Date: 2023-09-05T10:17:41+00:00

Actual source code: bvimpl.h
slepc-3.19.2 2023-09-05
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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: */

     11: #if !defined(SLEPCBVIMPL_H)
     12: #define SLEPCBVIMPL_H

     14: #include <slepcbv.h>
     15: #include <slepc/private/slepcimpl.h>

     17: /* SUBMANSEC = BV */

     19: SLEPC_EXTERN PetscBool BVRegisterAllCalled;
     20: SLEPC_EXTERN PetscErrorCode BVRegisterAll(void);

     22: SLEPC_EXTERN PetscLogEvent BV_Create,BV_Copy,BV_Mult,BV_MultVec,BV_MultInPlace,BV_Dot,BV_DotVec,BV_Orthogonalize,BV_OrthogonalizeVec,BV_Scale,BV_Norm,BV_NormVec,BV_Normalize,BV_SetRandom,BV_MatMult,BV_MatMultVec,BV_MatProject,BV_SVDAndRank;

     24: typedef struct _BVOps *BVOps;

     26: struct _BVOps {
     27:   PetscErrorCode (*mult)(BV,PetscScalar,PetscScalar,BV,Mat);
     28:   PetscErrorCode (*multvec)(BV,PetscScalar,PetscScalar,Vec,PetscScalar*);
     29:   PetscErrorCode (*multinplace)(BV,Mat,PetscInt,PetscInt);
     30:   PetscErrorCode (*multinplacetrans)(BV,Mat,PetscInt,PetscInt);
     31:   PetscErrorCode (*dot)(BV,BV,Mat);
     32:   PetscErrorCode (*dotvec)(BV,Vec,PetscScalar*);
     33:   PetscErrorCode (*dotvec_local)(BV,Vec,PetscScalar*);
     34:   PetscErrorCode (*dotvec_begin)(BV,Vec,PetscScalar*);
     35:   PetscErrorCode (*dotvec_end)(BV,Vec,PetscScalar*);
     36:   PetscErrorCode (*scale)(BV,PetscInt,PetscScalar);
     37:   PetscErrorCode (*norm)(BV,PetscInt,NormType,PetscReal*);
     38:   PetscErrorCode (*norm_local)(BV,PetscInt,NormType,PetscReal*);
     39:   PetscErrorCode (*norm_begin)(BV,PetscInt,NormType,PetscReal*);
     40:   PetscErrorCode (*norm_end)(BV,PetscInt,NormType,PetscReal*);
     41:   PetscErrorCode (*normalize)(BV,PetscScalar*);
     42:   PetscErrorCode (*matmult)(BV,Mat,BV);
     43:   PetscErrorCode (*copy)(BV,BV);
     44:   PetscErrorCode (*copycolumn)(BV,PetscInt,PetscInt);
     45:   PetscErrorCode (*resize)(BV,PetscInt,PetscBool);
     46:   PetscErrorCode (*getcolumn)(BV,PetscInt,Vec*);
     47:   PetscErrorCode (*restorecolumn)(BV,PetscInt,Vec*);
     48:   PetscErrorCode (*getarray)(BV,PetscScalar**);
     49:   PetscErrorCode (*restorearray)(BV,PetscScalar**);
     50:   PetscErrorCode (*getarrayread)(BV,const PetscScalar**);
     51:   PetscErrorCode (*restorearrayread)(BV,const PetscScalar**);
     52:   PetscErrorCode (*restoresplit)(BV,BV*,BV*);
     53:   PetscErrorCode (*gramschmidt)(BV,PetscInt,Vec,PetscBool*,PetscScalar*,PetscScalar*,PetscReal*,PetscReal*);
     54:   PetscErrorCode (*getmat)(BV,Mat*);
     55:   PetscErrorCode (*restoremat)(BV,Mat*);
     56:   PetscErrorCode (*duplicate)(BV,BV);
     57:   PetscErrorCode (*create)(BV);
     58:   PetscErrorCode (*setfromoptions)(BV,PetscOptionItems*);
     59:   PetscErrorCode (*view)(BV,PetscViewer);
     60:   PetscErrorCode (*destroy)(BV);
     61: };

