Date: 2021-02-01T14:41:51+00:00

Actual source code: sinvert.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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 STBackTransform_Sinvert(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
     17: {
     18:   PetscInt    j;
     19: #if !defined(PETSC_USE_COMPLEX)
     20:   PetscScalar t;
     21: #endif

     24: #if !defined(PETSC_USE_COMPLEX)
     25:   for (j=0;j<n;j++) {
     26:     if (eigi[j] == 0) eigr[j] = 1.0 / eigr[j] + st->sigma;
     27:     else {
     28:       t = eigr[j] * eigr[j] + eigi[j] * eigi[j];
     29:       eigr[j] = eigr[j] / t + st->sigma;
     30:       eigi[j] = - eigi[j] / t;
     31:     }
     32:   }
     33: #else
     34:   for (j=0;j<n;j++) {
     35:     eigr[j] = 1.0 / eigr[j] + st->sigma;
     36:   }
     37: #endif
     38:   return(0);
     39: }

     41: PetscErrorCode STPostSolve_Sinvert(ST st)
     42: {

     46:   if (st->matmode == ST_MATMODE_INPLACE) {
     47:     if (st->nmat>1) {
     48:       MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
     49:     } else {
     50:       MatShift(st->A[0],st->sigma);
     51:     }
     52:     st->Astate[0] = ((PetscObject)st->A[0])->state;
     53:     st->state   = ST_STATE_INITIAL;
     54:     st->opready = PETSC_FALSE;
     55:   }
     56:   return(0);
     57: }

     59: /*
     60:    Operator (sinvert):
     61:                Op               P         M
     62:    if nmat=1:  (A-sI)^-1        A-sI      NULL
     63:    if nmat=2:  (A-sB)^-1 B      A-sB      B
     64: */
     65: PetscErrorCode STComputeOperator_Sinvert(ST st)
     66: {

     70:   /* if the user did not set the shift, use the target value */
     71:   if (!st->sigma_set) st->sigma = st->defsigma;
     72:   PetscObjectReference((PetscObject)st->A[1]);
     73:   MatDestroy(&st->T[0]);
     74:   st->T[0] = st->A[1];
     75:   STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[1]);
     76:   PetscObjectReference((PetscObject)st->T[1]);
     77:   MatDestroy(&st->P);
     78:   st->P = st->T[1];
     79:   st->M = (st->nmat>1)? st->T[0]: NULL;
     80:   return(0);
     81: }

     83: PetscErrorCode STSetUp_Sinvert(ST st)
     84: {
     86:   PetscInt       k,nc,nmat=st->nmat;
     87:   PetscScalar    *coeffs=NULL;

     90:   if (nmat>1) {
     91:     STSetWorkVecs(st,1);
     92:   }
     93:   /* if the user did not set the shift, use the target value */
     94:   if (!st->sigma_set) st->sigma = st->defsigma;
     95:   if (nmat>2) {  /* set-up matrices for polynomial eigenproblems */
     96:     if (st->transform) {
     97:       nc = (nmat*(nmat+1))/2;
     98:       PetscMalloc1(nc,&coeffs);
     99:       /* Compute coeffs */
    100:       STCoeffs_Monomial(st,coeffs);
    101:       /* T[0] = A_n */
    102:       k = nmat-1;
    103:       PetscObjectReference((PetscObject)st->A[k]);
    104:       MatDestroy(&st->T[0]);
    105:       st->T[0] = st->A[k];
    106:       for (k=1;k<nmat;k++) {
    107:         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]);
    108:       }
    109:       PetscFree(coeffs);
    110:       PetscObjectReference((PetscObject)st->T[nmat-1]);
    111:       MatDestroy(&st->P);
    112:       st->P = st->T[nmat-1];
    113:       if (!st->ksp) { STGetKSP(st,&st->ksp); }
    114:       STCheckFactorPackage(st);
    115:       KSPSetOperators(st->ksp,st->P,st->P);
    116:     } else {
    117:       for (k=0;k<nmat;k++) {
    118:         PetscObjectReference((PetscObject)st->A[k]);
    119:         MatDestroy(&st->T[k]);
    120:         st->T[k] = st->A[k];
    121:       }
    122:     }
    123:   }
    124:   if (st->P) {
    125:     KSPSetUp(st->ksp);
    126:   }
    127:   return(0);
    128: }

    130: PetscErrorCode STSetShift_Sinvert(ST st,PetscScalar newshift)
    131: {
    133:   PetscInt       nmat=PetscMax(st->nmat,2),k,nc;
    134:   PetscScalar    *coeffs=NULL;

    137:   if (st->transform) {
    138:     if (st->matmode == ST_MATMODE_COPY && nmat>2) {
    139:       nc = (nmat*(nmat+1))/2;
    140:       PetscMalloc1(nc,&coeffs);
    141:       /* Compute coeffs */
    142:       STCoeffs_Monomial(st,coeffs);
    143:     }
    144:     for (k=1;k<nmat;k++) {
    145:       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]);
    146:     }
    147:     if (st->matmode == ST_MATMODE_COPY && nmat>2) {
    148:       PetscFree(coeffs);
    149:     }
    150:     if (st->P!=st->T[nmat-1]) {
    151:       PetscObjectReference((PetscObject)st->T[nmat-1]);
    152:       MatDestroy(&st->P);
    153:       st->P = st->T[nmat-1];
    154:     }
    155:   }
    156:   if (st->P) {
    157:     if (!st->ksp) { STGetKSP(st,&st->ksp); }
    158:     KSPSetOperators(st->ksp,st->P,st->P);
    159:     KSPSetUp(st->ksp);
    160:   }
    161:   return(0);
    162: }

    164: SLEPC_EXTERN PetscErrorCode STCreate_Sinvert(ST st)
    165: {
    167:   st->usesksp = PETSC_TRUE;

    169:   st->ops->apply           = STApply_Generic;
    170:   st->ops->applytrans      = STApplyTranspose_Generic;
    171:   st->ops->backtransform   = STBackTransform_Sinvert;
    172:   st->ops->setshift        = STSetShift_Sinvert;
    173:   st->ops->getbilinearform = STGetBilinearForm_Default;
    174:   st->ops->setup           = STSetUp_Sinvert;
    175:   st->ops->computeoperator = STComputeOperator_Sinvert;
    176:   st->ops->postsolve       = STPostSolve_Sinvert;
    177:   st->ops->checknullspace  = STCheckNullSpace_Default;
    178:   st->ops->setdefaultksp   = STSetDefaultKSP_Default;
    179:   return(0);
    180: }