Actual source code: bvtensor.c

slepc-3.9.2 2018-07-02
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2018, 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>      /*I "slepcbv.h" I*/
 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 BVMult_Tensor(BV Y,PetscScalar alpha,PetscScalar beta,BV X,Mat Q)
 29: {
 31:   SETERRQ(PetscObjectComm((PetscObject)Y),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
 32: }

 34: PetscErrorCode BVMultVec_Tensor(BV X,PetscScalar alpha,PetscScalar beta,Vec y,PetscScalar *q)
 35: {
 37:   SETERRQ(PetscObjectComm((PetscObject)X),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
 38: }

 40: PetscErrorCode BVMultInPlace_Tensor(BV V,Mat Q,PetscInt s,PetscInt e)
 41: {
 43:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
 44:   PetscScalar    *pS,*q;
 45:   PetscInt       ldq,lds = ctx->ld*ctx->d;

 48:   MatGetSize(Q,&ldq,NULL);
 49:   MatDenseGetArray(ctx->S,&pS);
 50:   MatDenseGetArray(Q,&q);
 51:   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);
 52:   MatDenseRestoreArray(Q,&q);
 53:   MatDenseRestoreArray(ctx->S,&pS);
 54:   return(0);
 55: }

 57: PetscErrorCode BVMultInPlaceTranspose_Tensor(BV V,Mat Q,PetscInt s,PetscInt e)
 58: {
 60:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
 61:   PetscScalar    *pS,*q;
 62:   PetscInt       ldq,lds = ctx->ld*ctx->d;

 65:   MatGetSize(Q,&ldq,NULL);
 66:   MatDenseGetArray(ctx->S,&pS);
 67:   MatDenseGetArray(Q,&q);
 68:   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);
 69:   MatDenseRestoreArray(Q,&q);
 70:   MatDenseRestoreArray(ctx->S,&pS);
 71:   return(0);
 72: }

 74: PetscErrorCode BVDot_Tensor(BV X,BV Y,Mat M)
 75: {
 77:   BV_TENSOR      *x = (BV_TENSOR*)X->data,*y = (BV_TENSOR*)Y->data;
 78:   PetscScalar    *m,*px,*py;
 79:   PetscInt       ldm,lds = x->ld*x->d;

 82:   if (x->U!=y->U) SETERRQ(PetscObjectComm((PetscObject)X),PETSC_ERR_SUP,"BVDot() in BVTENSOR requires that both operands have the same U factor");
 83:   if (lds!=y->ld*y->d) SETERRQ2(PetscObjectComm((PetscObject)X),PETSC_ERR_ARG_SIZ,"Mismatching dimensions ld*d %D %D",lds,y->ld*y->d);
 84:   MatGetSize(M,&ldm,NULL);
 85:   MatDenseGetArray(x->S,&px);
 86:   MatDenseGetArray(y->S,&py);
 87:   MatDenseGetArray(M,&m);
 88:   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);
 89:   MatDenseRestoreArray(M,&m);
 90:   MatDenseRestoreArray(x->S,&px);
 91:   MatDenseRestoreArray(y->S,&py);
 92:   return(0);
 93: }

 95: PetscErrorCode BVDotVec_Tensor(BV X,Vec y,PetscScalar *q)
 96: {
 98:   SETERRQ(PetscObjectComm((PetscObject)X),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
 99: }

101: PetscErrorCode BVDotVec_Local_Tensor(BV X,Vec y,PetscScalar *m)
102: {
104:   SETERRQ(PetscObjectComm((PetscObject)X),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
105: }

107: PetscErrorCode BVScale_Tensor(BV bv,PetscInt j,PetscScalar alpha)
108: {
110:   BV_TENSOR      *ctx = (BV_TENSOR*)bv->data;
111:   PetscScalar    *pS;
112:   PetscInt       lds = ctx->ld*ctx->d;

115:   MatDenseGetArray(ctx->S,&pS);
116:   if (j<0) {
117:     BVScale_BLAS_Private(bv,(bv->k-bv->l)*lds,pS+(bv->nc+bv->l)*lds,alpha);
118:   } else {
119:     BVScale_BLAS_Private(bv,lds,pS+(bv->nc+j)*lds,alpha);
120:   }
121:   MatDenseRestoreArray(ctx->S,&pS);
122:   return(0);
123: }

125: PetscErrorCode BVNorm_Tensor(BV bv,PetscInt j,NormType type,PetscReal *val)
126: {
128:   BV_TENSOR      *ctx = (BV_TENSOR*)bv->data;
129:   PetscScalar    *pS;
130:   PetscInt       lds = ctx->ld*ctx->d;

