Actual source code: cayley.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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> /*I "slepcst.h" I*/
16: typedef struct {
17: PetscScalar nu;
18: PetscBool nu_set;
19: } ST_CAYLEY;
21: PetscErrorCode STApply_Cayley(ST st,Vec x,Vec y)
22: {
26: /* standard eigenproblem: y = (A - sI)^-1 (A + tI)x */
27: /* generalized eigenproblem: y = (A - sB)^-1 (A + tB)x */
28: MatMult(st->T[0],x,st->work[0]);
29: STMatSolve(st,st->work[0],y);
30: return(0);
31: }
33: PetscErrorCode STApplyTranspose_Cayley(ST st,Vec x,Vec y)
34: {
38: /* standard eigenproblem: y = (A + tI)^T (A - sI)^-T x */
39: /* generalized eigenproblem: y = (A + tB)^T (A - sB)^-T x */
40: STMatSolveTranspose(st,x,st->work[0]);
41: MatMultTranspose(st->T[0],st->work[0],y);
42: return(0);
43: }
45: static PetscErrorCode MatMult_Cayley(Mat B,Vec x,Vec y)
46: {
48: ST st;
49: ST_CAYLEY *ctx;
50: PetscScalar nu;
53: MatShellGetContext(B,(void**)&st);
54: ctx = (ST_CAYLEY*)st->data;
55: nu = ctx->nu;
57: if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };
59: if (st->nmat>1) {
60: /* generalized eigenproblem: y = (A + tB)x */
61: MatMult(st->A[0],x,y);
62: MatMult(st->A[1],x,st->work[1]);
63: VecAXPY(y,nu,st->work[1]);
64: } else {
65: /* standard eigenproblem: y = (A + tI)x */
66: MatMult(st->A[0],x,y);
67: VecAXPY(y,nu,x);
68: }
69: return(0);
70: }
72: static PetscErrorCode MatMultTranspose_Cayley(Mat B,Vec x,Vec y)
73: {
75: ST st;
76: ST_CAYLEY *ctx;
77: PetscScalar nu;
80: MatShellGetContext(B,(void**)&st);
81: ctx = (ST_CAYLEY*)st->data;
82: nu = ctx->nu;
84: if (st->shift_matrix == ST_MATMODE_INPLACE) { nu = nu + st->sigma; };
85: nu = PetscConj(nu);
87: if (st->nmat>1) {
88: /* generalized eigenproblem: y = (A + tB)x */
89: MatMultTranspose(st->A[0],x,y);
90: MatMultTranspose(st->A[1],x,st->work[1]);
91: VecAXPY(y,nu,st->work[1]);
92: } else {
93: /* standard eigenproblem: y = (A + tI)x */
94: MatMultTranspose(st->A[0],x,y);
95: VecAXPY(y,nu,x);
96: }
97: return(0);
98: }
100: PetscErrorCode STGetBilinearForm_Cayley(ST st,Mat *B)
101: {
105: STSetUp(st);
106: *B = st->T[0];
107: PetscObjectReference((PetscObject)*B);
108: return(0);
109: }
111: PetscErrorCode STBackTransform_Cayley(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
112: {
113: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
114: PetscInt j;
115: #if !defined(PETSC_USE_COMPLEX)
116: PetscScalar t,i,r;
117: #endif
120: #if !defined(PETSC_USE_COMPLEX)
121: for (j=0;j<n;j++) {
122: if (eigi[j] == 0.0) eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
123: else {
124: r = eigr[j];
125: i = eigi[j];
126: r = st->sigma * (r * r + i * i - r) + ctx->nu * (r - 1);
127: i = - st->sigma * i - ctx->nu * i;
128: t = i * i + r * (r - 2.0) + 1.0;
129: eigr[j] = r / t;
130: eigi[j] = i / t;
131: }
132: }
133: #else
134: for (j=0;j<n;j++) {
135: eigr[j] = (ctx->nu + eigr[j] * st->sigma) / (eigr[j] - 1.0);
136: }
137: #endif
138: return(0);
139: }
141: PetscErrorCode STPostSolve_Cayley(ST st)
142: {
146: if (st->shift_matrix == ST_MATMODE_INPLACE) {
147: if (st->nmat>1) {
148: MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
149: } else {
