Date: 2020-01-13T11:59:50+00:00

Actual source code: cayley.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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 Cayley spectral transform
     12: */

     14: #include <slepc/private/stimpl.h>          /*I "slepcst.h" I*/

     16: typedef struct {
     17:   PetscScalar nu;
     18:   PetscBool   nu_set;
     19: } ST_CAYLEY;

     21: PetscErrorCode STApply_Cayley(ST st,Vec x,Vec y)
     22: {

     26:   /* standard eigenproblem: y = (A - sI)^-1 (A + tI)x */
     27:   /* generalized eigenproblem: y = (A - sB)^-1 (A + tB)x */
     28:   MatMult(st->T[0],x,st->work[0]);
     29:   STMatSolve(st,st->work[0],y);
     30:   return(0);
     31: }

     33: PetscErrorCode STApplyTranspose_Cayley(ST st,Vec x,Vec y)
     34: {

     38:   /* standard eigenproblem: y =  (A + tI)^T (A - sI)^-T x */
     39:   /* generalized eigenproblem: y = (A + tB)^T (A - sB)^-T x */
     40:   STMatSolveTranspose(st,x,st->work[0]);
     41:   MatMultTranspose(st->T[0],st->work[0],y);
     42:   return(0);
     43: }

     45: static PetscErrorCode MatMult_Cayley(Mat B,Vec x,Vec y)
     46: {
     48:   ST             st;
     49:   ST_CAYLEY      *ctx;
     50:   PetscScalar    nu;

     53:   MatShellGetContext(B,(void**)&st);
     54:   ctx = (ST_CAYLEY*)st->data;
     55:   nu = ctx->nu;

     57:   if (st->matmode == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };

     59:   if (st->nmat>1) {
     60:     /* generalized eigenproblem: y = (A + tB)x */
     61:     MatMult(st->A[0],x,y);
     62:     MatMult(st->A[1],x,st->work[1]);
     63:     VecAXPY(y,nu,st->work[1]);
     64:   } else {
     65:     /* standard eigenproblem: y = (A + tI)x */
     66:     MatMult(st->A[0],x,y);
     67:     VecAXPY(y,nu,x);
     68:   }
     69:   return(0);
     70: }

     72: static PetscErrorCode MatMultTranspose_Cayley(Mat B,Vec x,Vec y)
     73: {
     75:   ST             st;
     76:   ST_CAYLEY      *ctx;
     77:   PetscScalar    nu;

     80:   MatShellGetContext(B,(void**)&st);
     81:   ctx = (ST_CAYLEY*)st->data;
     82:   nu = ctx->nu;

     84:   if (st->matmode == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };
     85:   nu = PetscConj(nu);

     87:   if (st->nmat>1) {
     88:     /* generalized eigenproblem: y = (A + tB)x */
     89:     MatMultTranspose(st->A[0],x,y);
     90:     MatMultTranspose(st->A[1],x,st->work[1]);
     91:     VecAXPY(y,nu,st->work[1]);
     92:   } else {
     93:     /* standard eigenproblem: y = (A + tI)x */
     94:     MatMultTranspose(st->A[0],x,y);
     95:     VecAXPY(y,nu,x);
     96:   }
     97:   return(0);
     98: }

    100: PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)
    101: {

    105:   STSetUp(st);
    106:   *B = st->T[0];
    107:   PetscObjectReference((PetscObject)*B);
    108:   return(0);
    109: }

    111: PetscErrorCode STBackTransform_Cayley(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
    112: {
    113:   ST_CAYLEY   *ctx = (ST_CAYLEY*)st->data;
    114:   PetscInt    j;
    115: #if !defined(PETSC_USE_COMPLEX)
    116:   PetscScalar t,i,r;
    117: #endif

    120: #if !defined(PETSC_USE_COMPLEX)
    121:   for (j=0;j<n;j++) {
    122:     if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
    123:     else {
    124:       r = eigr[j];
    125:       i = eigi[j];
    126:       r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
    127:       i = - st->sigma * i - ctx->nu * i;
    128:       t = i * i + r * (r - 2.0) + 1.0;
    129:       eigr[j] = r / t;
    130:       eigi[j] = i / t;
    131:     }
    132:   }
    133: #else
    134:   for (j=0;j<n;j++) {
    135:     eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
    136:   }
    137: #endif
    138:   return(0);
    139: }

    141: PetscErrorCode STPostSolve_Cayley(ST st)
    142: {

    146:   if (st->matmode == ST_MATMODE_INPLACE) {
    147:     if (st->nmat>1) {
    148:       MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
    149:     } else {
    150:       MatShift(st->A[0],st->sigma);
    151:     }
    152:     st->Astate[0] = ((PetscObject)st->A[0])->state;
    153:     st->state = ST_STATE_INITIAL;
    154:   }
    155:   return(0);
    156: }

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

    165:   STSetWorkVecs(st,2);

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

    170:   if (!ctx->nu_set) ctx->nu = st->sigma;
    171:   if (ctx->nu == 0.0 && st->sigma == 0.0) SETERRQ(PetscObjectComm((PetscObject)st),1,"Values of shift and antishift cannot be zero simultaneously");
    172:   if (ctx->nu == -st->sigma) SETERRQ(PetscObjectComm((PetscObject)st),1,"It is not allowed to set the antishift equal to minus the shift (the target)");

