Actual source code: cyclic.c
slepc-3.21.1 2024-04-26
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    SLEPc singular value solver: "cyclic"

     13:    Method: Uses a Hermitian eigensolver for H(A) = [ 0  A ; A^T 0 ]
     14: */

     16: #include <slepc/private/svdimpl.h>
     17: #include <slepc/private/bvimpl.h>
     18: #include "cyclic.h"

     20: static PetscErrorCode MatMult_Cyclic(Mat B,Vec x,Vec y)
     21: {
     22:   SVD_CYCLIC_SHELL  *ctx;
     23:   const PetscScalar *px;
     24:   PetscScalar       *py;
     25:   PetscInt          m;

     27:   PetscFunctionBegin;
     28:   PetscCall(MatShellGetContext(B,&ctx));
     29:   PetscCall(MatGetLocalSize(ctx->A,&m,NULL));
     30:   PetscCall(VecGetArrayRead(x,&px));
     31:   PetscCall(VecGetArrayWrite(y,&py));
     32:   PetscCall(VecPlaceArray(ctx->x1,px));
     33:   PetscCall(VecPlaceArray(ctx->x2,px+m));
     34:   PetscCall(VecPlaceArray(ctx->y1,py));
     35:   PetscCall(VecPlaceArray(ctx->y2,py+m));
     36:   PetscCall(MatMult(ctx->A,ctx->x2,ctx->y1));
     37:   PetscCall(MatMult(ctx->AT,ctx->x1,ctx->y2));
     38:   PetscCall(VecResetArray(ctx->x1));
     39:   PetscCall(VecResetArray(ctx->x2));
     40:   PetscCall(VecResetArray(ctx->y1));
     41:   PetscCall(VecResetArray(ctx->y2));
     42:   PetscCall(VecRestoreArrayRead(x,&px));
     43:   PetscCall(VecRestoreArrayWrite(y,&py));
     44:   PetscFunctionReturn(PETSC_SUCCESS);
     45: }

     47: static PetscErrorCode MatGetDiagonal_Cyclic(Mat B,Vec diag)
     48: {
     49:   PetscFunctionBegin;
     50:   PetscCall(VecSet(diag,0.0));
     51:   PetscFunctionReturn(PETSC_SUCCESS);
     52: }

     54: static PetscErrorCode MatDestroy_Cyclic(Mat B)
     55: {
     56:   SVD_CYCLIC_SHELL *ctx;

     58:   PetscFunctionBegin;
     59:   PetscCall(MatShellGetContext(B,&ctx));
     60:   PetscCall(VecDestroy(&ctx->x1));
     61:   PetscCall(VecDestroy(&ctx->x2));
     62:   PetscCall(VecDestroy(&ctx->y1));
     63:   PetscCall(VecDestroy(&ctx->y2));
     64:   if (ctx->misaligned) {
     65:     PetscCall(VecDestroy(&ctx->wx2));
     66:     PetscCall(VecDestroy(&ctx->wy2));
     67:   }
     68:   PetscCall(PetscFree(ctx));
     69:   PetscFunctionReturn(PETSC_SUCCESS);
     70: }

     72: /*
     73:    Builds cyclic matrix   C = | 0   A |
     74:                               | AT  0 |
     75: */
     76: static PetscErrorCode SVDCyclicGetCyclicMat(SVD svd,Mat A,Mat AT,Mat *C)
     77: {
     78:   SVD_CYCLIC       *cyclic = (SVD_CYCLIC*)svd->data;
     79:   SVD_CYCLIC_SHELL *ctx;
     80:   PetscInt         i,M,N,m,n,Istart,Iend;
     81:   VecType          vtype;
     82:   Mat              Zm,Zn;
     83: #if defined(PETSC_HAVE_CUDA)
     84:   PetscBool        cuda;
     85:   const PetscInt   *ranges;
     86:   PetscMPIInt      size;
     87: #endif

     89:   PetscFunctionBegin;
     90:   PetscCall(MatGetSize(A,&M,&N));
     91:   PetscCall(MatGetLocalSize(A,&m,&n));

     93:   if (cyclic->explicitmatrix) {
     94:     PetscCheck(svd->expltrans,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Cannot use explicit cyclic matrix with implicit transpose");
     95:     PetscCall(MatCreate(PetscObjectComm((PetscObject)svd),&Zm));
     96:     PetscCall(MatSetSizes(Zm,m,m,M,M));
     97:     PetscCall(MatSetFromOptions(Zm));
     98:     PetscCall(MatGetOwnershipRange(Zm,&Istart,&Iend));
     99:     for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(Zm,i,i,0.0,INSERT_VALUES));
    100:     PetscCall(MatAssemblyBegin(Zm,MAT_FINAL_ASSEMBLY));
    101:     PetscCall(MatAssemblyEnd(Zm,MAT_FINAL_ASSEMBLY));
    102:     PetscCall(MatCreate(PetscObjectComm((PetscObject)svd),&Zn));
    103:     PetscCall(MatSetSizes(Zn,n,n,N,N));
    104:     PetscCall(MatSetFromOptions(Zn));
    105:     PetscCall(MatGetOwnershipRange(Zn,&Istart,&Iend));
    106:     for (i=Istart;i<Iend;i++) PetscCall(MatSetValue(Zn,i,i,0.0,INSERT_VALUES));
    107:     PetscCall(MatAssemblyBegin(Zn,MAT_FINAL_ASSEMBLY));
    108:     PetscCall(MatAssemblyEnd(Zn,MAT_FINAL_ASSEMBLY));
    109:     PetscCall(MatCreateTile(1.0,Zm,1.0,A,1.0,AT,1.0,Zn,C));
    110:     PetscCall(MatDestroy(&Zm));
    111:     PetscCall(MatDestroy(&Zn));
    112:   } else {
    113:     PetscCall(PetscNew(&ctx));
    114:     ctx->A       = A;
    115:     ctx->AT      = AT;
    116:     ctx->swapped = svd->swapped;
    117:     PetscCall(MatCreateVecsEmpty(A,&ctx->x2,&ctx->x1));
    118:     PetscCall(MatCreateVecsEmpty(A,&ctx->y2,&ctx->y1));
    119:     PetscCall(MatCreateShell(PetscObjectComm((PetscObject)svd),m+n,m+n,M+N,M+N,ctx,C));
    120:     PetscCall(MatShellSetOperation(*C,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_Cyclic));
    121:     PetscCall(MatShellSetOperation(*C,MATOP_DESTROY,(void(*)(void))MatDestroy_Cyclic));
    122: #if defined(PETSC_HAVE_CUDA)
    123:     PetscCall(PetscObjectTypeCompareAny((PetscObject)(svd->swapped?AT:A),&cuda,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,""));
    124:     if (cuda) PetscCall(MatShellSetOperation(*C,MATOP_MULT,(void(*)(void))MatMult_Cyclic_CUDA));
    125:     else
    126: #endif
    127:       PetscCall(MatShellSetOperation(*C,MATOP_MULT,(void(*)(void))MatMult_Cyclic));
    128:     PetscCall(MatGetVecType(A,&vtype));
    129:     PetscCall(MatSetVecType(*C,vtype));
    130: #if defined(PETSC_HAVE_CUDA)
    131:     if (cuda) {
    132:       /* check alignment of bottom block */
    133:       PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)ctx->x1),&size));
    134:       PetscCall(VecGetOwnershipRanges(ctx->x1,&ranges));
    135:       for (i=0;i<size;i++) {
    136:         ctx->misaligned = (((ranges[i+1]-ranges[i])*sizeof(PetscScalar))%16)? PETSC_TRUE: PETSC_FALSE;
    137:         if (ctx->misaligned) break;
    138:       }
    139:       if (ctx->misaligned) {  /* create work vectors for MatMult */
    140:         PetscCall(VecDuplicate(ctx->x2,&ctx->wx2));
    141:         PetscCall(VecDuplicate(ctx->y2,&ctx->wy2));
    142:       }
    143:     }
    144: #endif
    145:   }
    146:   PetscFunctionReturn(PETSC_SUCCESS);
    147: }

