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


/*********************************************************************************/
/* Symmetric Band Diagonal matrix with half band width W (+1 for diagonal)       */
/* Only lower triangle is stored in the "profile" format                         */ 
/*                                                                               */ 
/*                                                                               */
/* Author: ruben.shahoyan@cern.ch                                                */
/*                                                                               */ 
/*********************************************************************************/
#include <stdlib.h>
#include <stdio.h>
#include <iostream>
#include <float.h>
//
#include "TClass.h"
#include "TMath.h"
#include "AliSymBDMatrix.h"
//

using namespace std;

ClassImp(AliSymBDMatrix)


//___________________________________________________________
AliSymBDMatrix::AliSymBDMatrix() 
: fElems(0)
{
  // def. c-tor
  fSymmetric = kTRUE;
}

//___________________________________________________________
AliSymBDMatrix::AliSymBDMatrix(Int_t size, Int_t w)
  : AliMatrixSq(),fElems(0)
{
  // c-tor for given size
  //
  fNcols = size;    // number of rows
  if (w<0) w = 0;
  if (w>=size) w = size-1;
  fNrows = w;
  fRowLwb = w+1;
  fSymmetric = kTRUE;
  //
  // total number of stored elements
  fNelems = size*(w+1) - w*(w+1)/2;
  //
  fElems = new Double_t[fNcols*fRowLwb];
  memset(fElems,0,fNcols*fRowLwb*sizeof(Double_t));
  //
}

//___________________________________________________________
AliSymBDMatrix::AliSymBDMatrix(const AliSymBDMatrix &src) 
  : AliMatrixSq(src),fElems(0)
{
  // copy c-tor
  if (src.GetSize()<1) return;
  fNcols = src.GetSize();
  fNrows = src.GetBandHWidth();
  fRowLwb = fNrows+1;
  fNelems = src.GetNElemsStored();
  fElems = new Double_t[fNcols*fRowLwb];
  memcpy(fElems,src.fElems,fNcols*fRowLwb*sizeof(Double_t));
  //
}

//___________________________________________________________
AliSymBDMatrix::~AliSymBDMatrix() 
{
  // d-tor
  Clear();
}

//___________________________________________________________
AliSymBDMatrix&  AliSymBDMatrix::operator=(const AliSymBDMatrix& src)
{
  // assignment
  //
  if (this != &src) {
    TObject::operator=(src);
    if (fNcols!=src.fNcols) {
      // recreate the matrix
      if (fElems) delete[] fElems;
      fNcols = src.GetSize();
      fNrows = src.GetBandHWidth();
      fNelems = src.GetNElemsStored();
      fRowLwb = src.fRowLwb;
      fElems = new Double_t[fNcols*fRowLwb];
    }
    memcpy(fElems,src.fElems,fNcols*fRowLwb*sizeof(Double_t));     
    fSymmetric = kTRUE;
  }
  //
  return *this;
  //
}

//___________________________________________________________
void AliSymBDMatrix::Clear(Option_t*)
{
  // clear dynamic part
  if (fElems) {delete[] fElems; fElems = 0;}
  //  
  fNelems = fNcols = fNrows = fRowLwb = 0;
  //
}

//___________________________________________________________
Float_t AliSymBDMatrix::GetDensity() const
{
  // get fraction of non-zero elements
  if (!fNelems) return 0;
  Int_t nel = 0;
  for (int i=fNelems;i--;) if (!IsZero(fElems[i])) nel++;
  return nel/fNelems;
}

//___________________________________________________________
void AliSymBDMatrix::Print(Option_t* option) const
{
  // print data
  printf("Symmetric Band-Diagonal Matrix : Size = %d, half bandwidth = %d\n",
	 GetSize(),GetBandHWidth());
  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<GetSize();i++) {
    printf(opt,i);
    for (Int_t j=TMath::Max(0,i-GetBandHWidth());j<=i;j++) printf("%+.3e|",GetEl(i,j));
    printf("\n");
  }
}