     63: struct _p_BV {
     64:   PETSCHEADER(struct _BVOps);
     65:   /*------------------------- User parameters --------------------------*/
     66:   Vec                t;            /* template vector */
     67:   PetscInt           n,N;          /* dimensions of vectors (local, global) */
     68:   PetscInt           m;            /* number of vectors */
     69:   PetscInt           l;            /* number of leading columns */
     70:   PetscInt           k;            /* number of active columns */
     71:   PetscInt           nc;           /* number of constraints */
     72:   BVOrthogType       orthog_type;  /* the method of vector orthogonalization */
     73:   BVOrthogRefineType orthog_ref;   /* refinement method */
     74:   PetscReal          orthog_eta;   /* refinement threshold */
     75:   BVOrthogBlockType  orthog_block; /* the method of block orthogonalization */
     76:   Mat                matrix;       /* inner product matrix */
     77:   PetscBool          indef;        /* matrix is indefinite */
     78:   BVMatMultType      vmm;          /* version of matmult operation */
     79:   PetscBool          rrandom;      /* reproducible random vectors */
     80:   PetscReal          deftol;       /* tolerance for BV_SafeSqrt */

     82:   /*---------------------- Cached data and workspace -------------------*/
     83:   Vec                buffer;       /* buffer vector used in orthogonalization */
     84:   Mat                Abuffer;      /* auxiliary seqdense matrix that wraps the buffer */
     85:   Vec                Bx;           /* result of matrix times a vector x */
     86:   PetscObjectId      xid;          /* object id of vector x */
     87:   PetscObjectState   xstate;       /* state of vector x */
     88:   Vec                cv[2];        /* column vectors obtained with BVGetColumn() */
     89:   PetscInt           ci[2];        /* column indices of obtained vectors */
     90:   PetscObjectState   st[2];        /* state of obtained vectors */
     91:   PetscObjectId      id[2];        /* object id of obtained vectors */
     92:   PetscScalar        *h,*c;        /* orthogonalization coefficients */
     93:   Vec                omega;        /* signature matrix values for indefinite case */
     94:   PetscBool          defersfo;     /* deferred call to setfromoptions */
     95:   BV                 cached;       /* cached BV to store result of matrix times BV */
     96:   PetscObjectState   bvstate;      /* state of BV when BVApplyMatrixBV() was called */
     97:   BV                 L,R;          /* BV objects obtained with BVGetSplit() */
     98:   PetscObjectState   lstate,rstate;/* state of L and R when BVGetSplit() was called */
     99:   PetscInt           lsplit;       /* the value of l when BVGetSplit() was called */
    100:   PetscInt           issplit;      /* >0 if this BV has been created by splitting (1=left, 2=right) */
    101:   BV                 splitparent;  /* my parent if I am a split BV */
    102:   PetscRandom        rand;         /* random number generator */
    103:   Mat                Acreate;      /* matrix given at BVCreateFromMat() */
    104:   Mat                Aget;         /* matrix returned for BVGetMat() */
    105:   PetscBool          cuda;         /* true if GPU must be used in SVEC */
    106:   PetscBool          sfocalled;    /* setfromoptions has been called */
    107:   PetscScalar        *work;
    108:   PetscInt           lwork;
    109:   void               *data;
    110: };

    112: /*
    113:   BV_SafeSqrt - Computes the square root of a scalar value alpha, which is
    114:   assumed to be z'*B*z. The result is
    115:     if definite inner product:     res = sqrt(alpha)
    116:     if indefinite inner product:   res = sgn(alpha)*sqrt(abs(alpha))
    117: */
    118: static inline PetscErrorCode BV_SafeSqrt(BV bv,PetscScalar alpha,PetscReal *res)
    119: {
    120:   PetscReal      absal,realp;

