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) */
7 /* fNRowIndex: total size (fNCols+fNRows), GetSize */
8 /* fRowLwb : actual size to used for given operation, by default = total size, GetSizeUsed */
10 /* Author: ruben.shahoyan@cern.ch */
12 /**********************************************************************************************/
21 #include "AliSymMatrix.h"
27 ClassImp(AliSymMatrix)
30 AliSymMatrix* AliSymMatrix::fgBuffer = 0;
31 Int_t AliSymMatrix::fgCopyCnt = 0;
32 //___________________________________________________________
33 AliSymMatrix::AliSymMatrix()
34 : fElems(0),fElemsAdd(0)
36 // default constructor
41 //___________________________________________________________
42 AliSymMatrix::AliSymMatrix(Int_t size)
43 : AliMatrixSq(),fElems(0),fElemsAdd(0)
45 //constructor for matrix with defined size
47 fNrowIndex = fNcols = fRowLwb = size;
48 fElems = new Double_t[fNcols*(fNcols+1)/2];
55 //___________________________________________________________
56 AliSymMatrix::AliSymMatrix(const AliSymMatrix &src)
57 : AliMatrixSq(src),fElems(0),fElemsAdd(0)
60 fNrowIndex = fNcols = src.GetSize();
62 fRowLwb = src.GetSizeUsed();
64 int nmainel = fNcols*(fNcols+1)/2;
65 fElems = new Double_t[nmainel];
66 nmainel = src.fNcols*(src.fNcols+1)/2;
67 memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
68 if (src.GetSizeAdded()) { // transfer extra rows to main matrix
69 Double_t *pnt = fElems + nmainel;
70 int ncl = src.GetSizeBooked() + 1;
71 for (int ir=0;ir<src.GetSizeAdded();ir++) {
72 memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
84 //___________________________________________________________
85 AliSymMatrix::~AliSymMatrix()
88 if (--fgCopyCnt < 1 && fgBuffer) {delete fgBuffer; fgBuffer = 0;}
91 //___________________________________________________________
92 AliSymMatrix& AliSymMatrix::operator=(const AliSymMatrix& src)
94 // assignment operator
96 TObject::operator=(src);
97 if (GetSizeBooked()!=src.GetSizeBooked() && GetSizeAdded()!=src.GetSizeAdded()) {
98 // recreate the matrix
99 if (fElems) delete[] fElems;
100 for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i];
103 fNrowIndex = src.GetSize();
104 fNcols = src.GetSize();
106 fRowLwb = src.GetSizeUsed();
107 fElems = new Double_t[GetSize()*(GetSize()+1)/2];
108 int nmainel = src.GetSizeBooked()*(src.GetSizeBooked()+1);
109 memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
110 if (src.GetSizeAdded()) { // transfer extra rows to main matrix
111 Double_t *pnt = fElems + nmainel;//*sizeof(Double_t);
112 int ncl = src.GetSizeBooked() + 1;
113 for (int ir=0;ir<src.GetSizeAdded();ir++) {
115 memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
116 pnt += ncl;//*sizeof(Double_t);
122 memcpy(fElems,src.fElems,GetSizeBooked()*(GetSizeBooked()+1)/2*sizeof(Double_t));
123 int ncl = GetSizeBooked() + 1;
124 for (int ir=0;ir<GetSizeAdded();ir++) { // dynamic rows
126 memcpy(fElemsAdd[ir],src.fElemsAdd[ir],ncl*sizeof(Double_t));
134 //___________________________________________________________
135 AliSymMatrix& AliSymMatrix::operator+=(const AliSymMatrix& src)
138 if (GetSizeUsed() != src.GetSizeUsed()) {
139 AliError("Matrix sizes are different");
142 for (int i=0;i<GetSizeUsed();i++) for (int j=i;j<GetSizeUsed();j++) (*this)(j,i) += src(j,i);
146 //___________________________________________________________
147 void AliSymMatrix::Clear(Option_t*)
149 // clear dynamic part
150 if (fElems) {delete[] fElems; fElems = 0;}
153 for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i];
157 fNrowIndex = fNcols = fNrows = fRowLwb = 0;
161 //___________________________________________________________
162 Float_t AliSymMatrix::GetDensity() const
