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CrystVector.cpp

/*  ObjCryst++ Object-Oriented Crystallographic Library
    (c) 2000-2002 Vincent Favre-Nicolin vincefn@users.sourceforge.net
        2000-2001 University of Geneva (Switzerland)

    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 of the License, 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 "CrystVector/CrystVector.h"
#include "Quirks/VFNStreamFormat.h"

#ifdef __LIBCRYST_VECTOR_USE_BLITZ__

#define CrystVector Array<REAL,1>
#define CrystMatrix Array<REAL,2>

template<class T> T MaxDifference(const Array<T,1> &a,const Array<T,1> &b)
{
   return max(fabs(a-b));
}

template<class T> T MaxDifference(const Array<T,2> &a,const Array<T,2> &b)
{
   return max(fabs(a-b));
}

#else  // __LIBCRYST_VECTOR_USE_BLITZ__

//Still using pointers instead of blitz for geometrical structure factor, 
//due to huge memory requirements with gcc when using blitz.
#define __VFN_GEOM_STRUCT_FACTOR_USE_POINTERS

#include "Quirks/VFNDebug.h"
#include "Quirks/VFNStreamFormat.h"

//######################################################################
//  CrystVector
//######################################################################
template<class T> CrystVector<T>::CrystVector():mpData(0),mNumElements(0),mIsAreference(false) {}
   
template<class T> CrystVector<T>::CrystVector(const long nbElements):
mNumElements(nbElements),mIsAreference(false)
{
   mpData=new T[mNumElements];
}
   
template<class T> CrystVector<T>::CrystVector(const CrystVector &old):
mNumElements(old.numElements()),mIsAreference(false)
{
   mpData=new T[mNumElements];
   T *p1=mpData;
   const T *p2=old.data();
   for(long i=0;i<mNumElements;i++) *p1++=*p2++;
}
   
template<class T> CrystVector<T>::~CrystVector()
{ 
   if(!mIsAreference)
   {
      delete[] mpData;
   }
}
template<class T> void CrystVector<T>::operator=(const CrystVector &old)
{
   VFN_DEBUG_MESSAGE("CrystVector<T>::operator=()",0)
   this->resize(old.numElements());
   mIsAreference=false;
   T *p1=mpData;
   const T *p2=old.data();
   for(long i=0;i<mNumElements;i++) *p1++=*p2++;
}

template<class T> void CrystVector<T>::reference(CrystVector &old)
{
   if(!mIsAreference)
   {
      delete[] mpData ;
   }
   mNumElements=old.numElements();
   mpData=old.data();
   mIsAreference=true;
}
   
template<class T> long CrystVector<T>::numElements()const {return mNumElements;}
   
template<class T> T CrystVector<T>::sum()const
{
   register T tmp=0;
   register const T *p=this->data();
   for(long i=0;i<this->numElements();i++) tmp += *p++ ;
   return tmp;
}
template<class T> T CrystVector<T>::min()const
{
   register T tmp=0;
   register const T *p=this->data();
   tmp=*p++;
   for(long i=1;i<this->numElements();i++)
   {
      if(tmp>*p) tmp=*p;
      p++;
   }
   return tmp;
}
template<class T> T CrystVector<T>::max()const
{
   register T tmp=0;
   register const T *p=this->data();
   tmp=*p++;
   for(long i=1;i<this->numElements();i++)
   {
      if(tmp<*p) tmp=*p;
      p++;
   }
   return tmp;
}

00128 template<class T> unsigned long CrystVector<T>::imin(const unsigned long start0,const unsigned long finish0)const
{
   unsigned long start=start0,finish=finish0;
   if(start0==finish0)
   {
      start=0;
      finish=this->numElements();
   }
   register T tmp=0;
   register const T *p=this->data()+start;
   tmp=*p++;
   long im=0;
   for(long i=start+1;i<finish;i++)
   {
      if(tmp>*p) {tmp=*p;im=i;}
      p++;
   }
   return (unsigned long)im;
}
00147 template<class T> unsigned long CrystVector<T>::imax(const unsigned long start0,const unsigned long finish0)const
{
   unsigned long start=start0,finish=finish0;
   if(start0==finish0)
   {
      start=0;
      finish=this->numElements();
   }
   register T tmp=0;
   register const T *p=this->data()+start;
   tmp=*p++;
   long im=start;
   for(long i=start+1;i<finish;i++)
   {
      if(tmp<*p) {tmp=*p;im=i;}
      p++;
   }
   return (unsigned long)im;
}

template<class T> T * CrystVector<T>::data() {return mpData;}
template<class T> const T * CrystVector<T>::data() const {return mpData;}

template<class T> void CrystVector<T>::resize(const long newNbElements)
{  
   if(mNumElements==newNbElements) return;
   VFN_DEBUG_MESSAGE("CrystVector<T>::resize():("<<mNumElements<<"->"
      <<newNbElements<<").",0)
   if((mIsAreference==false) && (mNumElements != 0))
   {
      delete[] mpData ;
   }
   mpData=0;
   mNumElements=newNbElements;
   if(mNumElements>0)
   {
      mpData=new T[mNumElements];
   }
   mIsAreference=false;
}

template<class T> void CrystVector<T>::resizeAndPreserve(const long newNbElements)
{
   //:TODO: check memory allocation
   if(newNbElements == mNumElements) return;
   register T * RESTRICT p=mpData;
   register T * RESTRICT p2,*p1;
   mpData=0;
   mpData=new T[newNbElements];
   p2=mpData;
   p1=p;
   const long tmp= (newNbElements > mNumElements) ? mNumElements : newNbElements ;
   for(long i=tmp;i>0;i--) *p2++ = *p1++ ;
   if(mIsAreference==false)
   {
      delete[] p ;
   }
   mNumElements=newNbElements;
   mIsAreference=false;
}

template<class T> void CrystVector<T>::operator*=(const T num)
{
   register T * RESTRICT p=mpData;
   for(int i=mNumElements;i>0;i--) *p++ *= num;
}

template<class T> void CrystVector<T>::operator*=(const CrystVector<T> &vect)
{
   #ifdef __DEBUG__
   if( vect.numElements() != mNumElements)
   {
      cout<<"CrystVector::operator*=(&vect)(i): Number of elements differ:"<< mNumElements \
            << "!="<< vect.numElements() <<endl;
      //throw 0;
   }
   #endif
   if(mpData!=vect.data())
   {
      register T * RESTRICT p=mpData;
      register const T * RESTRICT rhs=vect.data();
      for(int i=mNumElements;i>0;i--) { *p *= *rhs; p++ ; rhs++;}
   }
   else
   {
      register T *p=mpData;
      for(int i=mNumElements;i>0;i--) { *p *= *p; p++ ;}
   }
}

