Date: 2021-02-01T14:41:56+00:00

Actual source code: dvdcalcpairs.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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 eigensolver: "davidson"

     13:    Step: calculate the best eigenpairs in the subspace V

     15:    For that, performs these steps:
     16:      1) Update W <- A * V
     17:      2) Update H <- V' * W
     18:      3) Obtain eigenpairs of H
     19:      4) Select some eigenpairs
     20:      5) Compute the Ritz pairs of the selected ones
     21: */

     23: #include "davidson.h"
     24: #include <slepcblaslapack.h>

     26: static PetscErrorCode dvd_calcpairs_qz_start(dvdDashboard *d)
     27: {

     31:   BVSetActiveColumns(d->eps->V,0,0);
     32:   if (d->W) { BVSetActiveColumns(d->W,0,0); }
     33:   BVSetActiveColumns(d->AX,0,0);
     34:   if (d->BX) { BVSetActiveColumns(d->BX,0,0); }
     35:   return(0);
     36: }

     38: static PetscErrorCode dvd_calcpairs_qz_d(dvdDashboard *d)
     39: {
     40:   PetscErrorCode  ierr;

     43:   BVDestroy(&d->W);
     44:   BVDestroy(&d->AX);
     45:   BVDestroy(&d->BX);
     46:   BVDestroy(&d->auxBV);
     47:   MatDestroy(&d->H);
     48:   MatDestroy(&d->G);
     49:   MatDestroy(&d->auxM);
     50:   SlepcVecPoolDestroy(&d->auxV);
     51:   PetscFree(d->nBds);
     52:   return(0);
     53: }

     55: /* in complex, d->size_H real auxiliary values are needed */
     56: static PetscErrorCode dvd_calcpairs_projeig_solve(dvdDashboard *d)
     57: {
     58:   PetscErrorCode    ierr;
     59:   Vec               v;
     60:   PetscScalar       *pA;
     61:   const PetscScalar *pv;
     62:   PetscInt          i,lV,kV,n,ld;

     65:   BVGetActiveColumns(d->eps->V,&lV,&kV);
     66:   n = kV-lV;
     67:   DSSetDimensions(d->eps->ds,n,0,0,0);
     68:   DSCopyMat(d->eps->ds,DS_MAT_A,0,0,d->H,lV,lV,n,n,PETSC_FALSE);
     69:   if (d->G) {
     70:     DSCopyMat(d->eps->ds,DS_MAT_B,0,0,d->G,lV,lV,n,n,PETSC_FALSE);
     71:   }
     72:   /* Set the signature on projected matrix B */
     73:   if (DVD_IS(d->sEP,DVD_EP_INDEFINITE)) {
     74:     DSGetLeadingDimension(d->eps->ds,&ld);
     75:     DSGetArray(d->eps->ds,DS_MAT_B,&pA);
     76:     PetscArrayzero(pA,n*ld);
     77:     VecCreateSeq(PETSC_COMM_SELF,kV,&v);
     78:     BVGetSignature(d->eps->V,v);
     79:     VecGetArrayRead(v,&pv);
     80:     for (i=0;i<n;i++) {
     81:       pA[i+ld*i] = d->nBds[i] = PetscRealPart(pv[lV+i]);
     82:     }
     83:     VecRestoreArrayRead(v,&pv);
     84:     VecDestroy(&v);
     85:     DSRestoreArray(d->eps->ds,DS_MAT_B,&pA);
     86:   }
     87:   DSSetState(d->eps->ds,DS_STATE_RAW);
     88:   DSSolve(d->eps->ds,d->eigr,d->eigi);
     89:   return(0);
     90: }

