Date: 2026-03-09T09:12:15+00:00

Actual source code: dsghep.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: */

     11: #include <slepc/private/dsimpl.h>
     12: #include <slepcblaslapack.h>

     14: static PetscErrorCode DSAllocate_GHEP(DS ds,PetscInt ld)
     15: {
     16:   PetscFunctionBegin;
     17:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_A));
     18:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_B));
     19:   PetscCall(DSAllocateMat_Private(ds,DS_MAT_Q));
     20:   PetscCall(PetscFree(ds->perm));
     21:   PetscCall(PetscMalloc1(ld,&ds->perm));
     22:   PetscFunctionReturn(PETSC_SUCCESS);
     23: }

     25: static PetscErrorCode DSView_GHEP(DS ds,PetscViewer viewer)
     26: {
     27:   PetscViewerFormat format;

     29:   PetscFunctionBegin;
     30:   PetscCall(PetscViewerGetFormat(viewer,&format));
     31:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscFunctionReturn(PETSC_SUCCESS);
     32:   PetscCall(DSViewMat(ds,viewer,DS_MAT_A));
     33:   PetscCall(DSViewMat(ds,viewer,DS_MAT_B));
     34:   if (ds->state>DS_STATE_INTERMEDIATE) PetscCall(DSViewMat(ds,viewer,DS_MAT_Q));
     35:   if (ds->omat[DS_MAT_X]) PetscCall(DSViewMat(ds,viewer,DS_MAT_X));
     36:   PetscFunctionReturn(PETSC_SUCCESS);
     37: }

     39: static PetscErrorCode DSVectors_GHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
     40: {
     41:   PetscScalar       *Z;
     42:   const PetscScalar *Q;
     43:   PetscInt          ld = ds->ld;

     45:   PetscFunctionBegin;
     46:   PetscCheck(!rnorm,PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
     47:   switch (mat) {
     48:     case DS_MAT_X:
     49:     case DS_MAT_Y:
     50:       if (j) {
     51:         PetscCall(MatDenseGetArray(ds->omat[mat],&Z));
     52:         if (ds->state>=DS_STATE_CONDENSED) {
     53:           PetscCall(MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q));
     54:           PetscCall(PetscArraycpy(Z+(*j)*ld,Q+(*j)*ld,ld));
     55:           PetscCall(MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q));
     56:         } else {
     57:           PetscCall(PetscArrayzero(Z+(*j)*ld,ld));
     58:           Z[(*j)+(*j)*ld] = 1.0;
     59:         }
     60:         PetscCall(MatDenseRestoreArray(ds->omat[mat],&Z));
     61:       } else {
     62:         if (ds->state>=DS_STATE_CONDENSED) PetscCall(MatCopy(ds->omat[DS_MAT_Q],ds->omat[mat],SAME_NONZERO_PATTERN));
     63:         else PetscCall(DSSetIdentity(ds,mat));
     64:       }
     65:       break;
     66:     case DS_MAT_U:
     67:     case DS_MAT_V:
     68:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
     69:     default:
     70:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
     71:   }
     72:   PetscFunctionReturn(PETSC_SUCCESS);
     73: }

     75: static PetscErrorCode DSSort_GHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
     76: {
     77:   PetscInt       n,l,i,*perm,ld=ds->ld;
     78:   PetscScalar    *A;

     80:   PetscFunctionBegin;
     81:   if (!ds->sc) PetscFunctionReturn(PETSC_SUCCESS);
     82:   n = ds->n;
     83:   l = ds->l;
     84:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
     85:   perm = ds->perm;
     86:   for (i=l;i<n;i++) wr[i] = A[i+i*ld];
     87:   if (rr) PetscCall(DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE));
     88:   else PetscCall(DSSortEigenvalues_Private(ds,wr,NULL,perm,PETSC_FALSE));
     89:   for (i=l;i<n;i++) A[i+i*ld] = wr[perm[i]];
     90:   for (i=l;i<n;i++) wr[i] = A[i+i*ld];
     91:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
     92:   PetscCall(DSPermuteColumns_Private(ds,l,n,n,DS_MAT_Q,perm));
     93:   PetscFunctionReturn(PETSC_SUCCESS);
     94: }

