Date: 2026-01-20T11:35:12+00:00

Actual source code: pjd.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

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

     13:    Method: Jacobi-Davidson

     15:    Algorithm:

     17:        Jacobi-Davidson for polynomial eigenvalue problems.

     19:    References:

     21:        [1] C. Campos and J.E. Roman, "A polynomial Jacobi-Davidson solver
     22:            with support for non-monomial bases and deflation", BIT Numer.
     23:            Math. 60:295-318, 2020.

     25:        [2] G.L.G. Sleijpen et al., "Jacobi-Davidson type methods for
     26:            generalized eigenproblems and polynomial eigenproblems", BIT
     27:            36(3):595-633, 1996.

     29:        [3] Feng-Nan Hwang, Zih-Hao Wei, Tsung-Ming Huang, Weichung Wang,
     30:            "A Parallel Additive Schwarz Preconditioned Jacobi-Davidson
     31:            Algorithm for Polynomial Eigenvalue Problems in Quantum Dot
     32:            Simulation", J. Comput. Phys. 229(8):2932-2947, 2010.
     33: */

     35: #include <slepc/private/pepimpl.h>
     36: #include <slepcblaslapack.h>

     38: static PetscBool  cited = PETSC_FALSE;
     39: static const char citation[] =
     40:   "@Article{slepc-slice-qep,\n"
     41:   "   author = \"C. Campos and J. E. Roman\",\n"
     42:   "   title = \"A polynomial {Jacobi-Davidson} solver with support for non-monomial bases and deflation\",\n"
     43:   "   journal = \"{BIT} Numer. Math.\",\n"
     44:   "   volume = \"60\",\n"
     45:   "   pages = \"295--318\",\n"
     46:   "   year = \"2020,\"\n"
     47:   "   doi = \"https://doi.org/10.1007/s10543-019-00778-z\"\n"
     48:   "}\n";

     50: typedef struct {
     51:   PetscReal   keep;          /* restart parameter */
     52:   PetscReal   fix;           /* fix parameter */
     53:   PetscBool   reusepc;       /* flag indicating whether pc is rebuilt or not */
     54:   BV          V;             /* work basis vectors to store the search space */
     55:   BV          W;             /* work basis vectors to store the test space */
     56:   BV          *TV;           /* work basis vectors to store T*V (each TV[i] is the coefficient for \lambda^i of T*V for the extended T) */
     57:   BV          *AX;           /* work basis vectors to store A_i*X for locked eigenvectors */
     58:   BV          N[2];          /* auxiliary work BVs */
     59:   BV          X;             /* locked eigenvectors */
     60:   PetscScalar *T;            /* matrix of the invariant pair */
     61:   PetscScalar *Tj;           /* matrix containing the powers of the invariant pair matrix */
     62:   PetscScalar *XpX;          /* X^H*X */
     63:   PetscInt    ld;            /* leading dimension for Tj and XpX */
     64:   PC          pcshell;       /* preconditioner including basic precond+projector */
     65:   Mat         Pshell;        /* auxiliary shell matrix */
     66:   PetscInt    nlock;         /* number of locked vectors in the invariant pair */
     67:   Vec         vtempl;        /* reference nested vector */
     68:   PetscInt    midx;          /* minimality index */
     69:   PetscInt    mmidx;         /* maximum allowed minimality index */
     70:   PEPJDProjection proj;      /* projection type (orthogonal, harmonic) */
     71: } PEP_JD;

     73: typedef struct {
     74:   PEP         pep;
     75:   PC          pc;            /* basic preconditioner */
     76:   Vec         Bp[2];         /* preconditioned residual of derivative polynomial, B\p */
     77:   Vec         u[2];          /* Ritz vector */
     78:   PetscScalar gamma[2];      /* precomputed scalar u'*B\p */
     79:   PetscScalar theta;
     80:   PetscScalar *M;
     81:   PetscScalar *ps;
     82:   PetscInt    ld;
     83:   Vec         *work;
     84:   Mat         PPr;
     85:   BV          X;
     86:   PetscInt    n;
     87: } PEP_JD_PCSHELL;

     89: typedef struct {
     90:   Mat         Pr,Pi;         /* matrix polynomial evaluated at theta */
     91:   PEP         pep;
     92:   Vec         *work;
     93:   PetscScalar theta[2];
     94: } PEP_JD_MATSHELL;

     96: /*
     97:    Duplicate and resize auxiliary basis
     98: */
     99: static PetscErrorCode PEPJDDuplicateBasis(PEP pep,BV *basis)
    100: {
    101:   PEP_JD             *pjd = (PEP_JD*)pep->data;
    102:   PetscInt           nloc,m;
    103:   BVType             type;
    104:   BVOrthogType       otype;
    105:   BVOrthogRefineType oref;
    106:   PetscReal          oeta;
    107:   BVOrthogBlockType  oblock;
    108:   VecType            vtype;

    110:   PetscFunctionBegin;
    111:   if (pjd->ld>1) {
    112:     PetscCall(BVCreate(PetscObjectComm((PetscObject)pep),basis));
    113:     PetscCall(BVGetSizes(pep->V,&nloc,NULL,&m));
    114:     nloc += pjd->ld-1;
    115:     PetscCall(BVSetSizes(*basis,nloc,PETSC_DECIDE,m));
    116:     PetscCall(BVGetType(pep->V,&type));
    117:     PetscCall(BVSetType(*basis,type));
    118:     PetscCall(BVGetVecType(pep->V,&vtype));
    119:     PetscCall(BVSetVecType(*basis,vtype));
    120:     PetscCall(BVGetOrthogonalization(pep->V,&otype,&oref,&oeta,&oblock));
    121:     PetscCall(BVSetOrthogonalization(*basis,otype,oref,oeta,oblock));
    122:     PetscCall(PetscObjectStateIncrease((PetscObject)*basis));
    123:   } else PetscCall(BVDuplicate(pep->V,basis));
    124:   PetscFunctionReturn(PETSC_SUCCESS);
    125: }

    127: static PetscErrorCode PEPSetUp_JD(PEP pep)
    128: {
    129:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    130:   PetscBool      isprecond,flg;
    131:   PetscRandom    rand;
    132:   PetscInt       i;

    134:   PetscFunctionBegin;
    135:   PetscCall(PEPSetDimensions_Default(pep,pep->nev,&pep->ncv,&pep->mpd));
    136:   if (pep->max_it==PETSC_DETERMINE) pep->max_it = PetscMax(100,2*pep->n/pep->ncv);
    137:   if (!pep->which) pep->which = PEP_TARGET_MAGNITUDE;
    138:   PetscCheck(pep->which==PEP_TARGET_MAGNITUDE || pep->which==PEP_TARGET_REAL || pep->which==PEP_TARGET_IMAGINARY,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"The JD solver supports only target which, see PEPSetWhichEigenpairs()");

    140:   PetscCall(PetscObjectTypeCompare((PetscObject)pep->st,STPRECOND,&isprecond));
    141:   PetscCheck(isprecond,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"The JD solver only works with PRECOND spectral transformation");

    143:   PetscCall(STGetTransform(pep->st,&flg));
    144:   PetscCheck(!flg,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"The JD solver requires the ST transform flag unset, see STSetTransform()");
    145:   PEPCheckIgnored(pep,PEP_FEATURE_EXTRACT);

    147:   if (!pjd->mmidx) pjd->mmidx = pep->nmat-1;
    148:   pjd->mmidx = PetscMin(pjd->mmidx,pep->nmat-1);
    149:   if (!pjd->keep) pjd->keep = 0.5;
    150:   PetscCall(PEPBasisCoefficients(pep,pep->pbc));
    151:   PetscCall(PEPAllocateSolution(pep,0));
    152:   PetscCall(BVGetRandomContext(pep->V,&rand));  /* make sure the random context is available when duplicating */
    153:   PetscCall(PEPSetWorkVecs(pep,5));
    154:   pjd->ld = pep->nev;
    155: #if !defined (PETSC_USE_COMPLEX)
    156:   pjd->ld++;
    157: #endif
    158:   PetscCall(PetscMalloc2(pep->nmat,&pjd->TV,pep->nmat,&pjd->AX));
    159:   for (i=0;i<pep->nmat;i++) PetscCall(PEPJDDuplicateBasis(pep,pjd->TV+i));
    160:   if (pjd->ld>1) {
    161:     PetscCall(PEPJDDuplicateBasis(pep,&pjd->V));
    162:     PetscCall(BVSetFromOptions(pjd->V));
    163:     for (i=0;i<pep->nmat;i++) PetscCall(BVDuplicateResize(pep->V,pjd->ld-1,pjd->AX+i));
    164:     PetscCall(BVDuplicateResize(pep->V,pjd->ld-1,pjd->N));
    165:     PetscCall(BVDuplicateResize(pep->V,pjd->ld-1,pjd->N+1));
    166:     pjd->X = pep->V;
    167:     PetscCall(PetscCalloc3(pjd->ld*pjd->ld,&pjd->XpX,pep->ncv*pep->ncv,&pjd->T,pjd->ld*pjd->ld*pep->nmat,&pjd->Tj));
    168:   } else pjd->V = pep->V;
    169:   if (pjd->proj==PEP_JD_PROJECTION_HARMONIC) PetscCall(PEPJDDuplicateBasis(pep,&pjd->W));
    170:   else pjd->W = pjd->V;
    171:   PetscCall(DSSetType(pep->ds,DSPEP));
    172:   PetscCall(DSPEPSetDegree(pep->ds,pep->nmat-1));
    173:   if (pep->basis!=PEP_BASIS_MONOMIAL) PetscCall(DSPEPSetCoefficients(pep->ds,pep->pbc));
    174:   PetscCall(DSAllocate(pep->ds,pep->ncv));
    175:   PetscFunctionReturn(PETSC_SUCCESS);
    176: }

    178: /*
    179:    Updates columns (low to (high-1)) of TV[i]
    180: */
    181: static PetscErrorCode PEPJDUpdateTV(PEP pep,PetscInt low,PetscInt high,Vec *w)
    182: {
    183:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    184:   PetscInt       pp,col,i,nloc,nconv;
    185:   Vec            v1,v2,t1,t2;
    186:   PetscScalar    *array1,*array2,*x2,*xx,*N,*Np,*y2=NULL,zero=0.0,sone=1.0,*pT,fact,*psc;
    187:   PetscReal      *cg,*ca,*cb;
    188:   PetscMPIInt    rk,np;
    189:   PetscBLASInt   n_,ld_,one=1;
    190:   Mat            T;
    191:   BV             pbv;

    193:   PetscFunctionBegin;
    194:   ca = pep->pbc; cb = ca+pep->nmat; cg = cb + pep->nmat;
    195:   nconv = pjd->nlock;
    196:   PetscCall(PetscMalloc5(nconv,&x2,nconv,&xx,nconv*nconv,&pT,nconv*nconv,&N,nconv*nconv,&Np));
    197:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pep),&rk));
    198:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pep),&np));
    199:   PetscCall(BVGetSizes(pep->V,&nloc,NULL,NULL));
    200:   t1 = w[0];
    201:   t2 = w[1];
    202:   PetscCall(PetscBLASIntCast(pjd->nlock,&n_));
    203:   PetscCall(PetscBLASIntCast(pjd->ld,&ld_));
    204:   if (nconv) {
    205:     for (i=0;i<nconv;i++) PetscCall(PetscArraycpy(pT+i*nconv,pjd->T+i*pep->ncv,nconv));
    206:     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nconv,nconv,pT,&T));
    207:   }
    208:   for (col=low;col<high;col++) {
    209:     PetscCall(BVGetColumn(pjd->V,col,&v1));
    210:     PetscCall(VecGetArray(v1,&array1));
    211:     if (nconv>0) {
    212:       for (i=0;i<nconv;i++) x2[i] = array1[nloc+i]* PetscSqrtReal(np);
    213:     }
    214:     PetscCall(VecPlaceArray(t1,array1));
    215:     if (nconv) {
    216:       PetscCall(BVSetActiveColumns(pjd->N[0],0,nconv));
    217:       PetscCall(BVSetActiveColumns(pjd->N[1],0,nconv));
    218:       PetscCall(BVDotVec(pjd->X,t1,xx));
    219:     }
    220:     for (pp=pep->nmat-1;pp>=0;pp--) {
    221:       PetscCall(BVGetColumn(pjd->TV[pp],col,&v2));
    222:       PetscCall(VecGetArray(v2,&array2));
    223:       PetscCall(VecPlaceArray(t2,array2));
    224:       PetscCall(MatMult(pep->A[pp],t1,t2));
    225:       if (nconv) {
    226:         if (pp<pep->nmat-3) {
    227:           PetscCall(BVMult(pjd->N[0],1.0,-cg[pp+2],pjd->AX[pp+1],NULL));
    228:           PetscCall(MatShift(T,-cb[pp+1]));
    229:           PetscCall(BVMult(pjd->N[0],1.0/ca[pp],1.0/ca[pp],pjd->N[1],T));
    230:           pbv = pjd->N[0]; pjd->N[0] = pjd->N[1]; pjd->N[1] = pbv;
    231:           PetscCall(BVMultVec(pjd->N[1],1.0,1.0,t2,x2));
    232:           PetscCall(MatShift(T,cb[pp+1]));
    233:         } else if (pp==pep->nmat-3) {
    234:           PetscCall(BVCopy(pjd->AX[pp+2],pjd->N[0]));
    235:           PetscCall(BVScale(pjd->N[0],1/ca[pp+1]));
    236:           PetscCall(BVCopy(pjd->AX[pp+1],pjd->N[1]));
    237:           PetscCall(MatShift(T,-cb[pp+1]));
    238:           PetscCall(BVMult(pjd->N[1],1.0/ca[pp],1.0/ca[pp],pjd->N[0],T));
    239:           PetscCall(BVMultVec(pjd->N[1],1.0,1.0,t2,x2));
    240:           PetscCall(MatShift(T,cb[pp+1]));
    241:         } else if (pp==pep->nmat-2) PetscCall(BVMultVec(pjd->AX[pp+1],1.0/ca[pp],1.0,t2,x2));
    242:         if (pp<pjd->midx) {
    243:           y2 = array2+nloc;
    244:           PetscCallBLAS("BLASgemv",BLASgemv_("C",&n_,&n_,&sone,pjd->Tj+pjd->ld*pjd->ld*pp,&ld_,xx,&one,&zero,y2,&one));
    245:           if (pp<pjd->midx-2) {
    246:             fact = -cg[pp+2];
    247:             PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n_,&n_,&n_,&sone,pjd->Tj+(pp+1)*pjd->ld*pjd->ld,&ld_,pjd->XpX,&ld_,&fact,Np,&n_));
    248:             fact = 1/ca[pp];
    249:             PetscCall(MatShift(T,-cb[pp+1]));
    250:             PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&fact,N,&n_,pT,&n_,&fact,Np,&n_));
    251:             PetscCall(MatShift(T,cb[pp+1]));
    252:             psc = Np; Np = N; N = psc;
    253:             PetscCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,N,&n_,x2,&one,&sone,y2,&one));
    254:           } else if (pp==pjd->midx-2) {
    255:             fact = 1/ca[pp];
    256:             PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n_,&n_,&n_,&fact,pjd->Tj+(pp+1)*pjd->ld*pjd->ld,&ld_,pjd->XpX,&ld_,&zero,N,&n_));
    257:             PetscCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,N,&n_,x2,&one,&sone,y2,&one));
    258:           } else if (pp==pjd->midx-1) PetscCall(PetscArrayzero(Np,nconv*nconv));
    259:         }
    260:         for (i=0;i<nconv;i++) array2[nloc+i] /= PetscSqrtReal(np);
    261:       }
    262:       PetscCall(VecResetArray(t2));
    263:       PetscCall(VecRestoreArray(v2,&array2));
    264:       PetscCall(BVRestoreColumn(pjd->TV[pp],col,&v2));
    265:     }
    266:     PetscCall(VecResetArray(t1));
    267:     PetscCall(VecRestoreArray(v1,&array1));
    268:     PetscCall(BVRestoreColumn(pjd->V,col,&v1));
    269:   }
    270:   if (nconv) PetscCall(MatDestroy(&T));
    271:   PetscCall(PetscFree5(x2,xx,pT,N,Np));
    272:   PetscFunctionReturn(PETSC_SUCCESS);
    273: }

