[u/mrichter/AliRoot.git] / STEER / AliSymMatrix.cxx

/**********************************************************************************************/
/* Fast symmetric matrix with dynamically expandable size.                                    */
/* Only part can be used for matrix operations. It is defined as:                             */ 
/* fNCols: rows built by constructor (GetSizeBooked)                                          */ 
/* fNRows: number of rows added dynamically (automatically added on assignment to row)        */ 
/*         GetNRowAdded                                                                       */ 
/* fNRowIndex: total size (fNCols+fNRows), GetSize                                            */ 
/* fRowLwb   : actual size to used for given operation, by default = total size, GetSizeUsed  */ 
/*                                                                                            */ 
/* Author: ruben.shahoyan@cern.ch                                                             */
/*                                                                                            */ 
/**********************************************************************************************/
#include <stdlib.h>
#include <stdio.h>
#include <iostream>
#include <float.h>
//
#include <TClass.h>
#include <TMath.h>
#include "AliSymMatrix.h"
#include "AliLog.h"
//

using namespace std;

ClassImp(AliSymMatrix)


AliSymMatrix* AliSymMatrix::fgBuffer = 0; 
Int_t         AliSymMatrix::fgCopyCnt = 0; 
//___________________________________________________________
AliSymMatrix::AliSymMatrix() 
: fElems(0),fElemsAdd(0)
{
  fSymmetric = kTRUE;
  fgCopyCnt++;
}

//___________________________________________________________
AliSymMatrix::AliSymMatrix(Int_t size)
  : AliMatrixSq(),fElems(0),fElemsAdd(0)
{
  //
  fNrows = 0;
  fNrowIndex = fNcols = fRowLwb = size;
  fElems     = new Double_t[fNcols*(fNcols+1)/2];
  fSymmetric = kTRUE;
  Reset();
  fgCopyCnt++;
  //
}

//___________________________________________________________
AliSymMatrix::AliSymMatrix(const AliSymMatrix &src) 
  : AliMatrixSq(src),fElems(0),fElemsAdd(0)
{
  fNrowIndex = fNcols = src.GetSize();
  fNrows = 0;
  fRowLwb = src.GetSizeUsed();
  if (fNcols) {
    int nmainel = fNcols*(fNcols+1)/2;
    fElems     = new Double_t[nmainel];
    nmainel = src.fNcols*(src.fNcols+1)/2;
    memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
    if (src.GetSizeAdded()) { // transfer extra rows to main matrix
      Double_t *pnt = fElems + nmainel;
      int ncl = src.GetSizeBooked() + 1;
      for (int ir=0;ir<src.GetSizeAdded();ir++) {
	memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
	pnt += ncl;
	ncl++; 
      }
    }
  }
  else fElems = 0;
  fElemsAdd = 0;
  fgCopyCnt++;
  //
}

//___________________________________________________________
AliSymMatrix::~AliSymMatrix() 
{
  Clear();
  if (--fgCopyCnt < 1 && fgBuffer) {delete fgBuffer; fgBuffer = 0;}
}

//___________________________________________________________
AliSymMatrix&  AliSymMatrix::operator=(const AliSymMatrix& src)
{
  //
  if (this != &src) {
    TObject::operator=(src);
    if (GetSizeBooked()!=src.GetSizeBooked() && GetSizeAdded()!=src.GetSizeAdded()) {
      // recreate the matrix
      if (fElems) delete[] fElems;
      for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i]; 
      delete[] fElemsAdd;
      //
      fNrowIndex = src.GetSize(); 
      fNcols = src.GetSize();
      fNrows = 0;
      fRowLwb = src.GetSizeUsed();
      fElems     = new Double_t[GetSize()*(GetSize()+1)/2];
      int nmainel = src.GetSizeBooked()*(src.GetSizeBooked()+1);
      memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
      if (src.GetSizeAdded()) { // transfer extra rows to main matrix
	Double_t *pnt = fElems + nmainel*sizeof(Double_t);
	int ncl = src.GetSizeBooked() + 1;
	for (int ir=0;ir<src.GetSizeAdded();ir++) {
	  ncl += ir; 
	  memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
	  pnt += ncl*sizeof(Double_t);
	}
      }
      //
    }
    else {
      memcpy(fElems,src.fElems,GetSizeBooked()*(GetSizeBooked()+1)/2*sizeof(Double_t));
      int ncl = GetSizeBooked() + 1;
      for (int ir=0;ir<GetSizeAdded();ir++) { // dynamic rows
	ncl += ir; 
	memcpy(fElemsAdd[ir],src.fElemsAdd[ir],ncl*sizeof(Double_t));
      }
    }
  }
  //
  return *this;
}

//___________________________________________________________
AliSymMatrix& AliSymMatrix::operator+=(const AliSymMatrix& src)
{
  //
  if (GetSizeUsed() != src.GetSizeUsed()) {
    AliError("Matrix sizes are different");
    return *this;
  }
  for (int i=0;i<GetSizeUsed();i++) for (int j=i;j<GetSizeUsed();j++) (*this)(j,i) += src(j,i);
  return *this;
}

//___________________________________________________________
void AliSymMatrix::Clear(Option_t*)
{
  if (fElems) {delete[] fElems; fElems = 0;}
  //  
  if (fElemsAdd) {
    for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i]; 
    delete[] fElemsAdd;
    fElemsAdd = 0;
  }
  fNrowIndex = fNcols = fNrows = fRowLwb = 0;
  //
}

//___________________________________________________________
Float_t AliSymMatrix::GetDensity() const
{
  // get fraction of non-zero elements
  Int_t nel = 0;
  for (int i=GetSizeUsed();i--;) for (int j=i+1;j--;) if (TMath::Abs(GetEl(i,j))>DBL_MIN) nel++;
  return 2.*nel/( (GetSizeUsed()+1)*GetSizeUsed() );
}

