Actual source code: lsqr.c

petsc-3.4.4 2014-03-13
  2: /* lourens.vanzanen@shell.com contributed the standard error estimates of the solution, Jul 25, 2006 */
  3: /* Bas van't Hof contributed the preconditioned aspects Feb 10, 2010 */

  5: #define SWAP(a,b,c) { c = a; a = b; b = c; }

  7: #include <petsc-private/kspimpl.h>
  8: #include <../src/ksp/ksp/impls/lsqr/lsqr.h>

 10: typedef struct {
 11:   PetscInt  nwork_n,nwork_m;
 12:   Vec       *vwork_m;   /* work vectors of length m, where the system is size m x n */
 13:   Vec       *vwork_n;   /* work vectors of length n */
 14:   Vec       se;         /* Optional standard error vector */
 15:   PetscBool se_flg;     /* flag for -ksp_lsqr_set_standard_error */
 16:   PetscReal arnorm;     /* Norm of the vector A.r */
 17:   PetscReal anorm;      /* Frobenius norm of the matrix A */
 18:   PetscReal rhs_norm;   /* Norm of the right hand side */
 19: } KSP_LSQR;

 21: extern PetscErrorCode  VecSquare(Vec);

 25: static PetscErrorCode KSPSetUp_LSQR(KSP ksp)
 26: {
 28:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
 29:   PetscBool      nopreconditioner;

 32:   PetscObjectTypeCompare((PetscObject)ksp->pc,PCNONE,&nopreconditioner);
 33:   /*  nopreconditioner =PETSC_FALSE; */

 35:   lsqr->nwork_m = 2;
 36:   if (lsqr->vwork_m) {
 37:     VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
 38:   }
 39:   if (nopreconditioner) lsqr->nwork_n = 4;
 40:   else lsqr->nwork_n = 5;

 42:   if (lsqr->vwork_n) {
 43:     VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
 44:   }
 45:   KSPGetVecs(ksp,lsqr->nwork_n,&lsqr->vwork_n,lsqr->nwork_m,&lsqr->vwork_m);
 46:   if (lsqr->se_flg && !lsqr->se) {
 47:     /* lsqr->se is not set by user, get it from pmat */
 48:     Vec *se;
 49:     KSPGetVecs(ksp,1,&se,0,NULL);
 50:     lsqr->se = *se;
 51:     PetscFree(se);
 52:   }
 53:   return(0);
 54: }

 58: static PetscErrorCode KSPSolve_LSQR(KSP ksp)
 59: {
 61:   PetscInt       i,size1,size2;
 62:   PetscScalar    rho,rhobar,phi,phibar,theta,c,s,tmp,tau;
 63:   PetscReal      beta,alpha,rnorm;
 64:   Vec            X,B,V,V1,U,U1,TMP,W,W2,SE,Z = NULL;
 65:   Mat            Amat,Pmat;
 66:   MatStructure   pflag;
 67:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
 68:   PetscBool      diagonalscale,nopreconditioner;

 71:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
 72:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);

 74:   PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);
 75:   PetscObjectTypeCompare((PetscObject)ksp->pc,PCNONE,&nopreconditioner);

 77:   /*  nopreconditioner =PETSC_FALSE; */
 78:   /* Calculate norm of right hand side */
 79:   VecNorm(ksp->vec_rhs,NORM_2,&lsqr->rhs_norm);

 81:   /* mark norm of matrix with negative number to indicate it has not yet been computed */
 82:   lsqr->anorm = -1.0;

 84:   /* vectors of length m, where system size is mxn */
 85:   B  = ksp->vec_rhs;
 86:   U  = lsqr->vwork_m[0];
 87:   U1 = lsqr->vwork_m[1];

 89:   /* vectors of length n */
 90:   X  = ksp->vec_sol;
 91:   W  = lsqr->vwork_n[0];
 92:   V  = lsqr->vwork_n[1];
 93:   V1 = lsqr->vwork_n[2];
 94:   W2 = lsqr->vwork_n[3];
 95:   if (!nopreconditioner) Z = lsqr->vwork_n[4];

