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

Actual source code: cayley.c
slepc-3.7.4 2017-05-17
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      1: /*
      2:       Implements the Cayley spectral transform.

      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>          /*I "slepcst.h" I*/

     26: typedef struct {
     27:   PetscScalar nu;
     28:   PetscBool   nu_set;
     29:   Vec         w2;
     30: } ST_CAYLEY;

     34: PetscErrorCode STApply_Cayley(ST st,Vec x,Vec y)
     35: {

     39:   /* standard eigenproblem: y = (A - sI)^-1 (A + tI)x */
     40:   /* generalized eigenproblem: y = (A - sB)^-1 (A + tB)x */
     41:   MatMult(st->T[0],x,st->w);
     42:   STMatSolve(st,st->w,y);
     43:   return(0);
     44: }

     48: PetscErrorCode STApplyTranspose_Cayley(ST st,Vec x,Vec y)
     49: {

     53:   /* standard eigenproblem: y =  (A + tI)^T (A - sI)^-T x */
     54:   /* generalized eigenproblem: y = (A + tB)^T (A - sB)^-T x */
     55:   STMatSolveTranspose(st,x,st->w);
     56:   MatMultTranspose(st->T[0],st->w,y);
     57:   return(0);
     58: }

     62: static PetscErrorCode MatMult_Cayley(Mat B,Vec x,Vec y)
     63: {
     65:   ST             st;
     66:   ST_CAYLEY      *ctx;
     67:   PetscScalar    nu;

     70:   MatShellGetContext(B,(void**)&st);
     71:   ctx = (ST_CAYLEY*)st->data;
     72:   nu = ctx->nu;

     74:   if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };

     76:   if (st->nmat>1) {
     77:     /* generalized eigenproblem: y = (A + tB)x */
     78:     MatMult(st->A[0],x,y);
     79:     MatMult(st->A[1],x,ctx->w2);
     80:     VecAXPY(y,nu,ctx->w2);
     81:   } else {
     82:     /* standard eigenproblem: y = (A + tI)x */
     83:     MatMult(st->A[0],x,y);
     84:     VecAXPY(y,nu,x);
     85:   }
     86:   return(0);
     87: }

     91: PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)
     92: {

     96:   STSetUp(st);
     97:   *B = st->T[0];
     98:   PetscObjectReference((PetscObject)*B);
     99:   return(0);
    100: }

    104: PetscErrorCode STBackTransform_Cayley(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
    105: {
    106:   ST_CAYLEY   *ctx = (ST_CAYLEY*)st->data;
    107:   PetscInt    j;
    108: #if !defined(PETSC_USE_COMPLEX)
    109:   PetscScalar t,i,r;
    110: #endif

    113: #if !defined(PETSC_USE_COMPLEX)
    114:   for (j=0;j<n;j++) {
    115:     if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
    116:     else {
    117:       r = eigr[j];
    118:       i = eigi[j];
    119:       r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
    120:       i = - st->sigma * i - ctx->nu * i;
    121:       t = i * i + r * (r - 2.0) + 1.0;
    122:       eigr[j] = r / t;
    123:       eigi[j] = i / t;
    124:     }
    125:   }
    126: #else
    127:   for (j=0;j<n;j++) {
    128:     eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
    129:   }
    130: #endif
    131:   return(0);
    132: }

    136: PetscErrorCode STPostSolve_Cayley(ST st)
    137: {

    141:   if (st->shift_matrix == ST_MATMODE_INPLACE) {
    142:     if (st->nmat>1) {
    143:       MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
    144:     } else {
    145:       MatShift(st->A[0],st->sigma);
    146:     }
    147:     st->Astate[0] = ((PetscObject)st->A[0])->state;
    148:     st->state = ST_STATE_INITIAL;
    149:   }
    150:   return(0);
    151: }

    155: PetscErrorCode STSetUp_Cayley(ST st)
    156: {
    158:   PetscInt       n,m;
    159:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

