Signal.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_SIGNAL_HPP
#define SLIP_SIGNAL_HPP

#include <iostream>
#include <iterator>
#include <cassert>
#include <numeric>
#include <algorithm>
#include <cmath>
#include <cstddef>
#include <complex>
#include <string>
#include "Vector.hpp"
#include "Box1d.hpp"
#include "stride_iterator.hpp"
#include "apply.hpp"
#include "norms.hpp"
#include "linear_algebra_traits.hpp"
#include "linear_algebra.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 <typename T>
class Signal;

template <typename T>
std::ostream& operator<<(std::ostream & out, 
                                                 const Signal<T>& v);

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

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

template<typename T>
bool operator<(const Signal<T>& x, 
                       const Signal<T>& y);

template<typename T>
bool operator>(const Signal<T>& x, 
                       const Signal<T>& y);

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

template<typename T>
bool operator>=(const Signal<T>& x, 
                                const Signal<T>& y);
template <typename T>
class Signal
{
public :

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

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

  typedef ptrdiff_t difference_type;
  typedef std::size_t size_type;

  typedef pointer iterator;
  typedef const_pointer const_iterator;

  typedef slip::stride_iterator<pointer> iterator_range;
  typedef slip::stride_iterator<const_pointer> const_iterator_range;

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

  typedef std::reverse_iterator<iterator_range> reverse_iterator_range;
  typedef std::reverse_iterator<const_iterator_range> const_reverse_iterator_range;

  typedef typename slip::lin_alg_traits<value_type>::value_type norm_type;

   //default iterator of the container
  typedef iterator default_iterator;
  typedef const_iterator const_default_iterator;


  static const std::size_t DIM = 1;

public:
  
  Signal();
 
  Signal(const size_type n);
  
  Signal(const size_type n,
                 const T& val);
 
  Signal(const size_type n,
                 const T* val);
 
  template<typename InputIterator>
  Signal(InputIterator first,
                 InputIterator last):
    vector_(new slip::Vector<T>(first,last))
  {}

  Signal(const self& rhs);

  ~Signal();
  

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

 
 
  iterator begin();

  const_iterator begin() const;

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

  reverse_iterator rend();

  const_reverse_iterator rend() const;
 

  iterator_range begin(const slip::Range<int>& range);
 
  const_iterator_range begin(const slip::Range<int>& range) const;

  iterator_range end(const slip::Range<int>& range);
 
  const_iterator_range end(const slip::Range<int>& range) const;



  iterator begin(const slip::Box1d<int>& box);
 
  const_iterator begin(const slip::Box1d<int>& box) const;

  iterator end(const slip::Box1d<int>& box);
 
  const_iterator end(const slip::Box1d<int>& box) const;

  //
  reverse_iterator_range rbegin(const slip::Range<int>& range);
 
  const_reverse_iterator_range rbegin(const slip::Range<int>& range) const;

  reverse_iterator_range rend(const slip::Range<int>& range);
 
  const_reverse_iterator_range rend(const slip::Range<int>& range) const;



  reverse_iterator rbegin(const slip::Box1d<int>& box);
 
  const_reverse_iterator rbegin(const slip::Box1d<int>& box) const;

  reverse_iterator rend(const slip::Box1d<int>& box);
 
  const_reverse_iterator rend(const slip::Box1d<int>& box) const;
  friend std::ostream& operator<< <>(std::ostream & out, 
                                                                     const self& v);

  void write_ascii(const std::string& file_path_name) const
  {
    //    slip::write_ascii_2d<self,value_type>(*this,file_path_name);
  }

  void read_ascii(const std::string& file_path_name)
  {
    //slip::read_ascii_2d<self>(*this,file_path_name);
  }
  self& 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 Signal<T>& x, 
                                                    const Signal<T>& y);

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

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

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

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

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


  reference operator[](const size_type i);

  const_reference operator[](const size_type i) const;

  reference operator()(const size_type i);

  const_reference operator()(const size_type i) const;

  reference operator()(const slip::Point1d<size_type>& p);
  
  const_reference operator()(const slip::Point1d<size_type>& p) const;

  self operator()(const slip::Range<int>& range);


  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);
    

  std::string name() const;

  size_type size() const;

  size_type max_size() const;

  bool empty()const;

  void swap(self& M);

  T& min() const;


  T& max() const;

