libthepeg-dev 1.8.0-3build1 / usr / include / ThePEG / ACDC / ACDCGen.icc

// -*- C++ -*-
//
// ACDCGen.icc is a part of ThePEG - Toolkit for HEP Event Generation
// Copyright (C) 1999-2011 Leif Lonnblad
//
// ThePEG is licenced under version 2 of the GPL, see COPYING for details.
// Please respect the MCnet academic guidelines, see GUIDELINES for details.
//

namespace ACDCGenerator {

template <typename Rnd, typename FncPtr>
inline ACDCGen<Rnd,FncPtr>::ACDCGen(Rnd * r)
  : theRnd(r), theNAcc(0), theN(0), theNI(1, 0),
    theSumW(1, 0.0), theSumW2(1, 0.0),
    theEps(100*std::numeric_limits<double>::epsilon()), theMargin(1.1),
    theNTry(100), theMaxTry(10000), useCheapRandom(false), theFunctions(1),
    theDimensions(1, 0), thePrimaryCells(1), theSumMaxInts(1, 0.0), theLast(0),
    theLastCell(0), theLastF(0.0) {
  maxsize = 0;
}

template <typename Rnd, typename FncPtr>
inline ACDCGen<Rnd,FncPtr>::ACDCGen()
  : theRnd(0), theNAcc(0), theN(0), theNI(1, 0),
    theSumW(1, 0.0), theSumW2(1, 0.0),
    theEps(100*std::numeric_limits<double>::epsilon()), theMargin(1.1),
    theNTry(100), theMaxTry(10000), useCheapRandom(false), theFunctions(1),
    theDimensions(1, 0), thePrimaryCells(1), theSumMaxInts(1, 0.0), theLast(0),
    theLastCell(0), theLastF(0.0) {
  maxsize = 0;
}

template <typename Rnd, typename FncPtr>
inline ACDCGen<Rnd,FncPtr>::~ACDCGen() {
  clear();
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::setRnd(Rnd * r) {
  theRnd = r;
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::clear() {
  theNAcc = 0;
  theN = 0;
  theNI = vector<long>(1, 0);
  theSumW = DVector(1, 0.0);
  theSumW2 = DVector(1, 0.0);
  theFunctions = FncVector(1);
  theDimensions = DimVector(1, 0);
  for ( int i = 0, N = thePrimaryCells.size(); i < N; ++i )
    if ( thePrimaryCells[i] ) delete thePrimaryCells[i];
  thePrimaryCells = CellVector(1);
  theSumMaxInts = DVector(1, 0.0);
  theLast = 0;
  theLastCell = 0;
  theLastPoint.clear();
  theLastF = 0.0;
  levels.clear();
}

template <typename Rnd, typename FncPtr>
inline bool ACDCGen<Rnd,FncPtr>::
addFunction(DimType dim, FncPtrType fnc, double maxrat) {
  if ( maxrat < 0.0 ) maxrat = 1.0/nTry();
  typedef map<double,DVector> PointMap;
  theLast = theFunctions.size();
  theFunctions.push_back(fnc);
  theNI.push_back(0);
  theSumW.push_back(0.0);
  theSumW2.push_back(0.0);
  theDimensions.push_back(dim);

  // Generate nTry() points with non-zero function value
  DVector x(dim);
  PointMap pmap;
  long itry = 0;
  while ( pmap.size() < nTry() ) {
    if ( ++itry > maxTry() ) {
      thePrimaryCells.push_back(new ACDCGenCell(0.0));
      theSumMaxInts.push_back(theSumMaxInts.back() + cells().back()->doMaxInt());
      return false;
    }
    rnd(dim, x);
    double val = FncTraits::value(fnc, x);
    if ( val > 0.0 ) {
      pmap[val] = x;
      itry = 0;
    }
  }

  // Create the root cell and set its overestimated function value to
  // the smallest non-zero value found
  double minf = pmap.begin()->first;
  double maxf = (--pmap.end())->first;
  minf = max(minf, maxrat*maxf);
  //  thePrimaryCells.push_back(new ACDCGenCell(pmap.begin()->first));
  thePrimaryCells.push_back(new ACDCGenCell(minf));
  theLastF = pmap.begin()->first;
  pmap.erase(pmap.begin());
  theSumMaxInts.push_back(theSumMaxInts.back() + cells().back()->doMaxInt());

