Actual source code: cayley.c

slepc-main 2024-11-09
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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:   PetscFunctionBegin;
 28:   PetscCall(MatShellGetContext(B,&st));
 29:   ctx = (ST_CAYLEY*)st->data;
 30:   nu = ctx->nu;

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

 34:   if (st->nmat>1) {
 35:     /* generalized eigenproblem: y = (A + tB)x */
 36:     PetscCall(MatMult(st->A[0],x,y));
 37:     PetscCall(MatMult(st->A[1],x,st->work[1]));
 38:     PetscCall(VecAXPY(y,nu,st->work[1]));
 39:   } else {
 40:     /* standard eigenproblem: y = (A + tI)x */
 41:     PetscCall(MatMult(st->A[0],x,y));
 42:     PetscCall(VecAXPY(y,nu,x));
 43:   }
 44:   PetscFunctionReturn(PETSC_SUCCESS);
 45: }

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

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

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

 61:   if (st->nmat>1) {
 62:     /* generalized eigenproblem: y = (A + tB)x */
 63:     PetscCall(MatMultTranspose(st->A[0],x,y));
 64:     PetscCall(MatMultTranspose(st->A[1],x,st->work[1]));
 65:     PetscCall(VecAXPY(y,nu,st->work[1]));
 66:   } else {
 67:     /* standard eigenproblem: y = (A + tI)x */
 68:     PetscCall(MatMultTranspose(st->A[0],x,y));
 69:     PetscCall(VecAXPY(y,nu,x));
 70:   }
 71:   PetscFunctionReturn(PETSC_SUCCESS);
 72: }

 74: static PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)
 75: {
 76:   PetscFunctionBegin;
 77:   PetscCall(STSetUp(st));
 78:   *B = st->T[0];
 79:   PetscCall(PetscObjectReference((PetscObject)*B));
 80:   PetscFunctionReturn(PETSC_SUCCESS);
 81: }

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

 91:   PetscFunctionBegin;
 92: #if !defined(PETSC_USE_COMPLEX)
 93:   for (j=0;j<n;j++) {
 94:     if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
 95:     else {
 96:       r = eigr[j];
 97:       i = eigi[j];
 98:       r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
 99:       i = - st->sigma * i - ctx->nu * i;
100:       t = i * i + r * (r - 2.0) + 1.0;
101:       eigr[j] = r / t;
102:       eigi[j] = i / t;
103:     }
104:   }
105: #else
106:   for (j=0;j<n;j++) {
107:     eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
108:   }
109: #endif
110:   PetscFunctionReturn(PETSC_SUCCESS);
111: }

113: static PetscErrorCode STPostSolve_Cayley(ST st)
114: {
115:   PetscFunctionBegin;
116:   if (st->matmode == ST_MATMODE_INPLACE) {
117:     if (st->nmat>1) PetscCall(MatAXPY(st->A[0],st->sigma,st->A[1],st->str));
118:     else PetscCall(MatShift(st->A[0],st->sigma));
119:     st->Astate[0] = ((PetscObject)st->A[0])->state;
120:     st->state   = ST_STATE_INITIAL;
121:     st->opready = PETSC_FALSE;
122:   }
123:   PetscFunctionReturn(PETSC_SUCCESS);
124: }

126: /*
127:    Operator (cayley):
128:                Op                  P         M
129:    if nmat=1:  (A-sI)^-1 (A+tI)    A-sI      A+tI
130:    if nmat=2:  (A-sB)^-1 (A+tB)    A-sB      A+tI
131: */
132: static PetscErrorCode STComputeOperator_Cayley(ST st)
133: {
134:   PetscInt       n,m;
135:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

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

141:   if (!ctx->nu_set) ctx->nu = st->sigma;
142:   PetscCheck(ctx->nu!=0.0 || st->sigma!=0.0,PetscObjectComm((PetscObject)st),PETSC_ERR_USER_INPUT,"Values of shift and antishift cannot be zero simultaneously");
143:   PetscCheck(ctx->nu!=-st->sigma,PetscObjectComm((PetscObject)st),PETSC_ERR_USER_INPUT,"It is not allowed to set the antishift equal to minus the shift (the target)");

