Date: 2022-08-09T09:05:29+00:00

Actual source code: cayley.c
slepc-3.17.2 2022-08-09
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, 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>

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

     21: static PetscErrorCode MatMult_Cayley(Mat B,Vec x,Vec y)
     22: {
     23:   ST             st;
     24:   ST_CAYLEY      *ctx;
     25:   PetscScalar    nu;

     27:   MatShellGetContext(B,&st);
     28:   ctx = (ST_CAYLEY*)st->data;
     29:   nu = ctx->nu;

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

     33:   if (st->nmat>1) {
     34:     /* generalized eigenproblem: y = (A + tB)x */
     35:     MatMult(st->A[0],x,y);
     36:     MatMult(st->A[1],x,st->work[1]);
     37:     VecAXPY(y,nu,st->work[1]);
     38:   } else {
     39:     /* standard eigenproblem: y = (A + tI)x */
     40:     MatMult(st->A[0],x,y);
     41:     VecAXPY(y,nu,x);
     42:   }
     43:   PetscFunctionReturn(0);
     44: }

     46: static PetscErrorCode MatMultTranspose_Cayley(Mat B,Vec x,Vec y)
     47: {
     48:   ST             st;
     49:   ST_CAYLEY      *ctx;
     50:   PetscScalar    nu;

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

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

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

     72: PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)
     73: {
     74:   STSetUp(st);
     75:   *B = st->T[0];
     76:   PetscObjectReference((PetscObject)*B);
     77:   PetscFunctionReturn(0);
     78: }

     80: PetscErrorCode STBackTransform_Cayley(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
     81: {
     82:   ST_CAYLEY   *ctx = (ST_CAYLEY*)st->data;
     83:   PetscInt    j;
     84: #if !defined(PETSC_USE_COMPLEX)
     85:   PetscScalar t,i,r;
     86: #endif

     88: #if !defined(PETSC_USE_COMPLEX)
     89:   for (j=0;j<n;j++) {
     90:     if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
     91:     else {
     92:       r = eigr[j];
     93:       i = eigi[j];
     94:       r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
     95:       i = - st->sigma * i - ctx->nu * i;
     96:       t = i * i + r * (r - 2.0) + 1.0;
     97:       eigr[j] = r / t;
     98:       eigi[j] = i / t;
     99:     }
    100:   }
    101: #else
    102:   for (j=0;j<n;j++) {
    103:     eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
    104:   }
    105: #endif
    106:   PetscFunctionReturn(0);
    107: }

    109: PetscErrorCode STPostSolve_Cayley(ST st)
    110: {
    111:   if (st->matmode == ST_MATMODE_INPLACE) {
    112:     if (st->nmat>1) MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
    113:     else MatShift(st->A[0],st->sigma);
    114:     st->Astate[0] = ((PetscObject)st->A[0])->state;
    115:     st->state   = ST_STATE_INITIAL;
    116:     st->opready = PETSC_FALSE;
    117:   }
    118:   PetscFunctionReturn(0);
    119: }

    121: /*
    122:    Operator (cayley):
    123:                Op                  P         M
    124:    if nmat=1:  (A-sI)^-1 (A+tI)    A-sI      A+tI
    125:    if nmat=2:  (A-sB)^-1 (A+tB)    A-sB      A+tI
    126: */
    127: PetscErrorCode STComputeOperator_Cayley(ST st)
    128: {
    129:   PetscInt       n,m;
    130:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

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

    135:   if (!ctx->nu_set) ctx->nu = st->sigma;

    139:   /* T[0] = A+nu*B */
    140:   if (st->matmode==ST_MATMODE_INPLACE) {
    141:     MatGetLocalSize(st->A[0],&n,&m);
    142:     MatCreateShell(PetscObjectComm((PetscObject)st),n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,&st->T[0]);
    143:     MatShellSetOperation(st->T[0],MATOP_MULT,(void(*)(void))MatMult_Cayley);
    144:     MatShellSetOperation(st->T[0],MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Cayley);
    145:     PetscLogObjectParent((PetscObject)st,(PetscObject)st->T[0]);
    146:   } else STMatMAXPY_Private(st,ctx->nu,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[0]);
    147:   st->M = st->T[0];

    149:   /* T[1] = A-sigma*B */
    150:   STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[1]);
    151:   PetscObjectReference((PetscObject)st->T[1]);
    152:   MatDestroy(&st->P);
    153:   st->P = st->T[1];
    154:   if (st->Psplit) {  /* build custom preconditioner from the split matrices */
    155:     STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PETSC_TRUE,PETSC_TRUE,&st->Pmat);
    156:   }
    157:   PetscFunctionReturn(0);
    158: }

    160: PetscErrorCode STSetUp_Cayley(ST st)
    161: {
    163:   STSetWorkVecs(st,2);
    164:   KSPSetUp(st->ksp);
    165:   PetscFunctionReturn(0);
    166: }