    122:   PetscFunctionBegin;
    123:   absal = PetscAbsScalar(alpha);
    124:   realp = PetscRealPart(alpha);
    125:   if (PetscUnlikely(absal<PETSC_MACHINE_EPSILON)) PetscCall(PetscInfo(bv,"Zero norm %g, either the vector is zero or a semi-inner product is being used\n",(double)absal));
    126: #if defined(PETSC_USE_COMPLEX)
    127:   PetscCheck(PetscAbsReal(PetscImaginaryPart(alpha))<bv->deftol || PetscAbsReal(PetscImaginaryPart(alpha))/absal<10*bv->deftol,PetscObjectComm((PetscObject)bv),PETSC_ERR_USER_INPUT,"The inner product is not well defined: nonzero imaginary part %g",(double)PetscImaginaryPart(alpha));
    128: #endif
    129:   if (PetscUnlikely(bv->indef)) {
    130:     *res = (realp<0.0)? -PetscSqrtReal(-realp): PetscSqrtReal(realp);
    131:   } else {
    132:     PetscCheck(realp>-bv->deftol,PetscObjectComm((PetscObject)bv),PETSC_ERR_USER_INPUT,"The inner product is not well defined: indefinite matrix %g",(double)realp);
    133:     *res = (realp<0.0)? 0.0: PetscSqrtReal(realp);
    134:   }
    135:   PetscFunctionReturn(PETSC_SUCCESS);
    136: }

    138: /*
    139:   BV_IPMatMult - Multiply a vector x by the inner-product matrix, cache the
    140:   result in Bx.
    141: */
    142: static inline PetscErrorCode BV_IPMatMult(BV bv,Vec x)
    143: {
    144:   PetscFunctionBegin;
    145:   if (((PetscObject)x)->id != bv->xid || ((PetscObject)x)->state != bv->xstate) {
    146:     if (PetscUnlikely(!bv->Bx)) PetscCall(MatCreateVecs(bv->matrix,&bv->Bx,NULL));
    147:     PetscCall(MatMult(bv->matrix,x,bv->Bx));
    148:     PetscCall(PetscObjectGetId((PetscObject)x,&bv->xid));
    149:     PetscCall(PetscObjectStateGet((PetscObject)x,&bv->xstate));
    150:   }
    151:   PetscFunctionReturn(PETSC_SUCCESS);
    152: }

    154: /*
    155:   BV_IPMatMultBV - Multiply BV by the inner-product matrix, cache the
    156:   result internally in bv->cached.
    157: */
    158: static inline PetscErrorCode BV_IPMatMultBV(BV bv)
    159: {
    160:   PetscFunctionBegin;
    161:   PetscCall(BVGetCachedBV(bv,&bv->cached));
    162:   if (((PetscObject)bv)->state != bv->bvstate || bv->l != bv->cached->l || bv->k != bv->cached->k) {
    163:     PetscCall(BVSetActiveColumns(bv->cached,bv->l,bv->k));
    164:     if (bv->matrix) PetscCall(BVMatMult(bv,bv->matrix,bv->cached));
    165:     else PetscCall(BVCopy(bv,bv->cached));
    166:     bv->bvstate = ((PetscObject)bv)->state;
    167:   }
    168:   PetscFunctionReturn(PETSC_SUCCESS);
    169: }

    171: /*
    172:   BV_AllocateCoeffs - Allocate orthogonalization coefficients if not done already.
    173: */
    174: static inline PetscErrorCode BV_AllocateCoeffs(BV bv)
    175: {
    176:   PetscFunctionBegin;
    177:   if (!bv->h) PetscCall(PetscMalloc2(bv->nc+bv->m,&bv->h,bv->nc+bv->m,&bv->c));
    178:   PetscFunctionReturn(PETSC_SUCCESS);
    179: }

