matpackIV.cc

Go to the documentation of this file.

/* Copyright (C) 2002-2008 Stefan Buehler <sbuehler@ltu.se>

   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. */

#include "matpackIV.h"
#include "exceptions.h"

Tensor3View* Iterator4D::operator->()
{
  return &msv;
}

Tensor3View& Iterator4D::operator*()
{
  return msv;
}

const ConstTensor3View* ConstIterator4D::operator->() const
{
  return &msv;
}

const ConstTensor3View& ConstIterator4D::operator*() const
{
  return msv;
}



// Functions for ConstTensor4View:
// ------------------------------

Index ConstTensor4View::nbooks() const
{
  return mbr.mextent;
}

Index ConstTensor4View::npages() const
{
  return mpr.mextent;
}

Index ConstTensor4View::nrows() const
{
  return mrr.mextent;
}

Index ConstTensor4View::ncols() const
{
  return mcr.mextent;
}

ConstTensor4View ConstTensor4View::operator()(const Range& b,
                                                     const Range& p,
                                                     const Range& r,
                                                     const Range& c) const
{
  return ConstTensor4View(mdata,
                          mbr, mpr, mrr, mcr,
                          b,   p,   r,   c);
}

ConstTensor3View ConstTensor4View::operator()(const Range& b,
                                                     const Range& p,
                                                     const Range& r,
                                                     Index c       ) const
{
  // Check that c is valid:
  assert( 0 <= c );
  assert( c < mcr.mextent );

  return ConstTensor3View(mdata +
                          mcr.mstart + c * mcr.mstride,
                          mbr, mpr, mrr,
                          b,   p,   r);
}

ConstTensor3View ConstTensor4View::operator()(const Range& b,
                                                     const Range& p,
                                                     Index r,
                                                     const Range& c) const
{
  // Check that r is valid:
  assert( 0 <= r );
  assert( r < mrr.mextent );

  return ConstTensor3View(mdata +
                          mrr.mstart + r * mrr.mstride,
                          mbr, mpr, mcr,
                          b,   p,   c);
}

ConstTensor3View ConstTensor4View::operator()(const Range& b,
                                                     Index p,
                                                     const Range& r,
                                                     const Range& c) const
{
  // Check that p is valid:
  assert( 0 <= p );
  assert( p < mpr.mextent );

  return ConstTensor3View(mdata +
                          mpr.mstart + p * mpr.mstride,
                          mbr, mrr, mcr,
                          b,   r,   c);
}

ConstTensor3View ConstTensor4View::operator()(Index b,
                                                     const Range& p,
                                                     const Range& r,
                                                     const Range& c) const
{
  // Check that b is valid:
  assert( 0 <= b );
  assert( b < mbr.mextent );

  return ConstTensor3View(mdata +
                          mbr.mstart + b * mbr.mstride,
                          mpr, mrr, mcr,
                          p,   r,   c);
}

ConstMatrixView ConstTensor4View::operator()(const Range& b,
                                                    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 ConstMatrixView(mdata +
                         mrr.mstart + r * mrr.mstride +
                         mcr.mstart + c * mcr.mstride,
                         mbr, mpr,
                         b,   p);
}

ConstMatrixView ConstTensor4View::operator()(const Range& b,
                                                    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 ConstMatrixView(mdata +
                         mpr.mstart + p * mpr.mstride +
                         mcr.mstart + c * mcr.mstride,
                         mbr, mrr,
                         b,   r);
}

ConstMatrixView ConstTensor4View::operator()(const Range& b,
                                                    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 ConstMatrixView(mdata +
                         mpr.mstart + p * mpr.mstride +
                         mrr.mstart + r * mrr.mstride,
                         mbr, mcr,
                         b,   c);
}

ConstMatrixView ConstTensor4View::operator()(Index b,
                                                    const Range& p,
                                                    Index r,
                                                    const Range& c) const
{
  // Check that b and r are valid:
  assert( 0 <= b );
  assert( 0 <= r );
  assert( b < mbr.mextent );
  assert( r < mrr.mextent );

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

ConstMatrixView ConstTensor4View::operator()(Index b,
                                                    const Range& p,
                                                    const Range& r,
                                                    Index c       ) const
{
  // Check that b and c are valid:
  assert( 0 <= b );
  assert( 0 <= c );
  assert( b < mbr.mextent );
  assert( c < mcr.mextent );

