[u/mrichter/AliRoot.git] / STEER / 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 <string.h>
//
#include <TClass.h>
#include <TMath.h>
#include "AliSymMatrix.h"
#include "AliLog.h"
//

ClassImp(AliSymMatrix)


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

//___________________________________________________________
AliSymMatrix::AliSymMatrix(Int_t size)
  : AliMatrixSq(),fElems(0),fElemsAdd(0)
{
  //constructor for matrix with defined size
  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)
{
  // copy constructor
  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)
{
  // assignment operator
  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)
{
  // add operator
  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*)
{
  // clear dynamic part
  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 (!IsZero(GetEl(i,j))) nel++;
  return 2.*nel/( (GetSizeUsed()+1)*GetSizeUsed() );
}

//___________________________________________________________
void AliSymMatrix::Print(Option_t* option) const
{
  // print itself
  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(const 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; 
    fgBuffer = new AliSymMatrix(*this);
  }
  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
	  AliInfo(Form("The matrix is not positive definite [%e]\n"
		       "Choleski decomposition is not possible",sum));
	  Print("l");
	  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) {
    AliInfo("Failed to invert the matrix");
    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) {
    AliInfo("SolveChol failed");
    //    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(const TVectorD &brhs, TVectorD &bsol,Bool_t invert) 
{
  bsol = brhs;
  return SolveChol(bsol,invert);
}

//___________________________________________________________
void AliSymMatrix::AddRows(int nrows)
{
  // add empty rows
  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)
{
  // get pointer on the row
  if (r>=GetSize()) {
    int nn = GetSize();
    AddRows(r-GetSize()+1); 
    AliDebug(2,Form("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 (IsZero(vl)) 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 (!IsZero(rowMax[i])) rowMax[i] = 1./rowMax[i]; // Max elemt of row i
      if (!IsZero(colMax[i])) 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; 
    fgBuffer = new AliSymMatrix(*this);
  }
  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 (!IsZero(vl)) 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 (!IsZero(vl)) 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
    }
  }
  //
  if (stabilize) 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>
68f76645	17	#include <string.h>
8a9ab0eb	18	//
7c3070ec	19	#include <TClass.h>
7c3070ec	20	#include <TMath.h>
8a9ab0eb	21	#include "AliSymMatrix.h"
7c3070ec	22	#include "AliLog.h"
8a9ab0eb	23	//
8a9ab0eb	24
8a9ab0eb	25	ClassImp(AliSymMatrix)
	26
	27
	28	AliSymMatrix* AliSymMatrix::fgBuffer = 0;
	29	Int_t AliSymMatrix::fgCopyCnt = 0;
	30	//___________________________________________________________
	31	AliSymMatrix::AliSymMatrix()
	32	: fElems(0),fElemsAdd(0)
	33	{
68f76645	34	// default constructor
8a9ab0eb	35	fSymmetric = kTRUE;