    181: /*
    182:   BV_AllocateSignature - Allocate signature coefficients if not done already.
    183: */
    184: static inline PetscErrorCode BV_AllocateSignature(BV bv)
    185: {
    186:   PetscFunctionBegin;
    187:   if (bv->indef && !bv->omega) {
    188:     if (bv->cuda) {
    189: #if defined(PETSC_HAVE_CUDA)
    190:       PetscCall(VecCreateSeqCUDA(PETSC_COMM_SELF,bv->nc+bv->m,&bv->omega));
    191: #else
    192:       SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_PLIB,"Something wrong happened");
    193: #endif
    194:     } else PetscCall(VecCreateSeq(PETSC_COMM_SELF,bv->nc+bv->m,&bv->omega));
    195:     PetscCall(VecSet(bv->omega,1.0));
    196:   }
    197:   PetscFunctionReturn(PETSC_SUCCESS);
    198: }

    200: /*
    201:   BV_SetMatrixDiagonal - sets the inner product matrix for BV as a diagonal matrix
    202:   with the diagonal specified by vector vomega, using the same matrix type as matrix M
    203: */
    204: static inline PetscErrorCode BV_SetMatrixDiagonal(BV bv,Vec vomega,Mat M)
    205: {
    206:   Mat      Omega;
    207:   MatType  Mtype;

    209:   PetscFunctionBegin;
    210:   PetscCall(MatGetType(M,&Mtype));
    211:   PetscCall(MatCreate(PetscObjectComm((PetscObject)bv),&Omega));
    212:   PetscCall(MatSetSizes(Omega,bv->n,bv->n,bv->N,bv->N));
    213:   PetscCall(MatSetType(Omega,Mtype));
    214:   PetscCall(MatSetUp(Omega));
    215:   PetscCall(MatDiagonalSet(Omega,vomega,INSERT_VALUES));
    216:   PetscCall(BVSetMatrix(bv,Omega,PETSC_TRUE));
    217:   PetscCall(MatDestroy(&Omega));
    218:   PetscFunctionReturn(PETSC_SUCCESS);
    219: }

    221: /*
    222:   BVAvailableVec: First (0) or second (1) vector available for
    223:   getcolumn operation (or -1 if both vectors already fetched).
    224: */
    225: #define BVAvailableVec (((bv->ci[0]==-bv->nc-1)? 0: (bv->ci[1]==-bv->nc-1)? 1: -1))

    227: /*
    228:     Macros to test valid BV arguments
    229: */
    230: #if !defined(PETSC_USE_DEBUG)

    232: #define BVCheckSizes(h,arg) do {(void)(h);} while (0)
    233: #define BVCheckOp(h,arg,op) do {(void)(h);} while (0)

    235: #else

    237: #define BVCheckSizes(h,arg) \
    238:   do { \
    239:     PetscCheck((h)->m,PetscObjectComm((PetscObject)(h)),PETSC_ERR_ARG_WRONGSTATE,"BV sizes have not been defined: Parameter #%d",arg); \
    240:   } while (0)

    242: #define BVCheckOp(h,arg,op) \
    243:   do { \
    244:     PetscCheck((h)->ops->op,PetscObjectComm((PetscObject)(h)),PETSC_ERR_SUP,"Operation not implemented in this BV type: Parameter #%d",arg); \
    245:   } while (0)

    247: #endif

    249: SLEPC_INTERN PetscErrorCode BVView_Vecs(BV,PetscViewer);

    251: SLEPC_INTERN PetscErrorCode BVAllocateWork_Private(BV,PetscInt);