    275: /*
    276:    RRQR of X. Xin*P=Xou*R. Rank of R is rk
    277: */
    278: static PetscErrorCode PEPJDOrthogonalize(PetscInt row,PetscInt col,PetscScalar *X,PetscInt ldx,PetscInt *rk,PetscInt *P,PetscScalar *R,PetscInt ldr)
    279: {
    280:   PetscInt       i,j,n,r;
    281:   PetscBLASInt   row_,col_,ldx_,*p,lwork,info,n_;
    282:   PetscScalar    *tau,*work;
    283:   PetscReal      tol,*rwork;

    285:   PetscFunctionBegin;
    286:   PetscCall(PetscBLASIntCast(row,&row_));
    287:   PetscCall(PetscBLASIntCast(col,&col_));
    288:   PetscCall(PetscBLASIntCast(ldx,&ldx_));
    289:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    290:   n = PetscMin(row,col);
    291:   PetscCall(PetscBLASIntCast(n,&n_));
    292:   lwork = 3*col_+1;
    293:   PetscCall(PetscMalloc4(col,&p,n,&tau,lwork,&work,2*col,&rwork));
    294:   for (i=1;i<col;i++) p[i] = 0;
    295:   p[0] = 1;

    297:   /* rank revealing QR */
    298: #if defined(PETSC_USE_COMPLEX)
    299:   PetscCallBLAS("LAPACKgeqp3",LAPACKgeqp3_(&row_,&col_,X,&ldx_,p,tau,work,&lwork,rwork,&info));
    300: #else
    301:   PetscCallBLAS("LAPACKgeqp3",LAPACKgeqp3_(&row_,&col_,X,&ldx_,p,tau,work,&lwork,&info));
    302: #endif
    303:   SlepcCheckLapackInfo("geqp3",info);
    304:   if (P) for (i=0;i<col;i++) P[i] = p[i]-1;

    306:   /* rank computation */
    307:   tol = PetscMax(row,col)*PETSC_MACHINE_EPSILON*PetscAbsScalar(X[0]);
    308:   r = 1;
    309:   for (i=1;i<n;i++) {
    310:     if (PetscAbsScalar(X[i+ldx*i])>tol) r++;
    311:     else break;
    312:   }
    313:   if (rk) *rk=r;

    315:   /* copy upper triangular matrix if requested */
    316:   if (R) {
    317:      for (i=0;i<r;i++) {
    318:        PetscCall(PetscArrayzero(R+i*ldr,r));
    319:        for (j=0;j<=i;j++) R[i*ldr+j] = X[i*ldx+j];
    320:      }
    321:   }
    322:   PetscCallBLAS("LAPACKorgqr",LAPACKorgqr_(&row_,&n_,&n_,X,&ldx_,tau,work,&lwork,&info));
    323:   SlepcCheckLapackInfo("orgqr",info);
    324:   PetscCall(PetscFPTrapPop());
    325:   PetscCall(PetscFree4(p,tau,work,rwork));
    326:   PetscFunctionReturn(PETSC_SUCCESS);
    327: }

    329: /*
    330:    Application of extended preconditioner
    331: */
    332: static PetscErrorCode PEPJDExtendedPCApply(PC pc,Vec x,Vec y)
    333: {
    334:   PetscInt          i,j,nloc,n,ld=0;
    335:   PetscMPIInt       np;
    336:   Vec               tx,ty;
    337:   PEP_JD_PCSHELL    *ctx;
    338:   const PetscScalar *array1;
    339:   PetscScalar       *x2=NULL,*t=NULL,*ps=NULL,*array2,zero=0.0,sone=1.0;
    340:   PetscBLASInt      one=1,ld_,n_,ncv_;
    341:   PEP_JD            *pjd=NULL;

    343:   PetscFunctionBegin;
    344:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pc),&np));
    345:   PetscCall(PCShellGetContext(pc,&ctx));
    346:   n  = ctx->n;
    347:   if (n) {
    348:     pjd = (PEP_JD*)ctx->pep->data;
    349:     ps = ctx->ps;
    350:     ld = pjd->ld;
    351:     PetscCall(PetscMalloc2(n,&x2,n,&t));
    352:     PetscCall(VecGetLocalSize(ctx->work[0],&nloc));
    353:     PetscCall(VecGetArrayRead(x,&array1));
    354:     for (i=0;i<n;i++) x2[i] = array1[nloc+i]* PetscSqrtReal(np);
    355:     PetscCall(VecRestoreArrayRead(x,&array1));
    356:   }

    358:   /* y = B\x apply PC */
    359:   tx = ctx->work[0];
    360:   ty = ctx->work[1];
    361:   PetscCall(VecGetArrayRead(x,&array1));
    362:   PetscCall(VecPlaceArray(tx,array1));
    363:   PetscCall(VecGetArray(y,&array2));
    364:   PetscCall(VecPlaceArray(ty,array2));
    365:   PetscCall(PCApply(ctx->pc,tx,ty));
    366:   if (n) {
    367:     PetscCall(PetscBLASIntCast(ld,&ld_));
    368:     PetscCall(PetscBLASIntCast(n,&n_));
    369:     for (i=0;i<n;i++) {
    370:       t[i] = 0.0;
    371:       for (j=0;j<n;j++) t[i] += ctx->M[i+j*ld]*x2[j];
    372:     }
    373:     if (pjd->midx==1) {
    374:       PetscCall(PetscBLASIntCast(ctx->pep->ncv,&ncv_));
    375:       for (i=0;i<n;i++) pjd->T[i*(1+ctx->pep->ncv)] -= ctx->theta;
    376:       PetscCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,pjd->T,&ncv_,t,&one,&zero,x2,&one));
    377:       for (i=0;i<n;i++) pjd->T[i*(1+ctx->pep->ncv)] += ctx->theta;
    378:       for (i=0;i<n;i++) array2[nloc+i] = x2[i];
    379:       for (i=0;i<n;i++) x2[i] = -t[i];
    380:     } else {
    381:       for (i=0;i<n;i++) array2[nloc+i] = t[i];
    382:       PetscCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,ps,&ld_,t,&one,&zero,x2,&one));
    383:     }
    384:     for (i=0;i<n;i++) array2[nloc+i] /= PetscSqrtReal(np);
    385:     PetscCall(BVSetActiveColumns(pjd->X,0,n));
    386:     PetscCall(BVMultVec(pjd->X,-1.0,1.0,ty,x2));
    387:     PetscCall(PetscFree2(x2,t));
    388:   }
    389:   PetscCall(VecResetArray(tx));
    390:   PetscCall(VecResetArray(ty));
    391:   PetscCall(VecRestoreArrayRead(x,&array1));
    392:   PetscCall(VecRestoreArray(y,&array2));
    393:   PetscFunctionReturn(PETSC_SUCCESS);
    394: }

    396: /*
    397:    Application of shell preconditioner:
    398:       y = B\x - eta*B\p,  with eta = (u'*B\x)/(u'*B\p)
    399: */
    400: static PetscErrorCode PCShellApply_PEPJD(PC pc,Vec x,Vec y)
    401: {
    402:   PetscScalar    rr,eta;
    403:   PEP_JD_PCSHELL *ctx;
    404:   PetscInt       sz;
    405:   const Vec      *xs,*ys;
    406: #if !defined(PETSC_USE_COMPLEX)
    407:   PetscScalar    rx,xr,xx;
    408: #endif

    410:   PetscFunctionBegin;
    411:   PetscCall(PCShellGetContext(pc,&ctx));
    412:   PetscCall(VecCompGetSubVecs(x,&sz,&xs));
    413:   PetscCall(VecCompGetSubVecs(y,NULL,&ys));
    414:   /* y = B\x apply extended PC */
    415:   PetscCall(PEPJDExtendedPCApply(pc,xs[0],ys[0]));
    416: #if !defined(PETSC_USE_COMPLEX)
    417:   if (sz==2) PetscCall(PEPJDExtendedPCApply(pc,xs[1],ys[1]));
    418: #endif

    420:   /* Compute eta = u'*y / u'*Bp */
    421:   PetscCall(VecDot(ys[0],ctx->u[0],&rr));
    422:   eta  = -rr*ctx->gamma[0];
    423: #if !defined(PETSC_USE_COMPLEX)
    424:   if (sz==2) {
    425:     PetscCall(VecDot(ys[0],ctx->u[1],&xr));
    426:     PetscCall(VecDot(ys[1],ctx->u[0],&rx));
    427:     PetscCall(VecDot(ys[1],ctx->u[1],&xx));
    428:     eta += -ctx->gamma[0]*xx-ctx->gamma[1]*(-xr+rx);
    429:   }
    430: #endif
    431:   eta /= ctx->gamma[0]*ctx->gamma[0]+ctx->gamma[1]*ctx->gamma[1];

    433:   /* y = y - eta*Bp */
    434:   PetscCall(VecAXPY(ys[0],eta,ctx->Bp[0]));
    435: #if !defined(PETSC_USE_COMPLEX)
    436:   if (sz==2) {
    437:     PetscCall(VecAXPY(ys[1],eta,ctx->Bp[1]));
    438:     eta = -ctx->gamma[1]*(rr+xx)+ctx->gamma[0]*(-xr+rx);
    439:     eta /= ctx->gamma[0]*ctx->gamma[0]+ctx->gamma[1]*ctx->gamma[1];
    440:     PetscCall(VecAXPY(ys[0],eta,ctx->Bp[1]));
    441:     PetscCall(VecAXPY(ys[1],-eta,ctx->Bp[0]));
    442:   }
    443: #endif
    444:   PetscFunctionReturn(PETSC_SUCCESS);
    445: }

    447: static PetscErrorCode PEPJDCopyToExtendedVec(PEP pep,Vec v,PetscScalar *a,PetscInt na,PetscInt off,Vec vex,PetscBool back)
    448: {
    449:   PetscMPIInt    np,rk,count;
    450:   PetscScalar    *array1,*array2;
    451:   PetscInt       nloc;

    453:   PetscFunctionBegin;
    454:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pep),&rk));
    455:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pep),&np));
    456:   PetscCall(BVGetSizes(pep->V,&nloc,NULL,NULL));
    457:   if (v) {
    458:     PetscCall(VecGetArray(v,&array1));
    459:     PetscCall(VecGetArray(vex,&array2));
    460:     if (back) PetscCall(PetscArraycpy(array1,array2,nloc));
    461:     else PetscCall(PetscArraycpy(array2,array1,nloc));
    462:     PetscCall(VecRestoreArray(v,&array1));
    463:     PetscCall(VecRestoreArray(vex,&array2));
    464:   }
    465:   if (a) {
    466:     PetscCall(VecGetArray(vex,&array2));
    467:     if (back) {
    468:       PetscCall(PetscArraycpy(a,array2+nloc+off,na));
    469:       PetscCall(PetscMPIIntCast(na,&count));
    470:       PetscCallMPI(MPI_Bcast(a,count,MPIU_SCALAR,np-1,PetscObjectComm((PetscObject)pep)));
    471:     } else {
    472:       PetscCall(PetscArraycpy(array2+nloc+off,a,na));
    473:       PetscCall(PetscMPIIntCast(na,&count));
    474:       PetscCallMPI(MPI_Bcast(array2+nloc+off,count,MPIU_SCALAR,np-1,PetscObjectComm((PetscObject)pep)));
    475:     }
    476:     PetscCall(VecRestoreArray(vex,&array2));
    477:   }
    478:   PetscFunctionReturn(PETSC_SUCCESS);
    479: }

    481: /* Computes Phi^hat(lambda) times a vector or its derivative (depends on beval)
    482:      if no vector is provided returns a matrix
    483:  */
    484: static PetscErrorCode PEPJDEvaluateHatBasis(PEP pep,PetscInt n,PetscScalar *H,PetscInt ldh,PetscScalar *beval,PetscScalar *t,PetscInt idx,PetscScalar *qpp,PetscScalar *qp,PetscScalar *q)
    485: {
    486:   PetscInt       j,i;
    487:   PetscBLASInt   n_,ldh_,one=1;
    488:   PetscReal      *a,*b,*g;
    489:   PetscScalar    sone=1.0,zero=0.0;

    491:   PetscFunctionBegin;
    492:   a = pep->pbc; b=a+pep->nmat; g=b+pep->nmat;
    493:   PetscCall(PetscBLASIntCast(n,&n_));
    494:   PetscCall(PetscBLASIntCast(ldh,&ldh_));
    495:   if (idx<1) PetscCall(PetscArrayzero(q,t?n:n*n));
    496:   else if (idx==1) {
    497:     if (t) {for (j=0;j<n;j++) q[j] = t[j]*beval[idx-1]/a[0];}
    498:     else {
    499:       PetscCall(PetscArrayzero(q,n*n));
    500:       for (j=0;j<n;j++) q[(j+1)*n] = beval[idx-1]/a[0];
    501:     }
    502:   } else {
    503:     if (t) {
    504:       PetscCallBLAS("BLASgemv",BLASgemv_("N",&n_,&n_,&sone,H,&ldh_,qp,&one,&zero,q,&one));
    505:       for (j=0;j<n;j++) {
    506:         q[j] += beval[idx-1]*t[j]-b[idx-1]*qp[j]-g[idx-1]*qpp[j];
    507:         q[j] /= a[idx-1];
    508:       }
    509:     } else {
    510:       PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,H,&ldh_,qp,&n_,&zero,q,&n_));
    511:       for (j=0;j<n;j++) {
    512:         q[j+n*j] += beval[idx-1];
    513:         for (i=0;i<n;i++) {
    514:           q[i+n*j] += -b[idx-1]*qp[j*n+i]-g[idx-1]*qpp[j*n+i];
    515:           q[i+n*j] /= a[idx-1];
    516:         }
    517:       }
    518:     }
    519:   }
    520:   PetscFunctionReturn(PETSC_SUCCESS);
    521: }

