Date: 2013-07-02T14:48:19+00:00

Actual source code: lsqr.c
petsc-3.4.2 2013-07-02

      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: }