    162:   ST_AllocateWorkVec(st);

    164:   /* if the user did not set the shift, use the target value */
    165:   if (!st->sigma_set) st->sigma = st->defsigma;

    167:   if (!ctx->nu_set) ctx->nu = st->sigma;
    168:   if (ctx->nu == 0.0 && st->sigma == 0.0) SETERRQ(PetscObjectComm((PetscObject)st),1,"Values of shift and antishift cannot be zero simultaneously");

    170:   /* T[0] = A+nu*B */
    171:   if (st->shift_matrix==ST_MATMODE_INPLACE) {
    172:     MatGetLocalSize(st->A[0],&n,&m);
    173:     MatCreateShell(PetscObjectComm((PetscObject)st),n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,&st->T[0]);
    174:     MatShellSetOperation(st->T[0],MATOP_MULT,(void(*)(void))MatMult_Cayley);
    175:     PetscLogObjectParent((PetscObject)st,(PetscObject)st->T[0]);
    176:   } else {
    177:     STMatMAXPY_Private(st,ctx->nu,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[0]);
    178:   }

    180:   /* T[1] = A-sigma*B */
    181:   STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[1]);
    182:   PetscObjectReference((PetscObject)st->T[1]);
    183:   MatDestroy(&st->P);
    184:   st->P = st->T[1];
    185:   if (st->nmat>1) {
    186:     VecDestroy(&ctx->w2);
    187:     MatCreateVecs(st->A[1],&ctx->w2,NULL);
    188:     PetscLogObjectParent((PetscObject)st,(PetscObject)ctx->w2);
    189:   }
    190:   if (!st->ksp) { STGetKSP(st,&st->ksp); }
    191:   STCheckFactorPackage(st);
    192:   KSPSetOperators(st->ksp,st->P,st->P);
    193:   KSPSetErrorIfNotConverged(st->ksp,PETSC_TRUE);
    194:   KSPSetUp(st->ksp);
    195:   return(0);
    196: }

    200: PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
    201: {
    203:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

    206:   if (newshift==0.0 && (!ctx->nu_set || (ctx->nu_set && ctx->nu==0.0))) SETERRQ(PetscObjectComm((PetscObject)st),1,"Values of shift and antishift cannot be zero simultaneously");

    208:   if (!ctx->nu_set) {
    209:     if (st->shift_matrix!=ST_MATMODE_INPLACE) {
    210:       STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,&st->T[0]);
    211:     }
    212:     ctx->nu = newshift;
    213:   }
    214:   STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,&st->T[1]);
    215:   if (st->P!=st->T[1]) {
    216:     MatDestroy(&st->P);
    217:     st->P = st->T[1];
    218:     PetscObjectReference((PetscObject)st->P);
    219:   }
    220:   KSPSetOperators(st->ksp,st->P,st->P);
    221:   KSPSetUp(st->ksp);
    222:   return(0);
    223: }

    227: PetscErrorCode STSetFromOptions_Cayley(PetscOptionItems *PetscOptionsObject,ST st)
    228: {
    230:   PetscScalar    nu;
    231:   PetscBool      flg;
    232:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;
    233:   PC             pc;
    234:   PCType         pctype;
    235:   KSPType        ksptype;

    238:   if (!st->ksp) { STGetKSP(st,&st->ksp); }
    239:   KSPGetPC(st->ksp,&pc);
    240:   KSPGetType(st->ksp,&ksptype);
    241:   PCGetType(pc,&pctype);
    242:   if (!pctype && !ksptype) {
    243:     if (st->shift_matrix == ST_MATMODE_SHELL) {
    244:       /* in shell mode use GMRES with Jacobi as the default */
    245:       KSPSetType(st->ksp,KSPGMRES);
    246:       PCSetType(pc,PCJACOBI);
    247:     } else {
    248:       /* use direct solver as default */
    249:       KSPSetType(st->ksp,KSPPREONLY);
    250:       PCSetType(pc,PCLU);
    251:     }
    252:   }