    523: static PetscErrorCode PEPJDComputeResidual(PEP pep,PetscBool derivative,PetscInt sz,Vec *u,PetscScalar *theta,Vec *p,Vec *work)
    524: {
    525:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    526:   PetscMPIInt    rk,np,count;
    527:   Vec            tu,tp,w;
    528:   PetscScalar    *dval,*dvali,*array1,*array2,*x2=NULL,*y2,*qj=NULL,*tt=NULL,*xx=NULL,*xxi=NULL,sone=1.0;
    529:   PetscInt       i,j,nconv,nloc;
    530:   PetscBLASInt   n,ld,one=1;
    531: #if !defined(PETSC_USE_COMPLEX)
    532:   Vec            tui=NULL,tpi=NULL;
    533:   PetscScalar    *x2i=NULL,*qji=NULL,*qq,*y2i,*arrayi1,*arrayi2;
    534: #endif

    536:   PetscFunctionBegin;
    537:   nconv = pjd->nlock;
    538:   if (!nconv) PetscCall(PetscMalloc1(2*sz*pep->nmat,&dval));
    539:   else {
    540:     PetscCall(PetscMalloc5(2*pep->nmat,&dval,2*nconv,&xx,nconv,&tt,sz*nconv,&x2,(sz==2?3:1)*nconv*pep->nmat,&qj));
    541:     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pep),&rk));
    542:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pep),&np));
    543:     PetscCall(BVGetSizes(pep->V,&nloc,NULL,NULL));
    544:     PetscCall(VecGetArray(u[0],&array1));
    545:     for (i=0;i<nconv;i++) x2[i] = array1[nloc+i]*PetscSqrtReal(np);
    546:     PetscCall(VecRestoreArray(u[0],&array1));
    547: #if !defined(PETSC_USE_COMPLEX)
    548:     if (sz==2) {
    549:       x2i = x2+nconv;
    550:       PetscCall(VecGetArray(u[1],&arrayi1));
    551:       for (i=0;i<nconv;i++) x2i[i] = arrayi1[nloc+i]*PetscSqrtReal(np);
    552:       PetscCall(VecRestoreArray(u[1],&arrayi1));
    553:     }
    554: #endif
    555:   }
    556:   dvali = dval+pep->nmat;
    557:   tu = work[0];
    558:   tp = work[1];
    559:   w  = work[2];
    560:   PetscCall(VecGetArray(u[0],&array1));
    561:   PetscCall(VecPlaceArray(tu,array1));
    562:   PetscCall(VecGetArray(p[0],&array2));
    563:   PetscCall(VecPlaceArray(tp,array2));
    564:   PetscCall(VecSet(tp,0.0));
    565: #if !defined(PETSC_USE_COMPLEX)
    566:   if (sz==2) {
    567:     tui = work[3];
    568:     tpi = work[4];
    569:     PetscCall(VecGetArray(u[1],&arrayi1));
    570:     PetscCall(VecPlaceArray(tui,arrayi1));
    571:     PetscCall(VecGetArray(p[1],&arrayi2));
    572:     PetscCall(VecPlaceArray(tpi,arrayi2));
    573:     PetscCall(VecSet(tpi,0.0));
    574:   }
    575: #endif
    576:   if (derivative) PetscCall(PEPEvaluateBasisDerivative(pep,theta[0],theta[1],dval,dvali));
    577:   else PetscCall(PEPEvaluateBasis(pep,theta[0],theta[1],dval,dvali));
    578:   for (i=derivative?1:0;i<pep->nmat;i++) {
    579:     PetscCall(MatMult(pep->A[i],tu,w));
    580:     PetscCall(VecAXPY(tp,dval[i],w));
    581: #if !defined(PETSC_USE_COMPLEX)
    582:     if (sz==2) {
    583:       PetscCall(VecAXPY(tpi,dvali[i],w));
    584:       PetscCall(MatMult(pep->A[i],tui,w));
    585:       PetscCall(VecAXPY(tpi,dval[i],w));
    586:       PetscCall(VecAXPY(tp,-dvali[i],w));
    587:     }
    588: #endif
    589:   }
    590:   if (nconv) {
    591:     for (i=0;i<pep->nmat;i++) PetscCall(PEPJDEvaluateHatBasis(pep,nconv,pjd->T,pep->ncv,dval,x2,i,i>1?qj+(i-2)*nconv:NULL,i>0?qj+(i-1)*nconv:NULL,qj+i*nconv));
    592: #if !defined(PETSC_USE_COMPLEX)
    593:     if (sz==2) {
    594:       qji = qj+nconv*pep->nmat;
    595:       qq = qji+nconv*pep->nmat;
    596:       for (i=0;i<pep->nmat;i++) PetscCall(PEPJDEvaluateHatBasis(pep,nconv,pjd->T,pep->ncv,dvali,x2i,i,i>1?qji+(i-2)*nconv:NULL,i>0?qji+(i-1)*nconv:NULL,qji+i*nconv));
    597:       for (i=0;i<nconv*pep->nmat;i++) qj[i] -= qji[i];
    598:       for (i=0;i<pep->nmat;i++) {
    599:         PetscCall(PEPJDEvaluateHatBasis(pep,nconv,pjd->T,pep->ncv,dval,x2i,i,i>1?qji+(i-2)*nconv:NULL,i>0?qji+(i-1)*nconv:NULL,qji+i*nconv));
    600:         PetscCall(PEPJDEvaluateHatBasis(pep,nconv,pjd->T,pep->ncv,dvali,x2,i,i>1?qq+(i-2)*nconv:NULL,i>0?qq+(i-1)*nconv:NULL,qq+i*nconv));
    601:       }
    602:       for (i=0;i<nconv*pep->nmat;i++) qji[i] += qq[i];
    603:       for (i=derivative?2:1;i<pep->nmat;i++) PetscCall(BVMultVec(pjd->AX[i],1.0,1.0,tpi,qji+i*nconv));
    604:     }
    605: #endif
    606:     for (i=derivative?2:1;i<pep->nmat;i++) PetscCall(BVMultVec(pjd->AX[i],1.0,1.0,tp,qj+i*nconv));

    608:     /* extended vector part */
    609:     PetscCall(BVSetActiveColumns(pjd->X,0,nconv));
    610:     PetscCall(BVDotVec(pjd->X,tu,xx));
    611:     xxi = xx+nconv;
    612: #if !defined(PETSC_USE_COMPLEX)
    613:     if (sz==2) PetscCall(BVDotVec(pjd->X,tui,xxi));
    614: #endif
    615:     if (sz==1) PetscCall(PetscArrayzero(xxi,nconv));
    616:     if (rk==np-1) {
    617:       PetscCall(PetscBLASIntCast(nconv,&n));
    618:       PetscCall(PetscBLASIntCast(pjd->ld,&ld));
    619:       y2  = array2+nloc;
    620:       PetscCall(PetscArrayzero(y2,nconv));
    621:       for (j=derivative?1:0;j<pjd->midx;j++) {
    622:         for (i=0;i<nconv;i++) tt[i] = dval[j]*xx[i]-dvali[j]*xxi[i];
    623:         PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,pjd->XpX,&ld,qj+j*nconv,&one,&sone,tt,&one));
    624:         PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&sone,pjd->Tj+j*ld*ld,&ld,tt,&one,&sone,y2,&one));
    625:       }
    626:       for (i=0;i<nconv;i++) array2[nloc+i] /= PetscSqrtReal(np);
    627: #if !defined(PETSC_USE_COMPLEX)
    628:       if (sz==2) {
    629:         y2i = arrayi2+nloc;
    630:         PetscCall(PetscArrayzero(y2i,nconv));
    631:         for (j=derivative?1:0;j<pjd->midx;j++) {
    632:           for (i=0;i<nconv;i++) tt[i] = dval[j]*xxi[i]+dvali[j]*xx[i];
    633:           PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,pjd->XpX,&ld,qji+j*nconv,&one,&sone,tt,&one));
    634:           PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&sone,pjd->Tj+j*ld*ld,&ld,tt,&one,&sone,y2i,&one));
    635:         }
    636:         for (i=0;i<nconv;i++) arrayi2[nloc+i] /= PetscSqrtReal(np);
    637:       }
    638: #endif
    639:     }
    640:     PetscCall(PetscMPIIntCast(nconv,&count));
    641:     PetscCallMPI(MPI_Bcast(array2+nloc,count,MPIU_SCALAR,np-1,PetscObjectComm((PetscObject)pep)));
    642: #if !defined(PETSC_USE_COMPLEX)
    643:     if (sz==2) PetscCallMPI(MPI_Bcast(arrayi2+nloc,count,MPIU_SCALAR,np-1,PetscObjectComm((PetscObject)pep)));
    644: #endif
    645:   }
    646:   if (nconv) PetscCall(PetscFree5(dval,xx,tt,x2,qj));
    647:   else PetscCall(PetscFree(dval));
    648:   PetscCall(VecResetArray(tu));
    649:   PetscCall(VecRestoreArray(u[0],&array1));
    650:   PetscCall(VecResetArray(tp));
    651:   PetscCall(VecRestoreArray(p[0],&array2));
    652: #if !defined(PETSC_USE_COMPLEX)
    653:   if (sz==2) {
    654:     PetscCall(VecResetArray(tui));
    655:     PetscCall(VecRestoreArray(u[1],&arrayi1));
    656:     PetscCall(VecResetArray(tpi));
    657:     PetscCall(VecRestoreArray(p[1],&arrayi2));
    658:   }
    659: #endif
    660:   PetscFunctionReturn(PETSC_SUCCESS);
    661: }

    663: static PetscErrorCode PEPJDProcessInitialSpace(PEP pep,Vec *w)
    664: {
    665:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    666:   PetscScalar    *tt,target[2];
    667:   Vec            vg,wg;
    668:   PetscInt       i;
    669:   PetscReal      norm;

    671:   PetscFunctionBegin;
    672:   PetscCall(PetscMalloc1(pjd->ld-1,&tt));
    673:   PetscCheck(pep->nini==0,PETSC_COMM_SELF,PETSC_ERR_SUP,"Support for initial vectors not implemented yet");
    674:   PetscCall(BVSetRandomColumn(pjd->V,0));
    675:   for (i=0;i<pjd->ld-1;i++) tt[i] = 0.0;
    676:   PetscCall(BVGetColumn(pjd->V,0,&vg));
    677:   PetscCall(PEPJDCopyToExtendedVec(pep,NULL,tt,pjd->ld-1,0,vg,PETSC_FALSE));
    678:   PetscCall(BVRestoreColumn(pjd->V,0,&vg));
    679:   PetscCall(BVNormColumn(pjd->V,0,NORM_2,&norm));
    680:   PetscCall(BVScaleColumn(pjd->V,0,1.0/norm));
    681:   if (pjd->proj==PEP_JD_PROJECTION_HARMONIC) {
    682:     PetscCall(BVGetColumn(pjd->V,0,&vg));
    683:     PetscCall(BVGetColumn(pjd->W,0,&wg));
    684:     PetscCall(VecSet(wg,0.0));
    685:     target[0] = pep->target; target[1] = 0.0;
    686:     PetscCall(PEPJDComputeResidual(pep,PETSC_TRUE,1,&vg,target,&wg,w));
    687:     PetscCall(BVRestoreColumn(pjd->W,0,&wg));
    688:     PetscCall(BVRestoreColumn(pjd->V,0,&vg));
    689:     PetscCall(BVNormColumn(pjd->W,0,NORM_2,&norm));
    690:     PetscCall(BVScaleColumn(pjd->W,0,1.0/norm));
    691:   }
    692:   PetscCall(PetscFree(tt));
    693:   PetscFunctionReturn(PETSC_SUCCESS);
    694: }

    696: static PetscErrorCode MatMult_PEPJD(Mat P,Vec x,Vec y)
    697: {
    698:   PEP_JD_MATSHELL *matctx;
    699:   PEP_JD          *pjd;
    700:   PetscInt        i,j,nconv,nloc,nmat,ldt,ncv,sz;
    701:   Vec             tx,ty;
    702:   const Vec       *xs,*ys;
    703:   PetscScalar     *array1,*array2,*x2=NULL,*y2,*tt=NULL,*xx=NULL,*xxi,theta[2],sone=1.0,*qj,*val,*vali=NULL;
    704:   PetscBLASInt    n,ld,one=1;
    705:   PetscMPIInt     np;
    706: #if !defined(PETSC_USE_COMPLEX)
    707:   Vec             txi=NULL,tyi=NULL;
    708:   PetscScalar     *x2i=NULL,*qji=NULL,*qq,*y2i,*arrayi1,*arrayi2;
    709: #endif