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

ConstMatrixView ConstTensor4View::operator()(Index b,
                                                    Index p,
                                                    const Range& r,
                                                    const Range& c) const
{
  // Check that b and p are valid:
  assert( 0 <= b );
  assert( 0 <= p );
  assert( b < mbr.mextent );
  assert( p < mpr.mextent );

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

ConstVectorView ConstTensor4View::operator()(const Range& b,
                                                    Index p,
                                                    Index r,
                                                    Index c       ) const
{
  // Check that p, r and c are valid:
  assert( 0 <= p );
  assert( 0 <= r );
  assert( 0 <= c );
  assert( p < mpr.mextent );
  assert( r < mrr.mextent );
  assert( c < mcr.mextent );

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

ConstVectorView ConstTensor4View::operator()(Index b,
                                                    const Range& p,
                                                    Index r,
                                                    Index c       ) const
{
  // Check that b, r and c are valid:
  assert( 0 <= b );
  assert( 0 <= r );
  assert( 0 <= c );
  assert( b < mbr.mextent );
  assert( r < mrr.mextent );
  assert( c < mcr.mextent );

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

ConstVectorView ConstTensor4View::operator()(Index b,
                                                    Index p,
                                                    const Range& r,
                                                    Index c       ) const
{
  // Check that b, p and c are valid:
  assert( 0 <= b );
  assert( 0 <= p );
  assert( 0 <= c );
  assert( b < mbr.mextent );
  assert( p < mpr.mextent );
  assert( c < mcr.mextent );

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

ConstVectorView ConstTensor4View::operator()(Index b,
                                                    Index p,
                                                    Index r,
                                                    const Range& c) const
{
  // Check that b, p and r are valid:
  assert( 0 <= b );
  assert( 0 <= p );
  assert( 0 <= r );
  assert( b < mbr.mextent );
  assert( p < mpr.mextent );
  assert( r < mrr.mextent );

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

Numeric *Tensor4View::get_c_array()
{
  if (mbr.mstart != 0 || mbr.mstride != mpr.mextent * mrr.mextent * mcr.mextent
      || mpr.mstart != 0 || mpr.mstride != mrr.mextent * mcr.mextent
      || mrr.mstart != 0 || mrr.mstride != mcr.mextent
      || mcr.mstart != 0 || mcr.mstride != 1)
    throw runtime_error("A Tensor4View can only be converted to a plain C-array if mbr.mstart == 0 and mbr.mstride == mrp.extent*mrr.extent*mcr.extent and mpr.mstart == 0 and mpr.mstride == mrr.extent*mcr.extent and mrr.mstart == 0 and mrr.mstride == mcr.extent and mcr.mstart == 0 and mcr.mstride == 1");

  return mdata;
}

const Numeric *Tensor4View::get_c_array() const
{
  if (mbr.mstart != 0 || mbr.mstride != mpr.mextent * mrr.mextent * mcr.mextent
      || mpr.mstart != 0 || mpr.mstride != mrr.mextent * mcr.mextent
      || mrr.mstart != 0 || mrr.mstride != mcr.mextent
      || mcr.mstart != 0 || mcr.mstride != 1)
    throw runtime_error("A Tensor4View can only be converted to a plain C-array if mbr.mstart == 0 and mbr.mstride == mrp.extent*mrr.extent*mcr.extent and mpr.mstart == 0 and mpr.mstride == mrr.extent*mcr.extent and mrr.mstart == 0 and mrr.mstride == mcr.extent and mcr.mstart == 0 and mcr.mstride == 1");

  return mdata;
}

ConstIterator4D ConstTensor4View::begin() const
{
  return ConstIterator4D( ConstTensor3View(mdata + mbr.mstart,
                                           mpr, mrr, mcr),
                          mbr.mstride );
}

ConstIterator4D ConstTensor4View::end() const
{
  return ConstIterator4D( ConstTensor3View(mdata + mbr.mstart +
                                           (mbr.mextent) * mbr.mstride,
                                           mpr, mrr, mcr),
                          mbr.mstride );
}

ConstTensor4View::ConstTensor4View(const ConstTensor3View& a) :
  mbr(0,1,a.mpr.mextent*a.mrr.mextent*a.mcr.mextent),
  mpr(a.mpr),
  mrr(a.mrr),
  mcr(a.mcr),
  mdata(a.mdata) 
{
  // Nothing to do here.
}

