Actual source code: lsqr.c

petsc-master 2017-10-17
Report Typos and Errors

  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>

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

 20: static PetscErrorCode  VecSquare(Vec v)
 21: {
 23:   PetscScalar    *x;
 24:   PetscInt       i, n;

 27:   VecGetLocalSize(v, &n);
 28:   VecGetArray(v, &x);
 29:   for (i = 0; i < n; i++) x[i] *= PetscConj(x[i]);
 30:   VecRestoreArray(v, &x);
 31:   return(0);
 32: }

 34: static PetscErrorCode KSPSetUp_LSQR(KSP ksp)
 35: {
 37:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
 38:   PetscBool      nopreconditioner;

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

 44:   lsqr->nwork_m = 2;
 45:   if (lsqr->vwork_m) {
 46:     VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
 47:   }
 48:   if (nopreconditioner) lsqr->nwork_n = 4;
 49:   else lsqr->nwork_n = 5;

 51:   if (lsqr->vwork_n) {
 52:     VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
 53:   }
 54:   KSPCreateVecs(ksp,lsqr->nwork_n,&lsqr->vwork_n,lsqr->nwork_m,&lsqr->vwork_m);
 55:   if (lsqr->se_flg && !lsqr->se) {
 56:     /* lsqr->se is not set by user, get it from pmat */
 57:     Vec *se;
 58:     KSPCreateVecs(ksp,1,&se,0,NULL);
 59:     lsqr->se = *se;
 60:     PetscFree(se);
 61:   }
 62:   return(0);
 63: }

 65: static PetscErrorCode KSPSolve_LSQR(KSP ksp)
 66: {
 68:   PetscInt       i,size1,size2;
 69:   PetscScalar    rho,rhobar,phi,phibar,theta,c,s,tmp,tau;
 70:   PetscReal      beta,alpha,rnorm;
 71:   Vec            X,B,V,V1,U,U1,TMP,W,W2,SE,Z = NULL;
 72:   Mat            Amat,Pmat;
 73:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
 74:   PetscBool      diagonalscale,nopreconditioner;

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

 80:   PCGetOperators(ksp->pc,&Amat,&Pmat);
 81:   PetscObjectTypeCompare((PetscObject)ksp->pc,PCNONE,&nopreconditioner);

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

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

 90:   /* vectors of length m, where system size is mxn */
 91:   B  = ksp->vec_rhs;
 92:   U  = lsqr->vwork_m[0];
 93:   U1 = lsqr->vwork_m[1];

 95:   /* vectors of length n */
 96:   X  = ksp->vec_sol;
 97:   W  = lsqr->vwork_n[0];
 98:   V  = lsqr->vwork_n[1];
 99:   V1 = lsqr->vwork_n[2];
100:   W2 = lsqr->vwork_n[3];
101:   if (!nopreconditioner) Z = lsqr->vwork_n[4];

103:   /* standard error vector */
104:   SE = lsqr->se;
105:   if (SE) {
106:     VecGetSize(SE,&size1);
107:     VecGetSize(X,&size2);
108:     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);
109:     VecSet(SE,0.0);
110:   }

112:   /* Compute initial residual, temporarily use work vector u */
113:   if (!ksp->guess_zero) {
114:     KSP_MatMult(ksp,Amat,X,U);       /*   u <- b - Ax     */
115:     VecAYPX(U,-1.0,B);
116:   } else {
117:     VecCopy(B,U);            /*   u <- b (x is 0) */
118:   }

120:   /* Test for nothing to do */
121:   VecNorm(U,NORM_2,&rnorm);
122:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
123:   ksp->its   = 0;
124:   ksp->rnorm = rnorm;
125:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
126:   KSPLogResidualHistory(ksp,rnorm);
127:   KSPMonitor(ksp,0,rnorm);
128:   (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
129:   if (ksp->reason) return(0);

131:   beta = rnorm;
132:   VecScale(U,1.0/beta);
133:   KSP_MatMultTranspose(ksp,Amat,U,V);
134:   if (nopreconditioner) {
135:     VecNorm(V,NORM_2,&alpha);
136:   } else {
137:     PCApply(ksp->pc,V,Z);
138:     VecDotRealPart(V,Z,&alpha);
139:     if (alpha <= 0.0) {
140:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
141:       return(0);
142:     }
143:     alpha = PetscSqrtReal(alpha);
144:     VecScale(Z,1.0/alpha);
145:   }
146:   VecScale(V,1.0/alpha);

148:   if (nopreconditioner) {
149:     VecCopy(V,W);
150:   } else {
151:     VecCopy(Z,W);
152:   }