     92: /*
     93:    A(lA:kA-1,lA:kA-1) <- Z(l:k-1)'*A(l:k-1,l:k-1)*Q(l,k-1), where k=l+kA-lA
     94:  */
     95: static PetscErrorCode EPSXDUpdateProj(Mat Q,Mat Z,PetscInt l,Mat A,PetscInt lA,PetscInt kA,Mat aux)
     96: {
     98:   PetscScalar    one=1.0,zero=0.0;
     99:   PetscInt       i,j,dA_=kA-lA,m0,n0,ldA_,ldQ_,ldZ_,nQ_;
    100:   PetscBLASInt   dA,nQ,ldA,ldQ,ldZ;
    101:   PetscScalar    *pA,*pQ,*pZ,*pW;
    102:   PetscBool      symm=PETSC_FALSE,set,flg;

    105:   MatGetSize(A,&m0,&n0); ldA_=m0;
    106:   if (m0!=n0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"A should be square");
    107:   if (lA<0 || lA>m0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid initial row, column in A");
    108:   if (kA<0 || kA<lA || kA>m0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid final row, column in A");
    109:   MatIsHermitianKnown(A,&set,&flg);
    110:   symm = set? flg: PETSC_FALSE;
    111:   MatGetSize(Q,&m0,&n0); ldQ_=nQ_=m0;
    112:   if (l<0 || l>n0 || l+dA_>n0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid initial column in Q");
    113:   MatGetSize(Z,&m0,&n0); ldZ_=m0;
    114:   if (l<0 || l>n0 || l+dA_>n0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid initial column in Z");
    115:   MatGetSize(aux,&m0,&n0);
    116:   if (m0*n0<nQ_*dA_) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"aux should be larger");
    117:   PetscBLASIntCast(dA_,&dA);
    118:   PetscBLASIntCast(nQ_,&nQ);
    119:   PetscBLASIntCast(ldA_,&ldA);
    120:   PetscBLASIntCast(ldQ_,&ldQ);
    121:   PetscBLASIntCast(ldZ_,&ldZ);
    122:   MatDenseGetArray(A,&pA);
    123:   MatDenseGetArray(Q,&pQ);
    124:   if (Q!=Z) { MatDenseGetArray(Z,&pZ); }
    125:   else pZ = pQ;
    126: #if PETSC_USE_DEBUG
    127:   /* Avoid valgrind warning in xgemm and xsymm */
    128:   MatZeroEntries(aux);
    129: #endif
    130:   MatDenseGetArray(aux,&pW);
    131:   /* W = A*Q */
    132:   if (symm) {
    133:     /* symmetrize before multiplying */
    134:     for (i=lA+1;i<lA+nQ;i++) {
    135:       for (j=lA;j<i;j++) pA[i+j*ldA] = PetscConj(pA[j+i*ldA]);
    136:     }
    137:   }
    138:   PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&nQ,&dA,&nQ,&one,&pA[ldA*lA+lA],&ldA,&pQ[ldQ*l+l],&ldQ,&zero,pW,&nQ));
    139:   /* A = Q'*W */
    140:   PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&dA,&dA,&nQ,&one,&pZ[ldZ*l+l],&ldZ,pW,&nQ,&zero,&pA[ldA*lA+lA],&ldA));
    141:   MatDenseRestoreArray(A,&pA);
    142:   MatDenseRestoreArray(Q,&pQ);
    143:   if (Q!=Z) { MatDenseGetArray(Z,&pZ); }
    144:   else pZ = pQ;
    145:   MatDenseRestoreArray(aux,&pW);
    146:   return(0);
    147: }

    149: static PetscErrorCode dvd_calcpairs_updateproj(dvdDashboard *d)
    150: {
    152:   Mat            Q,Z;
    153:   PetscInt       lV,kV;
    154:   PetscBool      symm;

    157:   DSGetMat(d->eps->ds,DS_MAT_Q,&Q);
    158:   if (d->W) { DSGetMat(d->eps->ds,DS_MAT_Z,&Z); }
    159:   else Z = Q;
    160:   BVGetActiveColumns(d->eps->V,&lV,&kV);
    161:   EPSXDUpdateProj(Q,Z,0,d->H,lV,lV+d->V_tra_e,d->auxM);
    162:   if (d->G) { EPSXDUpdateProj(Q,Z,0,d->G,lV,lV+d->V_tra_e,d->auxM); }
    163:   MatDestroy(&Q);
    164:   if (d->W) { MatDestroy(&Z); }

