Actual source code: ibcgs.c

      2: #include <petsc/private/kspimpl.h>
      3: #include <petsc/private/vecimpl.h>

      5: static PetscErrorCode KSPSetUp_IBCGS(KSP ksp)
      6: {
      8:   PetscBool      diagonalscale;

     11:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
     12:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
     13:   KSPSetWorkVecs(ksp,9);
     14:   return(0);
     15: }

     17: /*
     18:     The code below "cheats" from PETSc style
     19:        1) VecRestoreArray() is called immediately after VecGetArray() and the array values are still accessed; the reason for the immediate
     20:           restore is that Vec operations are done on some of the vectors during the solve and if we did not restore immediately it would
     21:           generate two VecGetArray() (the second one inside the Vec operation) calls without a restore between them.
     22:        2) The vector operations on done directly on the arrays instead of with VecXXXX() calls

     24:        For clarity in the code we name single VECTORS with two names, for example, Rn_1 and R, but they actually always
     25:      the exact same memory. We do this with macro defines so that compiler won't think they are
     26:      two different variables.

     28: */
     29: #define Xn_1 Xn
     30: #define xn_1 xn
     31: #define Rn_1 Rn
     32: #define rn_1 rn
     33: #define Un_1 Un
     34: #define un_1 un
     35: #define Vn_1 Vn
     36: #define vn_1 vn
     37: #define Qn_1 Qn
     38: #define qn_1 qn
     39: #define Zn_1 Zn
     40: #define zn_1 zn
     41: static PetscErrorCode  KSPSolve_IBCGS(KSP ksp)
     42: {
     44:   PetscInt       i,N;
     45:   PetscReal      rnorm = 0.0,rnormin = 0.0;
     46: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
     47:   /* Because of possible instabilities in the algorithm (as indicated by different residual histories for the same problem
     48:      on the same number of processes  with different runs) we support computing the inner products using Intel's 80 bit arithmetic
     49:      rather than just 64 bit. Thus we copy our double precision values into long doubles (hoping this keeps the 16 extra bits)
     50:      and tell MPI to do its ALlreduces with MPI_LONG_DOUBLE.

     52:      Note for developers that does not effect the code. Intel's long double is implemented by storing the 80 bits of extended double
     53:      precision into a 16 byte space (the rest of the space is ignored)  */
     54:   long double insums[7],outsums[7];
     55: #else
     56:   PetscScalar insums[7],outsums[7];
     57: #endif
     58:   PetscScalar                       sigman_2, sigman_1, sigman, pin_1, pin, phin_1, phin,tmp1,tmp2;
     59:   PetscScalar                       taun_1, taun, rhon, alphan_1, alphan, omegan_1, omegan;
     60:   const PetscScalar *PETSC_RESTRICT r0, *PETSC_RESTRICT f0, *PETSC_RESTRICT qn, *PETSC_RESTRICT b, *PETSC_RESTRICT un;
     61:   PetscScalar *PETSC_RESTRICT       rn, *PETSC_RESTRICT xn, *PETSC_RESTRICT vn, *PETSC_RESTRICT zn;
     62:   /* the rest do not have to keep n_1 values */
     63:   PetscScalar                       kappan, thetan, etan, gamman, betan, deltan;
     64:   const PetscScalar *PETSC_RESTRICT tn;
     65:   PetscScalar *PETSC_RESTRICT       sn;
     66:   Vec                               R0,Rn,Xn,F0,Vn,Zn,Qn,Tn,Sn,B,Un;
     67:   Mat                               A;

     70:   if (!ksp->vec_rhs->petscnative) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Only coded for PETSc vectors");

     72:  #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
     73:   /* since 80 bit long doubls do not fill the upper bits, we fill them initially so that
     74:      valgrind won't detect MPI_Allreduce() with uninitialized data */
     75:   PetscMemzero(insums,sizeof(insums));
     76:   PetscMemzero(insums,sizeof(insums));
     77: #endif

