Actual source code: interpol.c
slepc-3.6.1 2015-09-03
1: /*
3: SLEPc nonlinear eigensolver: "interpol"
5: Method: Polynomial interpolation
7: Algorithm:
9: Uses a PEP object to solve the interpolated NEP. Currently supports
10: only Chebyshev interpolation on an interval.
12: References:
14: [1] C. Effenberger and D. Kresser, "Chebyshev interpolation for
15: nonlinear eigenvalue problems", BIT 52:933-951, 2012.
17: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
18: SLEPc - Scalable Library for Eigenvalue Problem Computations
19: Copyright (c) 2002-2015, Universitat Politecnica de Valencia, Spain
21: This file is part of SLEPc.
23: SLEPc is free software: you can redistribute it and/or modify it under the
24: terms of version 3 of the GNU Lesser General Public License as published by
25: the Free Software Foundation.
27: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
28: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
29: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
30: more details.
32: You should have received a copy of the GNU Lesser General Public License
33: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
34: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
35: */
37: #include <slepc/private/nepimpl.h> /*I "slepcnep.h" I*/
38: #include <slepc/private/pepimpl.h>
40: typedef struct {
41: PEP pep;
42: PetscInt deg;
43: } NEP_INTERPOL;
47: PetscErrorCode NEPSetUp_Interpol(NEP nep)
48: {
50: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
51: ST st;
52: RG rg;
53: PetscReal a,b,c,d,s,tol;
54: PetscBool flg,istrivial;
55: PetscInt its;
58: if (nep->ncv) { /* ncv set */
59: if (nep->ncv<nep->nev) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must be at least nev");
60: } else if (nep->mpd) { /* mpd set */
61: nep->ncv = PetscMin(nep->n,nep->nev+nep->mpd);
62: } else { /* neither set: defaults depend on nev being small or large */
63: if (nep->nev<500) nep->ncv = PetscMin(nep->n,PetscMax(2*nep->nev,nep->nev+15));
64: else {
65: nep->mpd = 500;
66: nep->ncv = PetscMin(nep->n,nep->nev+nep->mpd);
67: }
68: }
69: if (!nep->mpd) nep->mpd = nep->ncv;
70: if (nep->ncv>nep->nev+nep->mpd) SETERRQ(PetscObjectComm((PetscObject)nep),1,"The value of ncv must not be larger than nev+mpd");
71: if (!nep->max_it) nep->max_it = PetscMax(5000,2*nep->n/nep->ncv);
72: if (!nep->max_funcs) nep->max_funcs = nep->max_it;
73: if (!nep->split) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NEPINTERPOL only available for split operator");
75: /* transfer PEP options */
76: if (!ctx->pep) { NEPInterpolGetPEP(nep,&ctx->pep); }
77: PEPSetBV(ctx->pep,nep->V);
78: PEPSetBasis(ctx->pep,PEP_BASIS_CHEBYSHEV1);
79: PEPSetWhichEigenpairs(ctx->pep,PEP_TARGET_MAGNITUDE);
80: PEPSetTarget(ctx->pep,0.0);
81: PEPGetST(ctx->pep,&st);
82: STSetType(st,STSINVERT);
83: PEPSetDimensions(ctx->pep,nep->nev,nep->ncv?nep->ncv:PETSC_DEFAULT,nep->mpd?nep->mpd:PETSC_DEFAULT);
84: tol=ctx->pep->tol;
85: if (tol==PETSC_DEFAULT) tol = (nep->rtol==PETSC_DEFAULT)?SLEPC_DEFAULT_TOL/10.0:nep->rtol/10.0;
86: its=ctx->pep->max_it;
87: if (!its) its = nep->max_it?nep->max_it:PETSC_DEFAULT;
88: PEPSetTolerances(ctx->pep,tol,its);
90: /* transfer region options */
91: RGIsTrivial(nep->rg,&istrivial);
92: if (istrivial) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"NEPINTERPOL requires a nontrivial region");
93: PetscObjectTypeCompare((PetscObject)nep->rg,RGINTERVAL,&flg);
94: if (!flg) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Only implemented for interval regions");
95: RGIntervalGetEndpoints(nep->rg,&a,&b,&c,&d);
96: if (a<=-PETSC_MAX_REAL || b>=PETSC_MAX_REAL) SETERRQ(PetscObjectComm((PetscObject)nep),PETSC_ERR_SUP,"Only implemented for bounded intervals");
97: PEPGetRG(ctx->pep,&rg);
98: RGIsTrivial(rg,&istrivial);
99: if (istrivial) { /* user did not give region options */
100: RGSetType(rg,RGINTERVAL);