133:   MatDenseGetArray(ctx->S,&pS);
134:   if (j<0) {
135:     BVNorm_LAPACK_Private(bv,lds,bv->k-bv->l,pS+(bv->nc+bv->l)*lds,type,val,PETSC_FALSE);
136:   } else {
137:     BVNorm_LAPACK_Private(bv,lds,1,pS+(bv->nc+j)*lds,type,val,PETSC_FALSE);
138:   }
139:   MatDenseRestoreArray(ctx->S,&pS);
140:   return(0);
141: }

143: PetscErrorCode BVNorm_Local_Tensor(BV bv,PetscInt j,NormType type,PetscReal *val)
144: {
146:   SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
147: }

149: PetscErrorCode BVMatMult_Tensor(BV V,Mat A,BV W)
150: {
152:   SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
153: }

155: PetscErrorCode BVCopy_Tensor(BV V,BV W)
156: {
158:   SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
159: }

161: PetscErrorCode BVCopyColumn_Tensor(BV V,PetscInt j,PetscInt i)
162: {
164:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
165:   PetscScalar    *pS;
166:   PetscInt       lds = ctx->ld*ctx->d;

169:   MatDenseGetArray(ctx->S,&pS);
170:   PetscMemcpy(pS+(V->nc+i)*lds,pS+(V->nc+j)*lds,lds*sizeof(PetscScalar));
171:   MatDenseRestoreArray(ctx->S,&pS);
172:   return(0);
173: }

175: PetscErrorCode BVResize_Tensor(BV bv,PetscInt m,PetscBool copy)
176: {
178:   SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
179: }

181: PetscErrorCode BVGetColumn_Tensor(BV bv,PetscInt j,Vec *v)
182: {
184:   SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
185: }

187: PetscErrorCode BVRestoreColumn_Tensor(BV bv,PetscInt j,Vec *v)
188: {
190:   SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
191: }

193: PetscErrorCode BVGetArray_Tensor(BV bv,PetscScalar **a)
194: {
196:   SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
197: }

199: PetscErrorCode BVRestoreArray_Tensor(BV bv,PetscScalar **a)
200: {
202:   SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
203: }

205: PetscErrorCode BVGetArrayRead_Tensor(BV bv,const PetscScalar **a)
206: {
208:   SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
209: }

211: PetscErrorCode BVRestoreArrayRead_Tensor(BV bv,const PetscScalar **a)
212: {
214:   SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Operation not implemented in BVTENSOR");
215: }

217: static PetscErrorCode BVTensorNormColumn(BV bv,PetscInt j,PetscReal *norm)
218: {
220:   BV_TENSOR      *ctx = (BV_TENSOR*)bv->data;
221:   PetscBLASInt   one=1,lds_;
222:   PetscScalar    sone=1.0,szero=0.0,*S,*x,dot;
223:   PetscReal      alpha=1.0,scale=0.0,aval;
224:   PetscInt       i,lds,ld=ctx->ld;

227:   lds = ld*ctx->d;
228:   MatDenseGetArray(ctx->S,&S);
229:   PetscBLASIntCast(lds,&lds_);
230:   if (ctx->qB) {
231:     x = ctx->sw;
232:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&lds_,&sone,ctx->qB,&lds_,S+j*lds,&one,&szero,x,&one));
233:     dot = BLASdot_(&lds_,S+j*lds,&one,x,&one);
234:     BV_SafeSqrt(bv,dot,norm);
235:   } else {
236:     /* Compute *norm = BLASnrm2_(&lds_,S+j*lds,&one); */
237:     if (lds==1) *norm = PetscAbsScalar(S[j*lds]);
238:     else {
239:       for (i=0;i<lds;i++) {
240:         aval = PetscAbsScalar(S[i+j*lds]);
241:         if (aval!=0.0) {
242:           if (scale<aval) {
243:             alpha = 1.0 + alpha*PetscSqr(scale/aval);
244:             scale = aval;
245:           } else alpha += PetscSqr(aval/scale);
246:         }
247:       }
248:       *norm = scale*PetscSqrtReal(alpha);
249:     }
250:   }
251:   return(0);
252: }

254: PetscErrorCode BVOrthogonalizeGS1_Tensor(BV bv,PetscInt k,Vec v,PetscBool *which,PetscScalar *h,PetscScalar *c,PetscReal *onorm,PetscReal *norm)
255: {
256:   PetscErrorCode    ierr;
257:   BV_TENSOR         *ctx = (BV_TENSOR*)bv->data;
258:   PetscScalar       *pS,*cc,*x,dot,sonem=-1.0,sone=1.0,szero=0.0;
259:   PetscInt          i,lds = ctx->ld*ctx->d;
260:   PetscBLASInt      lds_,k_,one=1;
261:   const PetscScalar *omega;