     96: static PetscErrorCode DSSolve_GHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
     97: {
     98:   PetscScalar    *work,*A,*B,*Q;
     99:   PetscBLASInt   itype = 1,*iwork,info,n1,liwork,ld,lrwork=0,lwork;
    100:   PetscInt       off,i;
    101: #if defined(PETSC_USE_COMPLEX)
    102:   PetscReal      *rwork,*rr;
    103: #endif

    105:   PetscFunctionBegin;
    106:   PetscCall(PetscBLASIntCast(ds->n-ds->l,&n1));
    107:   PetscCall(PetscBLASIntCast(ds->ld,&ld));
    108:   PetscCall(PetscBLASIntCast(5*ds->n+3,&liwork));
    109: #if defined(PETSC_USE_COMPLEX)
    110:   PetscCall(PetscBLASIntCast(ds->n*ds->n+2*ds->n,&lwork));
    111:   PetscCall(PetscBLASIntCast(2*ds->n*ds->n+5*ds->n+1+n1,&lrwork));
    112: #else
    113:   PetscCall(PetscBLASIntCast(2*ds->n*ds->n+6*ds->n+1,&lwork));
    114: #endif
    115:   PetscCall(DSAllocateWork_Private(ds,lwork,lrwork,liwork));
    116:   work = ds->work;
    117:   iwork = ds->iwork;
    118:   off = ds->l+ds->l*ld;
    119:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    120:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
    121:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
    122: #if defined(PETSC_USE_COMPLEX)
    123:   rr = ds->rwork;
    124:   rwork = ds->rwork+n1;
    125:   PetscCall(PetscBLASIntCast(ds->lrwork-n1,&lrwork));
    126:   PetscCallBLAS("LAPACKsygvd",LAPACKsygvd_(&itype,"V","U",&n1,A+off,&ld,B+off,&ld,rr,work,&lwork,rwork,&lrwork,iwork,&liwork,&info));
    127:   for (i=0;i<n1;i++) wr[ds->l+i] = rr[i];
    128: #else
    129:   PetscCallBLAS("LAPACKsygvd",LAPACKsygvd_(&itype,"V","U",&n1,A+off,&ld,B+off,&ld,wr+ds->l,work,&lwork,iwork,&liwork,&info));
    130: #endif
    131:   SlepcCheckLapackInfo("sygvd",info);
    132:   PetscCall(PetscArrayzero(Q+ds->l*ld,n1*ld));
    133:   for (i=ds->l;i<ds->n;i++) PetscCall(PetscArraycpy(Q+ds->l+i*ld,A+ds->l+i*ld,n1));
    134:   PetscCall(PetscArrayzero(B+ds->l*ld,n1*ld));
    135:   PetscCall(PetscArrayzero(A+ds->l*ld,n1*ld));
    136:   for (i=ds->l;i<ds->n;i++) {
    137:     if (wi) wi[i] = 0.0;
    138:     B[i+i*ld] = 1.0;
    139:     A[i+i*ld] = wr[i];
    140:   }
    141:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    142:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
    143:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
    144:   PetscFunctionReturn(PETSC_SUCCESS);
    145: }

    147: #if !defined(PETSC_HAVE_MPIUNI)
    148: static PetscErrorCode DSSynchronize_GHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    149: {
    150:   PetscScalar    *A,*B,*Q;
    151:   PetscInt       ld=ds->ld,l=ds->l,k;
    152:   PetscMPIInt    n,rank,off=0,size,ldn;