//___________________________________________________________
void AliSymBDMatrix::MultiplyByVec(const Double_t *vecIn,Double_t *vecOut) const
{
  // fill vecOut by matrix*vecIn
  // vector should be of the same size as the matrix
  if (IsDecomposed()) {
    for (int i=0;i<GetSize();i++) {
      double sm = 0;
      int jmax = TMath::Min(GetSize(),i+fRowLwb);
      for (int j=i+1;j<jmax;j++) sm += vecIn[j]*Query(j,i);
      vecOut[i] = QueryDiag(i)*(vecIn[i]+sm);
    }
    for (int i=GetSize();i--;) {
      double sm = 0;
      int jmin = TMath::Max(0,i - GetBandHWidth());
      int jmax = i-1;
      for (int j=jmin;j<jmax;j++) sm += vecOut[j]*Query(i,j);
      vecOut[i] += sm;
    }
  }
  else { // not decomposed
    for (int i=GetSize();i--;) {
      vecOut[i] = 0.0;
      int jmin = TMath::Max(0,i - GetBandHWidth());
      int jmax = TMath::Min(GetSize(),i + fRowLwb);
      for (int j=jmin;j<jmax;j++) vecOut[i] += vecIn[j]*Query(i,j);
    }
  }
  //
}

//___________________________________________________________
void AliSymBDMatrix::Reset()
{
  // set all elems to 0
  if (fElems) memset(fElems,0,fNcols*fRowLwb*sizeof(Double_t));
  SetDecomposed(kFALSE);
  //
}

//___________________________________________________________
void AliSymBDMatrix::AddToRow(Int_t r, Double_t *valc,Int_t *indc,Int_t n)
{
  // add list of elements to row r
  for (int i=0;i<n;i++) (*this)(r,indc[i]) = valc[i];
}

//___________________________________________________________
void AliSymBDMatrix::DecomposeLDLT()
{
  // decomposition to L Diag L^T
  if (IsDecomposed()) return;
  //
  Double_t eps = std::numeric_limits<double>::epsilon()*std::numeric_limits<double>::epsilon();
  //
  Double_t dtmp,gamma=0.0,xi=0.0;
  int iDiag;
  //
  // find max diag and number of non-0 diag.elements
  for (dtmp=0.0,iDiag=0;iDiag<GetSize();iDiag++) {
    if ( (dtmp=QueryDiag(iDiag)) <=0.0) break;
    if (gamma < dtmp) gamma = dtmp; 
  }
  //
  // find max. off-diag element
  for (int ir=1;ir<iDiag;ir++) {
    for (int ic=ir-GetBandHWidth();ic<ir;ic++) {
      if (ic<0) continue;
      dtmp = TMath::Abs(Query(ir,ic));
      if (xi<dtmp) xi = dtmp;
    }
  }
  double delta = eps*TMath::Max(1.0,xi+gamma);
  //
  double sn = GetSize()>1 ? 1.0/TMath::Sqrt( GetSize()*GetSize() - 1.0) : 1.0;
  double beta = TMath::Sqrt(TMath::Max(eps,TMath::Max(gamma,xi*sn))); 
  //
  for (int kr=1;kr<GetSize();kr++) {
    int colKmin = TMath::Max(0,kr - GetBandHWidth());
    double theta = 0.0;
    //
    for (int jr=colKmin;jr<=kr;jr++) {
      int colJmin = TMath::Max(0,jr - GetBandHWidth());
      //
      dtmp = 0.0;
      for (int i=TMath::Max(colKmin,colJmin);i<jr;i++) 
	dtmp += Query(kr,i)*QueryDiag(i)*Query(jr,i);
      dtmp = (*this)(kr,jr) -= dtmp;
      //
      theta = TMath::Max(theta, TMath::Abs(dtmp));
      //
      if (jr!=kr) {
	if (!IsZero(QueryDiag(jr))) (*this)(kr,jr) /= QueryDiag(jr);
	else                        (*this)(kr,jr) = 0.0;
      }
      else if (kr<iDiag) {
	dtmp = theta/beta;
	dtmp *= dtmp;
	dtmp = TMath::Max(dtmp, delta);
	(*this)(kr,jr) = TMath::Max( TMath::Abs(Query(kr,jr)), dtmp); 
      }
    } // jr
  } // kr
  //
  for (int i=0;i<GetSize();i++) {
    dtmp = QueryDiag(i);
    if (!IsZero(dtmp)) DiagElem(i) = 1./dtmp;
  }
  //
  SetDecomposed();
}