    711:   PetscFunctionBegin;
    712:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)P),&np));
    713:   PetscCall(MatShellGetContext(P,&matctx));
    714:   pjd   = (PEP_JD*)matctx->pep->data;
    715:   nconv = pjd->nlock;
    716:   nmat  = matctx->pep->nmat;
    717:   ncv   = matctx->pep->ncv;
    718:   ldt   = pjd->ld;
    719:   PetscCall(VecCompGetSubVecs(x,&sz,&xs));
    720:   PetscCall(VecCompGetSubVecs(y,NULL,&ys));
    721:   theta[0] = matctx->theta[0];
    722:   theta[1] = (sz==2)?matctx->theta[1]:0.0;
    723:   if (nconv>0) {
    724:     PetscCall(PetscMalloc5(nconv,&tt,sz*nconv,&x2,(sz==2?3:1)*nconv*nmat,&qj,2*nconv,&xx,2*nmat,&val));
    725:     PetscCall(BVGetSizes(matctx->pep->V,&nloc,NULL,NULL));
    726:     PetscCall(VecGetArray(xs[0],&array1));
    727:     for (i=0;i<nconv;i++) x2[i] = array1[nloc+i]* PetscSqrtReal(np);
    728:     PetscCall(VecRestoreArray(xs[0],&array1));
    729: #if !defined(PETSC_USE_COMPLEX)
    730:     if (sz==2) {
    731:       x2i = x2+nconv;
    732:       PetscCall(VecGetArray(xs[1],&arrayi1));
    733:       for (i=0;i<nconv;i++) x2i[i] = arrayi1[nloc+i]* PetscSqrtReal(np);
    734:       PetscCall(VecRestoreArray(xs[1],&arrayi1));
    735:     }
    736: #endif
    737:     vali = val+nmat;
    738:   }
    739:   tx = matctx->work[0];
    740:   ty = matctx->work[1];
    741:   PetscCall(VecGetArray(xs[0],&array1));
    742:   PetscCall(VecPlaceArray(tx,array1));
    743:   PetscCall(VecGetArray(ys[0],&array2));
    744:   PetscCall(VecPlaceArray(ty,array2));
    745:   PetscCall(MatMult(matctx->Pr,tx,ty));
    746: #if !defined(PETSC_USE_COMPLEX)
    747:   if (sz==2) {
    748:     txi = matctx->work[2];
    749:     tyi = matctx->work[3];
    750:     PetscCall(VecGetArray(xs[1],&arrayi1));
    751:     PetscCall(VecPlaceArray(txi,arrayi1));
    752:     PetscCall(VecGetArray(ys[1],&arrayi2));
    753:     PetscCall(VecPlaceArray(tyi,arrayi2));
    754:     PetscCall(MatMult(matctx->Pr,txi,tyi));
    755:     if (theta[1]!=0.0) {
    756:       PetscCall(MatMult(matctx->Pi,txi,matctx->work[4]));
    757:       PetscCall(VecAXPY(ty,-1.0,matctx->work[4]));
    758:       PetscCall(MatMult(matctx->Pi,tx,matctx->work[4]));
    759:       PetscCall(VecAXPY(tyi,1.0,matctx->work[4]));
    760:     }
    761:   }
    762: #endif
    763:   if (nconv>0) {
    764:     PetscCall(PEPEvaluateBasis(matctx->pep,theta[0],theta[1],val,vali));
    765:     for (i=0;i<nmat;i++) PetscCall(PEPJDEvaluateHatBasis(matctx->pep,nconv,pjd->T,ncv,val,x2,i,i>1?qj+(i-2)*nconv:NULL,i>0?qj+(i-1)*nconv:NULL,qj+i*nconv));
    766: #if !defined(PETSC_USE_COMPLEX)
    767:     if (sz==2) {
    768:       qji = qj+nconv*nmat;
    769:       qq = qji+nconv*nmat;
    770:       for (i=0;i<nmat;i++) PetscCall(PEPJDEvaluateHatBasis(matctx->pep,nconv,pjd->T,matctx->pep->ncv,vali,x2i,i,i>1?qji+(i-2)*nconv:NULL,i>0?qji+(i-1)*nconv:NULL,qji+i*nconv));
    771:       for (i=0;i<nconv*nmat;i++) qj[i] -= qji[i];
    772:       for (i=0;i<nmat;i++) {
    773:         PetscCall(PEPJDEvaluateHatBasis(matctx->pep,nconv,pjd->T,matctx->pep->ncv,val,x2i,i,i>1?qji+(i-2)*nconv:NULL,i>0?qji+(i-1)*nconv:NULL,qji+i*nconv));
    774:         PetscCall(PEPJDEvaluateHatBasis(matctx->pep,nconv,pjd->T,matctx->pep->ncv,vali,x2,i,i>1?qq+(i-2)*nconv:NULL,i>0?qq+(i-1)*nconv:NULL,qq+i*nconv));
    775:       }
    776:       for (i=0;i<nconv*nmat;i++) qji[i] += qq[i];
    777:       for (i=1;i<matctx->pep->nmat;i++) PetscCall(BVMultVec(pjd->AX[i],1.0,1.0,tyi,qji+i*nconv));
    778:     }
    779: #endif
    780:     for (i=1;i<nmat;i++) PetscCall(BVMultVec(pjd->AX[i],1.0,1.0,ty,qj+i*nconv));

    782:     /* extended vector part */
    783:     PetscCall(BVSetActiveColumns(pjd->X,0,nconv));
    784:     PetscCall(BVDotVec(pjd->X,tx,xx));
    785:     xxi = xx+nconv;
    786: #if !defined(PETSC_USE_COMPLEX)
    787:     if (sz==2) PetscCall(BVDotVec(pjd->X,txi,xxi));
    788: #endif
    789:     if (sz==1) PetscCall(PetscArrayzero(xxi,nconv));
    790:     PetscCall(PetscBLASIntCast(pjd->nlock,&n));
    791:     PetscCall(PetscBLASIntCast(ldt,&ld));
    792:     y2 = array2+nloc;
    793:     PetscCall(PetscArrayzero(y2,nconv));
    794:     for (j=0;j<pjd->midx;j++) {
    795:       for (i=0;i<nconv;i++) tt[i] = val[j]*xx[i]-vali[j]*xxi[i];
    796:       PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,pjd->XpX,&ld,qj+j*nconv,&one,&sone,tt,&one));
    797:       PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&sone,pjd->Tj+j*ld*ld,&ld,tt,&one,&sone,y2,&one));
    798:     }
    799: #if !defined(PETSC_USE_COMPLEX)
    800:     if (sz==2) {
    801:       y2i = arrayi2+nloc;
    802:       PetscCall(PetscArrayzero(y2i,nconv));
    803:       for (j=0;j<pjd->midx;j++) {
    804:         for (i=0;i<nconv;i++) tt[i] = val[j]*xxi[i]+vali[j]*xx[i];
    805:         PetscCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&sone,pjd->XpX,&ld,qji+j*nconv,&one,&sone,tt,&one));
    806:         PetscCallBLAS("BLASgemv",BLASgemv_("C",&n,&n,&sone,pjd->Tj+j*ld*ld,&ld,tt,&one,&sone,y2i,&one));
    807:       }
    808:       for (i=0;i<nconv;i++) arrayi2[nloc+i] /= PetscSqrtReal(np);
    809:     }
    810: #endif
    811:     for (i=0;i<nconv;i++) array2[nloc+i] /= PetscSqrtReal(np);
    812:     PetscCall(PetscFree5(tt,x2,qj,xx,val));
    813:   }
    814:   PetscCall(VecResetArray(tx));
    815:   PetscCall(VecRestoreArray(xs[0],&array1));
    816:   PetscCall(VecResetArray(ty));
    817:   PetscCall(VecRestoreArray(ys[0],&array2));
    818: #if !defined(PETSC_USE_COMPLEX)
    819:   if (sz==2) {
    820:     PetscCall(VecResetArray(txi));
    821:     PetscCall(VecRestoreArray(xs[1],&arrayi1));
    822:     PetscCall(VecResetArray(tyi));
    823:     PetscCall(VecRestoreArray(ys[1],&arrayi2));
    824:   }
    825: #endif
    826:   PetscFunctionReturn(PETSC_SUCCESS);
    827: }

    829: static PetscErrorCode MatCreateVecs_PEPJD(Mat A,Vec *right,Vec *left)
    830: {
    831:   PEP_JD_MATSHELL *matctx;
    832:   PEP_JD          *pjd;
    833:   PetscInt        kspsf=1,i;
    834:   Vec             v[2];

    836:   PetscFunctionBegin;
    837:   PetscCall(MatShellGetContext(A,&matctx));
    838:   pjd   = (PEP_JD*)matctx->pep->data;
    839: #if !defined (PETSC_USE_COMPLEX)
    840:   kspsf = 2;
    841: #endif
    842:   for (i=0;i<kspsf;i++) PetscCall(BVCreateVec(pjd->V,v+i));
    843:   if (right) PetscCall(VecCreateCompWithVecs(v,kspsf,pjd->vtempl,right));
    844:   if (left) PetscCall(VecCreateCompWithVecs(v,kspsf,pjd->vtempl,left));
    845:   for (i=0;i<kspsf;i++) PetscCall(VecDestroy(&v[i]));
    846:   PetscFunctionReturn(PETSC_SUCCESS);
    847: }

    849: static PetscErrorCode PEPJDUpdateExtendedPC(PEP pep,PetscScalar theta)
    850: {
    851:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    852:   PEP_JD_PCSHELL *pcctx;
    853:   PetscInt       i,j,k,n=pjd->nlock,ld=pjd->ld,deg=pep->nmat-1;
    854:   PetscScalar    *M,*ps,*work,*U,*V,*S,*Sp,*Spp,snone=-1.0,sone=1.0,zero=0.0,*val;
    855:   PetscReal      tol,maxeig=0.0,*sg,*rwork;
    856:   PetscBLASInt   n_,info,ld_,*p,lw_,rk=0;

    858:   PetscFunctionBegin;
    859:   if (n) {
    860:     PetscCall(PCShellGetContext(pjd->pcshell,&pcctx));
    861:     pcctx->theta = theta;
    862:     pcctx->n = n;
    863:     M  = pcctx->M;
    864:     PetscCall(PetscBLASIntCast(n,&n_));
    865:     PetscCall(PetscBLASIntCast(ld,&ld_));
    866:     PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    867:     if (pjd->midx==1) {
    868:       PetscCall(PetscArraycpy(M,pjd->XpX,ld*ld));
    869:       PetscCall(PetscCalloc2(10*n,&work,n,&p));
    870:     } else {
    871:       ps = pcctx->ps;
    872:       PetscCall(PetscCalloc7(2*n*n,&U,3*n*n,&S,n,&sg,10*n,&work,5*n,&rwork,n,&p,deg+1,&val));
    873:       V = U+n*n;
    874:       /* pseudo-inverse */
    875:       for (j=0;j<n;j++) {
    876:         for (i=0;i<n;i++) S[n*j+i] = -pjd->T[pep->ncv*j+i];
    877:         S[n*j+j] += theta;
    878:       }
    879:       lw_ = 10*n_;
    880: #if !defined (PETSC_USE_COMPLEX)
    881:       PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&n_,&n_,S,&n_,sg,U,&n_,V,&n_,work,&lw_,&info));
    882: #else
    883:       PetscCallBLAS("LAPACKgesvd",LAPACKgesvd_("S","S",&n_,&n_,S,&n_,sg,U,&n_,V,&n_,work,&lw_,rwork,&info));
    884: #endif
    885:       SlepcCheckLapackInfo("gesvd",info);
    886:       for (i=0;i<n;i++) maxeig = PetscMax(maxeig,sg[i]);
    887:       tol = 10*PETSC_MACHINE_EPSILON*n*maxeig;
    888:       for (j=0;j<n;j++) {
    889:         if (sg[j]>tol) {
    890:           for (i=0;i<n;i++) U[j*n+i] /= sg[j];
    891:           rk++;
    892:         } else break;
    893:       }
    894:       PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&rk,&sone,U,&n_,V,&n_,&zero,ps,&ld_));

    896:       /* compute M */
    897:       PetscCall(PEPEvaluateBasis(pep,theta,0.0,val,NULL));
    898:       PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&snone,pjd->XpX,&ld_,ps,&ld_,&zero,M,&ld_));
    899:       PetscCall(PetscArrayzero(S,2*n*n));
    900:       Sp = S+n*n;
    901:       for (j=0;j<n;j++) S[j*(n+1)] = 1.0;
    902:       for (k=1;k<pjd->midx;k++) {
    903:         for (j=0;j<n;j++) for (i=0;i<n;i++) V[j*n+i] = S[j*n+i] - ps[j*ld+i]*val[k];
    904:         PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,pjd->XpX,&ld_,V,&n_,&zero,U,&n_));
    905:         PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n_,&n_,&n_,&sone,pjd->Tj+k*ld*ld,&ld_,U,&n_,&sone,M,&ld_));
    906:         Spp = Sp; Sp = S;
    907:         PetscCall(PEPJDEvaluateHatBasis(pep,n,pjd->T,pep->ncv,val,NULL,k+1,Spp,Sp,S));
    908:       }
    909:     }
    910:     /* inverse */
    911:     PetscCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n_,&n_,M,&ld_,p,&info));
    912:     SlepcCheckLapackInfo("getrf",info);
    913:     PetscCallBLAS("LAPACKgetri",LAPACKgetri_(&n_,M,&ld_,p,work,&n_,&info));
    914:     SlepcCheckLapackInfo("getri",info);
    915:     PetscCall(PetscFPTrapPop());
    916:     if (pjd->midx==1) PetscCall(PetscFree2(work,p));
    917:     else PetscCall(PetscFree7(U,S,sg,work,rwork,p,val));
    918:   }
    919:   PetscFunctionReturn(PETSC_SUCCESS);
    920: }

    922: static PetscErrorCode PEPJDMatSetUp(PEP pep,PetscInt sz,PetscScalar *theta)
    923: {
    924:   PEP_JD          *pjd = (PEP_JD*)pep->data;
    925:   PEP_JD_MATSHELL *matctx;
    926:   PEP_JD_PCSHELL  *pcctx;
    927:   MatStructure    str;
    928:   PetscScalar     *vals,*valsi;
    929:   PetscBool       skipmat=PETSC_FALSE;
    930:   PetscInt        i;
    931:   Mat             Pr=NULL;

    933:   PetscFunctionBegin;
    934:   if (sz==2 && theta[1]==0.0) sz = 1;
    935:   PetscCall(MatShellGetContext(pjd->Pshell,&matctx));
    936:   PetscCall(PCShellGetContext(pjd->pcshell,&pcctx));
    937:   if (matctx->Pr && matctx->theta[0]==theta[0] && ((!matctx->Pi && sz==1) || (sz==2 && matctx->theta[1]==theta[1]))) {
    938:     if (pcctx->n == pjd->nlock) PetscFunctionReturn(PETSC_SUCCESS);
    939:     skipmat = PETSC_TRUE;
    940:   }
    941:   if (!skipmat) {
    942:     PetscCall(PetscMalloc2(pep->nmat,&vals,pep->nmat,&valsi));
    943:     PetscCall(STGetMatStructure(pep->st,&str));
    944:     PetscCall(PEPEvaluateBasis(pep,theta[0],theta[1],vals,valsi));
    945:     if (!matctx->Pr) PetscCall(MatDuplicate(pep->A[0],MAT_COPY_VALUES,&matctx->Pr));
    946:     else PetscCall(MatCopy(pep->A[0],matctx->Pr,str));
    947:     for (i=1;i<pep->nmat;i++) PetscCall(MatAXPY(matctx->Pr,vals[i],pep->A[i],str));
    948:     if (!pjd->reusepc) {
    949:       if (pcctx->PPr && sz==2) {
    950:         PetscCall(MatCopy(matctx->Pr,pcctx->PPr,str));
    951:         Pr = pcctx->PPr;
    952:       } else Pr = matctx->Pr;
    953:     }
    954:     matctx->theta[0] = theta[0];
    955: #if !defined(PETSC_USE_COMPLEX)
    956:     if (sz==2) {
    957:       if (!matctx->Pi) PetscCall(MatDuplicate(pep->A[0],MAT_COPY_VALUES,&matctx->Pi));
    958:       else PetscCall(MatCopy(pep->A[1],matctx->Pi,str));
    959:       PetscCall(MatScale(matctx->Pi,valsi[1]));
    960:       for (i=2;i<pep->nmat;i++) PetscCall(MatAXPY(matctx->Pi,valsi[i],pep->A[i],str));
    961:       matctx->theta[1] = theta[1];
    962:     }
    963: #endif
    964:     PetscCall(PetscFree2(vals,valsi));
    965:   }
    966:   if (!pjd->reusepc) {
    967:     if (!skipmat) {
    968:       PetscCall(PCSetOperators(pcctx->pc,Pr,Pr));
    969:       PetscCall(PCSetUp(pcctx->pc));
    970:     }
    971:     PetscCall(PEPJDUpdateExtendedPC(pep,theta[0]));
    972:   }
    973:   PetscFunctionReturn(PETSC_SUCCESS);
    974: }

