Date: 2023-01-26T12:18:14+00:00

Actual source code: bvtensor.c
slepc-3.18.2 2023-01-26
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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:    Tensor BV that is represented in compact form as V = (I otimes U) S
     12: */

     14: #include <slepc/private/bvimpl.h>
     15: #include <slepcblaslapack.h>

     17: typedef struct {
     18:   BV          U;        /* first factor */
     19:   Mat         S;        /* second factor */
     20:   PetscScalar *qB;      /* auxiliary matrix used in non-standard inner products */
     21:   PetscScalar *sw;      /* work space */
     22:   PetscInt    d;        /* degree of the tensor BV */
     23:   PetscInt    ld;       /* leading dimension of a single block in S */
     24:   PetscInt    puk;      /* copy of the k value */
     25:   Vec         u;        /* auxiliary work vector */
     26: } BV_TENSOR;

     28: PetscErrorCode BVMultInPlace_Tensor(BV V,Mat Q,PetscInt s,PetscInt e)
     29: {
     30:   BV_TENSOR         *ctx = (BV_TENSOR*)V->data;
     31:   PetscScalar       *pS;
     32:   const PetscScalar *q;
     33:   PetscInt          ldq,lds = ctx->ld*ctx->d;

     35:   MatDenseGetLDA(Q,&ldq);
     36:   MatDenseGetArray(ctx->S,&pS);
     37:   MatDenseGetArrayRead(Q,&q);
     38:   BVMultInPlace_BLAS_Private(V,lds,V->k-V->l,ldq,s-V->l,e-V->l,pS+(V->nc+V->l)*lds,q+V->l*ldq+V->l,PETSC_FALSE);
     39:   MatDenseRestoreArrayRead(Q,&q);
     40:   MatDenseRestoreArray(ctx->S,&pS);
     41:   return 0;
     42: }

     44: PetscErrorCode BVMultInPlaceHermitianTranspose_Tensor(BV V,Mat Q,PetscInt s,PetscInt e)
     45: {
     46:   BV_TENSOR         *ctx = (BV_TENSOR*)V->data;
     47:   PetscScalar       *pS;
     48:   const PetscScalar *q;
     49:   PetscInt          ldq,lds = ctx->ld*ctx->d;

     51:   MatDenseGetLDA(Q,&ldq);
     52:   MatDenseGetArray(ctx->S,&pS);
     53:   MatDenseGetArrayRead(Q,&q);
     54:   BVMultInPlace_BLAS_Private(V,lds,V->k-V->l,ldq,s-V->l,e-V->l,pS+(V->nc+V->l)*lds,q+V->l*ldq+V->l,PETSC_TRUE);
     55:   MatDenseRestoreArrayRead(Q,&q);
     56:   MatDenseRestoreArray(ctx->S,&pS);
     57:   return 0;
     58: }

     60: PetscErrorCode BVDot_Tensor(BV X,BV Y,Mat M)
     61: {
     62:   BV_TENSOR         *x = (BV_TENSOR*)X->data,*y = (BV_TENSOR*)Y->data;
     63:   PetscScalar       *m;
     64:   const PetscScalar *px,*py;
     65:   PetscInt          ldm,lds = x->ld*x->d;

     69:   MatDenseGetLDA(M,&ldm);
     70:   MatDenseGetArrayRead(x->S,&px);
     71:   MatDenseGetArrayRead(y->S,&py);
     72:   MatDenseGetArray(M,&m);
     73:   BVDot_BLAS_Private(X,Y->k-Y->l,X->k-X->l,lds,ldm,py+(Y->nc+Y->l)*lds,px+(X->nc+X->l)*lds,m+X->l*ldm+Y->l,PETSC_FALSE);
     74:   MatDenseRestoreArray(M,&m);
     75:   MatDenseRestoreArrayRead(x->S,&px);
     76:   MatDenseRestoreArrayRead(y->S,&py);
     77:   return 0;
     78: }

     80: PetscErrorCode BVScale_Tensor(BV bv,PetscInt j,PetscScalar alpha)
     81: {
     82:   BV_TENSOR      *ctx = (BV_TENSOR*)bv->data;
     83:   PetscScalar    *pS;
     84:   PetscInt       lds = ctx->ld*ctx->d;

     86:   MatDenseGetArray(ctx->S,&pS);
     87:   if (PetscUnlikely(j<0)) BVScale_BLAS_Private(bv,(bv->k-bv->l)*lds,pS+(bv->nc+bv->l)*lds,alpha);
     88:   else BVScale_BLAS_Private(bv,lds,pS+(bv->nc+j)*lds,alpha);
     89:   MatDenseRestoreArray(ctx->S,&pS);
     90:   return 0;
     91: }

     93: PetscErrorCode BVNorm_Tensor(BV bv,PetscInt j,NormType type,PetscReal *val)
     94: {
     95:   BV_TENSOR         *ctx = (BV_TENSOR*)bv->data;
     96:   const PetscScalar *pS;
     97:   PetscInt          lds = ctx->ld*ctx->d;