    253: SLEPC_INTERN PetscErrorCode BVMult_BLAS_Private(BV,PetscInt,PetscInt,PetscInt,PetscInt,PetscScalar,const PetscScalar*,const PetscScalar*,PetscScalar,PetscScalar*);
    254: SLEPC_INTERN PetscErrorCode BVMultVec_BLAS_Private(BV,PetscInt,PetscInt,PetscScalar,const PetscScalar*,const PetscScalar*,PetscScalar,PetscScalar*);
    255: SLEPC_INTERN PetscErrorCode BVMultInPlace_BLAS_Private(BV,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscScalar*,const PetscScalar*,PetscBool);
    256: SLEPC_INTERN PetscErrorCode BVMultInPlace_Vecs_Private(BV,PetscInt,PetscInt,PetscInt,Vec*,const PetscScalar*,PetscBool);
    257: SLEPC_INTERN PetscErrorCode BVAXPY_BLAS_Private(BV,PetscInt,PetscInt,PetscScalar,const PetscScalar*,PetscScalar,PetscScalar*);
    258: SLEPC_INTERN PetscErrorCode BVDot_BLAS_Private(BV,PetscInt,PetscInt,PetscInt,PetscInt,const PetscScalar*,const PetscScalar*,PetscScalar*,PetscBool);
    259: SLEPC_INTERN PetscErrorCode BVDotVec_BLAS_Private(BV,PetscInt,PetscInt,const PetscScalar*,const PetscScalar*,PetscScalar*,PetscBool);
    260: SLEPC_INTERN PetscErrorCode BVScale_BLAS_Private(BV,PetscInt,PetscScalar*,PetscScalar);
    261: SLEPC_INTERN PetscErrorCode BVNorm_LAPACK_Private(BV,PetscInt,PetscInt,const PetscScalar*,NormType,PetscReal*,PetscBool);
    262: SLEPC_INTERN PetscErrorCode BVNormalize_LAPACK_Private(BV,PetscInt,PetscInt,const PetscScalar*,PetscScalar*,PetscBool);
    263: SLEPC_INTERN PetscErrorCode BVGetMat_Default(BV,Mat*);
    264: SLEPC_INTERN PetscErrorCode BVRestoreMat_Default(BV,Mat*);
    265: SLEPC_INTERN PetscErrorCode BVMatCholInv_LAPACK_Private(BV,Mat,Mat);
    266: SLEPC_INTERN PetscErrorCode BVMatTriInv_LAPACK_Private(BV,Mat,Mat);
    267: SLEPC_INTERN PetscErrorCode BVMatSVQB_LAPACK_Private(BV,Mat,Mat);
    268: SLEPC_INTERN PetscErrorCode BVOrthogonalize_LAPACK_TSQR(BV,PetscInt,PetscInt,PetscScalar*,PetscScalar*,PetscInt);
    269: SLEPC_INTERN PetscErrorCode BVOrthogonalize_LAPACK_TSQR_OnlyR(BV,PetscInt,PetscInt,PetscScalar*,PetscScalar*,PetscInt);

    271: /* reduction operations used in BVOrthogonalize and BVNormalize */
    272: SLEPC_EXTERN MPI_Op MPIU_TSQR, MPIU_LAPY2;
    273: SLEPC_EXTERN void MPIAPI SlepcGivensPacked(void*,void*,PetscMPIInt*,MPI_Datatype*);
    274: SLEPC_EXTERN void MPIAPI SlepcPythag(void*,void*,PetscMPIInt*,MPI_Datatype*);

    276: /*
    277:    BV_CleanCoefficients_Default - Sets to zero all entries of column j of the bv buffer
    278: */
    279: static inline PetscErrorCode BV_CleanCoefficients_Default(BV bv,PetscInt j,PetscScalar *h)
    280: {
    281:   PetscScalar    *hh=h,*a;
    282:   PetscInt       i;

    284:   PetscFunctionBegin;
    285:   if (!h) {
    286:     PetscCall(VecGetArray(bv->buffer,&a));
    287:     hh = a + j*(bv->nc+bv->m);
    288:   }
    289:   for (i=0;i<bv->nc+j;i++) hh[i] = 0.0;
    290:   if (!h) PetscCall(VecRestoreArray(bv->buffer,&a));
    291:   PetscFunctionReturn(PETSC_SUCCESS);
    292: }

