matpackIII.h

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/* Copyright (C) 2001 Stefan Buehler <sbuehler@uni-bremen.de>

   This program is free software; 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, or (at your option) any
   later version.

   This program 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 General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,
   USA. */

#ifndef matpackIII_h
#define matpackIII_h

#include <iomanip>
#include "matpackI.h"

class Iterator3D {
public:
  // Constructors:
  Iterator3D();
  Iterator3D(const Iterator3D& o);
  Iterator3D(const MatrixView& x, Index stride);

  // Operators:
  Iterator3D& operator++();
  bool operator!=(const Iterator3D& other) const;
  MatrixView* const operator->();
  MatrixView& operator*();
  
private:
  MatrixView msv;
  Index mstride;
};

class ConstIterator3D {
public:
  // Constructors:
  ConstIterator3D();
  ConstIterator3D(const ConstIterator3D& o);
  ConstIterator3D(const ConstMatrixView& x, Index stride);

  // Operators:
  ConstIterator3D& operator++();
  bool operator!=(const ConstIterator3D& other) const;
  const ConstMatrixView* operator->() const;
  const ConstMatrixView& operator*() const;

private:
  ConstMatrixView msv;
  Index mstride;
};


// Declare class Tensor3:
class Tensor3;


class ConstTensor3View {
public:
  // Member functions:
  Index npages() const;
  Index nrows() const;
  Index ncols() const;

  // Const index operators:
  ConstTensor3View operator()( const Range& p, const Range& r, const Range& c ) const;

  ConstMatrixView  operator()( const Range& p, const Range& r, Index c        ) const;
  ConstMatrixView  operator()( const Range& p, Index r,        const Range& c ) const;
  ConstMatrixView  operator()( Index p,        const Range& r, const Range& c ) const;

  ConstVectorView  operator()( Index p,        Index r,        const Range& c ) const;
  ConstVectorView  operator()( Index p,        const Range& r, Index c        ) const;
  ConstVectorView  operator()( const Range& p, Index r,        Index c        ) const;

  Numeric          operator()( Index p,        Index r,        Index c        ) const;

  // Functions returning iterators:
  ConstIterator3D begin() const;
  ConstIterator3D end() const;
  
  // Friends:
  friend class Tensor3View;


protected:
  // Constructors:
  ConstTensor3View();
  ConstTensor3View(Numeric *data,
                   const Range& p, const Range& r, const Range& c);
  ConstTensor3View(Numeric *data,
                   const Range& pp, const Range& pr, const Range& pc,
                   const Range& np, const Range& nr, const Range& nc);

  // Data members:
  // -------------
  Range mpr;
  Range mrr;
  Range mcr;
  Numeric *mdata;
};

class Tensor3View : public ConstTensor3View {
public:

  // Const index operators:
  ConstTensor3View operator()( const Range& p, const Range& r, const Range& c ) const;

  ConstMatrixView  operator()( const Range& p, const Range& r, Index c        ) const;
  ConstMatrixView  operator()( const Range& p, Index r,        const Range& c ) const;
  ConstMatrixView  operator()( Index p,        const Range& r, const Range& c ) const;

  ConstVectorView  operator()( Index p,        Index r,        const Range& c ) const;
  ConstVectorView  operator()( Index p,        const Range& r, Index c        ) const;
  ConstVectorView  operator()( const Range& p, Index r,        Index c        ) const;

  Numeric          operator()( Index p,        Index r,        Index c        ) const;

  // Non-const index operators:

  Tensor3View operator()( const Range& p, const Range& r, const Range& c );

  MatrixView  operator()( const Range& p, const Range& r, Index c        );
  MatrixView  operator()( const Range& p, Index r,        const Range& c );
  MatrixView  operator()( Index p,        const Range& r, const Range& c );

  VectorView  operator()( Index p,        Index r,        const Range& c );
  VectorView  operator()( Index p,        const Range& r, Index c        );
  VectorView  operator()( const Range& p, Index r,        Index c        );

  Numeric&    operator()( Index p,        Index r,        Index c        );

  // Functions returning const iterators:
  ConstIterator3D begin() const;
  ConstIterator3D end() const;
  // Functions returning iterators:
  Iterator3D begin();
  Iterator3D end();
  