164 // get fraction of non-zero elements
166 for (int i=GetSizeUsed();i--;) for (int j=i+1;j--;) if (!IsZero(GetEl(i,j))) nel++;
167 return 2.*nel/( (GetSizeUsed()+1)*GetSizeUsed() );
170 //___________________________________________________________
171 void AliSymMatrix::Print(Option_t* option) const
174 printf("Symmetric Matrix: Size = %d (%d rows added dynamically), %d used\n",GetSize(),GetSizeAdded(),GetSizeUsed());
175 TString opt = option; opt.ToLower();
176 if (opt.IsNull()) return;
177 opt = "%"; opt += 1+int(TMath::Log10(double(GetSize()))); opt+="d|";
178 for (Int_t i=0;i<GetSizeUsed();i++) {
180 for (Int_t j=0;j<=i;j++) printf("%+.3e|",GetEl(i,j));
185 //___________________________________________________________
186 void AliSymMatrix::MultiplyByVec(const Double_t *vecIn,Double_t *vecOut) const
188 // fill vecOut by matrix*vecIn
189 // vector should be of the same size as the matrix
190 for (int i=GetSizeUsed();i--;) {
192 for (int j=GetSizeUsed();j--;) vecOut[i] += vecIn[j]*GetEl(i,j);
197 //___________________________________________________________
198 AliSymMatrix* AliSymMatrix::DecomposeChol()
200 // Return a matrix with Choleski decomposition
201 // Adopted from Numerical Recipes in C, ch.2-9, http://www.nr.com
202 // consturcts Cholesky decomposition of SYMMETRIC and
203 // POSITIVELY-DEFINED matrix a (a=L*Lt)
204 // Only upper triangle of the matrix has to be filled.
205 // In opposite to function from the book, the matrix is modified:
206 // lower triangle and diagonal are refilled.
208 if (!fgBuffer || fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
211 fgBuffer = new AliSymMatrix(*this);
214 AliInfo("Failed to allocate memory for Choleski decompostions");
218 else (*fgBuffer) = *this;
220 AliSymMatrix& mchol = *fgBuffer;
222 for (int i=0;i<GetSizeUsed();i++) {
223 Double_t *rowi = mchol.GetRow(i);
224 for (int j=i;j<GetSizeUsed();j++) {
225 Double_t *rowj = mchol.GetRow(j);
226 double sum = rowj[i];
227 for (int k=i-1;k>=0;k--) if (rowi[k]&&rowj[k]) sum -= rowi[k]*rowj[k];
229 if (sum <= 0.0) { // not positive-definite
230 AliInfo(Form("The matrix is not positive definite [%e]\n"
231 "Choleski decomposition is not possible",sum));
235 rowi[i] = TMath::Sqrt(sum);
237 } else rowj[i] = sum/rowi[i];
243 //___________________________________________________________
244 Bool_t AliSymMatrix::InvertChol()
246 // Invert matrix using Choleski decomposition
248 AliSymMatrix* mchol = DecomposeChol();
250 AliInfo("Failed to invert the matrix");
259 //___________________________________________________________
260 void AliSymMatrix::InvertChol(AliSymMatrix* pmchol)
262 // Invert matrix using Choleski decomposition, provided the Cholseki's L matrix
265 AliSymMatrix& mchol = *pmchol;
267 // Invert decomposed triangular L matrix (Lower triangle is filled)
268 for (int i=0;i<GetSizeUsed();i++) {
269 mchol(i,i) = 1.0/mchol(i,i);
270 for (int j=i+1;j<GetSizeUsed();j++) {
271 Double_t *rowj = mchol.GetRow(j);
273 for (int k=i;k<j;k++) if (rowj[k]) {
274 double &mki = mchol(k,i); if (mki) sum -= rowj[k]*mki;
276 rowj[i] = sum/rowj[j];
280 // take product of the inverted Choleski L matrix with its transposed
281 for (int i=GetSizeUsed();i--;) {
282 for (int j=i+1;j--;) {
284 for (int k=i;k<GetSizeUsed();k++) {
285 double &mik = mchol(i,k);
287 double &mjk = mchol(j,k);
288 if (mjk) sum += mik*mjk;
298 //___________________________________________________________
299 Bool_t AliSymMatrix::SolveChol(Double_t *b, Bool_t invert)
301 // Adopted from Numerical Recipes in C, ch.2-9, http://www.nr.com
302 // Solves the set of n linear equations A x = b,
303 // where a is a positive-definite symmetric matrix.
