrix<T>::const_reverse_iterator2d_range 
  Matrix<T>::rbottom_right(const Range<int>& range) const
  {
    return this->rbottom_right(range,range);
  }

  template <typename T>
  inline
  std::ostream& operator<<(std::ostream & out, const Matrix<T>& a)
  {
    out<<*(a.array_);
    return out;
  }



  template<typename T>
  inline
  typename Matrix<T>::pointer 
  Matrix<T>::operator[](const typename Matrix<T>::size_type i)
  {
    return (*array_)[i];
  }
  
  template<typename T>
  inline
  typename Matrix<T>::const_pointer 
  Matrix<T>::operator[](const typename Matrix<T>::size_type i) const 
  {
    return (*array_)[i];
  }
  
  template<typename T>
  inline
  typename Matrix<T>::reference 
  Matrix<T>::operator()(const typename Matrix<T>::size_type i,
                                                const typename Matrix<T>::size_type j)
  {
    return (*array_)[i][j];
  }
  
  template<typename T>
  inline
  typename Matrix<T>::const_reference 
  Matrix<T>::operator()(const typename Matrix<T>::size_type i,
                                                const typename Matrix<T>::size_type j) const
  {
    return (*array_)[i][j];
  }

  template<typename T>
  inline
  typename Matrix<T>::reference 
  Matrix<T>::operator()(const Point2d<typename Matrix<T>::size_type>& point2d)
   {
     return (*array_)(point2d);
   }

  template<typename T>
  inline
  typename Matrix<T>::const_reference 
  Matrix<T>::operator()(const Point2d<typename Matrix<T>::size_type>& point2d) const
   {
     return (*array_)(point2d);
   }


  template<typename T>
  inline
  Matrix<T> 
  Matrix<T>::operator()(const Range<int>& row_range,
                                                 const Range<int>& col_range)
  {
    assert((*this)[0] != 0);
    assert(row_range.is_valid());
    assert(row_range.start() < int(this->dim2()));
    assert(row_range.stop()  < int(this->dim2()));
    assert(col_range.is_valid());
    assert(col_range.start() < int(this->dim1()));
    assert(col_range.stop()  < int(this->dim1()));
    std::size_t rows = row_range.iterations();
    std::size_t cols = col_range.iterations();
    return Matrix<T>(rows+1,cols+1,array_->upper_left(row_range,col_range),
                                       array_->bottom_right(row_range,col_range));
  } 

  template<typename T>
  inline
  std::string 
  Matrix<T>::name() const {return "Matrix";} 
 

  template<typename T>
  inline
  typename Matrix<T>::size_type Matrix<T>::dim1() const {return array_->dim1();} 
  
  template<typename T>
  inline
  typename Matrix<T>::size_type Matrix<T>::rows() const {return this->dim1();} 
  

  template<typename T>
  inline
  typename Matrix<T>::size_type Matrix<T>::dim2() const {return array_->dim2();} 
  
  template<typename T>
  inline
  typename Matrix<T>::size_type Matrix<T>::columns() const {return this->dim2();} 
 
  template<typename T>
  inline
  typename Matrix<T>::size_type Matrix<T>::cols() const {return this->dim2();} 
 
  template<typename T>
  inline
  typename Matrix<T>::size_type Matrix<T>::size() const {return array_->size();}

  template<typename T>
  inline
  typename Matrix<T>::size_type Matrix<T>::max_size() const {return array_->max_size();}


  template<typename T>
  inline
  bool Matrix<T>::empty()const {return array_->empty();}

  template<typename T>
  inline
  void Matrix<T>::swap(Matrix<T>& M)
  {
    array_->swap(*(M.array_));
  }


  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator+=(const T& val)
  {
    std::transform(array_->begin(),array_->end(),array_->begin(),std::bind2nd(std::plus<T>(),val));
    return *this;
  }
  
  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator-=(const T& val)
  {
    std::transform(array_->begin(),array_->end(),array_->begin(),std::bind2nd(std::minus<T>(),val));
    return *this;
  }

  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator*=(const T& val)
  {
    std::transform(array_->begin(),array_->end(),array_->begin(),std::bind2nd(std::multiplies<T>(),val));
    return *this;
  }
  
