Date: 2016-07-24T17:06:54+00:00

Actual source code: lsqr.c
petsc-3.7.3 2016-07-24
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      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;

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

     30:   VecGetLocalSize(v, &n);
     31:   VecGetArray(v, &x);
     32:   for (i = 0; i < n; i++) x[i] *= PetscConj(x[i]);
     33:   VecRestoreArray(v, &x);
     34:   return(0);
     35: }

     39: static PetscErrorCode KSPSetUp_LSQR(KSP ksp)
     40: {
     42:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
     43:   PetscBool      nopreconditioner;

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

     49:   lsqr->nwork_m = 2;
     50:   if (lsqr->vwork_m) {
     51:     VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
     52:   }
     53:   if (nopreconditioner) lsqr->nwork_n = 4;
     54:   else lsqr->nwork_n = 5;

     56:   if (lsqr->vwork_n) {
     57:     VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
     58:   }
     59:   KSPCreateVecs(ksp,lsqr->nwork_n,&lsqr->vwork_n,lsqr->nwork_m,&lsqr->vwork_m);
     60:   if (lsqr->se_flg && !lsqr->se) {
     61:     /* lsqr->se is not set by user, get it from pmat */
     62:     Vec *se;
     63:     KSPCreateVecs(ksp,1,&se,0,NULL);
     64:     lsqr->se = *se;
     65:     PetscFree(se);
     66:   }
     67:   return(0);
     68: }

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

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

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

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

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

     97:   /* vectors of length m, where system size is mxn */
     98:   B  = ksp->vec_rhs;
     99:   U  = lsqr->vwork_m[0];
    100:   U1 = lsqr->vwork_m[1];

    102:   /* vectors of length n */
    103:   X  = ksp->vec_sol;
    104:   W  = lsqr->vwork_n[0];
    105:   V  = lsqr->vwork_n[1];
    106:   V1 = lsqr->vwork_n[2];
    107:   W2 = lsqr->vwork_n[3];
    108:   if (!nopreconditioner) Z = lsqr->vwork_n[4];

    110:   /* standard error vector */
    111:   SE = lsqr->se;
    112:   if (SE) {
    113:     VecGetSize(SE,&size1);
    114:     VecGetSize(X,&size2);
    115:     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);
    116:     VecSet(SE,0.0);
    117:   }

    119:   /* Compute initial residual, temporarily use work vector u */
    120:   if (!ksp->guess_zero) {
    121:     KSP_MatMult(ksp,Amat,X,U);       /*   u <- b - Ax     */
    122:     VecAYPX(U,-1.0,B);
    123:   } else {
    124:     VecCopy(B,U);            /*   u <- b (x is 0) */
    125:   }

    127:   /* Test for nothing to do */
    128:   VecNorm(U,NORM_2,&rnorm);
    129:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
    130:   ksp->its   = 0;
    131:   ksp->rnorm = rnorm;
    132:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
    133:   KSPLogResidualHistory(ksp,rnorm);
    134:   KSPMonitor(ksp,0,rnorm);
    135:   (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
    136:   if (ksp->reason) return(0);

    138:   beta = rnorm;
    139:   VecScale(U,1.0/beta);
    140:   KSP_MatMultTranspose(ksp,Amat,U,V);
    141:   if (nopreconditioner) {
    142:     VecNorm(V,NORM_2,&alpha);
    143:   } else {
    144:     PCApply(ksp->pc,V,Z);
    145:     VecDotRealPart(V,Z,&alpha);
    146:     if (alpha <= 0.0) {
    147:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
    148:       return(0);
    149:     }
    150:     alpha = PetscSqrtReal(alpha);
    151:     VecScale(Z,1.0/alpha);
    152:   }
    153:   VecScale(V,1.0/alpha);

    155:   if (nopreconditioner) {
    156:     VecCopy(V,W);
    157:   } else {
    158:     VecCopy(Z,W);
    159:   }

    161:   lsqr->arnorm = alpha * beta;
    162:   phibar       = beta;
    163:   rhobar       = alpha;
    164:   i            = 0;
    165:   do {
    166:     if (nopreconditioner) {
    167:       KSP_MatMult(ksp,Amat,V,U1);
    168:     } else {
    169:       KSP_MatMult(ksp,Amat,Z,U1);
    170:     }
    171:     VecAXPY(U1,-alpha,U);
    172:     VecNorm(U1,NORM_2,&beta);
    173:     if (beta > 0.0) {
    174:       VecScale(U1,1.0/beta); /* beta*U1 = Amat*V - alpha*U */
    175:     }