    294: /*
    295:    BV_AddCoefficients_Default - Add the contents of the scratch (0-th column) of the bv buffer
    296:    into column j of the bv buffer
    297: */
    298: static inline PetscErrorCode BV_AddCoefficients_Default(BV bv,PetscInt j,PetscScalar *h,PetscScalar *c)
    299: {
    300:   PetscScalar    *hh=h,*cc=c;
    301:   PetscInt       i;

    303:   PetscFunctionBegin;
    304:   if (!h) {
    305:     PetscCall(VecGetArray(bv->buffer,&cc));
    306:     hh = cc + j*(bv->nc+bv->m);
    307:   }
    308:   for (i=0;i<bv->nc+j;i++) hh[i] += cc[i];
    309:   if (!h) PetscCall(VecRestoreArray(bv->buffer,&cc));
    310:   PetscCall(PetscLogFlops(1.0*(bv->nc+j)));
    311:   PetscFunctionReturn(PETSC_SUCCESS);
    312: }

    314: /*
    315:    BV_SetValue_Default - Sets value in row j (counted after the constraints) of column k
    316:    of the coefficients array
    317: */
    318: static inline PetscErrorCode BV_SetValue_Default(BV bv,PetscInt j,PetscInt k,PetscScalar *h,PetscScalar value)
    319: {
    320:   PetscScalar    *hh=h,*a;

    322:   PetscFunctionBegin;
    323:   if (!h) {
    324:     PetscCall(VecGetArray(bv->buffer,&a));
    325:     hh = a + k*(bv->nc+bv->m);
    326:   }
    327:   hh[bv->nc+j] = value;
    328:   if (!h) PetscCall(VecRestoreArray(bv->buffer,&a));
    329:   PetscFunctionReturn(PETSC_SUCCESS);
    330: }

    332: /*
    333:    BV_SquareSum_Default - Returns the value h'*h, where h represents the contents of the
    334:    coefficients array (up to position j)
    335: */
    336: static inline PetscErrorCode BV_SquareSum_Default(BV bv,PetscInt j,PetscScalar *h,PetscReal *sum)
    337: {
    338:   PetscScalar    *hh=h;
    339:   PetscInt       i;

    341:   PetscFunctionBegin;
    342:   *sum = 0.0;
    343:   if (!h) PetscCall(VecGetArray(bv->buffer,&hh));
    344:   for (i=0;i<bv->nc+j;i++) *sum += PetscRealPart(hh[i]*PetscConj(hh[i]));
    345:   if (!h) PetscCall(VecRestoreArray(bv->buffer,&hh));
    346:   PetscCall(PetscLogFlops(2.0*(bv->nc+j)));
    347:   PetscFunctionReturn(PETSC_SUCCESS);
    348: }

    350: /*
    351:    BV_ApplySignature_Default - Computes the pointwise product h*omega, where h represents
    352:    the contents of the coefficients array (up to position j) and omega is the signature;
    353:    if inverse=TRUE then the operation is h/omega
    354: */
    355: static inline PetscErrorCode BV_ApplySignature_Default(BV bv,PetscInt j,PetscScalar *h,PetscBool inverse)
    356: {
    357:   PetscScalar       *hh=h;
    358:   PetscInt          i;
    359:   const PetscScalar *omega;

    361:   PetscFunctionBegin;
    362:   if (PetscUnlikely(!(bv->nc+j))) PetscFunctionReturn(PETSC_SUCCESS);
    363:   if (!h) PetscCall(VecGetArray(bv->buffer,&hh));
    364:   PetscCall(VecGetArrayRead(bv->omega,&omega));
    365:   if (inverse) for (i=0;i<bv->nc+j;i++) hh[i] /= PetscRealPart(omega[i]);
    366:   else for (i=0;i<bv->nc+j;i++) hh[i] *= PetscRealPart(omega[i]);
    367:   PetscCall(VecRestoreArrayRead(bv->omega,&omega));
    368:   if (!h) PetscCall(VecRestoreArray(bv->buffer,&hh));
    369:   PetscCall(PetscLogFlops(1.0*(bv->nc+j)));
    370:   PetscFunctionReturn(PETSC_SUCCESS);
    371: }

