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SymMatrix.cc

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// -*- C++ -*-
// ---------------------------------------------------------------------------
//
// This file is a part of the CLHEP - a Class Library for High Energy Physics.
// 
// 
// Copyright Cornell University 1993, 1996, All Rights Reserved.
// 
// This software written by Nobu Katayama and Mike Smyth, Cornell University.
// 
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
// 1. Redistributions of source code must retain the above copyright
//    notice and author attribution, this list of conditions and the
//    following disclaimer. 
// 2. Redistributions in binary form must reproduce the above copyright
//    notice and author attribution, this list of conditions and the
//    following disclaimer in the documentation and/or other materials
//    provided with the distribution.
// 3. Neither the name of the University nor the names of its contributors
//    may be used to endorse or promote products derived from this software
//    without specific prior written permission.
// 
// Creation of derivative forms of this software for commercial
// utilization may be subject to restriction; written permission may be
// obtained from Cornell University.
// 
// CORNELL MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED.  By way
// of example, but not limitation, CORNELL MAKES NO REPRESENTATIONS OR
// WARRANTIES OF MERCANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE OR THAT
// THE USE OF THIS SOFTWARE OR DOCUMENTATION WILL NOT INFRINGE ANY PATENTS,
// COPYRIGHTS, TRADEMARKS, OR OTHER RIGHTS.  Cornell University shall not be
// held liable for any liability with respect to any claim by the user or any
// other party arising from use of the program.
//

#ifdef GNUPRAGMA
#pragma implementation
#endif

#include <string.h>
#include <float.h>        // for DBL_EPSILON

#include "CLHEP/Matrix/defs.h"
#include "CLHEP/Random/Random.h"
#include "CLHEP/Matrix/SymMatrix.h"
#include "CLHEP/Matrix/Matrix.h"
#include "CLHEP/Matrix/DiagMatrix.h"
#include "CLHEP/Matrix/Vector.h"

#ifdef HEP_DEBUG_INLINE
#include "CLHEP/Matrix/SymMatrix.icc"
#endif

namespace CLHEP {

// Simple operation for all elements

#define SIMPLE_UOP(OPER)          \
   register HepMatrix::mIter a=m.begin();            \
   register HepMatrix::mIter e=m.begin()+num_size(); \
   for(;a<e; a++) (*a) OPER t;

#define SIMPLE_BOP(OPER)          \
   register HepMatrix::mIter a=m.begin();            \
   register HepMatrix::mcIter b=m2.m.begin();         \
   register HepMatrix::mcIter e=m.begin()+num_size(); \
   for(;a<e; a++, b++) (*a) OPER (*b);

#define SIMPLE_TOP(OPER)          \
   register HepMatrix::mcIter a=m1.m.begin();           \
   register HepMatrix::mcIter b=m2.m.begin();         \
   register HepMatrix::mIter t=mret.m.begin();         \
   register HepMatrix::mcIter e=m1.m.begin()+m1.num_size(); \
   for( ;a<e; a++, b++, t++) (*t) = (*a) OPER (*b);

#define CHK_DIM_2(r1,r2,c1,c2,fun) \
   if (r1!=r2 || c1!=c2)  { \
     HepGenMatrix::error("Range error in SymMatrix function " #fun "(1)."); \
   }

#define CHK_DIM_1(c1,r2,fun) \
   if (c1!=r2) { \
     HepGenMatrix::error("Range error in SymMatrix function " #fun "(2)."); \
   }

// Constructors. (Default constructors are inlined and in .icc file)

HepSymMatrix::HepSymMatrix(int p)
   : m(p*(p+1)/2), nrow(p)
{
   size = nrow * (nrow+1) / 2;
   m.assign(size,0);
}

HepSymMatrix::HepSymMatrix(int p, int init)
   : m(p*(p+1)/2), nrow(p)
{
   size = nrow * (nrow+1) / 2;

   m.assign(size,0);
   switch(init)
   {
   case 0:
      break;
      
   case 1:
      {
         HepMatrix::mIter a; 
         for(int i=0;i<nrow;++i) {
            a = m.begin() + (i+1)*i/2 + i;
            *a = 1.0;
         }
         break;
      }
   default:
      error("SymMatrix: initialization must be either 0 or 1.");
   }
}

HepSymMatrix::HepSymMatrix(int p, HepRandom &r)
   : m(p*(p+1)/2), nrow(p)
{
   size = nrow * (nrow+1) / 2;
   HepMatrix::mIter a = m.begin();
   HepMatrix::mIter b = m.begin() + size;
   for(;a<b;a++) *a = r();
}

//
// Destructor
//
HepSymMatrix::~HepSymMatrix() {
}

HepSymMatrix::HepSymMatrix(const HepSymMatrix &m1)
   : m(m1.size), nrow(m1.nrow), size(m1.size)
{
   m = m1.m;
}

HepSymMatrix::HepSymMatrix(const HepDiagMatrix &m1)
   : m(m1.nrow*(m1.nrow+1)/2), nrow(m1.nrow)
{
   size = nrow * (nrow+1) / 2;

   int n = num_row();
   m.assign(size,0);

   HepMatrix::mIter mrr = m.begin();
   HepMatrix::mcIter mr = m1.m.begin();
   for(int r=1;r<=n;r++) {
      *mrr = *(mr++);
      if(r<n) mrr += (r+1);
   }
}

//
//
// Sub matrix
//
//

HepSymMatrix HepSymMatrix::sub(int min_row, int max_row) const
#ifdef HEP_GNU_OPTIMIZED_RETURN
return mret(max_row-min_row+1);
{
#else
{
  HepSymMatrix mret(max_row-min_row+1);
#endif
  if(max_row > num_row())
    error("HepSymMatrix::sub: Index out of range");
  HepMatrix::mIter a = mret.m.begin();
  HepMatrix::mcIter b1 = m.begin() + (min_row+2)*(min_row-1)/2;
  int rowsize=mret.num_row();
  for(int irow=1; irow<=rowsize; irow++) {
    HepMatrix::mcIter b = b1;
    for(int icol=0; icol<irow; ++icol) {
      *(a++) = *(b++);
    }
    if(irow<rowsize) b1 += irow+min_row-1;
  }
  return mret;
}