ConstTensor4View::ConstTensor4View() :
  mbr(0,0,1),
  mpr(0,0,1),
  mrr(0,0,1),
  mcr(0,0,1),
  mdata(NULL)
{
  // Nothing to do here.
}

ConstTensor4View::ConstTensor4View(Numeric *data,
                                          const Range& br,
                                          const Range& pr,
                                          const Range& rr,
                                          const Range& cr) :
  mbr(br),
  mpr(pr),
  mrr(rr),
  mcr(cr),
  mdata(data)
{
  // Nothing to do here.
}

ConstTensor4View::ConstTensor4View(Numeric *data,
                                          const Range& pb,
                                          const Range& pp,
                                          const Range& pr,
                                          const Range& pc,
                                          const Range& nb,
                                          const Range& np,
                                          const Range& nr,
                                          const Range& nc) :
  mbr(pb,nb),
  mpr(pp,np),
  mrr(pr,nr),
  mcr(pc,nc),
  mdata(data)
{
  // Nothing to do here.
}

ostream& operator<<(ostream& os, const ConstTensor4View& v)
{
  // Page iterators:
  ConstIterator4D ib = v.begin();
  const ConstIterator4D end_book = v.end();

  if ( ib != end_book ) {
    os << *ib;
    ++ib;
  }

  for ( ; ib != end_book; ++ib ) {
    os << "\n\n";
    os << *ib;
  }

  return os;
}


// Functions for Tensor4View:
// -------------------------

ConstTensor4View Tensor4View::operator()(const Range& b,
                                                const Range& p,
                                                const Range& r,
                                                const Range& c) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstTensor3View Tensor4View::operator()(const Range& b,
                                                const Range& p,
                                                const Range& r,
                                                Index c       ) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstTensor3View Tensor4View::operator()(const Range& b,
                                                const Range& p,
                                                Index r,
                                                const Range& c) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstTensor3View Tensor4View::operator()(const Range& b,
                                                Index p,
                                                const Range& r,
                                                const Range& c) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstTensor3View Tensor4View::operator()(Index b,
                                                const Range& p,
                                                const Range& r,
                                                const Range& c) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstMatrixView Tensor4View::operator()(const Range& b,
                                               const Range& p,
                                               Index r,
                                               Index c       ) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstMatrixView Tensor4View::operator()(const Range& b,
                                               Index p,
                                               const Range& r,
                                               Index c       ) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstMatrixView Tensor4View::operator()(const Range& b,
                                               Index p,
                                               Index r,
                                               const Range& c) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstMatrixView Tensor4View::operator()(Index b,
                                               const Range& p,
                                               Index r,
                                               const Range& c) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstMatrixView Tensor4View::operator()(Index b,
                                               const Range& p,
                                               const Range& r,
                                               Index c       ) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstMatrixView Tensor4View::operator()(Index b,
                                               Index p,
                                               const Range& r,
                                               const Range& c) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstVectorView Tensor4View::operator()(const Range& b,
                                               Index p,
                                               Index r,
                                               Index c       ) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstVectorView Tensor4View::operator()(Index b,
                                               const Range& p,
                                               Index r,
                                               Index c       ) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstVectorView Tensor4View::operator()(Index b,
                                               Index p,
                                               const Range& r,
                                               Index c       ) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

ConstVectorView Tensor4View::operator()(Index b,
                                               Index p,
                                               Index r,
                                               const Range& c) const
{
  return ConstTensor4View::operator()(b,p,r,c);
}

Tensor4View Tensor4View::operator()(const Range& b,
                                           const Range& p,
                                           const Range& r,
                                           const Range& c)
{
  return Tensor4View(mdata,
                     mbr, mpr, mrr, mcr,
                     b,   p,   r,   c);
}

Tensor3View Tensor4View::operator()(const Range& b,
                                           const Range& p,
                                           const Range& r,
                                           Index c)
{
  // Check that c is valid:
  assert( 0 <= c );
  assert( c < mcr.mextent );

  return Tensor3View(mdata +
                     mcr.mstart + c * mcr.mstride,
                     mbr, mpr, mrr,
                     b,   p,   r);
}

Tensor3View Tensor4View::operator()(const Range& b,
                                           const Range& p,
                                           Index r,
                                           const Range& c)
{
  // Check that r is valid:
  assert( 0 <= r );
  assert( r < mrr.mextent );

  return Tensor3View(mdata +
                     mrr.mstart + r * mrr.mstride,
                     mbr, mpr, mcr,
                     b,   p,   c);
}