 97:   /* standard error vector */
 98:   SE = lsqr->se;
 99:   if (SE) {
100:     VecGetSize(SE,&size1);
101:     VecGetSize(X,&size2);
102:     if (size1 != size2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Standard error vector (size %d) does not match solution vector (size %d)",size1,size2);
103:     VecSet(SE,0.0);
104:   }

106:   /* Compute initial residual, temporarily use work vector u */
107:   if (!ksp->guess_zero) {
108:     KSP_MatMult(ksp,Amat,X,U);       /*   u <- b - Ax     */
109:     VecAYPX(U,-1.0,B);
110:   } else {
111:     VecCopy(B,U);            /*   u <- b (x is 0) */
112:   }

114:   /* Test for nothing to do */
115:   VecNorm(U,NORM_2,&rnorm);
116:   PetscObjectAMSTakeAccess((PetscObject)ksp);
117:   ksp->its   = 0;
118:   ksp->rnorm = rnorm;
119:   PetscObjectAMSGrantAccess((PetscObject)ksp);
120:   KSPLogResidualHistory(ksp,rnorm);
121:   KSPMonitor(ksp,0,rnorm);
122:   (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
123:   if (ksp->reason) return(0);

125:   beta = rnorm;
126:   VecScale(U,1.0/beta);
127:   KSP_MatMultTranspose(ksp,Amat,U,V);
128:   if (nopreconditioner) {
129:     VecNorm(V,NORM_2,&alpha);
130:   } else {
131:     PCApply(ksp->pc,V,Z);
132:     VecDotRealPart(V,Z,&alpha);
133:     if (alpha <= 0.0) {
134:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
135:       return(0);
136:     }
137:     alpha = PetscSqrtReal(alpha);
138:     VecScale(Z,1.0/alpha);
139:   }
140:   VecScale(V,1.0/alpha);

142:   if (nopreconditioner) {
143:     VecCopy(V,W);
144:   } else {
145:     VecCopy(Z,W);
146:   }

148:   lsqr->arnorm = alpha * beta;
149:   phibar       = beta;
150:   rhobar       = alpha;
151:   i            = 0;
152:   do {
153:     if (nopreconditioner) {
154:       KSP_MatMult(ksp,Amat,V,U1);
155:     } else {
156:       KSP_MatMult(ksp,Amat,Z,U1);
157:     }
158:     VecAXPY(U1,-alpha,U);
159:     VecNorm(U1,NORM_2,&beta);
160:     if (beta == 0.0) {
161:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
162:       break;
163:     }
164:     VecScale(U1,1.0/beta);

166:     KSP_MatMultTranspose(ksp,Amat,U1,V1);
167:     VecAXPY(V1,-beta,V);
168:     if (nopreconditioner) {
169:       VecNorm(V1,NORM_2,&alpha);
170:     } else {
171:       PCApply(ksp->pc,V1,Z);
172:       VecDotRealPart(V1,Z,&alpha);
173:       if (alpha <= 0.0) {
174:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
175:         break;
176:       }
177:       alpha = PetscSqrtReal(alpha);
178:       VecScale(Z,1.0/alpha);
179:     }
180:     VecScale(V1,1.0/alpha);
181:     rho    = PetscSqrtScalar(rhobar*rhobar + beta*beta);
182:     c      = rhobar / rho;
183:     s      = beta / rho;
184:     theta  = s * alpha;
185:     rhobar = -c * alpha;
186:     phi    = c * phibar;
187:     phibar = s * phibar;
188:     tau    = s * phi;

