Date: 2026-03-31T13:23:32+00:00

Actual source code: lapack.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:    This file implements a wrapper to the LAPACK eigenvalue subroutines.
     12:    Generalized problems are transformed to standard ones only if necessary.
     13: */

     15: #include <slepc/private/epsimpl.h>

     17: static PetscErrorCode EPSSetUp_LAPACK(EPS eps)
     18: {
     19:   int            ierra,ierrb;
     20:   PetscBool      isshift,flg,denseok=PETSC_FALSE;
     21:   Mat            A,B,OP,shell,Ar,Br,Adense=NULL,Bdense=NULL,Ads,Bds;
     22:   PetscScalar    shift;
     23:   PetscInt       nmat;
     24:   KSP            ksp;
     25:   PC             pc;

     27:   PetscFunctionBegin;
     28:   EPSCheckNotStructured(eps);
     29:   if (eps->nev==0) eps->nev = 1;
     30:   eps->ncv = eps->n;
     31:   if (eps->mpd!=PETSC_DETERMINE) PetscCall(PetscInfo(eps,"Warning: parameter mpd ignored\n"));
     32:   if (eps->max_it==PETSC_DETERMINE) eps->max_it = 1;
     33:   if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps));
     34:   PetscCheck(eps->which!=EPS_ALL || eps->inta==eps->intb,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support interval computation");
     35:   EPSCheckUnsupported(eps,EPS_FEATURE_BALANCE | EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION);
     36:   EPSCheckIgnored(eps,EPS_FEATURE_EXTRACTION | EPS_FEATURE_CONVERGENCE | EPS_FEATURE_STOPPING);
     37:   PetscCall(EPSAllocateSolution(eps,0));

     39:   /* attempt to get dense representations of A and B separately */
     40:   PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STSHIFT,&isshift));
     41:   if (isshift) {
     42:     PetscCall(STGetNumMatrices(eps->st,&nmat));
     43:     PetscCall(STGetMatrix(eps->st,0,&A));
     44:     PetscCall(MatHasOperation(A,MATOP_CREATE_SUBMATRICES,&flg));
     45:     if (flg) {
     46:       PetscCall(PetscPushErrorHandler(PetscReturnErrorHandler,NULL));
     47:       ierra  = MatCreateRedundantMatrix(A,0,PETSC_COMM_SELF,MAT_INITIAL_MATRIX,&Ar);
     48:       if (!ierra) ierra |= MatConvert(Ar,MATSEQDENSE,MAT_INITIAL_MATRIX,&Adense);
     49:       ierra |= MatDestroy(&Ar);
     50:       PetscCall(PetscPopErrorHandler());
     51:     } else ierra = 1;
     52:     if (nmat>1) {
     53:       PetscCall(STGetMatrix(eps->st,1,&B));
     54:       PetscCall(MatHasOperation(B,MATOP_CREATE_SUBMATRICES,&flg));
     55:       if (flg) {
     56:         PetscCall(PetscPushErrorHandler(PetscReturnErrorHandler,NULL));
     57:         ierrb  = MatCreateRedundantMatrix(B,0,PETSC_COMM_SELF,MAT_INITIAL_MATRIX,&Br);
     58:         if (!ierrb) ierrb |= MatConvert(Br,MATSEQDENSE,MAT_INITIAL_MATRIX,&Bdense);
     59:         ierrb |= MatDestroy(&Br);
     60:         PetscCall(PetscPopErrorHandler());
     61:       } else ierrb = 1;
     62:     } else ierrb = 0;
     63:     denseok = PetscNot(ierra || ierrb);
     64:   }

     66:   /* setup DS */
     67:   if (denseok) {
     68:     if (eps->isgeneralized) {
     69:       if (eps->ishermitian) {
     70:         if (eps->ispositive) PetscCall(DSSetType(eps->ds,DSGHEP));
     71:         else PetscCall(DSSetType(eps->ds,DSGNHEP)); /* TODO: should be DSGHIEP */
     72:       } else PetscCall(DSSetType(eps->ds,DSGNHEP));
     73:     } else {
     74:       if (eps->ishermitian) PetscCall(DSSetType(eps->ds,DSHEP));
     75:       else PetscCall(DSSetType(eps->ds,DSNHEP));
     76:     }
     77:   } else PetscCall(DSSetType(eps->ds,DSNHEP));
     78:   PetscCall(DSAllocate(eps->ds,eps->ncv));
     79:   PetscCall(DSSetDimensions(eps->ds,eps->ncv,0,0));

     81:   if (denseok) {
     82:     PetscCall(STGetShift(eps->st,&shift));
     83:     if (shift != 0.0) {
     84:       if (nmat>1) PetscCall(MatAXPY(Adense,-shift,Bdense,SAME_NONZERO_PATTERN));
     85:       else PetscCall(MatShift(Adense,-shift));
     86:     }
     87:     /* use dummy pc and ksp to avoid problems when B is not positive definite */
     88:     PetscCall(STGetKSP(eps->st,&ksp));
     89:     PetscCall(KSPSetType(ksp,KSPPREONLY));
     90:     PetscCall(KSPGetPC(ksp,&pc));
     91:     PetscCall(PCSetType(pc,PCNONE));
     92:   } else {
     93:     PetscCall(PetscInfo(eps,"Using slow explicit operator\n"));
     94:     PetscCall(STGetOperator(eps->st,&shell));
     95:     PetscCall(MatComputeOperator(shell,MATDENSE,&OP));
     96:     PetscCall(STRestoreOperator(eps->st,&shell));
     97:     PetscCall(MatDestroy(&Adense));
     98:     PetscCall(MatCreateRedundantMatrix(OP,0,PETSC_COMM_SELF,MAT_INITIAL_MATRIX,&Adense));
     99:     PetscCall(MatDestroy(&OP));
    100:   }