    166:   PetscObjectTypeCompareAny((PetscObject)d->eps->ds,&symm,DSHEP,DSGHIEP,DSGHEP,"");
    167:   if (d->V_tra_s==0 || symm) return(0);
    168:   /* Compute upper part of H (and G): H(0:l-1,l:k-1) <- W(0:l-1)' * AV(l:k-1), where
    169:      k=l+d->V_tra_s */
    170:   BVSetActiveColumns(d->W?d->W:d->eps->V,0,lV);
    171:   BVSetActiveColumns(d->AX,lV,lV+d->V_tra_s);
    172:   BVDot(d->AX,d->W?d->W:d->eps->V,d->H);
    173:   if (d->G) {
    174:     BVSetActiveColumns(d->BX?d->BX:d->eps->V,lV,lV+d->V_tra_s);
    175:     BVDot(d->BX?d->BX:d->eps->V,d->W?d->W:d->eps->V,d->G);
    176:   }
    177:   PetscObjectTypeCompare((PetscObject)d->eps->ds,DSGHEP,&symm);
    178:   if (!symm) {
    179:     BVSetActiveColumns(d->W?d->W:d->eps->V,lV,lV+d->V_tra_s);
    180:     BVSetActiveColumns(d->AX,0,lV);
    181:     BVDot(d->AX,d->W?d->W:d->eps->V,d->H);
    182:     if (d->G) {
    183:       BVSetActiveColumns(d->BX?d->BX:d->eps->V,0,lV);
    184:       BVDot(d->BX?d->BX:d->eps->V,d->W?d->W:d->eps->V,d->G);
    185:     }
    186:   }
    187:   BVSetActiveColumns(d->eps->V,lV,kV);
    188:   BVSetActiveColumns(d->AX,lV,kV);
    189:   if (d->BX) { BVSetActiveColumns(d->BX,lV,kV); }
    190:   if (d->W) { BVSetActiveColumns(d->W,lV,kV); }
    191:   if (d->W) { dvd_harm_updateproj(d); }
    192:   return(0);
    193: }

    195: /*
    196:    BV <- BV*MT
    197:  */
    198: PETSC_STATIC_INLINE PetscErrorCode dvd_calcpairs_updateBV0_gen(dvdDashboard *d,BV bv,DSMatType mat)
    199: {
    201:   PetscInt       l,k,n;
    202:   Mat            auxM;

    205:   BVGetActiveColumns(d->eps->V,&l,&k);
    206:   MatCreateSeqDense(PETSC_COMM_SELF,k,k,NULL,&auxM);
    207:   MatZeroEntries(auxM);
    208:   DSGetDimensions(d->eps->ds,&n,NULL,NULL,NULL,NULL);
    209:   if (k-l!=n) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
    210:   DSCopyMat(d->eps->ds,mat,0,0,auxM,l,l,n,d->V_tra_e,PETSC_TRUE);
    211:   BVMultInPlace(bv,auxM,l,l+d->V_tra_e);
    212:   MatDestroy(&auxM);
    213:   return(0);
    214: }

    216: static PetscErrorCode dvd_calcpairs_proj(dvdDashboard *d)
    217: {
    219:   PetscInt       i,l,k;
    220:   Vec            v1,v2;
    221:   PetscScalar    *pv;