  T sum() const;

  norm_type Euclidean_norm() const
  { 
    return (this->vector_)->Euclidean_norm();
  }

  norm_type L2_norm() const
  {
    return (this->vector_)->L2_norm();
  }

  norm_type L1_norm() const
  {
    
    return (this->vector_)->L1_norm();
  }

  norm_type L22_norm() const
  {
    return (this->vector_)->L22_norm();
  }

  norm_type infinite_norm() const
  {
    return (this->vector_)->infinite_norm();
  }
  Signal<T>& apply(T (*fun)(T));

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

 private:
  slip::Vector<T>* vector_;

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

  typedef slip::Signal<double> Signal_d;
  typedef slip::Signal<float> Signal_f;
  typedef slip::Signal<long> Signal_l;
  typedef slip::Signal<unsigned long> Signal_ul;
  typedef slip::Signal<short> Signal_s;
  typedef slip::Signal<unsigned short> Signal_us;
  typedef slip::Signal<int> Signal_i;
  typedef slip::Signal<unsigned int> Signal_ui;
  typedef slip::Signal<char> Signal_c;
  typedef slip::Signal<unsigned char> Signal_uc;

template<typename T>
Signal<T> operator+(const Signal<T>& V1, 
                                    const Signal<T>& V2);

template<typename T>
Signal<T> operator+(const Signal<T>& V, 
                                    const T& val);

template<typename T>
Signal<T> operator+(const T& val, 
                                    const Signal<T>& V);


template<typename T>
Signal<T> operator-(const Signal<T>& V1, 
                                    const Signal<T>& V2);

template<typename T>
Signal<T> operator-(const Signal<T>& V, 
                                    const T& val);

template<typename T>
Signal<T> operator-(const T& val, 
                                    const Signal<T>& V);

template<typename T>
Signal<T> operator*(const Signal<T>& V1, 
                                    const Signal<T>& V2);

template<typename T>
Signal<T> operator*(const Signal<T>& V, 
                                    const T& val);

template<typename T>
Signal<T> operator*(const T& val, 
                                    const Signal<T>& V);

  template<typename T>
  Signal<T> operator/(const Signal<T>& V1, 
                                      const Signal<T>& V2);

  template<typename T>
  Signal<T> operator/(const Signal<T>& V, 
                                      const T& val);



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

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

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

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

  Signal<float> acos(const Signal<float>& V);
  Signal<double> acos(const Signal<double>& V);
  Signal<long double> acos(const Signal<long double>& V);
  
  template<typename T>
  Signal<T> sin(const Signal<T>& V);

  Signal<float> asin(const Signal<float>& V);
  Signal<double> asin(const Signal<double>& V);
  Signal<long double> asin(const Signal<long double>& V);
  
  template<typename T>
  Signal<T> tan(const Signal<T>& V);

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

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

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

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

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

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

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

}//slip::

namespace slip
{
  template<typename T>
  inline
  Signal<T>::Signal():
    vector_(new slip::Vector<T>())
  {}

  template<typename T>
  inline
  Signal<T>::Signal(typename Signal<T>::size_type n):
    vector_(new slip::Vector<T>(n))
  {}
  
  template<typename T>
  inline
  Signal<T>::Signal(typename Signal<T>::size_type n,
                                    const T& val):
    vector_(new slip::Vector<T>(n,val))
  {}

  template<typename T>
  inline
  Signal<T>::Signal(typename Signal<T>::size_type n,
                                    const T* val):
    vector_(new slip::Vector<T>(n,val))   
  {}
  
  template<typename T>
  inline
  Signal<T>::Signal(const Signal<T>& rhs):
    vector_(new slip::Vector<T>((*rhs.vector_)))
  {}
  
  template<typename T>
  inline
  Signal<T>& Signal<T>::operator=(const Signal<T> & rhs)
  {
    if(this != &rhs)
      {
                *(this->vector_) = *(rhs.vector_);
      }
    return *this;
  }

  template<typename T>
  inline
  Signal<T>::~Signal()
  {
    delete vector_;
  }

  template<typename T>
  inline
  Signal<T>& Signal<T>::operator=(const T& val)
  {
    (this->vector_)->operator=(val);
    return *this;
  }
  
  template<typename T>
  inline
  void Signal<T>::resize(typename Signal<T>::size_type new_size,
                                                 const T& val)
  {
    (this->vector_)->resize(new_size,val);
  }