//___________________________________________________________
void AliSymBDMatrix::Solve(Double_t *rhs)
{
  // solve matrix equation
  //
  if (!IsDecomposed()) DecomposeLDLT();
  //
  for (int kr=0;kr<GetSize();kr++) 
    for (int jr=TMath::Max(0,kr-GetBandHWidth());jr<kr;jr++) rhs[kr] -= Query(kr,jr)*rhs[jr];
  //
  for (int kr=GetSize();kr--;) rhs[kr] *= QueryDiag(kr);
  //
  for (int kr=GetSize();kr--;)
    for (int jr=TMath::Max(0,kr - GetBandHWidth());jr<kr;jr++) rhs[jr] -= Query(kr,jr)*rhs[kr];
  //
}

//___________________________________________________________
void AliSymBDMatrix::Solve(const Double_t *rhs,Double_t *sol)
{
  // solve matrix equation
  memcpy(sol,rhs,GetSize()*sizeof(Double_t));
  Solve(sol);
  //
}
Commit	Line	Data
7c3070ec	1
	2	/*********************************************************************************/
	3	/* Symmetric Band Diagonal matrix with half band width W (+1 for diagonal) */
	4	/* Only lower triangle is stored in the "profile" format */
	5	/* */
	6	/* */
	7	/* Author: ruben.shahoyan@cern.ch */
	8	/* */
	9	/*********************************************************************************/
	10	#include <stdlib.h>
	11	#include <stdio.h>
	12	#include <iostream>
	13	#include <float.h>
	14	//
	15	#include "TClass.h"
	16	#include "TMath.h"
	17	#include "AliSymBDMatrix.h"
	18	//
	19
	20	using namespace std;
	21
	22	ClassImp(AliSymBDMatrix)
	23
	24
	25	//___________________________________________________________
	26	AliSymBDMatrix::AliSymBDMatrix()
	27	: fElems(0)
	28	{
	29	// def. c-tor
	30	fSymmetric = kTRUE;
	31	}
	32
	33	//___________________________________________________________
	34	AliSymBDMatrix::AliSymBDMatrix(Int_t size, Int_t w)
	35	: AliMatrixSq(),fElems(0)
	36	{
	37	// c-tor for given size
	38	//
	39	fNcols = size; // number of rows
	40	if (w<0) w = 0;
	41	if (w>=size) w = size-1;
	42	fNrows = w;
	43	fRowLwb = w+1;
	44	fSymmetric = kTRUE;
	45	//
	46	// total number of stored elements
	47	fNelems = size(w+1) - w(w+1)/2;
	48	//
	49	fElems = new Double_t[fNcols*fRowLwb];
	50	memset(fElems,0,fNcolsfRowLwbsizeof(Double_t));
	51	//
	52	}
	53
	54	//___________________________________________________________
	55	AliSymBDMatrix::AliSymBDMatrix(const AliSymBDMatrix &src)
	56	: AliMatrixSq(src),fElems(0)
	57	{
	58	// copy c-tor
	59	if (src.GetSize()<1) return;
	60	fNcols = src.GetSize();
	61	fNrows = src.GetBandHWidth();
	62	fRowLwb = fNrows+1;
	63	fNelems = src.GetNElemsStored();
	64	fElems = new Double_t[fNcols*fRowLwb];
65	memcpy(fElems,src.fElems,fNcolsfRowLwbsizeof(Double_t));
66	//
67	}
68
69	//___________________________________________________________
70	AliSymBDMatrix::~AliSymBDMatrix()
71	{
72	// d-tor
73	Clear();
74	}
75
76	//___________________________________________________________
77	AliSymBDMatrix& AliSymBDMatrix::operator=(const AliSymBDMatrix& src)
78	{
79	// assignment
80	//
81	if (this != &src) {
82	TObject::operator=(src);
83	if (fNcols!=src.fNcols) {