    224:   BVGetActiveColumns(d->eps->V,&l,&k);
    225:   /* Update AV, BV, W and the projected matrices */
    226:   /* 1. S <- S*MT */
    227:   if (d->V_tra_s != d->V_tra_e || d->V_tra_e > 0) {
    228:     dvd_calcpairs_updateBV0_gen(d,d->eps->V,DS_MAT_Q);
    229:     if (d->W) { dvd_calcpairs_updateBV0_gen(d,d->W,DS_MAT_Z); }
    230:     dvd_calcpairs_updateBV0_gen(d,d->AX,DS_MAT_Q);
    231:     if (d->BX) { dvd_calcpairs_updateBV0_gen(d,d->BX,DS_MAT_Q); }
    232:     dvd_calcpairs_updateproj(d);
    233:     /* Update signature */
    234:     if (d->nBds) {
    235:       VecCreateSeq(PETSC_COMM_SELF,l+d->V_tra_e,&v1);
    236:       BVSetActiveColumns(d->eps->V,0,l+d->V_tra_e);
    237:       BVGetSignature(d->eps->V,v1);
    238:       VecGetArray(v1,&pv);
    239:       for (i=0;i<d->V_tra_e;i++) pv[l+i] = d->nBds[i];
    240:       VecRestoreArray(v1,&pv);
    241:       BVSetSignature(d->eps->V,v1);
    242:       BVSetActiveColumns(d->eps->V,l,k);
    243:       VecDestroy(&v1);
    244:     }
    245:     k = l+d->V_tra_e;
    246:     l+= d->V_tra_s;
    247:   } else {
    248:     /* 2. V <- orth(V, V_new) */
    249:     dvd_orthV(d->eps->V,l+d->V_new_s,l+d->V_new_e);
    250:     /* 3. AV <- [AV A * V(V_new_s:V_new_e-1)] */
    251:     /* Check consistency */
    252:     if (k-l != d->V_new_s) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
    253:     for (i=l+d->V_new_s;i<l+d->V_new_e;i++) {
    254:       BVGetColumn(d->eps->V,i,&v1);
    255:       BVGetColumn(d->AX,i,&v2);
    256:       MatMult(d->A,v1,v2);
    257:       BVRestoreColumn(d->eps->V,i,&v1);
    258:       BVRestoreColumn(d->AX,i,&v2);
    259:     }
    260:     /* 4. BV <- [BV B * V(V_new_s:V_new_e-1)] */
    261:     if (d->BX) {
    262:       /* Check consistency */
    263:       if (k-l != d->V_new_s) SETERRQ(PETSC_COMM_SELF,1,"Consistency broken");
    264:       for (i=l+d->V_new_s;i<l+d->V_new_e;i++) {
    265:         BVGetColumn(d->eps->V,i,&v1);
    266:         BVGetColumn(d->BX,i,&v2);
    267:         MatMult(d->B,v1,v2);
    268:         BVRestoreColumn(d->eps->V,i,&v1);
    269:         BVRestoreColumn(d->BX,i,&v2);
    270:       }
    271:     }
    272:     /* 5. W <- [W f(AV,BV)] */
    273:     if (d->W) {
    274:       d->calcpairs_W(d);
    275:       dvd_orthV(d->W,l+d->V_new_s,l+d->V_new_e);
    276:     }
    277:     /* 6. H <- W' * AX; G <- W' * BX */
    278:     BVSetActiveColumns(d->eps->V,l+d->V_new_s,l+d->V_new_e);
    279:     BVSetActiveColumns(d->AX,l+d->V_new_s,l+d->V_new_e);
    280:     if (d->BX) { BVSetActiveColumns(d->BX,l+d->V_new_s,l+d->V_new_e); }
    281:     if (d->W) { BVSetActiveColumns(d->W,l+d->V_new_s,l+d->V_new_e); }
    282:     BVMatProject(d->AX,NULL,d->W?d->W:d->eps->V,d->H);
    283:     if (d->G) { BVMatProject(d->BX?d->BX:d->eps->V,NULL,d->W?d->W:d->eps->V,d->G); }
    284:     BVSetActiveColumns(d->eps->V,l,k);
    285:     BVSetActiveColumns(d->AX,l,k);
    286:     if (d->BX) { BVSetActiveColumns(d->BX,l,k); }
    287:     if (d->W) { BVSetActiveColumns(d->W,l,k); }

    289:     /* Perform the transformation on the projected problem */
    290:     if (d->W) {
    291:       d->calcpairs_proj_trans(d);
    292:     }
    293:     k = l+d->V_new_e;
    294:   }
    295:   BVSetActiveColumns(d->eps->V,l,k);
    296:   BVSetActiveColumns(d->AX,l,k);
    297:   if (d->BX) { BVSetActiveColumns(d->BX,l,k); }
    298:   if (d->W) { BVSetActiveColumns(d->W,l,k); }