HepSymMatrix HepSymMatrix::sub(int min_row, int max_row) 
{
  HepSymMatrix mret(max_row-min_row+1);
  if(max_row > num_row())
    error("HepSymMatrix::sub: Index out of range");
  HepMatrix::mIter a = mret.m.begin();
  HepMatrix::mIter b1 = m.begin() + (min_row+2)*(min_row-1)/2;
  int rowsize=mret.num_row();
  for(int irow=1; irow<=rowsize; irow++) {
    HepMatrix::mIter b = b1;
    for(int icol=0; icol<irow; ++icol) {
      *(a++) = *(b++);
    }
    if(irow<rowsize) b1 += irow+min_row-1;
  }
  return mret;
}

void HepSymMatrix::sub(int row,const HepSymMatrix &m1)
{
  if(row <1 || row+m1.num_row()-1 > num_row() )
    error("HepSymMatrix::sub: Index out of range");
  HepMatrix::mcIter a = m1.m.begin();
  HepMatrix::mIter b1 = m.begin() + (row+2)*(row-1)/2;
  int rowsize=m1.num_row();
  for(int irow=1; irow<=rowsize; ++irow) {
    HepMatrix::mIter b = b1;
    for(int icol=0; icol<irow; ++icol) {
      *(b++) = *(a++);
    }
    if(irow<rowsize) b1 += irow+row-1;
  }
}

//
// Direct sum of two matricies
//

HepSymMatrix dsum(const HepSymMatrix &m1,
                                     const HepSymMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
  return mret(m1.num_row() + m2.num_row(), 0);
{
#else
{
  HepSymMatrix mret(m1.num_row() + m2.num_row(),
                                       0);
#endif
  mret.sub(1,m1);
  mret.sub(m1.num_row()+1,m2);
  return mret;
}

/* -----------------------------------------------------------------------
   This section contains support routines for matrix.h. This section contains
   The two argument functions +,-. They call the copy constructor and +=,-=.
   ----------------------------------------------------------------------- */
HepSymMatrix HepSymMatrix::operator- () const 
#ifdef HEP_GNU_OPTIMIZED_RETURN
      return m2(nrow);
{
#else
{
   HepSymMatrix m2(nrow);
#endif
   register HepMatrix::mcIter a=m.begin();
   register HepMatrix::mIter b=m2.m.begin();
   register HepMatrix::mcIter e=m.begin()+num_size();
   for(;a<e; a++, b++) (*b) = -(*a);
   return m2;
}

   

HepMatrix operator+(const HepMatrix &m1,const HepSymMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1);
{
#else
{
  HepMatrix mret(m1);
#endif
  CHK_DIM_2(m1.num_row(),m2.num_row(), m1.num_col(),m2.num_col(),+);
  mret += m2;
  return mret;
}
HepMatrix operator+(const HepSymMatrix &m1,const HepMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m2);
{
#else
{
  HepMatrix mret(m2);
#endif
  CHK_DIM_2(m1.num_row(),m2.num_row(),m1.num_col(),m2.num_col(),+);
  mret += m1;
  return mret;
}

HepSymMatrix operator+(const HepSymMatrix &m1,const HepSymMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.nrow);
{
#else
{
  HepSymMatrix mret(m1.nrow);
#endif
  CHK_DIM_1(m1.nrow, m2.nrow,+);
  SIMPLE_TOP(+)
  return mret;
}

//
// operator -
//

HepMatrix operator-(const HepMatrix &m1,const HepSymMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1);
{
#else
{
  HepMatrix mret(m1);
#endif
  CHK_DIM_2(m1.num_row(),m2.num_row(),
                         m1.num_col(),m2.num_col(),-);
  mret -= m2;
  return mret;
}
HepMatrix operator-(const HepSymMatrix &m1,const HepMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1);
{
#else
{
  HepMatrix mret(m1);
#endif
  CHK_DIM_2(m1.num_row(),m2.num_row(),
                         m1.num_col(),m2.num_col(),-);
  mret -= m2;
  return mret;
}

HepSymMatrix operator-(const HepSymMatrix &m1,const HepSymMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.num_row());
{
#else
{
  HepSymMatrix mret(m1.num_row());
#endif
  CHK_DIM_1(m1.num_row(),m2.num_row(),-);
  SIMPLE_TOP(-)
  return mret;
}

/* -----------------------------------------------------------------------
   This section contains support routines for matrix.h. This file contains
   The two argument functions *,/. They call copy constructor and then /=,*=.
   ----------------------------------------------------------------------- */

HepSymMatrix operator/(
const HepSymMatrix &m1,double t)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1);
{
#else
{
  HepSymMatrix mret(m1);
#endif
  mret /= t;
  return mret;
}

HepSymMatrix operator*(const HepSymMatrix &m1,double t)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1);
{
#else
{
  HepSymMatrix mret(m1);
#endif
  mret *= t;
  return mret;
}

HepSymMatrix operator*(double t,const HepSymMatrix &m1)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1);
{
#else
{
  HepSymMatrix mret(m1);
#endif
  mret *= t;
  return mret;
}


HepMatrix operator*(const HepMatrix &m1,const HepSymMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.num_row(),m2.num_col());
{
#else
  {
    HepMatrix mret(m1.num_row(),m2.num_col());
#endif
    CHK_DIM_1(m1.num_col(),m2.num_row(),*);
    HepMatrix::mcIter mit1, mit2, sp,snp; //mit2=0
    double temp;
    HepMatrix::mIter mir=mret.m.begin();
    for(mit1=m1.m.begin();
        mit1<m1.m.begin()+m1.num_row()*m1.num_col();
        mit1 = mit2)
    {
      snp=m2.m.begin();
      for(int step=1;step<=m2.num_row();++step)
        {
          mit2=mit1;
          sp=snp;
          snp+=step;
          temp=0;
          while(sp<snp)
            temp+=*(sp++)*(*(mit2++));
          if( step<m2.num_row() ) {     // only if we aren't on the last row
            sp+=step-1;
            for(int stept=step+1;stept<=m2.num_row();stept++)
              {
                temp+=*sp*(*(mit2++));
                if(stept<m2.num_row()) sp+=stept;
              }
            }   // if(step
          *(mir++)=temp;
        }       // for(step
      } // for(mit1
    return mret;
  }