	36	fgCopyCnt++;
	37	}
	38
	39	//___________________________________________________________
	40	AliSymMatrix::AliSymMatrix(Int_t size)
	41	: AliMatrixSq(),fElems(0),fElemsAdd(0)
	42	{
68f76645	43	//constructor for matrix with defined size
8a9ab0eb	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	{
68f76645	57	// copy constructor
8a9ab0eb	58	fNrowIndex = fNcols = src.GetSize();
8a9ab0eb	59	fNrows = 0;
7c3070ec	60	fRowLwb = src.GetSizeUsed();
8a9ab0eb	61	if (fNcols) {
	62	int nmainel = fNcols*(fNcols+1)/2;
	63	fElems = new Double_t[nmainel];
	64	nmainel = src.fNcols*(src.fNcols+1)/2;
	65	memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
7c3070ec	66	if (src.GetSizeAdded()) { // transfer extra rows to main matrix
8a9ab0eb	67	Double_t *pnt = fElems + nmainel;
7c3070ec	68	int ncl = src.GetSizeBooked() + 1;
7c3070ec	69	for (int ir=0;ir<src.GetSizeAdded();ir++) {
8a9ab0eb	70	memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
	71	pnt += ncl;
	72	ncl++;
	73	}
	74	}
	75	}
	76	else fElems = 0;
	77	fElemsAdd = 0;
	78	fgCopyCnt++;
	79	//
	80	}
	81
	82	//___________________________________________________________
	83	AliSymMatrix::~AliSymMatrix()
	84	{
	85	Clear();
	86	if (--fgCopyCnt < 1 && fgBuffer) {delete fgBuffer; fgBuffer = 0;}
	87	}
	88
	89	//___________________________________________________________
	90	AliSymMatrix& AliSymMatrix::operator=(const AliSymMatrix& src)
	91	{
68f76645	92	// assignment operator
8a9ab0eb	93	if (this != &src) {
8a9ab0eb	94	TObject::operator=(src);
7c3070ec	95	if (GetSizeBooked()!=src.GetSizeBooked() && GetSizeAdded()!=src.GetSizeAdded()) {
8a9ab0eb	96	// recreate the matrix
8a9ab0eb	97	if (fElems) delete[] fElems;
7c3070ec	98	for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i];
8a9ab0eb	99	delete[] fElemsAdd;
8a9ab0eb	100	//
de34b538	101	fNrowIndex = src.GetSize();
de34b538	102	fNcols = src.GetSize();
8a9ab0eb	103	fNrows = 0;
7c3070ec	104	fRowLwb = src.GetSizeUsed();
	105	fElems = new Double_t[GetSize()*(GetSize()+1)/2];
	106	int nmainel = src.GetSizeBooked()*(src.GetSizeBooked()+1);
8a9ab0eb	107	memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
7c3070ec	108	if (src.GetSizeAdded()) { // transfer extra rows to main matrix
c8f37c50	109	Double_t pnt = fElems + nmainel;//sizeof(Double_t);
7c3070ec	110	int ncl = src.GetSizeBooked() + 1;
7c3070ec	111	for (int ir=0;ir<src.GetSizeAdded();ir++) {
8a9ab0eb	112	ncl += ir;
8a9ab0eb	113	memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
c8f37c50	114	pnt += ncl;//*sizeof(Double_t);
8a9ab0eb	115	}
	116	}
	117	//
	118	}
	119	else {
7c3070ec	120	memcpy(fElems,src.fElems,GetSizeBooked()(GetSizeBooked()+1)/2sizeof(Double_t));
	121	int ncl = GetSizeBooked() + 1;
	122	for (int ir=0;ir<GetSizeAdded();ir++) { // dynamic rows
8a9ab0eb	123	ncl += ir;
	124	memcpy(fElemsAdd[ir],src.fElemsAdd[ir],ncl*sizeof(Double_t));
	125	}
	126	}
	127	}
	128	//
	129	return *this;
	130	}
	131
7c3070ec	132	//___________________________________________________________
	133	AliSymMatrix& AliSymMatrix::operator+=(const AliSymMatrix& src)
	134	{
68f76645	135	// add operator
7c3070ec	136	if (GetSizeUsed() != src.GetSizeUsed()) {
	137	AliError("Matrix sizes are different");
	138	return *this;
	139	}