//___________________________________________________________
void AliSymMatrix::Print(Option_t* option) const
{
  printf("Symmetric Matrix: Size = %d (%d rows added dynamically), %d used\n",GetSize(),GetSizeAdded(),GetSizeUsed());
  TString opt = option; opt.ToLower();
  if (opt.IsNull()) return;
  opt = "%"; opt += 1+int(TMath::Log10(double(GetSize()))); opt+="d|";
  for (Int_t i=0;i<GetSizeUsed();i++) {
    printf(opt,i);
    for (Int_t j=0;j<=i;j++) printf("%+.3e|",GetEl(i,j));
    printf("\n");
  }
}

//___________________________________________________________
void AliSymMatrix::MultiplyByVec(Double_t *vecIn,Double_t *vecOut) const
{
  // fill vecOut by matrix*vecIn
  // vector should be of the same size as the matrix
  for (int i=GetSizeUsed();i--;) {
    vecOut[i] = 0.0;
    for (int j=GetSizeUsed();j--;) vecOut[i] += vecIn[j]*GetEl(i,j);
  }
  //
}

//___________________________________________________________
AliSymMatrix* AliSymMatrix::DecomposeChol() 
{
  // Return a matrix with Choleski decomposition
  // Adopted from Numerical Recipes in C, ch.2-9, http://www.nr.com
  // consturcts Cholesky decomposition of SYMMETRIC and
  // POSITIVELY-DEFINED matrix a (a=L*Lt)
  // Only upper triangle of the matrix has to be filled.
  // In opposite to function from the book, the matrix is modified:
  // lower triangle and diagonal are refilled.
  //
  if (!fgBuffer || fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
    delete fgBuffer; 
    try {
      fgBuffer = new AliSymMatrix(*this);
    }
    catch(bad_alloc&) {
      printf("Failed to allocate memory for Choleski decompostions\n");
      return 0;
    }
  }
  else (*fgBuffer) = *this;
  //
  AliSymMatrix& mchol = *fgBuffer;
  //
  for (int i=0;i<GetSizeUsed();i++) {
    Double_t *rowi = mchol.GetRow(i);
    for (int j=i;j<GetSizeUsed();j++) {
      Double_t *rowj = mchol.GetRow(j);
      double sum = rowj[i];
      for (int k=i-1;k>=0;k--) if (rowi[k]&&rowj[k]) sum -= rowi[k]*rowj[k];
      if (i == j) {
	if (sum <= 0.0) { // not positive-definite
	  printf("The matrix is not positive definite [%e]\n"
		 "Choleski decomposition is not possible\n",sum);
	  return 0;
	}
	rowi[i] = TMath::Sqrt(sum);
	//
      } else rowj[i] = sum/rowi[i];
    }
  }
  return fgBuffer;
}

//___________________________________________________________
Bool_t AliSymMatrix::InvertChol() 
{
  // Invert matrix using Choleski decomposition
  //
  AliSymMatrix* mchol = DecomposeChol();
  if (!mchol) {
    printf("Failed to invert the matrix\n");
    return kFALSE;
  }
  //
  InvertChol(mchol);
  return kTRUE;
  //
}

//___________________________________________________________
void AliSymMatrix::InvertChol(AliSymMatrix* pmchol) 
{
  // Invert matrix using Choleski decomposition, provided the Cholseki's L matrix
  //
  Double_t sum;
  AliSymMatrix& mchol = *pmchol;
  //
  // Invert decomposed triangular L matrix (Lower triangle is filled)
  for (int i=0;i<GetSizeUsed();i++) { 
    mchol(i,i) =  1.0/mchol(i,i);
    for (int j=i+1;j<GetSizeUsed();j++) { 
      Double_t *rowj = mchol.GetRow(j);
      sum = 0.0; 
      for (int k=i;k<j;k++) if (rowj[k]) { 
	double &mki = mchol(k,i); if (mki) sum -= rowj[k]*mki;
      }
      rowj[i] = sum/rowj[j];
    } 
  }
  //
  // take product of the inverted Choleski L matrix with its transposed
  for (int i=GetSizeUsed();i--;) {
    for (int j=i+1;j--;) {
      sum = 0;
      for (int k=i;k<GetSizeUsed();k++) {
	double &mik = mchol(i,k); 
	if (mik) {
	  double &mjk = mchol(j,k);
	  if (mjk) sum += mik*mjk;
	}
      }
      (*this)(j,i) = sum;
    }
  }
  //
}


//___________________________________________________________
Bool_t AliSymMatrix::SolveChol(Double_t *b, Bool_t invert) 
{
  // Adopted from Numerical Recipes in C, ch.2-9, http://www.nr.com
  // Solves the set of n linear equations A x = b, 
  // where a is a positive-definite symmetric matrix. 
  // a[1..n][1..n] is the output of the routine CholDecomposw. 
  // Only the lower triangle of a is accessed. b[1..n] is input as the 
  // right-hand side vector. The solution vector is returned in b[1..n].
  //
  Int_t i,k;
  Double_t sum;
  //
  AliSymMatrix *pmchol = DecomposeChol();
  if (!pmchol) {
    printf("SolveChol failed\n");
    //    Print("l");
    return kFALSE;
  }
  AliSymMatrix& mchol = *pmchol;
  //
  for (i=0;i<GetSizeUsed();i++) {
    Double_t *rowi = mchol.GetRow(i);
    for (sum=b[i],k=i-1;k>=0;k--) if (rowi[k]&&b[k]) sum -= rowi[k]*b[k];
    b[i]=sum/rowi[i];
  }
  //
  for (i=GetSizeUsed()-1;i>=0;i--) {
    for (sum=b[i],k=i+1;k<GetSizeUsed();k++) if (b[k]) {
      double &mki=mchol(k,i); if (mki) sum -= mki*b[k];
    }
    b[i]=sum/mchol(i,i);
  }
  //
  if (invert) InvertChol(pmchol);
  return kTRUE;
  //
}

