Removing try/catch-es
[u/mrichter/AliRoot.git] / STEER / STEER / AliSymMatrix.cxx
CommitLineData
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>
20#include <TMath.h>
8a9ab0eb 21#include "AliSymMatrix.h"
7c3070ec 22#include "AliLog.h"
8a9ab0eb 23//
24
25using namespace std;
26
27ClassImp(AliSymMatrix)
28
29
30AliSymMatrix* AliSymMatrix::fgBuffer = 0;
31Int_t AliSymMatrix::fgCopyCnt = 0;
32//___________________________________________________________
33AliSymMatrix::AliSymMatrix()
34: fElems(0),fElemsAdd(0)
35{
68f76645 36 // default constructor
8a9ab0eb 37 fSymmetric = kTRUE;
38 fgCopyCnt++;
39}
40
41//___________________________________________________________
42AliSymMatrix::AliSymMatrix(Int_t size)
43 : AliMatrixSq(),fElems(0),fElemsAdd(0)
44{
68f76645 45 //constructor for matrix with defined size
8a9ab0eb 46 fNrows = 0;
7c3070ec 47 fNrowIndex = fNcols = fRowLwb = size;
8a9ab0eb 48 fElems = new Double_t[fNcols*(fNcols+1)/2];
49 fSymmetric = kTRUE;
50 Reset();
51 fgCopyCnt++;
52 //
53}
54
55//___________________________________________________________
56AliSymMatrix::AliSymMatrix(const AliSymMatrix &src)
57 : AliMatrixSq(src),fElems(0),fElemsAdd(0)
58{
68f76645 59 // copy constructor
8a9ab0eb 60 fNrowIndex = fNcols = src.GetSize();
61 fNrows = 0;
7c3070ec 62 fRowLwb = src.GetSizeUsed();
8a9ab0eb 63 if (fNcols) {
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));
7c3070ec 68 if (src.GetSizeAdded()) { // transfer extra rows to main matrix
8a9ab0eb 69 Double_t *pnt = fElems + nmainel;
7c3070ec 70 int ncl = src.GetSizeBooked() + 1;
71 for (int ir=0;ir<src.GetSizeAdded();ir++) {
8a9ab0eb 72 memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
73 pnt += ncl;
74 ncl++;
75 }
76 }
77 }
78 else fElems = 0;
79 fElemsAdd = 0;
80 fgCopyCnt++;
81 //
82}
83
84//___________________________________________________________
85AliSymMatrix::~AliSymMatrix()
86{
87 Clear();
88 if (--fgCopyCnt < 1 && fgBuffer) {delete fgBuffer; fgBuffer = 0;}
89}
90
91//___________________________________________________________
92AliSymMatrix& AliSymMatrix::operator=(const AliSymMatrix& src)
93{
68f76645 94 // assignment operator
8a9ab0eb 95 if (this != &src) {
96 TObject::operator=(src);
7c3070ec 97 if (GetSizeBooked()!=src.GetSizeBooked() && GetSizeAdded()!=src.GetSizeAdded()) {
8a9ab0eb 98 // recreate the matrix
99 if (fElems) delete[] fElems;
7c3070ec 100 for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i];
8a9ab0eb 101 delete[] fElemsAdd;
102 //
de34b538 103 fNrowIndex = src.GetSize();
104 fNcols = src.GetSize();
8a9ab0eb 105 fNrows = 0;
7c3070ec 106 fRowLwb = src.GetSizeUsed();
107 fElems = new Double_t[GetSize()*(GetSize()+1)/2];
108 int nmainel = src.GetSizeBooked()*(src.GetSizeBooked()+1);
8a9ab0eb 109 memcpy(fElems,src.fElems,nmainel*sizeof(Double_t));
7c3070ec 110 if (src.GetSizeAdded()) { // transfer extra rows to main matrix
c8f37c50 111 Double_t *pnt = fElems + nmainel;//*sizeof(Double_t);