264:   if (v) SETERRQ(PetscObjectComm((PetscObject)bv),PETSC_ERR_SUP,"Orthogonalization against an external vector is not allowed in BVTENSOR");
265:   MatDenseGetArray(ctx->S,&pS);
266:   if (!c) {
267:     VecGetArray(bv->buffer,&cc);
268:   } else cc = c;
269:   PetscBLASIntCast(lds,&lds_);
270:   PetscBLASIntCast(k,&k_);

272:   if (onorm) { BVTensorNormColumn(bv,k,onorm); }

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

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

279:     if (bv->indef) { /* signature */
280:       VecGetArrayRead(bv->omega,&omega);
281:     }
282:     for (i=-bv->nc;i<k;i++) {
283:       if (which && i>=0 && !which[i]) continue;
284:       if (ctx->qB) PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&lds_,&sone,ctx->qB,&lds_,pS+k*lds,&one,&szero,x,&one));
285:       /* c_i = ( s_k, s_i ) */
286:       dot = BLASdot_(&lds_,pS+i*lds,&one,x,&one);
287:       if (bv->indef) dot /= PetscRealPart(omega[i]);
288:       BV_SetValue(bv,i,0,cc,dot);
289:       /* s_k = s_k - c_i s_i */
290:       dot = -dot;
291:       PetscStackCallBLAS("BLASaxpy",BLASaxpy_(&lds_,&dot,pS+i*lds,&one,pS+k*lds,&one));
292:     }
293:     if (bv->indef) {
294:       VecRestoreArrayRead(bv->omega,&omega);
295:     }

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

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

303:     /* s_k = s_k - S_{0:k-1} cc */
304:     if (bv->indef) { BV_ApplySignature(bv,k,cc,PETSC_TRUE); }
305:      PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&lds_,&k_,&sonem,pS,&lds_,cc,&one,&sone,pS+k*lds,&one));
306:     if (bv->indef) { BV_ApplySignature(bv,k,cc,PETSC_FALSE); }
307:   }

309:   if (norm) { BVTensorNormColumn(bv,k,norm); }
310:   BV_AddCoefficients(bv,k,h,cc);
311:   MatDenseRestoreArray(ctx->S,&pS);
312:   VecRestoreArray(bv->buffer,&cc);
313:   return(0);
314: }

316: PetscErrorCode BVView_Tensor(BV bv,PetscViewer viewer)
317: {
318:   PetscErrorCode    ierr;
319:   BV_TENSOR         *ctx = (BV_TENSOR*)bv->data;
320:   PetscViewerFormat format;
321:   PetscBool         isascii;
322:   const char        *bvname,*uname,*sname;

325:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
326:   if (isascii) {
327:     PetscViewerGetFormat(viewer,&format);
328:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
329:       PetscViewerASCIIPrintf(viewer,"number of tensor blocks (degree): %D\n",ctx->d);
330:       PetscViewerASCIIPrintf(viewer,"number of columns of U factor: %D\n",ctx->ld);
331:       return(0);
332:     }
333:     BVView(ctx->U,viewer);
334:     MatView(ctx->S,viewer);
335:     if (format == PETSC_VIEWER_ASCII_MATLAB) {
336:       PetscObjectGetName((PetscObject)bv,&bvname);
337:       PetscObjectGetName((PetscObject)ctx->U,&uname);
338:       PetscObjectGetName((PetscObject)ctx->S,&sname);
339:       PetscViewerASCIIPrintf(viewer,"%s=kron(eye(%D),%s)*%s(:,1:%D);\n",bvname,ctx->d,uname,sname,bv->k);
340:     }
341:   } else {
342:     BVView(ctx->U,viewer);
343:     MatView(ctx->S,viewer);
344:   }
345:   return(0);
346: }

348: static PetscErrorCode BVTensorUpdateMatrix(BV V,PetscInt ini,PetscInt end)
349: {
351:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
352:   PetscInt       i,j,r,c,l,k,ld=ctx->ld,lds=ctx->d*ctx->ld;
353:   PetscScalar    *qB,*sqB;
354:   Vec            u;
355:   Mat            A;

