Actual source code: linear.c
slepc-3.18.0 2022-10-01
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: Explicit linearization for polynomial eigenproblems
12: */
14: #include <slepc/private/pepimpl.h>
15: #include "linear.h"
17: static PetscErrorCode MatMult_Linear_Shift(Mat M,Vec x,Vec y)
18: {
19: PEP_LINEAR *ctx;
20: PEP pep;
21: const PetscScalar *px;
22: PetscScalar *py,a,sigma=0.0;
23: PetscInt nmat,deg,i,m;
24: Vec x1,x2,x3,y1,aux;
25: PetscReal *ca,*cb,*cg;
26: PetscBool flg;
28: MatShellGetContext(M,&ctx);
29: pep = ctx->pep;
30: STGetTransform(pep->st,&flg);
31: if (!flg) STGetShift(pep->st,&sigma);
32: nmat = pep->nmat;
33: deg = nmat-1;
34: m = pep->nloc;
35: ca = pep->pbc;
36: cb = pep->pbc+nmat;
37: cg = pep->pbc+2*nmat;
38: x1=ctx->w[0];x2=ctx->w[1];x3=ctx->w[2];y1=ctx->w[3];aux=ctx->w[4];
40: VecSet(y,0.0);
41: VecGetArrayRead(x,&px);
42: VecGetArray(y,&py);
43: a = 1.0;
45: /* first block */
46: VecPlaceArray(x2,px);
47: VecPlaceArray(x3,px+m);
48: VecPlaceArray(y1,py);
49: VecAXPY(y1,cb[0]-sigma,x2);
50: VecAXPY(y1,ca[0],x3);
51: VecResetArray(x2);
52: VecResetArray(x3);
53: VecResetArray(y1);
55: /* inner blocks */
56: for (i=1;i<deg-1;i++) {
57: VecPlaceArray(x1,px+(i-1)*m);
58: VecPlaceArray(x2,px+i*m);
59: VecPlaceArray(x3,px+(i+1)*m);
60: VecPlaceArray(y1,py+i*m);
61: VecAXPY(y1,cg[i],x1);
62: VecAXPY(y1,cb[i]-sigma,x2);
63: VecAXPY(y1,ca[i],x3);
64: VecResetArray(x1);
65: VecResetArray(x2);
66: VecResetArray(x3);
67: VecResetArray(y1);
68: }
70: /* last block */
71: VecPlaceArray(y1,py+(deg-1)*m);
72: for (i=0;i<deg;i++) {
73: VecPlaceArray(x1,px+i*m);
74: STMatMult(pep->st,i,x1,aux);
75: VecAXPY(y1,a,aux);
76: VecResetArray(x1);
77: a *= pep->sfactor;
78: }
79: VecCopy(y1,aux);
80: STMatSolve(pep->st,aux,y1);
81: VecScale(y1,-ca[deg-1]/a);
82: VecPlaceArray(x1,px+(deg-2)*m);
83: VecPlaceArray(x2,px+(deg-1)*m);
84: VecAXPY(y1,cg[deg-1],x1);
85: VecAXPY(y1,cb[deg-1]-sigma,x2);
86: VecResetArray(x1);
87: VecResetArray(x2);
88: VecResetArray(y1);
90: VecRestoreArrayRead(x,&px);
91: VecRestoreArray(y,&py);
92: return 0;
93: }
95: static PetscErrorCode MatMult_Linear_Sinvert(Mat M,Vec x,Vec y)
96: {
97: PEP_LINEAR *ctx;
98: PEP pep;
99: const PetscScalar *px;
100: PetscScalar *py,a,sigma,t=1.0,tp=0.0,tt;
101: PetscInt nmat,deg,i,m;
102: Vec x1,y1,y2,y3,aux,aux2;
103: PetscReal *ca,*cb,*cg;
105: MatShellGetContext(M,&ctx);
106: pep = ctx->pep;
107: nmat = pep->nmat;
108: deg = nmat-1;
109: m = pep->nloc;
110: ca = pep->pbc;
111: cb = pep->pbc+nmat;
112: cg = pep->pbc+2*nmat;
113: x1=ctx->w[0];y1=ctx->w[1];y2=ctx->w[2];y3=ctx->w[3];aux=ctx->w[4];aux2=ctx->w[5];
114: EPSGetTarget(ctx->eps,&sigma);
115: VecSet(y,0.0);
116: VecGetArrayRead(x,&px);
117: VecGetArray(y,&py);
118: a = pep->sfactor;
120: /* first block */
121: VecPlaceArray(x1,px);
122: VecPlaceArray(y1,py+m);
123: VecCopy(x1,y1);
124: VecScale(y1,1.0/ca[0]);
125: VecResetArray(x1);
126: VecResetArray(y1);
128: /* second block */
129: if (deg>2) {
130: VecPlaceArray(x1,px+m);
131: VecPlaceArray(y1,py+m);
132: VecPlaceArray(y2,py+2*m);
133: VecCopy(x1,y2);
134: VecAXPY(y2,sigma-cb[1],y1);
135: VecScale(y2,1.0/ca[1]);
136: VecResetArray(x1);
137: VecResetArray(y1);
138: VecResetArray(y2);
139: }
141: /* inner blocks */
142: for (i=2;i<deg-1;i++) {
143: VecPlaceArray(x1,px+i*m);