    149: static PetscErrorCode MatMult_ECross(Mat B,Vec x,Vec y)
    150: {
    151:   SVD_CYCLIC_SHELL  *ctx;
    152:   const PetscScalar *px;
    153:   PetscScalar       *py;
    154:   PetscInt          mn,m,n;

    156:   PetscFunctionBegin;
    157:   PetscCall(MatShellGetContext(B,&ctx));
    158:   PetscCall(MatGetLocalSize(ctx->A,NULL,&n));
    159:   PetscCall(VecGetLocalSize(y,&mn));
    160:   m = mn-n;
    161:   PetscCall(VecGetArrayRead(x,&px));
    162:   PetscCall(VecGetArrayWrite(y,&py));
    163:   PetscCall(VecPlaceArray(ctx->x1,px));
    164:   PetscCall(VecPlaceArray(ctx->x2,px+m));
    165:   PetscCall(VecPlaceArray(ctx->y1,py));
    166:   PetscCall(VecPlaceArray(ctx->y2,py+m));
    167:   PetscCall(VecCopy(ctx->x1,ctx->y1));
    168:   PetscCall(MatMult(ctx->A,ctx->x2,ctx->w));
    169:   PetscCall(MatMult(ctx->AT,ctx->w,ctx->y2));
    170:   PetscCall(VecResetArray(ctx->x1));
    171:   PetscCall(VecResetArray(ctx->x2));
    172:   PetscCall(VecResetArray(ctx->y1));
    173:   PetscCall(VecResetArray(ctx->y2));
    174:   PetscCall(VecRestoreArrayRead(x,&px));
    175:   PetscCall(VecRestoreArrayWrite(y,&py));
    176:   PetscFunctionReturn(PETSC_SUCCESS);
    177: }

    179: static PetscErrorCode MatGetDiagonal_ECross(Mat B,Vec d)
    180: {
    181:   SVD_CYCLIC_SHELL  *ctx;
    182:   PetscScalar       *pd;
    183:   PetscMPIInt       len;
    184:   PetscInt          mn,m,n,N,i,j,start,end,ncols;
    185:   PetscScalar       *work1,*work2,*diag;
    186:   const PetscInt    *cols;
    187:   const PetscScalar *vals;

    189:   PetscFunctionBegin;
    190:   PetscCall(MatShellGetContext(B,&ctx));
    191:   PetscCall(MatGetLocalSize(ctx->A,NULL,&n));
    192:   PetscCall(VecGetLocalSize(d,&mn));
    193:   m = mn-n;
    194:   PetscCall(VecGetArrayWrite(d,&pd));
    195:   PetscCall(VecPlaceArray(ctx->y1,pd));
    196:   PetscCall(VecSet(ctx->y1,1.0));
    197:   PetscCall(VecResetArray(ctx->y1));
    198:   PetscCall(VecPlaceArray(ctx->y2,pd+m));
    199:   if (!ctx->diag) {
    200:     /* compute diagonal from rows and store in ctx->diag */
    201:     PetscCall(VecDuplicate(ctx->y2,&ctx->diag));
    202:     PetscCall(MatGetSize(ctx->A,NULL,&N));
    203:     PetscCall(PetscCalloc2(N,&work1,N,&work2));
    204:     if (ctx->swapped) {
    205:       PetscCall(MatGetOwnershipRange(ctx->AT,&start,&end));
    206:       for (i=start;i<end;i++) {
    207:         PetscCall(MatGetRow(ctx->AT,i,&ncols,NULL,&vals));
    208:         for (j=0;j<ncols;j++) work1[i] += vals[j]*vals[j];
    209:         PetscCall(MatRestoreRow(ctx->AT,i,&ncols,NULL,&vals));
    210:       }
    211:     } else {
    212:       PetscCall(MatGetOwnershipRange(ctx->A,&start,&end));
    213:       for (i=start;i<end;i++) {
    214:         PetscCall(MatGetRow(ctx->A,i,&ncols,&cols,&vals));
    215:         for (j=0;j<ncols;j++) work1[cols[j]] += vals[j]*vals[j];
    216:         PetscCall(MatRestoreRow(ctx->A,i,&ncols,&cols,&vals));
    217:       }
    218:     }
    219:     PetscCall(PetscMPIIntCast(N,&len));
    220:     PetscCall(MPIU_Allreduce(work1,work2,len,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)B)));
    221:     PetscCall(VecGetOwnershipRange(ctx->diag,&start,&end));
    222:     PetscCall(VecGetArrayWrite(ctx->diag,&diag));
    223:     for (i=start;i<end;i++) diag[i-start] = work2[i];
    224:     PetscCall(VecRestoreArrayWrite(ctx->diag,&diag));
    225:     PetscCall(PetscFree2(work1,work2));
    226:   }
    227:   PetscCall(VecCopy(ctx->diag,ctx->y2));
    228:   PetscCall(VecResetArray(ctx->y2));
    229:   PetscCall(VecRestoreArrayWrite(d,&pd));
    230:   PetscFunctionReturn(PETSC_SUCCESS);
    231: }

    233: static PetscErrorCode MatDestroy_ECross(Mat B)
    234: {
    235:   SVD_CYCLIC_SHELL *ctx;

    237:   PetscFunctionBegin;
    238:   PetscCall(MatShellGetContext(B,&ctx));
    239:   PetscCall(VecDestroy(&ctx->x1));
    240:   PetscCall(VecDestroy(&ctx->x2));
    241:   PetscCall(VecDestroy(&ctx->y1));
    242:   PetscCall(VecDestroy(&ctx->y2));
    243:   PetscCall(VecDestroy(&ctx->diag));
    244:   PetscCall(VecDestroy(&ctx->w));
    245:   if (ctx->misaligned) {
    246:     PetscCall(VecDestroy(&ctx->wx2));
    247:     PetscCall(VecDestroy(&ctx->wy2));
    248:   }
    249:   PetscCall(PetscFree(ctx));
    250:   PetscFunctionReturn(PETSC_SUCCESS);
    251: }

    253: /*
    254:    Builds extended cross product matrix   C = | I_m   0  |
    255:                                               |  0  AT*A |
    256:    t is an auxiliary Vec used to take the dimensions of the upper block
    257: */
    258: static PetscErrorCode SVDCyclicGetECrossMat(SVD svd,Mat A,Mat AT,Mat *C,Vec t)
    259: {
    260:   SVD_CYCLIC       *cyclic = (SVD_CYCLIC*)svd->data;
    261:   SVD_CYCLIC_SHELL *ctx;
    262:   PetscInt         i,M,N,m,n,Istart,Iend;
    263:   VecType          vtype;
    264:   Mat              Id,Zm,Zn,ATA;
    265: #if defined(PETSC_HAVE_CUDA)
    266:   PetscBool        cuda;
    267:   const PetscInt   *ranges;
    268:   PetscMPIInt      size;
    269: #endif

    271:   PetscFunctionBegin;
    272:   PetscCall(MatGetSize(A,NULL,&N));
    273:   PetscCall(MatGetLocalSize(A,NULL,&n));
    274:   PetscCall(VecGetSize(t,&M));
    275:   PetscCall(VecGetLocalSize(t,&m));