Tensor3View Tensor4View::operator()(const Range& b,
                                           Index p,
                                           const Range& r,
                                           const Range& c)
{
  // Check that p is valid:
  assert( 0 <= p );
  assert( p < mpr.mextent );

  return Tensor3View(mdata +
                     mpr.mstart + p * mpr.mstride,
                     mbr, mrr, mcr,
                     b,   r,   c);
}

Tensor3View Tensor4View::operator()(Index b,
                                           const Range& p,
                                           const Range& r,
                                           const Range& c)
{
  // Check that b is valid:
  assert( 0 <= b );
  assert( b < mbr.mextent );

  return Tensor3View(mdata +
                     mbr.mstart + b * mbr.mstride,
                     mpr, mrr, mcr,
                     p,   r,   c);
}

MatrixView Tensor4View::operator()(const Range& b,
                                          const Range& p,
                                          Index r,
                                          Index c)
{
  // Check that r and c are valid:
  assert( 0 <= r );
  assert( 0 <= c );
  assert( r < mrr.mextent );
  assert( c < mcr.mextent );

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

MatrixView Tensor4View::operator()(const Range& b,
                                          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 MatrixView(mdata +
                    mpr.mstart + p * mpr.mstride +
                    mcr.mstart + c * mcr.mstride,
                    mbr, mrr,
                    b,   r);
}

MatrixView Tensor4View::operator()(const Range& b,
                                          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 MatrixView(mdata +
                    mpr.mstart + p * mpr.mstride +
                    mrr.mstart + r * mrr.mstride,
                    mbr, mcr,
                    b,   c);
}

MatrixView Tensor4View::operator()(Index b,
                               const Range& p,
                               Index r,
                               const Range& c)
{
  // Check that b and r are valid:
  assert( 0 <= b );
  assert( 0 <= r );
  assert( b < mbr.mextent );
  assert( r < mrr.mextent );

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

MatrixView Tensor4View::operator()(Index b,
                                          const Range& p,
                                          const Range& r,
                                          Index c)
{
  // Check that b and c are valid:
  assert( 0 <= b );
  assert( 0 <= c );
  assert( b < mbr.mextent );
  assert( c < mcr.mextent );

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

MatrixView Tensor4View::operator()(Index b,
                                          Index p,
                                          const Range& r,
                                          const Range& c)
{
  // Check that b and p are valid:
  assert( 0 <= b );
  assert( 0 <= p );
  assert( b < mbr.mextent );
  assert( p < mpr.mextent );

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

VectorView Tensor4View::operator()(const Range& b,
                                          Index p,
                                          Index r,
                                          Index c)
{
  // Check that p, r and c are valid:
  assert( 0 <= p );
  assert( 0 <= r );
  assert( 0 <= c );
  assert( p < mpr.mextent );
  assert( r < mrr.mextent );
  assert( c < mcr.mextent );

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

VectorView Tensor4View::operator()(Index b,
                                          const Range& p,
                                          Index r,
                                          Index c)
{
  // Check that b, r and c are valid:
  assert( 0 <= b );
  assert( 0 <= r );
  assert( 0 <= c );
  assert( b < mbr.mextent );
  assert( r < mrr.mextent );
  assert( c < mcr.mextent );

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

VectorView Tensor4View::operator()(Index b,
                                          Index p,
                                          const Range& r,
                                          Index c)
{
  // Check that b, p and c are valid:
  assert( 0 <= b );
  assert( 0 <= p );
  assert( 0 <= c );
  assert( b < mbr.mextent );
  assert( p < mpr.mextent );
  assert( c < mcr.mextent );

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

VectorView Tensor4View::operator()(Index b,
                                          Index p,
                                          Index r,
                                          const Range& c)
{
  // Check that b, p and r are valid:
  assert( 0 <= b );
  assert( 0 <= p );
  assert( 0 <= r );
  assert( b < mbr.mextent );
  assert( p < mpr.mextent );
  assert( r < mrr.mextent );

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

ConstIterator4D Tensor4View::begin() const
{
  return ConstTensor4View::begin();
}

ConstIterator4D Tensor4View::end() const
{
  return ConstTensor4View::end();
}

Iterator4D Tensor4View::begin()
{
  return Iterator4D( Tensor3View(mdata + mbr.mstart,
                                 mpr, mrr, mcr),
                     mbr.mstride );
}