    373: /*
    374:    BV_SquareRoot_Default - Returns the square root of position j (counted after the constraints)
    375:    of the coefficients array
    376: */
    377: static inline PetscErrorCode BV_SquareRoot_Default(BV bv,PetscInt j,PetscScalar *h,PetscReal *beta)
    378: {
    379:   PetscScalar    *hh=h;

    381:   PetscFunctionBegin;
    382:   if (!h) PetscCall(VecGetArray(bv->buffer,&hh));
    383:   PetscCall(BV_SafeSqrt(bv,hh[bv->nc+j],beta));
    384:   if (!h) PetscCall(VecRestoreArray(bv->buffer,&hh));
    385:   PetscFunctionReturn(PETSC_SUCCESS);
    386: }

    388: /*
    389:    BV_StoreCoefficients_Default - Copy the contents of the coefficients array to an array dest
    390:    provided by the caller (only values from l to j are copied)
    391: */
    392: static inline PetscErrorCode BV_StoreCoefficients_Default(BV bv,PetscInt j,PetscScalar *h,PetscScalar *dest)
    393: {
    394:   PetscScalar    *hh=h,*a;
    395:   PetscInt       i;

    397:   PetscFunctionBegin;
    398:   if (!h) {
    399:     PetscCall(VecGetArray(bv->buffer,&a));
    400:     hh = a + j*(bv->nc+bv->m);
    401:   }
    402:   for (i=bv->l;i<j;i++) dest[i-bv->l] = hh[bv->nc+i];
    403:   if (!h) PetscCall(VecRestoreArray(bv->buffer,&a));
    404:   PetscFunctionReturn(PETSC_SUCCESS);
    405: }

    407: /*
    408:   BV_GetEigenvector - retrieves k-th eigenvector from basis vectors V.
    409:   The argument eigi is the imaginary part of the corresponding eigenvalue.
    410: */
    411: static inline PetscErrorCode BV_GetEigenvector(BV V,PetscInt k,PetscScalar eigi,Vec Vr,Vec Vi)
    412: {
    413:   PetscFunctionBegin;
    414: #if defined(PETSC_USE_COMPLEX)
    415:   if (Vr) PetscCall(BVCopyVec(V,k,Vr));
    416:   if (Vi) PetscCall(VecSet(Vi,0.0));
    417: #else
    418:   if (eigi > 0.0) { /* first value of conjugate pair */
    419:     if (Vr) PetscCall(BVCopyVec(V,k,Vr));
    420:     if (Vi) PetscCall(BVCopyVec(V,k+1,Vi));
    421:   } else if (eigi < 0.0) { /* second value of conjugate pair */
    422:     if (Vr) PetscCall(BVCopyVec(V,k-1,Vr));
    423:     if (Vi) {
    424:       PetscCall(BVCopyVec(V,k,Vi));
    425:       PetscCall(VecScale(Vi,-1.0));
    426:     }
    427:   } else { /* real eigenvalue */
    428:     if (Vr) PetscCall(BVCopyVec(V,k,Vr));
    429:     if (Vi) PetscCall(VecSet(Vi,0.0));
    430:   }
    431: #endif
    432:   PetscFunctionReturn(PETSC_SUCCESS);
    433: }

    435: /*
    436:    BV_OrthogonalizeColumn_Safe - this is intended for cases where we know that
    437:    the resulting vector is going to be numerically zero, so normalization or
    438:    iterative refinement may cause problems in parallel (collective operation
    439:    not being called by all processes)
    440: */
    441: static inline PetscErrorCode BV_OrthogonalizeColumn_Safe(BV bv,PetscInt j,PetscScalar *H,PetscReal *norm,PetscBool *lindep)
    442: {
    443:   BVOrthogRefineType orthog_ref;