HepMatrix operator*(const HepSymMatrix &m1,const HepMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.num_row(),m2.num_col());
{
#else
{
  HepMatrix mret(m1.num_row(),m2.num_col());
#endif
  CHK_DIM_1(m1.num_col(),m2.num_row(),*);
  int step,stept;
  HepMatrix::mcIter mit1,mit2,sp,snp;
  double temp;
  HepMatrix::mIter mir=mret.m.begin();
  for(step=1,snp=m1.m.begin();step<=m1.num_row();snp+=step++)
    for(mit1=m2.m.begin();mit1<m2.m.begin()+m2.num_col();mit1++)
      {
        mit2=mit1;
        sp=snp;
        temp=0;
        while(sp<snp+step)
          {
            temp+=*mit2*(*(sp++));
            if( m2.num_size()-(mit2-m2.m.begin())>m2.num_col() ){
              mit2+=m2.num_col();
            }
          }
        if(step<m1.num_row()) { // only if we aren't on the last row
          sp+=step-1;
          for(stept=step+1;stept<=m1.num_row();stept++)
            {
              temp+=*mit2*(*sp);
              if(stept<m1.num_row()) {
                mit2+=m2.num_col();
                sp+=stept;
              }
            }
          }     // if(step
        *(mir++)=temp;
      } // for(mit1
  return mret;
}

HepMatrix operator*(const HepSymMatrix &m1,const HepSymMatrix &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.num_row(),m1.num_row());
{
#else
{
  HepMatrix mret(m1.num_row(),m1.num_row());
#endif
  CHK_DIM_1(m1.num_col(),m2.num_row(),*);
  int step1,stept1,step2,stept2;
  HepMatrix::mcIter snp1,sp1,snp2,sp2;
  double temp;
  HepMatrix::mIter mr = mret.m.begin();
  snp1=m1.m.begin();
  for(step1=1;step1<=m1.num_row();++step1) {
    snp2=m2.m.begin();
    for(step2=1;step2<=m2.num_row();++step2)
      {
        sp1=snp1;
        sp2=snp2;
        snp2+=step2;
        temp=0;
        if(step1<step2)
          {
            while(sp1<snp1+step1) {
              temp+=(*(sp1++))*(*(sp2++));
              }
            sp1+=step1-1;
            for(stept1=step1+1;stept1!=step2+1;++stept1) {
              temp+=(*sp1)*(*(sp2++));
              if(stept1<m2.num_row()) sp1+=stept1;
              }
            if(step2<m2.num_row()) {    // only if we aren't on the last row
              sp2+=step2-1;
              for(stept2=step2+1;stept2<=m2.num_row();stept1++,stept2++) {
                temp+=(*sp1)*(*sp2);
                if(stept2<m2.num_row()) {
                   sp1+=stept1;
                   sp2+=stept2;
                   }
                }       // for(stept2
              } // if(step2
          }     // step1<step2
        else
          {
            while(sp2<snp2) {
              temp+=(*(sp1++))*(*(sp2++));
              }
            if(step2<m2.num_row()) {    // only if we aren't on the last row
              sp2+=step2-1;
              for(stept2=step2+1;stept2!=step1+1;stept2++) {
                temp+=(*(sp1++))*(*sp2);
                if(stept2<m1.num_row()) sp2+=stept2;
                }
              if(step1<m1.num_row()) {  // only if we aren't on the last row
                sp1+=step1-1;
                for(stept1=step1+1;stept1<=m1.num_row();stept1++,stept2++) {
                  temp+=(*sp1)*(*sp2);
                  if(stept1<m1.num_row()) {
                     sp1+=stept1;
                     sp2+=stept2;
                     }
                  }     // for(stept1
                }       // if(step1
              } // if(step2
          }     // else
        *(mr++)=temp;
      } // for(step2
    if(step1<m1.num_row()) snp1+=step1;
    }   // for(step1
  return mret;
}

HepVector operator*(const HepSymMatrix &m1,const HepVector &m2)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.num_row());
{
#else
{
  HepVector mret(m1.num_row());
#endif
  CHK_DIM_1(m1.num_col(),m2.num_row(),*);
  HepMatrix::mcIter sp,snp,vpt;
  double temp;
  int step,stept;
  HepMatrix::mIter vrp=mret.m.begin();
  for(step=1,snp=m1.m.begin();step<=m1.num_row();++step)
    {
      sp=snp;
      vpt=m2.m.begin();
      snp+=step;
      temp=0;
      while(sp<snp)
        temp+=*(sp++)*(*(vpt++));
      if(step<m1.num_row()) sp+=step-1;
      for(stept=step+1;stept<=m1.num_row();stept++)
        { 
          temp+=*sp*(*(vpt++));
          if(stept<m1.num_row()) sp+=stept;
        }
      *(vrp++)=temp;
    }   // for(step
  return mret;
}

HepSymMatrix vT_times_v(const HepVector &v)
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(v.num_row());
{
#else
{
  HepSymMatrix mret(v.num_row());
#endif
  HepMatrix::mIter mr=mret.m.begin();
  HepMatrix::mcIter vt1,vt2;
  for(vt1=v.m.begin();vt1<v.m.begin()+v.num_row();vt1++)
    for(vt2=v.m.begin();vt2<=vt1;vt2++)
      *(mr++)=(*vt1)*(*vt2);
  return mret;
}