145:   /* T[0] = A+nu*B */
146:   if (st->matmode==ST_MATMODE_INPLACE) {
147:     PetscCall(MatGetLocalSize(st->A[0],&n,&m));
148:     PetscCall(MatCreateShell(PetscObjectComm((PetscObject)st),n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,&st->T[0]));
149:     PetscCall(MatShellSetOperation(st->T[0],MATOP_MULT,(void(*)(void))MatMult_Cayley));
150:     PetscCall(MatShellSetOperation(st->T[0],MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Cayley));
151:   } else PetscCall(STMatMAXPY_Private(st,ctx->nu,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[0]));
152:   st->M = st->T[0];

154:   /* T[1] = A-sigma*B */
155:   PetscCall(STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[1]));
156:   PetscCall(PetscObjectReference((PetscObject)st->T[1]));
157:   PetscCall(MatDestroy(&st->P));
158:   st->P = st->T[1];
159:   if (st->Psplit) {  /* build custom preconditioner from the split matrices */
160:     PetscCall(STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PETSC_TRUE,PETSC_TRUE,&st->Pmat));
161:   }
162:   PetscFunctionReturn(PETSC_SUCCESS);
163: }

165: static PetscErrorCode STSetUp_Cayley(ST st)
166: {
167:   PetscFunctionBegin;
168:   PetscCheck(st->nmat<=2,PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"Cayley transform cannot be used in polynomial eigenproblems");
169:   PetscCall(STSetWorkVecs(st,2));
170:   PetscCall(KSPSetUp(st->ksp));
171:   PetscFunctionReturn(PETSC_SUCCESS);
172: }

174: static PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
175: {
176:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

178:   PetscFunctionBegin;
179:   PetscCheck(newshift!=0.0 || (ctx->nu_set && ctx->nu!=0.0),PetscObjectComm((PetscObject)st),PETSC_ERR_USER_INPUT,"Values of shift and antishift cannot be zero simultaneously");
180:   PetscCheck(ctx->nu!=-newshift,PetscObjectComm((PetscObject)st),PETSC_ERR_USER_INPUT,"It is not allowed to set the shift equal to minus the antishift");

182:   if (!ctx->nu_set) {
183:     if (st->matmode!=ST_MATMODE_INPLACE) PetscCall(STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,PETSC_FALSE,&st->T[0]));
184:     ctx->nu = newshift;
185:   }
186:   PetscCall(STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,PETSC_FALSE,&st->T[1]));
187:   if (st->P!=st->T[1]) {
188:     PetscCall(PetscObjectReference((PetscObject)st->T[1]));
189:     PetscCall(MatDestroy(&st->P));
190:     st->P = st->T[1];
191:   }
192:   if (st->Psplit) {  /* build custom preconditioner from the split matrices */
193:     PetscCall(STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,PETSC_TRUE,&st->Pmat));
194:   }
195:   PetscCall(ST_KSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P));
196:   PetscCall(KSPSetUp(st->ksp));
197:   PetscFunctionReturn(PETSC_SUCCESS);
198: }

200: static PetscErrorCode STSetFromOptions_Cayley(ST st,PetscOptionItems *PetscOptionsObject)
201: {
202:   PetscScalar    nu;
203:   PetscBool      flg;
204:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;

206:   PetscFunctionBegin;
207:   PetscOptionsHeadBegin(PetscOptionsObject,"ST Cayley Options");

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

212:   PetscOptionsHeadEnd();
213:   PetscFunctionReturn(PETSC_SUCCESS);
214: }

216: static PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
217: {
218:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

220:   PetscFunctionBegin;
221:   if (ctx->nu != newshift) {
222:     STCheckNotSeized(st,1);
223:     if (st->state && st->matmode!=ST_MATMODE_INPLACE) PetscCall(STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,PETSC_FALSE,&st->T[0]));
224:     ctx->nu = newshift;
225:   }
226:   ctx->nu_set = PETSC_TRUE;
227:   PetscFunctionReturn(PETSC_SUCCESS);
228: }

230: /*@
231:    STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
232:    spectral transformation.