     79:   PCGetOperators(ksp->pc,&A,NULL);
     80:   VecGetLocalSize(ksp->vec_sol,&N);
     81:   Xn   = ksp->vec_sol; VecGetArray(Xn_1,(PetscScalar**)&xn_1); VecRestoreArray(Xn_1,NULL);
     82:   B    = ksp->vec_rhs; VecGetArrayRead(B,(const PetscScalar**)&b); VecRestoreArrayRead(B,NULL);
     83:   R0   = ksp->work[0]; VecGetArrayRead(R0,(const PetscScalar**)&r0); VecRestoreArrayRead(R0,NULL);
     84:   Rn   = ksp->work[1]; VecGetArray(Rn_1,(PetscScalar**)&rn_1); VecRestoreArray(Rn_1,NULL);
     85:   Un   = ksp->work[2]; VecGetArrayRead(Un_1,(const PetscScalar**)&un_1); VecRestoreArrayRead(Un_1,NULL);
     86:   F0   = ksp->work[3]; VecGetArrayRead(F0,(const PetscScalar**)&f0); VecRestoreArrayRead(F0,NULL);
     87:   Vn   = ksp->work[4]; VecGetArray(Vn_1,(PetscScalar**)&vn_1); VecRestoreArray(Vn_1,NULL);
     88:   Zn   = ksp->work[5]; VecGetArray(Zn_1,(PetscScalar**)&zn_1); VecRestoreArray(Zn_1,NULL);
     89:   Qn   = ksp->work[6]; VecGetArrayRead(Qn_1,(const PetscScalar**)&qn_1); VecRestoreArrayRead(Qn_1,NULL);
     90:   Tn   = ksp->work[7]; VecGetArrayRead(Tn,(const PetscScalar**)&tn); VecRestoreArrayRead(Tn,NULL);
     91:   Sn   = ksp->work[8]; VecGetArrayRead(Sn,(const PetscScalar**)&sn); VecRestoreArrayRead(Sn,NULL);

     93:   /* r0 = rn_1 = b - A*xn_1; */
     94:   /* KSP_PCApplyBAorAB(ksp,Xn_1,Rn_1,Tn);
     95:      VecAYPX(Rn_1,-1.0,B); */
     96:   KSPInitialResidual(ksp,Xn_1,Tn,Sn,Rn_1,B);
     97:   if (ksp->normtype != KSP_NORM_NONE) {
     98:     VecNorm(Rn_1,NORM_2,&rnorm);
     99:     KSPCheckNorm(ksp,rnorm);
    100:   }
    101:   KSPMonitor(ksp,0,rnorm);
    102:   (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
    103:   if (ksp->reason) return(0);

    105:   VecCopy(Rn_1,R0);

    107:   /* un_1 = A*rn_1; */
    108:   KSP_PCApplyBAorAB(ksp,Rn_1,Un_1,Tn);

    110:   /* f0   = A'*rn_1; */
    111:   if (ksp->pc_side == PC_RIGHT) { /* B' A' */
    112:     KSP_MatMultTranspose(ksp,A,R0,Tn);
    113:     KSP_PCApplyTranspose(ksp,Tn,F0);
    114:   } else if (ksp->pc_side == PC_LEFT) { /* A' B' */
    115:     KSP_PCApplyTranspose(ksp,R0,Tn);
    116:     KSP_MatMultTranspose(ksp,A,Tn,F0);
    117:   }

    119:   /*qn_1 = vn_1 = zn_1 = 0.0; */
    120:   VecSet(Qn_1,0.0);
    121:   VecSet(Vn_1,0.0);
    122:   VecSet(Zn_1,0.0);

    124:   sigman_2 = pin_1 = taun_1 = 0.0;

    126:   /* the paper says phin_1 should be initialized to zero, it is actually R0'R0 */
    127:   VecDot(R0,R0,&phin_1);
    128:   KSPCheckDot(ksp,phin_1);

    130:   /* sigman_1 = rn_1'un_1  */
    131:   VecDot(R0,Un_1,&sigman_1);

    133:   alphan_1 = omegan_1 = 1.0;

    135:   for (ksp->its = 1; ksp->its<ksp->max_it+1; ksp->its++) {
    136:     rhon = phin_1 - omegan_1*sigman_2 + omegan_1*alphan_1*pin_1;
    137:     if (ksp->its == 1) deltan = rhon;
    138:     else deltan = rhon/taun_1;
    139:     betan = deltan/omegan_1;
    140:     taun  = sigman_1 + betan*taun_1  - deltan*pin_1;
    141:     if (taun == 0.0) {
    142:       if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to taun is zero, iteration %D",ksp->its);
    143:       else {
    144:         ksp->reason = KSP_DIVERGED_NANORINF;
    145:         return(0);
    146:       }
    147:     }
    148:     alphan = rhon/taun;
    149:     PetscLogFlops(15.0);