84	// recreate the matrix
85	if (fElems) delete[] fElems;
86	fNcols = src.GetSize();
87	fNrows = src.GetBandHWidth();
88	fNelems = src.GetNElemsStored();
89	fRowLwb = src.fRowLwb;
90	fElems = new Double_t[fNcols*fRowLwb];
91	}
92	memcpy(fElems,src.fElems,fNcolsfRowLwbsizeof(Double_t));
93	fSymmetric = kTRUE;
94	}
95	//
96	return *this;
97	//
98	}
99
100	//___________________________________________________________
101	void AliSymBDMatrix::Clear(Option_t*)
102	{
103	// clear dynamic part
104	if (fElems) {delete[] fElems; fElems = 0;}
105	//
106	fNelems = fNcols = fNrows = fRowLwb = 0;
107	//
108	}
109
110	//___________________________________________________________
111	Float_t AliSymBDMatrix::GetDensity() const
112	{
113	// get fraction of non-zero elements
114	if (!fNelems) return 0;
115	Int_t nel = 0;
7c185459	116	for (int i=fNelems;i--;) if (!IsZero(fElems[i])) nel++;
7c3070ec	117	return nel/fNelems;
	118	}
	119
	120	//___________________________________________________________
	121	void AliSymBDMatrix::Print(Option_t* option) const
	122	{
	123	// print data
	124	printf("Symmetric Band-Diagonal Matrix : Size = %d, half bandwidth = %d\n",
	125	GetSize(),GetBandHWidth());
	126	TString opt = option; opt.ToLower();
	127	if (opt.IsNull()) return;
	128	opt = "%"; opt += 1+int(TMath::Log10(double(GetSize()))); opt+="d\|";
	129	for (Int_t i=0;i<GetSize();i++) {
	130	printf(opt,i);
	131	for (Int_t j=TMath::Max(0,i-GetBandHWidth());j<=i;j++) printf("%+.3e\|",GetEl(i,j));
	132	printf("\n");
	133	}
	134	}
	135
	136	//___________________________________________________________
551c9e69	137	void AliSymBDMatrix::MultiplyByVec(const Double_t vecIn,Double_t vecOut) const
7c3070ec	138	{
	139	// fill vecOut by matrix*vecIn
	140	// vector should be of the same size as the matrix
	141	if (IsDecomposed()) {
	142	for (int i=0;i<GetSize();i++) {
	143	double sm = 0;
	144	int jmax = TMath::Min(GetSize(),i+fRowLwb);
	145	for (int j=i+1;j<jmax;j++) sm += vecIn[j]*Query(j,i);
	146	vecOut[i] = QueryDiag(i)*(vecIn[i]+sm);
	147	}
	148	for (int i=GetSize();i--;) {
	149	double sm = 0;
	150	int jmin = TMath::Max(0,i - GetBandHWidth());
	151	int jmax = i-1;
	152	for (int j=jmin;j<jmax;j++) sm += vecOut[j]*Query(i,j);
	153	vecOut[i] += sm;
	154	}
	155	}
	156	else { // not decomposed
	157	for (int i=GetSize();i--;) {
	158	vecOut[i] = 0.0;
	159	int jmin = TMath::Max(0,i - GetBandHWidth());
	160	int jmax = TMath::Min(GetSize(),i + fRowLwb);
	161	for (int j=jmin;j<jmax;j++) vecOut[i] += vecIn[j]*Query(i,j);
	162	}
	163	}
	164	//
	165	}
	166
	167	//___________________________________________________________
	168	void AliSymBDMatrix::Reset()
	169	{
	170	// set all elems to 0
	171	if (fElems) memset(fElems,0,fNcolsfRowLwbsizeof(Double_t));
c130d912	172	SetDecomposed(kFALSE);
7c3070ec	173	//
	174	}
	175
	176	//___________________________________________________________
	177	void AliSymBDMatrix::AddToRow(Int_t r, Double_t valc,Int_t indc,Int_t n)