7c3070ec 112 int ncl = src.GetSizeBooked() + 1;
113 for (int ir=0;ir<src.GetSizeAdded();ir++) {
8a9ab0eb 114 ncl += ir;
115 memcpy(pnt,src.fElemsAdd[ir],ncl*sizeof(Double_t));
c8f37c50 116 pnt += ncl;//*sizeof(Double_t);
8a9ab0eb 117 }
118 }
119 //
120 }
121 else {
7c3070ec 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
8a9ab0eb 125 ncl += ir;
126 memcpy(fElemsAdd[ir],src.fElemsAdd[ir],ncl*sizeof(Double_t));
127 }
128 }
129 }
130 //
131 return *this;
132}
133
7c3070ec 134//___________________________________________________________
135AliSymMatrix& AliSymMatrix::operator+=(const AliSymMatrix& src)
136{
68f76645 137 // add operator
7c3070ec 138 if (GetSizeUsed() != src.GetSizeUsed()) {
139 AliError("Matrix sizes are different");
140 return *this;
141 }
142 for (int i=0;i<GetSizeUsed();i++) for (int j=i;j<GetSizeUsed();j++) (*this)(j,i) += src(j,i);
143 return *this;
144}
145
8a9ab0eb 146//___________________________________________________________
147void AliSymMatrix::Clear(Option_t*)
148{
68f76645 149 // clear dynamic part
8a9ab0eb 150 if (fElems) {delete[] fElems; fElems = 0;}
151 //
152 if (fElemsAdd) {
7c3070ec 153 for (int i=0;i<GetSizeAdded();i++) delete[] fElemsAdd[i];
8a9ab0eb 154 delete[] fElemsAdd;
155 fElemsAdd = 0;
156 }
7c3070ec 157 fNrowIndex = fNcols = fNrows = fRowLwb = 0;
8a9ab0eb 158 //
159}
160
161//___________________________________________________________
162Float_t AliSymMatrix::GetDensity() const
163{
164 // get fraction of non-zero elements
165 Int_t nel = 0;
7c185459 166 for (int i=GetSizeUsed();i--;) for (int j=i+1;j--;) if (!IsZero(GetEl(i,j))) nel++;
7c3070ec 167 return 2.*nel/( (GetSizeUsed()+1)*GetSizeUsed() );
8a9ab0eb 168}
169
170//___________________________________________________________
171void AliSymMatrix::Print(Option_t* option) const
172{
68f76645 173 // print itself
7c3070ec 174 printf("Symmetric Matrix: Size = %d (%d rows added dynamically), %d used\n",GetSize(),GetSizeAdded(),GetSizeUsed());
8a9ab0eb 175 TString opt = option; opt.ToLower();
176 if (opt.IsNull()) return;
177 opt = "%"; opt += 1+int(TMath::Log10(double(GetSize()))); opt+="d|";
7c3070ec 178 for (Int_t i=0;i<GetSizeUsed();i++) {
8a9ab0eb 179 printf(opt,i);
180 for (Int_t j=0;j<=i;j++) printf("%+.3e|",GetEl(i,j));
181 printf("\n");
182 }
183}
184
185//___________________________________________________________
551c9e69 186void AliSymMatrix::MultiplyByVec(const Double_t *vecIn,Double_t *vecOut) const
8a9ab0eb 187{
188 // fill vecOut by matrix*vecIn
189 // vector should be of the same size as the matrix
7c3070ec 190 for (int i=GetSizeUsed();i--;) {
8a9ab0eb 191 vecOut[i] = 0.0;
7c3070ec 192 for (int j=GetSizeUsed();j--;) vecOut[i] += vecIn[j]*GetEl(i,j);
8a9ab0eb 193 }
194 //
195}
196
197//___________________________________________________________
198AliSymMatrix* AliSymMatrix::DecomposeChol()
199{
200 // Return a matrix with Choleski decomposition
de34b538 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.