    102:   /* fill DS matrices */
    103:   PetscCall(DSGetMat(eps->ds,DS_MAT_A,&Ads));
    104:   PetscCall(MatCopy(Adense,Ads,SAME_NONZERO_PATTERN));
    105:   PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&Ads));
    106:   if (denseok && eps->isgeneralized) {
    107:     PetscCall(DSGetMat(eps->ds,DS_MAT_B,&Bds));
    108:     PetscCall(MatCopy(Bdense,Bds,SAME_NONZERO_PATTERN));
    109:     PetscCall(DSRestoreMat(eps->ds,DS_MAT_B,&Bds));
    110:   }
    111:   PetscCall(DSSetState(eps->ds,DS_STATE_RAW));
    112:   PetscCall(MatDestroy(&Adense));
    113:   PetscCall(MatDestroy(&Bdense));
    114:   PetscFunctionReturn(PETSC_SUCCESS);
    115: }

    117: static PetscErrorCode EPSSolve_LAPACK(EPS eps)
    118: {
    119:   PetscInt       n=eps->n,i,low,high;
    120:   PetscScalar    *array,*pX,*pY;
    121:   Vec            v,w;

    123:   PetscFunctionBegin;
    124:   PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi));
    125:   PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL));
    126:   PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));

    128:   /* right eigenvectors */
    129:   PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL));
    130:   PetscCall(DSGetArray(eps->ds,DS_MAT_X,&pX));
    131:   for (i=0;i<eps->ncv;i++) {
    132:     PetscCall(BVGetColumn(eps->V,i,&v));
    133:     PetscCall(VecGetOwnershipRange(v,&low,&high));
    134:     PetscCall(VecGetArray(v,&array));
    135:     PetscCall(PetscArraycpy(array,pX+i*n+low,high-low));
    136:     PetscCall(VecRestoreArray(v,&array));
    137:     PetscCall(BVRestoreColumn(eps->V,i,&v));
    138:   }
    139:   PetscCall(DSRestoreArray(eps->ds,DS_MAT_X,&pX));

    141:   /* left eigenvectors */
    142:   if (eps->twosided) {
    143:     PetscCall(DSVectors(eps->ds,DS_MAT_Y,NULL,NULL));
    144:     PetscCall(DSGetArray(eps->ds,DS_MAT_Y,&pY));
    145:     for (i=0;i<eps->ncv;i++) {
    146:       PetscCall(BVGetColumn(eps->W,i,&w));
    147:       PetscCall(VecGetOwnershipRange(w,&low,&high));
    148:       PetscCall(VecGetArray(w,&array));
    149:       PetscCall(PetscArraycpy(array,pY+i*n+low,high-low));
    150:       PetscCall(VecRestoreArray(w,&array));
    151:       PetscCall(BVRestoreColumn(eps->W,i,&w));
    152:     }
    153:     PetscCall(DSRestoreArray(eps->ds,DS_MAT_Y,&pY));
    154:   }

    156:   eps->nconv  = eps->ncv;
    157:   eps->its    = 1;
    158:   eps->reason = EPS_CONVERGED_TOL;
    159:   PetscFunctionReturn(PETSC_SUCCESS);
    160: }

    162: /*MC
    163:    EPSLAPACK - EPSLAPACK = "lapack" - A wrapper to LAPACK eigensolvers.

    165:    Notes:
    166:    This is not really a full-featured eigensolver but simply an interface to
    167:    some LAPACK routines {cite:p}`And99`. These routines operate sequentially
    168:    in dense mode and therefore are suitable only for small size problems.
    169:    This solver should be used only for debugging purposes.

    171:    The LAPACK routine is not called directly, instead a `DS` object of
    172:    the appropriate type is set up.

    174:    Level: beginner

    176: .seealso: [](ch:eps), `EPS`, `EPSType`, `EPSSetType()`, `DS`
    177: M*/
    178: SLEPC_EXTERN PetscErrorCode EPSCreate_LAPACK(EPS eps)
    179: {
    180:   PetscFunctionBegin;
    181:   eps->useds = PETSC_TRUE;
    182:   eps->categ = EPS_CATEGORY_OTHER;

    184:   eps->ops->solve          = EPSSolve_LAPACK;
    185:   eps->ops->setup          = EPSSetUp_LAPACK;
    186:   eps->ops->setupsort      = EPSSetUpSort_Default;
    187:   eps->ops->backtransform  = EPSBackTransform_Default;
    188:   PetscFunctionReturn(PETSC_SUCCESS);
    189: }