template<class T> void CrystVector<T>::operator/=(const T num)
{
   register T * RESTRICT p=mpData;
   const REAL d=1/num;
   for(int i=mNumElements;i>0;i--) *p++ *= d;
}

template<class T> void CrystVector<T>::operator/=(const CrystVector<T> &vect)
{
   #ifdef __DEBUG__
   if( vect.numElements() != mNumElements)
   {
      cout<<"CrystVector::operator/=(&vect)(i): Number of elements differ:"<< mNumElements \
            << "!="<< vect.numElements() <<endl;
      //throw 0;
   }
   #endif
   if(mpData!=vect.data())
   {
      register T * RESTRICT p=mpData;
      register const T * RESTRICT rhs=vect.data();
      for(int i=mNumElements;i>0;i--) { *p /= *rhs; p++ ; rhs++;}
   }
   else *this=1;
}

template<class T> void CrystVector<T>::operator+=(const T num)
{
   register T * RESTRICT p=mpData;
   for(int i=mNumElements;i>0;i--) *p++ += num;
}

template<class T> void CrystVector<T>::operator+=(const CrystVector<T> &vect)
{
   #ifdef __DEBUG__
   if( vect.numElements() != mNumElements)
   {
      cout<<"CrystVector::operator+=(&vect)(i): Number of elements differ:"<< mNumElements \
            << "!="<< vect.numElements() <<endl;
      //throw 0;
   }
   #endif
   if(mpData!=vect.data())
   {
      register T * RESTRICT p=mpData;
      const T * RESTRICT rhs=vect.data();
      for(int i=mNumElements;i>0;i--) *p++ += *rhs++;
   }
   else
   {
      register T *p=mpData;
      for(int i=mNumElements;i>0;i--) {*p += *p; p++;}
   }
}

template<class T> void CrystVector<T>::operator-=(const CrystVector<T> &vect)
{
   #ifdef __DEBUG__
   if( vect.numElements() != mNumElements)
   {
      cout<<"CrystVector::operator-=(&vect)(i): Number of elements differ:"<< mNumElements \
            << "!="<< vect.numElements() <<endl;
      //throw 0;
   }
   #endif
   if(mpData!=vect.data())
   {
      register T * RESTRICT p=mpData;
      const T * RESTRICT rhs=vect.data();
      for(int i=mNumElements;i>0;i--) *p++ -= *rhs++;
   }
   else (*this)=0;
}

template<class T> void CrystVector<T>::operator=(const T num)
{
   register T *p=mpData;
   for(int i=mNumElements;i>0;i--) *p++ = num;
}

template<class T> T CrystVector<T>::operator()(const long i) const
{
   #ifdef __DEBUG__
   if( (i<0) || (i>=mNumElements))
   {
      cout<<"CrystVector::operator()(i): Tried to access an element out of bounds :"<<i<<endl;
      //throw 0;
   }
   #endif
   return mpData[i];
}

template<class T> T& CrystVector<T>::operator()(const long i)
{
   #ifdef __DEBUG__
   if( (i<0) || (i>=mNumElements))
   {
      cout<<"CrystVector::operator()(i): Tried to access an element out of bounds !"<<i<<endl;
      //throw 0;
   }
   #endif
   return mpData[i];
}
//######################################################################
//  CrystVector functions
//######################################################################

template<class T> ostream& operator<<(ostream &os, CrystVector<T> &vect)
{
   //return os << FormatHorizVector(vect);
   for(long i=0;i<vect.numElements();i++) os << vect(i) <<endl;
   return os;
}

template<class T> CrystVector<long> SortSubs(const CrystVector<T> &vect)
{
   CrystVector<long> subscript(vect.numElements());
   {
      long *pLong=subscript.data();
      for(long i=0;i<subscript.numElements();i++) *pLong++ = i;
   }
   CrystVector<T> v;
   v=vect;
   QuickSortSubs(v,subscript,v.numElements()-1,0,0);
   return subscript;
}

template<class T> long QuickSortSubs(CrystVector<T> &vect,
                                     CrystVector<long> &subscript,
                                     long last,long first, int depth)
{
   //assert(depth++ <50);//for up to 2^50 elements
   static long count=0;
   long low, high;
   T tmpT, sepValeur ;
   long tmpSubs;
   low = first;
   high = last;
   sepValeur = vect( (first + last) / 2 );
   do 
   {
      while( vect(low) < sepValeur ) low++;
      while( vect(high) > sepValeur ) high--;
      if( low <= high )
      {
         count++;
         tmpT = vect(low);
         vect(low) = vect(high);
         vect(high) = tmpT;
         tmpSubs = subscript(low);
         subscript(low++) = subscript(high);
         subscript(high--) = tmpSubs;
      }
   } while( low <= high);
   if( first < high ) QuickSortSubs(vect,subscript, high, first,depth);
   if( low < last ) QuickSortSubs(vect,subscript, last, low,depth);
   return count ;
}

template<class T> CrystVector<T> cos(const CrystVector<T> &vect)
{
   CrystVector<T> cosVect(vect.numElements());
   for(long i=0;i<vect.numElements();i++) cosVect(i) = (T) cos(vect(i));
   return cosVect;
}

template<class T> CrystVector<T> sin(const CrystVector<T> &vect)
{
   CrystVector<T> sinVect(vect.numElements());
   for(long i=0;i<vect.numElements();i++) sinVect(i) = (T) sin(vect(i));
   return sinVect;
}

template<class T> CrystVector<T> tan(const CrystVector<T> &vect)
{
   CrystVector<T> tanVect(vect.numElements());
   for(long i=0;i<vect.numElements();i++) tanVect(i) = (T) tan(vect(i));
   return tanVect;
}

template<class T> CrystVector<T> sqrt(const CrystVector<T> &vect)
{
   CrystVector<T> tanVect(vect.numElements());
   for(long i=0;i<vect.numElements();i++) tanVect(i) = (T) sqrt(vect(i));
   return tanVect;
}