    277:   if (cyclic->explicitmatrix) {
    278:     PetscCheck(svd->expltrans,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Cannot use explicit cyclic matrix with implicit transpose");
    279:     PetscCall(MatCreateConstantDiagonal(PetscObjectComm((PetscObject)svd),m,m,M,M,1.0,&Id));
    280:     PetscCall(MatCreate(PetscObjectComm((PetscObject)svd),&Zm));
    281:     PetscCall(MatSetSizes(Zm,m,n,M,N));
    282:     PetscCall(MatSetFromOptions(Zm));
    283:     PetscCall(MatGetOwnershipRange(Zm,&Istart,&Iend));
    284:     for (i=Istart;i<Iend;i++) {
    285:       if (i<N) PetscCall(MatSetValue(Zm,i,i,0.0,INSERT_VALUES));
    286:     }
    287:     PetscCall(MatAssemblyBegin(Zm,MAT_FINAL_ASSEMBLY));
    288:     PetscCall(MatAssemblyEnd(Zm,MAT_FINAL_ASSEMBLY));
    289:     PetscCall(MatCreate(PetscObjectComm((PetscObject)svd),&Zn));
    290:     PetscCall(MatSetSizes(Zn,n,m,N,M));
    291:     PetscCall(MatSetFromOptions(Zn));
    292:     PetscCall(MatGetOwnershipRange(Zn,&Istart,&Iend));
    293:     for (i=Istart;i<Iend;i++) {
    294:       if (i<m) PetscCall(MatSetValue(Zn,i,i,0.0,INSERT_VALUES));
    295:     }
    296:     PetscCall(MatAssemblyBegin(Zn,MAT_FINAL_ASSEMBLY));
    297:     PetscCall(MatAssemblyEnd(Zn,MAT_FINAL_ASSEMBLY));
    298:     PetscCall(MatProductCreate(AT,A,NULL,&ATA));
    299:     PetscCall(MatProductSetType(ATA,MATPRODUCT_AB));
    300:     PetscCall(MatProductSetFromOptions(ATA));
    301:     PetscCall(MatProductSymbolic(ATA));
    302:     PetscCall(MatProductNumeric(ATA));
    303:     PetscCall(MatCreateTile(1.0,Id,1.0,Zm,1.0,Zn,1.0,ATA,C));
    304:     PetscCall(MatDestroy(&Id));
    305:     PetscCall(MatDestroy(&Zm));
    306:     PetscCall(MatDestroy(&Zn));
    307:     PetscCall(MatDestroy(&ATA));
    308:   } else {
    309:     PetscCall(PetscNew(&ctx));
    310:     ctx->A       = A;
    311:     ctx->AT      = AT;
    312:     ctx->swapped = svd->swapped;
    313:     PetscCall(VecDuplicateEmpty(t,&ctx->x1));
    314:     PetscCall(VecDuplicateEmpty(t,&ctx->y1));
    315:     PetscCall(MatCreateVecsEmpty(A,&ctx->x2,NULL));
    316:     PetscCall(MatCreateVecsEmpty(A,&ctx->y2,NULL));
    317:     PetscCall(MatCreateVecs(A,NULL,&ctx->w));
    318:     PetscCall(MatCreateShell(PetscObjectComm((PetscObject)svd),m+n,m+n,M+N,M+N,ctx,C));
    319:     PetscCall(MatShellSetOperation(*C,MATOP_GET_DIAGONAL,(void(*)(void))MatGetDiagonal_ECross));
    320:     PetscCall(MatShellSetOperation(*C,MATOP_DESTROY,(void(*)(void))MatDestroy_ECross));
    321: #if defined(PETSC_HAVE_CUDA)
    322:     PetscCall(PetscObjectTypeCompareAny((PetscObject)(svd->swapped?AT:A),&cuda,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,""));
    323:     if (cuda) PetscCall(MatShellSetOperation(*C,MATOP_MULT,(void(*)(void))MatMult_ECross_CUDA));
    324:     else
    325: #endif
    326:       PetscCall(MatShellSetOperation(*C,MATOP_MULT,(void(*)(void))MatMult_ECross));
    327:     PetscCall(MatGetVecType(A,&vtype));
    328:     PetscCall(MatSetVecType(*C,vtype));
    329: #if defined(PETSC_HAVE_CUDA)
    330:     if (cuda) {
    331:       /* check alignment of bottom block */
    332:       PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)ctx->x1),&size));
    333:       PetscCall(VecGetOwnershipRanges(ctx->x1,&ranges));
    334:       for (i=0;i<size;i++) {
    335:         ctx->misaligned = (((ranges[i+1]-ranges[i])*sizeof(PetscScalar))%16)? PETSC_TRUE: PETSC_FALSE;
    336:         if (ctx->misaligned) break;
    337:       }
    338:       if (ctx->misaligned) {  /* create work vectors for MatMult */
    339:         PetscCall(VecDuplicate(ctx->x2,&ctx->wx2));
    340:         PetscCall(VecDuplicate(ctx->y2,&ctx->wy2));
    341:       }
    342:     }
    343: #endif
    344:   }
    345:   PetscFunctionReturn(PETSC_SUCCESS);
    346: }

    348: /* Convergence test relative to the norm of R (used in GSVD only) */
    349: static PetscErrorCode EPSConv_Cyclic(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
    350: {
    351:   SVD svd = (SVD)ctx;

    353:   PetscFunctionBegin;
    354:   *errest = res/PetscMax(svd->nrma,svd->nrmb);
    355:   PetscFunctionReturn(PETSC_SUCCESS);
    356: }

    358: static PetscErrorCode SVDSetUp_Cyclic(SVD svd)
    359: {
    360:   SVD_CYCLIC        *cyclic = (SVD_CYCLIC*)svd->data;
    361:   PetscInt          M,N,m,n,p,k,i,isl,offset,nev,ncv,mpd,maxit;
    362:   PetscReal         tol;
    363:   const PetscScalar *isa,*oa;
    364:   PetscScalar       *va;
    365:   EPSProblemType    ptype;
    366:   PetscBool         trackall,issinv;
    367:   Vec               v,t;
    368:   ST                st;
    369:   Mat               Omega;
    370:   MatType           Atype;