  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator/=(const T& val)
  {
    std::transform(array_->begin(),array_->end(),array_->begin(),std::bind2nd(std::divides<T>(),val));
    return *this;
  }
  
  template<typename T>
  inline
  Matrix<T> Matrix<T>::operator-() const
  {
    Matrix<T> tmp(*this);
    std::transform(array_->begin(),array_->end(),tmp.begin(),std::negate<T>());
    return tmp;
  }

  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator+=(const Matrix<T>& rhs)
  {
    assert(this->dim1() == rhs.dim1());
    assert(this->dim2() == rhs.dim2());
    std::transform(array_->begin(),array_->end(),(*(rhs.array_)).begin(),array_->begin(),std::plus<T>());
    return *this;
  }
  
  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator-=(const Matrix<T>& rhs)
  {
    assert(this->dim1() == rhs.dim1());
    assert(this->dim2() == rhs.dim2());
    std::transform(array_->begin(),array_->end(),(*(rhs.array_)).begin(),array_->begin(),std::minus<T>());
    return *this;
  }
  
  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator*=(const Matrix<T>& rhs)
  {
    assert(this->dim1() == rhs.dim1());
    assert(this->dim2() == rhs.dim2());
    std::transform(array_->begin(),array_->end(),(*(rhs.array_)).begin(),array_->begin(),std::multiplies<T>());
    return *this;
  }
  
  template<typename T>
  inline
  Matrix<T>& Matrix<T>::operator/=(const Matrix<T>& rhs)
  {
    assert(this->size() == rhs.size());
    std::transform(array_->begin(),array_->end(),(*(rhs.array_)).begin(),array_->begin(),std::divides<T>());
    return *this;
  }
                
 

  template<typename T>
  inline
  T& Matrix<T>::min() const
  {
    assert(array_->size() != 0);
    return *std::min_element(array_->begin(),array_->end(),std::less<T>());
  }

  template<typename T>
  inline
  T& Matrix<T>::max() const
  {
    assert(array_->size() != 0);
    return *std::max_element(array_->begin(),array_->end(),std::less<T>());
  }

  template<typename T>
  inline
  T Matrix<T>::sum() const
  {
    assert(array_->size() != 0);
    return std::accumulate(array_->begin(),array_->end(),T());
  }

  template<typename T>
  inline
  T Matrix<T>::trace() const
  {
    assert(array_->size() != 0);
    assert(this->rows() == this->cols());
    T sum = (*this)[0][0];
    for(std::size_t i = 1; i < this->rows(); ++i)
      {
                sum += (*this)[i][i];
      }
    return sum;
  }

  template<typename T>
  inline
  T Matrix<T>::det() const
  {
    assert(array_->size() != 0);
    assert(this->rows() == this->cols());
    return T(slip::lu_det(*this));
  }

  template<typename T>
  inline
  typename Matrix<T>::size_type Matrix<T>::rank() const
  {
    typename Matrix<T>::size_type r = typename Matrix<T>::size_type(0);
    //computes the SVD
    slip::Array2d<T> U(this->rows(),this->cols());
    slip::Array2d<T> V(this->cols(),this->cols());
    slip::Array<T> W(this->cols());
    slip::svd(*this,U,W.begin(),W.end(),V);
    norm_type max = std::abs(W[0]);
    norm_type tol = norm_type(std::max(this->rows(),this->cols())) * max * slip::epsilon<T>();
    for(std::size_t i = 0; i <  W.size(); ++i)
      {
                norm_type tmp = std::abs(W[i]);
                if(tmp > tol) 
                  {
                    r = (i + 1);
                  }
                else
                  {
                    break;
                  }
      }
    return r;
  }

  template<typename T>
  inline
  typename Matrix<T>::norm_type Matrix<T>::cond() const
  {
    assert(array_->size() != 0);
    assert(this->rows() == this->cols());
    slip::Array2d<T> U(this->rows(),this->cols());
    slip::Array2d<T> V(this->cols(),this->cols());
    slip::Array<T> W(this->cols());
    slip::svd(*this,U,W.begin(),W.end(),V);
    norm_type max = std::abs(W[0]);
    norm_type min = std::abs(W[0]);
    //norm_type cond = norm_type();
    norm_type tol = norm_type(std::max(this->rows(),this->cols())) * max * slip::epsilon<T>();
  
    for(std::size_t i = 1; i <  W.size(); ++i)
      {
                norm_type tmp = std::abs(W[i]);
                if(tmp > tol) 
                  {
                    min = tmp;
                  }
                else
                  {
                    break;
                  }
      }
    
    return max/min;
    