//___________________________________________________________
Bool_t AliSymMatrix::SolveChol(TVectorD &b, Bool_t invert) 
{
  return SolveChol((Double_t*)b.GetMatrixArray(),invert);
}


//___________________________________________________________
Bool_t AliSymMatrix::SolveChol(Double_t *brhs, Double_t *bsol,Bool_t invert) 
{
  memcpy(bsol,brhs,GetSizeUsed()*sizeof(Double_t));
  return SolveChol(bsol,invert);  
}

//___________________________________________________________
Bool_t AliSymMatrix::SolveChol(TVectorD &brhs, TVectorD &bsol,Bool_t invert) 
{
  bsol = brhs;
  return SolveChol(bsol,invert);
}

//___________________________________________________________
void AliSymMatrix::AddRows(int nrows)
{
  if (nrows<1) return;
  Double_t **pnew = new Double_t*[nrows+fNrows];
  for (int ir=0;ir<fNrows;ir++) pnew[ir] = fElemsAdd[ir]; // copy old extra rows
  for (int ir=0;ir<nrows;ir++) {
    int ncl = GetSize()+1;
    pnew[fNrows] = new Double_t[ncl];
    memset(pnew[fNrows],0,ncl*sizeof(Double_t));
    fNrows++;
    fNrowIndex++;
    fRowLwb++;
  }
  delete[] fElemsAdd;
  fElemsAdd = pnew;
  //
}

//___________________________________________________________
void AliSymMatrix::Reset()
{
  // if additional rows exist, regularize it
  if (fElemsAdd) {
    delete[] fElems;
    for (int i=0;i<fNrows;i++) delete[] fElemsAdd[i]; 
    delete[] fElemsAdd; fElemsAdd = 0;
    fNcols = fRowLwb = fNrowIndex;
    fElems = new Double_t[GetSize()*(GetSize()+1)/2];
    fNrows = 0;
  }
  if (fElems) memset(fElems,0,GetSize()*(GetSize()+1)/2*sizeof(Double_t));
  //
}

//___________________________________________________________
/*
void AliSymMatrix::AddToRow(Int_t r, Double_t *valc,Int_t *indc,Int_t n)
{
  //   for (int i=n;i--;) {
  //     (*this)(indc[i],r) += valc[i];
  //   }
  //   return;

  double *row;
  if (r>=fNrowIndex) {
    AddRows(r-fNrowIndex+1); 
    row = &((fElemsAdd[r-fNcols])[0]);
  }
  else row = &fElems[GetIndex(r,0)];
  //
  int nadd = 0;
  for (int i=n;i--;) {
    if (indc[i]>r) continue;
    row[indc[i]] += valc[i];
    nadd++;
  }
  if (nadd == n) return;
  //
  // add to col>row
  for (int i=n;i--;) {
    if (indc[i]>r) (*this)(indc[i],r) += valc[i];
  }
  //
}
*/

//___________________________________________________________
Double_t* AliSymMatrix::GetRow(Int_t r)
{
  if (r>=GetSize()) {
    int nn = GetSize();
    AddRows(r-GetSize()+1); 
    printf("create %d of %d\n",r, nn);
    return &((fElemsAdd[r-GetSizeBooked()])[0]);
  }
  else return &fElems[GetIndex(r,0)];
}


//___________________________________________________________
int AliSymMatrix::SolveSpmInv(double *vecB, Bool_t stabilize)
{
  //   Solution a la MP1: gaussian eliminations
  ///  Obtain solution of a system of linear equations with symmetric matrix 
  ///  and the inverse (using 'singular-value friendly' GAUSS pivot)
  //

