Actual source code: cayley.c
slepc-3.14.1 2020-12-08
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2020, 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: {
24: ST st;
25: ST_CAYLEY *ctx;
26: PetscScalar nu;
29: MatShellGetContext(B,(void**)&st);
30: ctx = (ST_CAYLEY*)st->data;
31: nu = ctx->nu;
33: if (st->matmode == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };
35: if (st->nmat>1) {
36: /* generalized eigenproblem: y = (A + tB)x */
37: MatMult(st->A[0],x,y);
38: MatMult(st->A[1],x,st->work[1]);
39: VecAXPY(y,nu,st->work[1]);
40: } else {
41: /* standard eigenproblem: y = (A + tI)x */
42: MatMult(st->A[0],x,y);
43: VecAXPY(y,nu,x);
44: }
45: return(0);
46: }
48: static PetscErrorCode MatMultTranspose_Cayley(Mat B,Vec x,Vec y)
49: {
51: ST st;
52: ST_CAYLEY *ctx;
53: PetscScalar nu;
56: MatShellGetContext(B,(void**)&st);
57: ctx = (ST_CAYLEY*)st->data;
58: nu = ctx->nu;
60: if (st->matmode == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };
61: nu = PetscConj(nu);
63: if (st->nmat>1) {
64: /* generalized eigenproblem: y = (A + tB)x */
65: MatMultTranspose(st->A[0],x,y);
66: MatMultTranspose(st->A[1],x,st->work[1]);
67: VecAXPY(y,nu,st->work[1]);
68: } else {
69: /* standard eigenproblem: y = (A + tI)x */
70: MatMultTranspose(st->A[0],x,y);
71: VecAXPY(y,nu,x);
72: }
73: return(0);
74: }
76: PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)
77: {
81: STSetUp(st);
82: *B = st->T[0];
83: PetscObjectReference((PetscObject)*B);
84: return(0);
85: }
87: PetscErrorCode STBackTransform_Cayley(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
88: {
89: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
90: PetscInt j;
91: #if !defined(PETSC_USE_COMPLEX)
92: PetscScalar t,i,r;
93: #endif
96: #if !defined(PETSC_USE_COMPLEX)
97: for (j=0;j<n;j++) {
98: if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
99: else {
100: r = eigr[j];
101: i = eigi[j];
102: r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
103: i = - st->sigma * i - ctx->nu * i;
104: t = i * i + r * (r - 2.0) + 1.0;
105: eigr[j] = r / t;
106: eigi[j] = i / t;
107: }
108: }
109: #else
110: for (j=0;j<n;j++) {
111: eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
112: }
113: #endif
114: return(0);
115: }
117: PetscErrorCode STPostSolve_Cayley(ST st)
118: {
122: if (st->matmode == ST_MATMODE_INPLACE) {
123: if (st->nmat>1) {
124: MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
125: } else {
126: MatShift(st->A[0],st->sigma);
127: }
128: st->Astate[0] = ((PetscObject)st->A[0])->state;
129: st->state = ST_STATE_INITIAL;
130: st->opready = PETSC_FALSE;
131: }
132: return(0);
133: }
135: /*
136: Operator (cayley):
137: Op P M
138: if nmat=1: (A-sI)^-1 (A+tI) A-sI A+tI
139: if nmat=2: (A-sB)^-1 (A+tB) A-sB A+tI
140: */
141: PetscErrorCode STComputeOperator_Cayley(ST st)
142: {
144: PetscInt n,m;
145: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
148: /* if the user did not set the shift, use the target value */
149: if (!st->sigma_set) st->sigma = st->defsigma;
151: if (!ctx->nu_set) ctx->nu = st->sigma;
152: if (ctx->nu == 0.0 && st->sigma == 0.0) SETERRQ(PetscObjectComm((PetscObject)st),1,"Values of shift and antishift cannot be zero simultaneously");
153: 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)");
155: /* T[0] = A+nu*B */
156: if (st->matmode==ST_MATMODE_INPLACE) {
157: MatGetLocalSize(st->A[0],&n,&m);
158: MatCreateShell(PetscObjectComm((PetscObject)st),n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,&st->T[0]);
159: MatShellSetOperation(st->T[0],MATOP_MULT,(void(*)(void))MatMult_Cayley);
160: MatShellSetOperation(st->T[0],MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Cayley);
161: PetscLogObjectParent((PetscObject)st,(PetscObject)st->T[0]);
162: } else {
163: STMatMAXPY_Private(st,ctx->nu,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[0]);
164: }
165: st->M = st->T[0];
167: /* T[1] = A-sigma*B */
168: STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[1]);
169: PetscObjectReference((PetscObject)st->T[1]);
170: MatDestroy(&st->P);
171: st->P = st->T[1];
172: return(0);
173: }
175: PetscErrorCode STSetUp_Cayley(ST st)
176: {
180: if (st->nmat>2) SETERRQ(PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"Cayley transform cannot be used in polynomial eigenproblems");
181: STSetWorkVecs(st,2);
182: KSPSetUp(st->ksp);
183: return(0);
184: }
186: PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
187: {
189: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
192: 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");