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

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

    203:     if (SE) {
    204:       VecCopy(W,W2);
    205:       VecSquare(W2);
    206:       VecScale(W2,1.0/(rho*rho));
    207:       VecAXPY(SE, 1.0, W2); /* SE <- SE + (w^2/rho^2) */
    208:     }
    209:     if (nopreconditioner) {
    210:       VecAYPX(W,-theta/rho,V1);  /* w <- v - (theta/rho) w */
    211:     } else {
    212:       VecAYPX(W,-theta/rho,Z);   /* w <- z - (theta/rho) w */
    213:     }

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

    218:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
    219:     ksp->its++;
    220:     ksp->rnorm = rnorm;
    221:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
    222:     KSPLogResidualHistory(ksp,rnorm);
    223:     KSPMonitor(ksp,i+1,rnorm);
    224:     (*ksp->converged)(ksp,i+1,rnorm,&ksp->reason,ksp->cnvP);
    225:     if (ksp->reason) break;
    226:     SWAP(U1,U,TMP);
    227:     SWAP(V1,V,TMP);

    229:     i++;
    230:   } while (i<ksp->max_it);
    231:   if (i >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;

    233:   /* Finish off the standard error estimates */
    234:   if (SE) {
    235:     tmp  = 1.0;
    236:     MatGetSize(Amat,&size1,&size2);
    237:     if (size1 > size2) tmp = size1 - size2;
    238:     tmp  = rnorm / PetscSqrtScalar(tmp);
    239:     VecSqrtAbs(SE);
    240:     VecScale(SE,tmp);
    241:   }
    242:   return(0);
    243: }

    248: PetscErrorCode KSPDestroy_LSQR(KSP ksp)
    249: {
    250:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

    254:   /* Free work vectors */
    255:   if (lsqr->vwork_n) {
    256:     VecDestroyVecs(lsqr->nwork_n,&lsqr->vwork_n);
    257:   }
    258:   if (lsqr->vwork_m) {
    259:     VecDestroyVecs(lsqr->nwork_m,&lsqr->vwork_m);
    260:   }
    261:   if (lsqr->se_flg) {
    262:     VecDestroy(&lsqr->se);
    263:   }
    264:   PetscFree(ksp->data);
    265:   return(0);
    266: }

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

    276:   VecDestroy(&lsqr->se);
    277:   lsqr->se = se;
    278:   return(0);
    279: }

    283: PetscErrorCode  KSPLSQRGetStandardErrorVec(KSP ksp,Vec *se)
    284: {
    285:   KSP_LSQR *lsqr = (KSP_LSQR*)ksp->data;

    288:   *se = lsqr->se;
    289:   return(0);
    290: }

    294: PetscErrorCode  KSPLSQRGetArnorm(KSP ksp,PetscReal *arnorm, PetscReal *rhs_norm, PetscReal *anorm)
    295: {
    296:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

    300:   *arnorm = lsqr->arnorm;
    301:   if (anorm) {
    302:     if (lsqr->anorm < 0.0) {
    303:       PC  pc;
    304:       Mat Amat;
    305:       KSPGetPC(ksp,&pc);
    306:       PCGetOperators(pc,&Amat,NULL);
    307:       MatNorm(Amat,NORM_FROBENIUS,&lsqr->anorm);
    308:     }
    309:     *anorm = lsqr->anorm;
    310:   }
    311:   if (rhs_norm) *rhs_norm = lsqr->rhs_norm;
    312:   return(0);
    313: }

    317: /*@C
    318:    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

    320:    Collective on KSP

    322:    Input Parameters:
    323: +  ksp   - iterative context
    324: .  n     - iteration number
    325: .  rnorm - 2-norm (preconditioned) residual value (may be estimated).
    326: -  dummy - viewer and format context

    328:    Level: intermediate

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

    332: .seealso: KSPMonitorSet(), KSPMonitorTrueResidualNorm(), KSPMonitorLGResidualNormCreate(), KSPMonitorDefault()
    333: @*/
    334: PetscErrorCode  KSPLSQRMonitorDefault(KSP ksp,PetscInt n,PetscReal rnorm,PetscViewerAndFormat *dummy)
    335: {
    337:   PetscViewer    viewer = dummy->viewer;
    338:   KSP_LSQR       *lsqr  = (KSP_LSQR*)ksp->data;

    341:   PetscViewerPushFormat(viewer,dummy->format);
    342:   PetscViewerASCIIAddTab(viewer,((PetscObject)ksp)->tablevel);
    343:   if (((PetscObject)ksp)->prefix) {
    344:     PetscViewerASCIIPrintf(viewer,"  Residual norm and norm of normal equations for %s solve.\n",((PetscObject)ksp)->prefix);
    345:   }
    346:   if (!n) {
    347:     PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e\n",n,rnorm);
    348:   } else {
    349:     PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e Residual norm normal equations %14.12e\n",n,rnorm,lsqr->arnorm);
    350:   }
    351:   PetscViewerASCIISubtractTab(viewer,((PetscObject)ksp)->tablevel);
    352:   PetscViewerPopFormat(viewer);
    353:   return(0);
    354: }