190:     VecAXPY(X,phi/rho,W);  /*    x <- x + (phi/rho) w   */

192:     if (SE) {
193:       VecCopy(W,W2);
194:       VecSquare(W2);
195:       VecScale(W2,1.0/(rho*rho));
196:       VecAXPY(SE, 1.0, W2); /* SE <- SE + (w^2/rho^2) */
197:     }
198:     if (nopreconditioner) {
199:       VecAYPX(W,-theta/rho,V1);  /* w <- v - (theta/rho) w */
200:     } else {
201:       VecAYPX(W,-theta/rho,Z);   /* w <- z - (theta/rho) w */
202:     }

204:     lsqr->arnorm = alpha*PetscAbsScalar(tau);
205:     rnorm        = PetscRealPart(phibar);

207:     PetscObjectAMSTakeAccess((PetscObject)ksp);
208:     ksp->its++;
209:     ksp->rnorm = rnorm;
210:     PetscObjectAMSGrantAccess((PetscObject)ksp);
211:     KSPLogResidualHistory(ksp,rnorm);
212:     KSPMonitor(ksp,i+1,rnorm);
213:     (*ksp->converged)(ksp,i+1,rnorm,&ksp->reason,ksp->cnvP);
214:     if (ksp->reason) break;
215:     SWAP(U1,U,TMP);
216:     SWAP(V1,V,TMP);

218:     i++;
219:   } while (i<ksp->max_it);
220:   if (i >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;

222:   /* Finish off the standard error estimates */
223:   if (SE) {
224:     tmp  = 1.0;
225:     MatGetSize(Amat,&size1,&size2);
226:     if (size1 > size2) tmp = size1 - size2;
227:     tmp  = rnorm / PetscSqrtScalar(tmp);
228:     VecSqrtAbs(SE);
229:     VecScale(SE,tmp);
230:   }
231:   return(0);
232: }


237: PetscErrorCode KSPDestroy_LSQR(KSP ksp)
238: {
239:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

243:   /* Free work vectors */
244:   if (lsqr->vwork_n) {
245:     VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
246:   }
247:   if (lsqr->vwork_m) {
248:     VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
249:   }
250:   if (lsqr->se_flg) {
251:     VecDestroy(&lsqr->se);
252:   }
253:   PetscFree(ksp->data);
254:   return(0);
255: }

259: PetscErrorCode  KSPLSQRSetStandardErrorVec(KSP ksp, Vec se)
260: {
261:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

265:   VecDestroy(&lsqr->se);
266:   lsqr->se = se;
267:   return(0);
268: }

272: PetscErrorCode  KSPLSQRGetStandardErrorVec(KSP ksp,Vec *se)
273: {
274:   KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;

277:   *se = lsqr->se;
278:   return(0);
279: }

283: PetscErrorCode  KSPLSQRGetArnorm(KSP ksp,PetscReal *arnorm, PetscReal *rhs_norm, PetscReal *anorm)
284: {
285:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

289:   *arnorm = lsqr->arnorm;
290:   if (anorm) {
291:     if (lsqr->anorm < 0.0) {
292:       PC  pc;
293:       Mat Amat;
294:       KSPGetPC(ksp,&pc);
295:       PCGetOperators(pc,&Amat,NULL,NULL);
296:       MatNorm(Amat,NORM_FROBENIUS,&lsqr->anorm);
297:     }
298:     *anorm = lsqr->anorm;
299:   }
300:   if (rhs_norm) *rhs_norm = lsqr->rhs_norm;
301:   return(0);
302: }

306: /*@C
307:    KSPLSQRMonitorDefault - Print the residual norm at each iteration of the LSQR method and the norm of the residual of the normal equations A'*A x = A' b

309:    Collective on KSP

311:    Input Parameters:
312: +  ksp   - iterative context
313: .  n     - iteration number
314: .  rnorm - 2-norm (preconditioned) residual value (may be estimated).
315: -  dummy - unused monitor context