Iterator4D Tensor4View::end()
{
  return Iterator4D( Tensor3View(mdata + mbr.mstart +
                                 (mbr.mextent) * mbr.mstride,
                                 mpr, mrr, mcr),
                     mbr.mstride );
}

Tensor4View& Tensor4View::operator=(const ConstTensor4View& m)
{
  // Check that sizes are compatible:
  assert( mbr.mextent == m.mbr.mextent );
  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;
}

Tensor4View& Tensor4View::operator=(const Tensor4View& m)
{
  // Check that sizes are compatible:
  assert( mbr.mextent == m.mbr.mextent );
  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;
}

Tensor4View& Tensor4View::operator=(const Tensor4& m)
{
  // Check that sizes are compatible:
  assert( mbr.mextent == m.mbr.mextent );
  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;
}

Tensor4View& Tensor4View::operator=(Numeric x)
{
  copy( x, begin(), end() );
  return *this;
}

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

Tensor4View& Tensor4View::operator*=(Numeric x)
{
  const Iterator4D eb = end();
  for ( Iterator4D b = begin(); b != eb ; ++b )
  {
    *b *= x;
  }
  return *this;
}

Tensor4View& Tensor4View::operator/=(Numeric x)
{
  const Iterator4D eb = end();
  for ( Iterator4D b = begin(); b != eb ; ++b )
  {
    *b /= x;
  }
  return *this;
}

Tensor4View& Tensor4View::operator+=(Numeric x)
{
  const Iterator4D eb = end();
  for ( Iterator4D b = begin(); b != eb ; ++b )
  {
    *b += x;
  }
  return *this;
}

Tensor4View& Tensor4View::operator-=(Numeric x)
{
  const Iterator4D eb = end();
  for ( Iterator4D b = begin(); b != eb ; ++b )
  {
    *b -= x;
  }
  return *this;
}

Tensor4View& Tensor4View::operator*=(const ConstTensor4View& x)
{
  assert( nbooks() == x.nbooks() );
  assert( npages() == x.npages() );
  assert( nrows()  == x.nrows()  );
  assert( ncols()  == x.ncols()  );
  ConstIterator4D  xb = x.begin();
  Iterator4D        b = begin();
  const Iterator4D eb = end();
  for ( ; b != eb ; ++b, ++xb )
    {
      *b *= *xb;
    }
  return *this;
}

Tensor4View& Tensor4View::operator/=(const ConstTensor4View& x)
{
  assert( nbooks() == x.nbooks() );
  assert( npages() == x.npages() );
  assert( nrows()  == x.nrows()  );
  assert( ncols()  == x.ncols()  );
  ConstIterator4D  xb = x.begin();
  Iterator4D        b = begin();
  const Iterator4D eb = end();
  for ( ; b != eb ; ++b, ++xb )
    {
      *b /= *xb;
    }
  return *this;
}

Tensor4View& Tensor4View::operator+=(const ConstTensor4View& x)
{
  assert( nbooks() == x.nbooks() );
  assert( npages() == x.npages() );
  assert( nrows()  == x.nrows()  );
  assert( ncols()  == x.ncols()  );
  ConstIterator4D  xb = x.begin();
  Iterator4D        b = begin();
  const Iterator4D eb = end();
  for ( ; b != eb ; ++b, ++xb )
    {
      *b += *xb;
    }
  return *this;
}

Tensor4View& Tensor4View::operator-=(const ConstTensor4View& x)
{
  assert( nbooks() == x.nbooks() );
  assert( npages() == x.npages() );
  assert( nrows()  == x.nrows()  );
  assert( ncols()  == x.ncols()  );
  ConstIterator4D  xb = x.begin();
  Iterator4D        b = begin();
  const Iterator4D eb = end();
  for ( ; b != eb ; ++b, ++xb )
    {
      *b -= *xb;
    }
  return *this;
}

Tensor4View::Tensor4View(const Tensor3View& a) :
  ConstTensor4View( a.mdata,
                    Range(0,1,
                          a.mpr.mextent*
                          a.mrr.mextent*
                          a.mcr.mextent),
                    a.mpr,
                    a.mrr,
                    a.mcr )
{
  // Nothing to do here.
}