    300:   /* Solve the projected problem */
    301:   dvd_calcpairs_projeig_solve(d);

    303:   d->V_tra_s = d->V_tra_e = 0;
    304:   d->V_new_s = d->V_new_e;
    305:   return(0);
    306: }

    308: static PetscErrorCode dvd_calcpairs_apply_arbitrary(dvdDashboard *d,PetscInt r_s,PetscInt r_e,PetscScalar *rr,PetscScalar *ri)
    309: {
    310:   PetscInt       i,k,ld;
    311:   PetscScalar    *pX;
    312:   Vec            *X,xr,xi;
    314: #if defined(PETSC_USE_COMPLEX)
    315:   PetscInt       N=1;
    316: #else
    317:   PetscInt       N=2,j;
    318: #endif

    321:   /* Quick exit without neither arbitrary selection nor harmonic extraction */
    322:   if (!d->eps->arbitrary && !d->calcpairs_eig_backtrans) return(0);

    324:   /* Quick exit without arbitrary selection, but with harmonic extraction */
    325:   if (d->calcpairs_eig_backtrans) {
    326:     for (i=r_s; i<r_e; i++) {
    327:       d->calcpairs_eig_backtrans(d,d->eigr[i],d->eigi[i],&rr[i-r_s],&ri[i-r_s]);
    328:     }
    329:   }
    330:   if (!d->eps->arbitrary) return(0);

    332:   SlepcVecPoolGetVecs(d->auxV,N,&X);
    333:   DSGetLeadingDimension(d->eps->ds,&ld);
    334:   for (i=r_s;i<r_e;i++) {
    335:     k = i;
    336:     DSVectors(d->eps->ds,DS_MAT_X,&k,NULL);
    337:     DSGetArray(d->eps->ds,DS_MAT_X,&pX);
    338:     dvd_improvex_compute_X(d,i,k+1,X,pX,ld);
    339:     DSRestoreArray(d->eps->ds,DS_MAT_X,&pX);
    340: #if !defined(PETSC_USE_COMPLEX)
    341:     if (d->nX[i] != 1.0) {
    342:       for (j=i;j<k+1;j++) {
    343:         VecScale(X[j-i],1.0/d->nX[i]);
    344:       }
    345:     }
    346:     xr = X[0];
    347:     xi = X[1];
    348:     if (i == k) {
    349:       VecSet(xi,0.0);
    350:     }
    351: #else
    352:     xr = X[0];
    353:     xi = NULL;
    354:     if (d->nX[i] != 1.0) {
    355:       VecScale(xr,1.0/d->nX[i]);
    356:     }
    357: #endif
    358:     (d->eps->arbitrary)(rr[i-r_s],ri[i-r_s],xr,xi,&rr[i-r_s],&ri[i-r_s],d->eps->arbitraryctx);
    359: #if !defined(PETSC_USE_COMPLEX)
    360:     if (i != k) {
    361:       rr[i+1-r_s] = rr[i-r_s];
    362:       ri[i+1-r_s] = ri[i-r_s];
    363:       i++;
    364:     }
    365: #endif
    366:   }
    367:   SlepcVecPoolRestoreVecs(d->auxV,N,&X);
    368:   return(0);
    369: }

    371: static PetscErrorCode dvd_calcpairs_selectPairs(dvdDashboard *d,PetscInt n)
    372: {
    373:   PetscInt       k,lV,kV,nV;
    374:   PetscScalar    *rr,*ri;