//######################################################################
//  CrystMatrix
//######################################################################
template<class T> CrystMatrix<T> ::CrystMatrix():
mpData(0),mNumElements(0),mXSize(0),mYSize(0),mIsAreference(false){}

template<class T> CrystMatrix<T>::CrystMatrix(const long ySize,const long xSize):
mNumElements(xSize*ySize),mXSize(xSize),mYSize(ySize),mIsAreference(false)
{
   mpData=new T[mNumElements];
}

template<class T> CrystMatrix<T>::CrystMatrix(const CrystMatrix &old):
mNumElements(old.numElements()),mXSize(old.cols()),mYSize(old.rows()),mIsAreference(false)
{
   mpData=new T[mNumElements];
   register T *p1=mpData;
   register const T *p2=old.data();
   for(long i=0;i<mNumElements;i++) *p1++=*p2++;
}

template<class T> CrystMatrix<T>::~CrystMatrix()
{
   if(!mIsAreference)
   {
      delete[] mpData;
   }
}

template<class T> void CrystMatrix<T>::operator=(const CrystMatrix<T> &old)
{
   mXSize=old.cols();
   mYSize=old.rows();
   mIsAreference=false;
   if(mNumElements!=old.numElements())
   {
      if(mIsAreference==false)
      {
         delete[] mpData ;
      }
      mNumElements=old.numElements();
      mpData=new T[mNumElements];
   }
   register T *p1=mpData;
   register const T *p2=old.data();
   for(long i=0;i<mNumElements;i++) *p1++=*p2++;
}

template<class T> void CrystMatrix<T>::reference(CrystMatrix<T> &old)
{
   if(mIsAreference==false)
   {
      delete[] mpData ;
   }
   mIsAreference=true;
   mNumElements=old.numElements();
   mpData=old.data();
}

template<class T> long CrystMatrix<T>::numElements()const {return mNumElements;}

template<class T> T CrystMatrix<T>::sum()const
{
   register T tmp=0;
   register const T *p=this->data();
   for(long i=0;i<this->numElements();i++) tmp += *p++ ;
   return tmp;
}

template<class T> T CrystMatrix<T>::min()const
{
   register T tmp=0;
   register const T *p=this->data();
   tmp=*p++;
   for(long i=1;i<this->numElements();i++)
   {
      if(tmp>*p) tmp=*p;
      p++;
   }
   return tmp;
}

template<class T> T CrystMatrix<T>::max()const
{
   register T tmp=0;
   register const T *p=this->data();
   tmp=*p++;
   for(long i=1;i<this->numElements();i++)
   {
      if(tmp<*p) tmp=*p;
      p++;
   }
   return tmp;
}

template<class T> long CrystMatrix<T>::cols()const {return mXSize;}

template<class T> long CrystMatrix<T>::rows()const {return mYSize;}

template<class T> T* CrystMatrix<T>::data() {return mpData;}
template<class T> const T* CrystMatrix<T>::data() const {return mpData;}

template<class T> void CrystMatrix<T>::resize(const long ySize,const long xSize)
{
   mXSize=xSize;
   mYSize=ySize;
   if(xSize*ySize == mNumElements) return;
   if(!mIsAreference)
   {
      delete[] mpData ;
   }
   mpData=0;
   mXSize=xSize;
   mYSize=ySize;
   mNumElements=xSize*ySize;
   if(mNumElements>0)
   {
      mpData=new T[mNumElements];
   }
}

template<class T> void CrystMatrix<T>::resizeAndPreserve(const long ySize,const long xSize)
{
   mXSize=xSize;
   mYSize=ySize;
   if(xSize*ySize == mNumElements) return;
   register T *p=mpData;
   register T *p2,*p1;
   mpData=0;
   mpData=new T[xSize*ySize];
   p2=mpData;
   p1=p;
   long tmp= ( (xSize*ySize) > mNumElements) ? mNumElements : xSize*ySize;
   for(long i=0;i<tmp;i++) *p2++ = *p1++ ;
   if(!mIsAreference)
   {
      delete[] p ;
   }
   mNumElements=xSize*ySize;
   mIsAreference=false;
}
/*
template<class T> void CrystMatrix<T>::operator=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ = num;
}
*/
template<class T> void CrystMatrix<T>::operator*=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ *= num;
}

template<class T> void CrystMatrix<T>::operator*=(const CrystMatrix<T> &vect)
{
   #ifdef __DEBUG__
   if( this->numElements() != vect.numElements())
   {
      cout<<"CrystMatrix::operator*=(): Number of elements differ !"<<endl;
      //throw 0;
   }
   #endif
   register T *p=mpData;
   register const T *rhs=vect.data();
   for(int i=0;i<mNumElements;i++) *p++ *= *rhs++;
}

template<class T> void CrystMatrix<T>::operator/=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ /= num;
}

template<class T> void CrystMatrix<T>::operator+=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ += num;
}

template<class T> void CrystMatrix<T>::operator-=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ -= num;
}

template<class T> T CrystMatrix<T>::operator()(const long i) const
{
   #ifdef __DEBUG__
   if( (i<0) || (i>=mNumElements))
   {
      cout<<"CrystMatrix::operator()(i): element out of bounds !"<<i<<endl;
      //throw 0;
   }
   #endif
   return mpData[i];
}

template<class T> T CrystMatrix<T>::operator()(const long i,const long j) const
{  
   #ifdef __DEBUG__
   if( (i<0) || (j<0) || (i>=mYSize) || (j>=mXSize) )
   {
      cout<<"CrystMatrix::operator()(i,j): element out of bounds:"<<i<<","<<j<<endl;
      cout<<"dimensions:"<<mYSize<<","<<mXSize<<endl;
      //throw 0;
   }
   #endif
   return mpData[i*mXSize+j];
}

template<class T> T& CrystMatrix<T>::operator()(const long i)
{
   #ifdef __DEBUG__
   if( (i<0) || (i>=mNumElements))
   {
      cout<<"CrystMatrix::operator()(i): element out of bounds !"<<i<<endl;
      //throw 0;
   }
   #endif
   return mpData[i];
}

template<class T> T& CrystMatrix<T>::operator()(const long i,const long j) 
{  
   #ifdef __DEBUG__
   if( (i<0) || (j<0) || (i>=mYSize) || (j>=mXSize) )
   {
      cout<<"CrystMatrix::operator()(i,j): element out of bounds:"<<i<<","<<j<<endl;
      //throw 0;
   }
   #endif
   return mpData[i*mXSize+j];
}

template<class T> CrystMatrix<T> CrystMatrix<T>::transpose(const int dim1, const int dim2)const
{
   CrystMatrix<T> newM(this->cols(),this->rows());
   for(long i=0;i<this->cols();i++)
      for(long j=0;j<this->rows();j++) newM(i,j)=(*this)(j,i);
   return newM;
}