    976: static PetscErrorCode PEPJDCreateShellPC(PEP pep,Vec *ww)
    977: {
    978:   PEP_JD          *pjd = (PEP_JD*)pep->data;
    979:   PEP_JD_PCSHELL  *pcctx;
    980:   PEP_JD_MATSHELL *matctx;
    981:   KSP             ksp;
    982:   PetscInt        nloc,mloc,kspsf=1;
    983:   Vec             v[2];
    984:   PetscScalar     target[2];
    985:   Mat             Pr;

    987:   PetscFunctionBegin;
    988:   /* Create the reference vector */
    989:   PetscCall(BVGetColumn(pjd->V,0,&v[0]));
    990:   v[1] = v[0];
    991: #if !defined (PETSC_USE_COMPLEX)
    992:   kspsf = 2;
    993: #endif
    994:   PetscCall(VecCreateCompWithVecs(v,kspsf,NULL,&pjd->vtempl));
    995:   PetscCall(BVRestoreColumn(pjd->V,0,&v[0]));

    997:   /* Replace preconditioner with one containing projectors */
    998:   PetscCall(PCCreate(PetscObjectComm((PetscObject)pep),&pjd->pcshell));
    999:   PetscCall(PCSetType(pjd->pcshell,PCSHELL));
    1000:   PetscCall(PCShellSetName(pjd->pcshell,"PCPEPJD"));
    1001:   PetscCall(PCShellSetApply(pjd->pcshell,PCShellApply_PEPJD));
    1002:   PetscCall(PetscNew(&pcctx));
    1003:   PetscCall(PCShellSetContext(pjd->pcshell,pcctx));
    1004:   PetscCall(STGetKSP(pep->st,&ksp));
    1005:   PetscCall(BVCreateVec(pjd->V,&pcctx->Bp[0]));
    1006:   PetscCall(VecDuplicate(pcctx->Bp[0],&pcctx->Bp[1]));
    1007:   PetscCall(KSPGetPC(ksp,&pcctx->pc));
    1008:   PetscCall(PetscObjectReference((PetscObject)pcctx->pc));
    1009:   PetscCall(MatGetLocalSize(pep->A[0],&mloc,&nloc));
    1010:   if (pjd->ld>1) {
    1011:     nloc += pjd->ld-1; mloc += pjd->ld-1;
    1012:   }
    1013:   PetscCall(PetscNew(&matctx));
    1014:   PetscCall(MatCreateShell(PetscObjectComm((PetscObject)pep),kspsf*nloc,kspsf*mloc,PETSC_DETERMINE,PETSC_DETERMINE,matctx,&pjd->Pshell));
    1015:   PetscCall(MatShellSetOperation(pjd->Pshell,MATOP_MULT,(PetscErrorCodeFn*)MatMult_PEPJD));
    1016:   PetscCall(MatShellSetOperation(pjd->Pshell,MATOP_CREATE_VECS,(PetscErrorCodeFn*)MatCreateVecs_PEPJD));
    1017:   matctx->pep = pep;
    1018:   target[0] = pep->target; target[1] = 0.0;
    1019:   PetscCall(PEPJDMatSetUp(pep,1,target));
    1020:   Pr = matctx->Pr;
    1021:   pcctx->PPr = NULL;
    1022: #if !defined(PETSC_USE_COMPLEX)
    1023:   if (!pjd->reusepc) {
    1024:     PetscCall(MatDuplicate(matctx->Pr,MAT_COPY_VALUES,&pcctx->PPr));
    1025:     Pr = pcctx->PPr;
    1026:   }
    1027: #endif
    1028:   PetscCall(PCSetOperators(pcctx->pc,Pr,Pr));
    1029:   PetscCall(PCSetErrorIfFailure(pcctx->pc,PETSC_TRUE));
    1030:   PetscCall(KSPSetPC(ksp,pjd->pcshell));
    1031:   if (pjd->reusepc) {
    1032:     PetscCall(PCSetReusePreconditioner(pcctx->pc,PETSC_TRUE));
    1033:     PetscCall(KSPSetReusePreconditioner(ksp,PETSC_TRUE));
    1034:   }
    1035:   PetscCall(PEP_KSPSetOperators(ksp,pjd->Pshell,pjd->Pshell));
    1036:   PetscCall(KSPSetUp(ksp));
    1037:   if (pjd->ld>1) {
    1038:     PetscCall(PetscMalloc2(pjd->ld*pjd->ld,&pcctx->M,pjd->ld*pjd->ld,&pcctx->ps));
    1039:     pcctx->pep = pep;
    1040:   }
    1041:   matctx->work = ww;
    1042:   pcctx->work  = ww;
    1043:   PetscFunctionReturn(PETSC_SUCCESS);
    1044: }

    1046: static PetscErrorCode PEPJDEigenvectors(PEP pep)
    1047: {
    1048:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    1049:   PetscBLASInt   ld,nconv,info,nc;
    1050:   PetscScalar    *Z;
    1051:   PetscReal      *wr;
    1052:   Mat            U;
    1053: #if defined(PETSC_USE_COMPLEX)
    1054:   PetscScalar    *w;
    1055: #endif

    1057:   PetscFunctionBegin;
    1058:   PetscCall(PetscBLASIntCast(pep->ncv,&ld));
    1059:   PetscCall(PetscBLASIntCast(pep->nconv,&nconv));
    1060:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    1061: #if !defined(PETSC_USE_COMPLEX)
    1062:   PetscCall(PetscMalloc2(pep->nconv*pep->nconv,&Z,3*pep->ncv,&wr));
    1063:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_("R","A",NULL,&nconv,pjd->T,&ld,NULL,&nconv,Z,&nconv,&nconv,&nc,wr,&info));
    1064: #else
    1065:   PetscCall(PetscMalloc3(pep->nconv*pep->nconv,&Z,3*pep->ncv,&wr,2*pep->ncv,&w));
    1066:   PetscCallBLAS("LAPACKtrevc",LAPACKtrevc_("R","A",NULL,&nconv,pjd->T,&ld,NULL,&nconv,Z,&nconv,&nconv,&nc,w,wr,&info));
    1067: #endif
    1068:   PetscCall(PetscFPTrapPop());
    1069:   SlepcCheckLapackInfo("trevc",info);
    1070:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nconv,nconv,Z,&U));
    1071:   PetscCall(BVSetActiveColumns(pjd->X,0,pep->nconv));
    1072:   PetscCall(BVMultInPlace(pjd->X,U,0,pep->nconv));
    1073:   PetscCall(BVNormalize(pjd->X,pep->eigi));
    1074:   PetscCall(MatDestroy(&U));
    1075: #if !defined(PETSC_USE_COMPLEX)
    1076:   PetscCall(PetscFree2(Z,wr));
    1077: #else
    1078:   PetscCall(PetscFree3(Z,wr,w));
    1079: #endif
    1080:   PetscFunctionReturn(PETSC_SUCCESS);
    1081: }

    1083: static PetscErrorCode PEPJDLockConverged(PEP pep,PetscInt *nv,PetscInt sz)
    1084: {
    1085:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    1086:   PetscInt       j,i,*P,ldds,rk=0,nvv=*nv;
    1087:   Vec            v,x,w;
    1088:   PetscScalar    *R,*r,*pX,target[2];
    1089:   Mat            X;
    1090:   PetscBLASInt   sz_,rk_,nv_,info;
    1091:   PetscMPIInt    np;

    1093:   PetscFunctionBegin;
    1094:   /* update AX and XpX */
    1095:   for (i=sz;i>0;i--) {
    1096:     PetscCall(BVGetColumn(pjd->X,pjd->nlock-i,&x));
    1097:     for (j=0;j<pep->nmat;j++) {
    1098:       PetscCall(BVGetColumn(pjd->AX[j],pjd->nlock-i,&v));
    1099:       PetscCall(MatMult(pep->A[j],x,v));
    1100:       PetscCall(BVRestoreColumn(pjd->AX[j],pjd->nlock-i,&v));
    1101:       PetscCall(BVSetActiveColumns(pjd->AX[j],0,pjd->nlock-i+1));
    1102:     }
    1103:     PetscCall(BVRestoreColumn(pjd->X,pjd->nlock-i,&x));
    1104:     PetscCall(BVDotColumn(pjd->X,(pjd->nlock-i),pjd->XpX+(pjd->nlock-i)*pjd->ld));
    1105:     pjd->XpX[(pjd->nlock-i)*(1+pjd->ld)] = 1.0;
    1106:     for (j=0;j<pjd->nlock-i;j++) pjd->XpX[j*pjd->ld+pjd->nlock-i] = PetscConj(pjd->XpX[(pjd->nlock-i)*pjd->ld+j]);
    1107:   }

    1109:   /* minimality index */
    1110:   pjd->midx = PetscMin(pjd->mmidx,pjd->nlock);

    1112:   /* evaluate the polynomial basis in T */
    1113:   PetscCall(PetscArrayzero(pjd->Tj,pjd->ld*pjd->ld*pep->nmat));
    1114:   for (j=0;j<pep->nmat;j++) PetscCall(PEPEvaluateBasisMat(pep,pjd->nlock,pjd->T,pep->ncv,j,(j>1)?pjd->Tj+(j-2)*pjd->ld*pjd->ld:NULL,pjd->ld,j?pjd->Tj+(j-1)*pjd->ld*pjd->ld:NULL,pjd->ld,pjd->Tj+j*pjd->ld*pjd->ld,pjd->ld));

    1116:   /* Extend search space */
    1117:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pep),&np));
    1118:   PetscCall(PetscCalloc3(nvv,&P,nvv*nvv,&R,nvv*sz,&r));
    1119:   PetscCall(DSGetLeadingDimension(pep->ds,&ldds));
    1120:   PetscCall(DSGetArray(pep->ds,DS_MAT_X,&pX));
    1121:   PetscCall(PEPJDOrthogonalize(nvv,nvv,pX,ldds,&rk,P,R,nvv));
    1122:   for (j=0;j<sz;j++) {
    1123:     for (i=0;i<rk;i++) r[i*sz+j] = PetscConj(R[nvv*i+j]*pep->eigr[P[i]]); /* first row scaled with permuted diagonal */
    1124:   }
    1125:   PetscCall(PetscBLASIntCast(rk,&rk_));
    1126:   PetscCall(PetscBLASIntCast(sz,&sz_));
    1127:   PetscCall(PetscBLASIntCast(nvv,&nv_));
    1128:   PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
    1129:   PetscCallBLAS("LAPACKtrtri",LAPACKtrtri_("U","N",&rk_,R,&nv_,&info));
    1130:   PetscCall(PetscFPTrapPop());
    1131:   SlepcCheckLapackInfo("trtri",info);
    1132:   for (i=0;i<sz;i++) PetscCallBLAS("BLAStrmv",BLAStrmv_("U","C","N",&rk_,R,&nv_,r+i,&sz_));
    1133:   for (i=0;i<sz*rk;i++) r[i] = PetscConj(r[i])/PetscSqrtReal(np); /* revert */
    1134:   PetscCall(BVSetActiveColumns(pjd->V,0,nvv));
    1135:   rk -= sz;
    1136:   for (j=0;j<rk;j++) PetscCall(PetscArraycpy(R+j*nvv,pX+(j+sz)*ldds,nvv));
    1137:   PetscCall(DSRestoreArray(pep->ds,DS_MAT_X,&pX));
    1138:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,nvv,rk,R,&X));
    1139:   PetscCall(BVMultInPlace(pjd->V,X,0,rk));
    1140:   PetscCall(MatDestroy(&X));
    1141:   PetscCall(BVSetActiveColumns(pjd->V,0,rk));
    1142:   for (j=0;j<rk;j++) {
    1143:     PetscCall(BVGetColumn(pjd->V,j,&v));
    1144:     PetscCall(PEPJDCopyToExtendedVec(pep,NULL,r+sz*(j+sz),sz,pjd->nlock-sz,v,PETSC_FALSE));
    1145:     PetscCall(BVRestoreColumn(pjd->V,j,&v));
    1146:   }
    1147:   PetscCall(BVOrthogonalize(pjd->V,NULL));

    1149:   if (pjd->proj==PEP_JD_PROJECTION_HARMONIC) {
    1150:     for (j=0;j<rk;j++) {
    1151:       /* W = P(target)*V */
    1152:       PetscCall(BVGetColumn(pjd->W,j,&w));
    1153:       PetscCall(BVGetColumn(pjd->V,j,&v));
    1154:       target[0] = pep->target; target[1] = 0.0;
    1155:       PetscCall(PEPJDComputeResidual(pep,PETSC_FALSE,1,&v,target,&w,pep->work));
    1156:       PetscCall(BVRestoreColumn(pjd->V,j,&v));
    1157:       PetscCall(BVRestoreColumn(pjd->W,j,&w));
    1158:     }
    1159:     PetscCall(BVSetActiveColumns(pjd->W,0,rk));
    1160:     PetscCall(BVOrthogonalize(pjd->W,NULL));
    1161:   }
    1162:   *nv = rk;
    1163:   PetscCall(PetscFree3(P,R,r));
    1164:   PetscFunctionReturn(PETSC_SUCCESS);
    1165: }

    1167: static PetscErrorCode PEPJDSystemSetUp(PEP pep,PetscInt sz,PetscScalar *theta,Vec *u,Vec *p,Vec *ww)
    1168: {
    1169:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    1170:   PEP_JD_PCSHELL *pcctx;
    1171: #if !defined(PETSC_USE_COMPLEX)
    1172:   PetscScalar    s[2];
    1173: #endif