  Int_t nRank = 0;
  int iPivot;
  double vPivot = 0.;
  double eps = 1e-14;
  int nGlo = GetSizeUsed();
  bool   *bUnUsed = new bool[nGlo];
  double *rowMax,*colMax=0;
  rowMax  = new double[nGlo];
  //
  if (stabilize) {
    colMax   = new double[nGlo];
    for (Int_t i=nGlo; i--;) rowMax[i] = colMax[i] = 0.0;
    for (Int_t i=nGlo; i--;) for (Int_t j=i+1;j--;) { 
	double vl = TMath::Abs(Query(i,j));
	if (vl<DBL_MIN) continue;
	if (vl > rowMax[i]) rowMax[i] = vl; // Max elemt of row i
	if (vl > colMax[j]) colMax[j] = vl; // Max elemt of column j
	if (i==j) continue;
	if (vl > rowMax[j]) rowMax[j] = vl; // Max elemt of row j
	if (vl > colMax[i]) colMax[i] = vl; // Max elemt of column i
      }
    //
    for (Int_t i=nGlo; i--;) {
      if (TMath::Abs(rowMax[i])>DBL_MIN) rowMax[i] = 1./rowMax[i]; // Max elemt of row i
      if (TMath::Abs(colMax[i])>DBL_MIN) colMax[i] = 1./colMax[i]; // Max elemt of column i
    }
    //
  }
  //
  for (Int_t i=nGlo; i--;) bUnUsed[i] = true;
  //  
  if (!fgBuffer || fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
    delete fgBuffer; 
    try {
      fgBuffer = new AliSymMatrix(*this);
    }
    catch(bad_alloc&) {
      printf("Failed to allocate memory for matrix inversion buffer\n");
      return 0;
    }
  }
  else (*fgBuffer) = *this;
  //
  if (stabilize) for (int i=0;i<nGlo; i++) { // Small loop for matrix equilibration (gives a better conditioning) 
      for (int j=0;j<=i; j++) {
	double vl = Query(i,j);
	if (TMath::Abs(vl)>DBL_MIN) SetEl(i,j, TMath::Sqrt(rowMax[i])*vl*TMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
      }
      for (int j=i+1;j<nGlo;j++) {
	double vl = Query(j,i);
	if (TMath::Abs(vl)>DBL_MIN) fgBuffer->SetEl(j,i,TMath::Sqrt(rowMax[i])*vl*TMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
      }
    }
  //
  for (Int_t j=nGlo; j--;) fgBuffer->DiagElem(j) = TMath::Abs(QueryDiag(j)); // save diagonal elem absolute values 
  //
  for (Int_t i=0; i<nGlo; i++) {
    vPivot = 0.0;
    iPivot = -1;
    //
    for (Int_t j=0; j<nGlo; j++) { // First look for the pivot, ie max unused diagonal element       
      double vl;
      if (bUnUsed[j] && (TMath::Abs(vl=QueryDiag(j))>TMath::Max(TMath::Abs(vPivot),eps*fgBuffer->QueryDiag(j)))) {    
	vPivot = vl;
	iPivot = j;
      }
    }
    //
    if (iPivot >= 0) {   // pivot found          
      nRank++;
      bUnUsed[iPivot] = false; // This value is used
      vPivot = 1.0/vPivot;
      DiagElem(iPivot) = -vPivot; // Replace pivot by its inverse
      //
      for (Int_t j=0; j<nGlo; j++) {      
	for (Int_t jj=0; jj<nGlo; jj++) {  
	  if (j != iPivot && jj != iPivot) {// Other elements (!!! do them first as you use old matV[k][j]'s !!!)	  
	    double &r = j>=jj ? (*this)(j,jj) : (*fgBuffer)(jj,j);
	    r -= vPivot* ( j>iPivot  ? Query(j,iPivot)  : fgBuffer->Query(iPivot,j) )
	      *          ( iPivot>jj ? Query(iPivot,jj) : fgBuffer->Query(jj,iPivot));
	  }
	}
      }
      //
      for (Int_t j=0; j<nGlo; j++) if (j != iPivot) { // Pivot row or column elements 
	  (*this)(j,iPivot)     *= vPivot;
	  (*fgBuffer)(iPivot,j) *= vPivot;
	}
      //
    }
    else {  // No more pivot value (clear those elements)
      for (Int_t j=0; j<nGlo; j++) {
	if (bUnUsed[j]) {
	  vecB[j] = 0.0;
	  for (Int_t k=0; k<nGlo; k++) {
	    (*this)(j,k) = 0.;
	    if (j!=k) (*fgBuffer)(j,k) = 0;
	  }
	}
      }
      break;  // No more pivots anyway, stop here
    }
  }
  //
  for (Int_t i=0; i<nGlo; i++) for (Int_t j=0; j<nGlo; j++) {
      double vl = TMath::Sqrt(colMax[i])*TMath::Sqrt(rowMax[j]); // Correct matrix V
      if (i>=j) (*this)(i,j) *= vl;
      else      (*fgBuffer)(j,i) *= vl;
    }
  //
  for (Int_t j=0; j<nGlo; j++) {
    rowMax[j] = 0.0;
    for (Int_t jj=0; jj<nGlo; jj++) { // Reverse matrix elements
      double vl;
      if (j>=jj) vl = (*this)(j,jj)     = -Query(j,jj);
      else       vl = (*fgBuffer)(j,jj) = -fgBuffer->Query(j,jj);
      rowMax[j] += vl*vecB[jj];
    }		
  }
  
  for (Int_t j=0; j<nGlo; j++) {
    vecB[j] = rowMax[j]; // The final result
  }
  //
  delete [] bUnUsed;
  delete [] rowMax;
  if (stabilize) delete [] colMax;