    378:   BVGetActiveColumns(d->eps->V,&lV,&kV);
    379:   nV = kV - lV;
    380:   n = PetscMin(n,nV);
    381:   if (n <= 0) return(0);
    382:   /* Put the best n pairs at the beginning. Useful for restarting */
    383:   if (d->eps->arbitrary || d->calcpairs_eig_backtrans) {
    384:     PetscMalloc1(nV,&rr);
    385:     PetscMalloc1(nV,&ri);
    386:     dvd_calcpairs_apply_arbitrary(d,0,nV,rr,ri);
    387:   } else {
    388:     rr = d->eigr;
    389:     ri = d->eigi;
    390:   }
    391:   k = n;
    392:   DSSort(d->eps->ds,d->eigr,d->eigi,rr,ri,&k);
    393:   /* Put the best pair at the beginning. Useful to check its residual */
    394: #if !defined(PETSC_USE_COMPLEX)
    395:   if (n != 1 && (n != 2 || d->eigi[0] == 0.0))
    396: #else
    397:   if (n != 1)
    398: #endif
    399:   {
    400:     dvd_calcpairs_apply_arbitrary(d,0,nV,rr,ri);
    401:     k = 1;
    402:     DSSort(d->eps->ds,d->eigr,d->eigi,rr,ri,&k);
    403:   }
    404:   DSSynchronize(d->eps->ds,d->eigr,d->eigi);

    406:   if (d->calcpairs_eigs_trans) {
    407:     d->calcpairs_eigs_trans(d);
    408:   }
    409:   if (d->eps->arbitrary || d->calcpairs_eig_backtrans) {
    410:     PetscFree(rr);
    411:     PetscFree(ri);
    412:   }
    413:   return(0);
    414: }

    416: static PetscErrorCode EPSXDComputeDSConv(dvdDashboard *d)
    417: {
    418:   PetscErrorCode    ierr;
    419:   PetscInt          i,ld;
    420:   Vec               v;
    421:   PetscScalar       *pA;
    422:   const PetscScalar *pv;
    423:   PetscBool         symm;

    426:   BVSetActiveColumns(d->eps->V,0,d->eps->nconv);
    427:   PetscObjectTypeCompare((PetscObject)d->eps->ds,DSHEP,&symm);
    428:   if (symm) return(0);
    429:   DSSetDimensions(d->eps->ds,d->eps->nconv,0,0,0);
    430:   DSCopyMat(d->eps->ds,DS_MAT_A,0,0,d->H,0,0,d->eps->nconv,d->eps->nconv,PETSC_FALSE);
    431:   if (d->G) {
    432:     DSCopyMat(d->eps->ds,DS_MAT_B,0,0,d->G,0,0,d->eps->nconv,d->eps->nconv,PETSC_FALSE);
    433:   }
    434:   /* Set the signature on projected matrix B */
    435:   if (DVD_IS(d->sEP,DVD_EP_INDEFINITE)) {
    436:     DSGetLeadingDimension(d->eps->ds,&ld);
    437:     DSGetArray(d->eps->ds,DS_MAT_B,&pA);
    438:     PetscArrayzero(pA,d->eps->nconv*ld);
    439:     VecCreateSeq(PETSC_COMM_SELF,d->eps->nconv,&v);
    440:     BVGetSignature(d->eps->V,v);
    441:     VecGetArrayRead(v,&pv);
    442:     for (i=0;i<d->eps->nconv;i++) pA[i+ld*i] = pv[i];
    443:     VecRestoreArrayRead(v,&pv);
    444:     VecDestroy(&v);
    445:     DSRestoreArray(d->eps->ds,DS_MAT_B,&pA);
    446:   }
    447:   DSSetState(d->eps->ds,DS_STATE_RAW);
    448:   DSSolve(d->eps->ds,d->eps->eigr,d->eps->eigi);
    449:   DSSynchronize(d->eps->ds,d->eps->eigr,d->eps->eigi);
    450:   if (d->W) {
    451:     for (i=0; i<d->eps->nconv; i++) {
    452:       d->calcpairs_eig_backtrans(d,d->eps->eigr[i],d->eps->eigi[i],&d->eps->eigr[i],&d->eps->eigi[i]);
    453:     }
    454:   }
    455:   return(0);
    456: }