    445:   PetscFunctionBegin;
    446:   PetscCall(PetscInfo(bv,"Orthogonalizing column %" PetscInt_FMT " without refinement\n",j));
    447:   orthog_ref     = bv->orthog_ref;
    448:   bv->orthog_ref = BV_ORTHOG_REFINE_NEVER;  /* avoid refinement */
    449:   PetscCall(BVOrthogonalizeColumn(bv,j,H,NULL,NULL));
    450:   bv->orthog_ref = orthog_ref;  /* restore refinement setting */
    451:   if (norm)   *norm  = 0.0;
    452:   if (lindep) *lindep = PETSC_TRUE;
    453:   PetscFunctionReturn(PETSC_SUCCESS);
    454: }

    456: #if defined(PETSC_HAVE_CUDA)
    457: SLEPC_INTERN PetscErrorCode BV_CleanCoefficients_CUDA(BV,PetscInt,PetscScalar*);
    458: SLEPC_INTERN PetscErrorCode BV_AddCoefficients_CUDA(BV,PetscInt,PetscScalar*,PetscScalar*);
    459: SLEPC_INTERN PetscErrorCode BV_SetValue_CUDA(BV,PetscInt,PetscInt,PetscScalar*,PetscScalar);
    460: SLEPC_INTERN PetscErrorCode BV_SquareSum_CUDA(BV,PetscInt,PetscScalar*,PetscReal*);
    461: SLEPC_INTERN PetscErrorCode BV_ApplySignature_CUDA(BV,PetscInt,PetscScalar*,PetscBool);
    462: SLEPC_INTERN PetscErrorCode BV_SquareRoot_CUDA(BV,PetscInt,PetscScalar*,PetscReal*);
    463: SLEPC_INTERN PetscErrorCode BV_StoreCoefficients_CUDA(BV,PetscInt,PetscScalar*,PetscScalar*);
    464: #define BV_CleanCoefficients(a,b,c)   ((a)->cuda?BV_CleanCoefficients_CUDA:BV_CleanCoefficients_Default)((a),(b),(c))
    465: #define BV_AddCoefficients(a,b,c,d)   ((a)->cuda?BV_AddCoefficients_CUDA:BV_AddCoefficients_Default)((a),(b),(c),(d))
    466: #define BV_SetValue(a,b,c,d,e)        ((a)->cuda?BV_SetValue_CUDA:BV_SetValue_Default)((a),(b),(c),(d),(e))
    467: #define BV_SquareSum(a,b,c,d)         ((a)->cuda?BV_SquareSum_CUDA:BV_SquareSum_Default)((a),(b),(c),(d))
    468: #define BV_ApplySignature(a,b,c,d)    ((a)->cuda?BV_ApplySignature_CUDA:BV_ApplySignature_Default)((a),(b),(c),(d))
    469: #define BV_SquareRoot(a,b,c,d)        ((a)->cuda?BV_SquareRoot_CUDA:BV_SquareRoot_Default)((a),(b),(c),(d))
    470: #define BV_StoreCoefficients(a,b,c,d) ((a)->cuda?BV_StoreCoefficients_CUDA:BV_StoreCoefficients_Default)((a),(b),(c),(d))
    471: #else
    472: #define BV_CleanCoefficients(a,b,c)   BV_CleanCoefficients_Default((a),(b),(c))
    473: #define BV_AddCoefficients(a,b,c,d)   BV_AddCoefficients_Default((a),(b),(c),(d))
    474: #define BV_SetValue(a,b,c,d,e)        BV_SetValue_Default((a),(b),(c),(d),(e))
    475: #define BV_SquareSum(a,b,c,d)         BV_SquareSum_Default((a),(b),(c),(d))
    476: #define BV_ApplySignature(a,b,c,d)    BV_ApplySignature_Default((a),(b),(c),(d))
    477: #define BV_SquareRoot(a,b,c,d)        BV_SquareRoot_Default((a),(b),(c),(d))
    478: #define BV_StoreCoefficients(a,b,c,d) BV_StoreCoefficients_Default((a),(b),(c),(d))
    479: #endif /* PETSC_HAVE_CUDA */

    481: #endif