  return nRank;
}
Commit	Line	Data
7c3070ec	1	/**********************************************************************************************/
	2	/* Fast symmetric matrix with dynamically expandable size. */
	3	/* Only part can be used for matrix operations. It is defined as: */
	4	/* fNCols: rows built by constructor (GetSizeBooked) */
	5	/* fNRows: number of rows added dynamically (automatically added on assignment to row) */
	6	/* GetNRowAdded */
	7	/* fNRowIndex: total size (fNCols+fNRows), GetSize */
	8	/* fRowLwb : actual size to used for given operation, by default = total size, GetSizeUsed */
	9	/* */
	10	/* Author: ruben.shahoyan@cern.ch */
	11	/* */
	12	/**********************************************************************************************/
8a9ab0eb	13	#include <stdlib.h>
	14	#include <stdio.h>
	15	#include <iostream>
7c3070ec	16	#include <float.h>
8a9ab0eb	17	//
7c3070ec	18	#include <TClass.h>
7c3070ec	19	#include <TMath.h>
8a9ab0eb	20	#include "AliSymMatrix.h"
7c3070ec	21	#include "AliLog.h"
8a9ab0eb	22	//
	23
	24	using namespace std;
	25
	26	ClassImp(AliSymMatrix)
	27
	28
	29	AliSymMatrix* AliSymMatrix::fgBuffer = 0;
	30	Int_t AliSymMatrix::fgCopyCnt = 0;
	31	//___________________________________________________________
	32	AliSymMatrix::AliSymMatrix()
	33	: fElems(0),fElemsAdd(0)
	34	{
	35	fSymmetric = kTRUE;
	36	fgCopyCnt++;
	37	}
	38
	39	//___________________________________________________________
	40	AliSymMatrix::AliSymMatrix(Int_t size)
	41	: AliMatrixSq(),fElems(0),fElemsAdd(0)
	42	{
	43	//
	44	fNrows = 0;
7c3070ec	45	fNrowIndex = fNcols = fRowLwb = size;
8a9ab0eb	46	fElems = new Double_t[fNcols*(fNcols+1)/2];
	47	fSymmetric = kTRUE;
	48	Reset();
	49	fgCopyCnt++;
	50	//
	51	}
	52
	53	//___________________________________________________________
	54	AliSymMatrix::AliSymMatrix(const AliSymMatrix &src)
	55	: AliMatrixSq(src),fElems(0),fElemsAdd(0)
	56	{
	57	fNrowIndex = fNcols = src.GetSize();
	58	fNrows = 0;
7c3070ec	59	fRowLwb = src.GetSizeUsed();
8a9ab0eb	60	if (fNcols) {
	61	int nmainel = fNcols*(fNcols+1)/2;
	62	fElems = new Double_t[nmainel];
	63	nmainel = src.fNcols*(src.fNcols+1)/2;
	64	memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
7c3070ec	65	if (src.GetSizeAdded()) { // transfer extra rows to main matrix
8a9ab0eb	66	Double_t *pnt = fElems + nmainel;
7c3070ec	67	int ncl = src.GetSizeBooked() + 1;
7c3070ec	68	for (int ir=0;ir<src.GetSizeAdded();ir++) {
8a9ab0eb	69	memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
	70	pnt += ncl;
	71	ncl++;
	72	}
	73	}
	74	}
	75	else fElems = 0;
	76	fElemsAdd = 0;
	77	fgCopyCnt++;
	78	//
	79	}
	80
	81	//___________________________________________________________
	82	AliSymMatrix::~AliSymMatrix()
	83	{
	84	Clear();
	85	if (--fgCopyCnt < 1 && fgBuffer) {delete fgBuffer; fgBuffer = 0;}
	86	}
	87
	88	//___________________________________________________________
	89	AliSymMatrix& AliSymMatrix::operator=(const AliSymMatrix& src)
	90	{
	91	//
	92	if (this != &src) {
	93	TObject::operator=(src);
7c3070ec	94	if (GetSizeBooked()!=src.GetSizeBooked() && GetSizeAdded()!=src.GetSizeAdded()) {
8a9ab0eb	95	// recreate the matrix
8a9ab0eb	96	if (fElems) delete[] fElems;
7c3070ec	97	for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i];
8a9ab0eb	98	delete[] fElemsAdd;
8a9ab0eb	99	//
de34b538	100	fNrowIndex = src.GetSize();
de34b538	101	fNcols = src.GetSize();
8a9ab0eb	102	fNrows = 0;
7c3070ec	103	fRowLwb = src.GetSizeUsed();
	104	fElems = new Double_t[GetSize()*(GetSize()+1)/2];
	105	int nmainel = src.GetSizeBooked()*(src.GetSizeBooked()+1);
8a9ab0eb	106	memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
7c3070ec	107	if (src.GetSizeAdded()) { // transfer extra rows to main matrix
8a9ab0eb	108	Double_t pnt = fElems + nmainelsizeof(Double_t);
7c3070ec	109	int ncl = src.GetSizeBooked() + 1;
7c3070ec	110	for (int ir=0;ir<src.GetSizeAdded();ir++) {
8a9ab0eb	111	ncl += ir;
	112	memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
	113	pnt += ncl*sizeof(Double_t);
	114	}
	115	}
	116	//
	117	}
	118	else {
7c3070ec	119	memcpy(fElems,src.fElems,GetSizeBooked()(GetSizeBooked()+1)/2sizeof(Double_t));
	120	int ncl = GetSizeBooked() + 1;
	121	for (int ir=0;ir<GetSizeAdded();ir++) { // dynamic rows
8a9ab0eb	122	ncl += ir;
	123	memcpy(fElemsAdd[ir],src.fElemsAdd[ir],ncl*sizeof(Double_t));
	124	}
	125	}
	126	}
	127	//
	128	return *this;
	129	}
	130
7c3070ec	131	//___________________________________________________________
	132	AliSymMatrix& AliSymMatrix::operator+=(const AliSymMatrix& src)
	133	{
	134	//
	135	if (GetSizeUsed() != src.GetSizeUsed()) {
	136	AliError("Matrix sizes are different");
	137	return *this;
	138	}
	139	for (int i=0;i<GetSizeUsed();i++) for (int j=i;j<GetSizeUsed();j++) (*this)(j,i) += src(j,i);