    458: /*
    459:    Compute the residual vectors R(i) <- (AV - BV*eigr(i))*pX(i), and also
    460:    the norm associated to the Schur pair, where i = r_s..r_e
    461: */
    462: static PetscErrorCode dvd_calcpairs_res_0(dvdDashboard *d,PetscInt r_s,PetscInt r_e)
    463: {
    464:   PetscInt       i,ldpX;
    465:   PetscScalar    *pX;
    467:   BV             BX = d->BX?d->BX:d->eps->V;
    468:   Vec            *R;

    471:   DSGetLeadingDimension(d->eps->ds,&ldpX);
    472:   DSGetArray(d->eps->ds,DS_MAT_Q,&pX);
    473:   /* nX(i) <- ||X(i)|| */
    474:   dvd_improvex_compute_X(d,r_s,r_e,NULL,pX,ldpX);
    475:   SlepcVecPoolGetVecs(d->auxV,r_e-r_s,&R);
    476:   for (i=r_s;i<r_e;i++) {
    477:     /* R(i-r_s) <- AV*pX(i) */
    478:     BVMultVec(d->AX,1.0,0.0,R[i-r_s],&pX[ldpX*i]);
    479:     /* R(i-r_s) <- R(i-r_s) - eigr(i)*BX*pX(i) */
    480:     BVMultVec(BX,-d->eigr[i],1.0,R[i-r_s],&pX[ldpX*i]);
    481:   }
    482:   DSRestoreArray(d->eps->ds,DS_MAT_Q,&pX);
    483:   d->calcpairs_proj_res(d,r_s,r_e,R);
    484:   SlepcVecPoolRestoreVecs(d->auxV,r_e-r_s,&R);
    485:   return(0);
    486: }

    488: static PetscErrorCode dvd_calcpairs_proj_res(dvdDashboard *d,PetscInt r_s,PetscInt r_e,Vec *R)
    489: {
    490:   PetscInt       i,l,k;
    492:   PetscBool      lindep=PETSC_FALSE;
    493:   BV             cX;

    496:   if (d->W) cX = d->W; /* If left subspace exists, R <- orth(cY, R), nR[i] <- ||R[i]|| */
    497:   else if (!(DVD_IS(d->sEP, DVD_EP_STD) && DVD_IS(d->sEP, DVD_EP_HERMITIAN))) cX = d->eps->V; /* If not HEP, R <- orth(cX, R), nR[i] <- ||R[i]|| */
    498:   else cX = NULL; /* Otherwise, nR[i] <- ||R[i]|| */

    500:   if (cX) {
    501:     BVGetActiveColumns(cX,&l,&k);
    502:     BVSetActiveColumns(cX,0,l);
    503:     for (i=0;i<r_e-r_s;i++) {
    504:       BVOrthogonalizeVec(cX,R[i],NULL,&d->nR[r_s+i],&lindep);
    505:     }
    506:     BVSetActiveColumns(cX,l,k);
    507:     if (lindep || (PetscAbs(d->nR[r_s+i]) < PETSC_MACHINE_EPSILON)) {
    508:       PetscInfo2(d->eps,"The computed eigenvector residual %D is too low, %g!\n",r_s+i,(double)(d->nR[r_s+i]));
    509:     }
    510:   } else {
    511:     for (i=0;i<r_e-r_s;i++) {
    512:       VecNormBegin(R[i],NORM_2,&d->nR[r_s+i]);
    513:     }
    514:     for (i=0;i<r_e-r_s;i++) {
    515:       VecNormEnd(R[i],NORM_2,&d->nR[r_s+i]);
    516:     }
    517:   }
    518:   return(0);
    519: }

    521: PetscErrorCode dvd_calcpairs_qz(dvdDashboard *d,dvdBlackboard *b,PetscBool borth,PetscBool harm)
    522: {
    524:   PetscBool      std_probl,her_probl,ind_probl;
    525:   DSType         dstype;
    526:   Vec            v1;