     99:   MatDenseGetArrayRead(ctx->S,&pS);
    100:   if (j<0) BVNorm_LAPACK_Private(bv,lds,bv->k-bv->l,pS+(bv->nc+bv->l)*lds,type,val,PETSC_FALSE);
    101:   else BVNorm_LAPACK_Private(bv,lds,1,pS+(bv->nc+j)*lds,type,val,PETSC_FALSE);
    102:   MatDenseRestoreArrayRead(ctx->S,&pS);
    103:   return 0;
    104: }

    106: PetscErrorCode BVCopyColumn_Tensor(BV V,PetscInt j,PetscInt i)
    107: {
    108:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
    109:   PetscScalar    *pS;
    110:   PetscInt       lds = ctx->ld*ctx->d;

    112:   MatDenseGetArray(ctx->S,&pS);
    113:   PetscArraycpy(pS+(V->nc+i)*lds,pS+(V->nc+j)*lds,lds);
    114:   MatDenseRestoreArray(ctx->S,&pS);
    115:   return 0;
    116: }

    118: static PetscErrorCode BVTensorNormColumn(BV bv,PetscInt j,PetscReal *norm)
    119: {
    120:   BV_TENSOR         *ctx = (BV_TENSOR*)bv->data;
    121:   PetscBLASInt      one=1,lds_;
    122:   PetscScalar       sone=1.0,szero=0.0,*x,dot;
    123:   const PetscScalar *S;
    124:   PetscReal         alpha=1.0,scale=0.0,aval;
    125:   PetscInt          i,lds,ld=ctx->ld;

    127:   lds = ld*ctx->d;
    128:   MatDenseGetArrayRead(ctx->S,&S);
    129:   PetscBLASIntCast(lds,&lds_);
    130:   if (PetscUnlikely(ctx->qB)) {
    131:     x = ctx->sw;
    132:     PetscCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&lds_,&sone,ctx->qB,&lds_,S+j*lds,&one,&szero,x,&one));
    133:     dot = PetscRealPart(BLASdot_(&lds_,S+j*lds,&one,x,&one));
    134:     BV_SafeSqrt(bv,dot,norm);
    135:   } else {
    136:     /* Compute *norm = BLASnrm2_(&lds_,S+j*lds,&one); */
    137:     if (lds==1) *norm = PetscAbsScalar(S[j*lds]);
    138:     else {
    139:       for (i=0;i<lds;i++) {
    140:         aval = PetscAbsScalar(S[i+j*lds]);
    141:         if (aval!=0.0) {
    142:           if (PetscUnlikely(scale<aval)) {
    143:             alpha = 1.0 + alpha*PetscSqr(scale/aval);
    144:             scale = aval;
    145:           } else alpha += PetscSqr(aval/scale);
    146:         }
    147:       }
    148:       *norm = scale*PetscSqrtReal(alpha);
    149:     }
    150:   }
    151:   MatDenseRestoreArrayRead(ctx->S,&S);
    152:   return 0;
    153: }

    155: PetscErrorCode BVOrthogonalizeGS1_Tensor(BV bv,PetscInt k,Vec v,PetscBool *which,PetscScalar *h,PetscScalar *c,PetscReal *onorm,PetscReal *norm)
    156: {
    157:   BV_TENSOR         *ctx = (BV_TENSOR*)bv->data;
    158:   PetscScalar       *pS,*cc,*x,dot,sonem=-1.0,sone=1.0,szero=0.0;
    159:   PetscInt          i,lds = ctx->ld*ctx->d;
    160:   PetscBLASInt      lds_,k_,one=1;
    161:   const PetscScalar *omega;

    164:   MatDenseGetArray(ctx->S,&pS);
    165:   if (!c) VecGetArray(bv->buffer,&cc);
    166:   else cc = c;
    167:   PetscBLASIntCast(lds,&lds_);
    168:   PetscBLASIntCast(k,&k_);

    170:   if (onorm) BVTensorNormColumn(bv,k,onorm);

    172:   if (ctx->qB) x = ctx->sw;
    173:   else x = pS+k*lds;

    175:   if (PetscUnlikely(bv->orthog_type==BV_ORTHOG_MGS)) {  /* modified Gram-Schmidt */

    177:     if (PetscUnlikely(bv->indef)) { /* signature */
    178:       VecGetArrayRead(bv->omega,&omega);
    179:     }
    180:     for (i=-bv->nc;i<k;i++) {
    181:       if (which && i>=0 && !which[i]) continue;
    182:       if (ctx->qB) PetscCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&lds_,&sone,ctx->qB,&lds_,pS+k*lds,&one,&szero,x,&one));
    183:       /* c_i = (s_k, s_i) */
    184:       dot = PetscRealPart(BLASdot_(&lds_,pS+i*lds,&one,x,&one));
    185:       if (bv->indef) dot /= PetscRealPart(omega[i]);
    186:       BV_SetValue(bv,i,0,cc,dot);
    187:       /* s_k = s_k - c_i s_i */
    188:       dot = -dot;
    189:       PetscCallBLAS("BLASaxpy",BLASaxpy_(&lds_,&dot,pS+i*lds,&one,pS+k*lds,&one));
    190:     }
    191:     if (PetscUnlikely(bv->indef)) VecRestoreArrayRead(bv->omega,&omega);