/* -----------------------------------------------------------------------
   This section contains the assignment and inplace operators =,+=,-=,*=,/=.
   ----------------------------------------------------------------------- */

HepMatrix & HepMatrix::operator+=(const HepSymMatrix &m2)
{
  CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),+=);
  HepMatrix::mcIter sjk = m2.m.begin();
  // j >= k
  for(int j=0; j!=nrow; ++j) {
     for(int k=0; k<=j; ++k) {
        m[j*ncol+k] += *sjk;
        // make sure this is not a diagonal element
        if(k!=j) m[k*nrow+j] += *sjk;
        ++sjk;
     } 
  }   
  return (*this);
}

HepSymMatrix & HepSymMatrix::operator+=(const HepSymMatrix &m2)
{
  CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),+=);
  SIMPLE_BOP(+=)
  return (*this);
}

HepMatrix & HepMatrix::operator-=(const HepSymMatrix &m2)
{
  CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),-=);
  HepMatrix::mcIter sjk = m2.m.begin();
  // j >= k
  for(int j=0; j!=nrow; ++j) {
     for(int k=0; k<=j; ++k) {
        m[j*ncol+k] -= *sjk;
        // make sure this is not a diagonal element
        if(k!=j) m[k*nrow+j] -= *sjk;
        ++sjk;
     } 
  }   
  return (*this);
}

HepSymMatrix & HepSymMatrix::operator-=(const HepSymMatrix &m2)
{
  CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),-=);
  SIMPLE_BOP(-=)
  return (*this);
}

HepSymMatrix & HepSymMatrix::operator/=(double t)
{
  SIMPLE_UOP(/=)
  return (*this);
}

HepSymMatrix & HepSymMatrix::operator*=(double t)
{
  SIMPLE_UOP(*=)
  return (*this);
}

HepMatrix & HepMatrix::operator=(const HepSymMatrix &m1)
{
   // define size, rows, and columns of *this
   nrow = ncol = m1.nrow;
   if(nrow*ncol != size)
   {
      size = nrow*ncol;
      m.resize(size);
   }
   // begin copy
   mcIter sjk = m1.m.begin();
   // j >= k
   for(int j=0; j!=nrow; ++j) {
      for(int k=0; k<=j; ++k) {
         m[j*ncol+k] = *sjk;
         // we could copy the diagonal element twice or check 
         // doing the check may be a tiny bit faster,
         // so we choose that option for now
         if(k!=j) m[k*nrow+j] = *sjk;
         ++sjk;
      } 
   }   
   return (*this);
}

HepSymMatrix & HepSymMatrix::operator=(const HepSymMatrix &m1)
{
   if(m1.nrow != nrow)
   {
      nrow = m1.nrow;
      size = m1.size;
      m.resize(size);
   }
   m = m1.m;
   return (*this);
}

HepSymMatrix & HepSymMatrix::operator=(const HepDiagMatrix &m1)
{
   if(m1.nrow != nrow)
   {
      nrow = m1.nrow;
      size = nrow * (nrow+1) / 2;
      m.resize(size);
   }

   m.assign(size,0);
   HepMatrix::mIter mrr = m.begin();
   HepMatrix::mcIter mr = m1.m.begin();
   for(int r=1; r<=nrow; r++) {
      *mrr = *(mr++);
      if(r<nrow) mrr += (r+1);
   }
   return (*this);
}

// Print the Matrix.

std::ostream& operator<<(std::ostream &s, const HepSymMatrix &q)
{
  s << std::endl;
/* Fixed format needs 3 extra characters for field, while scientific needs 7 */
  int width;
  if(s.flags() & std::ios::fixed)
    width = s.precision()+3;
  else
    width = s.precision()+7;
  for(int irow = 1; irow<= q.num_row(); irow++)
    {
      for(int icol = 1; icol <= q.num_col(); icol++)
        {
          s.width(width);
          s << q(irow,icol) << " ";
        }
      s << std::endl;
    }
  return s;
}

HepSymMatrix HepSymMatrix::
apply(double (*f)(double, int, int)) const
#ifdef HEP_GNU_OPTIMIZED_RETURN
return mret(num_row());
{
#else
{
  HepSymMatrix mret(num_row());
#endif
  HepMatrix::mcIter a = m.begin();
  HepMatrix::mIter b = mret.m.begin();
  for(int ir=1;ir<=num_row();ir++) {
    for(int ic=1;ic<=ir;ic++) {
      *(b++) = (*f)(*(a++), ir, ic);
    }
  }
  return mret;
}

void HepSymMatrix::assign (const HepMatrix &m1)
{
   if(m1.nrow != nrow)
   {
      nrow = m1.nrow;
      size = nrow * (nrow+1) / 2;
      m.resize(size);
   }
   HepMatrix::mcIter a = m1.m.begin();
   HepMatrix::mIter b = m.begin();
   for(int r=1;r<=nrow;r++) {
      HepMatrix::mcIter d = a;
      for(int c=1;c<=r;c++) {
         *(b++) = *(d++);
      }
      if(r<nrow) a += nrow;
   }
}

HepSymMatrix HepSymMatrix::similarity(const HepMatrix &m1) const
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.num_row());
{
#else
{
  HepSymMatrix mret(m1.num_row());
#endif
  HepMatrix temp = m1*(*this);
// If m1*(*this) has correct dimensions, then so will the m1.T multiplication.
// So there is no need to check dimensions again.
  int n = m1.num_col();
  HepMatrix::mIter mr = mret.m.begin();
  HepMatrix::mIter tempr1 = temp.m.begin();
  for(int r=1;r<=mret.num_row();r++) {
    HepMatrix::mcIter m1c1 = m1.m.begin();
    for(int c=1;c<=r;c++) {
      register double tmp = 0.0;
      HepMatrix::mIter tempri = tempr1;
      HepMatrix::mcIter m1ci = m1c1;
      for(int i=1;i<=m1.num_col();i++) {
        tmp+=(*(tempri++))*(*(m1ci++));
      }
      *(mr++) = tmp;
      m1c1 += n;
    }
    tempr1 += n;
  }
  return mret;
}