    1175:   PetscFunctionBegin;
    1176:   PetscCall(PCShellGetContext(pjd->pcshell,&pcctx));
    1177:   PetscCall(PEPJDMatSetUp(pep,sz,theta));
    1178:   pcctx->u[0] = u[0]; pcctx->u[1] = u[1];
    1179:   /* Compute r'. p is a work space vector */
    1180:   PetscCall(PEPJDComputeResidual(pep,PETSC_TRUE,sz,u,theta,p,ww));
    1181:   PetscCall(PEPJDExtendedPCApply(pjd->pcshell,p[0],pcctx->Bp[0]));
    1182:   PetscCall(VecDot(pcctx->Bp[0],u[0],pcctx->gamma));
    1183: #if !defined(PETSC_USE_COMPLEX)
    1184:   if (sz==2) {
    1185:     PetscCall(PEPJDExtendedPCApply(pjd->pcshell,p[1],pcctx->Bp[1]));
    1186:     PetscCall(VecDot(pcctx->Bp[0],u[1],pcctx->gamma+1));
    1187:     PetscCall(VecMDot(pcctx->Bp[1],2,u,s));
    1188:     pcctx->gamma[0] += s[1];
    1189:     pcctx->gamma[1] = -pcctx->gamma[1]+s[0];
    1190:   }
    1191: #endif
    1192:   if (sz==1) {
    1193:     PetscCall(VecZeroEntries(pcctx->Bp[1]));
    1194:     pcctx->gamma[1] = 0.0;
    1195:   }
    1196:   PetscFunctionReturn(PETSC_SUCCESS);
    1197: }

    1199: static PetscErrorCode PEPSolve_JD(PEP pep)
    1200: {
    1201:   PEP_JD          *pjd = (PEP_JD*)pep->data;
    1202:   PetscInt        k,nv,nvc,ld,minv,dim,bupdated=0,sz=1,kspsf=1,idx,off,maxits,nloc;
    1203:   PetscMPIInt     np,count;
    1204:   PetscScalar     theta[2]={0.0,0.0},ritz[2]={0.0,0.0},*pX,*eig,*eigi,*array;
    1205:   PetscReal       norm,*res,tol=0.0,rtol,abstol, dtol;
    1206:   PetscBool       lindep,ini=PETSC_TRUE;
    1207:   Vec             tc,t[2]={NULL,NULL},u[2]={NULL,NULL},p[2]={NULL,NULL};
    1208:   Vec             rc,rr[2],r[2]={NULL,NULL},*ww=pep->work,v[2];
    1209:   Mat             G,X,Y;
    1210:   KSP             ksp;
    1211:   PEP_JD_PCSHELL  *pcctx;
    1212:   PEP_JD_MATSHELL *matctx;
    1213: #if !defined(PETSC_USE_COMPLEX)
    1214:   PetscReal       norm1;
    1215: #endif

    1217:   PetscFunctionBegin;
    1218:   PetscCall(PetscCitationsRegister(citation,&cited));
    1219:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pep),&np));
    1220:   PetscCall(BVGetSizes(pep->V,&nloc,NULL,NULL));
    1221:   PetscCall(DSGetLeadingDimension(pep->ds,&ld));
    1222:   PetscCall(PetscCalloc3(pep->ncv+pep->nev,&eig,pep->ncv+pep->nev,&eigi,pep->ncv+pep->nev,&res));
    1223:   pjd->nlock = 0;
    1224:   PetscCall(STGetKSP(pep->st,&ksp));
    1225:   PetscCall(KSPGetTolerances(ksp,&rtol,&abstol,&dtol,&maxits));
    1226: #if !defined (PETSC_USE_COMPLEX)
    1227:   kspsf = 2;
    1228: #endif
    1229:   PetscCall(PEPJDProcessInitialSpace(pep,ww));
    1230:   nv = (pep->nini)?pep->nini:1;

    1232:   /* Replace preconditioner with one containing projectors */
    1233:   PetscCall(PEPJDCreateShellPC(pep,ww));
    1234:   PetscCall(PCShellGetContext(pjd->pcshell,&pcctx));

    1236:   /* Create auxiliary vectors */
    1237:   PetscCall(BVCreateVec(pjd->V,&u[0]));
    1238:   PetscCall(VecDuplicate(u[0],&p[0]));
    1239:   PetscCall(VecDuplicate(u[0],&r[0]));
    1240: #if !defined (PETSC_USE_COMPLEX)
    1241:   PetscCall(VecDuplicate(u[0],&u[1]));
    1242:   PetscCall(VecDuplicate(u[0],&p[1]));
    1243:   PetscCall(VecDuplicate(u[0],&r[1]));
    1244: #endif

    1246:   /* Restart loop */
    1247:   while (pep->reason == PEP_CONVERGED_ITERATING) {
    1248:     pep->its++;
    1249:     PetscCall(DSSetDimensions(pep->ds,nv,0,0));
    1250:     PetscCall(BVSetActiveColumns(pjd->V,bupdated,nv));
    1251:     PetscCall(PEPJDUpdateTV(pep,bupdated,nv,ww));
    1252:     if (pjd->proj==PEP_JD_PROJECTION_HARMONIC) PetscCall(BVSetActiveColumns(pjd->W,bupdated,nv));
    1253:     for (k=0;k<pep->nmat;k++) {
    1254:       PetscCall(BVSetActiveColumns(pjd->TV[k],bupdated,nv));
    1255:       PetscCall(DSGetMat(pep->ds,DSMatExtra[k],&G));
    1256:       PetscCall(BVMatProject(pjd->TV[k],NULL,pjd->W,G));
    1257:       PetscCall(DSRestoreMat(pep->ds,DSMatExtra[k],&G));
    1258:     }
    1259:     PetscCall(BVSetActiveColumns(pjd->V,0,nv));
    1260:     PetscCall(BVSetActiveColumns(pjd->W,0,nv));

    1262:     /* Solve projected problem */
    1263:     PetscCall(DSSetState(pep->ds,DS_STATE_RAW));
    1264:     PetscCall(DSSolve(pep->ds,pep->eigr,pep->eigi));
    1265:     PetscCall(DSSort(pep->ds,pep->eigr,pep->eigi,NULL,NULL,NULL));
    1266:     PetscCall(DSSynchronize(pep->ds,pep->eigr,pep->eigi));
    1267:     idx = 0;
    1268:     do {
    1269:       ritz[0] = pep->eigr[idx];
    1270: #if !defined(PETSC_USE_COMPLEX)
    1271:       ritz[1] = pep->eigi[idx];
    1272:       sz = (ritz[1]==0.0)?1:2;
    1273: #endif
    1274:       /* Compute Ritz vector u=V*X(:,1) */
    1275:       PetscCall(DSGetArray(pep->ds,DS_MAT_X,&pX));
    1276:       PetscCall(BVSetActiveColumns(pjd->V,0,nv));
    1277:       PetscCall(BVMultVec(pjd->V,1.0,0.0,u[0],pX+idx*ld));
    1278: #if !defined(PETSC_USE_COMPLEX)
    1279:       if (sz==2) PetscCall(BVMultVec(pjd->V,1.0,0.0,u[1],pX+(idx+1)*ld));
    1280: #endif
    1281:       PetscCall(DSRestoreArray(pep->ds,DS_MAT_X,&pX));
    1282:       PetscCall(PEPJDComputeResidual(pep,PETSC_FALSE,sz,u,ritz,r,ww));
    1283:       /* Check convergence */
    1284:       PetscCall(VecNorm(r[0],NORM_2,&norm));
    1285: #if !defined(PETSC_USE_COMPLEX)
    1286:       if (sz==2) {
    1287:         PetscCall(VecNorm(r[1],NORM_2,&norm1));
    1288:         norm = SlepcAbs(norm,norm1);
    1289:       }
    1290: #endif
    1291:       PetscCall((*pep->converged)(pep,ritz[0],ritz[1],norm,&pep->errest[pep->nconv],pep->convergedctx));
    1292:       if (sz==2) pep->errest[pep->nconv+1] = pep->errest[pep->nconv];
    1293:       if (ini) {
    1294:         tol = PetscMin(.1,pep->errest[pep->nconv]); ini = PETSC_FALSE;
    1295:       } else tol = PetscMin(pep->errest[pep->nconv],tol/2);
    1296:       PetscCall((*pep->stopping)(pep,pep->its,pep->max_it,(pep->errest[pep->nconv]<pep->tol)?pep->nconv+sz:pep->nconv,pep->nev,&pep->reason,pep->stoppingctx));
    1297:       if (pep->errest[pep->nconv]<pep->tol) {
    1298:         /* Ritz pair converged */
    1299:         ini = PETSC_TRUE;
    1300:         minv = PetscMin(nv,(PetscInt)(pjd->keep*pep->ncv));
    1301:         if (pjd->ld>1) {
    1302:           PetscCall(BVGetColumn(pjd->X,pep->nconv,&v[0]));
    1303:           PetscCall(PEPJDCopyToExtendedVec(pep,v[0],pjd->T+pep->ncv*pep->nconv,pjd->ld-1,0,u[0],PETSC_TRUE));
    1304:           PetscCall(BVRestoreColumn(pjd->X,pep->nconv,&v[0]));
    1305:           PetscCall(BVSetActiveColumns(pjd->X,0,pep->nconv+1));
    1306:           PetscCall(BVNormColumn(pjd->X,pep->nconv,NORM_2,&norm));
    1307:           PetscCall(BVScaleColumn(pjd->X,pep->nconv,1.0/norm));
    1308:           for (k=0;k<pep->nconv;k++) pjd->T[pep->ncv*pep->nconv+k] *= PetscSqrtReal(np)/norm;
    1309:           pjd->T[(pep->ncv+1)*pep->nconv] = ritz[0];
    1310:           eig[pep->nconv] = ritz[0];
    1311:           idx++;
    1312: #if !defined(PETSC_USE_COMPLEX)
    1313:           if (sz==2) {
    1314:             PetscCall(BVGetColumn(pjd->X,pep->nconv+1,&v[0]));
    1315:             PetscCall(PEPJDCopyToExtendedVec(pep,v[0],pjd->T+pep->ncv*(pep->nconv+1),pjd->ld-1,0,u[1],PETSC_TRUE));
    1316:             PetscCall(BVRestoreColumn(pjd->X,pep->nconv+1,&v[0]));
    1317:             PetscCall(BVSetActiveColumns(pjd->X,0,pep->nconv+2));
    1318:             PetscCall(BVNormColumn(pjd->X,pep->nconv+1,NORM_2,&norm1));
    1319:             PetscCall(BVScaleColumn(pjd->X,pep->nconv+1,1.0/norm1));
    1320:             for (k=0;k<pep->nconv;k++) pjd->T[pep->ncv*(pep->nconv+1)+k] *= PetscSqrtReal(np)/norm1;
    1321:             pjd->T[(pep->ncv+1)*(pep->nconv+1)] = ritz[0];
    1322:             pjd->T[(pep->ncv+1)*pep->nconv+1] = -ritz[1]*norm1/norm;
    1323:             pjd->T[(pep->ncv+1)*(pep->nconv+1)-1] = ritz[1]*norm/norm1;
    1324:             eig[pep->nconv+1] = ritz[0];
    1325:             eigi[pep->nconv] = ritz[1]; eigi[pep->nconv+1] = -ritz[1];
    1326:             idx++;
    1327:           }
    1328: #endif
    1329:         } else PetscCall(BVInsertVec(pep->V,pep->nconv,u[0]));
    1330:         pep->nconv += sz;
    1331:       }
    1332:     } while (pep->errest[pep->nconv]<pep->tol && pep->nconv<nv);