  // Assignment operators:
  Tensor3View& operator=(const ConstTensor3View& v);
  Tensor3View& operator=(const Tensor3View& v);
  Tensor3View& operator=(const Tensor3& v);
  Tensor3View& operator=(Numeric x);

  // Other operators:
  Tensor3View& operator*=(Numeric x);
  Tensor3View& operator/=(Numeric x);
  Tensor3View& operator+=(Numeric x);
  Tensor3View& operator-=(Numeric x);

  Tensor3View& operator*=(const ConstTensor3View& x);
  Tensor3View& operator/=(const ConstTensor3View& x);
  Tensor3View& operator+=(const ConstTensor3View& x);
  Tensor3View& operator-=(const ConstTensor3View& x);

  // Friends:
//   friend class VectorView;
//   friend ConstTensor3View transpose(ConstTensor3View m);
//   friend Tensor3View transpose(Tensor3View m);

protected:
  // Constructors:
  Tensor3View();
  Tensor3View(Numeric *data, const Range& p, const Range& r, const Range& c);
  Tensor3View(Numeric *data,
              const Range& pp, const Range& pr, const Range& pc,
              const Range& np, const Range& nr, const Range& nc);
};

class Tensor3 : public Tensor3View {
public:
  // Constructors:
  Tensor3();
  Tensor3(Index p, Index r, Index c);
  Tensor3(Index p, Index r, Index c, Numeric fill);
  Tensor3(const ConstTensor3View& v);
  Tensor3(const Tensor3& v);

  // Assignment operators:
  Tensor3& operator=(const Tensor3& x);
  Tensor3& operator=(Numeric x);

  // Resize function:
  void resize(Index p, Index r, Index c);

  // Destructor:
  ~Tensor3();
};


// Function declarations:
// ----------------------

inline void copy(ConstIterator3D origin,
                 const ConstIterator3D& end,
                 Iterator3D target);

inline void copy(Numeric x,
                 Iterator3D target,
                 const Iterator3D& end);



// Declare the existance of class Array:
template<class base>
class Array;

typedef Array<Tensor3> ArrayOfTensor3;



// Functions for Iterator3D
// ------------------------

inline Iterator3D::Iterator3D()
{
  // Nothing to do here.
}

inline Iterator3D::Iterator3D(const Iterator3D& o) :
  msv(o.msv), mstride(o.mstride)
{
  // Nothing to do here.
}

inline Iterator3D::Iterator3D(const MatrixView& x, Index stride) :
  msv(x), mstride(stride)
{
  // Nothing to do here. 
}

inline Iterator3D& Iterator3D::operator++()
{
  msv.mdata += mstride;
  return *this;
}

inline bool Iterator3D::operator!=(const Iterator3D& other) const
{
  if ( msv.mdata +
       msv.mrr.mstart +
       msv.mcr.mstart 
       !=
       other.msv.mdata +
       other.msv.mrr.mstart +
       other.msv.mcr.mstart )
    return true;
  else
    return false;
}

inline MatrixView* const Iterator3D::operator->()
{
  return &msv;
}

inline MatrixView& Iterator3D::operator*()
{
  return msv;
}

// Functions for ConstIterator3D
// -----------------------------

inline ConstIterator3D::ConstIterator3D()
{
  // Nothing to do here.
}

inline ConstIterator3D::ConstIterator3D(const ConstIterator3D& o) :
  msv(o.msv), mstride(o.mstride)
{
  // Nothing to do here.
}

inline ConstIterator3D::ConstIterator3D(const ConstMatrixView& x, Index stride) :
  msv(x), mstride(stride)
{
  // Nothing to do here. 
}

inline ConstIterator3D& ConstIterator3D::operator++()
{
  msv.mdata += mstride;
  return *this;
}

inline bool ConstIterator3D::operator!=(const ConstIterator3D& other) const
{
  if ( msv.mdata +
       msv.mrr.mstart +
       msv.mcr.mstart
       !=
       other.msv.mdata +
       other.msv.mrr.mstart +
       other.msv.mcr.mstart )
    return true;
  else
    return false;
}

inline const ConstMatrixView* ConstIterator3D::operator->() const
{
  return &msv;
}

inline const ConstMatrixView& ConstIterator3D::operator*() const
{
  return msv;
}