	140	for (int i=0;i<GetSizeUsed();i++) for (int j=i;j<GetSizeUsed();j++) (*this)(j,i) += src(j,i);
	141	return *this;
	142	}
	143
8a9ab0eb	144	//___________________________________________________________
	145	void AliSymMatrix::Clear(Option_t*)
	146	{
68f76645	147	// clear dynamic part
8a9ab0eb	148	if (fElems) {delete[] fElems; fElems = 0;}
	149	//
	150	if (fElemsAdd) {
7c3070ec	151	for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i];
8a9ab0eb	152	delete[] fElemsAdd;
	153	fElemsAdd = 0;
	154	}
7c3070ec	155	fNrowIndex = fNcols = fNrows = fRowLwb = 0;
8a9ab0eb	156	//
	157	}
	158
	159	//___________________________________________________________
	160	Float_t AliSymMatrix::GetDensity() const
	161	{
	162	// get fraction of non-zero elements
	163	Int_t nel = 0;
7c185459	164	for (int i=GetSizeUsed();i--;) for (int j=i+1;j--;) if (!IsZero(GetEl(i,j))) nel++;
7c3070ec	165	return 2.nel/( (GetSizeUsed()+1)GetSizeUsed() );
8a9ab0eb	166	}
	167
	168	//___________________________________________________________
	169	void AliSymMatrix::Print(Option_t* option) const
	170	{
68f76645	171	// print itself
7c3070ec	172	printf("Symmetric Matrix: Size = %d (%d rows added dynamically), %d used\n",GetSize(),GetSizeAdded(),GetSizeUsed());
8a9ab0eb	173	TString opt = option; opt.ToLower();
	174	if (opt.IsNull()) return;
	175	opt = "%"; opt += 1+int(TMath::Log10(double(GetSize()))); opt+="d\|";
7c3070ec	176	for (Int_t i=0;i<GetSizeUsed();i++) {
8a9ab0eb	177	printf(opt,i);
	178	for (Int_t j=0;j<=i;j++) printf("%+.3e\|",GetEl(i,j));
	179	printf("\n");
	180	}
	181	}
	182
	183	//___________________________________________________________
551c9e69	184	void AliSymMatrix::MultiplyByVec(const Double_t vecIn,Double_t vecOut) const
8a9ab0eb	185	{
	186	// fill vecOut by matrix*vecIn
	187	// vector should be of the same size as the matrix
7c3070ec	188	for (int i=GetSizeUsed();i--;) {
8a9ab0eb	189	vecOut[i] = 0.0;
7c3070ec	190	for (int j=GetSizeUsed();j--;) vecOut[i] += vecIn[j]*GetEl(i,j);
8a9ab0eb	191	}
	192	//
	193	}
	194
	195	//___________________________________________________________
	196	AliSymMatrix* AliSymMatrix::DecomposeChol()
	197	{
	198	// Return a matrix with Choleski decomposition
de34b538	199	// Adopted from Numerical Recipes in C, ch.2-9, http://www.nr.com
	200	// consturcts Cholesky decomposition of SYMMETRIC and
	201	// POSITIVELY-DEFINED matrix a (a=L*Lt)
	202	// Only upper triangle of the matrix has to be filled.
	203	// In opposite to function from the book, the matrix is modified:
	204	// lower triangle and diagonal are refilled.
8a9ab0eb	205	//
7c3070ec	206	if (!fgBuffer \|\| fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
8a9ab0eb	207	delete fgBuffer;
3c5b4cc8	208	fgBuffer = new AliSymMatrix(*this);
8a9ab0eb	209	}
	210	else (fgBuffer) = this;
	211	//
	212	AliSymMatrix& mchol = *fgBuffer;
	213	//
7c3070ec	214	for (int i=0;i<GetSizeUsed();i++) {
de34b538	215	Double_t *rowi = mchol.GetRow(i);
7c3070ec	216	for (int j=i;j<GetSizeUsed();j++) {
de34b538	217	Double_t *rowj = mchol.GetRow(j);
	218	double sum = rowj[i];
	219	for (int k=i-1;k>=0;k--) if (rowi[k]&&rowj[k]) sum -= rowi[k]*rowj[k];
8a9ab0eb	220	if (i == j) {
8a9ab0eb	221	if (sum <= 0.0) { // not positive-definite