    1334:     if (pep->reason==PEP_CONVERGED_ITERATING) {
    1335:       nvc = nv;
    1336:       if (idx) {
    1337:         pjd->nlock +=idx;
    1338:         PetscCall(PEPJDLockConverged(pep,&nv,idx));
    1339:       }
    1340:       if (nv+sz>=pep->ncv-1) {
    1341:         /* Basis full, force restart */
    1342:         minv = PetscMin(nv,(PetscInt)(pjd->keep*pep->ncv));
    1343:         PetscCall(DSGetDimensions(pep->ds,&dim,NULL,NULL,NULL));
    1344:         PetscCall(DSGetArray(pep->ds,DS_MAT_X,&pX));
    1345:         PetscCall(PEPJDOrthogonalize(dim,minv,pX,ld,&minv,NULL,NULL,ld));
    1346:         PetscCall(DSRestoreArray(pep->ds,DS_MAT_X,&pX));
    1347:         PetscCall(DSGetArray(pep->ds,DS_MAT_Y,&pX));
    1348:         PetscCall(PEPJDOrthogonalize(dim,minv,pX,ld,&minv,NULL,NULL,ld));
    1349:         PetscCall(DSRestoreArray(pep->ds,DS_MAT_Y,&pX));
    1350:         PetscCall(DSGetMat(pep->ds,DS_MAT_X,&X));
    1351:         PetscCall(BVMultInPlace(pjd->V,X,0,minv));
    1352:         PetscCall(DSRestoreMat(pep->ds,DS_MAT_X,&X));
    1353:         if (pjd->proj==PEP_JD_PROJECTION_HARMONIC) {
    1354:          PetscCall(DSGetMat(pep->ds,DS_MAT_Y,&Y));
    1355:          PetscCall(BVMultInPlace(pjd->W,Y,pep->nconv,minv));
    1356:          PetscCall(DSRestoreMat(pep->ds,DS_MAT_Y,&Y));
    1357:         }
    1358:         nv = minv;
    1359:         bupdated = 0;
    1360:       } else {
    1361:         if (!idx && pep->errest[pep->nconv]<pjd->fix) {theta[0] = ritz[0]; theta[1] = ritz[1];}
    1362:         else {theta[0] = pep->target; theta[1] = 0.0;}
    1363:         /* Update system mat */
    1364:         PetscCall(PEPJDSystemSetUp(pep,sz,theta,u,p,ww));
    1365:         /* Solve correction equation to expand basis */
    1366:         PetscCall(BVGetColumn(pjd->V,nv,&t[0]));
    1367:         rr[0] = r[0];
    1368:         if (sz==2) {
    1369:           PetscCall(BVGetColumn(pjd->V,nv+1,&t[1]));
    1370:           rr[1] = r[1];
    1371:         } else {
    1372:           t[1] = NULL;
    1373:           rr[1] = NULL;
    1374:         }
    1375:         PetscCall(VecCreateCompWithVecs(t,kspsf,pjd->vtempl,&tc));
    1376:         PetscCall(VecCreateCompWithVecs(rr,kspsf,pjd->vtempl,&rc));
    1377:         PetscCall(VecCompSetSubVecs(pjd->vtempl,sz,NULL));
    1378:         tol  = PetscMax(rtol,tol/2);
    1379:         PetscCall(KSPSetTolerances(ksp,tol,abstol,dtol,maxits));
    1380:         PetscCall(KSPSolve(ksp,rc,tc));
    1381:         PetscCall(VecDestroy(&tc));
    1382:         PetscCall(VecDestroy(&rc));
    1383:         PetscCall(VecGetArray(t[0],&array));
    1384:         PetscCall(PetscMPIIntCast(pep->nconv,&count));
    1385:         PetscCallMPI(MPI_Bcast(array+nloc,count,MPIU_SCALAR,np-1,PetscObjectComm((PetscObject)pep)));
    1386:         PetscCall(VecRestoreArray(t[0],&array));
    1387:         PetscCall(BVRestoreColumn(pjd->V,nv,&t[0]));
    1388:         PetscCall(BVOrthogonalizeColumn(pjd->V,nv,NULL,&norm,&lindep));
    1389:         if (lindep || norm==0.0) {
    1390:           PetscCheck(sz!=1,PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"Linearly dependent continuation vector");
    1391:           off = 1;
    1392:         } else {
    1393:           off = 0;
    1394:           PetscCall(BVScaleColumn(pjd->V,nv,1.0/norm));
    1395:         }
    1396: #if !defined(PETSC_USE_COMPLEX)
    1397:         if (sz==2) {
    1398:           PetscCall(VecGetArray(t[1],&array));
    1399:           PetscCallMPI(MPI_Bcast(array+nloc,count,MPIU_SCALAR,np-1,PetscObjectComm((PetscObject)pep)));
    1400:           PetscCall(VecRestoreArray(t[1],&array));
    1401:           PetscCall(BVRestoreColumn(pjd->V,nv+1,&t[1]));
    1402:           if (off) PetscCall(BVCopyColumn(pjd->V,nv+1,nv));
    1403:           PetscCall(BVOrthogonalizeColumn(pjd->V,nv+1-off,NULL,&norm,&lindep));
    1404:           if (lindep || norm==0.0) {
    1405:             PetscCheck(off==0,PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"Linearly dependent continuation vector");
    1406:             off = 1;
    1407:           } else PetscCall(BVScaleColumn(pjd->V,nv+1-off,1.0/norm));
    1408:         }
    1409: #endif
    1410:         if (pjd->proj==PEP_JD_PROJECTION_HARMONIC) {
    1411:           PetscCall(BVInsertVec(pjd->W,nv,r[0]));
    1412:           if (sz==2 && !off) PetscCall(BVInsertVec(pjd->W,nv+1,r[1]));
    1413:           PetscCall(BVOrthogonalizeColumn(pjd->W,nv,NULL,&norm,&lindep));
    1414:           PetscCheck(!lindep && norm>0.0,PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"Linearly dependent continuation vector");
    1415:           PetscCall(BVScaleColumn(pjd->W,nv,1.0/norm));
    1416:           if (sz==2 && !off) {
    1417:             PetscCall(BVOrthogonalizeColumn(pjd->W,nv+1,NULL,&norm,&lindep));
    1418:             PetscCheck(!lindep && norm>0.0,PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"Linearly dependent continuation vector");
    1419:             PetscCall(BVScaleColumn(pjd->W,nv+1,1.0/norm));
    1420:           }
    1421:         }
    1422:         bupdated = idx?0:nv;
    1423:         nv += sz-off;
    1424:       }
    1425:       for (k=0;k<nvc;k++) {
    1426:         eig[pep->nconv-idx+k] = pep->eigr[k];
    1427: #if !defined(PETSC_USE_COMPLEX)
    1428:         eigi[pep->nconv-idx+k] = pep->eigi[k];
    1429: #endif
    1430:       }
    1431:       PetscCall(PEPMonitor(pep,pep->its,pep->nconv,eig,eigi,pep->errest,pep->nconv+1));
    1432:     }
    1433:   }
    1434:   if (pjd->ld>1) {
    1435:     for (k=0;k<pep->nconv;k++) {
    1436:       pep->eigr[k] = eig[k];
    1437:       pep->eigi[k] = eigi[k];
    1438:     }
    1439:     if (pep->nconv>0) PetscCall(PEPJDEigenvectors(pep));
    1440:     PetscCall(PetscFree2(pcctx->M,pcctx->ps));
    1441:   }
    1442:   PetscCall(VecDestroy(&u[0]));
    1443:   PetscCall(VecDestroy(&r[0]));
    1444:   PetscCall(VecDestroy(&p[0]));
    1445: #if !defined (PETSC_USE_COMPLEX)
    1446:   PetscCall(VecDestroy(&u[1]));
    1447:   PetscCall(VecDestroy(&r[1]));
    1448:   PetscCall(VecDestroy(&p[1]));
    1449: #endif
    1450:   PetscCall(KSPSetTolerances(ksp,rtol,abstol,dtol,maxits));
    1451:   PetscCall(KSPSetPC(ksp,pcctx->pc));
    1452:   PetscCall(VecDestroy(&pcctx->Bp[0]));
    1453:   PetscCall(VecDestroy(&pcctx->Bp[1]));
    1454:   PetscCall(MatShellGetContext(pjd->Pshell,&matctx));
    1455:   PetscCall(MatDestroy(&matctx->Pr));
    1456:   PetscCall(MatDestroy(&matctx->Pi));
    1457:   PetscCall(MatDestroy(&pjd->Pshell));
    1458:   PetscCall(MatDestroy(&pcctx->PPr));
    1459:   PetscCall(PCDestroy(&pcctx->pc));
    1460:   PetscCall(PetscFree(pcctx));
    1461:   PetscCall(PetscFree(matctx));
    1462:   PetscCall(PCDestroy(&pjd->pcshell));
    1463:   PetscCall(PetscFree3(eig,eigi,res));
    1464:   PetscCall(VecDestroy(&pjd->vtempl));
    1465:   PetscFunctionReturn(PETSC_SUCCESS);
    1466: }

    1468: static PetscErrorCode PEPJDSetRestart_JD(PEP pep,PetscReal keep)
    1469: {
    1470:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1472:   PetscFunctionBegin;
    1473:   if (keep==(PetscReal)PETSC_DEFAULT || keep==(PetscReal)PETSC_DECIDE) pjd->keep = 0.5;
    1474:   else {
    1475:     PetscCheck(keep>=0.1 && keep<=0.9,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The keep argument must be in the range [0.1,0.9]");
    1476:     pjd->keep = keep;
    1477:   }
    1478:   PetscFunctionReturn(PETSC_SUCCESS);
    1479: }

    1481: /*@
    1482:    PEPJDSetRestart - Sets the restart parameter for the Jacobi-Davidson
    1483:    method, in particular the proportion of basis vectors that must be kept
    1484:    after restart.

    1486:    Logically Collective

    1488:    Input Parameters:
    1489: +  pep  - the polynomial eigensolver context
    1490: -  keep - the number of vectors to be kept at restart

    1492:    Options Database Key:
    1493: .  -pep_jd_restart \<keep\> - sets the restart parameter

    1495:    Notes:
    1496:    Allowed values are in the range [0.1,0.9]. The default is 0.5.

    1498:    Level: advanced

    1500: .seealso: [](ch:pep), `PEPJD`, `PEPJDGetRestart()`
    1501: @*/
    1502: PetscErrorCode PEPJDSetRestart(PEP pep,PetscReal keep)
    1503: {
    1504:   PetscFunctionBegin;
    1507:   PetscTryMethod(pep,"PEPJDSetRestart_C",(PEP,PetscReal),(pep,keep));
    1508:   PetscFunctionReturn(PETSC_SUCCESS);
    1509: }

    1511: static PetscErrorCode PEPJDGetRestart_JD(PEP pep,PetscReal *keep)
    1512: {
    1513:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1515:   PetscFunctionBegin;
    1516:   *keep = pjd->keep;
    1517:   PetscFunctionReturn(PETSC_SUCCESS);
    1518: }

    1520: /*@
    1521:    PEPJDGetRestart - Gets the restart parameter used in the Jacobi-Davidson method.

    1523:    Not Collective

    1525:    Input Parameter:
    1526: .  pep - the polynomial eigensolver context

    1528:    Output Parameter:
    1529: .  keep - the restart parameter

    1531:    Level: advanced

    1533: .seealso: [](ch:pep), `PEPJD`, `PEPJDSetRestart()`
    1534: @*/
    1535: PetscErrorCode PEPJDGetRestart(PEP pep,PetscReal *keep)
    1536: {
    1537:   PetscFunctionBegin;
    1539:   PetscAssertPointer(keep,2);
    1540:   PetscUseMethod(pep,"PEPJDGetRestart_C",(PEP,PetscReal*),(pep,keep));
    1541:   PetscFunctionReturn(PETSC_SUCCESS);
    1542: }

    1544: static PetscErrorCode PEPJDSetFix_JD(PEP pep,PetscReal fix)
    1545: {
    1546:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1548:   PetscFunctionBegin;
    1549:   if (fix == (PetscReal)PETSC_DEFAULT || fix == (PetscReal)PETSC_DECIDE) pjd->fix = 0.01;
    1550:   else {
    1551:     PetscCheck(fix>=0.0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid fix value, must be >0");
    1552:     pjd->fix = fix;
    1553:   }
    1554:   PetscFunctionReturn(PETSC_SUCCESS);
    1555: }

    1557: /*@
    1558:    PEPJDSetFix - Sets the threshold for changing the target in the correction
    1559:    equation.

    1561:    Logically Collective

    1563:    Input Parameters:
    1564: +  pep - the polynomial eigensolver context
    1565: -  fix - threshold for changing the target

    1567:    Options Database Key:
    1568: .  -pep_jd_fix \<fix\> - the fix value

    1570:    Notes:
    1571:    The target in the correction equation is fixed at the first iterations.
    1572:    When the norm of the residual vector is lower than the `fix` value,
    1573:    the target is set to the corresponding eigenvalue.

    1575:    Detailed information can be found at {cite:p}`Cam20a`.

    1577:    Level: advanced

    1579: .seealso: [](ch:pep), `PEPJD`, `PEPJDGetFix()`
    1580: @*/
    1581: PetscErrorCode PEPJDSetFix(PEP pep,PetscReal fix)
    1582: {
    1583:   PetscFunctionBegin;
    1586:   PetscTryMethod(pep,"PEPJDSetFix_C",(PEP,PetscReal),(pep,fix));
    1587:   PetscFunctionReturn(PETSC_SUCCESS);
    1588: }

    1590: static PetscErrorCode PEPJDGetFix_JD(PEP pep,PetscReal *fix)
    1591: {
    1592:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1594:   PetscFunctionBegin;
    1595:   *fix = pjd->fix;
    1596:   PetscFunctionReturn(PETSC_SUCCESS);
    1597: }

    1599: /*@
    1600:    PEPJDGetFix - Returns the threshold for changing the target in the correction
    1601:    equation.

    1603:    Not Collective

    1605:    Input Parameter:
    1606: .  pep - the polynomial eigensolver context

    1608:    Output Parameter:
    1609: .  fix - threshold for changing the target

    1611:    Level: advanced

    1613: .seealso: [](ch:pep), `PEPJD`, `PEPJDSetFix()`
    1614: @*/
    1615: PetscErrorCode PEPJDGetFix(PEP pep,PetscReal *fix)
    1616: {
    1617:   PetscFunctionBegin;
    1619:   PetscAssertPointer(fix,2);
    1620:   PetscUseMethod(pep,"PEPJDGetFix_C",(PEP,PetscReal*),(pep,fix));
    1621:   PetscFunctionReturn(PETSC_SUCCESS);
    1622: }

    1624: static PetscErrorCode PEPJDSetReusePreconditioner_JD(PEP pep,PetscBool reusepc)
    1625: {
    1626:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1628:   PetscFunctionBegin;
    1629:   pjd->reusepc = reusepc;
    1630:   PetscFunctionReturn(PETSC_SUCCESS);
    1631: }

    1633: /*@
    1634:    PEPJDSetReusePreconditioner - Sets a flag indicating whether the preconditioner
    1635:    must be reused or not.

    1637:    Logically Collective

    1639:    Input Parameters:
    1640: +  pep     - the polynomial eigensolver context
    1641: -  reusepc - the reuse flag

    1643:    Options Database Key:
    1644: .  -pep_jd_reuse_preconditioner - the reuse flag

    1646:    Note:
    1647:    The default value is `PETSC_FALSE`. If set to `PETSC_TRUE`, the preconditioner is built
    1648:    only at the beginning, using the target value. Otherwise, it may be rebuilt
    1649:    (depending on the `fix` parameter) at each iteration from the Ritz value.

    1651:    Level: advanced

    1653: .seealso: [](ch:pep), `PEPJD`, `PEPJDGetReusePreconditioner()`, `PEPJDSetFix()`
    1654: @*/
    1655: PetscErrorCode PEPJDSetReusePreconditioner(PEP pep,PetscBool reusepc)
    1656: {
    1657:   PetscFunctionBegin;
    1660:   PetscTryMethod(pep,"PEPJDSetReusePreconditioner_C",(PEP,PetscBool),(pep,reusepc));
    1661:   PetscFunctionReturn(PETSC_SUCCESS);
    1662: }

    1664: static PetscErrorCode PEPJDGetReusePreconditioner_JD(PEP pep,PetscBool *reusepc)
    1665: {
    1666:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1668:   PetscFunctionBegin;
    1669:   *reusepc = pjd->reusepc;
    1670:   PetscFunctionReturn(PETSC_SUCCESS);
    1671: }

    1673: /*@
    1674:    PEPJDGetReusePreconditioner - Returns the flag for reusing the preconditioner.

    1676:    Not Collective

    1678:    Input Parameter:
    1679: .  pep - the polynomial eigensolver context

    1681:    Output Parameter:
    1682: .  reusepc - the reuse flag

    1684:    Level: advanced

    1686: .seealso: [](ch:pep), `PEPJD`, `PEPJDSetReusePreconditioner()`
    1687: @*/
    1688: PetscErrorCode PEPJDGetReusePreconditioner(PEP pep,PetscBool *reusepc)
    1689: {
    1690:   PetscFunctionBegin;
    1692:   PetscAssertPointer(reusepc,2);
    1693:   PetscUseMethod(pep,"PEPJDGetReusePreconditioner_C",(PEP,PetscBool*),(pep,reusepc));
    1694:   PetscFunctionReturn(PETSC_SUCCESS);
    1695: }

    1697: static PetscErrorCode PEPJDSetMinimalityIndex_JD(PEP pep,PetscInt mmidx)
    1698: {
    1699:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1701:   PetscFunctionBegin;
    1702:   if (mmidx == PETSC_DEFAULT || mmidx == PETSC_DECIDE) {
    1703:     if (pjd->mmidx != 1) pep->state = PEP_STATE_INITIAL;
    1704:     pjd->mmidx = 1;
    1705:   } else {
    1706:     PetscCheck(mmidx>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mmidx value, should be >0");
    1707:     if (pjd->mmidx != mmidx) pep->state = PEP_STATE_INITIAL;
    1708:     pjd->mmidx = mmidx;
    1709:   }
    1710:   PetscFunctionReturn(PETSC_SUCCESS);
    1711: }

    1713: /*@
    1714:    PEPJDSetMinimalityIndex - Sets the maximum allowed value for the minimality index.