144: VecPlaceArray(y1,py+(i-1)*m);
145: VecPlaceArray(y2,py+i*m);
146: VecPlaceArray(y3,py+(i+1)*m);
147: VecCopy(x1,y3);
148: VecAXPY(y3,sigma-cb[i],y2);
149: VecAXPY(y3,-cg[i],y1);
150: VecScale(y3,1.0/ca[i]);
151: VecResetArray(x1);
152: VecResetArray(y1);
153: VecResetArray(y2);
154: VecResetArray(y3);
155: }
157: /* last block */
158: VecPlaceArray(y1,py);
159: for (i=0;i<deg-2;i++) {
160: VecPlaceArray(y2,py+(i+1)*m);
161: STMatMult(pep->st,i+1,y2,aux);
162: VecAXPY(y1,a,aux);
163: VecResetArray(y2);
164: a *= pep->sfactor;
165: }
166: i = deg-2;
167: VecPlaceArray(y2,py+(i+1)*m);
168: VecPlaceArray(y3,py+i*m);
169: VecCopy(y2,aux2);
170: VecAXPY(aux2,cg[i+1]/ca[i+1],y3);
171: STMatMult(pep->st,i+1,aux2,aux);
172: VecAXPY(y1,a,aux);
173: VecResetArray(y2);
174: VecResetArray(y3);
175: a *= pep->sfactor;
176: i = deg-1;
177: VecPlaceArray(x1,px+i*m);
178: VecPlaceArray(y3,py+i*m);
179: VecCopy(x1,aux2);
180: VecAXPY(aux2,sigma-cb[i],y3);
181: VecScale(aux2,1.0/ca[i]);
182: STMatMult(pep->st,i+1,aux2,aux);
183: VecAXPY(y1,a,aux);
184: VecResetArray(x1);
185: VecResetArray(y3);
187: VecCopy(y1,aux);
188: STMatSolve(pep->st,aux,y1);
189: VecScale(y1,-1.0);
191: /* final update */
192: for (i=1;i<deg;i++) {
193: VecPlaceArray(y2,py+i*m);
194: tt = t;
195: t = ((sigma-cb[i-1])*t-cg[i-1]*tp)/ca[i-1]; /* i-th basis polynomial */
196: tp = tt;
197: VecAXPY(y2,t,y1);
198: VecResetArray(y2);
199: }
200: VecResetArray(y1);
202: VecRestoreArrayRead(x,&px);
203: VecRestoreArray(y,&py);
204: return 0;
205: }
207: static PetscErrorCode BackTransform_Linear(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
208: {
209: PEP_LINEAR *ctx;
210: ST stctx;
212: STShellGetContext(st,&ctx);
213: PEPGetST(ctx->pep,&stctx);
214: STBackTransform(stctx,n,eigr,eigi);
215: return 0;
216: }
218: /*
219: Dummy backtransform operation
220: */
221: static PetscErrorCode BackTransform_Skip(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
222: {
223: return 0;
224: }
226: static PetscErrorCode Apply_Linear(ST st,Vec x,Vec y)
227: {
228: PEP_LINEAR *ctx;
230: STShellGetContext(st,&ctx);
231: MatMult(ctx->A,x,y);
232: return 0;
233: }
235: PetscErrorCode PEPSetUp_Linear(PEP pep)
236: {
237: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
238: ST st;
239: PetscInt i=0,deg=pep->nmat-1;
240: EPSWhich which = EPS_LARGEST_MAGNITUDE;
241: EPSProblemType ptype;
242: PetscBool trackall,istrivial,transf,sinv,ks;
243: PetscScalar sigma,*epsarray,*peparray;
244: Vec veps,w=NULL;
245: /* function tables */
246: PetscErrorCode (*fcreate[][2])(MPI_Comm,PEP_LINEAR*,Mat*) = {
247: { MatCreateExplicit_Linear_NA, MatCreateExplicit_Linear_NB },
248: { MatCreateExplicit_Linear_SA, MatCreateExplicit_Linear_SB },
249: { MatCreateExplicit_Linear_HA, MatCreateExplicit_Linear_HB },
250: };
252: PEPCheckShiftSinvert(pep);
253: PEPCheckUnsupported(pep,PEP_FEATURE_STOPPING);
254: PEPCheckIgnored(pep,PEP_FEATURE_CONVERGENCE);
255: STGetTransform(pep->st,&transf);
256: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
257: if (!pep->which) PEPSetWhichEigenpairs_Default(pep);
259: STSetUp(pep->st);
260: if (!ctx->eps) PEPLinearGetEPS(pep,&ctx->eps);
261: EPSGetST(ctx->eps,&st);
262: if (!transf && !ctx->usereps) EPSSetTarget(ctx->eps,pep->target);
263: if (sinv && !transf && !ctx->usereps) STSetDefaultShift(st,pep->target);