// Functions for ConstTensor3View:
// ------------------------------

inline Index ConstTensor3View::npages() const
{
  return mpr.mextent;
}

inline Index ConstTensor3View::nrows() const
{
  return mrr.mextent;
}

inline Index ConstTensor3View::ncols() const
{
  return mcr.mextent;
}

inline ConstTensor3View ConstTensor3View::operator()(const Range& p,
                                                     const Range& r,
                                                     const Range& c) const
{
  return ConstTensor3View(mdata, mpr, mrr, mcr, p, r, c);
}

inline ConstMatrixView ConstTensor3View::operator()(const Range& p,
                                                    const Range& r,
                                                    Index c) const
{
  // Check that c is valid:
  assert( 0 <= c );
  assert( c < mcr.mextent );

  return ConstMatrixView(mdata + mcr.mstart + c*mcr.mstride,
                         mpr, mrr, 
                         p,   r);
}

inline ConstMatrixView ConstTensor3View::operator()(const Range& p,
                                                    Index        r,
                                                    const Range& c) const
{
  // Check that r is valid:
  assert( 0 <= r );
  assert( r < mrr.mextent );

  return ConstMatrixView(mdata + mrr.mstart + r*mrr.mstride,
                         mpr, mcr, 
                         p,   c);
}

inline ConstMatrixView ConstTensor3View::operator()(Index p,
                                                    const Range& r,
                                                    const Range& c) const
{
  // Check that p is valid:
  assert( 0 <= p );
  assert( p < mpr.mextent );

  return ConstMatrixView(mdata + mpr.mstart + p*mpr.mstride,
                         mrr, mcr, 
                         r,   c);
}

inline ConstVectorView ConstTensor3View::operator()(Index p,
                                                    Index r,
                                                    const Range& c) const
{
  // Check that p and r are valid:
  assert( 0 <= p );
  assert( 0 <= r );
  assert( p < mpr.mextent );
  assert( r < mrr.mextent );

  return ConstVectorView(mdata +
                         mpr.mstart + p*mpr.mstride +
                         mrr.mstart + r*mrr.mstride,
                         mcr, c);
}

inline ConstVectorView ConstTensor3View::operator()(Index p,
                                                    const Range& r,
                                                    Index c) const
{
  // Check that p and c are valid:
  assert( 0 <= p );
  assert( 0 <= c );
  assert( p < mpr.mextent );
  assert( c < mcr.mextent );

  return ConstVectorView(mdata +
                         mpr.mstart + p*mpr.mstride +
                         mcr.mstart + c*mcr.mstride,
                         mrr, r);
}

inline ConstVectorView ConstTensor3View::operator()(const Range& p,
                                                    Index r,
                                                    Index c) const
{
  // Check that r and c are valid:
  assert( 0 <= r );
  assert( 0 <= c );
  assert( r < mrr.mextent );
  assert( c < mcr.mextent );

  return ConstVectorView(mdata +
                         mrr.mstart + r*mrr.mstride +
                         mcr.mstart + c*mcr.mstride,
                         mpr, p);
}

inline Numeric ConstTensor3View::operator()(Index p, Index r, Index c) const
{
  // Check if indices are valid:
  assert( 0<=p );
  assert( 0<=r );
  assert( 0<=c );
  assert( p<mpr.mextent );
  assert( r<mrr.mextent );
  assert( c<mcr.mextent );

  return *( mdata +
            mpr.mstart + p*mpr.mstride +
            mrr.mstart + r*mrr.mstride +
            mcr.mstart + c*mcr.mstride );
}

inline ConstIterator3D ConstTensor3View::begin() const
{
  return ConstIterator3D(ConstMatrixView(mdata+mpr.mstart,
                                         mrr,
                                         mcr),
                         mpr.mstride);
}

inline ConstIterator3D ConstTensor3View::end() const
{
  return ConstIterator3D( ConstMatrixView(mdata + mpr.mstart +
                                          (mpr.mextent)*mpr.mstride,
                                          mrr,
                                          mcr),
                          mpr.mstride );
}

inline ConstTensor3View::ConstTensor3View() :
  mpr(0,0,1), mrr(0,0,1), mcr(0,0,1), mdata(NULL)
{
  // Nothing to do here.
}