//######################################################################
//  CrystArray3D
//######################################################################
template<class T> CrystArray3D<T> ::CrystArray3D():
mpData(0),mNumElements(0),mXSize(0),mYSize(0),mZSize(0),mIsAreference(false){}

template<class T> CrystArray3D<T>::CrystArray3D(const long zSize,
                                                  const long ySize,
                                                  const long xSize):
mNumElements(xSize*ySize*zSize),mXSize(xSize),mYSize(ySize),mZSize(zSize),
mIsAreference(false)
{
   mpData=new T[mNumElements];
}

template<class T> CrystArray3D<T>::CrystArray3D(const CrystArray3D &old):
mNumElements(old.numElements()),
mXSize(old.cols()),mYSize(old.rows()),mZSize(old.depth()),
mIsAreference(false)
{
   mpData=new T[mNumElements];
   register T *p1=mpData;
   register const T *p2=old.data();
   for(long i=0;i<mNumElements;i++) *p1++=*p2++;
}

template<class T> CrystArray3D<T>::~CrystArray3D()
{ if(!mIsAreference)delete[] mpData;}

template<class T> void CrystArray3D<T>::operator=(const CrystArray3D<T> &old)
{
   mXSize=old.cols();
   mYSize=old.rows();
   mZSize=old.depth();
   mIsAreference=false;
   if(mNumElements!=old.numElements())
   {
      mNumElements=old.numElements();
      if(mIsAreference==false)delete[] mpData ;
      mpData=new T[mNumElements];
   }
   register T *p1=mpData;
   register const T *p2=old.data();
   for(long i=0;i<mNumElements;i++) *p1++=*p2++;
}

template<class T> void CrystArray3D<T>::reference(CrystArray3D<T> &old)
{
   if(mIsAreference==false) delete[] mpData ;
   mIsAreference=true;
   mNumElements=old.numElements();
   mpData=old.data();
}

template<class T> long CrystArray3D<T>::numElements()const{return mNumElements;}

template<class T> T CrystArray3D<T>::sum()const
{
   register T tmp=0;
   register const T *p=this->data();
   for(long i=0;i<this->numElements();i++) tmp += *p++ ;
   return tmp;
}

template<class T> T CrystArray3D<T>::min()const
{
   register T tmp=0;
   register const T *p=this->data();
   tmp=*p++;
   for(long i=1;i<this->numElements();i++)
   {
      if(tmp>*p) tmp=*p;
      p++;
   }
   return tmp;
}

template<class T> T CrystArray3D<T>::max()const
{
   register T tmp=0;
   register const T *p=this->data();
   tmp=*p++;
   for(long i=1;i<this->numElements();i++)
   {
      if(tmp<*p) tmp=*p;
      p++;
   }
   return tmp;
}

template<class T> long CrystArray3D<T>::cols()const {return mXSize;}

template<class T> long CrystArray3D<T>::rows()const {return mYSize;}

template<class T> long CrystArray3D<T>::depth()const {return mZSize;}

template<class T> T* CrystArray3D<T>::data() {return mpData;}
template<class T> const T* CrystArray3D<T>::data() const {return mpData;}

template<class T> void CrystArray3D<T>::resize(const long zSize,
                                                const long ySize,
                                                const long xSize)
{
   mXSize=xSize;
   mYSize=ySize;
   mZSize=zSize;
   if(xSize*ySize*zSize == mNumElements) return;
   if(!mIsAreference)delete[] mpData ;
   mpData=0;
   mNumElements=xSize*ySize*zSize;
   if(mNumElements>0) mpData=new T[mNumElements];
}

template<class T> void CrystArray3D<T>::resizeAndPreserve(const long zSize,
                                                           const long ySize,
                                                           const long xSize)
{
   mXSize=xSize;
   mYSize=ySize;
   mZSize=zSize;
   if(xSize*ySize*zSize == mNumElements) return;
   register T *p=mpData;
   register T *p2,*p1;
   mpData=new T[xSize*ySize*zSize];
   p2=mpData;
   p1=p;
   long tmp= ( (xSize*ySize*zSize) > mNumElements) ? mNumElements : xSize*ySize*zSize;
   for(long i=0;i<tmp;i++) *p2++ = *p1++ ;
   mNumElements=xSize*ySize*zSize;
   if(!mIsAreference)delete[] p ;
   mIsAreference=false;
}

template<class T> void CrystArray3D<T>::operator=(const T num)
{
   VFN_DEBUG_MESSAGE("CrystArray3D<T>::operator=():"<<num,1)
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ = num;
}
template<class T> void CrystArray3D<T>::operator*=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ *= num;
}

template<class T> void CrystArray3D<T>::operator*=(const CrystArray3D<T> &vect)
{
   #ifdef __DEBUG__
   if( this->numElements() != vect.numElements())
   {
      cout<<"CrystArray3D::operator*=(): Number of elements differ !"<<endl;
      //throw 0;
   }
   #endif
   register T *p=mpData;
   register const T *rhs=vect.data();
   for(int i=0;i<mNumElements;i++) *p++ *= *rhs++;
}

template<class T> void CrystArray3D<T>::operator/=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ /= num;
}

template<class T> void CrystArray3D<T>::operator+=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ += num;
}

template<class T> void CrystArray3D<T>::operator-=(const T num)
{
   register T *p=mpData;
   for(int i=0;i<mNumElements;i++) *p++ -= num;
}

template<class T> T CrystArray3D<T>::operator()(const long i) const
{
   #ifdef __DEBUG__
   if( (i<0) || (i>=mNumElements))
   {
      cout<<"CrystArray3D::operator()(i): element out of bounds !"<<i<<endl;
      //throw 0;
   }
   #endif
   return mpData[i];
}

template<class T> T CrystArray3D<T>::operator()(const long i,const long j,const long k) const
{  
   #ifdef __DEBUG__
   if( (i<0) || (j<0) || (k<0) || (i>=mZSize) || (j>=mYSize) || (k>=mXSize))
   {
      cout<<"CrystArray3D::operator()(i,j,k): element out of bounds:"<<i<<","<<j<<","<<k<<endl;
      cout<<"dimensions:"<<mZSize<<","<<mYSize<<","<<mXSize<<endl;
      //throw 0;
   }
   #endif
   return mpData[i*mYSize*mXSize+j*mXSize+k];
}

template<class T> T& CrystArray3D<T>::operator()(const long i)
{
   #ifdef __DEBUG__
   if( (i<0) || (i>=mNumElements))
   {
      cout<<"CrystArray3D::operator()(i): element out of bounds !"<<i<<endl;
      //throw 0;
   }
   #endif
   return mpData[i];
}

template<class T> T& CrystArray3D<T>::operator()(const long i,const long j,const long k) 
{  
   #ifdef __DEBUG__
   if( (i<0) || (j<0) || (k<0) || (i>=mZSize) || (j>=mYSize) || (k>=mXSize))
   {
      cout<<"CrystArray3D::operator()(i,j,k): element out of bounds:"<<i<<","<<j<<","<<k<<endl;
      cout<<"dimensions:"<<mZSize<<","<<mYSize<<","<<mXSize<<endl;
      //throw 0;
   }
   #endif
   return mpData[i*mYSize*mXSize+j*mXSize+k];
}