264: /* compute scale factor if not set by user */
265: PEPComputeScaleFactor(pep);
267: if (ctx->explicitmatrix) {
268: PEPCheckQuadraticCondition(pep,PETSC_TRUE," (with explicit matrix)");
269: PEPCheckUnsupportedCondition(pep,PEP_FEATURE_NONMONOMIAL,PETSC_TRUE," (with explicit matrix)");
272: if (sinv && !transf) STSetType(st,STSINVERT);
273: RGPushScale(pep->rg,1.0/pep->sfactor);
274: STGetMatrixTransformed(pep->st,0,&ctx->K);
275: STGetMatrixTransformed(pep->st,1,&ctx->C);
276: STGetMatrixTransformed(pep->st,2,&ctx->M);
277: ctx->sfactor = pep->sfactor;
278: ctx->dsfactor = pep->dsfactor;
280: MatDestroy(&ctx->A);
281: MatDestroy(&ctx->B);
282: VecDestroy(&ctx->w[0]);
283: VecDestroy(&ctx->w[1]);
284: VecDestroy(&ctx->w[2]);
285: VecDestroy(&ctx->w[3]);
287: switch (pep->problem_type) {
288: case PEP_GENERAL: i = 0; break;
289: case PEP_HERMITIAN:
290: case PEP_HYPERBOLIC: i = 1; break;
291: case PEP_GYROSCOPIC: i = 2; break;
292: }
294: (*fcreate[i][0])(PetscObjectComm((PetscObject)pep),ctx,&ctx->A);
295: (*fcreate[i][1])(PetscObjectComm((PetscObject)pep),ctx,&ctx->B);
297: } else { /* implicit matrix */
299: if (!((PetscObject)(ctx->eps))->type_name) EPSSetType(ctx->eps,EPSKRYLOVSCHUR);
300: else {
301: PetscObjectTypeCompare((PetscObject)ctx->eps,EPSKRYLOVSCHUR,&ks);
303: }
305: STSetType(st,STSHELL);
306: STShellSetContext(st,ctx);
307: if (!transf) STShellSetBackTransform(st,BackTransform_Linear);
308: else STShellSetBackTransform(st,BackTransform_Skip);
309: MatCreateVecsEmpty(pep->A[0],&ctx->w[0],&ctx->w[1]);
310: MatCreateVecsEmpty(pep->A[0],&ctx->w[2],&ctx->w[3]);
311: MatCreateVecs(pep->A[0],&ctx->w[4],&ctx->w[5]);
312: MatCreateShell(PetscObjectComm((PetscObject)pep),deg*pep->nloc,deg*pep->nloc,deg*pep->n,deg*pep->n,ctx,&ctx->A);
313: if (sinv && !transf) MatShellSetOperation(ctx->A,MATOP_MULT,(void(*)(void))MatMult_Linear_Sinvert);
314: else MatShellSetOperation(ctx->A,MATOP_MULT,(void(*)(void))MatMult_Linear_Shift);
315: STShellSetApply(st,Apply_Linear);
316: ctx->pep = pep;
318: PEPBasisCoefficients(pep,pep->pbc);
319: if (!transf) {
320: PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
321: if (sinv) PEPEvaluateBasis(pep,pep->target,0,pep->solvematcoeffs,NULL);
322: else {
323: for (i=0;i<deg;i++) pep->solvematcoeffs[i] = 0.0;
324: pep->solvematcoeffs[deg] = 1.0;
325: }
326: STScaleShift(pep->st,1.0/pep->sfactor);
327: RGPushScale(pep->rg,1.0/pep->sfactor);
328: }
329: if (pep->sfactor!=1.0) {
330: for (i=0;i<pep->nmat;i++) {
331: pep->pbc[pep->nmat+i] /= pep->sfactor;
332: pep->pbc[2*pep->nmat+i] /= pep->sfactor*pep->sfactor;
333: }
334: }
335: }
337: EPSSetOperators(ctx->eps,ctx->A,ctx->B);
338: EPSGetProblemType(ctx->eps,&ptype);
339: if (!ptype) {
340: if (ctx->explicitmatrix) EPSSetProblemType(ctx->eps,EPS_GNHEP);
341: else EPSSetProblemType(ctx->eps,EPS_NHEP);
342: }
343: if (!ctx->usereps) {
344: if (transf) which = EPS_LARGEST_MAGNITUDE;
345: else {
346: switch (pep->which) {
347: case PEP_LARGEST_MAGNITUDE: which = EPS_LARGEST_MAGNITUDE; break;
348: case PEP_SMALLEST_MAGNITUDE: which = EPS_SMALLEST_MAGNITUDE; break;
349: case PEP_LARGEST_REAL: which = EPS_LARGEST_REAL; break;
350: case PEP_SMALLEST_REAL: which = EPS_SMALLEST_REAL; break;
351: case PEP_LARGEST_IMAGINARY: which = EPS_LARGEST_IMAGINARY; break;
