Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
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 : */
13 :
14 : #include <slepc/private/stimpl.h> /*I "slepcst.h" I*/
15 :
16 : typedef struct {
17 : PetscScalar nu;
18 : PetscBool nu_set;
19 : } ST_CAYLEY;
20 :
21 10 : static PetscErrorCode MatMult_Cayley(Mat B,Vec x,Vec y)
22 : {
23 10 : ST st;
24 10 : ST_CAYLEY *ctx;
25 10 : PetscScalar nu;
26 :
27 10 : PetscFunctionBegin;
28 10 : PetscCall(MatShellGetContext(B,&st));
29 10 : ctx = (ST_CAYLEY*)st->data;
30 10 : nu = ctx->nu;
31 :
32 10 : if (st->matmode == ST_MATMODE_INPLACE) { nu = nu + st->sigma; }
33 :
34 10 : if (st->nmat>1) {
35 : /* generalized eigenproblem: y = (A + tB)x */
36 4 : PetscCall(MatMult(st->A[0],x,y));
37 4 : PetscCall(MatMult(st->A[1],x,st->work[1]));
38 4 : PetscCall(VecAXPY(y,nu,st->work[1]));
39 : } else {
40 : /* standard eigenproblem: y = (A + tI)x */
41 6 : PetscCall(MatMult(st->A[0],x,y));
42 6 : PetscCall(VecAXPY(y,nu,x));
43 : }
44 10 : PetscFunctionReturn(PETSC_SUCCESS);
45 : }
46 :
47 2 : static PetscErrorCode MatMultTranspose_Cayley(Mat B,Vec x,Vec y)
48 : {
49 2 : ST st;
50 2 : ST_CAYLEY *ctx;
51 2 : PetscScalar nu;
52 :
53 2 : PetscFunctionBegin;
54 2 : PetscCall(MatShellGetContext(B,&st));
55 2 : ctx = (ST_CAYLEY*)st->data;
56 2 : nu = ctx->nu;
57 :
58 2 : if (st->matmode == ST_MATMODE_INPLACE) { nu = nu + st->sigma; }
59 2 : nu = PetscConj(nu);
60 :
61 2 : if (st->nmat>1) {
62 : /* generalized eigenproblem: y = (A + tB)x */
63 0 : PetscCall(MatMultTranspose(st->A[0],x,y));
64 0 : PetscCall(MatMultTranspose(st->A[1],x,st->work[1]));
65 0 : PetscCall(VecAXPY(y,nu,st->work[1]));
66 : } else {
67 : /* standard eigenproblem: y = (A + tI)x */
68 2 : PetscCall(MatMultTranspose(st->A[0],x,y));
69 2 : PetscCall(VecAXPY(y,nu,x));
70 : }
71 2 : PetscFunctionReturn(PETSC_SUCCESS);
72 : }
73 :
74 7 : static PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)
75 : {
76 7 : PetscFunctionBegin;
77 7 : PetscCall(STSetUp(st));
78 7 : *B = st->T[0];
79 7 : PetscCall(PetscObjectReference((PetscObject)*B));
80 7 : PetscFunctionReturn(PETSC_SUCCESS);
81 : }
82 :
83 683 : static PetscErrorCode STBackTransform_Cayley(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
84 : {
85 683 : ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
86 683 : PetscInt j;
87 : #if !defined(PETSC_USE_COMPLEX)
88 683 : PetscScalar t,i,r;
89 : #endif
90 :
91 683 : PetscFunctionBegin;
92 : #if !defined(PETSC_USE_COMPLEX)
93 2047 : for (j=0;j<n;j++) {
94 1364 : if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
95 : else {
96 57 : r = eigr[j];
97 57 : i = eigi[j];
98 57 : r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
99 57 : i = - st->sigma * i - ctx->nu * i;
100 57 : t = i * i + r * (r - 2.0) + 1.0;
101 57 : eigr[j] = r / t;
102 57 : 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
110 683 : PetscFunctionReturn(PETSC_SUCCESS);
111 : }
112 :
113 5 : static PetscErrorCode STPostSolve_Cayley(ST st)
114 : {
115 5 : PetscFunctionBegin;
116 5 : if (st->matmode == ST_MATMODE_INPLACE) {
117 1 : if (st->nmat>1) PetscCall(MatAXPY(st->A[0],st->sigma,st->A[1],st->str));
118 1 : else PetscCall(MatShift(st->A[0],st->sigma));
119 1 : st->Astate[0] = ((PetscObject)st->A[0])->state;
120 1 : st->state = ST_STATE_INITIAL;
121 1 : st->opready = PETSC_FALSE;
122 : }
123 5 : PetscFunctionReturn(PETSC_SUCCESS);
124 : }
125 :
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 13 : static PetscErrorCode STComputeOperator_Cayley(ST st)
133 : {
134 13 : PetscInt n,m;
135 13 : ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
136 :
137 13 : PetscFunctionBegin;
138 : /* if the user did not set the shift, use the target value */
139 13 : if (!st->sigma_set) st->sigma = st->defsigma;
140 :
141 13 : if (!ctx->nu_set) ctx->nu = st->sigma;
142 13 : 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 13 : 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)");