  // Start the divide-and-conquer procedure using the point with the
  // highest function value found.
  theLastF = (--pmap.end())->first;
  theLastPoint =  (--pmap.end())->second;
  pmap.erase(--pmap.end());
  DVector up(dim, 1.0);
  DVector lo(dim, 0.0);
  theLastCell = cells().back()->getCell(lo, lastPoint(), up);
  if ( lastF() > lastCell()->g() ) {
    compensate(lo, up);
    levels.clear();
  }

  // For each other generated point check that it's below the
  // overestimated value of the corresponding cell. If not start the
  // divide-and-conquer using that point.
  while ( !pmap.empty() ) {
    theLastPoint = pmap.begin()->second;
    theLastF = pmap.begin()->first;
    pmap.erase(pmap.begin());
    DVector up(dim, 1.0);
    DVector lo(dim, 0.0);
    theLastCell = cells().back()->getCell(lo, lastPoint(), up);
    if ( lastF() > lastCell()->g() ) {
      compensate(lo, up);
      levels.clear();
    }
  }
  //  cells().back()->smooth(1.0/nTry());
  return true;
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::chooseCell(DVector & lo, DVector & up) {
  if ( compensating() ) {
    // If we are compensating, we must choose the cell to be compensated.
    up = levels.back().up;
    lo = levels.back().lo;
    theLastCell = levels.back().cell;
    theLast = levels.back().index;
  } else {
    // Otherwise, first choose the function to be used and choose the
    // corresponding root cell.
    theLast = upper_bound(sumMaxInts().begin(), sumMaxInts().end(),
			  rnd()*sumMaxInts().back())
      - sumMaxInts().begin();
    if(theLast>=sumMaxInts().size()) {
      throw ThePEG::Exception() << "Selected a function outside the allowed range"
				<< " in ACDCGen::chooseCell(). This is usually due"
				<< " to a floating point error (nan or inf) in the"
				<< " calculation of the weight"
				<< ThePEG::Exception::abortnow;
    }
    up = DVector(lastDimension(), 1.0);
    lo = DVector(lastDimension(), 0.0);
    theLastCell = lastPrimary();
  }

  // Now select randomly a sub-cell of the chosen cell
  if ( cheapRandom() ) {
    theLastCell = lastCell()->generate(lo, up, theRnd);
  } else {
    DVector rndv(lastDimension());
    rnd(lastDimension(), rndv);
    theLastCell = lastCell()->generate(lo, up, rndv);
  }
}

template <typename Rnd, typename FncPtr>
inline typename ACDCGen<Rnd,FncPtr>::FncPtrType
ACDCGen<Rnd,FncPtr>::generate() {
  long itry = 0;
  while ( true ) {
    if ( ++itry > maxTry() ) return FncPtrType();
    ++theN;

    // First choose a function and a cell to generate in.
    DVector up;
    DVector lo;
    chooseCell(lo, up);

    // Now choose a point in that cell according to a flat distribution.
    DimType D = lastDimension();
    theLastPoint.resize(D);
    for ( DimType d = 0; d < D; ++d ) theLastPoint[d] = rnd(lo[d], up[d]);

    // Calculate the function value in this point
    theLastF = FncTraits::value(lastFunction(), theLastPoint);
    if ( theLastF <= 0.0 ) continue;

    // If we are compensating we require the function value to be
    // above the previous overestimate of the function.
    if ( compensating() && lastF() < levels.back().g ) theLastF = 0.0;

    double w = lastF()/lastCell()->g();
    if ( w > 1.0 ) {
      // If the value was above the overestimate then we must start
      // the compensation procedure and the curren point is disregarded.
      --theN;
      compensate(lo, up);
      continue;
    }