358:   if (!V->matrix) return(0);
359:   l = ctx->U->l; k = ctx->U->k;
360:   /* update inner product matrix */
361:   if (!ctx->qB) {
362:     PetscCalloc2(lds*lds,&ctx->qB,lds,&ctx->sw);
363:     VecDuplicate(ctx->U->t,&ctx->u);
364:   }
365:   for (i=0;i<ctx->d;i++) { PetscMemzero(ctx->qB+i*lds*ld+ini*lds,(end-ini)*lds*sizeof(PetscScalar)); }
366:   ctx->U->l = 0;
367:   for (r=0;r<ctx->d;r++) {
368:     for (c=0;c<=r;c++) {
369:       MatNestGetSubMat(V->matrix,r,c,&A);
370:       if (A) {
371:         qB = ctx->qB+c*ld*lds+r*ld;
372:         for (i=ini;i<end;i++) {
373:           BVGetColumn(ctx->U,i,&u);
374:           MatMult(A,u,ctx->u);
375:           ctx->U->k = i+1;
376:           BVDotVec(ctx->U,ctx->u,qB+i*lds);
377:           BVRestoreColumn(ctx->U,i,&u);
378:           for (j=0;j<i;j++) qB[i+j*lds] = PetscConj(qB[j+i*lds]);
379:         }
380:         if (c!=r) {
381:           sqB = ctx->qB+r*ld*lds+c*ld;
382:           for (i=ini;i<end;i++) for (j=0;j<i;j++) sqB[i+j*lds] = PetscConj(qB[j+i*lds]);
383:         }
384:       }
385:     }
386:   }
387:   ctx->U->l = l; ctx->U->k = k;
388:   return(0);
389: }

391: static PetscErrorCode BVTensorBuildFirstColumn_Tensor(BV V,PetscInt k)
392: {
394:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
395:   PetscInt       i,nq=0;
396:   PetscScalar    *pS,*omega;
397:   PetscReal      norm;
398:   PetscBool      breakdown=PETSC_FALSE;

401:   MatDenseGetArray(ctx->S,&pS);
402:   for (i=0;i<ctx->d;i++) {
403:     if (i>=k) {
404:       BVSetRandomColumn(ctx->U,nq);
405:     } else {
406:       BVCopyColumn(ctx->U,i,nq);
407:     }
408:     BVOrthogonalizeColumn(ctx->U,nq,pS+i*ctx->ld,&norm,&breakdown);
409:     if (!breakdown) {
410:       BVScaleColumn(ctx->U,nq,1.0/norm);
411:       pS[nq+i*ctx->ld] = norm;
412:       nq++;
413:     }
414:   }
415:   MatDenseRestoreArray(ctx->S,&pS);
416:   if (!nq) SETERRQ1(PetscObjectComm((PetscObject)V),1,"Cannot build first column of tensor BV; U should contain k=%D nonzero columns",k);
417:   BVTensorUpdateMatrix(V,0,nq);
418:   BVTensorNormColumn(V,0,&norm);
419:   BVScale_Tensor(V,0,1.0/norm);
420:   if (V->indef) {
421:     BV_AllocateSignature(V);
422:     VecGetArray(V->omega,&omega);
423:     omega[0] = (norm<0.0)? -1.0: 1.0;
424:     VecRestoreArray(V->omega,&omega);
425:   }
426:   /* set active columns */
427:   ctx->U->l = 0;
428:   ctx->U->k = nq;
429:   return(0);
430: }

432: /*@
433:    BVTensorBuildFirstColumn - Builds the first column of the tensor basis vectors
434:    V from the data contained in the first k columns of U.

436:    Collective on BV

438:    Input Parameters:
439: +  V - the basis vectors context
440: -  k - the number of columns of U with relevant information

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

449:    The computed column has unit norm.

451:    Level: advanced

453: .seealso: BVCreateTensor()
454: @*/
455: PetscErrorCode BVTensorBuildFirstColumn(BV V,PetscInt k)
456: {

462:   PetscUseMethod(V,"BVTensorBuildFirstColumn_C",(BV,PetscInt),(V,k));
463:   return(0);
464: }

466: static PetscErrorCode BVTensorCompress_Tensor(BV V,PetscInt newc)
467: {
468: #if defined(PETSC_MISSING_LAPACK_GESVD) || defined(PETSC_MISSING_LAPACK_GEQRF) || defined(PETSC_MISSING_LAPACK_ORGQR)
470:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GESVD/GEQRF/ORGQR - Lapack routine is unavailable");
471: #else
473:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;
474:   PetscInt       nwu=0,nnc,nrow,lwa,r,c;
475:   PetscInt       i,j,k,n,lds=ctx->ld*ctx->d,deg=ctx->d,lock,cs1=V->k,rs1=ctx->U->k,rk=0,offu;
476:   PetscScalar    *S,*M,*Z,*pQ,*SS,*SS2,t,sone=1.0,zero=0.0,mone=-1.0,*p,*tau,*work,*qB,*sqB;
477:   PetscReal      *sg,tol,*rwork;
478:   PetscBLASInt   ld_,cs1_,rs1_,cs1tdeg,n_,info,lw_,newc_,newctdeg,nnc_,nrow_,nnctdeg,lds_,rk_;
479:   Mat            Q,A;