352: case PEP_SMALLEST_IMAGINARY: which = EPS_SMALLEST_IMAGINARY; break;
353: case PEP_TARGET_MAGNITUDE: which = EPS_TARGET_MAGNITUDE; break;
354: case PEP_TARGET_REAL: which = EPS_TARGET_REAL; break;
355: case PEP_TARGET_IMAGINARY: which = EPS_TARGET_IMAGINARY; break;
356: case PEP_ALL: which = EPS_ALL; break;
357: case PEP_WHICH_USER: which = EPS_WHICH_USER;
358: EPSSetEigenvalueComparison(ctx->eps,pep->sc->comparison,pep->sc->comparisonctx);
359: break;
360: }
361: }
362: EPSSetWhichEigenpairs(ctx->eps,which);
364: EPSSetDimensions(ctx->eps,pep->nev,pep->ncv,pep->mpd);
365: EPSSetTolerances(ctx->eps,SlepcDefaultTol(pep->tol),pep->max_it);
366: }
367: RGIsTrivial(pep->rg,&istrivial);
368: if (!istrivial) {
370: EPSSetRG(ctx->eps,pep->rg);
371: }
372: /* Transfer the trackall option from pep to eps */
373: PEPGetTrackAll(pep,&trackall);
374: EPSSetTrackAll(ctx->eps,trackall);
376: /* temporary change of target */
377: if (pep->sfactor!=1.0) {
378: EPSGetTarget(ctx->eps,&sigma);
379: EPSSetTarget(ctx->eps,sigma/pep->sfactor);
380: }
382: /* process initial vector */
383: if (pep->nini<0) {
384: VecCreateMPI(PetscObjectComm((PetscObject)ctx->eps),deg*pep->nloc,deg*pep->n,&veps);
385: VecGetArray(veps,&epsarray);
386: for (i=0;i<deg;i++) {
387: if (i<-pep->nini) {
388: VecGetArray(pep->IS[i],&peparray);
389: PetscArraycpy(epsarray+i*pep->nloc,peparray,pep->nloc);
390: VecRestoreArray(pep->IS[i],&peparray);
391: } else {
392: if (!w) VecDuplicate(pep->IS[0],&w);
393: VecSetRandom(w,NULL);
394: VecGetArray(w,&peparray);
395: PetscArraycpy(epsarray+i*pep->nloc,peparray,pep->nloc);
396: VecRestoreArray(w,&peparray);
397: }
398: }
399: VecRestoreArray(veps,&epsarray);
400: EPSSetInitialSpace(ctx->eps,1,&veps);
401: VecDestroy(&veps);
402: VecDestroy(&w);
403: SlepcBasisDestroy_Private(&pep->nini,&pep->IS);
404: }
406: EPSSetUp(ctx->eps);
407: EPSGetDimensions(ctx->eps,NULL,&pep->ncv,&pep->mpd);
408: EPSGetTolerances(ctx->eps,NULL,&pep->max_it);
409: PEPAllocateSolution(pep,0);
410: return 0;
411: }
413: /*
414: PEPLinearExtract_Residual - Auxiliary routine that copies the solution of the
415: linear eigenproblem to the PEP object. The eigenvector of the generalized
416: problem is supposed to be
417: z = [ x ]
418: [ l*x ]
419: The eigenvector is taken from z(1:n) or z(n+1:2*n) depending on the explicitly
420: computed residual norm.
421: Finally, x is normalized so that ||x||_2 = 1.
422: */
423: static PetscErrorCode PEPLinearExtract_Residual(PEP pep,EPS eps)
424: {
425: PetscInt i,k;
426: const PetscScalar *px;
427: PetscScalar *er=pep->eigr,*ei=pep->eigi;
428: PetscReal rn1,rn2;
429: Vec xr,xi=NULL,wr;
430: Mat A;
431: #if !defined(PETSC_USE_COMPLEX)
432: Vec wi;
433: const PetscScalar *py;
434: #endif
436: #if defined(PETSC_USE_COMPLEX)
437: PEPSetWorkVecs(pep,2);
438: #else
439: PEPSetWorkVecs(pep,4);
440: #endif
441: EPSGetOperators(eps,&A,NULL);
442: MatCreateVecs(A,&xr,NULL);
443: MatCreateVecsEmpty(pep->A[0],&wr,NULL);
444: #if !defined(PETSC_USE_COMPLEX)
445: VecDuplicate(xr,&xi);
446: VecDuplicateEmpty(wr,&wi);
447: #endif
448: for (i=0;i<pep->nconv;i++) {
449: EPSGetEigenpair(eps,i,NULL,NULL,xr,xi);
450: #if !defined(PETSC_USE_COMPLEX)
451: if (ei[i]!=0.0) { /* complex conjugate pair */
452: VecGetArrayRead(xr,&px);