//######################################################################
//  Other functions
//######################################################################

template<class T> ostream& operator<<(ostream &os, const CrystMatrix<T> &vect)
{
   //return os << FormatHorizVector(vect);
   for(long i=0;i<vect.rows();i++) 
   {
      for(long j=0;j<vect.cols();j++) os << FormatFloat(vect(i,j)) ;
      os << endl;
   }
   return os;
}

template<class T> ostream& operator<<(ostream &os, const CrystArray3D<T> &vect)
{
   for(long i=0;i<vect.depth();i++)
   {
      for(long j=0;j<vect.rows();j++) 
      {
       for(long k=0;k<vect.cols();k++) os << FormatFloat(vect(i,j,k)) ;
       os << endl;
      }
      os << endl;
   }
   return os;
}

template<class T> T MaxDifference(const CrystVector<T> &a,const CrystVector<T> &b)
{
   const T *p1=a.data();
   const T *p2=b.data();
   REAL max=0;
   REAL tmp=0;
   for(long i=0;i<a.numElements();i++)
   {
      tmp=(T)fabs((REAL) (*p1++ - *p2++));
      if(tmp>max) max=tmp;
   }
   return (T)max;
}

template<class T> T MaxDifference(const CrystMatrix<T> &a,const CrystMatrix<T> &b)
{
   const T *p1=a.data();
   const T *p2=b.data();
   T max=0;
   T tmp=0;
   for(long i=0;i<a.numElements();i++)
   {
      tmp=(T)fabs((REAL)(*p1++ - *p2++));
      if(tmp>max) max=tmp;
   }
   return max;
}

template<class T> CrystMatrix<T> product(const CrystMatrix<T> &a,const CrystMatrix<T> &b)
{
   VFN_DEBUG_ENTRY("CrystMatrix<T> product()",2)
   //:TODO: check a.cols()==b.rows()
   CrystMatrix<T> ab(a.rows(),b.cols());
   for(long i=0;i<ab.rows();i++)
   {
      for(long j=0;j<ab.cols();j++)
      {
         ab(i,j)=0;
         for(long k=0;k<b.rows();k++) ab(i,j) += a(i,k)*b(k,j);
      }
   }
   VFN_DEBUG_EXIT("CrystMatrix<T> product()",2)
   return ab;
}

//######################################################################
//  explicit instantiation
//######################################################################

template class CrystVector<REAL>;
template REAL MaxDifference(const CrystVector<REAL>&,const CrystVector<REAL>&);
template ostream& operator<<(ostream &os, CrystVector<REAL> &vect);
template CrystVector<long> SortSubs(const CrystVector<REAL> &vect);
template long QuickSortSubs(CrystVector<REAL> &vect,CrystVector<long> &subscript,
                            long last,long first, int depth);
template class CrystMatrix<REAL>;
template REAL MaxDifference(const CrystMatrix<REAL>&,const CrystMatrix<REAL>&);
template CrystMatrix<REAL> product(const CrystMatrix<REAL>&,const CrystMatrix<REAL>&);
template ostream& operator<<(ostream &os, const CrystMatrix<REAL> &vect);
template CrystVector<REAL> cos(const CrystVector<REAL>&);
template CrystVector<REAL> sin(const CrystVector<REAL>&);
template CrystVector<REAL> tan(const CrystVector<REAL>&);
template CrystVector<REAL> sqrt(const CrystVector<REAL>&);
template class CrystArray3D<REAL>;
template ostream& operator<<(ostream &os, const CrystArray3D<REAL> &vect);

template class CrystVector<long>;
template long MaxDifference(const CrystVector<long>&,const CrystVector<long>&);
template ostream& operator<<(ostream &os, CrystVector<long> &vect);
template CrystVector<long> SortSubs(const CrystVector<long> &vect);
template long QuickSortSubs(CrystVector<long> &vect,CrystVector<long> &subscript,
                            long last,long first, int depth);
template class CrystMatrix<long>;
template long MaxDifference(const CrystMatrix<long>&,const CrystMatrix<long>&);
template CrystMatrix<long> product(const CrystMatrix<long>&,const CrystMatrix<long>&);
template ostream& operator<<(ostream &os, const CrystMatrix<long> &vect);


template class CrystVector<int>;
template int MaxDifference(const CrystVector<int>&,const CrystVector<int>&);
template ostream& operator<<(ostream &os, CrystVector<int> &vect);
template CrystVector<long> SortSubs(const CrystVector<int> &vect);
template long QuickSortSubs(CrystVector<int> &vect,CrystVector<long> &subscript,
                            long last,long first, int depth);
template class CrystMatrix<int>;
template int MaxDifference(const CrystMatrix<int>&,const CrystMatrix<int>&);
template CrystMatrix<int> product(const CrystMatrix<int>&,const CrystMatrix<int>&);
template ostream& operator<<(ostream &os, const CrystMatrix<int> &vect);

template class CrystVector<unsigned int>;
template unsigned int MaxDifference(const CrystVector<unsigned int>&,const CrystVector<unsigned int>&);
template ostream& operator<<(ostream &os, CrystVector<unsigned int> &vect);
template CrystVector<long> SortSubs(const CrystVector<unsigned int> &vect);
template long QuickSortSubs(CrystVector<unsigned int> &vect,CrystVector<long> &subscript,
                            long last,long first, int depth);
template class CrystMatrix<unsigned int>;
template unsigned int MaxDifference(const CrystMatrix<unsigned int>&,const CrystMatrix<unsigned int>&);
template CrystMatrix<unsigned int> product(const CrystMatrix<unsigned int>&,const CrystMatrix<unsigned int>&);
template ostream& operator<<(ostream &os, const CrystMatrix<unsigned int> &vect);


template class CrystVector<bool>;
template ostream& operator<<(ostream &os, CrystVector<bool> &vect);
template class CrystMatrix<bool>;
template bool MaxDifference(const CrystMatrix<bool>&,const CrystMatrix<bool>&);
template ostream& operator<<(ostream &os, const CrystMatrix<bool> &vect);