317:    Level: intermediate

319: .keywords: KSP, default, monitor, residual

321: .seealso: KSPMonitorSet(), KSPMonitorTrueResidualNorm(), KSPMonitorLGResidualNormCreate(), KSPMonitorDefault()
322: @*/
323: PetscErrorCode  KSPLSQRMonitorDefault(KSP ksp,PetscInt n,PetscReal rnorm,void *dummy)
324: {
326:   PetscViewer    viewer = dummy ? (PetscViewer) dummy : PETSC_VIEWER_STDOUT_(PetscObjectComm((PetscObject)ksp));
327:   KSP_LSQR       *lsqr  = (KSP_LSQR*)ksp->data;

330:   PetscViewerASCIIAddTab(viewer,((PetscObject)ksp)->tablevel);
331:   if (((PetscObject)ksp)->prefix) {
332:     PetscViewerASCIIPrintf(viewer,"  Residual norm and norm of normal equations for %s solve.\n",((PetscObject)ksp)->prefix);
333:   }
334:   if (!n) {
335:     PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e\n",n,rnorm);
336:   } else {
337:     PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e Residual norm normal equations %14.12e\n",n,rnorm,lsqr->arnorm);
338:   }
339:   PetscViewerASCIISubtractTab(viewer,((PetscObject)ksp)->tablevel);
340:   return(0);
341: }

345: PetscErrorCode KSPSetFromOptions_LSQR(KSP ksp)
346: {
348:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
349:   char           monfilename[PETSC_MAX_PATH_LEN];
350:   PetscViewer    monviewer;
351:   PetscBool      flg;

354:   PetscOptionsHead("KSP LSQR Options");
355:   PetscOptionsName("-ksp_lsqr_set_standard_error","Set Standard Error Estimates of Solution","KSPLSQRSetStandardErrorVec",&lsqr->se_flg);
356:   PetscOptionsString("-ksp_lsqr_monitor","Monitor residual norm and norm of residual of normal equations","KSPMonitorSet","stdout",monfilename,PETSC_MAX_PATH_LEN,&flg);
357:   if (flg) {
358:     PetscViewerASCIIOpen(PetscObjectComm((PetscObject)ksp),monfilename,&monviewer);
359:     KSPMonitorSet(ksp,KSPLSQRMonitorDefault,monviewer,(PetscErrorCode (*)(void**))PetscViewerDestroy);
360:   }
361:   PetscOptionsTail();
362:   return(0);
363: }

367: PetscErrorCode KSPView_LSQR(KSP ksp,PetscViewer viewer)
368: {
369:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
371:   PetscBool      iascii;

374:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
375:   if (iascii) {
376:     if (lsqr->se) {
377:       PetscReal rnorm;
378:       KSPLSQRGetStandardErrorVec(ksp,&lsqr->se);
379:       VecNorm(lsqr->se,NORM_2,&rnorm);
380:       PetscViewerASCIIPrintf(viewer,"  Norm of Standard Error %G, Iterations %D\n",rnorm,ksp->its);
381:     }
382:   }
383:   return(0);
384: }

388: /*@C
389:    KSPLSQRDefaultConverged - Determines convergence of the LSQR Krylov method. This calls KSPDefaultConverged() and if that does not determine convergence then checks
390:       convergence for the least squares problem.

392:    Collective on KSP

394:    Input Parameters:
395: +  ksp   - iterative context
396: .  n     - iteration number
397: .  rnorm - 2-norm residual value (may be estimated)
398: -  ctx - convergence context which must be created by KSPDefaultConvergedCreate()

400:    reason is set to:
401: +   positive - if the iteration has converged;
402: .   negative - if residual norm exceeds divergence threshold;
403: -   0 - otherwise.

405:    Notes:
406:       Possible convergence for the least squares problem (which is based on the residual of the normal equations) are KSP_CONVERGED_RTOL_NORMAL norm and KSP_CONVERGED_ATOL_NORMAL.