453: VecGetArrayRead(xi,&py);
454: VecPlaceArray(wr,px);
455: VecPlaceArray(wi,py);
456: VecNormalizeComplex(wr,wi,PETSC_TRUE,NULL);
457: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,wi,pep->work,&rn1);
458: BVInsertVec(pep->V,i,wr);
459: BVInsertVec(pep->V,i+1,wi);
460: for (k=1;k<pep->nmat-1;k++) {
461: VecResetArray(wr);
462: VecResetArray(wi);
463: VecPlaceArray(wr,px+k*pep->nloc);
464: VecPlaceArray(wi,py+k*pep->nloc);
465: VecNormalizeComplex(wr,wi,PETSC_TRUE,NULL);
466: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,wi,pep->work,&rn2);
467: if (rn1>rn2) {
468: BVInsertVec(pep->V,i,wr);
469: BVInsertVec(pep->V,i+1,wi);
470: rn1 = rn2;
471: }
472: }
473: VecResetArray(wr);
474: VecResetArray(wi);
475: VecRestoreArrayRead(xr,&px);
476: VecRestoreArrayRead(xi,&py);
477: i++;
478: } else /* real eigenvalue */
479: #endif
480: {
481: VecGetArrayRead(xr,&px);
482: VecPlaceArray(wr,px);
483: VecNormalizeComplex(wr,NULL,PETSC_FALSE,NULL);
484: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,NULL,pep->work,&rn1);
485: BVInsertVec(pep->V,i,wr);
486: for (k=1;k<pep->nmat-1;k++) {
487: VecResetArray(wr);
488: VecPlaceArray(wr,px+k*pep->nloc);
489: VecNormalizeComplex(wr,NULL,PETSC_FALSE,NULL);
490: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,NULL,pep->work,&rn2);
491: if (rn1>rn2) {
492: BVInsertVec(pep->V,i,wr);
493: rn1 = rn2;
494: }
495: }
496: VecResetArray(wr);
497: VecRestoreArrayRead(xr,&px);
498: }
499: }
500: VecDestroy(&wr);
501: VecDestroy(&xr);
502: #if !defined(PETSC_USE_COMPLEX)
503: VecDestroy(&wi);
504: VecDestroy(&xi);
505: #endif
506: return 0;
507: }
509: /*
510: PEPLinearExtract_None - Same as PEPLinearExtract_Norm but always takes
511: the first block.
512: */
513: static PetscErrorCode PEPLinearExtract_None(PEP pep,EPS eps)
514: {
515: PetscInt i;
516: const PetscScalar *px;
517: Mat A;
518: Vec xr,xi=NULL,w;
519: #if !defined(PETSC_USE_COMPLEX)
520: PetscScalar *ei=pep->eigi;
521: #endif
523: EPSGetOperators(eps,&A,NULL);
524: MatCreateVecs(A,&xr,NULL);
525: #if !defined(PETSC_USE_COMPLEX)
526: VecDuplicate(xr,&xi);
527: #endif
528: MatCreateVecsEmpty(pep->A[0],&w,NULL);
529: for (i=0;i<pep->nconv;i++) {
530: EPSGetEigenvector(eps,i,xr,xi);
531: #if !defined(PETSC_USE_COMPLEX)
532: if (ei[i]!=0.0) { /* complex conjugate pair */
533: VecGetArrayRead(xr,&px);
534: VecPlaceArray(w,px);
535: BVInsertVec(pep->V,i,w);
536: VecResetArray(w);
537: VecRestoreArrayRead(xr,&px);
538: VecGetArrayRead(xi,&px);
539: VecPlaceArray(w,px);
540: BVInsertVec(pep->V,i+1,w);
541: VecResetArray(w);
542: VecRestoreArrayRead(xi,&px);
543: i++;
544: } else /* real eigenvalue */
545: #endif
546: {
547: VecGetArrayRead(xr,&px);
548: VecPlaceArray(w,px);
549: BVInsertVec(pep->V,i,w);
550: VecResetArray(w);
551: VecRestoreArrayRead(xr,&px);
552: }
553: }
554: VecDestroy(&w);
555: VecDestroy(&xr);
556: #if !defined(PETSC_USE_COMPLEX)
557: VecDestroy(&xi);
558: #endif
559: return 0;
560: }
562: /*
563: PEPLinearExtract_Norm - Auxiliary routine that copies the solution of the
564: linear eigenproblem to the PEP object. The eigenvector of the generalized
565: problem is supposed to be
566: z = [ x ]
567: [ l*x ]
568: If |l|<1.0, the eigenvector is taken from z(1:n), otherwise from z(n+1:2*n).
569: Finally, x is normalized so that ||x||_2 = 1.