inline ConstTensor3View::ConstTensor3View(Numeric *data,
                                          const Range& pr,
                                          const Range& rr,
                                          const Range& cr) :
  mpr(pr),
  mrr(rr),
  mcr(cr),
  mdata(data)
{
  // Nothing to do here.
}

inline ConstTensor3View::ConstTensor3View(Numeric *data,
                                          const Range& pp,
                                          const Range& pr,
                                          const Range& pc,
                                          const Range& np,
                                          const Range& nr,
                                          const Range& nc) :
  mpr(pp,np),
  mrr(pr,nr),
  mcr(pc,nc),
  mdata(data)
{
  // Nothing to do here.
}

inline std::ostream& operator<<(std::ostream& os, const ConstTensor3View& v)
{
  // Page iterators:
  ConstIterator3D ip=v.begin();
  const ConstIterator3D end_page=v.end();

  if ( ip!=end_page )
    {
      os << *ip;
      ++ip;
    }

  for ( ; ip!=end_page; ++ip )
    {
      os << "\n\n";
      os << *ip;
    }

  return os;
}


// Functions for Tensor3View:
// -------------------------

inline ConstTensor3View Tensor3View::operator()(const Range& p,
                                                const Range& r,
                                                const Range& c) const
{
  return ConstTensor3View::operator()(p,r,c);  
}

inline ConstMatrixView Tensor3View::operator()(const Range& p,
                                                    const Range& r,
                                                    Index c) const
{
  return ConstTensor3View::operator()(p,r,c);  
}

inline ConstMatrixView Tensor3View::operator()(const Range& p,
                                                    Index        r,
                                                    const Range& c) const
{
  return ConstTensor3View::operator()(p,r,c);  
}

inline ConstMatrixView Tensor3View::operator()(Index p,
                                                    const Range& r,
                                                    const Range& c) const
{
  return ConstTensor3View::operator()(p,r,c);  
}

inline ConstVectorView Tensor3View::operator()(Index p,
                                                    Index r,
                                                    const Range& c) const
{
  return ConstTensor3View::operator()(p,r,c);  
}

inline ConstVectorView Tensor3View::operator()(Index p,
                                                    const Range& r,
                                                    Index c) const
{
  return ConstTensor3View::operator()(p,r,c);  
}

inline ConstVectorView Tensor3View::operator()(const Range& p,
                                                    Index r,
                                                    Index c) const
{
  return ConstTensor3View::operator()(p,r,c);  
}

inline Numeric Tensor3View::operator()(Index p, Index r, Index c) const
{
  return ConstTensor3View::operator()(p,r,c);  
}

inline Tensor3View Tensor3View::operator()(const Range& p,
                                           const Range& r,
                                           const Range& c) 
{
  return Tensor3View(mdata, mpr, mrr, mcr, p, r, c);
}

inline MatrixView Tensor3View::operator()(const Range& p,
                                          const Range& r,
                                          Index c)
{
  // Check that c is valid:
  assert( 0 <= c );
  assert( c < mcr.mextent );

  return MatrixView(mdata + mcr.mstart + c*mcr.mstride,
                    mpr, mrr, 
                    p,   r);
}

inline MatrixView Tensor3View::operator()(const Range& p,
                                          Index        r,
                                          const Range& c) 
{
  // Check that r is valid:
  assert( 0 <= r );
  assert( r < mrr.mextent );

  return MatrixView(mdata + mrr.mstart + r*mrr.mstride,
                    mpr, mcr, 
                    p,   c);
}

inline MatrixView Tensor3View::operator()(Index p,
                                          const Range& r,
                                          const Range& c) 
{
  // Check that p is valid:
  assert( 0 <= p );
  assert( p < mpr.mextent );

  return MatrixView(mdata + mpr.mstart + p*mpr.mstride,
                    mrr, mcr, 
                    r,   c);
}

inline VectorView Tensor3View::operator()(Index p,
                                          Index r,
                                          const Range& c) 
{
  // Check that p and r are valid:
  assert( 0 <= p );
  assert( 0 <= r );
  assert( p < mpr.mextent );
  assert( r < mrr.mextent );

  return VectorView(mdata +
                    mpr.mstart + p*mpr.mstride +
                    mrr.mstart + r*mrr.mstride,
                    mcr, c);
}