482:   if (!cs1) return(0);
483:   lwa = 6*ctx->ld*lds+2*cs1;
484:   n = PetscMin(rs1,deg*cs1);
485:   lock = ctx->U->l;
486:   nnc = cs1-lock-newc;
487:   nrow = rs1-lock;
488:   PetscCalloc6(deg*newc*nnc,&SS,newc*nnc,&SS2,(rs1+lock+newc)*n,&pQ,deg*rs1,&tau,lwa,&work,6*n,&rwork);
489:   offu = lock*(rs1+1);
490:   M = work+nwu;
491:   nwu += rs1*cs1*deg;
492:   sg = rwork;
493:   Z = work+nwu;
494:   nwu += deg*cs1*n;
495:   PetscBLASIntCast(n,&n_);
496:   PetscBLASIntCast(nnc,&nnc_);
497:   PetscBLASIntCast(cs1,&cs1_);
498:   PetscBLASIntCast(rs1,&rs1_);
499:   PetscBLASIntCast(newc,&newc_);
500:   PetscBLASIntCast(newc*deg,&newctdeg);
501:   PetscBLASIntCast(nnc*deg,&nnctdeg);
502:   PetscBLASIntCast(cs1*deg,&cs1tdeg);
503:   PetscBLASIntCast(lwa-nwu,&lw_);
504:   PetscBLASIntCast(nrow,&nrow_);
505:   PetscBLASIntCast(lds,&lds_);
506:   MatDenseGetArray(ctx->S,&S);

508:   if (newc>0) {
509:     /* truncate columns associated with new converged eigenpairs */
510:     for (j=0;j<deg;j++) {
511:       for (i=lock;i<lock+newc;i++) {
512:         PetscMemcpy(M+(i-lock+j*newc)*nrow,S+i*lds+j*ctx->ld+lock,nrow*sizeof(PetscScalar));
513:       }
514:     }
515: #if !defined (PETSC_USE_COMPLEX)
516:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&newctdeg,M,&nrow_,sg,pQ+offu,&rs1_,Z,&n_,work+nwu,&lw_,&info));
517: #else
518:     PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&newctdeg,M,&nrow_,sg,pQ+offu,&rs1_,Z,&n_,work+nwu,&lw_,rwork+n,&info));
519: #endif
520:     SlepcCheckLapackInfo("gesvd",info);
521:     /* SVD has rank min(newc,nrow) */
522:     rk = PetscMin(newc,nrow);
523:     for (i=0;i<rk;i++) {
524:       t = sg[i];
525:       PetscStackCallBLAS("BLASscal",BLASscal_(&newctdeg,&t,Z+i,&n_));
526:     }
527:     for (i=0;i<deg;i++) {
528:       for (j=lock;j<lock+newc;j++) {
529:         PetscMemcpy(S+j*lds+i*ctx->ld+lock,Z+(newc*i+j-lock)*n,rk*sizeof(PetscScalar));
530:         PetscMemzero(S+j*lds+i*ctx->ld+lock+rk,(ctx->ld-lock-rk)*sizeof(PetscScalar));
531:       }
532:     }
533:     /*
534:       update columns associated with non-converged vectors, orthogonalize
535:       against pQ so that next M has rank nnc+d-1 insted of nrow+d-1
536:     */
537:     for (i=0;i<deg;i++) {
538:       PetscStackCallBLAS("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_));
539:       PetscStackCallBLAS("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_));
540:       /* repeat orthogonalization step */
541:       PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&newc_,&nnc_,&nrow_,&sone,pQ+offu,&rs1_,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_,&zero,SS2,&newc_));
542:       PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&nrow_,&nnc_,&newc_,&mone,pQ+offu,&rs1_,SS2,&newc_,&sone,S+(lock+newc)*lds+i*ctx->ld+lock,&lds_));
543:       for (j=0;j<newc*nnc;j++) *(SS+i*newc*nnc+j) += SS2[j];
544:     }
545:   }