	140	return *this;
	141	}
	142
8a9ab0eb	143	//___________________________________________________________
	144	void AliSymMatrix::Clear(Option_t*)
	145	{
	146	if (fElems) {delete[] fElems; fElems = 0;}
	147	//
	148	if (fElemsAdd) {
7c3070ec	149	for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i];
8a9ab0eb	150	delete[] fElemsAdd;
	151	fElemsAdd = 0;
	152	}
7c3070ec	153	fNrowIndex = fNcols = fNrows = fRowLwb = 0;
8a9ab0eb	154	//
	155	}
	156
	157	//___________________________________________________________
	158	Float_t AliSymMatrix::GetDensity() const
	159	{
	160	// get fraction of non-zero elements
	161	Int_t nel = 0;
7c3070ec	162	for (int i=GetSizeUsed();i--;) for (int j=i+1;j--;) if (TMath::Abs(GetEl(i,j))>DBL_MIN) nel++;
7c3070ec	163	return 2.nel/( (GetSizeUsed()+1)GetSizeUsed() );
8a9ab0eb	164	}
	165
	166	//___________________________________________________________
	167	void AliSymMatrix::Print(Option_t* option) const
	168	{
7c3070ec	169	printf("Symmetric Matrix: Size = %d (%d rows added dynamically), %d used\n",GetSize(),GetSizeAdded(),GetSizeUsed());
8a9ab0eb	170	TString opt = option; opt.ToLower();
	171	if (opt.IsNull()) return;
	172	opt = "%"; opt += 1+int(TMath::Log10(double(GetSize()))); opt+="d\|";
7c3070ec	173	for (Int_t i=0;i<GetSizeUsed();i++) {
8a9ab0eb	174	printf(opt,i);
	175	for (Int_t j=0;j<=i;j++) printf("%+.3e\|",GetEl(i,j));
	176	printf("\n");
	177	}
	178	}
	179
	180	//___________________________________________________________
	181	void AliSymMatrix::MultiplyByVec(Double_t vecIn,Double_t vecOut) const
	182	{
	183	// fill vecOut by matrix*vecIn
	184	// vector should be of the same size as the matrix
7c3070ec	185	for (int i=GetSizeUsed();i--;) {
8a9ab0eb	186	vecOut[i] = 0.0;
7c3070ec	187	for (int j=GetSizeUsed();j--;) vecOut[i] += vecIn[j]*GetEl(i,j);
8a9ab0eb	188	}
	189	//
	190	}
	191
	192	//___________________________________________________________
	193	AliSymMatrix* AliSymMatrix::DecomposeChol()
	194	{
	195	// Return a matrix with Choleski decomposition
de34b538	196	// Adopted from Numerical Recipes in C, ch.2-9, http://www.nr.com
	197	// consturcts Cholesky decomposition of SYMMETRIC and
	198	// POSITIVELY-DEFINED matrix a (a=L*Lt)
	199	// Only upper triangle of the matrix has to be filled.
	200	// In opposite to function from the book, the matrix is modified:
	201	// lower triangle and diagonal are refilled.
8a9ab0eb	202	//
7c3070ec	203	if (!fgBuffer \|\| fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
8a9ab0eb	204	delete fgBuffer;
	205	try {
	206	fgBuffer = new AliSymMatrix(*this);
	207	}
	208	catch(bad_alloc&) {
	209	printf("Failed to allocate memory for Choleski decompostions\n");
	210	return 0;
	211	}
	212	}
	213	else (fgBuffer) = this;
	214	//
	215	AliSymMatrix& mchol = *fgBuffer;
	216	//
7c3070ec	217	for (int i=0;i<GetSizeUsed();i++) {
de34b538	218	Double_t *rowi = mchol.GetRow(i);
7c3070ec	219	for (int j=i;j<GetSizeUsed();j++) {
de34b538	220	Double_t *rowj = mchol.GetRow(j);
	221	double sum = rowj[i];
	222	for (int k=i-1;k>=0;k--) if (rowi[k]&&rowj[k]) sum -= rowi[k]*rowj[k];
8a9ab0eb	223	if (i == j) {
	224	if (sum <= 0.0) { // not positive-definite
	225	printf("The matrix is not positive definite [%e]\n"
	226	"Choleski decomposition is not possible\n",sum);
	227	return 0;
	228	}
de34b538	229	rowi[i] = TMath::Sqrt(sum);
8a9ab0eb	230	//
de34b538	231	} else rowj[i] = sum/rowi[i];
8a9ab0eb	232	}
	233	}
	234	return fgBuffer;
	235	}
	236
	237	//___________________________________________________________
	238	Bool_t AliSymMatrix::InvertChol()
	239	{
	240	// Invert matrix using Choleski decomposition
	241	//
	242	AliSymMatrix* mchol = DecomposeChol();
	243	if (!mchol) {
	244	printf("Failed to invert the matrix\n");
	245	return kFALSE;
	246	}
	247	//
	248	InvertChol(mchol);
	249	return kTRUE;
	250	//
	251	}
de34b538	252
8a9ab0eb	253	//___________________________________________________________
	254	void AliSymMatrix::InvertChol(AliSymMatrix* pmchol)
	255	{
	256	// Invert matrix using Choleski decomposition, provided the Cholseki's L matrix
5d88242b	257	//
8a9ab0eb	258	Double_t sum;
	259	AliSymMatrix& mchol = *pmchol;
	260	//
	261	// Invert decomposed triangular L matrix (Lower triangle is filled)
7c3070ec	262	for (int i=0;i<GetSizeUsed();i++) {
8a9ab0eb	263	mchol(i,i) = 1.0/mchol(i,i);
7c3070ec	264	for (int j=i+1;j<GetSizeUsed();j++) {
de34b538	265	Double_t *rowj = mchol.GetRow(j);
8a9ab0eb	266	sum = 0.0;
de34b538	267	for (int k=i;k<j;k++) if (rowj[k]) {
	268	double &mki = mchol(k,i); if (mki) sum -= rowj[k]*mki;
	269	}
	270	rowj[i] = sum/rowj[j];
8a9ab0eb	271	}
	272	}
	273	//
	274	// take product of the inverted Choleski L matrix with its transposed
7c3070ec	275	for (int i=GetSizeUsed();i--;) {
