Actual source code: sinvert.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, 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:    Implements the shift-and-invert technique for eigenvalue problems
     12: */

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

     16: PetscErrorCode STApply_Sinvert(ST st,Vec x,Vec y)
     17: {

     21:   if (st->nmat>1) {
     22:     /* generalized eigenproblem: y = (A - sB)^-1 B x */
     23:     MatMult(st->T[0],x,st->work[0]);
     24:     STMatSolve(st,st->work[0],y);
     25:   } else {
     26:     /* standard eigenproblem: y = (A - sI)^-1 x */
     27:     STMatSolve(st,x,y);
     28:   }
     29:   return(0);
     30: }

     32: PetscErrorCode STApplyTranspose_Sinvert(ST st,Vec x,Vec y)
     33: {

     37:   if (st->nmat>1) {
     38:     /* generalized eigenproblem: y = B^T (A - sB)^-T x */
     39:     STMatSolveTranspose(st,x,st->work[0]);
     40:     MatMultTranspose(st->T[0],st->work[0],y);
     41:   } else {
     42:     /* standard eigenproblem: y = (A - sI)^-T x */
     43:     STMatSolveTranspose(st,x,y);
     44:   }
     45:   return(0);
     46: }

     48: PetscErrorCode STBackTransform_Sinvert(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
     49: {
     50:   PetscInt    j;
     51: #if !defined(PETSC_USE_COMPLEX)
     52:   PetscScalar t;
     53: #endif

     56: #if !defined(PETSC_USE_COMPLEX)
     57:   for (j=0;j<n;j++) {
     58:     if (eigi[j] == 0) eigr[j] = 1.0 / eigr[j] + st->sigma;
     59:     else {
     60:       t = eigr[j] * eigr[j] + eigi[j] * eigi[j];
     61:       eigr[j] = eigr[j] / t + st->sigma;
     62:       eigi[j] = - eigi[j] / t;
     63:     }
     64:   }
     65: #else
     66:   for (j=0;j<n;j++) {
     67:     eigr[j] = 1.0 / eigr[j] + st->sigma;
     68:   }
     69: #endif
     70:   return(0);
     71: }

     73: PetscErrorCode STPostSolve_Sinvert(ST st)
     74: {

     78:   if (st->shift_matrix == ST_MATMODE_INPLACE) {
     79:     if (st->nmat>1) {
     80:       MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
     81:     } else {
     82:       MatShift(st->A[0],st->sigma);
     83:     }
     84:     st->Astate[0] = ((PetscObject)st->A[0])->state;
     85:     st->state = ST_STATE_INITIAL;
     86:   }
     87:   return(0);
     88: }

     90: PetscErrorCode STSetUp_Sinvert(ST st)
     91: {
     93:   PetscInt       k,nc,nmat=PetscMax(st->nmat,2);
     94:   PetscScalar    *coeffs=NULL;

     97:   if (st->nmat>1) {
     98:     STSetWorkVecs(st,1);
     99:   }
    100:   /* if the user did not set the shift, use the target value */
    101:   if (!st->sigma_set) st->sigma = st->defsigma;
    102:   if (st->transform) {
    103:     if (nmat>2) {
    104:       nc = (nmat*(nmat+1))/2;
    105:       PetscMalloc1(nc,&coeffs);
    106:       /* Compute coeffs */
    107:       STCoeffs_Monomial(st,coeffs);
    108:     }
    109:     /* T[0] = A_n */
    110:     k = nmat-1;
    111:     PetscObjectReference((PetscObject)st->A[k]);
    112:     MatDestroy(&st->T[0]);
    113:     st->T[0] = st->A[k];
    114:     for (k=1;k<nmat;k++) {
    115:       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]);
    116:     }
    117:     if (nmat>2) { PetscFree(coeffs); }
    118:     PetscObjectReference((PetscObject)st->T[nmat-1]);
    119:     MatDestroy(&st->P);
    120:     st->P = st->T[nmat-1];
    121:   } else {
    122:     for (k=0;k<nmat;k++) {
    123:       PetscObjectReference((PetscObject)st->A[k]);
    124:       MatDestroy(&st->T[k]);
    125:       st->T[k] = st->A[k];
    126:     }
    127:   }
    128:   if (st->P) {
    129:     if (!st->ksp) { STGetKSP(st,&st->ksp); }
    130:     STCheckFactorPackage(st);
    131:     KSPSetOperators(st->ksp,st->P,st->P);
    132:     KSPSetUp(st->ksp);
    133:   }
    134:   return(0);
    135: }

    137: PetscErrorCode STSetShift_Sinvert(ST st,PetscScalar newshift)
    138: {
    140:   PetscInt       nmat=PetscMax(st->nmat,2),k,nc;
    141:   PetscScalar    *coeffs=NULL;

    144:   if (st->transform) {
    145:     if (st->shift_matrix == ST_MATMODE_COPY && nmat>2) {
    146:       nc = (nmat*(nmat+1))/2;
    147:       PetscMalloc1(nc,&coeffs);
    148:       /* Compute coeffs */
    149:       STCoeffs_Monomial(st,coeffs);
    150:     }
    151:     for (k=1;k<nmat;k++) {
    152:       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]);
    153:     }
    154:     if (st->shift_matrix == ST_MATMODE_COPY && nmat>2) {
    155:       PetscFree(coeffs);
    156:     }
    157:     if (st->P!=st->T[nmat-1]) {
    158:       PetscObjectReference((PetscObject)st->T[nmat-1]);
    159:       MatDestroy(&st->P);
    160:       st->P = st->T[nmat-1];
    161:     }
    162:   }
    163:   if (st->P) {
    164:     if (!st->ksp) { STGetKSP(st,&st->ksp); }
    165:     KSPSetOperators(st->ksp,st->P,st->P);
    166:     KSPSetUp(st->ksp);
    167:   }
    168:   return(0);
    169: }

    171: PETSC_EXTERN PetscErrorCode STCreate_Sinvert(ST st)
    172: {
    174:   st->ops->apply           = STApply_Sinvert;
    175:   st->ops->getbilinearform = STGetBilinearForm_Default;
    176:   st->ops->applytrans      = STApplyTranspose_Sinvert;
    177:   st->ops->postsolve       = STPostSolve_Sinvert;
    178:   st->ops->backtransform   = STBackTransform_Sinvert;
    179:   st->ops->setup           = STSetUp_Sinvert;
    180:   st->ops->setshift        = STSetShift_Sinvert;
    181:   st->ops->checknullspace  = STCheckNullSpace_Default;
    182:   st->ops->setdefaultksp   = STSetDefaultKSP_Default;
    183:   return(0);
    184: }