570: */
571: static PetscErrorCode PEPLinearExtract_Norm(PEP pep,EPS eps)
572: {
573: PetscInt i,offset;
574: const PetscScalar *px;
575: PetscScalar *er=pep->eigr;
576: Mat A;
577: Vec xr,xi=NULL,w;
578: #if !defined(PETSC_USE_COMPLEX)
579: PetscScalar *ei=pep->eigi;
580: #endif
582: EPSGetOperators(eps,&A,NULL);
583: MatCreateVecs(A,&xr,NULL);
584: #if !defined(PETSC_USE_COMPLEX)
585: VecDuplicate(xr,&xi);
586: #endif
587: MatCreateVecsEmpty(pep->A[0],&w,NULL);
588: for (i=0;i<pep->nconv;i++) {
589: EPSGetEigenpair(eps,i,NULL,NULL,xr,xi);
590: if (SlepcAbsEigenvalue(er[i],ei[i])>1.0) offset = (pep->nmat-2)*pep->nloc;
591: else offset = 0;
592: #if !defined(PETSC_USE_COMPLEX)
593: if (ei[i]!=0.0) { /* complex conjugate pair */
594: VecGetArrayRead(xr,&px);
595: VecPlaceArray(w,px+offset);
596: BVInsertVec(pep->V,i,w);
597: VecResetArray(w);
598: VecRestoreArrayRead(xr,&px);
599: VecGetArrayRead(xi,&px);
600: VecPlaceArray(w,px+offset);
601: BVInsertVec(pep->V,i+1,w);
602: VecResetArray(w);
603: VecRestoreArrayRead(xi,&px);
604: i++;
605: } else /* real eigenvalue */
606: #endif
607: {
608: VecGetArrayRead(xr,&px);
609: VecPlaceArray(w,px+offset);
610: BVInsertVec(pep->V,i,w);
611: VecResetArray(w);
612: VecRestoreArrayRead(xr,&px);
613: }
614: }
615: VecDestroy(&w);
616: VecDestroy(&xr);
617: #if !defined(PETSC_USE_COMPLEX)
618: VecDestroy(&xi);
619: #endif
620: return 0;
621: }
623: PetscErrorCode PEPExtractVectors_Linear(PEP pep)
624: {
625: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
627: switch (pep->extract) {
628: case PEP_EXTRACT_NONE:
629: PEPLinearExtract_None(pep,ctx->eps);
630: break;
631: case PEP_EXTRACT_NORM:
632: PEPLinearExtract_Norm(pep,ctx->eps);
633: break;
634: case PEP_EXTRACT_RESIDUAL:
635: PEPLinearExtract_Residual(pep,ctx->eps);
636: break;
637: case PEP_EXTRACT_STRUCTURED:
638: SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Extraction not implemented in this solver");
639: }
640: return 0;
641: }
643: PetscErrorCode PEPSolve_Linear(PEP pep)
644: {
645: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
646: PetscScalar sigma;
647: PetscBool flg;
648: PetscInt i;
650: EPSSolve(ctx->eps);
651: EPSGetConverged(ctx->eps,&pep->nconv);
652: EPSGetIterationNumber(ctx->eps,&pep->its);
653: EPSGetConvergedReason(ctx->eps,(EPSConvergedReason*)&pep->reason);
655: /* recover eigenvalues */
656: for (i=0;i<pep->nconv;i++) {
657: EPSGetEigenpair(ctx->eps,i,&pep->eigr[i],&pep->eigi[i],NULL,NULL);
658: pep->eigr[i] *= pep->sfactor;
659: pep->eigi[i] *= pep->sfactor;
660: }
662: /* restore target */
663: EPSGetTarget(ctx->eps,&sigma);
664: EPSSetTarget(ctx->eps,sigma*pep->sfactor);
666: STGetTransform(pep->st,&flg);
667: if (flg) PetscTryTypeMethod(pep,backtransform);
668: if (pep->sfactor!=1.0) {
669: /* Restore original values */
670: for (i=0;i<pep->nmat;i++) {
671: pep->pbc[pep->nmat+i] *= pep->sfactor;
672: pep->pbc[2*pep->nmat+i] *= pep->sfactor*pep->sfactor;
673: }
674: if (!flg && !ctx->explicitmatrix) STScaleShift(pep->st,pep->sfactor);
675: }
676: if (ctx->explicitmatrix || !flg) RGPopScale(pep->rg);
677: return 0;
678: }
680: static PetscErrorCode EPSMonitor_Linear(EPS eps,PetscInt its,PetscInt nconv,PetscScalar *eigr,PetscScalar *eigi,PetscReal *errest,PetscInt nest,void *ctx)
681: {
682: PEP pep = (PEP)ctx;
684: PEPMonitor(pep,its,nconv,eigr,eigi,errest,nest);
685: return 0;
686: }
688: PetscErrorCode PEPSetFromOptions_Linear(PEP pep,PetscOptionItems *PetscOptionsObject)
689: {
690: PetscBool set,val;
691: PetscInt k;
692: PetscReal array[2]={0,0};
693: PetscBool flg;
694: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
696: PetscOptionsHeadBegin(PetscOptionsObject,"PEP Linear Options");
698: k = 2;
699: PetscOptionsRealArray("-pep_linear_linearization","Parameters of the linearization","PEPLinearSetLinearization",array,&k,&flg);
700: if (flg) PEPLinearSetLinearization(pep,array[0],array[1]);
702: PetscOptionsBool("-pep_linear_explicitmatrix","Use explicit matrix in linearization","PEPLinearSetExplicitMatrix",ctx->explicitmatrix,&val,&set);
703: if (set) PEPLinearSetExplicitMatrix(pep,val);
705: PetscOptionsHeadEnd();
707: if (!ctx->eps) PEPLinearGetEPS(pep,&ctx->eps);
708: EPSSetFromOptions(ctx->eps);
709: return 0;
710: }
712: static PetscErrorCode PEPLinearSetLinearization_Linear(PEP pep,PetscReal alpha,PetscReal beta)
713: {
714: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
717: ctx->alpha = alpha;
718: ctx->beta = beta;
719: return 0;
720: }
722: /*@
723: PEPLinearSetLinearization - Set the coefficients that define
724: the linearization of a quadratic eigenproblem.