    193:   } else {  /* classical Gram-Schmidt */
    194:     if (ctx->qB) PetscCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&lds_,&sone,ctx->qB,&lds_,pS+k*lds,&one,&szero,x,&one));

    196:     /* cc = S_{0:k-1}^* s_k */
    197:     PetscCallBLAS("BLASgemv",BLASgemv_("C",&lds_,&k_,&sone,pS,&lds_,x,&one,&szero,cc,&one));

    199:     /* s_k = s_k - S_{0:k-1} cc */
    200:     if (PetscUnlikely(bv->indef)) BV_ApplySignature(bv,k,cc,PETSC_TRUE);
    201:     PetscCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&k_,&sonem,pS,&lds_,cc,&one,&sone,pS+k*lds,&one));
    202:     if (PetscUnlikely(bv->indef)) BV_ApplySignature(bv,k,cc,PETSC_FALSE);
    203:   }

    205:   if (norm) BVTensorNormColumn(bv,k,norm);
    206:   BV_AddCoefficients(bv,k,h,cc);
    207:   MatDenseRestoreArray(ctx->S,&pS);
    208:   VecRestoreArray(bv->buffer,&cc);
    209:   return 0;
    210: }

    212: PetscErrorCode BVView_Tensor(BV bv,PetscViewer viewer)
    213: {
    214:   BV_TENSOR         *ctx = (BV_TENSOR*)bv->data;
    215:   PetscViewerFormat format;
    216:   PetscBool         isascii;
    217:   const char        *bvname,*uname,*sname;

    219:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    220:   if (isascii) {
    221:     PetscViewerGetFormat(viewer,&format);
    222:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    223:       PetscViewerASCIIPrintf(viewer,"number of tensor blocks (degree): %" PetscInt_FMT "\n",ctx->d);
    224:       PetscViewerASCIIPrintf(viewer,"number of columns of U factor: %" PetscInt_FMT "\n",ctx->ld);
    225:       return 0;
    226:     }
    227:     BVView(ctx->U,viewer);
    228:     MatView(ctx->S,viewer);
    229:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
    230:       PetscObjectGetName((PetscObject)bv,&bvname);
    231:       PetscObjectGetName((PetscObject)ctx->U,&uname);
    232:       PetscObjectGetName((PetscObject)ctx->S,&sname);
    233:       PetscViewerASCIIPrintf(viewer,"%s=kron(eye(%" PetscInt_FMT "),%s)*%s(:,1:%" PetscInt_FMT ");\n",bvname,ctx->d,uname,sname,bv->k);
    234:     }
    235:   } else {
    236:     BVView(ctx->U,viewer);
    237:     MatView(ctx->S,viewer);
    238:   }
    239:   return 0;
    240: }

    242: static PetscErrorCode BVTensorUpdateMatrix(BV V,PetscInt ini,PetscInt end)
    243: {
    244:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
    245:   PetscInt       i,j,r,c,l,k,ld=ctx->ld,lds=ctx->d*ctx->ld;
    246:   PetscScalar    *qB,*sqB;
    247:   Vec            u;
    248:   Mat            A;

    250:   if (!V->matrix) return 0;
    251:   l = ctx->U->l; k = ctx->U->k;
    252:   /* update inner product matrix */
    253:   if (!ctx->qB) {
    254:     PetscCalloc2(lds*lds,&ctx->qB,lds,&ctx->sw);
    255:     VecDuplicate(ctx->U->t,&ctx->u);
    256:   }
    257:   ctx->U->l = 0;
    258:   for (r=0;r<ctx->d;r++) {
    259:     for (c=0;c<=r;c++) {
    260:       MatNestGetSubMat(V->matrix,r,c,&A);
    261:       if (A) {
    262:         qB = ctx->qB+c*ld*lds+r*ld;
    263:         for (i=ini;i<end;i++) {
    264:           BVGetColumn(ctx->U,i,&u);
    265:           MatMult(A,u,ctx->u);
    266:           ctx->U->k = i+1;
    267:           BVDotVec(ctx->U,ctx->u,qB+i*lds);
    268:           BVRestoreColumn(ctx->U,i,&u);
    269:           for (j=0;j<i;j++) qB[i+j*lds] = PetscConj(qB[j+i*lds]);
    270:           qB[i*lds+i] = PetscRealPart(qB[i+i*lds]);
    271:         }
    272:         if (PetscUnlikely(c!=r)) {
    273:           sqB = ctx->qB+r*ld*lds+c*ld;
    274:           for (i=ini;i<end;i++) for (j=0;j<=i;j++) {
    275:             sqB[i+j*lds] = PetscConj(qB[j+i*lds]);
    276:             sqB[j+i*lds] = qB[j+i*lds];
    277:           }
    278:         }
    279:       }
    280:     }
    281:   }
    282:   ctx->U->l = l; ctx->U->k = k;
    283:   return 0;
    284: }