  }

  template<typename T>
  inline
  Matrix<T> Matrix<T>::inv() const
  {
    assert(array_->size() != 0);
    assert(this->rows() == this->cols());
    slip::Matrix<T> tmp(this->rows(),this->cols());
    slip::lu_inv(*this,tmp);
    return tmp;
  }

  template<typename T>
  inline
  Matrix<T>& Matrix<T>::apply(T (*fun)(T))
  {
    slip::apply(this->begin(),this->end(),this->begin(),fun);
    return *this;
  }

  template<typename T>
  inline
  Matrix<T>& Matrix<T>::apply(T (*fun)(const T&))
  {
    slip::apply(this->begin(),this->end(),this->begin(),fun);
    return *this;
  }



  template<typename T>
  inline
  Matrix<T> operator+(const Matrix<T>& M1, 
                                      const Matrix<T>& M2)
  {
    assert(M1.dim1() == M2.dim1());
    assert(M1.dim2() == M2.dim2());
    Matrix<T> tmp(M1.dim1(),M1.dim2());
    std::transform(M1.begin(),M1.end(),M2.begin(),tmp.begin(),std::plus<T>());
    return tmp;
  }

  template<typename T>
  inline
  Matrix<T> operator+(const Matrix<T>& M1, 
                                      const T& val)
  {
    Matrix<T> tmp(M1);
    tmp+=val;
    return tmp;
  }

  template<typename T>
  inline
  Matrix<T> operator+(const T& val,
                                      const Matrix<T>& M1)
  {
    return M1 + val;
  }


template<typename T>
inline
Matrix<T> operator-(const Matrix<T>& M1, 
                                    const Matrix<T>& M2)
{
    assert(M1.dim1() == M2.dim1());
    assert(M1.dim2() == M2.dim2());
    Matrix<T> tmp(M1.dim1(),M1.dim2());
    std::transform(M1.begin(),M1.end(),M2.begin(),tmp.begin(),std::minus<T>());
    return tmp;
}

template<typename T>
inline
Matrix<T> operator-(const Matrix<T>& M1, 
                                    const T& val)
{
    Matrix<T> tmp(M1);
    tmp-=val;
    return tmp;
}

template<typename T>
inline
Matrix<T> operator-(const T& val,
                                    const Matrix<T>& M1)
{
  return -(M1 - val);
}

template<typename T>
inline
Matrix<T> operator*(const Matrix<T>& M1, 
                                    const Matrix<T>& M2)
{
    assert(M1.dim1() == M2.dim1());
    assert(M1.dim2() == M2.dim2());
    Matrix<T> tmp(M1.dim1(),M1.dim2());
    std::transform(M1.begin(),M1.end(),M2.begin(),tmp.begin(),std::multiplies<T>());
    return tmp;
}

template<typename T>
inline
Matrix<T> operator*(const Matrix<T>& M1, 
                                    const T& val)
{
  Matrix<T> tmp(M1.dim1(),M1.dim2(),
                                M1.begin(),M1.end());
    tmp*=val;
    return tmp;
}

template<typename T>
inline
Matrix<T> operator*(const T& val,
                                    const Matrix<T>& M1)
{
  return M1 * val;
}

template<typename T>
inline
Matrix<T> operator/(const Matrix<T>& M1, 
                                    const Matrix<T>& M2)
{
  assert(M1.dim1() == M2.dim1());
  assert(M1.dim2() == M2.dim2());
  Matrix<T> tmp(M1.dim1(),M1.dim2());
  std::transform(M1.begin(),M1.end(),M2.begin(),tmp.begin(),std::divides<T>());
    return tmp;
}

template<typename T>
inline
Matrix<T> operator/(const Matrix<T>& M1, 
                                    const T& val)
{
  Matrix<T> tmp(M1.dim1(),M1.dim2(),
                                M1.begin(),M1.end());
    tmp/=val;
    return tmp;
}