Tensor4View::Tensor4View() :
  ConstTensor4View()
{
  // Nothing to do here.
}

Tensor4View::Tensor4View(Numeric *data,
                                const Range& br,
                                const Range& pr,
                                const Range& rr,
                                const Range& cr) :
  ConstTensor4View(data, br, pr, rr, cr)
{
  // Nothing to do here.
}

Tensor4View::Tensor4View(Numeric *data,
                                const Range& pb,
                                const Range& pp,
                                const Range& pr,
                                const Range& pc,
                                const Range& nb,
                                const Range& np,
                                const Range& nr,
                                const Range& nc) :
  ConstTensor4View(data, pb, pp, pr, pc, nb, np, nr, nc)
{
  // Nothing to do here.
}

void copy(ConstIterator4D origin,
                 const ConstIterator4D& end,
                 Iterator4D 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() );
    }
}

void copy(Numeric x,
                 Iterator4D target,
                 const Iterator4D& 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 Tensor4:
// ---------------------

Tensor4::Tensor4() :
  Tensor4View::Tensor4View()
{
  // Nothing to do here. However, note that the default constructor
  // for Tensor4View has been called in the initializer list. That is
  // crucial, otherwise internal range objects will not be properly
  // initialized.
}

Tensor4::Tensor4(Index b, Index p, Index r, Index c) :
  Tensor4View( new Numeric[b*p*r*c],
               Range( 0, b, p*r*c ),
               Range( 0, p, r*c ),
               Range( 0, r, c ),
               Range( 0, c) )
{
  // Nothing to do here.
}

Tensor4::Tensor4(Index b, Index p, Index r, Index c, Numeric fill) :
  Tensor4View( new Numeric[b*p*r*c],
               Range( 0, b, 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:
  const Numeric *stop = mdata + b*p*r*c;
  for ( Numeric *x = mdata; x < stop; ++x )
    *x = fill;
}

Tensor4::Tensor4(const ConstTensor4View& m) :
  Tensor4View( new Numeric[m.nbooks()*m.npages()*m.nrows()*m.ncols()],
               Range( 0, m.nbooks(), 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() );
}

Tensor4::Tensor4(const Tensor4& m) :
  Tensor4View( new Numeric[m.nbooks()*m.npages()*m.nrows()*m.ncols()],
               Range( 0, m.nbooks(), 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());
}


Tensor4& Tensor4::operator=(const Tensor4& m)
{
  //  cout << "Tensor4 copy: m = " << m.nrows() << " " << m.ncols() << "\n";
  //  cout << "              n = " << nrows() << " " << ncols() << "\n";

  resize( m.mbr.mextent, m.mpr.mextent, m.mrr.mextent, m.mcr.mextent );
  copy( m.begin(), m.end(), begin() );
  return *this;
}

Tensor4& Tensor4::operator=(Numeric x)
{
  copy( x, begin(), end() );
  return *this;
}

void Tensor4::resize(Index b, Index p, Index r, Index c)
{
  assert( 0 <= b );
  assert( 0 <= p );
  assert( 0 <= r );
  assert( 0 <= c );

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

      mbr.mstart = 0;
      mbr.mextent = b;
      mbr.mstride = 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;
    }
}

Tensor4::~Tensor4()
{
//   cout << "Destroying a Tensor4:\n"
//        << *this << "\n........................................\n";
  delete[] mdata;
}


void transform( Tensor4View y,
                       double (&my_func)(double),
                       ConstTensor4View x )
{
  // Check dimensions:
  assert( y.nbooks() == x.nbooks() );
  assert( y.npages() == x.npages() );
  assert( y.nrows()  == x.nrows()  );
  assert( y.ncols()  == x.ncols()  );

  const ConstIterator4D xe = x.end();
  ConstIterator4D       xi = x.begin();
  Iterator4D            yi = y.begin();
  for ( ; xi != xe; ++xi, ++yi )
    {
      // Use the transform function of lower dimensional tensors
      // recursively:
      transform( *yi, my_func, *xi );
    }
}

Numeric max(const ConstTensor4View& x)
{
  const ConstIterator4D xe = x.end();
  ConstIterator4D       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;
}

Numeric min(const ConstTensor4View& x)
{
  const ConstIterator4D xe = x.end();
  ConstIterator4D       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;
}


// Helper function for debugging
#ifndef NDEBUG

Numeric debug_tensor4view_get_elem (Tensor4View& tv,
                                    Index b, Index p, Index r, Index c)
{
  return tv(b, p, r, c);
}

#endif

---