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

  template<typename T>
  inline
  typename Signal<T>::iterator Signal<T>::end()
  {
    return vector_->end();
  }
  
  template<typename T>
  inline
  typename Signal<T>::const_iterator Signal<T>::begin() const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->begin();
  }

  template<typename T>
  inline
  typename Signal<T>::const_iterator Signal<T>::end() const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->end();
  }
  

  template<typename T>
  inline
  typename Signal<T>::reverse_iterator Signal<T>::rbegin()
  {
    return vector_->rbegin();
  }

  template<typename T>
  inline
  typename Signal<T>::reverse_iterator Signal<T>::rend()
  {
    return vector_->rend();
  }

  template<typename T>
  inline
  typename Signal<T>::const_reverse_iterator Signal<T>::rbegin() const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->rbegin();
  }

  template<typename T>
  inline
  typename Signal<T>::const_reverse_iterator  Signal<T>::rend() const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->rend();
  }

  //
  template<typename T>
  inline
  typename Signal<T>::iterator_range 
  Signal<T>::begin(const slip::Range<int>& range)
  {
    return vector_->begin(range);
  }

  template<typename T>
  inline
  typename Signal<T>::iterator_range 
  Signal<T>::end(const slip::Range<int>& range)
  {
    return vector_->end(range);
  }
  
  template<typename T>
  inline
  typename Signal<T>::const_iterator_range 
  Signal<T>::begin(const slip::Range<int>& range) const
  {
   slip::Vector<T> const * tp(vector_);
    return tp->begin(range);
  }

  template<typename T>
  inline
  typename Signal<T>::const_iterator_range 
  Signal<T>::end(const slip::Range<int>& range) const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->end(range);
  }

  //
  template<typename T>
  inline
  typename Signal<T>::iterator
  Signal<T>::begin(const slip::Box1d<int>& box)
  {
    return vector_->begin(box);
  }

  template<typename T>
  inline
  typename Signal<T>::iterator 
  Signal<T>::end(const slip::Box1d<int>& box)
  {
    return vector_->end(box);
  }
  
  template<typename T>
  inline
  typename Signal<T>::const_iterator 
  Signal<T>::begin(const slip::Box1d<int>& box) const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->begin(box);
  }

  template<typename T>
  inline
  typename Signal<T>::const_iterator 
  Signal<T>::end(const slip::Box1d<int>& box) const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->end(box);
  }

  //
  template<typename T>
  inline
  typename Signal<T>::reverse_iterator Signal<T>::rbegin(const slip::Box1d<int>& box)
  {
    return vector_->rbegin(box);
  }

  template<typename T>
  inline
  typename Signal<T>::reverse_iterator 
  Signal<T>::rend(const slip::Box1d<int>& box)
  {
    return vector_->rend(box);
  }

  template<typename T>
  inline
  typename Signal<T>::const_reverse_iterator 
  Signal<T>::rbegin(const slip::Box1d<int>& box) const
  {
   slip::Vector<T> const * tp(vector_);
    return tp->rbegin(box);
  }

  template<typename T>
  inline
  typename Signal<T>::const_reverse_iterator 
  Signal<T>::rend(const slip::Box1d<int>& box) const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->rend(box);
  }
  //
  template<typename T>
  inline
  typename Signal<T>::reverse_iterator_range Signal<T>::rbegin(const slip::Range<int>& range)
  {
    return vector_->rbegin(range);
  }

  template<typename T>
  inline
  typename Signal<T>::reverse_iterator_range 
  Signal<T>::rend(const slip::Range<int>& range)
  {
    return vector_->rend(range);
  }

  template<typename T>
  inline
  typename Signal<T>::const_reverse_iterator_range 
  Signal<T>::rbegin(const slip::Range<int>& range) const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->rbegin(range);
  }

  template<typename T>
  inline
  typename Signal<T>::const_reverse_iterator_range 
  Signal<T>::rend(const slip::Range<int>& range) const
  {
    slip::Vector<T> const * tp(vector_);
    return tp->rend(range);
  }


  template <typename T>
  inline
  std::ostream& operator<<(std::ostream & out, 
                                                   const Signal<T>& v)
  {
    out<<*(v.vector_);
    return out;
  }

  template<typename T>
  inline
  typename Signal<T>::reference Signal<T>::operator[](typename Signal<T>::size_type i)
  {
    return (*vector_)[i];
  }
  
  template<typename T>
  inline
  typename Signal<T>::const_reference Signal<T>::operator[](typename Signal<T>::size_type i) const 
  {
    return (*vector_)[i];
  }
  
  template<typename T>
  inline
  typename Signal<T>::reference Signal<T>::operator()(typename Signal<T>::size_type i)
  {
    return (*vector_)(i);
  }
  
  template<typename T>
  inline
  typename Signal<T>::const_reference Signal<T>::operator()(typename Signal<T>::size_type i) const
  {
    return (*vector_)(i);
  }