    286: static PetscErrorCode BVTensorBuildFirstColumn_Tensor(BV V,PetscInt k)
    287: {
    288:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
    289:   PetscInt       i,nq=0;
    290:   PetscScalar    *pS,*omega;
    291:   PetscReal      norm;
    292:   PetscBool      breakdown=PETSC_FALSE;

    294:   MatDenseGetArray(ctx->S,&pS);
    295:   for (i=0;i<ctx->d;i++) {
    296:     if (i>=k) BVSetRandomColumn(ctx->U,nq);
    297:     else BVCopyColumn(ctx->U,i,nq);
    298:     BVOrthogonalizeColumn(ctx->U,nq,pS+i*ctx->ld,&norm,&breakdown);
    299:     if (!breakdown) {
    300:       BVScaleColumn(ctx->U,nq,1.0/norm);
    301:       pS[nq+i*ctx->ld] = norm;
    302:       nq++;
    303:     }
    304:   }
    305:   MatDenseRestoreArray(ctx->S,&pS);
    307:   BVTensorUpdateMatrix(V,0,nq);
    308:   BVTensorNormColumn(V,0,&norm);
    309:   BVScale_Tensor(V,0,1.0/norm);
    310:   if (V->indef) {
    311:     BV_AllocateSignature(V);
    312:     VecGetArray(V->omega,&omega);
    313:     omega[0] = (norm<0.0)? -1.0: 1.0;
    314:     VecRestoreArray(V->omega,&omega);
    315:   }
    316:   /* set active columns */
    317:   ctx->U->l = 0;
    318:   ctx->U->k = nq;
    319:   return 0;
    320: }

    322: /*@
    323:    BVTensorBuildFirstColumn - Builds the first column of the tensor basis vectors
    324:    V from the data contained in the first k columns of U.

    326:    Collective on V

    328:    Input Parameters:
    329: +  V - the basis vectors context
    330: -  k - the number of columns of U with relevant information

    332:    Notes:
    333:    At most d columns are considered, where d is the degree of the tensor BV.
    334:    Given V = (I otimes U) S, this function computes the first column of V, that
    335:    is, it computes the coefficients of the first column of S by orthogonalizing
    336:    the first d columns of U. If k is less than d (or linearly dependent columns
    337:    are found) then additional random columns are used.

    339:    The computed column has unit norm.

    341:    Level: advanced

    343: .seealso: BVCreateTensor()
    344: @*/
    345: PetscErrorCode BVTensorBuildFirstColumn(BV V,PetscInt k)
    346: {
    349:   PetscUseMethod(V,"BVTensorBuildFirstColumn_C",(BV,PetscInt),(V,k));
    350:   return 0;
    351: }

    353: static PetscErrorCode BVTensorCompress_Tensor(BV V,PetscInt newc)
    354: {
    355:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
    356:   PetscInt       nwu=0,nnc,nrow,lwa,r,c;
    357:   PetscInt       i,j,k,n,lds=ctx->ld*ctx->d,deg=ctx->d,lock,cs1=V->k,rs1=ctx->U->k,rk=0,offu;
    358:   PetscScalar    *S,*M,*Z,*pQ,*SS,*SS2,t,sone=1.0,zero=0.0,mone=-1.0,*p,*tau,*work,*qB,*sqB;
    359:   PetscReal      *sg,tol,*rwork;
    360:   PetscBLASInt   ld_,cs1_,rs1_,cs1tdeg,n_,info,lw_,newc_,newctdeg,nnc_,nrow_,nnctdeg,lds_,rk_;
    361:   Mat            Q,A;

    363:   if (!cs1) return 0;
    364:   lwa = 6*ctx->ld*lds+2*cs1;
    365:   n = PetscMin(rs1,deg*cs1);
    366:   lock = ctx->U->l;
    367:   nnc = cs1-lock-newc;
    368:   nrow = rs1-lock;
    369:   PetscCalloc6(deg*newc*nnc,&SS,newc*nnc,&SS2,(rs1+lock+newc)*n,&pQ,deg*rs1,&tau,lwa,&work,6*n,&rwork);
    370:   offu = lock*(rs1+1);
    371:   M = work+nwu;
    372:   nwu += rs1*cs1*deg;
    373:   sg = rwork;
    374:   Z = work+nwu;
    375:   nwu += deg*cs1*n;
    376:   PetscBLASIntCast(n,&n_);
    377:   PetscBLASIntCast(nnc,&nnc_);
    378:   PetscBLASIntCast(cs1,&cs1_);
    379:   PetscBLASIntCast(rs1,&rs1_);
    380:   PetscBLASIntCast(newc,&newc_);
    381:   PetscBLASIntCast(newc*deg,&newctdeg);
    382:   PetscBLASIntCast(nnc*deg,&nnctdeg);
    383:   PetscBLASIntCast(cs1*deg,&cs1tdeg);
    384:   PetscBLASIntCast(lwa-nwu,&lw_);
    385:   PetscBLASIntCast(nrow,&nrow_);
    386:   PetscBLASIntCast(lds,&lds_);
    387:   MatDenseGetArray(ctx->S,&S);