HepSymMatrix HepSymMatrix::similarity(const HepSymMatrix &m1) const
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.num_row());
{
#else
{
  HepSymMatrix mret(m1.num_row());
#endif
  HepMatrix temp = m1*(*this);
  int n = m1.num_col();
  HepMatrix::mIter mr = mret.m.begin();
  HepMatrix::mIter tempr1 = temp.m.begin();
  for(int r=1;r<=mret.num_row();r++) {
    HepMatrix::mcIter m1c1 = m1.m.begin();
    int c;
    for(c=1;c<=r;c++) {
      register double tmp = 0.0;
      HepMatrix::mIter tempri = tempr1;
      HepMatrix::mcIter m1ci = m1c1;
      int i;
      for(i=1;i<c;i++) {
        tmp+=(*(tempri++))*(*(m1ci++));
      }
      for(i=c;i<=m1.num_col();i++) {
        tmp+=(*(tempri++))*(*(m1ci));
        if(i<m1.num_col()) m1ci += i;
      }
      *(mr++) = tmp;
      m1c1 += c;
    }
    tempr1 += n;
  }
  return mret;
}

double HepSymMatrix::similarity(const HepVector &m1)
const {
  register double mret = 0.0;
  HepVector temp = (*this) *m1;
// If m1*(*this) has correct dimensions, then so will the m1.T multiplication.
// So there is no need to check dimensions again.
  HepMatrix::mIter a=temp.m.begin();
  HepMatrix::mcIter b=m1.m.begin();
  HepMatrix::mIter e=a+m1.num_row();
  for(;a<e;) mret += (*(a++)) * (*(b++));
  return mret;
}

HepSymMatrix HepSymMatrix::similarityT(const HepMatrix &m1) const
#ifdef HEP_GNU_OPTIMIZED_RETURN
     return mret(m1.num_col());
{
#else
{
  HepSymMatrix mret(m1.num_col());
#endif
  HepMatrix temp = (*this)*m1;
  int n = m1.num_col();
  HepMatrix::mIter mrc = mret.m.begin();
  HepMatrix::mIter temp1r = temp.m.begin();
  for(int r=1;r<=mret.num_row();r++) {
    HepMatrix::mcIter m11c = m1.m.begin();
    for(int c=1;c<=r;c++) {
      register double tmp = 0.0;
      for(int i=1;i<=m1.num_row();i++) {
        HepMatrix::mIter tempir = temp1r + n*(i-1);
        HepMatrix::mcIter m1ic = m11c + n*(i-1);
        tmp+=(*(tempir))*(*(m1ic));
      }
      *(mrc++) = tmp;
      m11c++;
    }
    temp1r++;
  }
  return mret;
}

void HepSymMatrix::invert(int &ifail) {
  
  ifail = 0;

  switch(nrow) {
  case 3:
    {
      double det, temp;
      double t1, t2, t3;
      double c11,c12,c13,c22,c23,c33;
      c11 = (*(m.begin()+2)) * (*(m.begin()+5)) - (*(m.begin()+4)) * (*(m.begin()+4));
      c12 = (*(m.begin()+4)) * (*(m.begin()+3)) - (*(m.begin()+1)) * (*(m.begin()+5));
      c13 = (*(m.begin()+1)) * (*(m.begin()+4)) - (*(m.begin()+2)) * (*(m.begin()+3));
      c22 = (*(m.begin()+5)) * (*m.begin()) - (*(m.begin()+3)) * (*(m.begin()+3));
      c23 = (*(m.begin()+3)) * (*(m.begin()+1)) - (*(m.begin()+4)) * (*m.begin());
      c33 = (*m.begin()) * (*(m.begin()+2)) - (*(m.begin()+1)) * (*(m.begin()+1));
      t1 = fabs(*m.begin());
      t2 = fabs(*(m.begin()+1));
      t3 = fabs(*(m.begin()+3));
      if (t1 >= t2) {
        if (t3 >= t1) {
          temp = *(m.begin()+3);
          det = c23*c12-c22*c13;
        } else {
          temp = *m.begin();
          det = c22*c33-c23*c23;
        }
      } else if (t3 >= t2) {
        temp = *(m.begin()+3);
        det = c23*c12-c22*c13;
      } else {
        temp = *(m.begin()+1);
        det = c13*c23-c12*c33;
      }
      if (det==0) {
        ifail = 1;
        return;
      }
      {
        double s = temp/det;
        HepMatrix::mIter mm = m.begin();
        *(mm++) = s*c11;
        *(mm++) = s*c12;
        *(mm++) = s*c22;
        *(mm++) = s*c13;
        *(mm++) = s*c23;
        *(mm) = s*c33;
      }
    }
    break;
 case 2:
    {
      double det, temp, s;
      det = (*m.begin())*(*(m.begin()+2)) - (*(m.begin()+1))*(*(m.begin()+1));
      if (det==0) {
        ifail = 1;
        return;
      }
      s = 1.0/det;
      *(m.begin()+1) *= -s;
      temp = s*(*(m.begin()+2));
      *(m.begin()+2) = s*(*m.begin());
      *m.begin() = temp;
      break;
    }
 case 1:
    {
      if ((*m.begin())==0) {
        ifail = 1;
        return;
      }
      *m.begin() = 1.0/(*m.begin());
      break;
    }
 case 5:
    {
      invert5(ifail);
      return;
    }
 case 6:
    {
      invert6(ifail);
      return;
    }
 case 4:
    {
      invert4(ifail);
      return;
    }
 default:
    {
      invertBunchKaufman(ifail);
      return;
    }
  }
  return; // inversion successful
}

double HepSymMatrix::determinant() const {
  static const int max_array = 20;
  // ir must point to an array which is ***1 longer than*** nrow
  static std::vector<int> ir_vec (max_array+1); 
  if (ir_vec.size() <= static_cast<unsigned int>(nrow)) ir_vec.resize(nrow+1);
  int * ir = &ir_vec[0];   