    174:   /* T[0] = A+nu*B */
    175:   if (st->matmode==ST_MATMODE_INPLACE) {
    176:     MatGetLocalSize(st->A[0],&n,&m);
    177:     MatCreateShell(PetscObjectComm((PetscObject)st),n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,&st->T[0]);
    178:     MatShellSetOperation(st->T[0],MATOP_MULT,(void(*)(void))MatMult_Cayley);
    179:     MatShellSetOperation(st->T[0],MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Cayley);
    180:     PetscLogObjectParent((PetscObject)st,(PetscObject)st->T[0]);
    181:   } else {
    182:     STMatMAXPY_Private(st,ctx->nu,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[0]);
    183:   }

    185:   /* T[1] = A-sigma*B */
    186:   STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[1]);
    187:   PetscObjectReference((PetscObject)st->T[1]);
    188:   MatDestroy(&st->P);
    189:   st->P = st->T[1];
    190:   if (!st->ksp) { STGetKSP(st,&st->ksp); }
    191:   STCheckFactorPackage(st);
    192:   KSPSetOperators(st->ksp,st->P,st->P);
    193:   KSPSetUp(st->ksp);
    194:   return(0);
    195: }

    197: PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
    198: {
    200:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

    203:   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");
    204:   if (ctx->nu == -newshift) SETERRQ(PetscObjectComm((PetscObject)st),1,"It is not allowed to set the shift equal to minus the antishift");

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

    223: PetscErrorCode STSetFromOptions_Cayley(PetscOptionItems *PetscOptionsObject,ST st)
    224: {
    226:   PetscScalar    nu;
    227:   PetscBool      flg;
    228:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

    231:   PetscOptionsHead(PetscOptionsObject,"ST Cayley Options");

    233:     PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg);
    234:     if (flg) { STCayleySetAntishift(st,nu); }

    236:   PetscOptionsTail();
    237:   return(0);
    238: }

    240: static PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
    241: {
    243:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

    246:   if (st->state && st->matmode!=ST_MATMODE_INPLACE) {
    247:     STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,&st->T[0]);
    248:   }
    249:   ctx->nu     = newshift;
    250:   ctx->nu_set = PETSC_TRUE;
    251:   return(0);
    252: }

    254: /*@
    255:    STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
    256:    spectral transformation.

    258:    Logically Collective on st

    260:    Input Parameters:
    261: +  st  - the spectral transformation context
    262: -  nu  - the anti-shift

    264:    Options Database Key:
    265: .  -st_cayley_antishift - Sets the value of the anti-shift

    267:    Level: intermediate

    269:    Note:
    270:    In the generalized Cayley transform, the operator can be expressed as
    271:    OP = inv(A - sigma B)*(A + nu B). This function sets the value of nu.
    272:    Use STSetShift() for setting sigma. The value nu=-sigma is not allowed.

    274: .seealso: STSetShift(), STCayleyGetAntishift()
    275: @*/
    276: PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
    277: {

    283:   PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));
    284:   return(0);
    285: }

    287: static PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)
    288: {
    289:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

    292:   *nu = ctx->nu;
    293:   return(0);
    294: }

    296: /*@
    297:    STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley
    298:    spectral transformation.

    300:    Not Collective

    302:    Input Parameter:
    303: .  st  - the spectral transformation context

    305:    Output Parameter:
    306: .  nu  - the anti-shift

    308:    Level: intermediate

    310: .seealso: STGetShift(), STCayleySetAntishift()
    311: @*/
    312: PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)
    313: {

    319:   PetscUseMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));
    320:   return(0);
    321: }

    323: PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
    324: {
    326:   char           str[50];
    327:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;
    328:   PetscBool      isascii;

    331:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    332:   if (isascii) {
    333:     SlepcSNPrintfScalar(str,50,ctx->nu,PETSC_FALSE);
    334:     PetscViewerASCIIPrintf(viewer,"  antishift: %s\n",str);
    335:   }
    336:   return(0);
    337: }

    339: PetscErrorCode STDestroy_Cayley(ST st)
    340: {

    344:   PetscFree(st->data);
    345:   PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",NULL);
    346:   PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",NULL);
    347:   return(0);
    348: }

    350: SLEPC_EXTERN PetscErrorCode STCreate_Cayley(ST st)
    351: {
    353:   ST_CAYLEY      *ctx;

    356:   PetscNewLog(st,&ctx);
    357:   st->data = (void*)ctx;

    359:   st->usesksp = PETSC_TRUE;

    361:   st->ops->apply           = STApply_Cayley;
    362:   st->ops->getbilinearform = STGetBilinearForm_Cayley;
    363:   st->ops->applytrans      = STApplyTranspose_Cayley;
    364:   st->ops->postsolve       = STPostSolve_Cayley;
    365:   st->ops->backtransform   = STBackTransform_Cayley;
    366:   st->ops->setfromoptions  = STSetFromOptions_Cayley;
    367:   st->ops->setup           = STSetUp_Cayley;
    368:   st->ops->setshift        = STSetShift_Cayley;
    369:   st->ops->destroy         = STDestroy_Cayley;
    370:   st->ops->view            = STView_Cayley;
    371:   st->ops->checknullspace  = STCheckNullSpace_Default;
    372:   st->ops->setdefaultksp   = STSetDefaultKSP_Default;
    373:   PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",STCayleySetAntishift_Cayley);
    374:   PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",STCayleyGetAntishift_Cayley);
    375:   return(0);
    376: }