    // Accept the point according to the ratio of the true and
    // overestimated function value.
    theSumW[last()] += w;
    theSumW2[last()] += w*w;
    ++theNI[last()];
    if ( w > rnd() ) {
      ++theNAcc;
      return lastFunction();
    }
  }
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::reject() {
  theSumW[last()] -= 1.0;
  theSumW2[last()] -= 1.0;
  --theNAcc;
}

template <typename Rnd, typename FncPtr>
inline bool ACDCGen<Rnd,FncPtr>::compensating() {
  while ( levels.size() && levels.back().lastN < N() ) levels.pop_back();
  // Leave all levels which has reached there 'expiry date'.

  return !levels.empty();
}

template <typename Rnd, typename FncPtr>
inline long ACDCGen<Rnd,FncPtr>::compleft() const {
  if ( levels.empty() ) return 0;
  long left = 1;
  for ( int i = 0, Ni = levels.size(); i < Ni; ++i )
    left = max(left, levels[i].lastN - N());

  return left;
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::
compensate(const DVector & lo, const DVector & up) {
  //Save the previous overestimated integral and create a new
  //compensation level.
  double i0 = maxInt();
  Level level;
  level.g = lastCell()->g();

  // Start the divide-and-conquer algorithm slicing up the selected
  // cell and specify it as the cell to compensate.
  Slicer slicer(lastDimension(), *this, lo, up);
  level.cell = slicer.first;
  level.index = last();
  level.up = slicer.firstup;
  level.lo = slicer.firstlo;

  // Now calculate the the new overestimated total integral and
  // calculate the number of attempted points needed to compensate.
  double rat = (doMaxInt())/i0;
  level.lastN = long(N()*rat);

  // If we are already compensating increase also the previous
  // compensation levels.
  for ( size_type i = 0; i < levels.size(); ++i )
    levels[i].lastN = long(levels[i].lastN*rat);
  levels.insert(levels.end(), level);
  maxsize = std::max(maxsize, levels.size());
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::eps(double newEps) {
  theEps = newEps;
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::margin(double newMargin) {
  theMargin = newMargin;
}

template <typename Rnd, typename FncPtr>
inline long ACDCGen<Rnd,FncPtr>::N() const {
  return theN;
}

template <typename Rnd, typename FncPtr>
inline long ACDCGen<Rnd,FncPtr>::n() const {
  return theNAcc;
}

template <typename Rnd, typename FncPtr>
inline typename ACDCGen<Rnd,FncPtr>::size_type
ACDCGen<Rnd,FncPtr>::nTry() const {
  return theNTry;
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::nTry(size_type newNTry) {
  theNTry = newNTry;
}

template <typename Rnd, typename FncPtr>
inline long ACDCGen<Rnd,FncPtr>::maxTry() const {
  return theMaxTry;
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::maxTry(long newMaxTry) {
  theMaxTry = newMaxTry;
}

template <typename Rnd, typename FncPtr>
inline bool ACDCGen<Rnd,FncPtr>::cheapRandom() const {
  return useCheapRandom;
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::cheapRandom(bool b) {
  useCheapRandom = b;
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::maxInt() const {
  return theSumMaxInts.back();
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::doMaxInt() {
  for ( size_type i = 1, imax = functions().size(); i < imax; ++i )
    theSumMaxInts[i] = sumMaxInts()[i - 1] + cells()[i]->doMaxInt();
  return maxInt();
}

template <typename Rnd, typename FncPtr>
inline int ACDCGen<Rnd,FncPtr>::nBins() const {
  int sum = 0;
  for ( size_type i = 1; i < functions().size(); ++i )
    sum += cell(i)->nBins();
  return sum;
}