547:   /* truncate columns associated with non-converged eigenpairs */
548:   for (j=0;j<deg;j++) {
549:     for (i=lock+newc;i<cs1;i++) {
550:       PetscMemcpy(M+(i-lock-newc+j*nnc)*nrow,S+i*lds+j*ctx->ld+lock,nrow*sizeof(PetscScalar));
551:     }
552:   }
553: #if !defined (PETSC_USE_COMPLEX)
554:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&nnctdeg,M,&nrow_,sg,pQ+offu+newc*rs1,&rs1_,Z,&n_,work+nwu,&lw_,&info));
555: #else
556:   PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&nrow_,&nnctdeg,M,&nrow_,sg,pQ+offu+newc*rs1,&rs1_,Z,&n_,work+nwu,&lw_,rwork+n,&info));
557: #endif
558:   SlepcCheckLapackInfo("gesvd",info);
559:   tol = PetscMax(rs1,deg*cs1)*PETSC_MACHINE_EPSILON*sg[0];
560:   rk = 0;
561:   for (i=0;i<PetscMin(nrow,nnctdeg);i++) if (sg[i]>tol) rk++;
562:   rk = PetscMin(nnc+deg-1,rk);
563:   /* the SVD has rank (at most) nnc+deg-1 */
564:   for (i=0;i<rk;i++) {
565:     t = sg[i];
566:     PetscStackCallBLAS("BLASscal",BLASscal_(&nnctdeg,&t,Z+i,&n_));
567:   }
568:   /* update S */
569:   PetscMemzero(S+cs1*lds,(V->m-cs1)*lds*sizeof(PetscScalar));
570:   k = ctx->ld-lock-newc-rk;
571:   for (i=0;i<deg;i++) {
572:     for (j=lock+newc;j<cs1;j++) {
573:       PetscMemcpy(S+j*lds+i*ctx->ld+lock+newc,Z+(nnc*i+j-lock-newc)*n,rk*sizeof(PetscScalar));
574:       PetscMemzero(S+j*lds+i*ctx->ld+lock+newc+rk,k*sizeof(PetscScalar));
575:     }
576:   }
577:   if (newc>0) {
578:     for (i=0;i<deg;i++) {
579:       p = SS+nnc*newc*i;
580:       for (j=lock+newc;j<cs1;j++) {
581:         for (k=0;k<newc;k++) S[j*lds+i*ctx->ld+lock+k] = *(p++);
582:       }
583:     }
584:   }

586:   /* orthogonalize pQ */
587:   rk = rk+newc;
588:   PetscBLASIntCast(rk,&rk_);
589:   PetscBLASIntCast(cs1-lock,&nnc_);
590:   PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&nrow_,&rk_,pQ+offu,&rs1_,tau,work+nwu,&lw_,&info));
591:   SlepcCheckLapackInfo("geqrf",info);
592:   for (i=0;i<deg;i++) {
593:     PetscStackCallBLAS("BLAStrmm",BLAStrmm_("L","U","N","N",&rk_,&nnc_,&sone,pQ+offu,&rs1_,S+lock*lds+lock+i*ctx->ld,&lds_));
594:   }
595:   PetscStackCallBLAS("LAPACKorgqr",LAPACKorgqr_(&nrow_,&rk_,&rk_,pQ+offu,&rs1_,tau,work+nwu,&lw_,&info));
596:   SlepcCheckLapackInfo("orgqr",info);

598:   /* update vectors U(:,idx) = U*Q(:,idx) */
599:   rk = rk+lock;
600:   for (i=0;i<lock;i++) pQ[i*(1+rs1)] = 1.0;
601:   MatCreateSeqDense(PETSC_COMM_SELF,rs1,rk,pQ,&Q);
602:   ctx->U->k = rs1;
603:   BVMultInPlace(ctx->U,Q,lock,rk);
604:   MatDestroy(&Q);

606:   if (ctx->qB) {
607:    /* update matrix qB */
608:     PetscBLASIntCast(ctx->ld,&ld_);
609:     PetscBLASIntCast(rk,&rk_);
610:     for (r=0;r<ctx->d;r++) {
611:       for (c=0;c<=r;c++) {
612:         MatNestGetSubMat(V->matrix,r,c,&A);
613:         if (A) {
614:           qB = ctx->qB+r*ctx->ld+c*ctx->ld*lds;
615:           PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&rs1_,&rk_,&rs1_,&sone,qB,&lds_,pQ,&rs1_,&zero,work+nwu,&rs1_));
616:           PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&rk_,&rk_,&rs1_,&sone,pQ,&rs1_,work+nwu,&rs1_,&zero,qB,&lds_));
617:           if (c!=r) {
618:             sqB = ctx->qB+r*ctx->ld*lds+c*ctx->ld;
619:             for (i=0;i<ctx->ld;i++) for (j=0;j<ctx->ld;j++) sqB[i+j*lds] = PetscConj(qB[j+i*lds]);
620:           }
621:         }
622:       }
623:     }
624:   }

626:   /* free work space */
627:   PetscFree6(SS,SS2,pQ,tau,work,rwork);
628:   MatDenseRestoreArray(ctx->S,&S);

630:   /* set active columns */
631:   if (newc) ctx->U->l += newc;
632:   ctx->U->k = rk;
633:   return(0);
634: #endif
635: }

637: /*@
638:    BVTensorCompress - Updates the U and S factors of the tensor basis vectors
639:    object V by means of an SVD, removing redundant information.