  double det;
  HepMatrix mt(*this);
  int i = mt.dfact_matrix(det, ir);
  if(i==0) return det;
  return 0.0;
}

double HepSymMatrix::trace() const {
   double t = 0.0;
   for (int i=0; i<nrow; i++) 
     t += *(m.begin() + (i+3)*i/2);
   return t;
}

void HepSymMatrix::invertBunchKaufman(int &ifail) {
  // Bunch-Kaufman diagonal pivoting method
  // It is decribed in J.R. Bunch, L. Kaufman (1977). 
  // "Some Stable Methods for Calculating Inertia and Solving Symmetric 
  // Linear Systems", Math. Comp. 31, p. 162-179. or in Gene H. Golub, 
  // Charles F. van Loan, "Matrix Computations" (the second edition 
  // has a bug.) and implemented in "lapack"
  // Mario Stanke, 09/97

  int i, j, k, s;
  int pivrow;

  // Establish the two working-space arrays needed:  x and piv are
  // used as pointers to arrays of doubles and ints respectively, each
  // of length nrow.  We do not want to reallocate each time through
  // unless the size needs to grow.  We do not want to leak memory, even
  // by having a new without a delete that is only done once.
  
  static const int max_array = 25;
#ifdef DISABLE_ALLOC
  static std::vector<double> xvec (max_array);
  static std::vector<int>    pivv (max_array);
  typedef std::vector<int>::iterator pivIter; 
#else
  static std::vector<double,Alloc<double,25> > xvec (max_array);
  static std::vector<int,   Alloc<int,   25> > pivv (max_array);
  typedef std::vector<int,Alloc<int,25> >::iterator pivIter; 
#endif  
  if (xvec.size() < static_cast<unsigned int>(nrow)) xvec.resize(nrow);
  if (pivv.size() < static_cast<unsigned int>(nrow)) pivv.resize(nrow);
     // Note - resize shuld do  nothing if the size is already larger than nrow,
     //        but on VC++ there are indications that it does so we check.
     // Note - the data elements in a vector are guaranteed to be contiguous,
     //        so x[i] and piv[i] are optimally fast.
  mIter   x   = xvec.begin();
  // x[i] is used as helper storage, needs to have at least size nrow.
  pivIter piv = pivv.begin();
  // piv[i] is used to store details of exchanges
      
  double temp1, temp2;
  HepMatrix::mIter ip, mjj, iq;
  double lambda, sigma;
  const double alpha = .6404; // = (1+sqrt(17))/8
  const double epsilon = 32*DBL_EPSILON;
  // whenever a sum of two doubles is below or equal to epsilon
  // it is set to zero.
  // this constant could be set to zero but then the algorithm
  // doesn't neccessarily detect that a matrix is singular
  
  for (i = 0; i < nrow; ++i) piv[i] = i+1;
      
  ifail = 0;
      
  // compute the factorization P*A*P^T = L * D * L^T 
  // L is unit lower triangular, D is direct sum of 1x1 and 2x2 matrices
  // L and D^-1 are stored in A = *this, P is stored in piv[]
        
  for (j=1; j < nrow; j+=s)  // main loop over columns
  {
      mjj = m.begin() + j*(j-1)/2 + j-1;
      lambda = 0;           // compute lambda = max of A(j+1:n,j)
      pivrow = j+1;
      //ip = m.begin() + (j+1)*j/2 + j-1;
      for (i=j+1; i <= nrow ; ++i) {
          // calculate ip to avoid going off end of storage array
          ip = m.begin() + (i-1)*i/2 + j-1;
          if (fabs(*ip) > lambda) {
              lambda = fabs(*ip);
              pivrow = i;
          }
      } // for i
      if (lambda == 0 ) {
          if (*mjj == 0) {
              ifail = 1;
              return;
          }
          s=1;
          *mjj = 1./ *mjj;
      } else {  // lambda == 0
          if (fabs(*mjj) >= lambda*alpha) {
              s=1;
              pivrow=j;
          } else {      // fabs(*mjj) >= lambda*alpha
              sigma = 0;  // compute sigma = max A(pivrow, j:pivrow-1)
              ip = m.begin() + pivrow*(pivrow-1)/2+j-1;
              for (k=j; k < pivrow; k++) {
                  if (fabs(*ip) > sigma) sigma = fabs(*ip);
                  ip++;
              } // for k
              if (sigma * fabs(*mjj) >= alpha * lambda * lambda) {
                  s=1;
                  pivrow = j;
              } else if (fabs(*(m.begin()+pivrow*(pivrow-1)/2+pivrow-1)) 
                            >= alpha * sigma) {
                s=1;
              } else {
                s=2;
              } // if sigma...
          }     // fabs(*mjj) >= lambda*alpha
          if (pivrow == j) { // no permutation neccessary
              piv[j-1] = pivrow;
              if (*mjj == 0) {
                  ifail=1;
                  return;
              }
              temp2 = *mjj = 1./ *mjj; // invert D(j,j)

              // update A(j+1:n, j+1,n)
              for (i=j+1; i <= nrow; i++) {
                  temp1 = *(m.begin() + i*(i-1)/2 + j-1) * temp2;
                  ip = m.begin()+i*(i-1)/2+j;
                  for (k=j+1; k<=i; k++) {
                      *ip -= temp1 * *(m.begin() + k*(k-1)/2 + j-1);
                      if (fabs(*ip) <= epsilon)
                        *ip=0;
                      ip++;
                  }
              } // for i
              // update L 
              //ip = m.begin() + (j+1)*j/2 + j-1; 
              for (i=j+1; i <= nrow; ++i) {
                  // calculate ip to avoid going off end of storage array
                  ip = m.begin() + (i-1)*i/2 + j-1;
                  *ip *= temp2;
              }
          } else if (s==1) { // 1x1 pivot 
              piv[j-1] = pivrow;