154:   lsqr->arnorm = alpha * beta;
155:   phibar       = beta;
156:   rhobar       = alpha;
157:   i            = 0;
158:   do {
159:     if (nopreconditioner) {
160:       KSP_MatMult(ksp,Amat,V,U1);
161:     } else {
162:       KSP_MatMult(ksp,Amat,Z,U1);
163:     }
164:     VecAXPY(U1,-alpha,U);
165:     VecNorm(U1,NORM_2,&beta);
166:     if (beta > 0.0) {
167:       VecScale(U1,1.0/beta); /* beta*U1 = Amat*V - alpha*U */
168:     }

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

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

196:     if (SE) {
197:       VecCopy(W,W2);
198:       VecSquare(W2);
199:       VecScale(W2,1.0/(rho*rho));
200:       VecAXPY(SE, 1.0, W2); /* SE <- SE + (w^2/rho^2) */
201:     }
202:     if (nopreconditioner) {
203:       VecAYPX(W,-theta/rho,V1);  /* w <- v - (theta/rho) w */
204:     } else {
205:       VecAYPX(W,-theta/rho,Z);   /* w <- z - (theta/rho) w */
206:     }

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

211:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
212:     ksp->its++;
213:     ksp->rnorm = rnorm;
214:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
215:     KSPLogResidualHistory(ksp,rnorm);
216:     KSPMonitor(ksp,i+1,rnorm);
217:     (*ksp->converged)(ksp,i+1,rnorm,&ksp->reason,ksp->cnvP);
218:     if (ksp->reason) break;
219:     SWAP(U1,U,TMP);
220:     SWAP(V1,V,TMP);

222:     i++;
223:   } while (i<ksp->max_it);
224:   if (i >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;

226:   /* Finish off the standard error estimates */
227:   if (SE) {
228:     tmp  = 1.0;
229:     MatGetSize(Amat,&size1,&size2);
230:     if (size1 > size2) tmp = size1 - size2;
231:     tmp  = rnorm / PetscSqrtScalar(tmp);
232:     VecSqrtAbs(SE);
233:     VecScale(SE,tmp);
234:   }
235:   return(0);
236: }


239: PetscErrorCode KSPDestroy_LSQR(KSP ksp)
240: {
241:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

245:   /* Free work vectors */
246:   if (lsqr->vwork_n) {
247:     VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
248:   }
249:   if (lsqr->vwork_m) {
250:     VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
251:   }
252:   if (lsqr->se_flg) {
253:     VecDestroy(&lsqr->se);
254:   }
255:   PetscFree(ksp->data);
256:   return(0);
257: }

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: }

270: PetscErrorCode  KSPLSQRGetStandardErrorVec(KSP ksp,Vec *se)
271: {
272:   KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;

275:   *se = lsqr->se;
276:   return(0);
277: }

279: PetscErrorCode  KSPLSQRGetArnorm(KSP ksp,PetscReal *arnorm, PetscReal *rhs_norm, PetscReal *anorm)
280: {
281:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

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

300: /*@C
301:    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

303:    Collective on KSP

305:    Input Parameters:
306: +  ksp   - iterative context
307: .  n     - iteration number
308: .  rnorm - 2-norm (preconditioned) residual value (may be estimated).
309: -  dummy - viewer and format context

311:    Level: intermediate

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

315: .seealso: KSPMonitorSet(), KSPMonitorTrueResidualNorm(), KSPMonitorLGResidualNormCreate(), KSPMonitorDefault()
316: @*/
317: PetscErrorCode  KSPLSQRMonitorDefault(KSP ksp,PetscInt n,PetscReal rnorm,PetscViewerAndFormat *dummy)
318: {
320:   PetscViewer    viewer = dummy->viewer;
321:   KSP_LSQR       *lsqr  = (KSP_LSQR*)ksp->data;

324:   PetscViewerPushFormat(viewer,dummy->format);
325:   PetscViewerASCIIAddTab(viewer,((PetscObject)ksp)->tablevel);
326:   if (((PetscObject)ksp)->prefix) {
327:     PetscViewerASCIIPrintf(viewer,"  Residual norm and norm of normal equations for %s solve.\n",((PetscObject)ksp)->prefix);
328:   }
329:   if (!n) {
330:     PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e\n",n,rnorm);
331:   } else {
332:     PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e Residual norm normal equations %14.12e\n",n,rnorm,lsqr->arnorm);
333:   }
334:   PetscViewerASCIISubtractTab(viewer,((PetscObject)ksp)->tablevel);
335:   PetscViewerPopFormat(viewer);
336:   return(0);
337: }

339: PetscErrorCode KSPSetFromOptions_LSQR(PetscOptionItems *PetscOptionsObject,KSP ksp)
340: {
342:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