template <typename Rnd, typename FncPtr>
inline int ACDCGen<Rnd,FncPtr>::depth() const {
  int mx = 0;
  for ( size_type i = 1; i < functions().size(); ++i )
    mx = max(mx, cell(i)->depth());
  return mx;
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::efficiency() const {
  return N() > 0? double(n())/double(N()): 0.0;
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::integral(FncPtrType f) const {
  if ( N() <= 0 ) return maxInt();
  double sumw = 0.0;
  for ( size_type i = 1; i < functions().size(); ++i )
    if ( functions()[i] == f || !f ) sumw += theSumW[i];
  return maxInt()*sumw/N();
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::integralErr(FncPtrType f) const {
  if ( N() <= 0 ) return maxInt();
  double sumw2 = 0.0;
  double sumw = 0.0;
  for ( size_type i = 1; i < functions().size(); ++i )
    if ( functions()[i] == f || !f ) {
      sumw2 += theSumW2[i];
      sumw += theSumW[i];
    }
  if ( f ) return maxInt()*sqrt(sumw2)/N();
  return maxInt()*sqrt(max(0.,sumw2 - sumw*sumw/N()))/N();
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::eps() const {
  return theEps;
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::margin() const {
  return theMargin;
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::rnd() const {
  return RndTraits::rnd(theRnd);
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::rnd(double lo, double up) const {
  return RndTraits::rnd(theRnd, lo, up);
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::
rnd(const DVector & lo, const DVector & up, DVector & r) const {
  RndTraits::rnd(theRnd, lo.begin(), lo.end(), up.begin(), r.begin());
}

template <typename Rnd, typename FncPtr>
inline void ACDCGen<Rnd,FncPtr>::
rnd(DimType D, DVector & r) const {
  RndTraits::rnd(theRnd, D, r.begin());
}

template <typename Rnd, typename FncPtr>
inline long ACDCGen<Rnd,FncPtr>::rndInt(long x) const {
  return RndTraits::rndInt(theRnd, x);
}

template <typename Rnd, typename FncPtr>
inline const typename ACDCGen<Rnd,FncPtr>::FncVector &
ACDCGen<Rnd,FncPtr>::functions() const {
  return theFunctions;
}

template <typename Rnd, typename FncPtr>
inline typename ACDCGen<Rnd,FncPtr>::FncPtrType
ACDCGen<Rnd,FncPtr>::function(size_type i) const {
  return functions()[i];
}

template <typename Rnd, typename FncPtr>
inline typename ACDCGen<Rnd,FncPtr>::FncPtrType
ACDCGen<Rnd,FncPtr>::lastFunction() const {
  return function(last());
}

template <typename Rnd, typename FncPtr>
inline const typename ACDCGen<Rnd,FncPtr>::DimVector &
ACDCGen<Rnd,FncPtr>::dimensions() const {
  return theDimensions;
}

template <typename Rnd, typename FncPtr>
inline DimType ACDCGen<Rnd,FncPtr>::dimension(size_type i) const {
  return dimensions()[i];
}

template <typename Rnd, typename FncPtr>
inline DimType ACDCGen<Rnd,FncPtr>::lastDimension() const {
  return dimension(last());
}

template <typename Rnd, typename FncPtr>
inline const typename ACDCGen<Rnd,FncPtr>::CellVector &
ACDCGen<Rnd,FncPtr>::cells() const {
  return thePrimaryCells;
}

template <typename Rnd, typename FncPtr>
inline ACDCGenCell * ACDCGen<Rnd,FncPtr>::cell(size_type i) const {
  return cells()[i];
}

template <typename Rnd, typename FncPtr>
inline ACDCGenCell * ACDCGen<Rnd,FncPtr>::lastPrimary() const {
  return cell(last());
}

template <typename Rnd, typename FncPtr>
inline const DVector & ACDCGen<Rnd,FncPtr>::sumMaxInts() const {
  return theSumMaxInts;
}

template <typename Rnd, typename FncPtr>
inline typename ACDCGen<Rnd,FncPtr>::size_type
ACDCGen<Rnd,FncPtr>::last() const {
  return theLast;
}

template <typename Rnd, typename FncPtr>
inline typename ACDCGen<Rnd,FncPtr>::size_type
ACDCGen<Rnd,FncPtr>::size() const {
  return cells().size() - 1;
}

template <typename Rnd, typename FncPtr>
inline ACDCGenCell * ACDCGen<Rnd,FncPtr>::lastCell() const {
  return theLastCell;
}

template <typename Rnd, typename FncPtr>
inline const DVector & ACDCGen<Rnd,FncPtr>::lastPoint() const {
  return theLastPoint;
}

template <typename Rnd, typename FncPtr>
inline double ACDCGen<Rnd,FncPtr>::lastF() const {
  return theLastF;
}

template <typename Rnd, typename FncPtr>
typename ACDCGen<Rnd,FncPtr>::size_type ACDCGen<Rnd,FncPtr>::maxsize = 0;