    389:   if (newc>0) {
    390:     /* truncate columns associated with new converged eigenpairs */
    391:     for (j=0;j<deg;j++) {
    392:       for (i=lock;i<lock+newc;i++) PetscArraycpy(M+(i-lock+j*newc)*nrow,S+i*lds+j*ctx->ld+lock,nrow);
    393:     }
    394:     PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    395: #if !defined (PETSC_USE_COMPLEX)
    396:     PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&newctdeg,M,&nrow_,sg,pQ+offu,&rs1_,Z,&n_,work+nwu,&lw_,&info));
    397: #else
    398:     PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&newctdeg,M,&nrow_,sg,pQ+offu,&rs1_,Z,&n_,work+nwu,&lw_,rwork+n,&info));
    399: #endif
    400:     SlepcCheckLapackInfo("gesvd",info);
    401:     PetscFPTrapPop();
    402:     /* SVD has rank min(newc,nrow) */
    403:     rk = PetscMin(newc,nrow);
    404:     for (i=0;i<rk;i++) {
    405:       t = sg[i];
    406:       PetscCallBLAS("BLASscal",BLASscal_(&newctdeg,&t,Z+i,&n_));
    407:     }
    408:     for (i=0;i<deg;i++) {
    409:       for (j=lock;j<lock+newc;j++) {
    410:         PetscArraycpy(S+j*lds+i*ctx->ld+lock,Z+(newc*i+j-lock)*n,rk);
    411:         PetscArrayzero(S+j*lds+i*ctx->ld+lock+rk,(ctx->ld-lock-rk));
    412:       }
    413:     }
    414:     /*
    415:       update columns associated with non-converged vectors, orthogonalize
    416:       against pQ so that next M has rank nnc+d-1 instead of nrow+d-1
    417:     */
    418:     for (i=0;i<deg;i++) {
    419:       PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&newc_,&nnc_,&nrow_,&sone,pQ+offu,&rs1_,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_,&zero,SS+i*newc*nnc,&newc_));
    420:       PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&nrow_,&nnc_,&newc_,&mone,pQ+offu,&rs1_,SS+i*newc*nnc,&newc_,&sone,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_));
    421:       /* repeat orthogonalization step */
    422:       PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&newc_,&nnc_,&nrow_,&sone,pQ+offu,&rs1_,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_,&zero,SS2,&newc_));
    423:       PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&nrow_,&nnc_,&newc_,&mone,pQ+offu,&rs1_,SS2,&newc_,&sone,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_));
    424:       for (j=0;j<newc*nnc;j++) *(SS+i*newc*nnc+j) += SS2[j];
    425:     }
    426:   }

    428:   /* truncate columns associated with non-converged eigenpairs */
    429:   for (j=0;j<deg;j++) {
    430:     for (i=lock+newc;i<cs1;i++) PetscArraycpy(M+(i-lock-newc+j*nnc)*nrow,S+i*lds+j*ctx->ld+lock,nrow);
    431:   }
    432:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    433: #if !defined (PETSC_USE_COMPLEX)
    434:   PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&nnctdeg,M,&nrow_,sg,pQ+offu+newc*rs1,&rs1_,Z,&n_,work+nwu,&lw_,&info));
    435: #else
    436:   PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&nnctdeg,M,&nrow_,sg,pQ+offu+newc*rs1,&rs1_,Z,&n_,work+nwu,&lw_,rwork+n,&info));
    437: #endif
    438:   SlepcCheckLapackInfo("gesvd",info);
    439:   PetscFPTrapPop();
    440:   tol = PetscMax(rs1,deg*cs1)*PETSC_MACHINE_EPSILON*sg[0];
    441:   rk = 0;
    442:   for (i=0;i<PetscMin(nrow,nnctdeg);i++) if (sg[i]>tol) rk++;
    443:   rk = PetscMin(nnc+deg-1,rk);
    444:   /* the SVD has rank (at most) nnc+deg-1 */
    445:   for (i=0;i<rk;i++) {
    446:     t = sg[i];
    447:     PetscCallBLAS("BLASscal",BLASscal_(&nnctdeg,&t,Z+i,&n_));
    448:   }
    449:   /* update S */
    450:   PetscArrayzero(S+cs1*lds,(V->m-cs1)*lds);
    451:   k = ctx->ld-lock-newc-rk;
    452:   for (i=0;i<deg;i++) {
    453:     for (j=lock+newc;j<cs1;j++) {
    454:       PetscArraycpy(S+j*lds+i*ctx->ld+lock+newc,Z+(nnc*i+j-lock-newc)*n,rk);
    455:       PetscArrayzero(S+j*lds+i*ctx->ld+lock+newc+rk,k);
    456:     }
    457:   }
    458:   if (newc>0) {
    459:     for (i=0;i<deg;i++) {
    460:       p = SS+nnc*newc*i;
    461:       for (j=lock+newc;j<cs1;j++) {
    462:         for (k=0;k<newc;k++) S[j*lds+i*ctx->ld+lock+k] = *(p++);
    463:       }
    464:     }
    465:   }