8a9ab0eb 207 //
7c3070ec 208 if (!fgBuffer || fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
8a9ab0eb 209 delete fgBuffer;
3c5b4cc8 210 fgBuffer = new AliSymMatrix(*this);
8a9ab0eb 211 }
212 else (*fgBuffer) = *this;
213 //
214 AliSymMatrix& mchol = *fgBuffer;
215 //
7c3070ec 216 for (int i=0;i<GetSizeUsed();i++) {
de34b538 217 Double_t *rowi = mchol.GetRow(i);
7c3070ec 218 for (int j=i;j<GetSizeUsed();j++) {
de34b538 219 Double_t *rowj = mchol.GetRow(j);
220 double sum = rowj[i];
221 for (int k=i-1;k>=0;k--) if (rowi[k]&&rowj[k]) sum -= rowi[k]*rowj[k];
8a9ab0eb 222 if (i == j) {
223 if (sum <= 0.0) { // not positive-definite
7c185459 224 AliInfo(Form("The matrix is not positive definite [%e]\n"
225 "Choleski decomposition is not possible",sum));
226 Print("l");
8a9ab0eb 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//___________________________________________________________
238Bool_t AliSymMatrix::InvertChol()
239{
240 // Invert matrix using Choleski decomposition
241 //
242 AliSymMatrix* mchol = DecomposeChol();
243 if (!mchol) {
7c185459 244 AliInfo("Failed to invert the matrix");
8a9ab0eb 245 return kFALSE;
246 }
247 //
248 InvertChol(mchol);
249 return kTRUE;
250 //
251}
de34b538 252
8a9ab0eb 253//___________________________________________________________
254void 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--;) {
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//___________________________________________________________
293Bool_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) {
7c185459 307 AliInfo("SolveChol failed");
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--) {
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];
322 }
8a9ab0eb 323 b[i]=sum/mchol(i,i);
324 }
325 //
326 if (invert) InvertChol(pmchol);
327 return kTRUE;
328 //
329}
330
331//___________________________________________________________
332Bool_t AliSymMatrix::SolveChol(TVectorD &b, Bool_t invert)
333{
334 return SolveChol((Double_t*)b.GetMatrixArray(),invert);
335}
336
337
338//___________________________________________________________
339Bool_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//___________________________________________________________
339fbe23 346Bool_t AliSymMatrix::SolveChol(const TVectorD &brhs, TVectorD &bsol,Bool_t invert)
8a9ab0eb 347{
348 bsol = brhs;
349 return SolveChol(bsol,invert);
350}
351
352//___________________________________________________________
353void AliSymMatrix::AddRows(int nrows)
354{
68f76645 355 // add empty rows
8a9ab0eb 356 if (nrows<1) return;
357 Double_t **pnew = new Double_t*[nrows+fNrows];
358 for (int ir=0;ir<fNrows;ir++) pnew[ir] = fElemsAdd[ir]; // copy old extra rows
359 for (int ir=0;ir<nrows;ir++) {
360 int ncl = GetSize()+1;
361 pnew[fNrows] = new Double_t[ncl];
362 memset(pnew[fNrows],0,ncl*sizeof(Double_t));
363 fNrows++;
364 fNrowIndex++;
7c3070ec 365 fRowLwb++;
8a9ab0eb 366 }
367 delete[] fElemsAdd;
368 fElemsAdd = pnew;
369 //
370}
371
372//___________________________________________________________
373void AliSymMatrix::Reset()