    254:   PetscOptionsHead(PetscOptionsObject,"ST Cayley Options");
    255:   PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg);
    256:   if (flg) {
    257:     STCayleySetAntishift(st,nu);
    258:   }
    259:   PetscOptionsTail();
    260:   return(0);
    261: }

    265: static PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
    266: {
    268:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

    271:   if (st->state && st->shift_matrix!=ST_MATMODE_INPLACE) {
    272:     STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,&st->T[0]);
    273:   }
    274:   ctx->nu     = newshift;
    275:   ctx->nu_set = PETSC_TRUE;
    276:   return(0);
    277: }

    281: /*@
    282:    STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
    283:    spectral transformation.

    285:    Logically Collective on ST

    287:    Input Parameters:
    288: +  st  - the spectral transformation context
    289: -  nu  - the anti-shift

    291:    Options Database Key:
    292: .  -st_cayley_antishift - Sets the value of the anti-shift

    294:    Level: intermediate

    296:    Note:
    297:    In the generalized Cayley transform, the operator can be expressed as
    298:    OP = inv(A - sigma B)*(A + nu B). This function sets the value of nu.
    299:    Use STSetShift() for setting sigma.

    301: .seealso: STSetShift(), STCayleyGetAntishift()
    302: @*/
    303: PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
    304: {

    310:   PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));
    311:   return(0);
    312: }
    315: static PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)
    316: {
    317:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

    320:   *nu = ctx->nu;
    321:   return(0);
    322: }

    326: /*@
    327:    STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley
    328:    spectral transformation.

    330:    Not Collective

    332:    Input Parameter:
    333: .  st  - the spectral transformation context

    335:    Output Parameter:
    336: .  nu  - the anti-shift

    338:    Level: intermediate

    340: .seealso: STGetShift(), STCayleySetAntishift()
    341: @*/
    342: PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)
    343: {

    349:   PetscUseMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));
    350:   return(0);
    351: }

    355: PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
    356: {
    358:   char           str[50];
    359:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;
    360:   PetscBool      isascii;

    363:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    364:   if (isascii) {
    365:     SlepcSNPrintfScalar(str,50,ctx->nu,PETSC_FALSE);
    366:     PetscViewerASCIIPrintf(viewer,"  Cayley: antishift: %s\n",str);
    367:   }
    368:   return(0);
    369: }

    373: PetscErrorCode STReset_Cayley(ST st)
    374: {
    376:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

    379:   VecDestroy(&ctx->w2);
    380:   return(0);
    381: }

    385: PetscErrorCode STDestroy_Cayley(ST st)
    386: {

    390:   PetscFree(st->data);
    391:   PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",NULL);
    392:   PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",NULL);
    393:   return(0);
    394: }

    398: PETSC_EXTERN PetscErrorCode STCreate_Cayley(ST st)
    399: {
    401:   ST_CAYLEY      *ctx;

    404:   PetscNewLog(st,&ctx);
    405:   st->data = (void*)ctx;

    407:   st->ops->apply           = STApply_Cayley;
    408:   st->ops->getbilinearform = STGetBilinearForm_Cayley;
    409:   st->ops->applytrans      = STApplyTranspose_Cayley;
    410:   st->ops->postsolve       = STPostSolve_Cayley;
    411:   st->ops->backtransform   = STBackTransform_Cayley;
    412:   st->ops->setfromoptions  = STSetFromOptions_Cayley;
    413:   st->ops->setup           = STSetUp_Cayley;
    414:   st->ops->setshift        = STSetShift_Cayley;
    415:   st->ops->destroy         = STDestroy_Cayley;
    416:   st->ops->reset           = STReset_Cayley;
    417:   st->ops->view            = STView_Cayley;
    418:   st->ops->checknullspace  = STCheckNullSpace_Default;
    419:   PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",STCayleySetAntishift_Cayley);
    420:   PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",STCayleyGetAntishift_Cayley);
    421:   return(0);
    422: }