    1716:    Logically Collective

    1718:    Input Parameters:
    1719: +  pep   - the polynomial eigensolver context
    1720: -  mmidx - maximum minimality index

    1722:    Options Database Key:
    1723: .  -pep_jd_minimality_index \<mmidx\> - the minimality index value

    1725:    Notes:
    1726:    The default value is equal to the degree of the polynomial. A smaller value
    1727:    can be used if the wanted eigenvectors are known to be linearly independent.

    1729:    Detailed information can be found at {cite:p}`Cam20a`.

    1731:    Level: advanced

    1733: .seealso: [](ch:pep), `PEPJD`, `PEPJDGetMinimalityIndex()`
    1734: @*/
    1735: PetscErrorCode PEPJDSetMinimalityIndex(PEP pep,PetscInt mmidx)
    1736: {
    1737:   PetscFunctionBegin;
    1740:   PetscTryMethod(pep,"PEPJDSetMinimalityIndex_C",(PEP,PetscInt),(pep,mmidx));
    1741:   PetscFunctionReturn(PETSC_SUCCESS);
    1742: }

    1744: static PetscErrorCode PEPJDGetMinimalityIndex_JD(PEP pep,PetscInt *mmidx)
    1745: {
    1746:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1748:   PetscFunctionBegin;
    1749:   *mmidx = pjd->mmidx;
    1750:   PetscFunctionReturn(PETSC_SUCCESS);
    1751: }

    1753: /*@
    1754:    PEPJDGetMinimalityIndex - Returns the maximum allowed value of the minimality
    1755:    index.

    1757:    Not Collective

    1759:    Input Parameter:
    1760: .  pep - the polynomial eigensolver context

    1762:    Output Parameter:
    1763: .  mmidx - minimality index

    1765:    Level: advanced

    1767: .seealso: [](ch:pep), `PEPJD`, `PEPJDSetMinimalityIndex()`
    1768: @*/
    1769: PetscErrorCode PEPJDGetMinimalityIndex(PEP pep,PetscInt *mmidx)
    1770: {
    1771:   PetscFunctionBegin;
    1773:   PetscAssertPointer(mmidx,2);
    1774:   PetscUseMethod(pep,"PEPJDGetMinimalityIndex_C",(PEP,PetscInt*),(pep,mmidx));
    1775:   PetscFunctionReturn(PETSC_SUCCESS);
    1776: }

    1778: static PetscErrorCode PEPJDSetProjection_JD(PEP pep,PEPJDProjection proj)
    1779: {
    1780:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1782:   PetscFunctionBegin;
    1783:   switch (proj) {
    1784:     case PEP_JD_PROJECTION_HARMONIC:
    1785:     case PEP_JD_PROJECTION_ORTHOGONAL:
    1786:       if (pjd->proj != proj) {
    1787:         pep->state = PEP_STATE_INITIAL;
    1788:         pjd->proj = proj;
    1789:       }
    1790:       break;
    1791:     default:
    1792:       SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid 'proj' value");
    1793:   }
    1794:   PetscFunctionReturn(PETSC_SUCCESS);
    1795: }

    1797: /*@
    1798:    PEPJDSetProjection - Sets the type of projection to be used in the Jacobi-Davidson solver.

    1800:    Logically Collective

    1802:    Input Parameters:
    1803: +  pep  - the polynomial eigensolver context
    1804: -  proj - the type of projection, see `PEPJDProjection` for possible values

    1806:    Options Database Key:
    1807: .  -pep_jd_projection \<proj\> - the projection type, either `orthogonal` or `harmonic`

    1809:    Note:
    1810:    Detailed information can be found at {cite:p}`Cam20a`.

    1812:    Level: advanced

    1814: .seealso: [](ch:pep), `PEPJD`, `PEPJDGetProjection()`
    1815: @*/
    1816: PetscErrorCode PEPJDSetProjection(PEP pep,PEPJDProjection proj)
    1817: {
    1818:   PetscFunctionBegin;
    1821:   PetscTryMethod(pep,"PEPJDSetProjection_C",(PEP,PEPJDProjection),(pep,proj));
    1822:   PetscFunctionReturn(PETSC_SUCCESS);
    1823: }

    1825: static PetscErrorCode PEPJDGetProjection_JD(PEP pep,PEPJDProjection *proj)
    1826: {
    1827:   PEP_JD *pjd = (PEP_JD*)pep->data;

    1829:   PetscFunctionBegin;
    1830:   *proj = pjd->proj;
    1831:   PetscFunctionReturn(PETSC_SUCCESS);
    1832: }

    1834: /*@
    1835:    PEPJDGetProjection - Returns the type of projection used by the Jacobi-Davidson solver.

    1837:    Not Collective

    1839:    Input Parameter:
    1840: .  pep - the polynomial eigensolver context

    1842:    Output Parameter:
    1843: .  proj - the type of projection

    1845:    Level: advanced

    1847: .seealso: [](ch:pep), `PEPJD`, `PEPJDSetProjection()`
    1848: @*/
    1849: PetscErrorCode PEPJDGetProjection(PEP pep,PEPJDProjection *proj)
    1850: {
    1851:   PetscFunctionBegin;
    1853:   PetscAssertPointer(proj,2);
    1854:   PetscUseMethod(pep,"PEPJDGetProjection_C",(PEP,PEPJDProjection*),(pep,proj));
    1855:   PetscFunctionReturn(PETSC_SUCCESS);
    1856: }

    1858: static PetscErrorCode PEPSetFromOptions_JD(PEP pep,PetscOptionItems PetscOptionsObject)
    1859: {
    1860:   PetscBool       flg,b1;
    1861:   PetscReal       r1;
    1862:   PetscInt        i1;
    1863:   PEPJDProjection proj;

    1865:   PetscFunctionBegin;
    1866:   PetscOptionsHeadBegin(PetscOptionsObject,"PEP JD Options");

    1868:     PetscCall(PetscOptionsReal("-pep_jd_restart","Proportion of vectors kept after restart","PEPJDSetRestart",0.5,&r1,&flg));
    1869:     if (flg) PetscCall(PEPJDSetRestart(pep,r1));

    1871:     PetscCall(PetscOptionsReal("-pep_jd_fix","Tolerance for changing the target in the correction equation","PEPJDSetFix",0.01,&r1,&flg));
    1872:     if (flg) PetscCall(PEPJDSetFix(pep,r1));

    1874:     PetscCall(PetscOptionsBool("-pep_jd_reuse_preconditioner","Whether to reuse the preconditioner","PEPJDSetReusePreconditoiner",PETSC_FALSE,&b1,&flg));
    1875:     if (flg) PetscCall(PEPJDSetReusePreconditioner(pep,b1));

    1877:     PetscCall(PetscOptionsInt("-pep_jd_minimality_index","Maximum allowed minimality index","PEPJDSetMinimalityIndex",1,&i1,&flg));
    1878:     if (flg) PetscCall(PEPJDSetMinimalityIndex(pep,i1));

    1880:     PetscCall(PetscOptionsEnum("-pep_jd_projection","Type of projection","PEPJDSetProjection",PEPJDProjectionTypes,(PetscEnum)PEP_JD_PROJECTION_HARMONIC,(PetscEnum*)&proj,&flg));
    1881:     if (flg) PetscCall(PEPJDSetProjection(pep,proj));

    1883:   PetscOptionsHeadEnd();
    1884:   PetscFunctionReturn(PETSC_SUCCESS);
    1885: }

    1887: static PetscErrorCode PEPView_JD(PEP pep,PetscViewer viewer)
    1888: {
    1889:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    1890:   PetscBool      isascii;

    1892:   PetscFunctionBegin;
    1893:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
    1894:   if (isascii) {
    1895:     PetscCall(PetscViewerASCIIPrintf(viewer,"  %d%% of basis vectors kept after restart\n",(int)(100*pjd->keep)));
    1896:     PetscCall(PetscViewerASCIIPrintf(viewer,"  threshold for changing the target in the correction equation (fix): %g\n",(double)pjd->fix));
    1897:     PetscCall(PetscViewerASCIIPrintf(viewer,"  projection type: %s\n",PEPJDProjectionTypes[pjd->proj]));
    1898:     PetscCall(PetscViewerASCIIPrintf(viewer,"  maximum allowed minimality index: %" PetscInt_FMT "\n",pjd->mmidx));
    1899:     if (pjd->reusepc) PetscCall(PetscViewerASCIIPrintf(viewer,"  reusing the preconditioner\n"));
    1900:   }
    1901:   PetscFunctionReturn(PETSC_SUCCESS);
    1902: }

    1904: static PetscErrorCode PEPSetDefaultST_JD(PEP pep)
    1905: {
    1906:   KSP            ksp;

    1908:   PetscFunctionBegin;
    1909:   if (!((PetscObject)pep->st)->type_name) {
    1910:     PetscCall(STSetType(pep->st,STPRECOND));
    1911:     PetscCall(STPrecondSetKSPHasMat(pep->st,PETSC_TRUE));
    1912:   }
    1913:   PetscCall(STSetTransform(pep->st,PETSC_FALSE));
    1914:   PetscCall(STGetKSP(pep->st,&ksp));
    1915:   if (!((PetscObject)ksp)->type_name) {
    1916:     PetscCall(KSPSetType(ksp,KSPBCGSL));
    1917:     PetscCall(KSPSetTolerances(ksp,1e-5,PETSC_CURRENT,PETSC_CURRENT,100));
    1918:   }
    1919:   PetscFunctionReturn(PETSC_SUCCESS);
    1920: }

    1922: static PetscErrorCode PEPReset_JD(PEP pep)
    1923: {
    1924:   PEP_JD         *pjd = (PEP_JD*)pep->data;
    1925:   PetscInt       i;

    1927:   PetscFunctionBegin;
    1928:   for (i=0;i<pep->nmat;i++) PetscCall(BVDestroy(pjd->TV+i));
    1929:   if (pjd->proj==PEP_JD_PROJECTION_HARMONIC) PetscCall(BVDestroy(&pjd->W));
    1930:   if (pjd->ld>1) {
    1931:     PetscCall(BVDestroy(&pjd->V));
    1932:     for (i=0;i<pep->nmat;i++) PetscCall(BVDestroy(pjd->AX+i));
    1933:     PetscCall(BVDestroy(&pjd->N[0]));
    1934:     PetscCall(BVDestroy(&pjd->N[1]));
    1935:     PetscCall(PetscFree3(pjd->XpX,pjd->T,pjd->Tj));
    1936:   }
    1937:   PetscCall(PetscFree2(pjd->TV,pjd->AX));
    1938:   PetscFunctionReturn(PETSC_SUCCESS);
    1939: }

    1941: static PetscErrorCode PEPDestroy_JD(PEP pep)
    1942: {
    1943:   PetscFunctionBegin;
    1944:   PetscCall(PetscFree(pep->data));
    1945:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetRestart_C",NULL));
    1946:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetRestart_C",NULL));
    1947:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetFix_C",NULL));
    1948:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetFix_C",NULL));
    1949:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetReusePreconditioner_C",NULL));
    1950:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetReusePreconditioner_C",NULL));
    1951:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetMinimalityIndex_C",NULL));
    1952:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetMinimalityIndex_C",NULL));
    1953:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetProjection_C",NULL));
    1954:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetProjection_C",NULL));
    1955:   PetscFunctionReturn(PETSC_SUCCESS);
    1956: }

    1958: /*MC
    1959:    PEPJD - PEPJD = "jd" - The Jacobi-Davidson method for polynomial eigenproblems.

    1961:    Notes:
    1962:    This is a preconditioned eigensolver, that is, it may be competitive
    1963:    when computing interior eigenvalues in case the shift-and-invert spectral
    1964:    transformation is too costly and a good preconditioner is available.

    1966:    The implemented method is polynomial Jacobi-Davidson {cite:p}`Sle96`.
    1967:    It is possible to set several options of the algorithm, such as the
    1968:    restart (`PEPJDSetRestart()`) or the fix parameter (`PEPJDSetFix()`).
    1969:    The details of the SLEPc implementation are in {cite:p}`Cam20a`.

    1971:    The preconditioner is specified via the internal `ST` object and its
    1972:    associated `KSP`. The preconditioner will be recomputed whenever the
    1973:    shift is updated, unless this is disabled with `PEPJDSetReusePreconditioner()`.

    1975:    Level: beginner

    1977: .seealso: [](ch:pep), `PEP`, `PEPType`, `PEPSetType()`, `PEPGetST()`, `PEPJDSetRestart()`, `PEPJDSetFix()`, `PEPJDSetReusePreconditioner()`
    1978: M*/
    1979: SLEPC_EXTERN PetscErrorCode PEPCreate_JD(PEP pep)
    1980: {
    1981:   PEP_JD         *pjd;

    1983:   PetscFunctionBegin;
    1984:   PetscCall(PetscNew(&pjd));
    1985:   pep->data = (void*)pjd;

    1987:   pep->lineariz = PETSC_FALSE;
    1988:   pjd->fix      = 0.01;
    1989:   pjd->mmidx    = 0;

    1991:   pep->ops->solve          = PEPSolve_JD;
    1992:   pep->ops->setup          = PEPSetUp_JD;
    1993:   pep->ops->setfromoptions = PEPSetFromOptions_JD;
    1994:   pep->ops->destroy        = PEPDestroy_JD;
    1995:   pep->ops->reset          = PEPReset_JD;
    1996:   pep->ops->view           = PEPView_JD;
    1997:   pep->ops->setdefaultst   = PEPSetDefaultST_JD;

    1999:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetRestart_C",PEPJDSetRestart_JD));
    2000:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetRestart_C",PEPJDGetRestart_JD));
    2001:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetFix_C",PEPJDSetFix_JD));
    2002:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetFix_C",PEPJDGetFix_JD));
    2003:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetReusePreconditioner_C",PEPJDSetReusePreconditioner_JD));
    2004:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetReusePreconditioner_C",PEPJDGetReusePreconditioner_JD));
    2005:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetMinimalityIndex_C",PEPJDSetMinimalityIndex_JD));
    2006:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetMinimalityIndex_C",PEPJDGetMinimalityIndex_JD));
    2007:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDSetProjection_C",PEPJDSetProjection_JD));
    2008:   PetscCall(PetscObjectComposeFunction((PetscObject)pep,"PEPJDGetProjection_C",PEPJDGetProjection_JD));
    2009:   PetscFunctionReturn(PETSC_SUCCESS);
    2010: }