641:    Collective on BV

643:    Input Parameters:
644: +  V - the tensor basis vectors context
645: -  newc - additional columns to be locked

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

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

659:    Level: advanced

661: .seealso: BVCreateTensor(), BVSetActiveColumns()
662: @*/
663: PetscErrorCode BVTensorCompress(BV V,PetscInt newc)
664: {

670:   PetscUseMethod(V,"BVTensorCompress_C",(BV,PetscInt),(V,newc));
671:   return(0);
672: }

674: static PetscErrorCode BVTensorGetDegree_Tensor(BV bv,PetscInt *d)
675: {
676:   BV_TENSOR *ctx = (BV_TENSOR*)bv->data;

679:   *d = ctx->d;
680:   return(0);
681: }

683: /*@
684:    BVTensorGetDegree - Returns the number of blocks (degree) of the tensor BV.

686:    Not collective

688:    Input Parameter:
689: .  bv - the basis vectors context

691:    Output Parameter:
692: .  d - the degree

694:    Level: advanced

696: .seealso: BVCreateTensor()
697: @*/
698: PetscErrorCode BVTensorGetDegree(BV bv,PetscInt *d)
699: {

705:   PetscUseMethod(bv,"BVTensorGetDegree_C",(BV,PetscInt*),(bv,d));
706:   return(0);
707: }

709: static PetscErrorCode BVTensorGetFactors_Tensor(BV V,BV *U,Mat *S)
710: {
711:   BV_TENSOR *ctx = (BV_TENSOR*)V->data;

714:   ctx->puk = ctx->U->k;
715:   if (U) *U = ctx->U;
716:   if (S) *S = ctx->S;
717:   return(0);
718: }

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

724:    Logically Collective on BV

726:    Input Parameter:
727: .  V - the basis vectors context

729:    Output Parameters:
730: +  U - the BV factor
731: -  S - the Mat factor

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

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

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

744:    Level: advanced

746: .seealso: BVTensorRestoreFactors()
747: @*/
748: PetscErrorCode BVTensorGetFactors(BV V,BV *U,Mat *S)
749: {
751:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;

755:   if (ctx->puk>-1) SETERRQ(PetscObjectComm((PetscObject)V),PETSC_ERR_ORDER,"Previous call to BVTensonGetFactors without a BVTensorRestoreFactors call");
756:   PetscUseMethod(V,"BVTensorGetFactors_C",(BV,BV*,Mat*),(V,U,S));
757:   return(0);
758: }

760: static PetscErrorCode BVTensorRestoreFactors_Tensor(BV V,BV *U,Mat *S)
761: {
763:   BV_TENSOR      *ctx = (BV_TENSOR*)V->data;

766:   PetscObjectStateIncrease((PetscObject)V);
767:   if (U) *U = NULL;
768:   if (S) *S = NULL;
769:   BVTensorUpdateMatrix(V,ctx->puk,ctx->U->k);
770:   ctx->puk = -1;
771:   return(0);
772: }

774: /*@C
775:    BVTensorRestoreFactors - Restore the two factors that were obtained with
776:    BVTensorGetFactors().

778:    Logically Collective on BV

780:    Input Parameters:
781: +  V - the basis vectors context
782: .  U - the BV factor (or NULL)
783: -  S - the Mat factor (or NULL)

785:    Nots:
786:    The arguments must match the corresponding call to BVTensorGetFactors().

788:    Level: advanced

790: .seealso: BVTensorGetFactors()
791: @*/
792: PetscErrorCode BVTensorRestoreFactors(BV V,BV *U,Mat *S)
793: {

800:   PetscUseMethod(V,"BVTensorRestoreFactors_C",(BV,BV*,Mat*),(V,U,S));
801:   return(0);
802: }

804: PetscErrorCode BVDestroy_Tensor(BV bv)
805: {
807:   BV_TENSOR      *ctx = (BV_TENSOR*)bv->data;

810:   BVDestroy(&ctx->U);
811:   MatDestroy(&ctx->S);
812:   if (ctx->u) {
813:     PetscFree2(ctx->qB,ctx->sw);
814:     VecDestroy(&ctx->u);
815:   }
816:   VecDestroy(&bv->cv[0]);
817:   VecDestroy(&bv->cv[1]);
818:   PetscFree(bv->data);
819:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorBuildFirstColumn_C",NULL);
820:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorCompress_C",NULL);
821:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetDegree_C",NULL);
822:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetFactors_C",NULL);
823:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorRestoreFactors_C",NULL);
824:   return(0);
825: }

827: PETSC_EXTERN PetscErrorCode BVCreate_Tensor(BV bv)
828: {
830:   BV_TENSOR      *ctx;

833:   PetscNewLog(bv,&ctx);
834:   bv->data = (void*)ctx;
835:   ctx->puk = -1;

837:   VecDuplicateEmpty(bv->t,&bv->cv[0]);
838:   VecDuplicateEmpty(bv->t,&bv->cv[1]);