    372:   PetscFunctionBegin;
    373:   PetscCall(MatGetSize(svd->A,&M,&N));
    374:   PetscCall(MatGetLocalSize(svd->A,&m,&n));
    375:   if (!cyclic->eps) PetscCall(SVDCyclicGetEPS(svd,&cyclic->eps));
    376:   PetscCall(MatDestroy(&cyclic->C));
    377:   PetscCall(MatDestroy(&cyclic->D));
    378:   if (svd->isgeneralized) {
    379:     if (svd->which==SVD_SMALLEST) {  /* alternative pencil */
    380:       PetscCall(MatCreateVecs(svd->B,NULL,&t));
    381:       PetscCall(SVDCyclicGetCyclicMat(svd,svd->B,svd->BT,&cyclic->C));
    382:       PetscCall(SVDCyclicGetECrossMat(svd,svd->A,svd->AT,&cyclic->D,t));
    383:     } else {
    384:       PetscCall(MatCreateVecs(svd->A,NULL,&t));
    385:       PetscCall(SVDCyclicGetCyclicMat(svd,svd->A,svd->AT,&cyclic->C));
    386:       PetscCall(SVDCyclicGetECrossMat(svd,svd->B,svd->BT,&cyclic->D,t));
    387:     }
    388:     PetscCall(VecDestroy(&t));
    389:     PetscCall(EPSSetOperators(cyclic->eps,cyclic->C,cyclic->D));
    390:     PetscCall(EPSGetProblemType(cyclic->eps,&ptype));
    391:     if (!ptype) PetscCall(EPSSetProblemType(cyclic->eps,EPS_GHEP));
    392:   } else if (svd->ishyperbolic) {
    393:     PetscCall(SVDCyclicGetCyclicMat(svd,svd->A,svd->AT,&cyclic->C));
    394:     PetscCall(MatCreateVecs(cyclic->C,&v,NULL));
    395:     PetscCall(VecSet(v,1.0));
    396:     PetscCall(VecGetArrayRead(svd->omega,&oa));
    397:     PetscCall(VecGetArray(v,&va));
    398:     if (svd->swapped) PetscCall(PetscArraycpy(va+m,oa,n));
    399:     else PetscCall(PetscArraycpy(va,oa,m));
    400:     PetscCall(VecRestoreArrayRead(svd->omega,&oa));
    401:     PetscCall(VecRestoreArray(v,&va));
    402:     PetscCall(MatGetType(svd->OP,&Atype));
    403:     PetscCall(MatCreate(PetscObjectComm((PetscObject)svd),&Omega));
    404:     PetscCall(MatSetSizes(Omega,m+n,m+n,M+N,M+N));
    405:     PetscCall(MatSetType(Omega,Atype));
    406:     PetscCall(MatDiagonalSet(Omega,v,INSERT_VALUES));
    407:     PetscCall(EPSSetOperators(cyclic->eps,cyclic->C,Omega));
    408:     PetscCall(EPSSetProblemType(cyclic->eps,EPS_GHIEP));
    409:     PetscCall(MatDestroy(&Omega));
    410:     PetscCall(VecDestroy(&v));
    411:   } else {
    412:     PetscCall(SVDCyclicGetCyclicMat(svd,svd->A,svd->AT,&cyclic->C));
    413:     PetscCall(EPSSetOperators(cyclic->eps,cyclic->C,NULL));
    414:     PetscCall(EPSSetProblemType(cyclic->eps,EPS_HEP));
    415:   }
    416:   if (!cyclic->usereps) {
    417:     if (svd->which == SVD_LARGEST) {
    418:       PetscCall(EPSGetST(cyclic->eps,&st));
    419:       PetscCall(PetscObjectTypeCompare((PetscObject)st,STSINVERT,&issinv));
    420:       if (issinv) PetscCall(EPSSetWhichEigenpairs(cyclic->eps,EPS_TARGET_MAGNITUDE));
    421:       else if (svd->ishyperbolic) PetscCall(EPSSetWhichEigenpairs(cyclic->eps,EPS_LARGEST_MAGNITUDE));
    422:       else PetscCall(EPSSetWhichEigenpairs(cyclic->eps,EPS_LARGEST_REAL));
    423:     } else {
    424:       if (svd->isgeneralized) {  /* computes sigma^{-1} via alternative pencil */
    425:         PetscCall(EPSSetWhichEigenpairs(cyclic->eps,EPS_LARGEST_REAL));
    426:       } else {
    427:         if (svd->ishyperbolic) PetscCall(EPSSetWhichEigenpairs(cyclic->eps,EPS_TARGET_MAGNITUDE));
    428:         else PetscCall(EPSSetEigenvalueComparison(cyclic->eps,SlepcCompareSmallestPosReal,NULL));
    429:         PetscCall(EPSSetTarget(cyclic->eps,0.0));
    430:       }
    431:     }
    432:     PetscCall(EPSGetDimensions(cyclic->eps,&nev,&ncv,&mpd));
    433:     PetscCheck(nev==1 || nev>=2*svd->nsv,PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_WRONG,"The number of requested eigenvalues %" PetscInt_FMT " must be at least 2*%" PetscInt_FMT,nev,svd->nsv);
    434:     nev = PetscMax(nev,2*svd->nsv);
    435:     if (ncv==PETSC_DEFAULT && svd->ncv!=PETSC_DEFAULT) ncv = PetscMax(3*svd->nsv,svd->ncv);
    436:     if (mpd==PETSC_DEFAULT && svd->mpd!=PETSC_DEFAULT) mpd = svd->mpd;
    437:     PetscCall(EPSSetDimensions(cyclic->eps,nev,ncv,mpd));
    438:     PetscCall(EPSGetTolerances(cyclic->eps,&tol,&maxit));
    439:     if (tol==(PetscReal)PETSC_DEFAULT) tol = svd->tol==(PetscReal)PETSC_DEFAULT? SLEPC_DEFAULT_TOL/10.0: svd->tol;
    440:     if (maxit==PETSC_DEFAULT && svd->max_it!=PETSC_DEFAULT) maxit = svd->max_it;
    441:     PetscCall(EPSSetTolerances(cyclic->eps,tol,maxit));
    442:     switch (svd->conv) {
    443:     case SVD_CONV_ABS:
    444:       PetscCall(EPSSetConvergenceTest(cyclic->eps,EPS_CONV_ABS));break;
    445:     case SVD_CONV_REL:
    446:       PetscCall(EPSSetConvergenceTest(cyclic->eps,EPS_CONV_REL));break;
    447:     case SVD_CONV_NORM:
    448:       if (svd->isgeneralized) {
    449:         if (!svd->nrma) PetscCall(MatNorm(svd->OP,NORM_INFINITY,&svd->nrma));
    450:         if (!svd->nrmb) PetscCall(MatNorm(svd->OPb,NORM_INFINITY,&svd->nrmb));
    451:         PetscCall(EPSSetConvergenceTestFunction(cyclic->eps,EPSConv_Cyclic,svd,NULL));
    452:       } else {
    453:         PetscCall(EPSSetConvergenceTest(cyclic->eps,EPS_CONV_NORM));break;
    454:       }
    455:       break;
    456:     case SVD_CONV_MAXIT:
    457:       SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Maxit convergence test not supported in this solver");
    458:     case SVD_CONV_USER:
    459:       SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"User-defined convergence test not supported in this solver");
    460:     }
    461:   }
    462:   SVDCheckUnsupported(svd,SVD_FEATURE_STOPPING);
    463:   /* Transfer the trackall option from svd to eps */
    464:   PetscCall(SVDGetTrackAll(svd,&trackall));
    465:   PetscCall(EPSSetTrackAll(cyclic->eps,trackall));
    466:   /* Transfer the initial subspace from svd to eps */
    467:   if (svd->nini<0 || svd->ninil<0) {
    468:     for (i=0;i<-PetscMin(svd->nini,svd->ninil);i++) {
    469:       PetscCall(MatCreateVecs(cyclic->C,&v,NULL));
    470:       PetscCall(VecGetArrayWrite(v,&va));
    471:       if (svd->isgeneralized) PetscCall(MatGetLocalSize(svd->B,&p,NULL));
    472:       k = (svd->isgeneralized && svd->which==SVD_SMALLEST)? p: m;  /* size of upper block row */
    473:       if (i<-svd->ninil) {
    474:         PetscCall(VecGetArrayRead(svd->ISL[i],&isa));
    475:         if (svd->isgeneralized) {
    476:           PetscCall(VecGetLocalSize(svd->ISL[i],&isl));
    477:           PetscCheck(isl==m+p,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Size mismatch for left initial vector");
    478:           offset = (svd->which==SVD_SMALLEST)? m: 0;
    479:           PetscCall(PetscArraycpy(va,isa+offset,k));
    480:         } else {
    481:           PetscCall(VecGetLocalSize(svd->ISL[i],&isl));
    482:           PetscCheck(isl==k,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Size mismatch for left initial vector");
    483:           PetscCall(PetscArraycpy(va,isa,k));
    484:         }
    485:         PetscCall(VecRestoreArrayRead(svd->IS[i],&isa));
    486:       } else PetscCall(PetscArrayzero(&va,k));
    487:       if (i<-svd->nini) {
    488:         PetscCall(VecGetLocalSize(svd->IS[i],&isl));
    489:         PetscCheck(isl==n,PetscObjectComm((PetscObject)svd),PETSC_ERR_SUP,"Size mismatch for right initial vector");
    490:         PetscCall(VecGetArrayRead(svd->IS[i],&isa));
    491:         PetscCall(PetscArraycpy(va+k,isa,n));
    492:         PetscCall(VecRestoreArrayRead(svd->IS[i],&isa));
    493:       } else PetscCall(PetscArrayzero(va+k,n));
    494:       PetscCall(VecRestoreArrayWrite(v,&va));
    495:       PetscCall(VecDestroy(&svd->IS[i]));
    496:       svd->IS[i] = v;
    497:     }
    498:     svd->nini = PetscMin(svd->nini,svd->ninil);
    499:     PetscCall(EPSSetInitialSpace(cyclic->eps,-svd->nini,svd->IS));
    500:     PetscCall(SlepcBasisDestroy_Private(&svd->nini,&svd->IS));
    501:     PetscCall(SlepcBasisDestroy_Private(&svd->ninil,&svd->ISL));
    502:   }
    503:   PetscCall(EPSSetUp(cyclic->eps));
    504:   PetscCall(EPSGetDimensions(cyclic->eps,NULL,&svd->ncv,&svd->mpd));
    505:   svd->ncv = PetscMin(svd->ncv,PetscMin(M,N));
    506:   PetscCall(EPSGetTolerances(cyclic->eps,NULL,&svd->max_it));
    507:   if (svd->tol==(PetscReal)PETSC_DEFAULT) svd->tol = SLEPC_DEFAULT_TOL;