#endif // __LIBCRYST_VECTOR_USE_BLITZ__

//######################################################################
//  Functions
//######################################################################


CrystMatrix_REAL InvertMatrix(const CrystMatrix_REAL &m)
{//:TODO: Check Pivoting...
   VFN_DEBUG_ENTRY("InvertMatrix()",2)
   VFN_DEBUG_MESSAGE("->Matrix to invert :"<<endl<<m,1)
   REAL eps = 1e-8;
   //check matrix is square
      if( (m.rows() != m.cols()) || (m.rows() <2))
      {//DoSomethingBad
         cout << "Matrix inversion: Cannot invert matrix !" <<endl;
         //throw 0;
      }
   //prepare...
      long size=m.rows();
      CrystMatrix_REAL im(size,size),cm(size,size);//(future) invert matrix & copy of matrix
      cm=m;
      im=0;
      for(long i=0;i<size;i++) im(i,i)=1.;
      CrystMatrix_long rowIndex(size,1);//Keep track of pivoted rows
      for(long i=0;i<size;i++) rowIndex(i)=i;
   //Make an upper triangular matrix
      for(long i=0;i<size;i++)
      {
         //get absolute maximum the ith column
            long rowMax=i;
            {
               REAL max=fabs(m(i,i));
               for(long j=i+1;j<m.rows();j++)
                  if(fabs(m(j,i)) > max)
                  {
                     max=fabs(m(j,i));
                     rowMax=j;
                  }
                  
               //Check if pivot is non-singular :TODO:
               /*
               if(max < eps)
               {
                  throw i;
               }
               */
            }
         //pivot
            if(rowMax != i)
            {
               //cout << "Exchanging rows: "<< i << " and " << rowMax <<endl;
               MatrixExchangeRows(cm,i,(long)rowMax);
               MatrixExchangeRows(im,i,(long)rowMax);
               MatrixExchangeRows(rowIndex,i,(long)rowMax);
            }
         //cout << cm <<endl;
         /*
         */
         //substract
            for(long j=i+1;j<size;j++)
            {
               const REAL a=cm(j,i)/cm(i,i);
               for(long k=0;k<size;k++) im(j,k) -= im(i,k)*a;
               for(long k=0;k<size;k++) cm(j,k) -= cm(i,k)*a;
            }
         //cout << cm <<endl;
         //cout << im <<endl;
      }
   VFN_DEBUG_MESSAGE("Finish solving from the upper triangular matrix...",1);
      for(long i=0;i<size;i++)
      {
         REAL a;
         for(long j=i-1;j>=0;j--)
         {
            a=cm(j,i)/cm(i,i);
            for(long k=0;k<size;k++) im(j,k) -= im(i,k)*a;
            for(long k=0;k<size;k++) cm(j,k) -= cm(i,k)*a;
         }
         a=cm(i,i);
         for(long k=0;k<size;k++) im(i,k) /= a;
         for(long k=0;k<size;k++) cm(i,k) /= a;
         //cout << cm <<endl;
         //cout << im <<endl;
      }
   //bring back to initial order of rows
   /*
   for(long i=0;i<size;i++)
   {
      if(rowIndex(i) != i)
      {
         long rowExch=0;
         for(; rowIndex(rowExch) != i ; rowExch++);
         cout << rowExch << endl;
         MatrixExchangeRows(im,i,rowExch);
      }
   }
   */
   VFN_DEBUG_MESSAGE("->Inverted Matrix :"<<endl<<im,1)
   VFN_DEBUG_EXIT("InvertMatrix()",2)
   return im;
}

template<class T> void MatrixExchangeRows(CrystMatrix_T &m, const long row1, const long row2)
{
   //cout << "Exchanging rows:begin" <<endl;
   if(row1 == row2) return;
   long rowSize=m.cols();
   T tmp;
   for(long i=0;i<rowSize;i++)
   {
      tmp=m(row1,i);
      m(row1,i)=m(row2,i);
      m(row2,i)=tmp;
   }
   //cout << "Exchanging rows:end" <<endl;
}

template void MatrixExchangeRows(CrystMatrix_REAL &m, const long row1, const long row2);



template<class T> T MaxAbs(const CrystVector_T &vector)
{
   const T* pData=vector.data();
   T max =(T) fabs((REAL) *pData++);
   for(long i=1;i<vector.numElements();i++)
   {
      if ( fabs((REAL) *pData) > max) max=(T) fabs((REAL) *pData);
      pData++;
   }
   return max;
}

//Explicit instatiation
template REAL  MaxAbs(const CrystVector_REAL &vector);
template int    MaxAbs(const CrystVector_int &vector);
template unsigned int    MaxAbs(const CrystVector_uint &vector);
template long   MaxAbs(const CrystVector_long &vector);


template<class T> T MinAbs(const CrystVector_T &vector)
{
   const T* pData=vector.data();
   T min =(T)  fabs((REAL) *pData++);
   for(long i=1;i<vector.numElements();i++)
   {
      if ( fabs((REAL) *pData) < min) min=(T) fabs((REAL) *pData);
      pData++;
   }
   return min;
}

//Explicit instatiation
template REAL  MinAbs(const CrystVector_REAL &vector);
template int    MinAbs(const CrystVector_int &vector);
template unsigned int    MinAbs(const CrystVector_uint &vector);
template long   MinAbs(const CrystVector_long &vector);

//######################################################################
//  CubicSpline
//######################################################################
01194 CubicSpline::CubicSpline():
mX(0),mY(0),mYsecond(0)
{}

01198 CubicSpline::CubicSpline(const CrystVector_REAL &x, const CrystVector_REAL &y, 
                         const REAL yp0, const REAL ypn)
{
   this->Init(x,y,yp0,ypn);
}

01204 CubicSpline::CubicSpline(const REAL *px, const REAL *py, const unsigned long nbPoints, 
                         const REAL yp0, const REAL ypn)
{
   this->Init(px,py,nbPoints,yp0,ypn);
}

01210 CubicSpline::CubicSpline(const CrystVector_REAL &x, const CrystVector_REAL &y)
{
   this->Init(x,y);
}

01215 CubicSpline::CubicSpline(const REAL *px, const REAL *py, const unsigned long nbPoints)
{
   this->Init(px,py,nbPoints);
}