template <typename Rnd, typename FncPtr>
vector<ACDCGenCellInfo> ACDCGen<Rnd,FncPtr>::extractCellInfo() const {
  vector<ACDCGenCellInfo> ret;
  for ( size_type i = 1; i < cells().size(); ++i ) {
    DVector lo(dimension(i), 0.0);
    DVector up(dimension(i), 1.0);
    cell(i)->extract(lo, up, ret);
  }
  return ret;
}

template <typename Rnd, typename FncPtr>
ACDCGen<Rnd,FncPtr>::Slicer::
Slicer(DimType Din, ACDCGen & gen, const DVector & loin, const DVector & upin)
  : D(Din), lo(loin), up(upin), xcl(loin), xcu(upin), xhl(loin), xhu(upin),
    fhl(Din, 0.0), fhu(Din, 0.0), xsel(gen.lastPoint()), fsel(gen.lastF()),
    current(gen.lastCell()), first(gen.lastCell()),
    firstlo(loin), firstup(upin),f(gen.lastFunction()),
    epsilon(gen.eps()), margin(gen.margin()), minf(0.0), wholecomp(false) {
  divideandconquer();
}

template <typename Rnd, typename FncPtr>
ACDCGen<Rnd,FncPtr>::Slicer::~Slicer() {
  // Added for debugging purposes.
}

template <typename Rnd, typename FncPtr>
void ACDCGen<Rnd,FncPtr>::Slicer::divideandconquer() {
  // If the current function value was just a little above the
  // overestimate, just increase the overestimate of this cell and
  // we're done.
  if ( fsel < current->g()*margin ) {
    current->g(current->g()*margin);
    return;
  }

  // First initialize and slice up the current cell and save the
  // resulting for the compensation procedure.
  init();
  slice();
  if ( !wholecomp ) {
    first = current;
    firstlo = lo;
    firstup = up;
  }

  // Find the largest function value in the current cell and as long
  // as it is above the current overestimate, increase the
  // overestimate and repeat the slicing.
  while ( shiftmaxmin() > current->g() ) {
    current->g(minf*margin);
    if ( current->g() > fsel ) return;
    init();
    slice();
  }   
}

template <typename Rnd, typename FncPtr>
double ACDCGen<Rnd,FncPtr>::Slicer::shiftmaxmin() {
  // Find the largest diagonal
  DVector test = xsel;
  double scale = 0.0;
  for ( DimType d = 0; d < D; ++d )
    if ( fhl[d] > fsel || fhu[d] > fsel ) scale += 1.0;
  scale = sqrt(scale);
  for ( DimType d = 0; d < D; ++d ) {
    if ( fhl[d] > fsel && fhl[d] > fhu[d] )
      test[d] = test[d] + (xhl[d] - test[d])/scale;
    if ( fhu[d] > fsel && fhu[d] > fhl[d] )
      test[d] = test[d] + (xhu[d] - test[d])/scale;
  }

  // Find the largest value above overestimate
  DimType dsel = -1;
  double x = 0;
  minf = fsel;
  for ( DimType d = 0; d < D; ++d ) {

    // Find the point with the function minimum value above the
    // current overestimate.
    minf = std::min(minf, fhl[d]);
    minf = std::min(minf, fhu[d]);

    // Find points with the maximum function value and shift the
    // current point to it.
    if ( fhu[d] > fsel ) {
      fsel = fhu[d];
      dsel = d;
      x = xhu[d];
    }
    if ( fhl[d] > fsel ) {
      fsel = fhl[d];
      dsel = d;
      x = xhl[d];
    }
  }

  // Check also the largest diagonal
  //  double ftest = (*f)(test);
//   if ( ftest > fsel ) {
//     xsel = test;
//     fsel = ftest;
//     dsel = -1;
//   }

  if ( dsel >= 0 ) xsel[dsel] = x;
  minf = std::max(minf, current->g());
  return fsel;
}

template <typename Rnd, typename FncPtr>
void ACDCGen<Rnd,FncPtr>::Slicer::dohalf(DimType d) {
  xcl[d] = lo[d];

