Date: 2013-09-02T10:06:09+00:00

Actual source code: sinvert.c

      1: /*
      2:       Implements the shift-and-invert technique for eigenvalue problems.

      4:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      5:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      6:    Copyright (c) 2002-2013, 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>          /*I "slepcst.h" I*/

     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,1,st->w,y);
     37:   } else {
     38:     /* standard eigenproblem: y = (A - sI)^-1 x */
     39:     STMatSolve(st,1,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,1,x,st->w);
     54:     MatMultTranspose(st->T[0],st->w,y);
     55:   } else {
     56:     /* standard eigenproblem: y = (A - sI)^-T x */
     57:     STMatSolveTranspose(st,1,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: {
     94:   PetscScalar    s;

     97:   if (st->shift_matrix == ST_MATMODE_INPLACE) {
     98:     if (st->nmat>1) {
     99:       if (st->nmat==3) {
    100:         MatAXPY(st->A[0],-st->sigma*st->sigma,st->A[2],st->str);
    101:         MatAXPY(st->A[1],-2.0*st->sigma,st->A[2],st->str);
    102:         s = -st->sigma;
    103:       } else s = st->sigma;
    104:       MatAXPY(st->A[0],s,st->A[1],st->str);
    105:     } else {
    106:       MatShift(st->A[0],st->sigma);
    107:     }
    108:     st->Astate[0] = ((PetscObject)st->A[0])->state;
    109:     st->setupcalled = 0;
    110:   }
    111:   return(0);
    112: }

    116: PetscErrorCode STSetUp_Sinvert(ST st)
    117: {
    119:   PetscScalar    gamma;

    122:   /* if the user did not set the shift, use the target value */
    123:   if (!st->sigma_set) st->sigma = st->defsigma;
    124:   if (st->nmat<3) {
    125:     /* T[0] = B */
    126:     if (st->nmat>1) { PetscObjectReference((PetscObject)st->A[1]); }
    127:     st->T[0] = st->A[1];
    128:     gamma = -st->sigma;
    129:   } else {
    130:     /* T[0] = C */
    131:     PetscObjectReference((PetscObject)st->A[2]);
    132:     st->T[0] = st->A[2];
    133:     /* T[2] = A+sigma*B+sigma*sigma*C */
    134:     STMatGAXPY_Private(st,st->sigma,0.0,2,2,PETSC_TRUE);
    135:     gamma = 2.0*st->sigma;
    136:   }
    137:   /* T[1] = A-sigma*B or B+2*sigma*C  */
    138:   STMatGAXPY_Private(st,gamma,0.0,1,1,PETSC_TRUE);
    139:   if (st->nmat<3) {
    140:     if (!st->ksp) { STGetKSP(st,&st->ksp); }
    141:     KSPSetOperators(st->ksp,st->T[1],st->T[1],DIFFERENT_NONZERO_PATTERN);
    142:     KSPSetUp(st->ksp);
    143:     st->kspidx = 1;
    144:   }
    145:   return(0);
    146: }

    150: PetscErrorCode STSetShift_Sinvert(ST st,PetscScalar newshift)
    151: {
    153:   MatStructure   flg;
    154:   PetscScalar    alpha,beta;

    157:   /* Nothing to be done if STSetUp has not been called yet */
    158:   if (!st->setupcalled) return(0);
    159:   if (st->nmat<3) {
    160:     alpha = -newshift; beta = -st->sigma;
    161:   } else {
    162:     STMatGAXPY_Private(st,newshift,st->sigma,2,2,PETSC_FALSE);
    163:     alpha = 2.0*newshift; beta = 2.0*st->sigma;
    164:   }
    165:   STMatGAXPY_Private(st,alpha,beta,1,1,PETSC_FALSE);
    166:   if (st->kspidx==1 || (st->nmat==3 && st->kspidx==2)) {  /* Update KSP operator */
    167:     /* Check if the new KSP matrix has the same zero structure */
    168:     if (st->nmat>1 && st->str == DIFFERENT_NONZERO_PATTERN && (st->sigma == 0.0 || newshift == 0.0)) flg = DIFFERENT_NONZERO_PATTERN;
    169:     else flg = SAME_NONZERO_PATTERN;
    170:     KSPSetOperators(st->ksp,st->T[st->kspidx],st->T[st->kspidx],flg);
    171:     KSPSetUp(st->ksp);
    172:   }
    173:   return(0);
    174: }

    178: PetscErrorCode STSetFromOptions_Sinvert(ST st)
    179: {
    181:   PC             pc;
    182:   PCType         pctype;
    183:   KSPType        ksptype;

    186:   if (!st->ksp) { STGetKSP(st,&st->ksp); }
    187:   KSPGetPC(st->ksp,&pc);
    188:   KSPGetType(st->ksp,&ksptype);
    189:   PCGetType(pc,&pctype);
    190:   if (!pctype && !ksptype) {
    191:     if (st->shift_matrix == ST_MATMODE_SHELL) {
    192:       /* in shell mode use GMRES with Jacobi as the default */
    193:       KSPSetType(st->ksp,KSPGMRES);
    194:       PCSetType(pc,PCJACOBI);
    195:     } else {
    196:       /* use direct solver as default */
    197:       KSPSetType(st->ksp,KSPPREONLY);
    198:       PCSetType(pc,PCREDUNDANT);
    199:     }
    200:   }
    201:   return(0);
    202: }

    206: PETSC_EXTERN PetscErrorCode STCreate_Sinvert(ST st)
    207: {
    209:   st->ops->apply           = STApply_Sinvert;
    210:   st->ops->getbilinearform = STGetBilinearForm_Default;
    211:   st->ops->applytrans      = STApplyTranspose_Sinvert;
    212:   st->ops->postsolve       = STPostSolve_Sinvert;
    213:   st->ops->backtransform   = STBackTransform_Sinvert;
    214:   st->ops->setup           = STSetUp_Sinvert;
    215:   st->ops->setshift        = STSetShift_Sinvert;
    216:   st->ops->setfromoptions  = STSetFromOptions_Sinvert;
    217:   st->ops->checknullspace  = STCheckNullSpace_Default;
    218:   return(0);
    219: }