01220 void CubicSpline::Init(const CrystVector_REAL &x, const CrystVector_REAL &y, 
                       const REAL yp0, const REAL ypn)
{
   VFN_DEBUG_ENTRY("CubicSpline::Init(x,y,yp0,ypn)",5)
   mX=x;
   mY=y;
   mYsecond.resize(x.numElements());
   this->InitSpline(yp0,ypn);
   VFN_DEBUG_EXIT("CubicSpline::Init(x,y,yp0,ypn)",5)
}
01230 void CubicSpline::Init(const REAL *px, const REAL *py, const unsigned long nbPoints, 
                       const REAL yp0, const REAL ypn)
{
   VFN_DEBUG_ENTRY("CubicSpline::Init(px,py,yp0,ypn)",5)
   mX.resize(nbPoints);
   mY.resize(nbPoints);
   mYsecond.resize(nbPoints);
   for(unsigned long i=0;i<nbPoints;i++)
   {
      mX(i)=px[i];
      mY(i)=py[i];
   }
   this->InitSpline(yp0,ypn);
   VFN_DEBUG_EXIT("CubicSpline::Init(x,y,yp0,ypn)",5)
}

01246 void CubicSpline::Init(const CrystVector_REAL &x, const CrystVector_REAL &y)
{
   VFN_DEBUG_ENTRY("CubicSpline::Init(x,y)",5)
   mX=x;
   mY=y;
   mYsecond.resize(x.numElements());
   this->InitNaturalSpline();
   VFN_DEBUG_EXIT("CubicSpline::Init(x,y)",5)
}

01256 void CubicSpline::Init(const REAL *px, const REAL *py, const unsigned long nbPoints)
{
   VFN_DEBUG_ENTRY("CubicSpline::Init(px,py,n)",5)
   mX.resize(nbPoints);
   mY.resize(nbPoints);
   mYsecond.resize(nbPoints);
   for(unsigned long i=0;i<nbPoints;i++)
   {
      mX(i)=px[i];
      mY(i)=py[i];
   }
   this->InitNaturalSpline();
   VFN_DEBUG_EXIT("CubicSpline::Init(x,y,n)",5)
}

CubicSpline::~CubicSpline()
{
}

01275 REAL CubicSpline::operator()(const REAL x) const
{
   //:TODO: faster!
   //:TODO: take into account beginning and end derivatives for out-of-bounds points
   long i;
   if(x<mX(0)) return mY(0);
   for(i=0;i<(mX.numElements()-1);i++)
      if(x<mX(i+1))
      {
         VFN_DEBUG_MESSAGE("CubicSpline::operator()(x):"<<x<<":"<<mX(i+1)<<":"<<i,0)
         const REAL e=mX(i+1)-mX(i);
         const REAL a=(mX(i+1)-x)/e;
         const REAL b=1.-a;
         const REAL c=1./6.*(a*a*a-a)*e*e;
         const REAL d=1./6.*(b*b*b-b)*e*e;
         return a*mY(i)+b*mY(i+1)+c*mYsecond(i)+d*mYsecond(i+1);
      }
   return mY(mY.numElements()-1);
}

01295 CrystVector_REAL CubicSpline::operator()(const CrystVector_REAL &x) const
{
   const long nb=x.numElements();
   CrystVector_REAL y(nb);
   //for(long i=0;i<nb;++i)y(i)=(*this)(x(i));
   //return y;
   const REAL *px=x.data();
   long i=0;
   REAL *py=y.data();
   const REAL *pX=mX.data();
   const REAL *pY=mY.data();
   const REAL *pY2=mYsecond.data();
   while((*px<*pX)&&(i<nb))
   {
      *py++=*pY;px++;i++;
   }
   
   for(long j=0;j<(mX.numElements()-1);j++)
   {
      while((*px<*(pX+1))&&(i<nb))
      {
         const REAL e= *(pX+1) - *pX;
         const REAL a= (*(pX+1)- *px)/e;
         const REAL b=1.-a;
         const REAL c=0.16666666666666666*(a*a*a-a)*e*e;
         const REAL d=0.16666666666666666*(b*b*b-b)*e*e;
         *py++ = a* *pY +b* *(pY+1) +c* *pY2 +d* *(pY2+1);
         px++;i++;
      }
      pX++;pY++;pY2++;
      if(i==nb) break;
   }
   for(;i<nb;++i) *py++ = *pY;
   return y;
}

01331 CrystVector_REAL CubicSpline::operator()(const REAL xmin,const REAL xstep, const long nb) const
{
   CrystVector_REAL y(nb);
   REAL x=xmin;
   long i=0;
   REAL *py=y.data();
   const REAL *pX=mX.data();
   const REAL *pY=mY.data();
   const REAL *pY2=mYsecond.data();
   while((x<*pX)&&(i<nb))
   {
      *py++=*pY;x += xstep;i++;
   }
   
   for(long j=0;j<(mX.numElements()-1);j++)
   {
      while((x<*(pX+1))&&(i<nb))
      {
         const REAL e= *(pX+1) - *pX;
         const REAL a= (*(pX+1)- x)/e;
         const REAL b=1.-a;
         const REAL c=0.16666666666666666*(a*a*a-a)*e*e;
         const REAL d=0.16666666666666666*(b*b*b-b)*e*e;
         *py++ = a* *pY +b* *(pY+1) +c* *pY2 +d* *(pY2+1);
         x+=xstep;i++;
      }
      pX++;pY++;pY2++;
      if(i==nb) break;
   }
   for(;i<nb;++i) *py++ = *pY;
   return y;
}

void CubicSpline::InitSpline(const REAL yp0, const REAL ypn)
{
   const long n=mX.numElements();
   CrystVector_REAL u(mX.numElements());
   mYsecond(0)=-0.5;
   u(0)=(3/(mX(1)-mX(0)))*((mY(1)-mY(0))/(mX(1)-mX(0))-yp0);
   REAL a,b;
   for(long i=1;i<(n-1);i++)
   {
      a=(mX(i)-mX(i-1))/(mX(i+1)-mX(i-1));
      b=a*mYsecond(i-1)+2;
      mYsecond(i)=(a-1.)/b;
      u(i)=(6*((mY(i+1)-mY(i))/(mX(i+1)-mX(i))-(mY(i)-mY(i-1))/(mX(i)-mX(i-1)))
           /(mX(i+1)-mX(i-1))-a*u(i-1))/b;
   }
   const REAL c=(3./(mX(n-1)-mX(n-2)))*(ypn-(mY(n-1)-mY(n-2))/(mX(n-1)-mX(n-2)));
   mYsecond(n-1)=(c-.5*u(n-2))/(0.5*mYsecond(n-2)+1);
   for(long i=(n-2);i>=0;i--) mYsecond(i)=mYsecond(i)*mYsecond(i+1)+u(i);
}

void CubicSpline::InitNaturalSpline()
{
   const long n=mX.numElements();
   CrystVector_REAL u(mX.numElements());
   mYsecond(0)=0;
   u(0)=0;
   REAL a,b;
   for(long i=1;i<=(n-2);i++)
   {
      a=(mX(i)-mX(i-1))/(mX(i+1)-mX(i-1));
      b=a*mYsecond(i-1)+2;
      mYsecond(i)=(a-1)/b;
      u(i)=(6*((mY(i+1)-mY(i))/(mX(i+1)-mX(i))-(mY(i)-mY(i-1))/(mX(i)-mX(i-1)))
           /(mX(i+1)-mX(i-1))-a*u(i-1))/b;
   }
   mYsecond(n-1)=0;
   for(long i=(n-2);i>=0;i--) mYsecond(i)=mYsecond(i)*mYsecond(i+1)+u(i);
}