8a9ab0eb	276	for (int j=i+1;j--;) {
8a9ab0eb	277	sum = 0;
7c3070ec	278	for (int k=i;k<GetSizeUsed();k++) {
de34b538	279	double &mik = mchol(i,k);
	280	if (mik) {
	281	double &mjk = mchol(j,k);
	282	if (mjk) sum += mik*mjk;
	283	}
	284	}
8a9ab0eb	285	(*this)(j,i) = sum;
	286	}
	287	}
	288	//
	289	}
	290
	291
	292	//___________________________________________________________
	293	Bool_t AliSymMatrix::SolveChol(Double_t *b, Bool_t invert)
	294	{
de34b538	295	// Adopted from Numerical Recipes in C, ch.2-9, http://www.nr.com
	296	// Solves the set of n linear equations A x = b,
	297	// where a is a positive-definite symmetric matrix.
	298	// a[1..n][1..n] is the output of the routine CholDecomposw.
	299	// Only the lower triangle of a is accessed. b[1..n] is input as the
	300	// right-hand side vector. The solution vector is returned in b[1..n].
8a9ab0eb	301	//
	302	Int_t i,k;
	303	Double_t sum;
	304	//
	305	AliSymMatrix *pmchol = DecomposeChol();
	306	if (!pmchol) {
	307	printf("SolveChol failed\n");
5d88242b	308	// Print("l");
8a9ab0eb	309	return kFALSE;
	310	}
	311	AliSymMatrix& mchol = *pmchol;
	312	//
7c3070ec	313	for (i=0;i<GetSizeUsed();i++) {
de34b538	314	Double_t *rowi = mchol.GetRow(i);
	315	for (sum=b[i],k=i-1;k>=0;k--) if (rowi[k]&&b[k]) sum -= rowi[k]*b[k];
	316	b[i]=sum/rowi[i];
8a9ab0eb	317	}
de34b538	318	//
7c3070ec	319	for (i=GetSizeUsed()-1;i>=0;i--) {
7c3070ec	320	for (sum=b[i],k=i+1;k<GetSizeUsed();k++) if (b[k]) {
de34b538	321	double &mki=mchol(k,i); if (mki) sum -= mki*b[k];
de34b538	322	}
8a9ab0eb	323	b[i]=sum/mchol(i,i);
	324	}
	325	//
	326	if (invert) InvertChol(pmchol);
	327	return kTRUE;
	328	//
	329	}
	330
	331	//___________________________________________________________
	332	Bool_t AliSymMatrix::SolveChol(TVectorD &b, Bool_t invert)
	333	{
	334	return SolveChol((Double_t*)b.GetMatrixArray(),invert);
	335	}
	336
	337
	338	//___________________________________________________________
	339	Bool_t AliSymMatrix::SolveChol(Double_t brhs, Double_t bsol,Bool_t invert)
	340	{
7c3070ec	341	memcpy(bsol,brhs,GetSizeUsed()*sizeof(Double_t));
8a9ab0eb	342	return SolveChol(bsol,invert);
	343	}
	344
	345	//___________________________________________________________
	346	Bool_t AliSymMatrix::SolveChol(TVectorD &brhs, TVectorD &bsol,Bool_t invert)
	347	{
	348	bsol = brhs;
	349	return SolveChol(bsol,invert);
	350	}
	351
	352	//___________________________________________________________
	353	void AliSymMatrix::AddRows(int nrows)
	354	{
	355	if (nrows<1) return;
	356	Double_t *pnew = new Double_t[nrows+fNrows];
	357	for (int ir=0;ir<fNrows;ir++) pnew[ir] = fElemsAdd[ir]; // copy old extra rows
	358	for (int ir=0;ir<nrows;ir++) {
	359	int ncl = GetSize()+1;
	360	pnew[fNrows] = new Double_t[ncl];
	361	memset(pnew[fNrows],0,ncl*sizeof(Double_t));
	362	fNrows++;
	363	fNrowIndex++;
7c3070ec	364	fRowLwb++;
8a9ab0eb	365	}
	366	delete[] fElemsAdd;
	367	fElemsAdd = pnew;
	368	//
	369	}
	370
	371	//___________________________________________________________
	372	void AliSymMatrix::Reset()
	373	{
	374	// if additional rows exist, regularize it
	375	if (fElemsAdd) {
	376	delete[] fElems;
	377	for (int i=0;i<fNrows;i++) delete[] fElemsAdd[i];
	378	delete[] fElemsAdd; fElemsAdd = 0;
7c3070ec	379	fNcols = fRowLwb = fNrowIndex;
7c3070ec	380	fElems = new Double_t[GetSize()*(GetSize()+1)/2];
8a9ab0eb	381	fNrows = 0;
8a9ab0eb	382	}
7c3070ec	383	if (fElems) memset(fElems,0,GetSize()(GetSize()+1)/2sizeof(Double_t));
8a9ab0eb	384	//
	385	}
	386
de34b538	387	//___________________________________________________________
	388	/*
	389	void AliSymMatrix::AddToRow(Int_t r, Double_t valc,Int_t indc,Int_t n)
	390	{
	391	// for (int i=n;i--;) {
	392	// (*this)(indc[i],r) += valc[i];
	393	// }
	394	// return;
	395
	396	double *row;
	397	if (r>=fNrowIndex) {
	398	AddRows(r-fNrowIndex+1);
	399	row = &((fElemsAdd[r-fNcols])[0]);
	400	}
	401	else row = &fElems[GetIndex(r,0)];
	402	//
	403	int nadd = 0;
	404	for (int i=n;i--;) {
	405	if (indc[i]>r) continue;
	406	row[indc[i]] += valc[i];
	407	nadd++;
	408	}
	409	if (nadd == n) return;
	410	//
	411	// add to col>row
	412	for (int i=n;i--;) {
	413	if (indc[i]>r) (*this)(indc[i],r) += valc[i];
	414	}
	415	//
	416	}
	417	*/
	418
	419	//___________________________________________________________
	420	Double_t* AliSymMatrix::GetRow(Int_t r)
	421	{
7c3070ec	422	if (r>=GetSize()) {
	423	int nn = GetSize();
	424	AddRows(r-GetSize()+1);
de34b538	425	printf("create %d of %d\n",r, nn);
7c3070ec	426	return &((fElemsAdd[r-GetSizeBooked()])[0]);
de34b538	427	}
	428	else return &fElems[GetIndex(r,0)];
	429	}
	430
	431
8a9ab0eb	432	//___________________________________________________________
	433	int AliSymMatrix::SolveSpmInv(double *vecB, Bool_t stabilize)