7c185459	222	AliInfo(Form("The matrix is not positive definite [%e]\n"
	223	"Choleski decomposition is not possible",sum));
	224	Print("l");
8a9ab0eb	225	return 0;
8a9ab0eb	226	}
de34b538	227	rowi[i] = TMath::Sqrt(sum);
8a9ab0eb	228	//
de34b538	229	} else rowj[i] = sum/rowi[i];
8a9ab0eb	230	}
	231	}
	232	return fgBuffer;
	233	}
	234
	235	//___________________________________________________________
	236	Bool_t AliSymMatrix::InvertChol()
	237	{
	238	// Invert matrix using Choleski decomposition
	239	//
	240	AliSymMatrix* mchol = DecomposeChol();
	241	if (!mchol) {
7c185459	242	AliInfo("Failed to invert the matrix");
8a9ab0eb	243	return kFALSE;
	244	}
	245	//
	246	InvertChol(mchol);
	247	return kTRUE;
	248	//
	249	}
de34b538	250
8a9ab0eb	251	//___________________________________________________________
	252	void AliSymMatrix::InvertChol(AliSymMatrix* pmchol)
	253	{
	254	// Invert matrix using Choleski decomposition, provided the Cholseki's L matrix
5d88242b	255	//
8a9ab0eb	256	Double_t sum;
	257	AliSymMatrix& mchol = *pmchol;
	258	//
	259	// Invert decomposed triangular L matrix (Lower triangle is filled)
7c3070ec	260	for (int i=0;i<GetSizeUsed();i++) {
8a9ab0eb	261	mchol(i,i) = 1.0/mchol(i,i);
7c3070ec	262	for (int j=i+1;j<GetSizeUsed();j++) {
de34b538	263	Double_t *rowj = mchol.GetRow(j);
8a9ab0eb	264	sum = 0.0;
de34b538	265	for (int k=i;k<j;k++) if (rowj[k]) {
	266	double &mki = mchol(k,i); if (mki) sum -= rowj[k]*mki;
	267	}
	268	rowj[i] = sum/rowj[j];
8a9ab0eb	269	}
	270	}
	271	//
	272	// take product of the inverted Choleski L matrix with its transposed
7c3070ec	273	for (int i=GetSizeUsed();i--;) {
8a9ab0eb	274	for (int j=i+1;j--;) {
8a9ab0eb	275	sum = 0;
7c3070ec	276	for (int k=i;k<GetSizeUsed();k++) {
de34b538	277	double &mik = mchol(i,k);
	278	if (mik) {
	279	double &mjk = mchol(j,k);
	280	if (mjk) sum += mik*mjk;
	281	}
	282	}
8a9ab0eb	283	(*this)(j,i) = sum;
	284	}
	285	}
	286	//
	287	}
	288
	289
	290	//___________________________________________________________
	291	Bool_t AliSymMatrix::SolveChol(Double_t *b, Bool_t invert)
	292	{
de34b538	293	// Adopted from Numerical Recipes in C, ch.2-9, http://www.nr.com
	294	// Solves the set of n linear equations A x = b,
	295	// where a is a positive-definite symmetric matrix.
	296	// a[1..n][1..n] is the output of the routine CholDecomposw.
	297	// Only the lower triangle of a is accessed. b[1..n] is input as the
	298	// right-hand side vector. The solution vector is returned in b[1..n].
8a9ab0eb	299	//
	300	Int_t i,k;
	301	Double_t sum;
	302	//
	303	AliSymMatrix *pmchol = DecomposeChol();
	304	if (!pmchol) {
7c185459	305	AliInfo("SolveChol failed");
5d88242b	306	// Print("l");
8a9ab0eb	307	return kFALSE;
	308	}
	309	AliSymMatrix& mchol = *pmchol;
	310	//
7c3070ec	311	for (i=0;i<GetSizeUsed();i++) {
de34b538	312	Double_t *rowi = mchol.GetRow(i);
	313	for (sum=b[i],k=i-1;k>=0;k--) if (rowi[k]&&b[k]) sum -= rowi[k]*b[k];
	314	b[i]=sum/rowi[i];
8a9ab0eb	315	}
de34b538	316	//
7c3070ec	317	for (i=GetSizeUsed()-1;i>=0;i--) {
7c3070ec	318	for (sum=b[i],k=i+1;k<GetSizeUsed();k++) if (b[k]) {
de34b538	319	double &mki=mchol(k,i); if (mki) sum -= mki*b[k];
de34b538	320	}
8a9ab0eb	321	b[i]=sum/mchol(i,i);
	322	}
	323	//