              // interchange rows and columns j and pivrow in
              // submatrix (j:n,j:n)
              ip = m.begin() + pivrow*(pivrow-1)/2 + j;
              for (i=j+1; i < pivrow; i++, ip++) {
                  temp1 = *(m.begin() + i*(i-1)/2 + j-1);
                  *(m.begin() + i*(i-1)/2 + j-1)= *ip;
                  *ip = temp1;
              } // for i
              temp1 = *mjj;
              *mjj = *(m.begin()+pivrow*(pivrow-1)/2+pivrow-1);
              *(m.begin()+pivrow*(pivrow-1)/2+pivrow-1) = temp1;
              ip = m.begin() + (pivrow+1)*pivrow/2 + j-1;
              iq = ip + pivrow-j;
              for (i = pivrow+1; i <= nrow; ip += i, iq += i++) {
                  temp1 = *iq;
                  *iq = *ip;
                  *ip = temp1;
              } // for i

              if (*mjj == 0) {
                  ifail = 1;
                  return;
              } // *mjj == 0
              temp2 = *mjj = 1./ *mjj; // invert D(j,j)

              // update A(j+1:n, j+1:n)
              for (i = j+1; i <= nrow; i++) {
                  temp1 = *(m.begin() + i*(i-1)/2 + j-1) * temp2;
                  ip = m.begin()+i*(i-1)/2+j;
                  for (k=j+1; k<=i; k++) {
                      *ip -= temp1 * *(m.begin() + k*(k-1)/2 + j-1);
                      if (fabs(*ip) <= epsilon)
                        *ip=0;
                      ip++;
                  }     // for k
              } // for i
              // update L 
              //ip = m.begin() + (j+1)*j/2 + j-1; 
              for (i=j+1; i <= nrow; ++i) {
                  // calculate ip to avoid going off end of storage array
                  ip = m.begin() + (i-1)*i/2 + j-1;
                  *ip *= temp2;
              }
          } else { // s=2, ie use a 2x2 pivot
              piv[j-1] = -pivrow;
              piv[j] = 0; // that means this is the second row of a 2x2 pivot

              if (j+1 != pivrow) {
                  // interchange rows and columns j+1 and pivrow in
                  // submatrix (j:n,j:n) 
                  ip = m.begin() + pivrow*(pivrow-1)/2 + j+1;
                  for (i=j+2; i < pivrow; i++, ip++) {
                      temp1 = *(m.begin() + i*(i-1)/2 + j);
                      *(m.begin() + i*(i-1)/2 + j) = *ip;
                      *ip = temp1;
                  }     // for i
                  temp1 = *(mjj + j + 1);
                  *(mjj + j + 1) = 
                    *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1);
                  *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1) = temp1;
                  temp1 = *(mjj + j);
                  *(mjj + j) = *(m.begin() + pivrow*(pivrow-1)/2 + j-1);
                  *(m.begin() + pivrow*(pivrow-1)/2 + j-1) = temp1;
                  ip = m.begin() + (pivrow+1)*pivrow/2 + j;
                  iq = ip + pivrow-(j+1);
                  for (i = pivrow+1; i <= nrow; ip += i, iq += i++) {
                      temp1 = *iq;
                      *iq = *ip;
                      *ip = temp1;
                  }     // for i
              } //  j+1 != pivrow
              // invert D(j:j+1,j:j+1)
              temp2 = *mjj * *(mjj + j + 1) - *(mjj + j) * *(mjj + j); 
              if (temp2 == 0) {
                std::cerr
                  << "SymMatrix::bunch_invert: error in pivot choice" 
                  << std::endl;
              }
              temp2 = 1. / temp2;
              // this quotient is guaranteed to exist by the choice 
              // of the pivot
              temp1 = *mjj;
              *mjj = *(mjj + j + 1) * temp2;
              *(mjj + j + 1) = temp1 * temp2;
              *(mjj + j) = - *(mjj + j) * temp2;

              if (j < nrow-1) { // otherwise do nothing
                  // update A(j+2:n, j+2:n)
                  for (i=j+2; i <= nrow ; i++) {
                      ip = m.begin() + i*(i-1)/2 + j-1;
                      temp1 = *ip * *mjj + *(ip + 1) * *(mjj + j);
                      if (fabs(temp1 ) <= epsilon) temp1 = 0;
                      temp2 = *ip * *(mjj + j) + *(ip + 1) * *(mjj + j + 1);
                      if (fabs(temp2 ) <= epsilon) temp2 = 0;
                      for (k = j+2; k <= i ; k++) {
                          ip = m.begin() + i*(i-1)/2 + k-1;
                          iq = m.begin() + k*(k-1)/2 + j-1;
                          *ip -= temp1 * *iq + temp2 * *(iq+1);
                          if (fabs(*ip) <= epsilon)
                            *ip = 0;
                      } // for k
                  }     // for i
                  // update L
                  for (i=j+2; i <= nrow ; i++) {
                      ip = m.begin() + i*(i-1)/2 + j-1;
                      temp1 = *ip * *mjj + *(ip+1) * *(mjj + j);
                      if (fabs(temp1) <= epsilon) temp1 = 0;
                      *(ip+1) = *ip * *(mjj + j) 
                                + *(ip+1) * *(mjj + j + 1);
                      if (fabs(*(ip+1)) <= epsilon) *(ip+1) = 0;
                      *ip = temp1;
                  }     // for k
              } // j < nrow-1
          }
      }
  } // end of main loop over columns

  if (j == nrow) { // the the last pivot is 1x1
      mjj = m.begin() + j*(j-1)/2 + j-1;
      if (*mjj == 0) {
          ifail = 1;
          return;
      } else { *mjj = 1. / *mjj; }
  } // end of last pivot code