    168: PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
    169: {
    170:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

    175:   if (!ctx->nu_set) {
    176:     if (st->matmode!=ST_MATMODE_INPLACE) STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,PETSC_FALSE,&st->T[0]);
    177:     ctx->nu = newshift;
    178:   }
    179:   STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,PETSC_FALSE,&st->T[1]);
    180:   if (st->P!=st->T[1]) {
    181:     PetscObjectReference((PetscObject)st->T[1]);
    182:     MatDestroy(&st->P);
    183:     st->P = st->T[1];
    184:   }
    185:   if (st->Psplit) {  /* build custom preconditioner from the split matrices */
    186:     STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,PETSC_TRUE,&st->Pmat);
    187:   }
    188:   ST_KSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P);
    189:   KSPSetUp(st->ksp);
    190:   PetscFunctionReturn(0);
    191: }

    193: PetscErrorCode STSetFromOptions_Cayley(PetscOptionItems *PetscOptionsObject,ST st)
    194: {
    195:   PetscScalar    nu;
    196:   PetscBool      flg;
    197:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

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

    201:     PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg);
    202:     if (flg) STCayleySetAntishift(st,nu);

    204:   PetscOptionsTail();
    205:   PetscFunctionReturn(0);
    206: }

    208: static PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
    209: {
    210:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

    212:   if (ctx->nu != newshift) {
    213:     STCheckNotSeized(st,1);
    214:     if (st->state && st->matmode!=ST_MATMODE_INPLACE) STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,PETSC_FALSE,&st->T[0]);
    215:     ctx->nu = newshift;
    216:   }
    217:   ctx->nu_set = PETSC_TRUE;
    218:   PetscFunctionReturn(0);
    219: }

    221: /*@
    222:    STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
    223:    spectral transformation.

    225:    Logically Collective on st

    227:    Input Parameters:
    228: +  st  - the spectral transformation context
    229: -  nu  - the anti-shift

    231:    Options Database Key:
    232: .  -st_cayley_antishift - Sets the value of the anti-shift

    234:    Level: intermediate

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

    241: .seealso: STSetShift(), STCayleyGetAntishift()
    242: @*/
    243: PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
    244: {
    247:   PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));
    248:   PetscFunctionReturn(0);
    249: }

    251: static PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)
    252: {
    253:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

    255:   *nu = ctx->nu;
    256:   PetscFunctionReturn(0);
    257: }

    259: /*@
    260:    STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley
    261:    spectral transformation.

    263:    Not Collective

    265:    Input Parameter:
    266: .  st  - the spectral transformation context

    268:    Output Parameter:
    269: .  nu  - the anti-shift

    271:    Level: intermediate

    273: .seealso: STGetShift(), STCayleySetAntishift()
    274: @*/
    275: PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)
    276: {
    279:   PetscUseMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));
    280:   PetscFunctionReturn(0);
    281: }

    283: PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
    284: {
    285:   char           str[50];
    286:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;
    287:   PetscBool      isascii;

    289:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    290:   if (isascii) {
    291:     SlepcSNPrintfScalar(str,sizeof(str),ctx->nu,PETSC_FALSE);
    292:     PetscViewerASCIIPrintf(viewer,"  antishift: %s\n",str);
    293:   }
    294:   PetscFunctionReturn(0);
    295: }

    297: PetscErrorCode STDestroy_Cayley(ST st)
    298: {
    299:   PetscFree(st->data);
    300:   PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",NULL);
    301:   PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",NULL);
    302:   PetscFunctionReturn(0);
    303: }

    305: SLEPC_EXTERN PetscErrorCode STCreate_Cayley(ST st)
    306: {
    307:   ST_CAYLEY      *ctx;

    309:   PetscNewLog(st,&ctx);
    310:   st->data = (void*)ctx;

    312:   st->usesksp = PETSC_TRUE;

    314:   st->ops->apply           = STApply_Generic;
    315:   st->ops->applytrans      = STApplyTranspose_Generic;
    316:   st->ops->backtransform   = STBackTransform_Cayley;
    317:   st->ops->setshift        = STSetShift_Cayley;
    318:   st->ops->getbilinearform = STGetBilinearForm_Cayley;
    319:   st->ops->setup           = STSetUp_Cayley;
    320:   st->ops->computeoperator = STComputeOperator_Cayley;
    321:   st->ops->setfromoptions  = STSetFromOptions_Cayley;
    322:   st->ops->postsolve       = STPostSolve_Cayley;
    323:   st->ops->destroy         = STDestroy_Cayley;
    324:   st->ops->view            = STView_Cayley;
    325:   st->ops->checknullspace  = STCheckNullSpace_Default;
    326:   st->ops->setdefaultksp   = STSetDefaultKSP_Default;

    328:   PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",STCayleySetAntishift_Cayley);
    329:   PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",STCayleyGetAntishift_Cayley);
    330:   PetscFunctionReturn(0);
    331: }