    529:   std_probl = DVD_IS(d->sEP,DVD_EP_STD)? PETSC_TRUE: PETSC_FALSE;
    530:   her_probl = DVD_IS(d->sEP,DVD_EP_HERMITIAN)? PETSC_TRUE: PETSC_FALSE;
    531:   ind_probl = DVD_IS(d->sEP,DVD_EP_INDEFINITE)? PETSC_TRUE: PETSC_FALSE;

    533:   /* Setting configuration constrains */
    534:   b->max_size_proj = PetscMax(b->max_size_proj,b->max_size_V);
    535:   d->W_shift = d->B? PETSC_TRUE: PETSC_FALSE;

    537:   /* Setup the step */
    538:   if (b->state >= DVD_STATE_CONF) {
    539:     d->max_size_P = b->max_size_P;
    540:     d->max_size_proj = b->max_size_proj;
    541:     /* Create a DS if the method works with Schur decompositions */
    542:     d->calcPairs = dvd_calcpairs_proj;
    543:     d->calcpairs_residual = dvd_calcpairs_res_0;
    544:     d->calcpairs_proj_res = dvd_calcpairs_proj_res;
    545:     d->calcpairs_selectPairs = dvd_calcpairs_selectPairs;
    546:     /* Create and configure a DS for solving the projected problems */
    547:     if (d->W) dstype = DSGNHEP;    /* If we use harmonics */
    548:     else {
    549:       if (ind_probl) dstype = DSGHIEP;
    550:       else if (std_probl) dstype = her_probl? DSHEP : DSNHEP;
    551:       else dstype = her_probl? DSGHEP : DSGNHEP;
    552:     }
    553:     DSSetType(d->eps->ds,dstype);
    554:     DSAllocate(d->eps->ds,d->eps->ncv);
    555:     /* Create various vector basis */
    556:     if (harm) {
    557:       BVDuplicateResize(d->eps->V,d->eps->ncv,&d->W);
    558:       BVSetMatrix(d->W,NULL,PETSC_FALSE);
    559:     } else d->W = NULL;
    560:     BVDuplicateResize(d->eps->V,d->eps->ncv,&d->AX);
    561:     BVSetMatrix(d->AX,NULL,PETSC_FALSE);
    562:     BVDuplicateResize(d->eps->V,d->eps->ncv,&d->auxBV);
    563:     BVSetMatrix(d->auxBV,NULL,PETSC_FALSE);
    564:     if (d->B) {
    565:       BVDuplicateResize(d->eps->V,d->eps->ncv,&d->BX);
    566:       BVSetMatrix(d->BX,NULL,PETSC_FALSE);
    567:     } else d->BX = NULL;
    568:     MatCreateVecsEmpty(d->A,&v1,NULL);
    569:     SlepcVecPoolCreate(v1,0,&d->auxV);
    570:     VecDestroy(&v1);
    571:     /* Create projected problem matrices */
    572:     MatCreateSeqDense(PETSC_COMM_SELF,d->eps->ncv,d->eps->ncv,NULL,&d->H);
    573:     if (!std_probl) {
    574:       MatCreateSeqDense(PETSC_COMM_SELF,d->eps->ncv,d->eps->ncv,NULL,&d->G);
    575:     } else d->G = NULL;
    576:     if (her_probl) {
    577:       MatSetOption(d->H,MAT_HERMITIAN,PETSC_TRUE);
    578:       if (d->G) { MatSetOption(d->G,MAT_HERMITIAN,PETSC_TRUE); }
    579:     }

    581:     if (ind_probl) {
    582:       PetscMalloc1(d->eps->ncv,&d->nBds);
    583:     } else d->nBds = NULL;
    584:     MatCreateSeqDense(PETSC_COMM_SELF,d->eps->ncv,d->eps->ncv,NULL,&d->auxM);

    586:     EPSDavidsonFLAdd(&d->startList,dvd_calcpairs_qz_start);
    587:     EPSDavidsonFLAdd(&d->endList,EPSXDComputeDSConv);
    588:     EPSDavidsonFLAdd(&d->destroyList,dvd_calcpairs_qz_d);
    589:   }
    590:   return(0);
    591: }