840:   bv->ops->mult             = BVMult_Tensor;
841:   bv->ops->multvec          = BVMultVec_Tensor;
842:   bv->ops->multinplace      = BVMultInPlace_Tensor;
843:   bv->ops->multinplacetrans = BVMultInPlaceTranspose_Tensor;
844:   bv->ops->dot              = BVDot_Tensor;
845:   bv->ops->dotvec           = BVDotVec_Tensor;
846:   bv->ops->dotvec_local     = BVDotVec_Local_Tensor;
847:   bv->ops->scale            = BVScale_Tensor;
848:   bv->ops->norm             = BVNorm_Tensor;
849:   bv->ops->norm_local       = BVNorm_Local_Tensor;
850:   bv->ops->matmult          = BVMatMult_Tensor;
851:   bv->ops->copy             = BVCopy_Tensor;
852:   bv->ops->copycolumn       = BVCopyColumn_Tensor;
853:   bv->ops->resize           = BVResize_Tensor;
854:   bv->ops->getcolumn        = BVGetColumn_Tensor;
855:   bv->ops->restorecolumn    = BVRestoreColumn_Tensor;
856:   bv->ops->getarray         = BVGetArray_Tensor;
857:   bv->ops->restorearray     = BVRestoreArray_Tensor;
858:   bv->ops->getarrayread     = BVGetArrayRead_Tensor;
859:   bv->ops->restorearrayread = BVRestoreArrayRead_Tensor;
860:   bv->ops->gramschmidt      = BVOrthogonalizeGS1_Tensor;
861:   bv->ops->destroy          = BVDestroy_Tensor;
862:   bv->ops->view             = BVView_Tensor;

864:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorBuildFirstColumn_C",BVTensorBuildFirstColumn_Tensor);
865:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorCompress_C",BVTensorCompress_Tensor);
866:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetDegree_C",BVTensorGetDegree_Tensor);
867:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorGetFactors_C",BVTensorGetFactors_Tensor);
868:   PetscObjectComposeFunction((PetscObject)bv,"BVTensorRestoreFactors_C",BVTensorRestoreFactors_Tensor);
869:   return(0);
870: }

872: /*@
873:    BVCreateTensor - Creates a tensor BV that is represented in compact form
874:    as V = (I otimes U) S, where U has orthonormal columns.

876:    Collective on BV

878:    Input Parameters:
879: +  U - a basis vectors object
880: -  d - the number of blocks (degree) of the tensor BV

882:    Output Parameter:
883: .  V - the new basis vectors context

885:    Notes:
886:    The new basis vectors object is V = (I otimes U) S, where otimes denotes
887:    the Kronecker product, I is the identity matrix of order d, and S is a
888:    sequential matrix allocated internally. This compact representation is
889:    used e.g. to represent the Krylov basis generated with the linearization
890:    of a matrix polynomial of degree d.

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

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

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

901:    Level: advanced

903: .seealso: BVTensorGetDegree(), BVTensorGetFactors(), BVTensorBuildFirstColumn()
904: @*/
905: PetscErrorCode BVCreateTensor(BV U,PetscInt d,BV *V)
906: {
908:   PetscBool      match;
909:   PetscInt       n,N,m;
910:   BV_TENSOR      *ctx;

915:   PetscObjectTypeCompare((PetscObject)U,BVTENSOR,&match);
916:   if (match) SETERRQ(PetscObjectComm((PetscObject)U),PETSC_ERR_SUP,"U cannot be of type tensor");

918:   BVCreate(PetscObjectComm((PetscObject)U),V);
919:   BVGetSizes(U,&n,&N,&m);
920:   if (m<d) SETERRQ2(PetscObjectComm((PetscObject)U),PETSC_ERR_ARG_SIZ,"U has %D columns, it should have at least d=%D",m,d);
921:   BVSetSizes(*V,d*n,d*N,m-d+1);
922:   PetscObjectChangeTypeName((PetscObject)*V,BVTENSOR);
923:   PetscLogEventBegin(BV_Create,*V,0,0,0);
924:   BVCreate_Tensor(*V);
925:   PetscLogEventEnd(BV_Create,*V,0,0,0);

927:   ctx = (BV_TENSOR*)(*V)->data;
928:   ctx->U  = U;
929:   ctx->d  = d;
930:   ctx->ld = m;
931:   PetscObjectReference((PetscObject)U);
932:   PetscLogObjectParent((PetscObject)*V,(PetscObject)U);
933:   MatCreateSeqDense(PETSC_COMM_SELF,d*m,m-d+1,NULL,&ctx->S);
934:   PetscLogObjectParent((PetscObject)*V,(PetscObject)ctx->S);
935:   PetscObjectSetName((PetscObject)ctx->S,"S");
936:   return(0);
937: }