	434	{
	435	// Solution a la MP1: gaussian eliminations
	436	/// Obtain solution of a system of linear equations with symmetric matrix
	437	/// and the inverse (using 'singular-value friendly' GAUSS pivot)
	438	//
	439
	440	Int_t nRank = 0;
	441	int iPivot;
	442	double vPivot = 0.;
7c3070ec	443	double eps = 1e-14;
7c3070ec	444	int nGlo = GetSizeUsed();
8a9ab0eb	445	bool *bUnUsed = new bool[nGlo];
	446	double rowMax,colMax=0;
	447	rowMax = new double[nGlo];
	448	//
	449	if (stabilize) {
	450	colMax = new double[nGlo];
	451	for (Int_t i=nGlo; i--;) rowMax[i] = colMax[i] = 0.0;
	452	for (Int_t i=nGlo; i--;) for (Int_t j=i+1;j--;) {
de34b538	453	double vl = TMath::Abs(Query(i,j));
7c3070ec	454	if (vl<DBL_MIN) continue;
8a9ab0eb	455	if (vl > rowMax[i]) rowMax[i] = vl; // Max elemt of row i
	456	if (vl > colMax[j]) colMax[j] = vl; // Max elemt of column j
	457	if (i==j) continue;
	458	if (vl > rowMax[j]) rowMax[j] = vl; // Max elemt of row j
	459	if (vl > colMax[i]) colMax[i] = vl; // Max elemt of column i
	460	}
	461	//
	462	for (Int_t i=nGlo; i--;) {
7c3070ec	463	if (TMath::Abs(rowMax[i])>DBL_MIN) rowMax[i] = 1./rowMax[i]; // Max elemt of row i
7c3070ec	464	if (TMath::Abs(colMax[i])>DBL_MIN) colMax[i] = 1./colMax[i]; // Max elemt of column i
8a9ab0eb	465	}
	466	//
	467	}
	468	//
	469	for (Int_t i=nGlo; i--;) bUnUsed[i] = true;
	470	//
7c3070ec	471	if (!fgBuffer \|\| fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
8a9ab0eb	472	delete fgBuffer;
	473	try {
	474	fgBuffer = new AliSymMatrix(*this);
	475	}
	476	catch(bad_alloc&) {
	477	printf("Failed to allocate memory for matrix inversion buffer\n");
	478	return 0;
	479	}
	480	}
	481	else (fgBuffer) = this;
	482	//
	483	if (stabilize) for (int i=0;i<nGlo; i++) { // Small loop for matrix equilibration (gives a better conditioning)
	484	for (int j=0;j<=i; j++) {
de34b538	485	double vl = Query(i,j);
7c3070ec	486	if (TMath::Abs(vl)>DBL_MIN) SetEl(i,j, TMath::Sqrt(rowMax[i])vlTMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
8a9ab0eb	487	}
8a9ab0eb	488	for (int j=i+1;j<nGlo;j++) {
de34b538	489	double vl = Query(j,i);
7c3070ec	490	if (TMath::Abs(vl)>DBL_MIN) fgBuffer->SetEl(j,i,TMath::Sqrt(rowMax[i])vlTMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
8a9ab0eb	491	}
	492	}
	493	//
de34b538	494	for (Int_t j=nGlo; j--;) fgBuffer->DiagElem(j) = TMath::Abs(QueryDiag(j)); // save diagonal elem absolute values
8a9ab0eb	495	//
	496	for (Int_t i=0; i<nGlo; i++) {
	497	vPivot = 0.0;
	498	iPivot = -1;
	499	//
	500	for (Int_t j=0; j<nGlo; j++) { // First look for the pivot, ie max unused diagonal element
	501	double vl;
de34b538	502	if (bUnUsed[j] && (TMath::Abs(vl=QueryDiag(j))>TMath::Max(TMath::Abs(vPivot),eps*fgBuffer->QueryDiag(j)))) {
8a9ab0eb	503	vPivot = vl;
	504	iPivot = j;
	505	}
	506	}
	507	//
	508	if (iPivot >= 0) { // pivot found
	509	nRank++;
	510	bUnUsed[iPivot] = false; // This value is used
	511	vPivot = 1.0/vPivot;
	512	DiagElem(iPivot) = -vPivot; // Replace pivot by its inverse
	513	//
	514	for (Int_t j=0; j<nGlo; j++) {
	515	for (Int_t jj=0; jj<nGlo; jj++) {
	516	if (j != iPivot && jj != iPivot) {// Other elements (!!! do them first as you use old matV[k][j]'s !!!)
	517	double &r = j>=jj ? (this)(j,jj) : (fgBuffer)(jj,j);
de34b538	518	r -= vPivot* ( j>iPivot ? Query(j,iPivot) : fgBuffer->Query(iPivot,j) )
de34b538	519	* ( iPivot>jj ? Query(iPivot,jj) : fgBuffer->Query(jj,iPivot));
8a9ab0eb	520	}
	521	}
	522	}
	523	//
	524	for (Int_t j=0; j<nGlo; j++) if (j != iPivot) { // Pivot row or column elements
	525	(this)(j,iPivot) = vPivot;
	526	(fgBuffer)(iPivot,j) = vPivot;
	527	}
	528	//
	529	}
	530	else { // No more pivot value (clear those elements)
	531	for (Int_t j=0; j<nGlo; j++) {
	532	if (bUnUsed[j]) {
	533	vecB[j] = 0.0;
	534	for (Int_t k=0; k<nGlo; k++) {
	535	(*this)(j,k) = 0.;
	536	if (j!=k) (*fgBuffer)(j,k) = 0;
	537	}
	538	}
	539	}
	540	break; // No more pivots anyway, stop here
	541	}
	542	}
	543	//
	544	for (Int_t i=0; i<nGlo; i++) for (Int_t j=0; j<nGlo; j++) {
	545	double vl = TMath::Sqrt(colMax[i])*TMath::Sqrt(rowMax[j]); // Correct matrix V
	546	if (i>=j) (this)(i,j) = vl;
	547	else (fgBuffer)(j,i) = vl;
	548	}
	549	//
	550	for (Int_t j=0; j<nGlo; j++) {
	551	rowMax[j] = 0.0;
	552	for (Int_t jj=0; jj<nGlo; jj++) { // Reverse matrix elements
	553	double vl;
de34b538	554	if (j>=jj) vl = (*this)(j,jj) = -Query(j,jj);
de34b538	555	else vl = (*fgBuffer)(j,jj) = -fgBuffer->Query(j,jj);
8a9ab0eb	556	rowMax[j] += vl*vecB[jj];
	557	}
	558	}
	559
	560	for (Int_t j=0; j<nGlo; j++) {
	561	vecB[j] = rowMax[j]; // The final result
	562	}
	563	//
	564	delete [] bUnUsed;
	565	delete [] rowMax;
	566	if (stabilize) delete [] colMax;
	567
	568	return nRank;
	569	}
5d88242b	570
5d88242b	571