    467:   /* orthogonalize pQ */
    468:   rk = rk+newc;
    469:   PetscBLASIntCast(rk,&rk_);
    470:   PetscBLASIntCast(cs1-lock,&nnc_);
    471:   PetscFPTrapPush(PETSC_FP_TRAP_OFF);
    472:   PetscCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&nrow_,&rk_,pQ+offu,&rs1_,tau,work+nwu,&lw_,&info));
    473:   SlepcCheckLapackInfo("geqrf",info);
    474:   for (i=0;i<deg;i++) {
    475:     PetscCallBLAS("BLAStrmm",BLAStrmm_("L","U","N","N",&rk_,&nnc_,&sone,pQ+offu,&rs1_,S+lock*lds+lock+i*ctx->ld,&lds_));
    476:   }
    477:   PetscCallBLAS("LAPACKorgqr",LAPACKorgqr_(&nrow_,&rk_,&rk_,pQ+offu,&rs1_,tau,work+nwu,&lw_,&info));
    478:   SlepcCheckLapackInfo("orgqr",info);
    479:   PetscFPTrapPop();

    481:   /* update vectors U(:,idx) = U*Q(:,idx) */
    482:   rk = rk+lock;
    483:   for (i=0;i<lock;i++) pQ[i*(1+rs1)] = 1.0;
    484:   MatCreateSeqDense(PETSC_COMM_SELF,rs1,rk,pQ,&Q);
    485:   ctx->U->k = rs1;
    486:   BVMultInPlace(ctx->U,Q,lock,rk);
    487:   MatDestroy(&Q);

    489:   if (ctx->qB) {
    490:    /* update matrix qB */
    491:     PetscBLASIntCast(ctx->ld,&ld_);
    492:     PetscBLASIntCast(rk,&rk_);
    493:     for (r=0;r<ctx->d;r++) {
    494:       for (c=0;c<=r;c++) {
    495:         MatNestGetSubMat(V->matrix,r,c,&A);
    496:         if (A) {
    497:           qB = ctx->qB+r*ctx->ld+c*ctx->ld*lds;
    498:           PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&rs1_,&rk_,&rs1_,&sone,qB,&lds_,pQ,&rs1_,&zero,work+nwu,&rs1_));
    499:           PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&rk_,&rk_,&rs1_,&sone,pQ,&rs1_,work+nwu,&rs1_,&zero,qB,&lds_));
    500:           for (i=0;i<rk;i++) {
    501:             for (j=0;j<i;j++) qB[i+j*lds] = PetscConj(qB[j+i*lds]);
    502:             qB[i+i*lds] = PetscRealPart(qB[i+i*lds]);
    503:           }
    504:           for (i=rk;i<ctx->ld;i++) PetscArrayzero(qB+i*lds,ctx->ld);
    505:           for (i=0;i<rk;i++) PetscArrayzero(qB+i*lds+rk,(ctx->ld-rk));
    506:           if (c!=r) {
    507:             sqB = ctx->qB+r*ctx->ld*lds+c*ctx->ld;
    508:             for (i=0;i<ctx->ld;i++) for (j=0;j<ctx->ld;j++) sqB[i+j*lds] = PetscConj(qB[j+i*lds]);
    509:           }
    510:         }
    511:       }
    512:     }
    513:   }

    515:   /* free work space */
    516:   PetscFree6(SS,SS2,pQ,tau,work,rwork);
    517:   MatDenseRestoreArray(ctx->S,&S);

    519:   /* set active columns */
    520:   if (newc) ctx->U->l += newc;
    521:   ctx->U->k = rk;
    522:   return 0;
    523: }

    525: /*@
    526:    BVTensorCompress - Updates the U and S factors of the tensor basis vectors
    527:    object V by means of an SVD, removing redundant information.