inline VectorView Tensor3View::operator()(Index p,
                                          const Range& r,
                                          Index c) 
{
  // Check that p and c are valid:
  assert( 0 <= p );
  assert( 0 <= c );
  assert( p < mpr.mextent );
  assert( c < mcr.mextent );

  return VectorView(mdata +
                    mpr.mstart + p*mpr.mstride +
                    mcr.mstart + c*mcr.mstride,
                    mrr, r);
}

inline VectorView Tensor3View::operator()(const Range& p,
                                          Index r,
                                          Index c)
{
  // Check that r and r are valid:
  assert( 0 <= r );
  assert( 0 <= c );
  assert( r < mrr.mextent );
  assert( c < mcr.mextent );

  return VectorView(mdata +
                    mrr.mstart + r*mrr.mstride +
                    mcr.mstart + c*mcr.mstride,
                    mpr, p);
}

inline Numeric& Tensor3View::operator()(Index p, Index r, Index c) 
{
  // Check if indices are valid:
  assert( 0<=p );
  assert( 0<=r );
  assert( 0<=c );
  assert( p<mpr.mextent );
  assert( r<mrr.mextent );
  assert( c<mcr.mextent );

  return *( mdata +
            mpr.mstart + p*mpr.mstride +
            mrr.mstart + r*mrr.mstride +
            mcr.mstart + c*mcr.mstride );
}

inline ConstIterator3D Tensor3View::begin() const
{
  return ConstTensor3View::begin();
}

inline ConstIterator3D Tensor3View::end() const
{
  return ConstTensor3View::end();
}

inline Iterator3D Tensor3View::begin()
{
  return Iterator3D(MatrixView(mdata+mpr.mstart,
                               mrr,
                               mcr),
                    mpr.mstride);
}

inline Iterator3D Tensor3View::end()
{
  return Iterator3D( MatrixView(mdata + mpr.mstart +
                                (mpr.mextent)*mpr.mstride,
                                mrr,
                                mcr),
                     mpr.mstride );
}

inline Tensor3View& Tensor3View::operator=(const ConstTensor3View& m)
{
  // Check that sizes are compatible:
  assert(mpr.mextent==m.mpr.mextent);
  assert(mrr.mextent==m.mrr.mextent);
  assert(mcr.mextent==m.mcr.mextent);

  copy( m.begin(), m.end(), begin() );
  return *this;
}

inline Tensor3View& Tensor3View::operator=(const Tensor3View& m)
{
  // Check that sizes are compatible:
  assert(mpr.mextent==m.mpr.mextent);
  assert(mrr.mextent==m.mrr.mextent);
  assert(mcr.mextent==m.mcr.mextent);

  copy( m.begin(), m.end(), begin() );
  return *this;
}

inline Tensor3View& Tensor3View::operator=(const Tensor3& m)
{
  // Check that sizes are compatible:
  assert(mpr.mextent==m.mpr.mextent);
  assert(mrr.mextent==m.mrr.mextent);
  assert(mcr.mextent==m.mcr.mextent);

  copy( m.begin(), m.end(), begin() );
  return *this;
}

inline Tensor3View& Tensor3View::operator=(Numeric x)
{
  copy( x, begin(), end() );
  return *this;
}

// Some little helper functions:
//------------------------------

inline Numeric add(Numeric x, Numeric y)
{
  return x+y;
}

inline Tensor3View& Tensor3View::operator*=(Numeric x)
{
  const Iterator3D ep=end();  
  for ( Iterator3D p=begin(); p!=ep ; ++p )
  {
    *p *= x;
  }
  return *this;
}

inline Tensor3View& Tensor3View::operator/=(Numeric x)
{
  const Iterator3D ep=end();  
  for ( Iterator3D p=begin(); p!=ep ; ++p )
  {
    *p /= x;
  }
  return *this;
}

inline Tensor3View& Tensor3View::operator+=(Numeric x)
{
  const Iterator3D ep=end();  
  for ( Iterator3D p=begin(); p!=ep ; ++p )
  {
    *p += x;
  }
  return *this;
}

inline Tensor3View& Tensor3View::operator-=(Numeric x)
{
  const Iterator3D ep=end();  
  for ( Iterator3D p=begin(); p!=ep ; ++p )
  {
    *p -= x;
  }
  return *this;
}