101: s = 2.0/(b-a);
102: c = (c==0)? -PETSC_MAX_REAL: c*s;
103: d = (d==0)? PETSC_MAX_REAL: d*s;
104: RGIntervalSetEndpoints(rg,-1.0,1.0,c,d);
105: }
107: NEPAllocateSolution(nep,0);
108: return(0);
109: }
113: /*
114: Input:
115: d, number of nodes to compute
116: a,b, interval extrems
117: Output:
118: *x, array containing the d Chebyshev nodes of the interval [a,b]
119: *dct2, coefficients to compute a discrete cosine transformation (DCT-II)
120: */
121: static PetscErrorCode ChebyshevNodes(PetscInt d,PetscReal a,PetscReal b,PetscScalar *x,PetscReal *dct2)
122: {
123: PetscInt j,i;
124: PetscReal t;
127: for (j=0;j<d+1;j++) {
128: t = ((2*j+1)*PETSC_PI)/(2*(d+1));
129: x[j] = (a+b)/2.0+((b-a)/2.0)*PetscCosReal(t);
130: for (i=0;i<d+1;i++) dct2[j*(d+1)+i] = PetscCosReal(i*t);
131: }
132: return(0);
133: }
137: PetscErrorCode NEPSolve_Interpol(NEP nep)
138: {
140: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
141: Mat *A; /*T=nep->function,Tp=nep->jacobian;*/
142: PetscScalar *x,*fx,t;
143: PetscReal *cs,a,b,s;
144: PetscInt i,j,k,deg=ctx->deg;
147: PetscMalloc4(deg+1,&A,(deg+1)*(deg+1),&cs,deg+1,&x,(deg+1)*nep->nt,&fx);
148: RGIntervalGetEndpoints(nep->rg,&a,&b,NULL,NULL);
149: ChebyshevNodes(deg,a,b,x,cs);
150: for (j=0;j<nep->nt;j++) {
151: for (i=0;i<=deg;i++) {
152: FNEvaluateFunction(nep->f[j],x[i],&fx[i+j*(deg+1)]);
153: }
154: }
156: /* Polynomial coefficients */
157: for (k=0;k<=deg;k++) {
158: MatDuplicate(nep->A[0],MAT_COPY_VALUES,&A[k]);
159: t = 0.0;
160: for (i=0;i<deg+1;i++) t += fx[i]*cs[i*(deg+1)+k];
161: t *= 2.0/(deg+1);
162: if (k==0) t /= 2.0;
163: MatScale(A[k],t);
164: for (j=1;j<nep->nt;j++) {
165: t = 0.0;
166: for (i=0;i<deg+1;i++) t += fx[i+j*(deg+1)]*cs[i*(deg+1)+k];
167: t *= 2.0/(deg+1);
168: if (k==0) t /= 2.0;
169: MatAXPY(A[k],t,nep->A[j],SUBSET_NONZERO_PATTERN);
170: }
171: }
173: PEPSetOperators(ctx->pep,deg+1,A);
174: for (k=0;k<=deg;k++) {
175: MatDestroy(&A[k]);
176: }
177: PetscFree4(A,cs,x,fx);
179: /* Solve polynomial eigenproblem */
180: PEPSolve(ctx->pep);
181: PEPGetConverged(ctx->pep,&nep->nconv);
182: PEPGetIterationNumber(ctx->pep,&nep->its);
183: PEPGetConvergedReason(ctx->pep,(PEPConvergedReason*)&nep->reason);
184: s = 2.0/(b-a);
185: for (i=0;i<nep->nconv;i++) {
186: PEPGetEigenpair(ctx->pep,i,&nep->eigr[i],&nep->eigi[i],NULL,NULL);
187: nep->eigr[i] /= s;
188: nep->eigr[i] += (a+b)/2.0;
189: nep->eigi[i] /= s;
190: }
191: nep->state = NEP_STATE_EIGENVECTORS;
192: return(0);
193: }
197: PetscErrorCode NEPSetFromOptions_Interpol(PetscOptions *PetscOptionsObject,NEP nep)
198: {
200: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
203: if (!ctx->pep) { NEPInterpolGetPEP(nep,&ctx->pep); }
204: PEPSetFromOptions(ctx->pep);
205: PetscOptionsHead(PetscOptionsObject,"NEP Interpol Options");
206: PetscOptionsInt("-nep_interpol_degree","Degree of interpolation polynomial","NEPInterpolSetDegree",ctx->deg,&ctx->deg,NULL);
207: PetscOptionsTail();
208: return(0);
209: }
213: static PetscErrorCode NEPInterpolSetDegree_Interpol(NEP nep,PetscInt deg)
214: {
215: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
218: ctx->deg = deg;
219: return(0);
220: }
224: /*@
225: NEPInterpolSetDegree - Sets the degree of the interpolation polynomial.
227: Collective on NEP
229: Input Parameters:
230: + nep - nonlinear eigenvalue solver
231: - deg - polynomial degree
233: Level: advanced
235: .seealso: NEPInterpolGetDegree()
236: @*/
237: PetscErrorCode NEPInterpolSetDegree(NEP nep,PetscInt deg)
238: {
244: PetscTryMethod(nep,"NEPInterpolSetDegree_C",(NEP,PetscInt),(nep,deg));
245: return(0);
246: }
250: static PetscErrorCode NEPInterpolGetDegree_Interpol(NEP nep,PetscInt *deg)
251: {
252: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
255: *deg = ctx->deg;
256: return(0);
257: }
261: /*@
262: NEPInterpolGetDegree - Gets the degree of the interpolation polynomial.