374{
375 // if additional rows exist, regularize it
376 if (fElemsAdd) {
377 delete[] fElems;
378 for (int i=0;i<fNrows;i++) delete[] fElemsAdd[i];
379 delete[] fElemsAdd; fElemsAdd = 0;
7c3070ec 380 fNcols = fRowLwb = fNrowIndex;
381 fElems = new Double_t[GetSize()*(GetSize()+1)/2];
8a9ab0eb 382 fNrows = 0;
383 }
7c3070ec 384 if (fElems) memset(fElems,0,GetSize()*(GetSize()+1)/2*sizeof(Double_t));
8a9ab0eb 385 //
386}
387
de34b538 388//___________________________________________________________
389/*
390void AliSymMatrix::AddToRow(Int_t r, Double_t *valc,Int_t *indc,Int_t n)
391{
392 // for (int i=n;i--;) {
393 // (*this)(indc[i],r) += valc[i];
394 // }
395 // return;
396
397 double *row;
398 if (r>=fNrowIndex) {
399 AddRows(r-fNrowIndex+1);
400 row = &((fElemsAdd[r-fNcols])[0]);
401 }
402 else row = &fElems[GetIndex(r,0)];
403 //
404 int nadd = 0;
405 for (int i=n;i--;) {
406 if (indc[i]>r) continue;
407 row[indc[i]] += valc[i];
408 nadd++;
409 }
410 if (nadd == n) return;
411 //
412 // add to col>row
413 for (int i=n;i--;) {
414 if (indc[i]>r) (*this)(indc[i],r) += valc[i];
415 }
416 //
417}
418*/
419
420//___________________________________________________________
421Double_t* AliSymMatrix::GetRow(Int_t r)
422{
68f76645 423 // get pointer on the row
7c3070ec 424 if (r>=GetSize()) {
425 int nn = GetSize();
426 AddRows(r-GetSize()+1);
7c185459 427 AliDebug(2,Form("create %d of %d\n",r, nn));
7c3070ec 428 return &((fElemsAdd[r-GetSizeBooked()])[0]);
de34b538 429 }
430 else return &fElems[GetIndex(r,0)];
431}
432
433
8a9ab0eb 434//___________________________________________________________
435int AliSymMatrix::SolveSpmInv(double *vecB, Bool_t stabilize)
436{
437 // Solution a la MP1: gaussian eliminations
438 /// Obtain solution of a system of linear equations with symmetric matrix
439 /// and the inverse (using 'singular-value friendly' GAUSS pivot)
440 //
441
442 Int_t nRank = 0;
443 int iPivot;
444 double vPivot = 0.;
7c3070ec 445 double eps = 1e-14;
446 int nGlo = GetSizeUsed();
8a9ab0eb 447 bool *bUnUsed = new bool[nGlo];
448 double *rowMax,*colMax=0;
449 rowMax = new double[nGlo];
450 //
451 if (stabilize) {
452 colMax = new double[nGlo];
453 for (Int_t i=nGlo; i--;) rowMax[i] = colMax[i] = 0.0;
454 for (Int_t i=nGlo; i--;) for (Int_t j=i+1;j--;) {
de34b538 455 double vl = TMath::Abs(Query(i,j));
7c185459 456 if (IsZero(vl)) continue;
8a9ab0eb 457 if (vl > rowMax[i]) rowMax[i] = vl; // Max elemt of row i
458 if (vl > colMax[j]) colMax[j] = vl; // Max elemt of column j
459 if (i==j) continue;
460 if (vl > rowMax[j]) rowMax[j] = vl; // Max elemt of row j
461 if (vl > colMax[i]) colMax[i] = vl; // Max elemt of column i
462 }
463 //
464 for (Int_t i=nGlo; i--;) {
7c185459 465 if (!IsZero(rowMax[i])) rowMax[i] = 1./rowMax[i]; // Max elemt of row i
466 if (!IsZero(colMax[i])) colMax[i] = 1./colMax[i]; // Max elemt of column i
8a9ab0eb 467 }
468 //
469 }
470 //
471 for (Int_t i=nGlo; i--;) bUnUsed[i] = true;
472 //
7c3070ec 473 if (!fgBuffer || fgBuffer->GetSizeUsed()!=GetSizeUsed()) {
8a9ab0eb 474 delete fgBuffer;