inline Tensor3View& Tensor3View::operator*=(const ConstTensor3View& x)
{
  assert( npages() == x.npages() );
  assert( nrows()  == x.nrows()  );
  assert( ncols()  == x.ncols()  );
  ConstIterator3D  xp = x.begin();
  Iterator3D        p = begin();
  const Iterator3D ep = end();
  for ( ; p!=ep ; ++p,++xp )
    {
      *p *= *xp;
    }
  return *this;
}

inline Tensor3View& Tensor3View::operator/=(const ConstTensor3View& x)
{
  assert( npages() == x.npages() );
  assert( nrows()  == x.nrows()  );
  assert( ncols()  == x.ncols()  );
  ConstIterator3D  xp = x.begin();
  Iterator3D        p = begin();
  const Iterator3D ep = end();
  for ( ; p!=ep ; ++p,++xp )
    {
      *p /= *xp;
    }
  return *this;
}

inline Tensor3View& Tensor3View::operator+=(const ConstTensor3View& x)
{
  assert( npages() == x.npages() );
  assert( nrows()  == x.nrows()  );
  assert( ncols()  == x.ncols()  );
  ConstIterator3D  xp = x.begin();
  Iterator3D        p = begin();
  const Iterator3D ep = end();
  for ( ; p!=ep ; ++p,++xp )
    {
      *p += *xp;
    }
  return *this;
}

inline Tensor3View& Tensor3View::operator-=(const ConstTensor3View& x)
{
  assert( npages() == x.npages() );
  assert( nrows()  == x.nrows()  );
  assert( ncols()  == x.ncols()  );
  ConstIterator3D  xp = x.begin();
  Iterator3D        p = begin();
  const Iterator3D ep = end();
  for ( ; p!=ep ; ++p,++xp )
    {
      *p -= *xp;
    }
  return *this;
}

inline Tensor3View::Tensor3View() :
  ConstTensor3View()
{
  // Nothing to do here.
}

inline Tensor3View::Tensor3View(Numeric *data,
                                const Range& pr,
                                const Range& rr,
                                const Range& cr) :
  ConstTensor3View(data, pr, rr, cr)
{
  // Nothing to do here.
}

inline Tensor3View::Tensor3View(Numeric *data,
                                const Range& pp,
                                const Range& pr,
                                const Range& pc,
                                const Range& np,
                                const Range& nr,
                                const Range& nc) :
  ConstTensor3View(data,pp,pr,pc,np,nr,nc)
{
  // Nothing to do here.
}

inline void copy(ConstIterator3D origin,
                 const ConstIterator3D& end,
                 Iterator3D target)
{
  for ( ; origin!=end ; ++origin,++target )
    {
      // We use the copy function for the next smaller rank of tensor
      // recursively:
      copy(origin->begin(),
           origin->end(),
           target->begin());
    }
}

inline void copy(Numeric x,
                 Iterator3D target,
                 const Iterator3D& end)
{
  for ( ; target!=end ; ++target )
    {
      // We use the copy function for the next smaller rank of tensor
      // recursively:
      copy(x,target->begin(),target->end());
    }
}


// Functions for Tensor3:
// ---------------------

inline Tensor3::Tensor3() :
  Tensor3View::Tensor3View()
{
  // Nothing to do here. However, note that the default constructor
  // for Tensor3View has been called in the initializer list. That is
  // crucial, otherwise internal range objects will not be properly
  // initialized. 
}

inline Tensor3::Tensor3(Index p, Index r, Index c) :
  Tensor3View( new Numeric[p*r*c],
             Range(0,p,r*c),
             Range(0,r,c),
             Range(0,c))
{
  // Nothing to do here.
}

inline Tensor3::Tensor3(Index p, Index r, Index c, Numeric fill) :
  Tensor3View( new Numeric[p*r*c],
              Range(0,p,r*c),
              Range(0,r,c),
              Range(0,c))
{
  // Here we can access the raw memory directly, for slightly
  // increased efficiency:
  for ( Numeric *x=mdata; x<mdata+p*r*c; ++x )
    *x = fill;
}