264: Not Collective
266: Input Parameter:
267: . nep - nonlinear eigenvalue solver
269: Output Parameter:
270: . pep - the polynomial degree
272: Level: advanced
274: .seealso: NEPInterpolSetDegree()
275: @*/
276: PetscErrorCode NEPInterpolGetDegree(NEP nep,PetscInt *deg)
277: {
283: PetscTryMethod(nep,"NEPInterpolGetDegree_C",(NEP,PetscInt*),(nep,deg));
284: return(0);
285: }
289: static PetscErrorCode NEPInterpolSetPEP_Interpol(NEP nep,PEP pep)
290: {
292: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
295: PetscObjectReference((PetscObject)pep);
296: PEPDestroy(&ctx->pep);
297: ctx->pep = pep;
298: PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->pep);
299: nep->state = NEP_STATE_INITIAL;
300: return(0);
301: }
305: /*@
306: NEPInterpolSetPEP - Associate a polynomial eigensolver object (PEP) to the
307: nonlinear eigenvalue solver.
309: Collective on NEP
311: Input Parameters:
312: + nep - nonlinear eigenvalue solver
313: - pep - the polynomial eigensolver object
315: Level: advanced
317: .seealso: NEPInterpolGetPEP()
318: @*/
319: PetscErrorCode NEPInterpolSetPEP(NEP nep,PEP pep)
320: {
327: PetscTryMethod(nep,"NEPInterpolSetPEP_C",(NEP,PEP),(nep,pep));
328: return(0);
329: }
333: static PetscErrorCode NEPInterpolGetPEP_Interpol(NEP nep,PEP *pep)
334: {
336: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
337: ST st;
340: if (!ctx->pep) {
341: PEPCreate(PetscObjectComm((PetscObject)nep),&ctx->pep);
342: PEPSetOptionsPrefix(ctx->pep,((PetscObject)nep)->prefix);
343: PEPAppendOptionsPrefix(ctx->pep,"nep_");
344: PEPGetST(ctx->pep,&st);
345: STSetOptionsPrefix(st,((PetscObject)ctx->pep)->prefix);
346: PetscObjectIncrementTabLevel((PetscObject)ctx->pep,(PetscObject)nep,1);
347: PetscLogObjectParent((PetscObject)nep,(PetscObject)ctx->pep);
348: }
349: *pep = ctx->pep;
350: return(0);
351: }
355: /*@
356: NEPInterpolGetPEP - Retrieve the polynomial eigensolver object (PEP)
357: associated with the nonlinear eigenvalue solver.
359: Not Collective
361: Input Parameter:
362: . nep - nonlinear eigenvalue solver
364: Output Parameter:
365: . pep - the polynomial eigensolver object
367: Level: advanced
369: .seealso: NEPInterpolSetPEP()
370: @*/
371: PetscErrorCode NEPInterpolGetPEP(NEP nep,PEP *pep)
372: {
378: PetscTryMethod(nep,"NEPInterpolGetPEP_C",(NEP,PEP*),(nep,pep));
379: return(0);
380: }
384: PetscErrorCode NEPView_Interpol(NEP nep,PetscViewer viewer)
385: {
387: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
390: if (!ctx->pep) { NEPInterpolGetPEP(nep,&ctx->pep); }
391: PetscViewerASCIIPrintf(viewer," Interpol: polynomial degree %D\n",ctx->deg);
392: PetscViewerASCIIPushTab(viewer);
393: PEPView(ctx->pep,viewer);
394: PetscViewerASCIIPopTab(viewer);
395: return(0);
396: }
400: PetscErrorCode NEPReset_Interpol(NEP nep)
401: {
403: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
406: if (!ctx->pep) { PEPReset(ctx->pep); }
407: return(0);
408: }
412: PetscErrorCode NEPDestroy_Interpol(NEP nep)
413: {
415: NEP_INTERPOL *ctx = (NEP_INTERPOL*)nep->data;
418: PEPDestroy(&ctx->pep);
419: PetscFree(nep->data);
420: PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetDegree_C",NULL);
421: PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetDegree_C",NULL);
422: PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NULL);
423: PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NULL);
424: return(0);
425: }
429: PETSC_EXTERN PetscErrorCode NEPCreate_Interpol(NEP nep)
430: {
432: NEP_INTERPOL *ctx;
435: PetscNewLog(nep,&ctx);
436: ctx->deg = 5;
437: nep->data = (void*)ctx;
439: nep->ops->solve = NEPSolve_Interpol;
440: nep->ops->setup = NEPSetUp_Interpol;
441: nep->ops->setfromoptions = NEPSetFromOptions_Interpol;
442: nep->ops->reset = NEPReset_Interpol;
443: nep->ops->destroy = NEPDestroy_Interpol;
444: nep->ops->view = NEPView_Interpol;
445: PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetDegree_C",NEPInterpolSetDegree_Interpol);
446: PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetDegree_C",NEPInterpolGetDegree_Interpol);
447: PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolSetPEP_C",NEPInterpolSetPEP_Interpol);
448: PetscObjectComposeFunction((PetscObject)nep,"NEPInterpolGetPEP_C",NEPInterpolGetPEP_Interpol);
449: return(0);
450: }