726: Logically Collective on pep
728: Input Parameters:
729: + pep - polynomial eigenvalue solver
730: . alpha - first parameter of the linearization
731: - beta - second parameter of the linearization
733: Options Database Key:
734: . -pep_linear_linearization <alpha,beta> - Sets the coefficients
736: Notes:
737: Cannot pass zero for both alpha and beta. The default values are
738: alpha=1 and beta=0.
740: Level: advanced
742: .seealso: PEPLinearGetLinearization()
743: @*/
744: PetscErrorCode PEPLinearSetLinearization(PEP pep,PetscReal alpha,PetscReal beta)
745: {
749: PetscTryMethod(pep,"PEPLinearSetLinearization_C",(PEP,PetscReal,PetscReal),(pep,alpha,beta));
750: return 0;
751: }
753: static PetscErrorCode PEPLinearGetLinearization_Linear(PEP pep,PetscReal *alpha,PetscReal *beta)
754: {
755: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
757: if (alpha) *alpha = ctx->alpha;
758: if (beta) *beta = ctx->beta;
759: return 0;
760: }
762: /*@
763: PEPLinearGetLinearization - Returns the coefficients that define
764: the linearization of a quadratic eigenproblem.
766: Not Collective
768: Input Parameter:
769: . pep - polynomial eigenvalue solver
771: Output Parameters:
772: + alpha - the first parameter of the linearization
773: - beta - the second parameter of the linearization
775: Level: advanced
777: .seealso: PEPLinearSetLinearization()
778: @*/
779: PetscErrorCode PEPLinearGetLinearization(PEP pep,PetscReal *alpha,PetscReal *beta)
780: {
782: PetscUseMethod(pep,"PEPLinearGetLinearization_C",(PEP,PetscReal*,PetscReal*),(pep,alpha,beta));
783: return 0;
784: }
786: static PetscErrorCode PEPLinearSetExplicitMatrix_Linear(PEP pep,PetscBool explicitmatrix)
787: {
788: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
790: if (ctx->explicitmatrix != explicitmatrix) {
791: ctx->explicitmatrix = explicitmatrix;
792: pep->state = PEP_STATE_INITIAL;
793: }
794: return 0;
795: }
797: /*@
798: PEPLinearSetExplicitMatrix - Indicate if the matrices A and B for the
799: linearization of the problem must be built explicitly.
801: Logically Collective on pep
803: Input Parameters:
804: + pep - polynomial eigenvalue solver
805: - explicitmat - boolean flag indicating if the matrices are built explicitly
807: Options Database Key:
808: . -pep_linear_explicitmatrix <boolean> - Indicates the boolean flag
810: Level: advanced
812: .seealso: PEPLinearGetExplicitMatrix()
813: @*/
814: PetscErrorCode PEPLinearSetExplicitMatrix(PEP pep,PetscBool explicitmat)
815: {
818: PetscTryMethod(pep,"PEPLinearSetExplicitMatrix_C",(PEP,PetscBool),(pep,explicitmat));
819: return 0;
820: }
822: static PetscErrorCode PEPLinearGetExplicitMatrix_Linear(PEP pep,PetscBool *explicitmat)
823: {
824: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
826: *explicitmat = ctx->explicitmatrix;
827: return 0;
828: }
830: /*@
831: PEPLinearGetExplicitMatrix - Returns the flag indicating if the matrices
832: A and B for the linearization are built explicitly.
834: Not Collective
836: Input Parameter:
837: . pep - polynomial eigenvalue solver
839: Output Parameter:
840: . explicitmat - the mode flag
842: Level: advanced
844: .seealso: PEPLinearSetExplicitMatrix()
845: @*/
846: PetscErrorCode PEPLinearGetExplicitMatrix(PEP pep,PetscBool *explicitmat)
847: {
850: PetscUseMethod(pep,"PEPLinearGetExplicitMatrix_C",(PEP,PetscBool*),(pep,explicitmat));
851: return 0;
852: }
854: static PetscErrorCode PEPLinearSetEPS_Linear(PEP pep,EPS eps)
855: {
856: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
858: PetscObjectReference((PetscObject)eps);
859: EPSDestroy(&ctx->eps);
860: ctx->eps = eps;
861: ctx->usereps = PETSC_TRUE;
862: pep->state = PEP_STATE_INITIAL;
863: return 0;
864: }
866: /*@
867: PEPLinearSetEPS - Associate an eigensolver object (EPS) to the
868: polynomial eigenvalue solver.