    151:     /*
    152:         zn = alphan*rn_1 + (alphan/alphan_1)betan*zn_1 - alphan*deltan*vn_1
    153:         vn = un_1 + betan*vn_1 - deltan*qn_1
    154:         sn = rn_1 - alphan*vn

    156:        The algorithm in the paper is missing the alphan/alphan_1 term in the zn update
    157:     */
    158:     PetscLogEventBegin(VEC_Ops,0,0,0,0);
    159:     tmp1 = (alphan/alphan_1)*betan;
    160:     tmp2 = alphan*deltan;
    161:     for (i=0; i<N; i++) {
    162:       zn[i] = alphan*rn_1[i] + tmp1*zn_1[i] - tmp2*vn_1[i];
    163:       vn[i] = un_1[i] + betan*vn_1[i] - deltan*qn_1[i];
    164:       sn[i] = rn_1[i] - alphan*vn[i];
    165:     }
    166:     PetscLogFlops(3.0+11.0*N);
    167:     PetscLogEventEnd(VEC_Ops,0,0,0,0);

    169:     /*
    170:         qn = A*vn
    171:     */
    172:     KSP_PCApplyBAorAB(ksp,Vn,Qn,Tn);

    174:     /*
    175:         tn = un_1 - alphan*qn
    176:     */
    177:     VecWAXPY(Tn,-alphan,Qn,Un_1);

    180:     /*
    181:         phin = r0'sn
    182:         pin  = r0'qn
    183:         gamman = f0'sn
    184:         etan   = f0'tn
    185:         thetan = sn'tn
    186:         kappan = tn'tn
    187:     */
    188:     PetscLogEventBegin(VEC_ReduceArithmetic,0,0,0,0);
    189:     phin = pin = gamman = etan = thetan = kappan = 0.0;
    190:     for (i=0; i<N; i++) {
    191:       phin   += r0[i]*sn[i];
    192:       pin    += r0[i]*qn[i];
    193:       gamman += f0[i]*sn[i];
    194:       etan   += f0[i]*tn[i];
    195:       thetan += sn[i]*tn[i];
    196:       kappan += tn[i]*tn[i];
    197:     }
    198:     PetscLogFlops(12.0*N);
    199:     PetscLogEventEnd(VEC_ReduceArithmetic,0,0,0,0);

    201:     insums[0] = phin;
    202:     insums[1] = pin;
    203:     insums[2] = gamman;
    204:     insums[3] = etan;
    205:     insums[4] = thetan;
    206:     insums[5] = kappan;
    207:     insums[6] = rnormin;

    209:     PetscLogEventBegin(VEC_ReduceCommunication,0,0,0,0);
    210: #if defined(PETSC_HAVE_MPI_LONG_DOUBLE) && !defined(PETSC_USE_COMPLEX) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
    211:     if (ksp->lagnorm && ksp->its > 1) {
    212:       MPIU_Allreduce(insums,outsums,7,MPI_LONG_DOUBLE,MPI_SUM,PetscObjectComm((PetscObject)ksp));
    213:     } else {
    214:       MPIU_Allreduce(insums,outsums,6,MPI_LONG_DOUBLE,MPI_SUM,PetscObjectComm((PetscObject)ksp));
    215:     }
    216: #else
    217:     if (ksp->lagnorm && ksp->its > 1 && ksp->normtype != KSP_NORM_NONE) {
    218:       MPIU_Allreduce(insums,outsums,7,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
    219:     } else {
    220:       MPIU_Allreduce(insums,outsums,6,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
    221:     }
    222: #endif
    223:     PetscLogEventEnd(VEC_ReduceCommunication,0,0,0,0);
    224:     phin   = outsums[0];
    225:     pin    = outsums[1];
    226:     gamman = outsums[2];
    227:     etan   = outsums[3];
    228:     thetan = outsums[4];
    229:     kappan = outsums[5];
    230:     if (ksp->lagnorm && ksp->its > 1 && ksp->normtype != KSP_NORM_NONE) rnorm = PetscSqrtReal(PetscRealPart(outsums[6]));

    232:     if (kappan == 0.0) {
    233:       if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to kappan is zero, iteration %D",ksp->its);
    234:       else {
    235:         ksp->reason = KSP_DIVERGED_NANORINF;
    236:         return(0);
    237:       }
    238:     }
    239:     if (thetan == 0.0) {
    240:       if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"KSPSolve has not converged due to thetan is zero, iteration %D",ksp->its);
    241:       else {
    242:         ksp->reason = KSP_DIVERGED_NANORINF;
    243:         return(0);
    244:       }
    245:     }
    246:     omegan = thetan/kappan;
    247:     sigman = gamman - omegan*etan;