	178	{
	179	// add list of elements to row r
	180	for (int i=0;i<n;i++) (*this)(r,indc[i]) = valc[i];
	181	}
	182
	183	//___________________________________________________________
	184	void AliSymBDMatrix::DecomposeLDLT()
	185	{
	186	// decomposition to L Diag L^T
	187	if (IsDecomposed()) return;
	188	//
	189	Double_t eps = std::numeric_limits<double>::epsilon()*std::numeric_limits<double>::epsilon();
	190	//
	191	Double_t dtmp,gamma=0.0,xi=0.0;
	192	int iDiag;
	193	//
	194	// find max diag and number of non-0 diag.elements
	195	for (dtmp=0.0,iDiag=0;iDiag<GetSize();iDiag++) {
	196	if ( (dtmp=QueryDiag(iDiag)) <=0.0) break;
	197	if (gamma < dtmp) gamma = dtmp;
	198	}
	199	//
	200	// find max. off-diag element
	201	for (int ir=1;ir<iDiag;ir++) {
	202	for (int ic=ir-GetBandHWidth();ic<ir;ic++) {
	203	if (ic<0) continue;
	204	dtmp = TMath::Abs(Query(ir,ic));
	205	if (xi<dtmp) xi = dtmp;
	206	}
	207	}
	208	double delta = eps*TMath::Max(1.0,xi+gamma);
	209	//
	210	double sn = GetSize()>1 ? 1.0/TMath::Sqrt( GetSize()*GetSize() - 1.0) : 1.0;
	211	double beta = TMath::Sqrt(TMath::Max(eps,TMath::Max(gamma,xi*sn)));
	212	//
	213	for (int kr=1;kr<GetSize();kr++) {
	214	int colKmin = TMath::Max(0,kr - GetBandHWidth());
	215	double theta = 0.0;
	216	//
	217	for (int jr=colKmin;jr<=kr;jr++) {
	218	int colJmin = TMath::Max(0,jr - GetBandHWidth());
	219	//
	220	dtmp = 0.0;
	221	for (int i=TMath::Max(colKmin,colJmin);i<jr;i++)
	222	dtmp += Query(kr,i)QueryDiag(i)Query(jr,i);
	223	dtmp = (*this)(kr,jr) -= dtmp;
	224	//
	225	theta = TMath::Max(theta, TMath::Abs(dtmp));
	226	//
	227	if (jr!=kr) {
7c185459	228	if (!IsZero(QueryDiag(jr))) (*this)(kr,jr) /= QueryDiag(jr);
7c185459	229	else (*this)(kr,jr) = 0.0;
7c3070ec	230	}
	231	else if (kr<iDiag) {
	232	dtmp = theta/beta;
	233	dtmp *= dtmp;
	234	dtmp = TMath::Max(dtmp, delta);
	235	(*this)(kr,jr) = TMath::Max( TMath::Abs(Query(kr,jr)), dtmp);
	236	}
	237	} // jr
	238	} // kr
	239	//
	240	for (int i=0;i<GetSize();i++) {
	241	dtmp = QueryDiag(i);
7c185459	242	if (!IsZero(dtmp)) DiagElem(i) = 1./dtmp;
7c3070ec	243	}
	244	//
	245	SetDecomposed();
	246	}
	247
	248	//___________________________________________________________
	249	void AliSymBDMatrix::Solve(Double_t *rhs)
	250	{
	251	// solve matrix equation
	252	//
	253	if (!IsDecomposed()) DecomposeLDLT();
	254	//
	255	for (int kr=0;kr<GetSize();kr++)
	256	for (int jr=TMath::Max(0,kr-GetBandHWidth());jr<kr;jr++) rhs[kr] -= Query(kr,jr)*rhs[jr];
	257	//
	258	for (int kr=GetSize();kr--;) rhs[kr] *= QueryDiag(kr);
	259	//
	260	for (int kr=GetSize();kr--;)
	261	for (int jr=TMath::Max(0,kr - GetBandHWidth());jr<kr;jr++) rhs[jr] -= Query(kr,jr)*rhs[kr];
	262	//
	263	}
	264
	265	//___________________________________________________________
	266	void AliSymBDMatrix::Solve(const Double_t rhs,Double_t sol)
	267	{
	268	// solve matrix equation
	269	memcpy(sol,rhs,GetSize()*sizeof(Double_t));
	270	Solve(sol);
	271	//
	272	}