870: Collective on pep
872: Input Parameters:
873: + pep - polynomial eigenvalue solver
874: - eps - the eigensolver object
876: Level: advanced
878: .seealso: PEPLinearGetEPS()
879: @*/
880: PetscErrorCode PEPLinearSetEPS(PEP pep,EPS eps)
881: {
885: PetscTryMethod(pep,"PEPLinearSetEPS_C",(PEP,EPS),(pep,eps));
886: return 0;
887: }
889: static PetscErrorCode PEPLinearGetEPS_Linear(PEP pep,EPS *eps)
890: {
891: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
893: if (!ctx->eps) {
894: EPSCreate(PetscObjectComm((PetscObject)pep),&ctx->eps);
895: PetscObjectIncrementTabLevel((PetscObject)ctx->eps,(PetscObject)pep,1);
896: EPSSetOptionsPrefix(ctx->eps,((PetscObject)pep)->prefix);
897: EPSAppendOptionsPrefix(ctx->eps,"pep_linear_");
898: PetscObjectSetOptions((PetscObject)ctx->eps,((PetscObject)pep)->options);
899: EPSMonitorSet(ctx->eps,EPSMonitor_Linear,pep,NULL);
900: }
901: *eps = ctx->eps;
902: return 0;
903: }
905: /*@
906: PEPLinearGetEPS - Retrieve the eigensolver object (EPS) associated
907: to the polynomial eigenvalue solver.
909: Not Collective
911: Input Parameter:
912: . pep - polynomial eigenvalue solver
914: Output Parameter:
915: . eps - the eigensolver object
917: Level: advanced
919: .seealso: PEPLinearSetEPS()
920: @*/
921: PetscErrorCode PEPLinearGetEPS(PEP pep,EPS *eps)
922: {
925: PetscUseMethod(pep,"PEPLinearGetEPS_C",(PEP,EPS*),(pep,eps));
926: return 0;
927: }
929: PetscErrorCode PEPView_Linear(PEP pep,PetscViewer viewer)
930: {
931: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
932: PetscBool isascii;
934: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
935: if (isascii) {
936: if (!ctx->eps) PEPLinearGetEPS(pep,&ctx->eps);
937: PetscViewerASCIIPrintf(viewer," %s matrices\n",ctx->explicitmatrix? "explicit": "implicit");
938: PetscViewerASCIIPrintf(viewer," linearization parameters: alpha=%g beta=%g\n",(double)ctx->alpha,(double)ctx->beta);
939: PetscViewerASCIIPushTab(viewer);
940: EPSView(ctx->eps,viewer);
941: PetscViewerASCIIPopTab(viewer);
942: }
943: return 0;
944: }
946: PetscErrorCode PEPReset_Linear(PEP pep)
947: {
948: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
950: if (!ctx->eps) EPSReset(ctx->eps);
951: MatDestroy(&ctx->A);
952: MatDestroy(&ctx->B);
953: VecDestroy(&ctx->w[0]);
954: VecDestroy(&ctx->w[1]);
955: VecDestroy(&ctx->w[2]);
956: VecDestroy(&ctx->w[3]);
957: VecDestroy(&ctx->w[4]);
958: VecDestroy(&ctx->w[5]);
959: return 0;
960: }
962: PetscErrorCode PEPDestroy_Linear(PEP pep)
963: {
964: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
966: EPSDestroy(&ctx->eps);
967: PetscFree(pep->data);
968: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetLinearization_C",NULL);
969: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetLinearization_C",NULL);
970: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetEPS_C",NULL);
971: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetEPS_C",NULL);
972: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetExplicitMatrix_C",NULL);
973: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetExplicitMatrix_C",NULL);
974: return 0;
975: }
977: SLEPC_EXTERN PetscErrorCode PEPCreate_Linear(PEP pep)
978: {
979: PEP_LINEAR *ctx;
981: PetscNew(&ctx);
982: pep->data = (void*)ctx;
984: pep->lineariz = PETSC_TRUE;
985: ctx->explicitmatrix = PETSC_FALSE;
986: ctx->alpha = 1.0;
987: ctx->beta = 0.0;
989: pep->ops->solve = PEPSolve_Linear;
990: pep->ops->setup = PEPSetUp_Linear;
991: pep->ops->setfromoptions = PEPSetFromOptions_Linear;
992: pep->ops->destroy = PEPDestroy_Linear;
993: pep->ops->reset = PEPReset_Linear;
994: pep->ops->view = PEPView_Linear;
995: pep->ops->backtransform = PEPBackTransform_Default;
996: pep->ops->computevectors = PEPComputeVectors_Default;
997: pep->ops->extractvectors = PEPExtractVectors_Linear;
999: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetLinearization_C",PEPLinearSetLinearization_Linear);
1000: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetLinearization_C",PEPLinearGetLinearization_Linear);
1001: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetEPS_C",PEPLinearSetEPS_Linear);
1002: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetEPS_C",PEPLinearGetEPS_Linear);
1003: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetExplicitMatrix_C",PEPLinearSetExplicitMatrix_Linear);
1004: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetExplicitMatrix_C",PEPLinearGetExplicitMatrix_Linear);
1005: return 0;
1006: }