  // Find the point closest below the current point in the given
  // dimension with a function value below the current overestimate,
  // also find the one furthest away from the current point with a
  // function value above the current overestimate. Use a crude
  // iterative mid-point selection.
  while ( true ) {
    xhl[d] = (xsel[d] + xcl[d])*0.5;

    std::swap(xsel[d], xhl[d]);
    fhl[d] = FncTraits::value(f, xsel);
    std::swap(xsel[d], xhl[d]);

    if ( fhl[d] > current->g() ) break;
    if ( xsel[d] - xcl[d] < epsilon ) break;

    xcl[d] = xhl[d];
  }

  // Check if the current slicing is worth doing...
  double cut = ( up[d] - xcl[d] )/( up[d] - lo[d] );
  if ( cut < 1.0 - current->g()/fsel && cut > 0.0 )
    rateslice.insert(std::make_pair(cut, -1-d));

  // Find the point closest above the current point in the given
  // dimension with a function value below the current overestimate,
  // also find the one furthest away from the current point with a
  // function value above the current overestimate. Use a crude
  // iterative mid-point selection.
  xcu[d] = up[d];
  while ( true ) {
    xhu[d] = (xsel[d] + xcu[d])*0.5;

    std::swap(xsel[d], xhu[d]);
    fhu[d] = FncTraits::value(f, xsel);
    std::swap(xsel[d], xhu[d]);

    if ( fhu[d] > current->g() ) break;
    if ( xcu[d] - xsel[d] < epsilon ) break;

    xcu[d] = xhu[d];
  }

  // Check if the current slicing is worth doing...
  cut = ( xcu[d] - lo[d] )/( up[d] - lo[d] );
  if ( cut < 1.0 - current->g()/fsel && cut > 0.0 )
    rateslice.insert(std::make_pair(cut, 1+d));

}

template <typename Rnd, typename FncPtr>
void ACDCGen<Rnd,FncPtr>::Slicer::init() {
  for ( DimType d = 0; d < D; ++d ) dohalf(d);
}

template <typename Rnd, typename FncPtr>
void ACDCGen<Rnd,FncPtr>::Slicer::slice() {
  while ( !rateslice.empty() ) {
    // Perform the slicing which reduces the volume of the cell the
    // most first.
    DimType d = rateslice.begin()->second;
    rateslice.erase(rateslice.begin());
    if ( d > 0 ) {
      // Slice from above.
      d = d - 1;
      current->splitme(lo[d], xcu[d], up[d], d);
      checkdiag(current->upper(), d, xcu[d], up[d]);
      current = current->lower();
      up[d] = xcu[d];
    } else {
      // Slice from below..
      d = -d - 1;
      current->splitme(lo[d], xcl[d], up[d], d);
      checkdiag(current->lower(), d, lo[d], xcl[d]);
      current = current->upper();
      lo[d] = xcl[d];
    }
    dohalf(d);
  }
}

template <typename Rnd, typename FncPtr>
void ACDCGen<Rnd,FncPtr>::Slicer::
checkdiag(ACDCGenCell * cell, DimType dc, double lod, double upd) {
  return;
  // Look at the midpoint in the dc direction in which a cell has been
  // chopped off.
  if ( upd - lod <= epsilon ) return;
  DVector newlo = lo;
  DVector newup = up;
  newlo[dc] = lod;
  newup[dc] = upd;
  DVector newsel = xsel;
  newsel[dc] = 0.5*(lod + upd);
  double newfsel = FncTraits::value(f, newsel);
  double newfh = newfsel;
  DVector newxsel = newsel;
  vector<int> dir(D, 0);

  // For each other direction look at the mid point between the point
  // chosen above and the borders of the cell. Save the point which
  // gives the highest function value.
  for ( DimType d = 0; d < D; ++d ) {
    if ( d == dc ) continue;
    double xdum = 0.5*(newlo[d] + newsel[d]);
    swap(xdum, newsel[d]);
    double fh1 = FncTraits::value(f, newsel);
    if ( fh1 > newfsel ) {
      newfsel = fh1;
      newxsel = newsel;
    }
    if ( fh1 > newfh ) dir[d] = -1;
    swap(xdum, newsel[d]);
    xdum = 0.5*(newsel[d] + newup[d]);
    swap(xdum, newsel[d]);
    double fh2 = FncTraits::value(f, newsel);
    if ( fh2 > newfsel ) {
      newfsel = fh2;
      newxsel = newsel;
    }
    if ( fh2 > newfh && fh2 > fh1 ) dir[d] = 1;
    swap(xdum, newsel[d]);
  }