150: MatShift(st->A[0],st->sigma);
151: }
152: st->Astate[0] = ((PetscObject)st->A[0])->state;
153: st->state = ST_STATE_INITIAL;
154: }
155: return(0);
156: }
158: PetscErrorCode STSetUp_Cayley(ST st)
159: {
161: PetscInt n,m;
162: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
165: STSetWorkVecs(st,2);
167: /* if the user did not set the shift, use the target value */
168: if (!st->sigma_set) st->sigma = st->defsigma;
170: if (!ctx->nu_set) ctx->nu = st->sigma;
171: if (ctx->nu == 0.0 && st->sigma == 0.0) SETERRQ(PetscObjectComm((PetscObject)st),1,"Values of shift and antishift cannot be zero simultaneously");
173: /* T[0] = A+nu*B */
174: if (st->shift_matrix==ST_MATMODE_INPLACE) {
175: MatGetLocalSize(st->A[0],&n,&m);
176: MatCreateShell(PetscObjectComm((PetscObject)st),n,m,PETSC_DETERMINE,PETSC_DETERMINE,st,&st->T[0]);
177: MatShellSetOperation(st->T[0],MATOP_MULT,(void(*)(void))MatMult_Cayley);
178: MatShellSetOperation(st->T[0],MATOP_MULT_TRANSPOSE,(void(*)(void))MatMultTranspose_Cayley);
179: PetscLogObjectParent((PetscObject)st,(PetscObject)st->T[0]);
180: } else {
181: STMatMAXPY_Private(st,ctx->nu,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[0]);
182: }
184: /* T[1] = A-sigma*B */
185: STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[1]);
186: PetscObjectReference((PetscObject)st->T[1]);
187: MatDestroy(&st->P);
188: st->P = st->T[1];
189: if (!st->ksp) { STGetKSP(st,&st->ksp); }
190: STCheckFactorPackage(st);
191: KSPSetOperators(st->ksp,st->P,st->P);
192: KSPSetUp(st->ksp);
193: return(0);
194: }
196: PetscErrorCode STSetShift_Cayley(ST st,PetscScalar newshift)
197: {
199: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
202: 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");
204: if (!ctx->nu_set) {
205: if (st->shift_matrix!=ST_MATMODE_INPLACE) {
206: STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,&st->T[0]);
207: }
208: ctx->nu = newshift;
209: }
210: STMatMAXPY_Private(st,-newshift,-st->sigma,0,NULL,PETSC_FALSE,&st->T[1]);
211: if (st->P!=st->T[1]) {
212: PetscObjectReference((PetscObject)st->T[1]);
213: MatDestroy(&st->P);
214: st->P = st->T[1];
215: }
216: KSPSetOperators(st->ksp,st->P,st->P);
217: KSPSetUp(st->ksp);
218: return(0);
219: }
221: PetscErrorCode STSetFromOptions_Cayley(PetscOptionItems *PetscOptionsObject,ST st)
222: {
224: PetscScalar nu;
225: PetscBool flg;
226: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
229: PetscOptionsHead(PetscOptionsObject,"ST Cayley Options");
231: PetscOptionsScalar("-st_cayley_antishift","Value of the antishift","STCayleySetAntishift",ctx->nu,&nu,&flg);
232: if (flg) { STCayleySetAntishift(st,nu); }
234: PetscOptionsTail();
235: return(0);
236: }
238: static PetscErrorCode STCayleySetAntishift_Cayley(ST st,PetscScalar newshift)
239: {
241: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
244: if (st->state && st->shift_matrix!=ST_MATMODE_INPLACE) {
245: STMatMAXPY_Private(st,newshift,ctx->nu,0,NULL,PETSC_FALSE,&st->T[0]);
246: }
247: ctx->nu = newshift;
248: ctx->nu_set = PETSC_TRUE;
249: return(0);
250: }
252: /*@
253: STCayleySetAntishift - Sets the value of the anti-shift for the Cayley
254: spectral transformation.