144 :
145 : /* T[0] = A+nu*B */
146 13 : if (st->matmode==ST_MATMODE_INPLACE) {
147 3 : PetscCall(MatGetLocalSize(st->A[0],&n,&m));
148 3 : PetscCall(MatCreateShell(PetscObjectComm((PetscObject)st),n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,&st->T[0]));
149 3 : PetscCall(MatShellSetOperation(st->T[0],MATOP_MULT,(void(*)(void))MatMult_Cayley));
150 3 : PetscCall(MatShellSetOperation(st->T[0],MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Cayley));
151 10 : } else PetscCall(STMatMAXPY_Private(st,ctx->nu,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[0]));
152 13 : st->M = st->T[0];
153 :
154 : /* T[1] = A-sigma*B */
155 13 : PetscCall(STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[1]));
156 13 : PetscCall(PetscObjectReference((PetscObject)st->T[1]));
157 13 : PetscCall(MatDestroy(&st->P));
158 13 : st->P = st->T[1];
159 13 : if (st->Psplit) { /* build custom preconditioner from the split matrices */
160 2 : PetscCall(STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PETSC_TRUE,PETSC_TRUE,&st->Pmat));
161 : }
162 13 : PetscFunctionReturn(PETSC_SUCCESS);
163 : }
164 :
165 13 : static PetscErrorCode STSetUp_Cayley(ST st)
166 : {
167 13 : PetscFunctionBegin;
168 13 : PetscCheck(st->nmat<=2,PetscObjectComm((PetscObject)st),PETSC_ERR_SUP,"Cayley transform cannot be used in polynomial eigenproblems");
169 13 : PetscCall(STSetWorkVecs(st,2));
170 13 : PetscCall(KSPSetUp(st->ksp));
171 13 : PetscFunctionReturn(PETSC_SUCCESS);
172 : }
173 :
174 8 : static PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
175 : {
176 8 : ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
177 :
178 8 : PetscFunctionBegin;
179 8 : 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 8 : PetscCheck(ctx->nu!=-newshift,PetscObjectComm((PetscObject)st),PETSC_ERR_USER_INPUT,"It is not allowed to set the shift equal to minus the antishift");
181 :
182 8 : if (!ctx->nu_set) {
183 6 : if (st->matmode!=ST_MATMODE_INPLACE) PetscCall(STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,PETSC_FALSE,&st->T[0]));
184 6 : ctx->nu = newshift;
185 : }
186 8 : PetscCall(STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,PETSC_FALSE,&st->T[1]));
187 8 : if (st->P!=st->T[1]) {
188 2 : PetscCall(PetscObjectReference((PetscObject)st->T[1]));
189 2 : PetscCall(MatDestroy(&st->P));
190 2 : st->P = st->T[1];
191 : }
192 8 : if (st->Psplit) { /* build custom preconditioner from the split matrices */
193 2 : PetscCall(STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,PETSC_TRUE,&st->Pmat));
194 : }
195 8 : PetscCall(ST_KSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P));
196 8 : PetscCall(KSPSetUp(st->ksp));
197 8 : PetscFunctionReturn(PETSC_SUCCESS);
198 : }
199 :
200 7 : static PetscErrorCode STSetFromOptions_Cayley(ST st,PetscOptionItems *PetscOptionsObject)
201 : {
202 7 : PetscScalar nu;
203 7 : PetscBool flg;
204 7 : ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
205 :
206 7 : PetscFunctionBegin;
207 7 : PetscOptionsHeadBegin(PetscOptionsObject,"ST Cayley Options");
208 :
209 7 : PetscCall(PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg));
210 7 : if (flg) PetscCall(STCayleySetAntishift(st,nu));
211 :
212 7 : PetscOptionsHeadEnd();
213 7 : PetscFunctionReturn(PETSC_SUCCESS);
214 : }
215 :
216 12 : static PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
217 : {
218 12 : ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
219 :
220 12 : PetscFunctionBegin;
221 12 : if (ctx->nu != newshift) {
222 12 : STCheckNotSeized(st,1);
223 12 : 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 12 : ctx->nu = newshift;
225 : }
226 12 : ctx->nu_set = PETSC_TRUE;
227 12 : PetscFunctionReturn(PETSC_SUCCESS);
228 : }
229 :
230 : /*@
231 : STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
232 : spectral transformation.
