Date: 2022-11-02T11:46:12+00:00

Actual source code: dsghep.c
slepc-3.18.1 2022-11-02
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

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

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

     14: PetscErrorCode DSAllocate_GHEP(DS ds,PetscInt ld)
     15: {
     16:   DSAllocateMat_Private(ds,DS_MAT_A);
     17:   DSAllocateMat_Private(ds,DS_MAT_B);
     18:   DSAllocateMat_Private(ds,DS_MAT_Q);
     19:   PetscFree(ds->perm);
     20:   PetscMalloc1(ld,&ds->perm);
     21:   return 0;
     22: }

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

     28:   PetscViewerGetFormat(viewer,&format);
     29:   if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) return 0;
     30:   DSViewMat(ds,viewer,DS_MAT_A);
     31:   DSViewMat(ds,viewer,DS_MAT_B);
     32:   if (ds->state>DS_STATE_INTERMEDIATE) DSViewMat(ds,viewer,DS_MAT_Q);
     33:   if (ds->omat[DS_MAT_X]) DSViewMat(ds,viewer,DS_MAT_X);
     34:   return 0;
     35: }

     37: PetscErrorCode DSVectors_GHEP(DS ds,DSMatType mat,PetscInt *j,PetscReal *rnorm)
     38: {
     39:   PetscScalar       *Z;
     40:   const PetscScalar *Q;
     41:   PetscInt          ld = ds->ld;

     44:   switch (mat) {
     45:     case DS_MAT_X:
     46:     case DS_MAT_Y:
     47:       if (j) {
     48:         MatDenseGetArray(ds->omat[mat],&Z);
     49:         if (ds->state>=DS_STATE_CONDENSED) {
     50:           MatDenseGetArrayRead(ds->omat[DS_MAT_Q],&Q);
     51:           PetscArraycpy(Z+(*j)*ld,Q+(*j)*ld,ld);
     52:           MatDenseRestoreArrayRead(ds->omat[DS_MAT_Q],&Q);
     53:         } else {
     54:           PetscArrayzero(Z+(*j)*ld,ld);
     55:           Z[(*j)+(*j)*ld] = 1.0;
     56:         }
     57:         MatDenseRestoreArray(ds->omat[mat],&Z);
     58:       } else {
     59:         if (ds->state>=DS_STATE_CONDENSED) MatCopy(ds->omat[DS_MAT_Q],ds->omat[mat],SAME_NONZERO_PATTERN);
     60:         else DSSetIdentity(ds,mat);
     61:       }
     62:       break;
     63:     case DS_MAT_U:
     64:     case DS_MAT_V:
     65:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_SUP,"Not implemented yet");
     66:     default:
     67:       SETERRQ(PetscObjectComm((PetscObject)ds),PETSC_ERR_ARG_OUTOFRANGE,"Invalid mat parameter");
     68:   }
     69:   return 0;
     70: }

     72: PetscErrorCode DSSort_GHEP(DS ds,PetscScalar *wr,PetscScalar *wi,PetscScalar *rr,PetscScalar *ri,PetscInt *k)
     73: {
     74:   PetscInt       n,l,i,*perm,ld=ds->ld;
     75:   PetscScalar    *A;

     77:   if (!ds->sc) return 0;
     78:   n = ds->n;
     79:   l = ds->l;
     80:   MatDenseGetArray(ds->omat[DS_MAT_A],&A);
     81:   perm = ds->perm;
     82:   for (i=l;i<n;i++) wr[i] = A[i+i*ld];
     83:   if (rr) DSSortEigenvalues_Private(ds,rr,ri,perm,PETSC_FALSE);
     84:   else DSSortEigenvalues_Private(ds,wr,NULL,perm,PETSC_FALSE);
     85:   for (i=l;i<n;i++) A[i+i*ld] = wr[perm[i]];
     86:   for (i=l;i<n;i++) wr[i] = A[i+i*ld];
     87:   MatDenseRestoreArray(ds->omat[DS_MAT_A],&A);
     88:   DSPermuteColumns_Private(ds,l,n,n,DS_MAT_Q,perm);
     89:   return 0;
     90: }

     92: PetscErrorCode DSSolve_GHEP(DS ds,PetscScalar *wr,PetscScalar *wi)
     93: {
     94:   PetscScalar    *work,*A,*B,*Q;
     95:   PetscBLASInt   itype = 1,*iwork,info,n1,liwork,ld,lrwork=0,lwork;
     96:   PetscInt       off,i;
     97: #if defined(PETSC_USE_COMPLEX)
     98:   PetscReal      *rwork,*rr;
     99: #endif

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

    142: #if !defined(PETSC_HAVE_MPIUNI)
    143: PetscErrorCode DSSynchronize_GHEP(DS ds,PetscScalar eigr[],PetscScalar eigi[])
    144: {
    145:   PetscScalar    *A,*B,*Q;
    146:   PetscInt       ld=ds->ld,l=ds->l,k;
    147:   PetscMPIInt    n,rank,off=0,size,ldn;

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

    180: PetscErrorCode DSHermitian_GHEP(DS ds,DSMatType m,PetscBool *flg)
    181: {
    182:   if (m==DS_MAT_A || m==DS_MAT_B) *flg = PETSC_TRUE;
    183:   else *flg = PETSC_FALSE;
    184:   return 0;
    185: }

    187: /*MC
    188:    DSGHEP - Dense Generalized Hermitian Eigenvalue Problem.

    190:    Level: beginner

    192:    Notes:
    193:    The problem is expressed as A*X = B*X*Lambda, where both A and B are
    194:    real symmetric (or complex Hermitian) and B is positive-definite. Lambda
    195:    is a diagonal matrix whose diagonal elements are the arguments of DSSolve().
    196:    After solve, A is overwritten with Lambda, and B is overwritten with I.

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

    200:    Used DS matrices:
    201: +  DS_MAT_A - first problem matrix
    202: .  DS_MAT_B - second problem matrix
    203: -  DS_MAT_Q - matrix of B-orthogonal eigenvectors, which is equal to X

    205:    Implemented methods:
    206: .  0 - Divide and Conquer (_sygvd)

    208: .seealso: DSCreate(), DSSetType(), DSType
    209: M*/
    210: SLEPC_EXTERN PetscErrorCode DSCreate_GHEP(DS ds)
    211: {
    212:   ds->ops->allocate      = DSAllocate_GHEP;
    213:   ds->ops->view          = DSView_GHEP;
    214:   ds->ops->vectors       = DSVectors_GHEP;
    215:   ds->ops->solve[0]      = DSSolve_GHEP;
    216:   ds->ops->sort          = DSSort_GHEP;
    217: #if !defined(PETSC_HAVE_MPIUNI)
    218:   ds->ops->synchronize   = DSSynchronize_GHEP;
    219: #endif
    220:   ds->ops->hermitian     = DSHermitian_GHEP;
    221:   return 0;
    222: }