  template <typename T>
  inline
  typename Signal<T>::reference 
  Signal<T>::operator()(const slip::Point1d<typename Signal<T>::size_type>& p)
  {
    return (*vector_)(p);
  }

  template <typename T>
  inline
  typename Signal<T>::const_reference 
  Signal<T>::operator()(const slip::Point1d<typename Signal<T>::size_type>& p) const
  {
    return (*vector_)(p);
  }

  template<typename T>
  inline
  Signal<T> Signal<T>::operator()(const slip::Range<int>& range)
  {
     assert(this->vector_ != 0);
     assert(range.is_valid());
     assert(range.start() < (int)this->size());
     assert(range.stop()  < (int)this->size());
     return Signal<T>(vector_->begin(range),vector_->end(range));

  }

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

  template<typename T>
  inline
  typename Signal<T>::size_type Signal<T>::size() const 
  {
    return (this->vector_)->size();
  }

  template<typename T>
  inline
  typename Signal<T>::size_type Signal<T>::max_size() const 
  {
    return (this->vector_)->max_size();
  }
  
  template<typename T>
  inline
  bool Signal<T>::empty()const 
  {
    return (this->vector_)->empty();
  }

  template<typename T>
  inline
  void Signal<T>::swap(Signal<T>& V)
  {
    (this->vector_)->swap(*(V.vector_));
  }


  template<typename T>
  inline
  Signal<T>& Signal<T>::operator+=(const T& val)
  {
    (this->vector_)->operator+=(val);
    return *this;
  }

  template<typename T>
  inline
  Signal<T>& Signal<T>::operator-=(const T& val)
  {
    (this->vector_)->operator-=(val);
    return *this;
  }

  template<typename T>
  inline
  Signal<T>& Signal<T>::operator*=(const T& val)
  {
    (this->vector_)->operator*=(val);
    return *this;
  }
  
  template<typename T>
  inline
  Signal<T>& Signal<T>::operator/=(const T& val)
  {
    (this->vector_)->operator/=(val);
    return *this;
  }
  

  template<typename T>
  inline
  Signal<T> Signal<T>::operator-() const
  {
    *(this->vector_) = (this->vector_)->operator-();
    return *this;
  }

  template<typename T>
  inline
  Signal<T>& Signal<T>::operator+=(const Signal<T>& rhs)
  {
    (this->vector_)->operator+=(*(rhs.vector_));
    return *this;
  }
  
  template<typename T>
  inline
  Signal<T>& Signal<T>::operator-=(const Signal<T>& rhs)
  {
    (this->vector_)->operator-=(*(rhs.vector_));
    return *this;
  }
  
  template<typename T>
  inline
  Signal<T>& Signal<T>::operator*=(const Signal<T>& rhs)
  {
    (this->vector_)->operator*=(*(rhs.vector_));
    return *this;
  }

   template<typename T>
  inline
  Signal<T>& Signal<T>::operator/=(const Signal<T>& rhs)
  {
    (this->vector_)->operator/=(*(rhs.vector_));
    return *this;
  }
  
  template<typename T>
  inline
  T& Signal<T>::min() const
  {
    return (this->vector_)->min();
  }

  template<typename T>
  inline
  T& Signal<T>::max() const
  {
    return (this->vector_)->max();
  }

  template<typename T>
  inline
  T Signal<T>::sum() const
  {
    return (this->vector_)->sum();
  }

  template<typename T>
  inline
  Signal<T>& Signal<T>::apply(T (*fun)(T))
  {
    (this->vector_)->apply(fun);
    return *this;

  }

  template<typename T>
  inline
  Signal<T>& Signal<T>::apply(T (*fun)(const T&))
  {
    (this->vector_)->apply(fun);
    return *this;
  }


  
  /* @{ */
template<typename T>
inline
Signal<T> operator+(const Signal<T>& V1, 
                                    const Signal<T>& V2)
{
    assert(V1.size() == V2.size());
    Signal<T> tmp(V1.size());
    std::transform(V1.begin(),V1.end(),V2.begin(),tmp.begin(),std::plus<T>());

    return tmp;
}

template<typename T>
inline
Signal<T> operator+(const Signal<T>& V1, 
                                    const T& val)
{
    Signal<T> tmp(V1);
    tmp+=val;
    return tmp;
}

template<typename T>
inline
Signal<T> operator+(const T& val,
                                    const Signal<T>& V1)
{
  return V1 + val;
}