//######################################################################
//  Savitzky-Golay interpolation
//######################################################################
// Coefficients for smoothing (deriv=0) - is there a general formula for these ?
REAL sgcoeffs_0_5[]={-0.08571429,  0.34285714,  0.48571429,  0.34285714, -0.08571429};
REAL sgcoeffs_0_7[]={-0.0952381 ,  0.14285714,  0.28571429,  0.33333333,  0.28571429,
                       0.14285714,  -0.0952381};
REAL sgcoeffs_0_9[]={-0.09090909,  0.06060606,  0.16883117,  0.23376623,  0.25541126,
                      0.23376623,   0.16883117,  0.06060606, -0.09090909};
REAL sgcoeffs_0_11[]={-0.08391608,  0.02097902,  0.1025641 ,  0.16083916,  0.1958042 ,  0.20745921,
                       0.1958042 ,  0.16083916,  0.1025641 ,  0.02097902, -0.08391608};
REAL sgcoeffs_0_13[]={-7.69230769e-02,   1.73472348e-18,   6.29370629e-02,   1.11888112e-01,
                       1.46853147e-01,   1.67832168e-01,   1.74825175e-01,   1.67832168e-01,
                       1.46853147e-01,   1.11888112e-01,   6.29370629e-02,   1.73472348e-18,
                      -7.69230769e-02};
REAL sgcoeffs_0_15[]={-0.07058824, -0.01176471,  0.03800905,  0.07873303,  0.11040724,  0.13303167,
                       0.14660633,  0.15113122,  0.14660633,  0.13303167,  0.11040724,
                       0.07873303,  0.03800905, -0.01176471, -0.07058824};
REAL sgcoeffs_0_17[]={-0.06501548, -0.01857585,  0.02167183,  0.05572755,  0.08359133,  0.10526316,
                       0.12074303,  0.13003096,  0.13312693,  0.13003096,  0.12074303,
                       0.10526316,  0.08359133,  0.05572755,  0.02167183, -0.01857585,
                      -0.06501548};
REAL sgcoeffs_0_19[]={-0.06015038, -0.02255639,  0.01061477,  0.03936311,  0.06368863,  0.08359133,
                       0.09907121,  0.11012826,  0.11676249,  0.11897391,  0.11676249,
                       0.11012826,  0.09907121,  0.08359133,  0.06368863,  0.03936311,
                       0.01061477, -0.02255639, -0.06015038};
REAL sgcoeffs_0_21[]={-0.05590062, -0.02484472,  0.00294214,  0.02745995,  0.04870873,  0.06668846,
                       0.08139915,  0.0928408 ,  0.1010134 ,  0.10591697,  0.10755149,
                       0.10591697,  0.1010134 ,  0.0928408 ,  0.08139915,  0.06668846,
                       0.04870873,  0.02745995,  0.00294214, -0.02484472, -0.05590062};
REAL sgcoeffs_0_23[]={-0.05217391, -0.02608696, -0.00248447,  0.01863354,  0.03726708,  0.05341615,
                       0.06708075,  0.07826087,  0.08695652,  0.0931677 ,  0.09689441,
                       0.09813665,  0.09689441,  0.0931677 ,  0.08695652,  0.07826087,
                       0.06708075,  0.05341615,  0.03726708,  0.01863354, -0.00248447,
                      -0.02608696, -0.05217391};
CrystVector_REAL SavitzkyGolay(const CrystVector_REAL &v, const unsigned int um, const unsigned int deriv)
{
   const int m=(int)um;
   REAL *sgcoeffs=0;
   if(deriv==0)
   {
      if(m==2)sgcoeffs=sgcoeffs_0_5;
      if(m==3)sgcoeffs=sgcoeffs_0_7;
      if(m==4)sgcoeffs=sgcoeffs_0_9;
      if(m==5)sgcoeffs=sgcoeffs_0_11;
      if(m==6)sgcoeffs=sgcoeffs_0_13;
      if(m==7)sgcoeffs=sgcoeffs_0_15;
      if(m==8)sgcoeffs=sgcoeffs_0_17;
      if(m==9)sgcoeffs=sgcoeffs_0_19;
      if(m==10)sgcoeffs=sgcoeffs_0_21;
      if(m==11)sgcoeffs=sgcoeffs_0_23;
   }
   if(deriv==1)
   {
      sgcoeffs=new REAL[2*m+1];
      REAL *p=sgcoeffs;
      const REAL f=3/(REAL) (m*(m+1)*(2*m+1));
      for(int j=-m;j<=m;++j) *p++ = f*j;
   }
   if(deriv==2)
   {
      sgcoeffs=new REAL[2*m+1];
      REAL *p=sgcoeffs;
      const REAL f1=45/(REAL) (m*(m+1)*(2*m+1)*(4*m*(m+1)-3));
      const REAL f2=-15/(REAL) ((2*m+1)*(4*m*(m+1)-3));
      for(int j=-m;j<=m;++j) *p++ = f1*j*j + f2;
   }
   //cout<<__FILE__<<":"<<__LINE__<<"Savitzky-Golay coeeficients(m="<<m<<",deriv="<<deriv<<"): ";
   //for(int j=-m;j<=m;++j) cout<<m<<"="<<sgcoeffs[m+j]<<" ";
   //cout<<endl;
   const unsigned int n=v.numElements();
   CrystVector_REAL d(n);
   d=0;
   const unsigned int nm=n-m;
   float *pd=d.data()+m;
   for(unsigned int i=m;i<nm;++i)
   {
      const REAL *c=sgcoeffs,*p=v.data()+i-m;
      for(int j=-m;j<=m;++j) *pd += *c++ * *p++;
      pd++;
   }
   if(deriv!=0) delete[]sgcoeffs;
   return d;
}

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