Actual source code: cayley.c
slepc-3.21.0 2024-03-30
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: }