  // Now check along the diagonal where we found the highest values.
  for ( DimType d = 0; d < D; ++d ) {
    if ( dir[d] == 0 ) continue;
    if ( dir[d] > 0 ) newsel[d] = 0.5*(newsel[d] + newup[d]);
    else newsel[d] = 0.5*(newlo[d] + newsel[d]);
  }
  newfh = FncTraits::value(f, newsel);
  if ( newfh > newfsel ) {
    newfsel = newfh;
    newxsel = newsel;
  }

  if ( newfsel < cell->g() ) return;

  // If this the highest value is above the overestimate, also this
  // cell needs to be divided up and conquered.
  wholecomp = true;
  Slicer dummy(D, *this, cell, newlo, newxsel, newup, newfsel);
}

template <typename Rnd, typename FncPtr>
ACDCGen<Rnd,FncPtr>::Slicer::
Slicer(DimType Din, const Slicer & s, ACDCGenCell * cellin,
       const DVector & loin, const DVector & xselin, const DVector & upin,
       double fselin)
  : D(Din), lo(loin), up(upin), xcl(loin), xcu(upin), xhl(loin), xhu(upin),
    fhl(Din, 0.0), fhu(Din, 0.0), xsel(xselin), fsel(fselin),
    current(cellin), first(cellin),
    firstlo(loin), firstup(upin),f(s.f),
    epsilon(s.epsilon), margin(s.margin), minf(0.0), wholecomp(false) {
  divideandconquer();
}

template <typename Rnd, typename FncPtr>
template <typename POStream>
void ACDCGen<Rnd,FncPtr>::output(POStream & os) const {
  os << theNAcc << theN << theEps << theMargin << theNTry << theMaxTry
     << useCheapRandom << theLast << theLastPoint << theLastF
     << theFunctions.size() << levels.size();
  for ( int i = 1, N = theFunctions.size(); i < N; ++i )
    os << theFunctions[i] << theDimensions [i] << theSumMaxInts[i]
       << *thePrimaryCells[i] << theNI[i] << theSumW[i] << theSumW2[i];
  os << thePrimaryCells[theLast]->getIndex(theLastCell);
  for ( int i = 0, N = levels.size(); i < N; ++i )
    os << levels[i].lastN << levels[i].g << levels[i].index
       << levels[i].up << levels[i].lo
       << thePrimaryCells[levels[i].index]->getIndex(levels[i].cell);
}

template <typename Rnd, typename FncPtr>
template <typename PIStream>
void ACDCGen<Rnd,FncPtr>::input(PIStream & is) {
  clear();
  long fsize = 0;
  long lsize = 0;
  is >> theNAcc >> theN >> theEps >> theMargin >> theNTry >> theMaxTry
     >> useCheapRandom >> theLast >> theLastPoint >> theLastF >> fsize >> lsize;
  while ( --fsize ) {
    theFunctions.push_back(FncPtrType());
    theDimensions.push_back(DimType());
    theSumMaxInts.push_back(0.0);
    theNI.push_back(0);
    theSumW.push_back(0.0);
    theSumW2.push_back(0.0);
    thePrimaryCells.push_back(new ACDCGenCell(0.0));
    is >> theFunctions.back() >> theDimensions.back() >> theSumMaxInts.back()
       >> *thePrimaryCells.back() >> theNI.back()
       >> theSumW.back() >> theSumW2.back();
  }
  long index = -1;
  is >> index;
  theLastCell = thePrimaryCells[theLast]->getCell(index);
  while ( lsize-- ) {
    levels.push_back(Level());
    is >> levels.back().lastN >> levels.back().g >> levels.back().index
       >> levels.back().up >> levels.back().lo >> index;
    levels.back().cell = thePrimaryCells[levels.back().index]->getCell(index);
  }
}

}