193: if (ctx->nu == -newshift) SETERRQ(PetscObjectComm((PetscObject)st),1,"It is not allowed to set the shift equal to minus the antishift");
195: if (!ctx->nu_set) {
196: if (st->matmode!=ST_MATMODE_INPLACE) {
197: STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,&st->T[0]);
198: }
199: ctx->nu = newshift;
200: }
201: STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,&st->T[1]);
202: if (st->P!=st->T[1]) {
203: PetscObjectReference((PetscObject)st->T[1]);
204: MatDestroy(&st->P);
205: st->P = st->T[1];
206: }
207: KSPSetOperators(st->ksp,st->P,st->P);
208: KSPSetUp(st->ksp);
209: return(0);
210: }
212: PetscErrorCode STSetFromOptions_Cayley(PetscOptionItems *PetscOptionsObject,ST st)
213: {
215: PetscScalar nu;
216: PetscBool flg;
217: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
220: PetscOptionsHead(PetscOptionsObject,"ST Cayley Options");
222: PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg);
223: if (flg) { STCayleySetAntishift(st,nu); }
225: PetscOptionsTail();
226: return(0);
227: }
229: static PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
230: {
232: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
235: if (ctx->nu != newshift) {
236: STCheckNotSeized(st,1);
237: if (st->state && st->matmode!=ST_MATMODE_INPLACE) {
238: STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,&st->T[0]);
239: }
240: ctx->nu = newshift;
241: }
242: ctx->nu_set = PETSC_TRUE;
243: return(0);
244: }
246: /*@
247: STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
248: spectral transformation.
250: Logically Collective on st
252: Input Parameters:
253: + st - the spectral transformation context
254: - nu - the anti-shift
256: Options Database Key:
257: . -st_cayley_antishift - Sets the value of the anti-shift
259: Level: intermediate
261: Note:
262: In the generalized Cayley transform, the operator can be expressed as
263: OP = inv(A - sigma B)*(A + nu B). This function sets the value of nu.
264: Use STSetShift() for setting sigma. The value nu=-sigma is not allowed.
266: .seealso: STSetShift(), STCayleyGetAntishift()
267: @*/
268: PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
269: {
275: PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));
276: return(0);
277: }
279: static PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)
280: {
281: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
284: *nu = ctx->nu;
285: return(0);
286: }
288: /*@
289: STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley
290: spectral transformation.
292: Not Collective
294: Input Parameter:
295: . st - the spectral transformation context
297: Output Parameter:
298: . nu - the anti-shift
300: Level: intermediate
302: .seealso: STGetShift(), STCayleySetAntishift()
303: @*/
304: PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)
305: {
311: PetscUseMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));
312: return(0);
313: }
315: PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
316: {
318: char str[50];
319: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
320: PetscBool isascii;
323: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
324: if (isascii) {
325: SlepcSNPrintfScalar(str,sizeof(str),ctx->nu,PETSC_FALSE);
326: PetscViewerASCIIPrintf(viewer," antishift: %s\n",str);
327: }
328: return(0);
329: }
331: PetscErrorCode STDestroy_Cayley(ST st)
332: {
336: PetscFree(st->data);
337: PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",NULL);
338: PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",NULL);
339: return(0);
340: }
342: SLEPC_EXTERN PetscErrorCode STCreate_Cayley(ST st)
343: {
345: ST_CAYLEY *ctx;
348: PetscNewLog(st,&ctx);
349: st->data = (void*)ctx;
351: st->usesksp = PETSC_TRUE;
353: st->ops->apply = STApply_Generic;
354: st->ops->applytrans = STApplyTranspose_Generic;
355: st->ops->backtransform = STBackTransform_Cayley;
356: st->ops->setshift = STSetShift_Cayley;
357: st->ops->getbilinearform = STGetBilinearForm_Cayley;
358: st->ops->setup = STSetUp_Cayley;
359: st->ops->computeoperator = STComputeOperator_Cayley;
360: st->ops->setfromoptions = STSetFromOptions_Cayley;
361: st->ops->postsolve = STPostSolve_Cayley;
362: st->ops->destroy = STDestroy_Cayley;
363: st->ops->view = STView_Cayley;
364: st->ops->checknullspace = STCheckNullSpace_Default;
365: st->ops->setdefaultksp = STSetDefaultKSP_Default;
367: PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",STCayleySetAntishift_Cayley);
368: PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",STCayleyGetAntishift_Cayley);
369: return(0);
370: }