408:    Level: intermediate

410: .keywords: KSP, default, convergence, residual

412: .seealso: KSPSetConvergenceTest(), KSPSetTolerances(), KSPSkipConverged(), KSPConvergedReason, KSPGetConvergedReason(),
413:           KSPDefaultConvergedSetUIRNorm(), KSPDefaultConvergedSetUMIRNorm(), KSPDefaultConvergedCreate(), KSPDefaultConvergedDestroy(), KSPDefaultConverged()
414: @*/
415: PetscErrorCode  KSPLSQRDefaultConverged(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
416: {
418:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

421:   KSPDefaultConverged(ksp,n,rnorm,reason,ctx);
422:   if (!n || *reason) return(0);
423:   if (lsqr->arnorm/lsqr->rhs_norm < ksp->rtol) *reason = KSP_CONVERGED_RTOL_NORMAL;
424:   if (lsqr->arnorm < ksp->abstol) *reason = KSP_CONVERGED_ATOL_NORMAL;
425:   return(0);
426: }



430: /*MC
431:      KSPLSQR - This implements LSQR

433:    Options Database Keys:
434: +   -ksp_lsqr_set_standard_error  - Set Standard Error Estimates of Solution see KSPLSQRSetStandardErrorVec()
435: .   -ksp_lsqr_monitor - Monitor residual norm and norm of residual of normal equations
436: -   see KSPSolve()

438:    Level: beginner

440:    Notes:
441:      This varient, when applied with no preconditioning is identical to the original algorithm in exact arithematic; however, in practice, with no preconditioning
442:      due to inexact arithematic, it can converge differently. Hence when no preconditioner is used (PCType PCNONE) it automatically reverts to the original algorithm.

444:      With the PETSc built-in preconditioners, such as ICC, one should call KSPSetOperators(ksp,A,A'*A,...) since the preconditioner needs to work
445:      for the normal equations A'*A.

447:      Supports only left preconditioning.

449:    References:The original unpreconditioned algorithm can be found in Paige and Saunders, ACM Transactions on Mathematical Software, Vol 8, pp 43-71, 1982.
450:      In exact arithmetic the LSQR method (with no preconditioning) is identical to the KSPCG algorithm applied to the normal equations.
451:      The preconditioned varient was implemented by Bas van't Hof and is essentially a left preconditioning for the Normal Equations. It appears the implementation with preconditioner
452:      track the true norm of the residual and uses that in the convergence test.

454:    Developer Notes: How is this related to the KSPCGNE implementation? One difference is that KSPCGNE applies
455:             the preconditioner transpose times the preconditioner,  so one does not need to pass A'*A as the third argument to KSPSetOperators().


458:    For least squares problems without a zero to A*x = b, there are additional convergence tests for the residual of the normal equations, A'*(b - Ax), see KSPLSQRDefaultConverged()

460: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPLSQRDefaultConverged()

462: M*/
465: PETSC_EXTERN PetscErrorCode KSPCreate_LSQR(KSP ksp)
466: {
467:   KSP_LSQR       *lsqr;

471:   PetscNewLog(ksp,KSP_LSQR,&lsqr);
472:   lsqr->se     = NULL;
473:   lsqr->se_flg = PETSC_FALSE;
474:   lsqr->arnorm = 0.0;
475:   ksp->data    = (void*)lsqr;
476:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,2);

478:   ksp->ops->setup          = KSPSetUp_LSQR;
479:   ksp->ops->solve          = KSPSolve_LSQR;
480:   ksp->ops->destroy        = KSPDestroy_LSQR;
481:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
482:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
483:   ksp->ops->setfromoptions = KSPSetFromOptions_LSQR;
484:   ksp->ops->view           = KSPView_LSQR;
485:   ksp->converged           = KSPLSQRDefaultConverged;
486:   return(0);
487: }

491: PetscErrorCode  VecSquare(Vec v)
492: {
494:   PetscScalar    *x;
495:   PetscInt       i, n;

498:   VecGetLocalSize(v, &n);
499:   VecGetArray(v, &x);
500:   for (i = 0; i < n; i++) x[i] *= x[i];
501:   VecRestoreArray(v, &x);
502:   return(0);
503: }