    249:     /*
    250:         rn = sn - omegan*tn
    251:         xn = xn_1 + zn + omegan*sn
    252:     */
    253:     PetscLogEventBegin(VEC_Ops,0,0,0,0);
    254:     rnormin = 0.0;
    255:     for (i=0; i<N; i++) {
    256:       rn[i]    = sn[i] - omegan*tn[i];
    257:       rnormin += PetscRealPart(PetscConj(rn[i])*rn[i]);
    258:       xn[i]   += zn[i] + omegan*sn[i];
    259:     }
    260:     PetscObjectStateIncrease((PetscObject)Xn);
    261:     PetscLogFlops(7.0*N);
    262:     PetscLogEventEnd(VEC_Ops,0,0,0,0);

    264:     if (!ksp->lagnorm && ksp->chknorm < ksp->its && ksp->normtype != KSP_NORM_NONE) {
    265:       PetscLogEventBegin(VEC_ReduceCommunication,0,0,0,0);
    266:       MPIU_Allreduce(&rnormin,&rnorm,1,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)ksp));
    267:       PetscLogEventEnd(VEC_ReduceCommunication,0,0,0,0);
    268:       rnorm = PetscSqrtReal(rnorm);
    269:     }

    271:     /* Test for convergence */
    272:     KSPMonitor(ksp,ksp->its,rnorm);
    273:     (*ksp->converged)(ksp,ksp->its,rnorm,&ksp->reason,ksp->cnvP);
    274:     if (ksp->reason) {
    275:       KSPUnwindPreconditioner(ksp,Xn,Tn);
    276:       return(0);
    277:     }

    279:     /* un = A*rn */
    280:     KSP_PCApplyBAorAB(ksp,Rn,Un,Tn);

    282:     /* Update n-1 locations with n locations */
    283:     sigman_2 = sigman_1;
    284:     sigman_1 = sigman;
    285:     pin_1    = pin;
    286:     phin_1   = phin;
    287:     alphan_1 = alphan;
    288:     taun_1   = taun;
    289:     omegan_1 = omegan;
    290:   }
    291:   if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    292:   KSPUnwindPreconditioner(ksp,Xn,Tn);
    293:   return(0);
    294: }

    297: /*MC
    298:      KSPIBCGS - Implements the IBiCGStab (Improved Stabilized version of BiConjugate Gradient) method
    299:             in an alternative form to have only a single global reduction operation instead of the usual 3 (or 4)

    301:    Options Database Keys:
    302: .   see KSPSolve()

    304:    Level: beginner

    306:    Notes:
    307:     Supports left and right preconditioning

    309:           See KSPBCGSL for additional stabilization

    311:           Unlike the Bi-CG-stab algorithm, this requires one multiplication be the transpose of the operator
    312:            before the iteration starts.

    314:           The paper has two errors in the algorithm presented, they are fixed in the code in KSPSolve_IBCGS()

    316:           For maximum reduction in the number of global reduction operations, this solver should be used with
    317:           KSPSetLagNorm().

    319:           This is not supported for complex numbers.

    321:    Reference: The Improved BiCGStab Method for Large and Sparse Unsymmetric Linear Systems on Parallel Distributed Memory
    322:                      Architectures. L. T. Yang and R. Brent, Proceedings of the Fifth International Conference on Algorithms and
    323:                      Architectures for Parallel Processing, 2002, IEEE.

    325: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPBICG, KSPBCGSL, KSPIBCGS, KSPSetLagNorm()
    326: M*/

    328: PETSC_EXTERN PetscErrorCode KSPCreate_IBCGS(KSP ksp)
    329: {

    334:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    335:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
    336:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);

    338:   ksp->ops->setup          = KSPSetUp_IBCGS;
    339:   ksp->ops->solve          = KSPSolve_IBCGS;
    340:   ksp->ops->destroy        = KSPDestroyDefault;
    341:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    342:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    343:   ksp->ops->setfromoptions = NULL;
    344:   ksp->ops->view           = NULL;
    345: #if defined(PETSC_USE_COMPLEX)
    346:   SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"This is not supported for complex numbers");
    347: #else
    348:   return(0);
    349: #endif
    350: }