233 :
234 : Logically Collective
235 :
236 : Input Parameters:
237 : + st - the spectral transformation context
238 : - nu - the anti-shift
239 :
240 : Options Database Key:
241 : . -st_cayley_antishift - Sets the value of the anti-shift
242 :
243 : Level: intermediate
244 :
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.
249 :
250 : .seealso: STSetShift(), STCayleyGetAntishift()
251 : @*/
252 16 : PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
253 : {
254 16 : PetscFunctionBegin;
255 16 : PetscValidHeaderSpecific(st,ST_CLASSID,1);
256 48 : PetscValidLogicalCollectiveScalar(st,nu,2);
257 16 : PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));
258 16 : PetscFunctionReturn(PETSC_SUCCESS);
259 : }
260 :
261 18 : static PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)
262 : {
263 18 : ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
264 :
265 18 : PetscFunctionBegin;
266 18 : *nu = ctx->nu;
267 18 : PetscFunctionReturn(PETSC_SUCCESS);
268 : }
269 :
270 : /*@
271 : STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley
272 : spectral transformation.
273 :
274 : Not Collective
275 :
276 : Input Parameter:
277 : . st - the spectral transformation context
278 :
279 : Output Parameter:
280 : . nu - the anti-shift
281 :
282 : Level: intermediate
283 :
284 : .seealso: STGetShift(), STCayleySetAntishift()
285 : @*/
286 18 : PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)
287 : {
288 18 : PetscFunctionBegin;
289 18 : PetscValidHeaderSpecific(st,ST_CLASSID,1);
290 18 : PetscAssertPointer(nu,2);
291 18 : PetscUseMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));
292 18 : PetscFunctionReturn(PETSC_SUCCESS);
293 : }
294 :
295 0 : static PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
296 : {
297 0 : char str[50];
298 0 : ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
299 0 : PetscBool isascii;
300 :
301 0 : PetscFunctionBegin;
302 0 : PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
303 0 : if (isascii) {
304 0 : PetscCall(SlepcSNPrintfScalar(str,sizeof(str),ctx->nu,PETSC_FALSE));
305 0 : PetscCall(PetscViewerASCIIPrintf(viewer," antishift: %s\n",str));
306 : }
307 0 : PetscFunctionReturn(PETSC_SUCCESS);
308 : }
309 :
310 13 : static PetscErrorCode STDestroy_Cayley(ST st)
311 : {
312 13 : PetscFunctionBegin;
313 13 : PetscCall(PetscFree(st->data));
314 13 : PetscCall(PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",NULL));
315 13 : PetscCall(PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",NULL));
316 13 : PetscFunctionReturn(PETSC_SUCCESS);
317 : }
318 :
319 13 : SLEPC_EXTERN PetscErrorCode STCreate_Cayley(ST st)
320 : {
321 13 : ST_CAYLEY *ctx;
322 :
323 13 : PetscFunctionBegin;
324 13 : PetscCall(PetscNew(&ctx));
325 13 : st->data = (void*)ctx;
326 :
327 13 : st->usesksp = PETSC_TRUE;
328 :
329 13 : st->ops->apply = STApply_Generic;
330 13 : st->ops->applytrans = STApplyTranspose_Generic;
331 13 : st->ops->applyhermtrans = STApplyHermitianTranspose_Generic;
332 13 : st->ops->backtransform = STBackTransform_Cayley;
333 13 : st->ops->setshift = STSetShift_Cayley;
334 13 : st->ops->getbilinearform = STGetBilinearForm_Cayley;
335 13 : st->ops->setup = STSetUp_Cayley;
336 13 : st->ops->computeoperator = STComputeOperator_Cayley;
337 13 : st->ops->setfromoptions = STSetFromOptions_Cayley;
338 13 : st->ops->postsolve = STPostSolve_Cayley;
339 13 : st->ops->destroy = STDestroy_Cayley;
340 13 : st->ops->view = STView_Cayley;
341 13 : st->ops->checknullspace = STCheckNullSpace_Default;
342 13 : st->ops->setdefaultksp = STSetDefaultKSP_Default;
343 :
344 13 : PetscCall(PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",STCayleySetAntishift_Cayley));
345 13 : PetscCall(PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",STCayleyGetAntishift_Cayley));
346 13 : PetscFunctionReturn(PETSC_SUCCESS);
347 : }
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