    154:   PetscFunctionBegin;
    155:   k = 2*(ds->n-l)*ld;
    156:   if (ds->state>DS_STATE_RAW) k += (ds->n-l)*ld;
    157:   if (eigr) k += (ds->n-l);
    158:   PetscCall(DSAllocateWork_Private(ds,k,0,0));
    159:   PetscCall(PetscMPIIntCast(k*sizeof(PetscScalar),&size));
    160:   PetscCall(PetscMPIIntCast(ds->n-l,&n));
    161:   PetscCall(PetscMPIIntCast(ld*(ds->n-l),&ldn));
    162:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_A],&A));
    163:   PetscCall(MatDenseGetArray(ds->omat[DS_MAT_B],&B));
    164:   if (ds->state>DS_STATE_RAW) PetscCall(MatDenseGetArray(ds->omat[DS_MAT_Q],&Q));
    165:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)ds),&rank));
    166:   if (!rank) {
    167:     PetscCallMPI(MPI_Pack(A+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    168:     PetscCallMPI(MPI_Pack(B+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    169:     if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Pack(Q+l*ld,ldn,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    170:     if (eigr) PetscCallMPI(MPI_Pack(eigr+l,n,MPIU_SCALAR,ds->work,size,&off,PetscObjectComm((PetscObject)ds)));
    171:   }
    172:   PetscCallMPI(MPI_Bcast(ds->work,size,MPI_BYTE,0,PetscObjectComm((PetscObject)ds)));
    173:   if (rank) {
    174:     PetscCallMPI(MPI_Unpack(ds->work,size,&off,A+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    175:     PetscCallMPI(MPI_Unpack(ds->work,size,&off,B+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    176:     if (ds->state>DS_STATE_RAW) PetscCallMPI(MPI_Unpack(ds->work,size,&off,Q+l*ld,ldn,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    177:     if (eigr) PetscCallMPI(MPI_Unpack(ds->work,size,&off,eigr+l,n,MPIU_SCALAR,PetscObjectComm((PetscObject)ds)));
    178:   }
    179:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_A],&A));
    180:   PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_B],&B));
    181:   if (ds->state>DS_STATE_RAW) PetscCall(MatDenseRestoreArray(ds->omat[DS_MAT_Q],&Q));
    182:   PetscFunctionReturn(PETSC_SUCCESS);
    183: }
    184: #endif

    186: static PetscErrorCode DSHermitian_GHEP(DS ds,DSMatType m,PetscBool *flg)
    187: {
    188:   PetscFunctionBegin;
    189:   if (m==DS_MAT_A || m==DS_MAT_B) *flg = PETSC_TRUE;
    190:   else *flg = PETSC_FALSE;
    191:   PetscFunctionReturn(PETSC_SUCCESS);
    192: }

    194: /*MC
    195:    DSGHEP - Dense Generalized Hermitian Eigenvalue Problem.

    197:    Notes:
    198:    The problem is expressed as $AX = BX\Lambda$, where both $A$ and $B$ are
    199:    real symmetric (or complex Hermitian) and $B$ is positive-definite. $\Lambda$
    200:    is a diagonal matrix whose diagonal elements are the arguments of `DSSolve()`.
    201:    After solve, $A$ is overwritten with $\Lambda$, and $B$ is overwritten with $I$.

    203:    No intermediate state is implemented, nor compact storage.

    205:    Used DS matrices:
    206: +  `DS_MAT_A` - first problem matrix
    207: .  `DS_MAT_B` - second problem matrix
    208: -  `DS_MAT_Q` - matrix of $B$-orthogonal eigenvectors, which is equal to $X$

    210:    Implemented methods:
    211: .  0 - Divide and Conquer (`_sygvd`)

    213:    Level: beginner

    215: .seealso: [](sec:ds), `DSCreate()`, `DSSetType()`, `DSType`
    216: M*/
    217: SLEPC_EXTERN PetscErrorCode DSCreate_GHEP(DS ds)
    218: {
    219:   PetscFunctionBegin;
    220:   ds->ops->allocate      = DSAllocate_GHEP;
    221:   ds->ops->view          = DSView_GHEP;
    222:   ds->ops->vectors       = DSVectors_GHEP;
    223:   ds->ops->solve[0]      = DSSolve_GHEP;
    224:   ds->ops->sort          = DSSort_GHEP;
    225: #if !defined(PETSC_HAVE_MPIUNI)
    226:   ds->ops->synchronize   = DSSynchronize_GHEP;
    227: #endif
    228:   ds->ops->hermitian     = DSHermitian_GHEP;
    229:   PetscFunctionReturn(PETSC_SUCCESS);
    230: }