    529:    Collective on V

    531:    Input Parameters:
    532: +  V - the tensor basis vectors context
    533: -  newc - additional columns to be locked

    535:    Notes:
    536:    This function is typically used when restarting Krylov solvers. Truncating a
    537:    tensor BV V = (I otimes U) S to its leading columns amounts to keeping the
    538:    leading columns of S. However, to effectively reduce the size of the
    539:    decomposition, it is necessary to compress it in a way that fewer columns of
    540:    U are employed. This can be achieved by means of an update that involves the
    541:    SVD of the low-rank matrix [S_0 S_1 ... S_{d-1}], where S_i are the pieces of S.

    543:    If newc is nonzero, then newc columns are added to the leading columns of V.
    544:    This means that the corresponding columns of the U and S factors will remain
    545:    invariant in subsequent operations.

    547:    Level: advanced

    549: .seealso: BVCreateTensor(), BVSetActiveColumns()
    550: @*/
    551: PetscErrorCode BVTensorCompress(BV V,PetscInt newc)
    552: {
    555:   PetscUseMethod(V,"BVTensorCompress_C",(BV,PetscInt),(V,newc));
    556:   return 0;
    557: }

    559: static PetscErrorCode BVTensorGetDegree_Tensor(BV bv,PetscInt *d)
    560: {
    561:   BV_TENSOR *ctx = (BV_TENSOR*)bv->data;

    563:   *d = ctx->d;
    564:   return 0;
    565: }

    567: /*@
    568:    BVTensorGetDegree - Returns the number of blocks (degree) of the tensor BV.

    570:    Not collective

    572:    Input Parameter:
    573: .  bv - the basis vectors context

    575:    Output Parameter:
    576: .  d - the degree

    578:    Level: advanced

    580: .seealso: BVCreateTensor()
    581: @*/
    582: PetscErrorCode BVTensorGetDegree(BV bv,PetscInt *d)
    583: {
    586:   PetscUseMethod(bv,"BVTensorGetDegree_C",(BV,PetscInt*),(bv,d));
    587:   return 0;
    588: }

    590: static PetscErrorCode BVTensorGetFactors_Tensor(BV V,BV *U,Mat *S)
    591: {
    592:   BV_TENSOR *ctx = (BV_TENSOR*)V->data;

    595:   ctx->puk = ctx->U->k;
    596:   if (U) *U = ctx->U;
    597:   if (S) *S = ctx->S;
    598:   return 0;
    599: }

    601: /*@C
    602:    BVTensorGetFactors - Returns the two factors involved in the definition of the
    603:    tensor basis vectors object, V = (I otimes U) S.

    605:    Logically Collective on V

    607:    Input Parameter:
    608: .  V - the basis vectors context

    610:    Output Parameters:
    611: +  U - the BV factor
    612: -  S - the Mat factor

    614:    Notes:
    615:    The returned factors are references (not copies) of the internal factors,
    616:    so modifying them will change the tensor BV as well. Some operations of the
    617:    tensor BV assume that U has orthonormal columns, so if the user modifies U
    618:    this restriction must be taken into account.

    620:    The returned factors must not be destroyed. BVTensorRestoreFactors() must
    621:    be called when they are no longer needed.

    623:    Pass a NULL vector for any of the arguments that is not needed.

    625:    Level: advanced

    627: .seealso: BVTensorRestoreFactors()
    628: @*/
    629: PetscErrorCode BVTensorGetFactors(BV V,BV *U,Mat *S)
    630: {
    632:   PetscUseMethod(V,"BVTensorGetFactors_C",(BV,BV*,Mat*),(V,U,S));
    633:   return 0;
    634: }

    636: static PetscErrorCode BVTensorRestoreFactors_Tensor(BV V,BV *U,Mat *S)
    637: {
    638:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;

    640:   PetscObjectStateIncrease((PetscObject)V);
    641:   if (U) *U = NULL;
    642:   if (S) *S = NULL;
    643:   BVTensorUpdateMatrix(V,ctx->puk,ctx->U->k);
    644:   ctx->puk = -1;
    645:   return 0;
    646: }

    648: /*@C
    649:    BVTensorRestoreFactors - Restore the two factors that were obtained with
    650:    BVTensorGetFactors().

    652:    Logically Collective on V

    654:    Input Parameters:
    655: +  V - the basis vectors context
    656: .  U - the BV factor (or NULL)
    657: -  S - the Mat factor (or NULL)

    659:    Notes:
    660:    The arguments must match the corresponding call to BVTensorGetFactors().