    509:   svd->leftbasis = PETSC_TRUE;
    510:   PetscCall(SVDAllocateSolution(svd,0));
    511:   PetscFunctionReturn(PETSC_SUCCESS);
    512: }

    514: static PetscErrorCode SVDCyclicCheckEigenvalue(SVD svd,PetscScalar er,PetscScalar ei,PetscReal *sigma,PetscBool *isreal)
    515: {
    516:   PetscFunctionBegin;
    517:   if (svd->ishyperbolic && PetscDefined(USE_COMPLEX) && PetscAbsReal(PetscImaginaryPart(er))>10*PetscAbsReal(PetscRealPart(er))) {
    518:     *sigma = PetscImaginaryPart(er);
    519:     if (isreal) *isreal = PETSC_FALSE;
    520:   } else if (svd->ishyperbolic && !PetscDefined(USE_COMPLEX) && PetscAbsScalar(ei)>10*PetscAbsScalar(er)) {
    521:     *sigma = PetscRealPart(ei);
    522:     if (isreal) *isreal = PETSC_FALSE;
    523:   } else {
    524:     *sigma = PetscRealPart(er);
    525:     if (isreal) *isreal = PETSC_TRUE;
    526:   }
    527:   PetscFunctionReturn(PETSC_SUCCESS);
    528: }

    530: static PetscErrorCode SVDSolve_Cyclic(SVD svd)
    531: {
    532:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;
    533:   PetscInt       i,j,nconv;
    534:   PetscScalar    er,ei;
    535:   PetscReal      sigma;

    537:   PetscFunctionBegin;
    538:   PetscCall(EPSSolve(cyclic->eps));
    539:   PetscCall(EPSGetConverged(cyclic->eps,&nconv));
    540:   PetscCall(EPSGetIterationNumber(cyclic->eps,&svd->its));
    541:   PetscCall(EPSGetConvergedReason(cyclic->eps,(EPSConvergedReason*)&svd->reason));
    542:   for (i=0,j=0;i<nconv;i++) {
    543:     PetscCall(EPSGetEigenvalue(cyclic->eps,i,&er,&ei));
    544:     PetscCall(SVDCyclicCheckEigenvalue(svd,er,ei,&sigma,NULL));
    545:     if (sigma>0.0) {
    546:       if (svd->isgeneralized && svd->which==SVD_SMALLEST) svd->sigma[j] = 1.0/sigma;
    547:       else svd->sigma[j] = sigma;
    548:       j++;
    549:     }
    550:   }
    551:   svd->nconv = j;
    552:   PetscFunctionReturn(PETSC_SUCCESS);
    553: }

    555: static PetscErrorCode SVDComputeVectors_Cyclic_Standard(SVD svd)
    556: {
    557:   SVD_CYCLIC        *cyclic = (SVD_CYCLIC*)svd->data;
    558:   PetscInt          i,j,m,nconv;
    559:   PetscScalar       er,ei;
    560:   PetscReal         sigma;
    561:   const PetscScalar *px;
    562:   Vec               x,x1,x2;

    564:   PetscFunctionBegin;
    565:   PetscCall(MatCreateVecs(cyclic->C,&x,NULL));
    566:   PetscCall(MatGetLocalSize(svd->A,&m,NULL));
    567:   PetscCall(MatCreateVecsEmpty(svd->A,&x2,&x1));
    568:   PetscCall(EPSGetConverged(cyclic->eps,&nconv));
    569:   for (i=0,j=0;i<nconv;i++) {
    570:     PetscCall(EPSGetEigenpair(cyclic->eps,i,&er,&ei,x,NULL));
    571:     PetscCall(SVDCyclicCheckEigenvalue(svd,er,ei,&sigma,NULL));
    572:     if (sigma<0.0) continue;
    573:     PetscCall(VecGetArrayRead(x,&px));
    574:     PetscCall(VecPlaceArray(x1,px));
    575:     PetscCall(VecPlaceArray(x2,px+m));
    576:     PetscCall(BVInsertVec(svd->U,j,x1));
    577:     PetscCall(BVScaleColumn(svd->U,j,PETSC_SQRT2));
    578:     PetscCall(BVInsertVec(svd->V,j,x2));
    579:     PetscCall(BVScaleColumn(svd->V,j,PETSC_SQRT2));
    580:     PetscCall(VecResetArray(x1));
    581:     PetscCall(VecResetArray(x2));
    582:     PetscCall(VecRestoreArrayRead(x,&px));
    583:     j++;
    584:   }
    585:   PetscCall(VecDestroy(&x));
    586:   PetscCall(VecDestroy(&x1));
    587:   PetscCall(VecDestroy(&x2));
    588:   PetscFunctionReturn(PETSC_SUCCESS);
    589: }

    591: static PetscErrorCode SVDComputeVectors_Cyclic_Generalized(SVD svd)
    592: {
    593:   SVD_CYCLIC        *cyclic = (SVD_CYCLIC*)svd->data;
    594:   PetscInt          i,j,m,p,nconv;
    595:   PetscScalar       *dst,er,ei;
    596:   PetscReal         sigma;
    597:   const PetscScalar *src,*px;
    598:   Vec               u,v,x,x1,x2,uv;

