Date: 2017-05-17T08:25:07+00:00

Actual source code: sinvert.c
slepc-3.7.4 2017-05-17
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      1: /*
      2:       Implements the shift-and-invert technique for eigenvalue problems.

      4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      6:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

      8:    This file is part of SLEPc.

     10:    SLEPc is free software: you can redistribute it and/or modify it under  the
     11:    terms of version 3 of the GNU Lesser General Public License as published by
     12:    the Free Software Foundation.

     14:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     15:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     16:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     17:    more details.

     19:    You  should have received a copy of the GNU Lesser General  Public  License
     20:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     21:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     22: */

     24: #include <slepc/private/stimpl.h>

     28: PetscErrorCode STApply_Sinvert(ST st,Vec x,Vec y)
     29: {

     33:   if (st->nmat>1) {
     34:     /* generalized eigenproblem: y = (A - sB)^-1 B x */
     35:     MatMult(st->T[0],x,st->w);
     36:     STMatSolve(st,st->w,y);
     37:   } else {
     38:     /* standard eigenproblem: y = (A - sI)^-1 x */
     39:     STMatSolve(st,x,y);
     40:   }
     41:   return(0);
     42: }

     46: PetscErrorCode STApplyTranspose_Sinvert(ST st,Vec x,Vec y)
     47: {

     51:   if (st->nmat>1) {
     52:     /* generalized eigenproblem: y = B^T (A - sB)^-T x */
     53:     STMatSolveTranspose(st,x,st->w);
     54:     MatMultTranspose(st->T[0],st->w,y);
     55:   } else {
     56:     /* standard eigenproblem: y = (A - sI)^-T x */
     57:     STMatSolveTranspose(st,x,y);
     58:   }
     59:   return(0);
     60: }

     64: PetscErrorCode STBackTransform_Sinvert(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
     65: {
     66:   PetscInt    j;
     67: #if !defined(PETSC_USE_COMPLEX)
     68:   PetscScalar t;
     69: #endif

     72: #if !defined(PETSC_USE_COMPLEX)
     73:   for (j=0;j<n;j++) {
     74:     if (eigi[j] == 0) eigr[j] = 1.0 / eigr[j] + st->sigma;
     75:     else {
     76:       t = eigr[j] * eigr[j] + eigi[j] * eigi[j];
     77:       eigr[j] = eigr[j] / t + st->sigma;
     78:       eigi[j] = - eigi[j] / t;
     79:     }
     80:   }
     81: #else
     82:   for (j=0;j<n;j++) {
     83:     eigr[j] = 1.0 / eigr[j] + st->sigma;
     84:   }
     85: #endif
     86:   return(0);
     87: }

     91: PetscErrorCode STPostSolve_Sinvert(ST st)
     92: {

     96:   if (st->shift_matrix == ST_MATMODE_INPLACE) {
     97:     if (st->nmat>1) {
     98:       MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
     99:     } else {
    100:       MatShift(st->A[0],st->sigma);
    101:     }
    102:     st->Astate[0] = ((PetscObject)st->A[0])->state;
    103:     st->state = ST_STATE_INITIAL;
    104:   }
    105:   return(0);
    106: }

    110: PetscErrorCode STSetUp_Sinvert(ST st)
    111: {
    113:   PetscInt       k,nc,nmat=PetscMax(st->nmat,2);
    114:   PetscScalar    *coeffs=NULL;

    117:   if (st->nmat>1) {
    118:     ST_AllocateWorkVec(st);
    119:   }
    120:   /* if the user did not set the shift, use the target value */
    121:   if (!st->sigma_set) st->sigma = st->defsigma;
    122:   if (st->transform) {
    123:     if (nmat>2) {
    124:       nc = (nmat*(nmat+1))/2;
    125:       PetscMalloc1(nc,&coeffs);
    126:       /* Compute coeffs */
    127:       STCoeffs_Monomial(st,coeffs);
    128:     }
    129:     /* T[0] = A_n */
    130:     k = nmat-1;
    131:     PetscObjectReference((PetscObject)st->A[k]);
    132:     MatDestroy(&st->T[0]);
    133:     st->T[0] = st->A[k];
    134:     for (k=1;k<nmat;k++) {
    135:       STMatMAXPY_Private(st,nmat>2?st->sigma:-st->sigma,0.0,nmat-k-1,coeffs?coeffs+(k*(k+1))/2:NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[k]);
    136:     }
    137:     if (nmat>2) { PetscFree(coeffs); }
    138:     PetscObjectReference((PetscObject)st->T[nmat-1]);
    139:     MatDestroy(&st->P);
    140:     st->P = st->T[nmat-1];
    141:   } else {
    142:     for (k=0;k<nmat;k++) {
    143:       PetscObjectReference((PetscObject)st->A[k]);
    144:       MatDestroy(&st->T[k]);
    145:       st->T[k] = st->A[k];
    146:     }
    147:   }
    148:   if (st->P) {
    149:     if (!st->ksp) { STGetKSP(st,&st->ksp); }
    150:     STCheckFactorPackage(st);
    151:     KSPSetOperators(st->ksp,st->P,st->P);
    152:     KSPSetErrorIfNotConverged(st->ksp,PETSC_TRUE);
    153:     KSPSetUp(st->ksp);
    154:   }
    155:   return(0);
    156: }