    662:    Level: advanced

    664: .seealso: BVTensorGetFactors()
    665: @*/
    666: PetscErrorCode BVTensorRestoreFactors(BV V,BV *U,Mat *S)
    667: {
    671:   PetscUseMethod(V,"BVTensorRestoreFactors_C",(BV,BV*,Mat*),(V,U,S));
    672:   return 0;
    673: }

    675: PetscErrorCode BVDestroy_Tensor(BV bv)
    676: {
    677:   BV_TENSOR      *ctx = (BV_TENSOR*)bv->data;

    679:   BVDestroy(&ctx->U);
    680:   MatDestroy(&ctx->S);
    681:   if (ctx->u) {
    682:     PetscFree2(ctx->qB,ctx->sw);
    683:     VecDestroy(&ctx->u);
    684:   }
    685:   PetscFree(bv->data);
    686:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorBuildFirstColumn_C",NULL);
    687:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorCompress_C",NULL);
    688:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetDegree_C",NULL);
    689:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetFactors_C",NULL);
    690:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorRestoreFactors_C",NULL);
    691:   return 0;
    692: }

    694: SLEPC_EXTERN PetscErrorCode BVCreate_Tensor(BV bv)
    695: {
    696:   BV_TENSOR      *ctx;

    698:   PetscNew(&ctx);
    699:   bv->data = (void*)ctx;
    700:   ctx->puk = -1;

    702:   bv->ops->multinplace      = BVMultInPlace_Tensor;
    703:   bv->ops->multinplacetrans = BVMultInPlaceHermitianTranspose_Tensor;
    704:   bv->ops->dot              = BVDot_Tensor;
    705:   bv->ops->scale            = BVScale_Tensor;
    706:   bv->ops->norm             = BVNorm_Tensor;
    707:   bv->ops->copycolumn       = BVCopyColumn_Tensor;
    708:   bv->ops->gramschmidt      = BVOrthogonalizeGS1_Tensor;
    709:   bv->ops->destroy          = BVDestroy_Tensor;
    710:   bv->ops->view             = BVView_Tensor;

    712:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorBuildFirstColumn_C",BVTensorBuildFirstColumn_Tensor);
    713:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorCompress_C",BVTensorCompress_Tensor);
    714:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetDegree_C",BVTensorGetDegree_Tensor);
    715:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetFactors_C",BVTensorGetFactors_Tensor);
    716:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorRestoreFactors_C",BVTensorRestoreFactors_Tensor);
    717:   return 0;
    718: }

    720: /*@
    721:    BVCreateTensor - Creates a tensor BV that is represented in compact form
    722:    as V = (I otimes U) S, where U has orthonormal columns.

    724:    Collective on U

    726:    Input Parameters:
    727: +  U - a basis vectors object
    728: -  d - the number of blocks (degree) of the tensor BV

    730:    Output Parameter:
    731: .  V - the new basis vectors context

    733:    Notes:
    734:    The new basis vectors object is V = (I otimes U) S, where otimes denotes
    735:    the Kronecker product, I is the identity matrix of order d, and S is a
    736:    sequential matrix allocated internally. This compact representation is
    737:    used e.g. to represent the Krylov basis generated with the linearization
    738:    of a matrix polynomial of degree d.

    740:    The size of V (number of rows) is equal to d times n, where n is the size
    741:    of U. The dimensions of S are d times m rows and m-d+1 columns, where m is
    742:    the number of columns of U, so m should be at least d.

    744:    The communicator of V will be the same as U.

    746:    On input, the content of U is irrelevant. Alternatively, it may contain
    747:    some nonzero columns that will be used by BVTensorBuildFirstColumn().

    749:    Level: advanced

    751: .seealso: BVTensorGetDegree(), BVTensorGetFactors(), BVTensorBuildFirstColumn()
    752: @*/
    753: PetscErrorCode BVCreateTensor(BV U,PetscInt d,BV *V)
    754: {
    755:   PetscBool      match;
    756:   PetscInt       n,N,m;
    757:   BV_TENSOR      *ctx;

    761:   PetscObjectTypeCompare((PetscObject)U,BVTENSOR,&match);

    764:   BVCreate(PetscObjectComm((PetscObject)U),V);
    765:   BVGetSizes(U,&n,&N,&m);
    767:   BVSetSizes(*V,d*n,d*N,m-d+1);
    768:   PetscObjectChangeTypeName((PetscObject)*V,BVTENSOR);
    769:   PetscLogEventBegin(BV_Create,*V,0,0,0);
    770:   BVCreate_Tensor(*V);
    771:   PetscLogEventEnd(BV_Create,*V,0,0,0);

    773:   ctx = (BV_TENSOR*)(*V)->data;
    774:   ctx->U  = U;
    775:   ctx->d  = d;
    776:   ctx->ld = m;
    777:   PetscObjectReference((PetscObject)U);
    778:   MatCreateSeqDense(PETSC_COMM_SELF,d*m,m-d+1,NULL,&ctx->S);
    779:   PetscObjectSetName((PetscObject)ctx->S,"S");

    781:   /* Copy user-provided attributes of U */
    782:   (*V)->orthog_type  = U->orthog_type;
    783:   (*V)->orthog_ref   = U->orthog_ref;
    784:   (*V)->orthog_eta   = U->orthog_eta;
    785:   (*V)->orthog_block = U->orthog_block;
    786:   (*V)->vmm          = U->vmm;
    787:   (*V)->rrandom      = U->rrandom;
    788:   return 0;
    789: }