    600:   PetscFunctionBegin;
    601:   PetscCall(MatGetLocalSize(svd->A,&m,NULL));
    602:   PetscCall(MatGetLocalSize(svd->B,&p,NULL));
    603:   PetscCall(MatCreateVecs(cyclic->C,&x,NULL));
    604:   if (svd->which==SVD_SMALLEST) PetscCall(MatCreateVecsEmpty(svd->B,&x1,&x2));
    605:   else PetscCall(MatCreateVecsEmpty(svd->A,&x2,&x1));
    606:   PetscCall(MatCreateVecs(svd->A,NULL,&u));
    607:   PetscCall(MatCreateVecs(svd->B,NULL,&v));
    608:   PetscCall(EPSGetConverged(cyclic->eps,&nconv));
    609:   for (i=0,j=0;i<nconv;i++) {
    610:     PetscCall(EPSGetEigenpair(cyclic->eps,i,&er,&ei,x,NULL));
    611:     PetscCall(SVDCyclicCheckEigenvalue(svd,er,ei,&sigma,NULL));
    612:     if (sigma<0.0) continue;
    613:     if (svd->which==SVD_SMALLEST) {
    614:       /* evec_i = 1/sqrt(2)*[ v_i; w_i ],  w_i = x_i/c_i */
    615:       PetscCall(VecGetArrayRead(x,&px));
    616:       PetscCall(VecPlaceArray(x2,px));
    617:       PetscCall(VecPlaceArray(x1,px+p));
    618:       PetscCall(VecCopy(x2,v));
    619:       PetscCall(VecScale(v,PETSC_SQRT2));  /* v_i = sqrt(2)*evec_i_1 */
    620:       PetscCall(VecScale(x1,PETSC_SQRT2)); /* w_i = sqrt(2)*evec_i_2 */
    621:       PetscCall(MatMult(svd->A,x1,u));     /* A*w_i = u_i */
    622:       PetscCall(VecScale(x1,1.0/PetscSqrtScalar(1.0+sigma*sigma)));  /* x_i = w_i*c_i */
    623:       PetscCall(BVInsertVec(svd->V,j,x1));
    624:       PetscCall(VecResetArray(x2));
    625:       PetscCall(VecResetArray(x1));
    626:       PetscCall(VecRestoreArrayRead(x,&px));
    627:     } else {
    628:       /* evec_i = 1/sqrt(2)*[ u_i; w_i ],  w_i = x_i/s_i */
    629:       PetscCall(VecGetArrayRead(x,&px));
    630:       PetscCall(VecPlaceArray(x1,px));
    631:       PetscCall(VecPlaceArray(x2,px+m));
    632:       PetscCall(VecCopy(x1,u));
    633:       PetscCall(VecScale(u,PETSC_SQRT2));  /* u_i = sqrt(2)*evec_i_1 */
    634:       PetscCall(VecScale(x2,PETSC_SQRT2)); /* w_i = sqrt(2)*evec_i_2 */
    635:       PetscCall(MatMult(svd->B,x2,v));     /* B*w_i = v_i */
    636:       PetscCall(VecScale(x2,1.0/PetscSqrtScalar(1.0+sigma*sigma)));  /* x_i = w_i*s_i */
    637:       PetscCall(BVInsertVec(svd->V,j,x2));
    638:       PetscCall(VecResetArray(x1));
    639:       PetscCall(VecResetArray(x2));
    640:       PetscCall(VecRestoreArrayRead(x,&px));
    641:     }
    642:     /* copy [u;v] to U[j] */
    643:     PetscCall(BVGetColumn(svd->U,j,&uv));
    644:     PetscCall(VecGetArrayWrite(uv,&dst));
    645:     PetscCall(VecGetArrayRead(u,&src));
    646:     PetscCall(PetscArraycpy(dst,src,m));
    647:     PetscCall(VecRestoreArrayRead(u,&src));
    648:     PetscCall(VecGetArrayRead(v,&src));
    649:     PetscCall(PetscArraycpy(dst+m,src,p));
    650:     PetscCall(VecRestoreArrayRead(v,&src));
    651:     PetscCall(VecRestoreArrayWrite(uv,&dst));
    652:     PetscCall(BVRestoreColumn(svd->U,j,&uv));
    653:     j++;
    654:   }
    655:   PetscCall(VecDestroy(&x));
    656:   PetscCall(VecDestroy(&x1));
    657:   PetscCall(VecDestroy(&x2));
    658:   PetscCall(VecDestroy(&u));
    659:   PetscCall(VecDestroy(&v));
    660:   PetscFunctionReturn(PETSC_SUCCESS);
    661: }

    663: #if defined(PETSC_USE_COMPLEX)
    664: /* VecMaxAbs: returns the entry of x that has max(abs(x(i))), using w as a workspace vector */
    665: static PetscErrorCode VecMaxAbs(Vec x,Vec w,PetscScalar *v)
    666: {
    667:   PetscMPIInt       size,rank,root;
    668:   const PetscScalar *xx;
    669:   const PetscInt    *ranges;
    670:   PetscReal         val;
    671:   PetscInt          p;

    673:   PetscFunctionBegin;
    674:   PetscCall(VecCopy(x,w));
    675:   PetscCall(VecAbs(w));
    676:   PetscCall(VecMax(w,&p,&val));
    677:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)x),&size));
    678:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)x),&rank));
    679:   PetscCall(VecGetOwnershipRanges(x,&ranges));
    680:   for (root=0;root<size;root++) if (p>=ranges[root] && p<ranges[root+1]) break;
    681:   if (rank==root) {
    682:     PetscCall(VecGetArrayRead(x,&xx));
    683:     *v = xx[p-ranges[root]];
    684:     PetscCall(VecRestoreArrayRead(x,&xx));
    685:   }
    686:   PetscCallMPI(MPI_Bcast(v,1,MPIU_SCALAR,root,PetscObjectComm((PetscObject)x)));
    687:   PetscFunctionReturn(PETSC_SUCCESS);
    688: }
    689: #endif

    691: static PetscErrorCode SVDComputeVectors_Cyclic_Hyperbolic(SVD svd)
    692: {
    693:   SVD_CYCLIC        *cyclic = (SVD_CYCLIC*)svd->data;
    694:   PetscInt          i,j,m,n,nconv;
    695:   PetscScalar       er,ei;
    696:   PetscReal         sigma,nrm;
    697:   PetscBool         isreal;
    698:   const PetscScalar *px;
    699:   Vec               u,x,xi=NULL,x1,x2,x1i=NULL,x2i;
    700:   BV                U=NULL,V=NULL;
    701: #if !defined(PETSC_USE_COMPLEX)
    702:   const PetscScalar *pxi;
    703:   PetscReal         nrmr,nrmi;
    704: #else
    705:   PetscScalar       alpha;
    706: #endif

    708:   PetscFunctionBegin;
    709:   PetscCall(MatCreateVecs(cyclic->C,&x,svd->ishyperbolic?&xi:NULL));
    710:   PetscCall(MatGetLocalSize(svd->A,&m,NULL));
    711:   PetscCall(MatCreateVecsEmpty(svd->OP,&x2,&x1));
    712: #if defined(PETSC_USE_COMPLEX)
    713:   PetscCall(MatCreateVecs(svd->OP,&x2i,&x1i));
    714: #else
    715:   PetscCall(MatCreateVecsEmpty(svd->OP,&x2i,&x1i));
    716: #endif
    717:   /* set-up Omega-normalization of U */
    718:   U = svd->swapped? svd->V: svd->U;
    719:   V = svd->swapped? svd->U: svd->V;
    720:   PetscCall(BVGetSizes(U,&n,NULL,NULL));
    721:   PetscCall(BV_SetMatrixDiagonal(U,svd->omega,svd->A));
    722:   PetscCall(EPSGetConverged(cyclic->eps,&nconv));
    723:   for (i=0,j=0;i<nconv;i++) {
    724:     PetscCall(EPSGetEigenpair(cyclic->eps,i,&er,&ei,x,xi));
    725:     PetscCall(SVDCyclicCheckEigenvalue(svd,er,ei,&sigma,&isreal));
    726:     if (sigma<0.0) continue;
    727:     PetscCall(VecGetArrayRead(x,&px));
    728:     if (svd->swapped) {
    729:       PetscCall(VecPlaceArray(x2,px));
    730:       PetscCall(VecPlaceArray(x1,px+m));
    731:     } else {
    732:       PetscCall(VecPlaceArray(x1,px));
    733:       PetscCall(VecPlaceArray(x2,px+n));
    734:     }
    735: #if defined(PETSC_USE_COMPLEX)
    736:     PetscCall(BVInsertVec(U,j,x1));
    737:     PetscCall(BVInsertVec(V,j,x2));
    738:     if (!isreal) {
    739:       PetscCall(VecMaxAbs(x1,x1i,&alpha));
    740:       PetscCall(BVScaleColumn(U,j,PetscAbsScalar(alpha)/alpha));
    741:       PetscCall(BVScaleColumn(V,j,PetscAbsScalar(alpha)/(alpha*PETSC_i)));
    742:     }
    743: #else
    744:     PetscCall(VecGetArrayRead(xi,&pxi));
    745:     if (svd->swapped) {
    746:       PetscCall(VecPlaceArray(x2i,pxi));
    747:       PetscCall(VecPlaceArray(x1i,pxi+m));
    748:     } else {
    749:       PetscCall(VecPlaceArray(x1i,pxi));
    750:       PetscCall(VecPlaceArray(x2i,pxi+n));
    751:     }
    752:     PetscCall(VecNorm(x2,NORM_2,&nrmr));
    753:     PetscCall(VecNorm(x2i,NORM_2,&nrmi));
    754:     if (nrmi>nrmr) {
    755:       if (isreal) {
    756:         PetscCall(BVInsertVec(U,j,x1i));
    757:         PetscCall(BVInsertVec(V,j,x2i));
    758:       } else {
    759:         PetscCall(BVInsertVec(U,j,x1));
    760:         PetscCall(BVInsertVec(V,j,x2i));
    761:       }
    762:     } else {
    763:       if (isreal) {
    764:         PetscCall(BVInsertVec(U,j,x1));
    765:         PetscCall(BVInsertVec(V,j,x2));
    766:       } else {
    767:         PetscCall(BVInsertVec(U,j,x1i));
    768:         PetscCall(BVScaleColumn(U,j,-1.0));
    769:         PetscCall(BVInsertVec(V,j,x2));
    770:       }
    771:     }
    772:     PetscCall(VecResetArray(x1i));
    773:     PetscCall(VecResetArray(x2i));
    774:     PetscCall(VecRestoreArrayRead(xi,&pxi));
    775: #endif
    776:     PetscCall(VecResetArray(x1));
    777:     PetscCall(VecResetArray(x2));
    778:     PetscCall(VecRestoreArrayRead(x,&px));
    779:     PetscCall(BVGetColumn(U,j,&u));
    780:     PetscCall(VecPointwiseMult(u,u,svd->omega));
    781:     PetscCall(BVRestoreColumn(U,j,&u));
    782:     PetscCall(BVNormColumn(U,j,NORM_2,&nrm));
    783:     PetscCall(BVScaleColumn(U,j,1.0/PetscAbs(nrm)));
    784:     svd->sign[j] = PetscSign(nrm);
    785:     PetscCall(BVNormColumn(V,j,NORM_2,&nrm));
    786:     PetscCall(BVScaleColumn(V,j,1.0/nrm));
    787:     j++;
    788:   }
    789:   PetscCall(VecDestroy(&x));
    790:   PetscCall(VecDestroy(&x1));
    791:   PetscCall(VecDestroy(&x2));
    792:   PetscCall(VecDestroy(&xi));
    793:   PetscCall(VecDestroy(&x1i));
    794:   PetscCall(VecDestroy(&x2i));
    795:   PetscFunctionReturn(PETSC_SUCCESS);
    796: }