345:   PetscOptionsHead(PetscOptionsObject,"KSP LSQR Options");
346:   PetscOptionsName("-ksp_lsqr_set_standard_error","Set Standard Error Estimates of Solution","KSPLSQRSetStandardErrorVec",&lsqr->se_flg);
347:   KSPMonitorSetFromOptions(ksp,"-ksp_lsqr_monitor","Monitor residual norm and norm of residual of normal equations","KSPMonitorSet",KSPLSQRMonitorDefault);
348:   PetscOptionsTail();
349:   return(0);
350: }

352: PetscErrorCode KSPView_LSQR(KSP ksp,PetscViewer viewer)
353: {
354:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
356:   PetscBool      iascii;

359:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
360:   if (iascii) {
361:     if (lsqr->se) {
362:       PetscReal rnorm;
363:       KSPLSQRGetStandardErrorVec(ksp,&lsqr->se);
364:       VecNorm(lsqr->se,NORM_2,&rnorm);
365:       PetscViewerASCIIPrintf(viewer,"  Norm of Standard Error %g, Iterations %D\n",(double)rnorm,ksp->its);
366:     }
367:   }
368:   return(0);
369: }

371: /*@C
372:    KSPLSQRDefaultConverged - Determines convergence of the LSQR Krylov method. This calls KSPConvergedDefault() and if that does not determine convergence then checks
373:       convergence for the least squares problem.

375:    Collective on KSP

377:    Input Parameters:
378: +  ksp   - iterative context
379: .  n     - iteration number
380: .  rnorm - 2-norm residual value (may be estimated)
381: -  ctx - convergence context which must be created by KSPConvergedDefaultCreate()

383:    reason is set to:
384: +   positive - if the iteration has converged;
385: .   negative - if residual norm exceeds divergence threshold;
386: -   0 - otherwise.

388:    Notes:
389:       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.

391:    Level: intermediate

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

395: .seealso: KSPSetConvergenceTest(), KSPSetTolerances(), KSPConvergedSkip(), KSPConvergedReason, KSPGetConvergedReason(),
396:           KSPConvergedDefaultSetUIRNorm(), KSPConvergedDefaultSetUMIRNorm(), KSPConvergedDefaultCreate(), KSPConvergedDefaultDestroy(), KSPConvergedDefault()
397: @*/
398: PetscErrorCode  KSPLSQRDefaultConverged(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
399: {
401:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

404:   KSPConvergedDefault(ksp,n,rnorm,reason,ctx);
405:   if (!n || *reason) return(0);
406:   if (lsqr->arnorm/lsqr->rhs_norm < ksp->rtol) *reason = KSP_CONVERGED_RTOL_NORMAL;
407:   if (lsqr->arnorm < ksp->abstol) *reason = KSP_CONVERGED_ATOL_NORMAL;
408:   return(0);
409: }

411: /*MC
412:      KSPLSQR - This implements LSQR

414:    Options Database Keys:
415: +   -ksp_lsqr_set_standard_error  - Set Standard Error Estimates of Solution see KSPLSQRSetStandardErrorVec()
416: .   -ksp_lsqr_monitor - Monitor residual norm and norm of residual of normal equations
417: -   see KSPSolve()

419:    Level: beginner

421:    Notes:
422:      Supports non-square (rectangular) matrices.

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

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

430:      Supports only left preconditioning.

432:    References:
433: .  1. - The original unpreconditioned algorithm can be found in Paige and Saunders, ACM Transactions on Mathematical Software, Vol 8, 1982.

435:      In exact arithmetic the LSQR method (with no preconditioning) is identical to the KSPCG algorithm applied to the normal equations.
436:      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
437:      track the true norm of the residual and uses that in the convergence test.

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


443:    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()

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

447: M*/
448: PETSC_EXTERN PetscErrorCode KSPCreate_LSQR(KSP ksp)
449: {
450:   KSP_LSQR       *lsqr;

454:   PetscNewLog(ksp,&lsqr);
455:   lsqr->se     = NULL;
456:   lsqr->se_flg = PETSC_FALSE;
457:   lsqr->arnorm = 0.0;
458:   ksp->data    = (void*)lsqr;
459:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,3);

461:   ksp->ops->setup          = KSPSetUp_LSQR;
462:   ksp->ops->solve          = KSPSolve_LSQR;
463:   ksp->ops->destroy        = KSPDestroy_LSQR;
464:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
465:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
466:   ksp->ops->setfromoptions = KSPSetFromOptions_LSQR;
467:   ksp->ops->view           = KSPView_LSQR;
468:   ksp->converged           = KSPLSQRDefaultConverged;
469:   return(0);
470: }