    358: PetscErrorCode KSPSetFromOptions_LSQR(PetscOptionItems *PetscOptionsObject,KSP ksp)
    359: {
    361:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

    364:   PetscOptionsHead(PetscOptionsObject,"KSP LSQR Options");
    365:   PetscOptionsName("-ksp_lsqr_set_standard_error","Set Standard Error Estimates of Solution","KSPLSQRSetStandardErrorVec",&lsqr->se_flg);
    366:   KSPMonitorSetFromOptions(ksp,"-ksp_lsqr_monitor","Monitor residual norm and norm of residual of normal equations","KSPMonitorSet",KSPLSQRMonitorDefault);
    367:   PetscOptionsTail();
    368:   return(0);
    369: }

    373: PetscErrorCode KSPView_LSQR(KSP ksp,PetscViewer viewer)
    374: {
    375:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;
    377:   PetscBool      iascii;

    380:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    381:   if (iascii) {
    382:     if (lsqr->se) {
    383:       PetscReal rnorm;
    384:       KSPLSQRGetStandardErrorVec(ksp,&lsqr->se);
    385:       VecNorm(lsqr->se,NORM_2,&rnorm);
    386:       PetscViewerASCIIPrintf(viewer,"  Norm of Standard Error %g, Iterations %D\n",(double)rnorm,ksp->its);
    387:     }
    388:   }
    389:   return(0);
    390: }

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

    398:    Collective on KSP

    400:    Input Parameters:
    401: +  ksp   - iterative context
    402: .  n     - iteration number
    403: .  rnorm - 2-norm residual value (may be estimated)
    404: -  ctx - convergence context which must be created by KSPConvergedDefaultCreate()

    406:    reason is set to:
    407: +   positive - if the iteration has converged;
    408: .   negative - if residual norm exceeds divergence threshold;
    409: -   0 - otherwise.

    411:    Notes:
    412:       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.

    414:    Level: intermediate

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

    418: .seealso: KSPSetConvergenceTest(), KSPSetTolerances(), KSPConvergedSkip(), KSPConvergedReason, KSPGetConvergedReason(),
    419:           KSPConvergedDefaultSetUIRNorm(), KSPConvergedDefaultSetUMIRNorm(), KSPConvergedDefaultCreate(), KSPConvergedDefaultDestroy(), KSPConvergedDefault()
    420: @*/
    421: PetscErrorCode  KSPLSQRDefaultConverged(KSP ksp,PetscInt n,PetscReal rnorm,KSPConvergedReason *reason,void *ctx)
    422: {
    424:   KSP_LSQR       *lsqr = (KSP_LSQR*)ksp->data;

    427:   KSPConvergedDefault(ksp,n,rnorm,reason,ctx);
    428:   if (!n || *reason) return(0);
    429:   if (lsqr->arnorm/lsqr->rhs_norm < ksp->rtol) *reason = KSP_CONVERGED_RTOL_NORMAL;
    430:   if (lsqr->arnorm < ksp->abstol) *reason = KSP_CONVERGED_ATOL_NORMAL;
    431:   return(0);
    432: }

    434: /*MC
    435:      KSPLSQR - This implements LSQR

    437:    Options Database Keys:
    438: +   -ksp_lsqr_set_standard_error  - Set Standard Error Estimates of Solution see KSPLSQRSetStandardErrorVec()
    439: .   -ksp_lsqr_monitor - Monitor residual norm and norm of residual of normal equations
    440: -   see KSPSolve()

    442:    Level: beginner

    444:    Notes:
    445:      Supports non-square (rectangular) matrices.

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

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

    453:      Supports only left preconditioning.

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

    458:      In exact arithmetic the LSQR method (with no preconditioning) is identical to the KSPCG algorithm applied to the normal equations.
    459:      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
    460:      track the true norm of the residual and uses that in the convergence test.

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

    466:    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()

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

    470: M*/
    473: PETSC_EXTERN PetscErrorCode KSPCreate_LSQR(KSP ksp)
    474: {
    475:   KSP_LSQR       *lsqr;

    479:   PetscNewLog(ksp,&lsqr);
    480:   lsqr->se     = NULL;
    481:   lsqr->se_flg = PETSC_FALSE;
    482:   lsqr->arnorm = 0.0;
    483:   ksp->data    = (void*)lsqr;
    484:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,3);

    486:   ksp->ops->setup          = KSPSetUp_LSQR;
    487:   ksp->ops->solve          = KSPSolve_LSQR;
    488:   ksp->ops->destroy        = KSPDestroy_LSQR;
    489:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    490:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    491:   ksp->ops->setfromoptions = KSPSetFromOptions_LSQR;
    492:   ksp->ops->view           = KSPView_LSQR;
    493:   ksp->converged           = KSPLSQRDefaultConverged;
    494:   return(0);
    495: }