    798: static PetscErrorCode SVDComputeVectors_Cyclic(SVD svd)
    799: {
    800:   PetscFunctionBegin;
    801:   switch (svd->problem_type) {
    802:     case SVD_STANDARD:
    803:       PetscCall(SVDComputeVectors_Cyclic_Standard(svd));
    804:       break;
    805:     case SVD_GENERALIZED:
    806:       PetscCall(SVDComputeVectors_Cyclic_Generalized(svd));
    807:       break;
    808:     case SVD_HYPERBOLIC:
    809:       PetscCall(SVDComputeVectors_Cyclic_Hyperbolic(svd));
    810:       break;
    811:     default:
    812:       SETERRQ(PetscObjectComm((PetscObject)svd),PETSC_ERR_ARG_WRONG,"Unknown singular value problem type");
    813:   }
    814:   PetscFunctionReturn(PETSC_SUCCESS);
    815: }

    817: static PetscErrorCode EPSMonitor_Cyclic(EPS eps,PetscInt its,PetscInt nconv,PetscScalar *eigr,PetscScalar *eigi,PetscReal *errest,PetscInt nest,void *ctx)
    818: {
    819:   PetscInt       i,j;
    820:   SVD            svd = (SVD)ctx;
    821:   PetscScalar    er,ei;
    822:   PetscReal      sigma;
    823:   ST             st;

    825:   PetscFunctionBegin;
    826:   nconv = 0;
    827:   PetscCall(EPSGetST(eps,&st));
    828:   for (i=0,j=0;i<PetscMin(nest,svd->ncv);i++) {
    829:     er = eigr[i]; ei = eigi[i];
    830:     PetscCall(STBackTransform(st,1,&er,&ei));
    831:     PetscCall(SVDCyclicCheckEigenvalue(svd,er,ei,&sigma,NULL));
    832:     if (sigma>0.0) {
    833:       svd->sigma[j]  = sigma;
    834:       svd->errest[j] = errest[i];
    835:       if (errest[i] && errest[i] < svd->tol) nconv++;
    836:       j++;
    837:     }
    838:   }
    839:   nest = j;
    840:   PetscCall(SVDMonitor(svd,its,nconv,svd->sigma,svd->errest,nest));
    841:   PetscFunctionReturn(PETSC_SUCCESS);
    842: }

    844: static PetscErrorCode SVDSetFromOptions_Cyclic(SVD svd,PetscOptionItems *PetscOptionsObject)
    845: {
    846:   PetscBool      set,val;
    847:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;
    848:   ST             st;

    850:   PetscFunctionBegin;
    851:   PetscOptionsHeadBegin(PetscOptionsObject,"SVD Cyclic Options");

    853:     PetscCall(PetscOptionsBool("-svd_cyclic_explicitmatrix","Use cyclic explicit matrix","SVDCyclicSetExplicitMatrix",cyclic->explicitmatrix,&val,&set));
    854:     if (set) PetscCall(SVDCyclicSetExplicitMatrix(svd,val));

    856:   PetscOptionsHeadEnd();

    858:   if (!cyclic->eps) PetscCall(SVDCyclicGetEPS(svd,&cyclic->eps));
    859:   if (!cyclic->explicitmatrix && !cyclic->usereps) {
    860:     /* use as default an ST with shell matrix and Jacobi */
    861:     PetscCall(EPSGetST(cyclic->eps,&st));
    862:     PetscCall(STSetMatMode(st,ST_MATMODE_SHELL));
    863:   }
    864:   PetscCall(EPSSetFromOptions(cyclic->eps));
    865:   PetscFunctionReturn(PETSC_SUCCESS);
    866: }

    868: static PetscErrorCode SVDCyclicSetExplicitMatrix_Cyclic(SVD svd,PetscBool explicitmat)
    869: {
    870:   SVD_CYCLIC *cyclic = (SVD_CYCLIC*)svd->data;

    872:   PetscFunctionBegin;
    873:   if (cyclic->explicitmatrix != explicitmat) {
    874:     cyclic->explicitmatrix = explicitmat;
    875:     svd->state = SVD_STATE_INITIAL;
    876:   }
    877:   PetscFunctionReturn(PETSC_SUCCESS);
    878: }

    880: /*@
    881:    SVDCyclicSetExplicitMatrix - Indicate if the eigensolver operator
    882:    H(A) = [ 0  A ; A^T 0 ] must be computed explicitly.

    884:    Logically Collective

    886:    Input Parameters:
    887: +  svd         - singular value solver
    888: -  explicitmat - boolean flag indicating if H(A) is built explicitly

    890:    Options Database Key:
    891: .  -svd_cyclic_explicitmatrix <boolean> - Indicates the boolean flag

    893:    Level: advanced

    895: .seealso: SVDCyclicGetExplicitMatrix()
    896: @*/
    897: PetscErrorCode SVDCyclicSetExplicitMatrix(SVD svd,PetscBool explicitmat)
    898: {
    899:   PetscFunctionBegin;
    902:   PetscTryMethod(svd,"SVDCyclicSetExplicitMatrix_C",(SVD,PetscBool),(svd,explicitmat));
    903:   PetscFunctionReturn(PETSC_SUCCESS);
    904: }

    906: static PetscErrorCode SVDCyclicGetExplicitMatrix_Cyclic(SVD svd,PetscBool *explicitmat)
    907: {
    908:   SVD_CYCLIC *cyclic = (SVD_CYCLIC*)svd->data;

    910:   PetscFunctionBegin;
    911:   *explicitmat = cyclic->explicitmatrix;
    912:   PetscFunctionReturn(PETSC_SUCCESS);
    913: }

    915: /*@
    916:    SVDCyclicGetExplicitMatrix - Returns the flag indicating if H(A) is built explicitly.