template<typename T>
inline
Signal<T> operator-(const Signal<T>& V1, 
                                    const Signal<T>& V2)
{
    assert(V1.size() == V2.size());
    Signal<T> tmp(V1.size());
    std::transform(V1.begin(),V1.end(),V2.begin(),tmp.begin(),std::minus<T>());
    return tmp;
}

template<typename T>
inline
Signal<T> operator-(const Signal<T>& V1, 
                                    const T& val)
{
    Signal<T> tmp(V1);
    tmp-=val;
    return tmp;
}

template<typename T>
inline
Signal<T> operator-(const T& val,
                                    const Signal<T>& V1)
{
  return -(V1 - val);
}

template<typename T>
inline
Signal<T> operator*(const Signal<T>& V1, 
                                    const Signal<T>& V2)
{
    assert(V1.size() == V2.size());
    Signal<T> tmp(V1.size());
    std::transform(V1.begin(),V1.end(),V2.begin(),tmp.begin(),std::multiplies<T>());
    return tmp;
}

template<typename T>
inline
Signal<T> operator*(const Signal<T>& V1, 
                                    const T& val)
{
    Signal<T> tmp(V1);
    tmp*=val;
    return tmp;
}

template<typename T>
inline
Signal<T> operator*(const T& val,
                                    const Signal<T>& V1)
{
  return V1 * val;
}

template<typename T>
inline
Signal<T> operator/(const Signal<T>& V1, 
                                    const Signal<T>& V2)
{
    assert(V1.size() == V2.size());
    Signal<T> tmp(V1.size());
    std::transform(V1.begin(),V1.end(),V2.begin(),tmp.begin(),std::divides<T>());
    return tmp;
}

template<typename T>
inline
Signal<T> operator/(const Signal<T>& V1, 
                                    const T& val)
{
    Signal<T> tmp(V1);
    tmp/=val;
    return tmp;
}

/* @} */

template<typename T>
inline
T& min(const Signal<T>& V1)
{
  return V1.min();
}

template<typename T>
inline
T& max(const Signal<T>& V1)
{
  return V1.max();
}

template<typename T>
inline
Signal<typename slip::lin_alg_traits<T>::value_type> abs(const Signal<T>& V)
{
  
  Signal<typename slip::lin_alg_traits<T>::value_type> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::abs);
  return tmp;
}

template<typename T>
inline
Signal<T> sqrt(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::sqrt);
  return tmp;
}

template<typename T>
inline
Signal<T> cos(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::cos);
  return tmp;
}


inline
Signal<float> acos(const Signal<float>& V)
{
  Signal<float> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::acos);
  return tmp;
}

inline
Signal<double> acos(const Signal<double>& V)
{
  Signal<double> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::acos);
  return tmp;
}

inline
Signal<long double> acos(const Signal<long double>& V)
{
  Signal<long double> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::acos);
  return tmp;
}

template<typename T>
inline
Signal<T> sin(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::sin);
  return tmp;
}



inline
Signal<float> asin(const Signal<float>& V)
{
  Signal<float> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::asin);
  return tmp;
}

inline
Signal<double> asin(const Signal<double>& V)
{
  Signal<double> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::asin);
  return tmp;
}

inline
Signal<long double> asin(const Signal<long double>& V)
{
  Signal<long double> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::asin);
  return tmp;
}

template<typename T>
inline
Signal<T> tan(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::tan);
  return tmp;
}

inline
Signal<float> atan(const Signal<float>& V)
{
  Signal<float> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::atan);
  return tmp;
}

inline
Signal<double> atan(const Signal<double>& V)
{
  Signal<double> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::atan);
  return tmp;
}

inline
Signal<long double> atan(const Signal<long double>& V)
{
  Signal<long double> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::atan);
  return tmp;
}

template<typename T>
inline
Signal<T> exp(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::exp);
  return tmp;
}

template<typename T>
inline
Signal<T> log(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::log);
  return tmp;
}

template<typename T>
inline
Signal<T> cosh(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::cosh);
  return tmp;
}

template<typename T>
inline
Signal<T> sinh(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::sinh);
  return tmp;
}

template<typename T>
inline
Signal<T> tanh(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::tanh);
  return tmp;
}

template<typename T>
inline
Signal<T> log10(const Signal<T>& V)
{
  Signal<T> tmp(V.size());
  slip::apply(V.begin(),V.end(),tmp.begin(),std::log10);
  return tmp;
}

  /* @{ */
template<typename T>
inline
bool operator==(const Signal<T>& x, 
                                const Signal<T>& y)
{
  return *(x.vector_) == *(y.vector_); 
}

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

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

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

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

#endif //SLIP_SIGNAL_HPP