// template<typename T>
// inline
// Matrix<T> operator/(const T& val,
//                                  const Matrix<T>& M1)
// {
//   return M1 / val;
// }


  template<typename T>
  inline
  T& min(const Matrix<T>& M1)
  {
    return M1.min();
  }

template<typename T>
inline
T& max(const Matrix<T>& M1)
{
  return M1.max();
}

template<typename T>
inline
Matrix<typename slip::lin_alg_traits<T>::value_type> abs(const Matrix<T>& M)
{
  
  Matrix<typename slip::lin_alg_traits<T>::value_type> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::abs);
  return tmp;
}

template<typename T>
inline
Matrix<T> sqrt(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::sqrt);
  return tmp;
}

template<typename T>
inline
Matrix<T> cos(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::cos);
  return tmp;
}


inline
Matrix<float> acos(const Matrix<float>& M)
{
  Matrix<float> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::acos);
  return tmp;
}

inline
Matrix<double> acos(const Matrix<double>& M)
{
  Matrix<double> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::acos);
  return tmp;
}

inline
Matrix<long double> acos(const Matrix<long double>& M)
{
  Matrix<long double> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::acos);
  return tmp;
}

template<typename T>
inline
Matrix<T> sin(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::sin);
  return tmp;
}


inline
Matrix<float> asin(const Matrix<float>& M)
{
  Matrix<float> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::asin);
  return tmp;
}

inline
Matrix<double> asin(const Matrix<double>& M)
{
  Matrix<double> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::asin);
  return tmp;
}

inline
Matrix<long double> asin(const Matrix<long double>& M)
{
  Matrix<long double> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::asin);
  return tmp;
}

template<typename T>
inline
Matrix<T> tan(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::tan);
  return tmp;
}


inline
Matrix<float> atan(const Matrix<float>& M)
{
  Matrix<float> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::atan);
  return tmp;
}

inline
Matrix<double> atan(const Matrix<double>& M)
{
  Matrix<double> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::atan);
  return tmp;
}

inline
Matrix<long double> atan(const Matrix<long double>& M)
{
  Matrix<long double> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::atan);
  return tmp;
}

template<typename T>
inline
Matrix<T> exp(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::exp);
  return tmp;
}

template<typename T>
inline
Matrix<T> log(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::log);
  return tmp;
}

template<typename T>
inline
Matrix<T> cosh(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::cosh);
  return tmp;
}

template<typename T>
inline
Matrix<T> sinh(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::sinh);
  return tmp;
}

template<typename T>
inline
Matrix<T> tanh(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::tanh);
  return tmp;
}

template<typename T>
inline
Matrix<T> log10(const Matrix<T>& M)
{
  Matrix<T> tmp(M.dim1(),M.dim2());
  slip::apply(M.begin(),M.end(),tmp.begin(),std::log10);
  return tmp;
}
  /* @{ */
template<typename T>
inline
bool operator==(const Matrix<T>& x, 
                                const Matrix<T>& y)
{
  return ( x.size() == y.size()
                   && std::equal(x.begin(),x.end(),y.begin())); 
}

template<typename T>
inline
bool operator!=(const Matrix<T>& x, 
                                const Matrix<T>& y)
{
  return !(x == y);
}

/* @} */

  /* @{ */
template<typename T>
inline
bool operator<(const Matrix<T>& x, 
                       const Matrix<T>& y)
{
  return std::lexicographical_compare(x.begin(), x.end(),
                                                                      y.begin(), y.end());
}

template<typename T>
inline
bool operator>(const Matrix<T>& x, 
                       const Matrix<T>& y)
{
  return (y < x);
}

template<typename T>
inline
bool operator<=(const Matrix<T>& x, 
                                const Matrix<T>& y)
{
  return !(y < x);
}

template<typename T>
inline
bool operator>=(const Matrix<T>& x, 
                                const Matrix<T>& y)
{
  return !(x < y);
} 
/* @} */
}//slip::

#endif //SLIP_MATRIX_HPP