304 // a[1..n][1..n] is the output of the routine CholDecomposw.
305 // Only the lower triangle of a is accessed. b[1..n] is input as the
306 // right-hand side vector. The solution vector is returned in b[1..n].
311 AliSymMatrix *pmchol = DecomposeChol();
313 AliInfo("SolveChol failed");
317 AliSymMatrix& mchol = *pmchol;
319 for (i=0;i<GetSizeUsed();i++) {
320 Double_t *rowi = mchol.GetRow(i);
321 for (sum=b[i],k=i-1;k>=0;k--) if (rowi[k]&&b[k]) sum -= rowi[k]*b[k];
325 for (i=GetSizeUsed()-1;i>=0;i--) {
326 for (sum=b[i],k=i+1;k<GetSizeUsed();k++) if (b[k]) {
327 double &mki=mchol(k,i); if (mki) sum -= mki*b[k];
332 if (invert) InvertChol(pmchol);
337 //___________________________________________________________
338 Bool_t AliSymMatrix::SolveChol(TVectorD &b, Bool_t invert)
340 return SolveChol((Double_t*)b.GetMatrixArray(),invert);
344 //___________________________________________________________
345 Bool_t AliSymMatrix::SolveChol(Double_t *brhs, Double_t *bsol,Bool_t invert)
347 memcpy(bsol,brhs,GetSizeUsed()*sizeof(Double_t));
348 return SolveChol(bsol,invert);
351 //___________________________________________________________
352 Bool_t AliSymMatrix::SolveChol(TVectorD &brhs, TVectorD &bsol,Bool_t invert)
355 return SolveChol(bsol,invert);
358 //___________________________________________________________
359 void AliSymMatrix::AddRows(int nrows)
363 Double_t **pnew = new Double_t*[nrows+fNrows];
364 for (int ir=0;ir<fNrows;ir++) pnew[ir] = fElemsAdd[ir]; // copy old extra rows
365 for (int ir=0;ir<nrows;ir++) {
366 int ncl = GetSize()+1;
367 pnew[fNrows] = new Double_t[ncl];
368 memset(pnew[fNrows],0,ncl*sizeof(Double_t));
378 //___________________________________________________________
379 void AliSymMatrix::Reset()
381 // if additional rows exist, regularize it
384 for (int i=0;i<fNrows;i++) delete[] fElemsAdd[i];
385 delete[] fElemsAdd; fElemsAdd = 0;
386 fNcols = fRowLwb = fNrowIndex;
387 fElems = new Double_t[GetSize()*(GetSize()+1)/2];
390 if (fElems) memset(fElems,0,GetSize()*(GetSize()+1)/2*sizeof(Double_t));
394 //___________________________________________________________
396 void AliSymMatrix::AddToRow(Int_t r, Double_t *valc,Int_t *indc,Int_t n)
398 // for (int i=n;i--;) {
399 // (*this)(indc[i],r) += valc[i];
405 AddRows(r-fNrowIndex+1);
406 row = &((fElemsAdd[r-fNcols])[0]);
408 else row = &fElems[GetIndex(r,0)];
412 if (indc[i]>r) continue;
413 row[indc[i]] += valc[i];
416 if (nadd == n) return;
420 if (indc[i]>r) (*this)(indc[i],r) += valc[i];
426 //___________________________________________________________
427 Double_t* AliSymMatrix::GetRow(Int_t r)
429 // get pointer on the row
432 AddRows(r-GetSize()+1);
433 AliDebug(2,Form("create %d of %d\n",r, nn));
434 return &((fElemsAdd[r-GetSizeBooked()])[0]);
436 else return &fElems[GetIndex(r,0)];
440 //___________________________________________________________
441 int AliSymMatrix::SolveSpmInv(double *vecB, Bool_t stabilize)
443 // Solution a la MP1: gaussian eliminations
444 /// Obtain solution of a system of linear equations with symmetric matrix
445 /// and the inverse (using 'singular-value friendly' GAUSS pivot)
452 int nGlo = GetSizeUsed();
453 bool *bUnUsed = new bool[nGlo];
454 double *rowMax,*colMax=0;