256: Logically Collective on ST
258: Input Parameters:
259: + st - the spectral transformation context
260: - nu - the anti-shift
262: Options Database Key:
263: . -st_cayley_antishift - Sets the value of the anti-shift
265: Level: intermediate
267: Note:
268: In the generalized Cayley transform, the operator can be expressed as
269: OP = inv(A - sigma B)*(A + nu B). This function sets the value of nu.
270: Use STSetShift() for setting sigma.
272: .seealso: STSetShift(), STCayleyGetAntishift()
273: @*/
274: PetscErrorCode STCayleySetAntishift(ST st,PetscScalar nu)
275: {
281: PetscTryMethod(st,"STCayleySetAntishift_C",(ST,PetscScalar),(st,nu));
282: return(0);
283: }
285: static PetscErrorCode STCayleyGetAntishift_Cayley(ST st,PetscScalar *nu)
286: {
287: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
290: *nu = ctx->nu;
291: return(0);
292: }
294: /*@
295: STCayleyGetAntishift - Gets the value of the anti-shift used in the Cayley
296: spectral transformation.
298: Not Collective
300: Input Parameter:
301: . st - the spectral transformation context
303: Output Parameter:
304: . nu - the anti-shift
306: Level: intermediate
308: .seealso: STGetShift(), STCayleySetAntishift()
309: @*/
310: PetscErrorCode STCayleyGetAntishift(ST st,PetscScalar *nu)
311: {
317: PetscUseMethod(st,"STCayleyGetAntishift_C",(ST,PetscScalar*),(st,nu));
318: return(0);
319: }
321: PetscErrorCode STView_Cayley(ST st,PetscViewer viewer)
322: {
324: char str[50];
325: ST_CAYLEY *ctx = (ST_CAYLEY*)st->data;
326: PetscBool isascii;
329: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
330: if (isascii) {
331: SlepcSNPrintfScalar(str,50,ctx->nu,PETSC_FALSE);
332: PetscViewerASCIIPrintf(viewer," antishift: %s\n",str);
333: }
334: return(0);
335: }
337: PetscErrorCode STDestroy_Cayley(ST st)
338: {
342: PetscFree(st->data);
343: PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",NULL);
344: PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",NULL);
345: return(0);
346: }
348: SLEPC_EXTERN PetscErrorCode STCreate_Cayley(ST st)
349: {
351: ST_CAYLEY *ctx;
354: PetscNewLog(st,&ctx);
355: st->data = (void*)ctx;
357: st->ops->apply = STApply_Cayley;
358: st->ops->getbilinearform = STGetBilinearForm_Cayley;
359: st->ops->applytrans = STApplyTranspose_Cayley;
360: st->ops->postsolve = STPostSolve_Cayley;
361: st->ops->backtransform = STBackTransform_Cayley;
362: st->ops->setfromoptions = STSetFromOptions_Cayley;
363: st->ops->setup = STSetUp_Cayley;
364: st->ops->setshift = STSetShift_Cayley;
365: st->ops->destroy = STDestroy_Cayley;
366: st->ops->view = STView_Cayley;
367: st->ops->checknullspace = STCheckNullSpace_Default;
368: st->ops->setdefaultksp = STSetDefaultKSP_Default;
369: PetscObjectComposeFunction((PetscObject)st,"STCayleySetAntishift_C",STCayleySetAntishift_Cayley);
370: PetscObjectComposeFunction((PetscObject)st,"STCayleyGetAntishift_C",STCayleyGetAntishift_Cayley);
371: return(0);
372: }