    160: PetscErrorCode STSetShift_Sinvert(ST st,PetscScalar newshift)
    161: {
    163:   PetscInt       nmat=PetscMax(st->nmat,2),k,nc;
    164:   PetscScalar    *coeffs=NULL;

    167:   if (st->transform) {
    168:     if (st->shift_matrix == ST_MATMODE_COPY && nmat>2) {
    169:       nc = (nmat*(nmat+1))/2;
    170:       PetscMalloc1(nc,&coeffs);
    171:       /* Compute coeffs */
    172:       STCoeffs_Monomial(st,coeffs);
    173:     }
    174:     for (k=1;k<nmat;k++) {
    175:       STMatMAXPY_Private(st,nmat>2?newshift:-newshift,nmat>2?st->sigma:-st->sigma,nmat-k-1,coeffs?coeffs+(k*(k+1))/2:NULL,PETSC_FALSE,&st->T[k]);
    176:     }
    177:     if (st->shift_matrix == ST_MATMODE_COPY && nmat>2) {
    178:       PetscFree(coeffs);
    179:     }
    180:     if (st->P!=st->T[nmat-1]) {
    181:       MatDestroy(&st->P);
    182:       st->P = st->T[nmat-1];
    183:       PetscObjectReference((PetscObject)st->P);
    184:     }
    185:   }
    186:   if (st->P) {
    187:     if (!st->ksp) { STGetKSP(st,&st->ksp); }
    188:     KSPSetOperators(st->ksp,st->P,st->P);
    189:     KSPSetUp(st->ksp);
    190:   }
    191:   return(0);
    192: }

    196: PetscErrorCode STSetFromOptions_Sinvert(PetscOptionItems *PetscOptionsObject,ST st)
    197: {
    199:   PC             pc;
    200:   PCType         pctype;
    201:   KSPType        ksptype;

    204:   if (!st->ksp) { STGetKSP(st,&st->ksp); }
    205:   KSPGetPC(st->ksp,&pc);
    206:   KSPGetType(st->ksp,&ksptype);
    207:   PCGetType(pc,&pctype);
    208:   if (!pctype && !ksptype) {
    209:     if (st->shift_matrix == ST_MATMODE_SHELL) {
    210:       /* in shell mode use GMRES with Jacobi as the default */
    211:       KSPSetType(st->ksp,KSPGMRES);
    212:       PCSetType(pc,PCJACOBI);
    213:     } else {
    214:       /* use direct solver as default */
    215:       KSPSetType(st->ksp,KSPPREONLY);
    216:       PCSetType(pc,PCLU);
    217:     }
    218:   }
    219:   return(0);
    220: }

    224: PETSC_EXTERN PetscErrorCode STCreate_Sinvert(ST st)
    225: {
    227:   st->ops->apply           = STApply_Sinvert;
    228:   st->ops->getbilinearform = STGetBilinearForm_Default;
    229:   st->ops->applytrans      = STApplyTranspose_Sinvert;
    230:   st->ops->postsolve       = STPostSolve_Sinvert;
    231:   st->ops->backtransform   = STBackTransform_Sinvert;
    232:   st->ops->setup           = STSetUp_Sinvert;
    233:   st->ops->setshift        = STSetShift_Sinvert;
    234:   st->ops->setfromoptions  = STSetFromOptions_Sinvert;
    235:   st->ops->checknullspace  = STCheckNullSpace_Default;
    236:   return(0);
    237: }