    918:    Not Collective

    920:    Input Parameter:
    921: .  svd  - singular value solver

    923:    Output Parameter:
    924: .  explicitmat - the mode flag

    926:    Level: advanced

    928: .seealso: SVDCyclicSetExplicitMatrix()
    929: @*/
    930: PetscErrorCode SVDCyclicGetExplicitMatrix(SVD svd,PetscBool *explicitmat)
    931: {
    932:   PetscFunctionBegin;
    934:   PetscAssertPointer(explicitmat,2);
    935:   PetscUseMethod(svd,"SVDCyclicGetExplicitMatrix_C",(SVD,PetscBool*),(svd,explicitmat));
    936:   PetscFunctionReturn(PETSC_SUCCESS);
    937: }

    939: static PetscErrorCode SVDCyclicSetEPS_Cyclic(SVD svd,EPS eps)
    940: {
    941:   SVD_CYCLIC      *cyclic = (SVD_CYCLIC*)svd->data;

    943:   PetscFunctionBegin;
    944:   PetscCall(PetscObjectReference((PetscObject)eps));
    945:   PetscCall(EPSDestroy(&cyclic->eps));
    946:   cyclic->eps     = eps;
    947:   cyclic->usereps = PETSC_TRUE;
    948:   svd->state      = SVD_STATE_INITIAL;
    949:   PetscFunctionReturn(PETSC_SUCCESS);
    950: }

    952: /*@
    953:    SVDCyclicSetEPS - Associate an eigensolver object (EPS) to the
    954:    singular value solver.

    956:    Collective

    958:    Input Parameters:
    959: +  svd - singular value solver
    960: -  eps - the eigensolver object

    962:    Level: advanced

    964: .seealso: SVDCyclicGetEPS()
    965: @*/
    966: PetscErrorCode SVDCyclicSetEPS(SVD svd,EPS eps)
    967: {
    968:   PetscFunctionBegin;
    971:   PetscCheckSameComm(svd,1,eps,2);
    972:   PetscTryMethod(svd,"SVDCyclicSetEPS_C",(SVD,EPS),(svd,eps));
    973:   PetscFunctionReturn(PETSC_SUCCESS);
    974: }

    976: static PetscErrorCode SVDCyclicGetEPS_Cyclic(SVD svd,EPS *eps)
    977: {
    978:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;

    980:   PetscFunctionBegin;
    981:   if (!cyclic->eps) {
    982:     PetscCall(EPSCreate(PetscObjectComm((PetscObject)svd),&cyclic->eps));
    983:     PetscCall(PetscObjectIncrementTabLevel((PetscObject)cyclic->eps,(PetscObject)svd,1));
    984:     PetscCall(EPSSetOptionsPrefix(cyclic->eps,((PetscObject)svd)->prefix));
    985:     PetscCall(EPSAppendOptionsPrefix(cyclic->eps,"svd_cyclic_"));
    986:     PetscCall(PetscObjectSetOptions((PetscObject)cyclic->eps,((PetscObject)svd)->options));
    987:     PetscCall(EPSSetWhichEigenpairs(cyclic->eps,EPS_LARGEST_REAL));
    988:     PetscCall(EPSMonitorSet(cyclic->eps,EPSMonitor_Cyclic,svd,NULL));
    989:   }
    990:   *eps = cyclic->eps;
    991:   PetscFunctionReturn(PETSC_SUCCESS);
    992: }

    994: /*@
    995:    SVDCyclicGetEPS - Retrieve the eigensolver object (EPS) associated
    996:    to the singular value solver.

    998:    Collective

    1000:    Input Parameter:
    1001: .  svd - singular value solver

    1003:    Output Parameter:
    1004: .  eps - the eigensolver object

    1006:    Level: advanced

    1008: .seealso: SVDCyclicSetEPS()
    1009: @*/
    1010: PetscErrorCode SVDCyclicGetEPS(SVD svd,EPS *eps)
    1011: {
    1012:   PetscFunctionBegin;
    1014:   PetscAssertPointer(eps,2);
    1015:   PetscUseMethod(svd,"SVDCyclicGetEPS_C",(SVD,EPS*),(svd,eps));
    1016:   PetscFunctionReturn(PETSC_SUCCESS);
    1017: }

    1019: static PetscErrorCode SVDView_Cyclic(SVD svd,PetscViewer viewer)
    1020: {
    1021:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;
    1022:   PetscBool      isascii;

    1024:   PetscFunctionBegin;
    1025:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    1026:   if (isascii) {
    1027:     if (!cyclic->eps) PetscCall(SVDCyclicGetEPS(svd,&cyclic->eps));
    1028:     PetscCall(PetscViewerASCIIPrintf(viewer,"  %s matrix\n",cyclic->explicitmatrix?"explicit":"implicit"));
    1029:     PetscCall(PetscViewerASCIIPushTab(viewer));
    1030:     PetscCall(EPSView(cyclic->eps,viewer));
    1031:     PetscCall(PetscViewerASCIIPopTab(viewer));
    1032:   }
    1033:   PetscFunctionReturn(PETSC_SUCCESS);
    1034: }

    1036: static PetscErrorCode SVDReset_Cyclic(SVD svd)
    1037: {
    1038:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;

    1040:   PetscFunctionBegin;
    1041:   PetscCall(EPSReset(cyclic->eps));
    1042:   PetscCall(MatDestroy(&cyclic->C));
    1043:   PetscCall(MatDestroy(&cyclic->D));
    1044:   PetscFunctionReturn(PETSC_SUCCESS);
    1045: }

    1047: static PetscErrorCode SVDDestroy_Cyclic(SVD svd)
    1048: {
    1049:   SVD_CYCLIC     *cyclic = (SVD_CYCLIC*)svd->data;

    1051:   PetscFunctionBegin;
    1052:   PetscCall(EPSDestroy(&cyclic->eps));
    1053:   PetscCall(PetscFree(svd->data));
    1054:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicSetEPS_C",NULL));
    1055:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicGetEPS_C",NULL));
    1056:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicSetExplicitMatrix_C",NULL));
    1057:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicGetExplicitMatrix_C",NULL));
    1058:   PetscFunctionReturn(PETSC_SUCCESS);
    1059: }

    1061: SLEPC_EXTERN PetscErrorCode SVDCreate_Cyclic(SVD svd)
    1062: {
    1063:   SVD_CYCLIC     *cyclic;

    1065:   PetscFunctionBegin;
    1066:   PetscCall(PetscNew(&cyclic));
    1067:   svd->data                = (void*)cyclic;
    1068:   svd->ops->solve          = SVDSolve_Cyclic;
    1069:   svd->ops->solveg         = SVDSolve_Cyclic;
    1070:   svd->ops->solveh         = SVDSolve_Cyclic;
    1071:   svd->ops->setup          = SVDSetUp_Cyclic;
    1072:   svd->ops->setfromoptions = SVDSetFromOptions_Cyclic;
    1073:   svd->ops->destroy        = SVDDestroy_Cyclic;
    1074:   svd->ops->reset          = SVDReset_Cyclic;
    1075:   svd->ops->view           = SVDView_Cyclic;
    1076:   svd->ops->computevectors = SVDComputeVectors_Cyclic;
    1077:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicSetEPS_C",SVDCyclicSetEPS_Cyclic));
    1078:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicGetEPS_C",SVDCyclicGetEPS_Cyclic));
    1079:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicSetExplicitMatrix_C",SVDCyclicSetExplicitMatrix_Cyclic));
    1080:   PetscCall(PetscObjectComposeFunction((PetscObject)svd,"SVDCyclicGetExplicitMatrix_C",SVDCyclicGetExplicitMatrix_Cyclic));
    1081:   PetscFunctionReturn(PETSC_SUCCESS);
    1082: }