inline Tensor3::Tensor3(const ConstTensor3View& m) :
  Tensor3View( new Numeric[m.npages()*m.nrows()*m.ncols()],
             Range( 0, m.npages(), m.nrows()*m.ncols() ),
             Range( 0, m.nrows(), m.ncols() ),
             Range( 0, m.ncols() ) )
{
  copy(m.begin(),m.end(),begin());
}

inline Tensor3::Tensor3(const Tensor3& m) :
  Tensor3View( new Numeric[m.npages()*m.nrows()*m.ncols()],
             Range( 0, m.npages(), m.nrows()*m.ncols() ),
             Range( 0, m.nrows(), m.ncols() ),
             Range( 0, m.ncols() ) )
{
  // There is a catch here: If m is an empty tensor, then it will have
  // dimensions of size 0. But these are used to initialize the stride
  // for higher dimensions! Thus, this method has to be consistent
  // with the behaviour of Range::Range. For now, Range::Range allows
  // also stride 0.
  copy(m.begin(),m.end(),begin());
}

inline Tensor3& Tensor3::operator=(const Tensor3& m)
{
  //  cout << "Tensor3 copy: m = " << m.nrows() << " " << m.ncols() << "\n";
  //  cout << "             n = " << nrows() << " " << ncols() << "\n";

  // None of the extents can be zero for a valid tensor, so we just
  // have to check one.
  if ( 0 == mcr.mextent )
    {
      // Adjust if previously empty.
      resize( m.mpr.mextent, m.mrr.mextent, m.mcr.mextent ); 
    }
  else
    {
      // Check that sizes are compatible:
      assert( mpr.mextent==m.mpr.mextent );
      assert( mrr.mextent==m.mrr.mextent );
      assert( mcr.mextent==m.mcr.mextent );
    }

  copy( m.begin(), m.end(), begin() );
  return *this;
}

inline Tensor3& Tensor3::operator=(Numeric x)
{
  copy( x, begin(), end() );
  return *this;
}

inline void Tensor3::resize(Index p, Index r, Index c)
{
  assert( 0<=p );
  assert( 0<=r );
  assert( 0<=c );

  if ( mpr.mextent!=p ||
       mrr.mextent!=r ||
       mcr.mextent!=c )
    {
      delete mdata;
      mdata = new Numeric[p*r*c];

      mpr.mstart = 0;
      mpr.mextent = p;
      mpr.mstride = r*c;

      mrr.mstart = 0;
      mrr.mextent = r;
      mrr.mstride = c;

      mcr.mstart = 0;
      mcr.mextent = c;
      mcr.mstride = 1;
    }
}

inline Tensor3::~Tensor3()
{
//   cout << "Destroying a Tensor3:\n"
//        << *this << "\n........................................\n";
  delete [] mdata;
}


inline void transform( Tensor3View y,
                       double (&my_func)(double),
                       ConstTensor3View x )
{
  // Check dimensions:
  assert( y.npages() == x.npages() );
  assert( y.nrows()  == x.nrows()  );
  assert( y.ncols()  == x.ncols()  );

  const ConstIterator3D xe = x.end();
  ConstIterator3D       xi = x.begin();
  Iterator3D            yi = y.begin();
  for ( ; xi!=xe; ++xi, ++yi )
    {
      // Use the transform function of lower dimensional tensors
      // recursively:
      transform(*yi,my_func,*xi);
    }
}

inline Numeric max(const ConstTensor3View& x)
{
  const ConstIterator3D xe = x.end();
  ConstIterator3D       xi = x.begin();

  // Initial value for max:
  Numeric themax = max(*xi);
  ++xi;

  for ( ; xi!=xe ; ++xi )
    {
      // Use the max function of lower dimensional tensors
      // recursively:
      Numeric maxi = max(*xi);
      if ( maxi > themax )
        themax = maxi;
    }

  return themax;
}

inline Numeric min(const ConstTensor3View& x)
{
  const ConstIterator3D xe = x.end();
  ConstIterator3D       xi = x.begin();

  // Initial value for min:
  Numeric themin = min(*xi);
  ++xi;

  for ( ; xi!=xe ; ++xi )
    {
      // Use the min function of lower dimensional tensors
      // recursively:
      Numeric mini = min(*xi);
      if ( mini < themin )
        themin = mini;
    }

  return themin;
}



#endif    // matpackIII_h

---