  // computing the inverse from the factorization
         
  for (j = nrow ; j >= 1 ; j -= s) // loop over columns
  {
      mjj = m.begin() + j*(j-1)/2 + j-1;
      if (piv[j-1] > 0) { // 1x1 pivot, compute column j of inverse
          s = 1; 
          if (j < nrow) {
              //ip = m.begin() + (j+1)*j/2 + j-1;
              //for (i=0; i < nrow-j; ip += 1+j+i++) x[i] = *ip;
              ip = m.begin() + (j+1)*j/2 - 1;
              for (i=0; i < nrow-j; ++i) {
                  ip += i + j;
                  x[i] = *ip;
              }
              for (i=j+1; i<=nrow ; i++) {
                  temp2=0;
                  ip = m.begin() + i*(i-1)/2 + j;
                  for (k=0; k <= i-j-1; k++) temp2 += *ip++ * x[k];
                  // avoid setting ip outside the bounds of the storage array
                  ip -= 1;
                  // using the value of k from the previous loop
                  for ( ; k < nrow-j; ++k) {
                      ip += j+k;
                      temp2 += *ip * x[k];
                  }
                  *(m.begin()+ i*(i-1)/2 + j-1) = -temp2;
              } // for i
              temp2 = 0;
              //ip = m.begin() + (j+1)*j/2 + j-1;
              //for (k=0; k < nrow-j; ip += 1+j+k++)
                //temp2 += x[k] * *ip;
              ip = m.begin() + (j+1)*j/2 - 1;
              for (k=0; k < nrow-j; ++k) {
                ip += j+k;
                temp2 += x[k] * *ip;
              }
              *mjj -= temp2;
          }     // j < nrow
      } else { //2x2 pivot, compute columns j and j-1 of the inverse
          if (piv[j-1] != 0)
            std::cerr << "error in piv" << piv[j-1] << std::endl;
          s=2; 
          if (j < nrow) {
              //ip = m.begin() + (j+1)*j/2 + j-1;
              //for (i=0; i < nrow-j; ip += 1+j+i++) x[i] = *ip;
              ip = m.begin() + (j+1)*j/2 - 1;
              for (i=0; i < nrow-j; ++i) {
                  ip += i + j;
                  x[i] = *ip;
              }
              for (i=j+1; i<=nrow ; i++) {
                  temp2 = 0;
                  ip = m.begin() + i*(i-1)/2 + j;
                  for (k=0; k <= i-j-1; k++)
                    temp2 += *ip++ * x[k];
                  for (ip += i-1; k < nrow-j; ip += 1+j+k++)
                    temp2 += *ip * x[k];
                  *(m.begin()+ i*(i-1)/2 + j-1) = -temp2;
              } // for i   
              temp2 = 0;
              //ip = m.begin() + (j+1)*j/2 + j-1;
              //for (k=0; k < nrow-j; ip += 1+j+k++) temp2 += x[k] * *ip;
              ip = m.begin() + (j+1)*j/2 - 1;
              for (k=0; k < nrow-j; ++k) {
                  ip += k + j;
                  temp2 += x[k] * *ip;
              }
              *mjj -= temp2;
              temp2 = 0;
              //ip = m.begin() + (j+1)*j/2 + j-2;
              //for (i=j+1; i <= nrow; ip += i++) temp2 += *ip * *(ip+1);
              ip = m.begin() + (j+1)*j/2 - 2;
              for (i=j+1; i <= nrow; ++i) {
                  ip += i - 1;
                  temp2 += *ip * *(ip+1);
              }
              *(mjj-1) -= temp2;
              //ip = m.begin() + (j+1)*j/2 + j-2;
              //for (i=0; i < nrow-j; ip += 1+j+i++) x[i] = *ip;
              ip = m.begin() + (j+1)*j/2 - 2;
              for (i=0; i < nrow-j; ++i) {
                  ip += i + j;
                  x[i] = *ip;
              }
              for (i=j+1; i <= nrow ; i++) {
                  temp2 = 0;
                  ip = m.begin() + i*(i-1)/2 + j;
                  for (k=0; k <= i-j-1; k++)
                      temp2 += *ip++ * x[k];
                  for (ip += i-1; k < nrow-j; ip += 1+j+k++)
                      temp2 += *ip * x[k];
                  *(m.begin()+ i*(i-1)/2 + j-2)= -temp2;
              } // for i
              temp2 = 0;
              //ip = m.begin() + (j+1)*j/2 + j-2;
              //for (k=0; k < nrow-j; ip += 1+j+k++)
                //  temp2 += x[k] * *ip;
              ip = m.begin() + (j+1)*j/2 - 2;
              for (k=0; k < nrow-j; ++k) {
                  ip += k + j;
                  temp2 += x[k] * *ip;
              }
              *(mjj-j) -= temp2;
          }     // j < nrow
      } // else  piv[j-1] > 0

      // interchange rows and columns j and piv[j-1] 
      // or rows and columns j and -piv[j-2]

      pivrow = (piv[j-1]==0)? -piv[j-2] : piv[j-1];
      ip = m.begin() + pivrow*(pivrow-1)/2 + j;
      for (i=j+1;i < pivrow; i++, ip++) {
          temp1 = *(m.begin() + i*(i-1)/2 + j-1);
          *(m.begin() + i*(i-1)/2 + j-1) = *ip;
          *ip = temp1;
      } // for i
      temp1 = *mjj;
      *mjj = *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1);
      *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1) = temp1;
      if (s==2) {
          temp1 = *(mjj-1);
          *(mjj-1) = *( m.begin() + pivrow*(pivrow-1)/2 + j-2);
          *( m.begin() + pivrow*(pivrow-1)/2 + j-2) = temp1;
      } // s==2

      // problem right here
      if( pivrow < nrow ) {
          ip = m.begin() + (pivrow+1)*pivrow/2 + j-1;  // &A(i,j)
          // adding parenthesis for VC++
          iq = ip + (pivrow-j);
          for (i = pivrow+1; i <= nrow; i++) {
              temp1 = *iq;
              *iq = *ip;
              *ip = temp1;
              if( i < nrow ) {
              ip += i;
              iq += i;
              }
          }     // for i 
      } // pivrow < nrow
  } // end of loop over columns (in computing inverse from factorization)

  return; // inversion successful

}

}  // namespace CLHEP

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