234:    Logically Collective

236:    Input Parameters:
237: +  st  - the spectral transformation context
238: -  nu  - the anti-shift

240:    Options Database Key:
241: .  -st_cayley_antishift - Sets the value of the anti-shift

243:    Level: intermediate

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

250: .seealso: STSetShift(), STCayleyGetAntishift()
251: @*/
252: PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
253: {
254:   PetscFunctionBegin;
257:   PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));
258:   PetscFunctionReturn(PETSC_SUCCESS);
259: }

261: static PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)
262: {
263:   ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;

265:   PetscFunctionBegin;
266:   *nu = ctx->nu;
267:   PetscFunctionReturn(PETSC_SUCCESS);
268: }

270: /*@
271:    STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley
272:    spectral transformation.

274:    Not Collective

276:    Input Parameter:
277: .  st  - the spectral transformation context

279:    Output Parameter:
280: .  nu  - the anti-shift

282:    Level: intermediate

284: .seealso: STGetShift(), STCayleySetAntishift()
285: @*/
286: PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)
287: {
288:   PetscFunctionBegin;
290:   PetscAssertPointer(nu,2);
291:   PetscUseMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));
292:   PetscFunctionReturn(PETSC_SUCCESS);
293: }

295: static PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
296: {
297:   char           str[50];
298:   ST_CAYLEY      *ctx = (ST_CAYLEY*)st->data;
299:   PetscBool      isascii;

301:   PetscFunctionBegin;
302:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
303:   if (isascii) {
304:     PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->nu,PETSC_FALSE));
305:     PetscCall(PetscViewerASCIIPrintf(viewer,"  antishift: %s\n",str));
306:   }
307:   PetscFunctionReturn(PETSC_SUCCESS);
308: }

310: static PetscErrorCode STDestroy_Cayley(ST st)
311: {
312:   PetscFunctionBegin;
313:   PetscCall(PetscFree(st->data));
314:   PetscCall(PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",NULL));
315:   PetscCall(PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",NULL));
316:   PetscFunctionReturn(PETSC_SUCCESS);
317: }

319: SLEPC_EXTERN PetscErrorCode STCreate_Cayley(ST st)
320: {
321:   ST_CAYLEY      *ctx;

323:   PetscFunctionBegin;
324:   PetscCall(PetscNew(&ctx));
325:   st->data = (void*)ctx;

327:   st->usesksp = PETSC_TRUE;

329:   st->ops->apply           = STApply_Generic;
330:   st->ops->applytrans      = STApplyTranspose_Generic;
331:   st->ops->applyhermtrans  = STApplyHermitianTranspose_Generic;
332:   st->ops->backtransform   = STBackTransform_Cayley;
333:   st->ops->setshift        = STSetShift_Cayley;
334:   st->ops->getbilinearform = STGetBilinearForm_Cayley;
335:   st->ops->setup           = STSetUp_Cayley;
336:   st->ops->computeoperator = STComputeOperator_Cayley;
337:   st->ops->setfromoptions  = STSetFromOptions_Cayley;
338:   st->ops->postsolve       = STPostSolve_Cayley;
339:   st->ops->destroy         = STDestroy_Cayley;
340:   st->ops->view            = STView_Cayley;
341:   st->ops->checknullspace  = STCheckNullSpace_Default;
342:   st->ops->setdefaultksp   = STSetDefaultKSP_Default;

344:   PetscCall(PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",STCayleySetAntishift_Cayley));
345:   PetscCall(PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",STCayleyGetAntishift_Cayley));
346:   PetscFunctionReturn(PETSC_SUCCESS);
347: }