	324	if (invert) InvertChol(pmchol);
	325	return kTRUE;
	326	//
	327	}
	328
	329	//___________________________________________________________
	330	Bool_t AliSymMatrix::SolveChol(TVectorD &b, Bool_t invert)
	331	{
	332	return SolveChol((Double_t*)b.GetMatrixArray(),invert);
	333	}
	334
	335
	336	//___________________________________________________________
	337	Bool_t AliSymMatrix::SolveChol(Double_t brhs, Double_t bsol,Bool_t invert)
	338	{
7c3070ec	339	memcpy(bsol,brhs,GetSizeUsed()*sizeof(Double_t));
8a9ab0eb	340	return SolveChol(bsol,invert);
	341	}
	342
	343	//___________________________________________________________
339fbe23	344	Bool_t AliSymMatrix::SolveChol(const TVectorD &brhs, TVectorD &bsol,Bool_t invert)
8a9ab0eb	345	{
	346	bsol = brhs;
	347	return SolveChol(bsol,invert);
	348	}
	349
	350	//___________________________________________________________
	351	void AliSymMatrix::AddRows(int nrows)
	352	{
68f76645	353	// add empty rows
8a9ab0eb	354	if (nrows<1) return;
	355	Double_t *pnew = new Double_t[nrows+fNrows];
	356	for (int ir=0;ir<fNrows;ir++) pnew[ir] = fElemsAdd[ir]; // copy old extra rows
	357	for (int ir=0;ir<nrows;ir++) {
	358	int ncl = GetSize()+1;
	359	pnew[fNrows] = new Double_t[ncl];
	360	memset(pnew[fNrows],0,ncl*sizeof(Double_t));
	361	fNrows++;
	362	fNrowIndex++;
7c3070ec	363	fRowLwb++;
8a9ab0eb	364	}
	365	delete[] fElemsAdd;
	366	fElemsAdd = pnew;
	367	//
	368	}
	369
	370	//___________________________________________________________
	371	void AliSymMatrix::Reset()
	372	{
	373	// if additional rows exist, regularize it
	374	if (fElemsAdd) {
	375	delete[] fElems;
	376	for (int i=0;i<fNrows;i++) delete[] fElemsAdd[i];
	377	delete[] fElemsAdd; fElemsAdd = 0;
7c3070ec	378	fNcols = fRowLwb = fNrowIndex;
7c3070ec	379	fElems = new Double_t[GetSize()*(GetSize()+1)/2];
8a9ab0eb	380	fNrows = 0;
8a9ab0eb	381	}
7c3070ec	382	if (fElems) memset(fElems,0,GetSize()(GetSize()+1)/2sizeof(Double_t));
8a9ab0eb	383	//
	384	}
	385
de34b538	386	//___________________________________________________________
	387	/*
	388	void AliSymMatrix::AddToRow(Int_t r, Double_t valc,Int_t indc,Int_t n)
	389	{
	390	// for (int i=n;i--;) {
	391	// (*this)(indc[i],r) += valc[i];
	392	// }
	393	// return;
	394
	395	double *row;
	396	if (r>=fNrowIndex) {
	397	AddRows(r-fNrowIndex+1);
	398	row = &((fElemsAdd[r-fNcols])[0]);
	399	}
	400	else row = &fElems[GetIndex(r,0)];
	401	//
	402	int nadd = 0;
	403	for (int i=n;i--;) {
	404	if (indc[i]>r) continue;
	405	row[indc[i]] += valc[i];
	406	nadd++;
	407	}
	408	if (nadd == n) return;
	409	//
	410	// add to col>row
	411	for (int i=n;i--;) {
	412	if (indc[i]>r) (*this)(indc[i],r) += valc[i];
	413	}
	414	//
	415	}
	416	*/
	417
	418	//___________________________________________________________
	419	Double_t* AliSymMatrix::GetRow(Int_t r)
	420	{
68f76645	421	// get pointer on the row
7c3070ec	422	if (r>=GetSize()) {
	423	int nn = GetSize();
	424	AddRows(r-GetSize()+1);
7c185459	425	AliDebug(2,Form("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));
7c185459	454	if (IsZero(vl)) 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--;) {
7c185459	463	if (!IsZero(rowMax[i])) rowMax[i] = 1./rowMax[i]; // Max elemt of row i