455 rowMax = new double[nGlo];
458 colMax = new double[nGlo];
459 for (Int_t i=nGlo; i--;) rowMax[i] = colMax[i] = 0.0;
460 for (Int_t i=nGlo; i--;) for (Int_t j=i+1;j--;) {
461 double vl = TMath::Abs(Query(i,j));
462 if (IsZero(vl)) continue;
463 if (vl > rowMax[i]) rowMax[i] = vl; // Max elemt of row i
464 if (vl > colMax[j]) colMax[j] = vl; // Max elemt of column j
466 if (vl > rowMax[j]) rowMax[j] = vl; // Max elemt of row j
467 if (vl > colMax[i]) colMax[i] = vl; // Max elemt of column i
470 for (Int_t i=nGlo; i--;) {
471 if (!IsZero(rowMax[i])) rowMax[i] = 1./rowMax[i]; // Max elemt of row i
472 if (!IsZero(colMax[i])) colMax[i] = 1./colMax[i]; // Max elemt of column i
477 for (Int_t i=nGlo; i--;) bUnUsed[i] = true;
479 if (!fgBuffer || fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
482 fgBuffer = new AliSymMatrix(*this);
485 AliError("Failed to allocate memory for matrix inversion buffer");
489 else (*fgBuffer) = *this;
491 if (stabilize) for (int i=0;i<nGlo; i++) { // Small loop for matrix equilibration (gives a better conditioning)
492 for (int j=0;j<=i; j++) {
493 double vl = Query(i,j);
494 if (!IsZero(vl)) SetEl(i,j, TMath::Sqrt(rowMax[i])*vl*TMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
496 for (int j=i+1;j<nGlo;j++) {
497 double vl = Query(j,i);
498 if (!IsZero(vl)) fgBuffer->SetEl(j,i,TMath::Sqrt(rowMax[i])*vl*TMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
502 for (Int_t j=nGlo; j--;) fgBuffer->DiagElem(j) = TMath::Abs(QueryDiag(j)); // save diagonal elem absolute values
504 for (Int_t i=0; i<nGlo; i++) {
508 for (Int_t j=0; j<nGlo; j++) { // First look for the pivot, ie max unused diagonal element
510 if (bUnUsed[j] && (TMath::Abs(vl=QueryDiag(j))>TMath::Max(TMath::Abs(vPivot),eps*fgBuffer->QueryDiag(j)))) {
516 if (iPivot >= 0) { // pivot found
518 bUnUsed[iPivot] = false; // This value is used
520 DiagElem(iPivot) = -vPivot; // Replace pivot by its inverse
522 for (Int_t j=0; j<nGlo; j++) {
523 for (Int_t jj=0; jj<nGlo; jj++) {
524 if (j != iPivot && jj != iPivot) {// Other elements (!!! do them first as you use old matV[k][j]'s !!!)
525 double &r = j>=jj ? (*this)(j,jj) : (*fgBuffer)(jj,j);
526 r -= vPivot* ( j>iPivot ? Query(j,iPivot) : fgBuffer->Query(iPivot,j) )
527 * ( iPivot>jj ? Query(iPivot,jj) : fgBuffer->Query(jj,iPivot));
532 for (Int_t j=0; j<nGlo; j++) if (j != iPivot) { // Pivot row or column elements
533 (*this)(j,iPivot) *= vPivot;
534 (*fgBuffer)(iPivot,j) *= vPivot;
538 else { // No more pivot value (clear those elements)
539 for (Int_t j=0; j<nGlo; j++) {
542 for (Int_t k=0; k<nGlo; k++) {
544 if (j!=k) (*fgBuffer)(j,k) = 0;
548 break; // No more pivots anyway, stop here
552 if (stabilize) for (Int_t i=0; i<nGlo; i++) for (Int_t j=0; j<nGlo; j++) {
553 double vl = TMath::Sqrt(colMax[i])*TMath::Sqrt(rowMax[j]); // Correct matrix V
554 if (i>=j) (*this)(i,j) *= vl;
555 else (*fgBuffer)(j,i) *= vl;
558 for (Int_t j=0; j<nGlo; j++) {
560 for (Int_t jj=0; jj<nGlo; jj++) { // Reverse matrix elements
562 if (j>=jj) vl = (*this)(j,jj) = -Query(j,jj);
563 else vl = (*fgBuffer)(j,jj) = -fgBuffer->Query(j,jj);
564 rowMax[j] += vl*vecB[jj];
568 for (Int_t j=0; j<nGlo; j++) {
569 vecB[j] = rowMax[j]; // The final result
574 if (stabilize) delete [] colMax;