3c5b4cc8 475 fgBuffer = new AliSymMatrix(*this);
8a9ab0eb 476 }
477 else (*fgBuffer) = *this;
478 //
479 if (stabilize) for (int i=0;i<nGlo; i++) { // Small loop for matrix equilibration (gives a better conditioning)
480 for (int j=0;j<=i; j++) {
de34b538 481 double vl = Query(i,j);
7c185459 482 if (!IsZero(vl)) SetEl(i,j, TMath::Sqrt(rowMax[i])*vl*TMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
8a9ab0eb 483 }
484 for (int j=i+1;j<nGlo;j++) {
de34b538 485 double vl = Query(j,i);
7c185459 486 if (!IsZero(vl)) fgBuffer->SetEl(j,i,TMath::Sqrt(rowMax[i])*vl*TMath::Sqrt(colMax[j]) ); // Equilibrate the V matrix
8a9ab0eb 487 }
488 }
489 //
de34b538 490 for (Int_t j=nGlo; j--;) fgBuffer->DiagElem(j) = TMath::Abs(QueryDiag(j)); // save diagonal elem absolute values
8a9ab0eb 491 //
492 for (Int_t i=0; i<nGlo; i++) {
493 vPivot = 0.0;
494 iPivot = -1;
495 //
496 for (Int_t j=0; j<nGlo; j++) { // First look for the pivot, ie max unused diagonal element
497 double vl;
de34b538 498 if (bUnUsed[j] && (TMath::Abs(vl=QueryDiag(j))>TMath::Max(TMath::Abs(vPivot),eps*fgBuffer->QueryDiag(j)))) {
8a9ab0eb 499 vPivot = vl;
500 iPivot = j;
501 }
502 }
503 //
504 if (iPivot >= 0) { // pivot found
505 nRank++;
506 bUnUsed[iPivot] = false; // This value is used
507 vPivot = 1.0/vPivot;
508 DiagElem(iPivot) = -vPivot; // Replace pivot by its inverse
509 //
510 for (Int_t j=0; j<nGlo; j++) {
511 for (Int_t jj=0; jj<nGlo; jj++) {
512 if (j != iPivot && jj != iPivot) {// Other elements (!!! do them first as you use old matV[k][j]'s !!!)
513 double &r = j>=jj ? (*this)(j,jj) : (*fgBuffer)(jj,j);
de34b538 514 r -= vPivot* ( j>iPivot ? Query(j,iPivot) : fgBuffer->Query(iPivot,j) )
515 * ( iPivot>jj ? Query(iPivot,jj) : fgBuffer->Query(jj,iPivot));
8a9ab0eb 516 }
517 }
518 }
519 //
520 for (Int_t j=0; j<nGlo; j++) if (j != iPivot) { // Pivot row or column elements
521 (*this)(j,iPivot) *= vPivot;
522 (*fgBuffer)(iPivot,j) *= vPivot;
523 }
524 //
525 }
526 else { // No more pivot value (clear those elements)
527 for (Int_t j=0; j<nGlo; j++) {
528 if (bUnUsed[j]) {
529 vecB[j] = 0.0;
530 for (Int_t k=0; k<nGlo; k++) {
531 (*this)(j,k) = 0.;
532 if (j!=k) (*fgBuffer)(j,k) = 0;
533 }
534 }
535 }
536 break; // No more pivots anyway, stop here
537 }
538 }
539 //
c8f37c50 540 if (stabilize) for (Int_t i=0; i<nGlo; i++) for (Int_t j=0; j<nGlo; j++) {
541 double vl = TMath::Sqrt(colMax[i])*TMath::Sqrt(rowMax[j]); // Correct matrix V
542 if (i>=j) (*this)(i,j) *= vl;
543 else (*fgBuffer)(j,i) *= vl;
544 }
8a9ab0eb 545 //
546 for (Int_t j=0; j<nGlo; j++) {
547 rowMax[j] = 0.0;
548 for (Int_t jj=0; jj<nGlo; jj++) { // Reverse matrix elements
549 double vl;
de34b538 550 if (j>=jj) vl = (*this)(j,jj) = -Query(j,jj);
551 else vl = (*fgBuffer)(j,jj) = -fgBuffer->Query(j,jj);
8a9ab0eb 552 rowMax[j] += vl*vecB[jj];
553 }
554 }
555
556 for (Int_t j=0; j<nGlo; j++) {
557 vecB[j] = rowMax[j]; // The final result
558 }
559 //
560 delete [] bUnUsed;
561 delete [] rowMax;
562 if (stabilize) delete [] colMax;
563
564 return nRank;
565}
5d88242b 566
567