7c185459	464	if (!IsZero(colMax[i])) 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;
3c5b4cc8	473	fgBuffer = new AliSymMatrix(*this);
8a9ab0eb	474	}
	475	else (fgBuffer) = this;
	476	//
	477	if (stabilize) for (int i=0;i<nGlo; i++) { // Small loop for matrix equilibration (gives a better conditioning)
	478	for (int j=0;j<=i; j++) {
de34b538	479	double vl = Query(i,j);
7c185459	480	if (!IsZero(vl)) SetEl(i,j, TMath::Sqrt(rowMax[i])vlTMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
8a9ab0eb	481	}
8a9ab0eb	482	for (int j=i+1;j<nGlo;j++) {
de34b538	483	double vl = Query(j,i);
7c185459	484	if (!IsZero(vl)) fgBuffer->SetEl(j,i,TMath::Sqrt(rowMax[i])vlTMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
8a9ab0eb	485	}
	486	}
	487	//
de34b538	488	for (Int_t j=nGlo; j--;) fgBuffer->DiagElem(j) = TMath::Abs(QueryDiag(j)); // save diagonal elem absolute values
8a9ab0eb	489	//
	490	for (Int_t i=0; i<nGlo; i++) {
	491	vPivot = 0.0;
	492	iPivot = -1;
	493	//
	494	for (Int_t j=0; j<nGlo; j++) { // First look for the pivot, ie max unused diagonal element
	495	double vl;
de34b538	496	if (bUnUsed[j] && (TMath::Abs(vl=QueryDiag(j))>TMath::Max(TMath::Abs(vPivot),eps*fgBuffer->QueryDiag(j)))) {
8a9ab0eb	497	vPivot = vl;
	498	iPivot = j;
	499	}
	500	}
	501	//
	502	if (iPivot >= 0) { // pivot found
	503	nRank++;
	504	bUnUsed[iPivot] = false; // This value is used
	505	vPivot = 1.0/vPivot;
	506	DiagElem(iPivot) = -vPivot; // Replace pivot by its inverse
	507	//
	508	for (Int_t j=0; j<nGlo; j++) {
	509	for (Int_t jj=0; jj<nGlo; jj++) {
	510	if (j != iPivot && jj != iPivot) {// Other elements (!!! do them first as you use old matV[k][j]'s !!!)
	511	double &r = j>=jj ? (this)(j,jj) : (fgBuffer)(jj,j);
de34b538	512	r -= vPivot* ( j>iPivot ? Query(j,iPivot) : fgBuffer->Query(iPivot,j) )
de34b538	513	* ( iPivot>jj ? Query(iPivot,jj) : fgBuffer->Query(jj,iPivot));
8a9ab0eb	514	}
	515	}
	516	}
	517	//
	518	for (Int_t j=0; j<nGlo; j++) if (j != iPivot) { // Pivot row or column elements
	519	(this)(j,iPivot) = vPivot;
	520	(fgBuffer)(iPivot,j) = vPivot;
	521	}
	522	//
	523	}
	524	else { // No more pivot value (clear those elements)
	525	for (Int_t j=0; j<nGlo; j++) {
	526	if (bUnUsed[j]) {
	527	vecB[j] = 0.0;
	528	for (Int_t k=0; k<nGlo; k++) {
	529	(*this)(j,k) = 0.;
	530	if (j!=k) (*fgBuffer)(j,k) = 0;
	531	}
	532	}
	533	}
	534	break; // No more pivots anyway, stop here
	535	}
	536	}
	537	//
c8f37c50	538	if (stabilize) for (Int_t i=0; i<nGlo; i++) for (Int_t j=0; j<nGlo; j++) {
	539	double vl = TMath::Sqrt(colMax[i])*TMath::Sqrt(rowMax[j]); // Correct matrix V
	540	if (i>=j) (this)(i,j) = vl;
	541	else (fgBuffer)(j,i) = vl;
	542	}
8a9ab0eb	543	//
	544	for (Int_t j=0; j<nGlo; j++) {
	545	rowMax[j] = 0.0;
	546	for (Int_t jj=0; jj<nGlo; jj++) { // Reverse matrix elements
	547	double vl;
de34b538	548	if (j>=jj) vl = (*this)(j,jj) = -Query(j,jj);
de34b538	549	else vl = (*fgBuffer)(j,jj) = -fgBuffer->Query(j,jj);
8a9ab0eb	550	rowMax[j] += vl*vecB[jj];
	551	}
	552	}
	553
	554	for (Int_t j=0; j<nGlo; j++) {
	555	vecB[j] = rowMax[j]; // The final result
	556	}
	557	//
	558	delete [] bUnUsed;
	559	delete [] rowMax;
	560	if (stabilize) delete [] colMax;
	561
	562	return nRank;
	563	}
5d88242b	564
5d88242b	565