Actual source code: linear.c
slepc-3.8.0 2017-10-20
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2017, 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> /*I "slepcpep.h" I*/
15: #include "linearp.h"
17: static PetscErrorCode MatMult_Linear_Shift(Mat M,Vec x,Vec y)
18: {
19: PetscErrorCode ierr;
20: PEP_LINEAR *ctx;
21: PEP pep;
22: const PetscScalar *px;
23: PetscScalar *py,a,sigma=0.0;
24: PetscInt nmat,deg,i,m;
25: Vec x1,x2,x3,y1,aux;
26: PetscReal *ca,*cb,*cg;
27: PetscBool flg;
30: MatShellGetContext(M,(void**)&ctx);
31: pep = ctx->pep;
32: STGetTransform(pep->st,&flg);
33: if (!flg) {
34: STGetShift(pep->st,&sigma);
35: }
36: nmat = pep->nmat;
37: deg = nmat-1;
38: m = pep->nloc;
39: ca = pep->pbc;
40: cb = pep->pbc+nmat;
41: cg = pep->pbc+2*nmat;
42: x1=ctx->w[0];x2=ctx->w[1];x3=ctx->w[2];y1=ctx->w[3];aux=ctx->w[4];
44: VecSet(y,0.0);
45: VecGetArrayRead(x,&px);
46: VecGetArray(y,&py);
47: a = 1.0;
49: /* first block */
50: VecPlaceArray(x2,px);
51: VecPlaceArray(x3,px+m);
52: VecPlaceArray(y1,py);
53: VecAXPY(y1,cb[0]-sigma,x2);
54: VecAXPY(y1,ca[0],x3);
55: VecResetArray(x2);
56: VecResetArray(x3);
57: VecResetArray(y1);
59: /* inner blocks */
60: for (i=1;i<deg-1;i++) {
61: VecPlaceArray(x1,px+(i-1)*m);
62: VecPlaceArray(x2,px+i*m);
63: VecPlaceArray(x3,px+(i+1)*m);
64: VecPlaceArray(y1,py+i*m);
65: VecAXPY(y1,cg[i],x1);
66: VecAXPY(y1,cb[i]-sigma,x2);
67: VecAXPY(y1,ca[i],x3);
68: VecResetArray(x1);
69: VecResetArray(x2);
70: VecResetArray(x3);
71: VecResetArray(y1);
72: }
74: /* last block */
75: VecPlaceArray(y1,py+(deg-1)*m);
76: for (i=0;i<deg;i++) {
77: VecPlaceArray(x1,px+i*m);
78: STMatMult(pep->st,i,x1,aux);
79: VecAXPY(y1,a,aux);
80: VecResetArray(x1);
81: a *= pep->sfactor;
82: }
83: VecCopy(y1,aux);
84: STMatSolve(pep->st,aux,y1);
85: VecScale(y1,-ca[deg-1]/a);
86: VecPlaceArray(x1,px+(deg-2)*m);
87: VecPlaceArray(x2,px+(deg-1)*m);
88: VecAXPY(y1,cg[deg-1],x1);
89: VecAXPY(y1,cb[deg-1]-sigma,x2);
90: VecResetArray(x1);
91: VecResetArray(x2);
92: VecResetArray(y1);
94: VecRestoreArrayRead(x,&px);
95: VecRestoreArray(y,&py);
96: return(0);
97: }
99: static PetscErrorCode MatMult_Linear_Sinvert(Mat M,Vec x,Vec y)
100: {
101: PetscErrorCode ierr;
102: PEP_LINEAR *ctx;
103: PEP pep;
104: const PetscScalar *px;
105: PetscScalar *py,a,sigma,t=1.0,tp=0.0,tt;
106: PetscInt nmat,deg,i,m;
107: Vec x1,y1,y2,y3,aux,aux2;
108: PetscReal *ca,*cb,*cg;
111: MatShellGetContext(M,(void**)&ctx);
112: pep = ctx->pep;
113: nmat = pep->nmat;
114: deg = nmat-1;
115: m = pep->nloc;
116: ca = pep->pbc;
117: cb = pep->pbc+nmat;
118: cg = pep->pbc+2*nmat;
119: x1=ctx->w[0];y1=ctx->w[1];y2=ctx->w[2];y3=ctx->w[3];aux=ctx->w[4];aux2=ctx->w[5];
120: EPSGetTarget(ctx->eps,&sigma);
121: VecSet(y,0.0);
122: VecGetArrayRead(x,&px);
123: VecGetArray(y,&py);
124: a = pep->sfactor;
126: /* first block */
127: VecPlaceArray(x1,px);
128: VecPlaceArray(y1,py+m);
129: VecCopy(x1,y1);
130: VecScale(y1,1.0/ca[0]);
131: VecResetArray(x1);
132: VecResetArray(y1);
134: /* second block */
135: if (deg>2) {
136: VecPlaceArray(x1,px+m);
137: VecPlaceArray(y1,py+m);
138: VecPlaceArray(y2,py+2*m);
139: VecCopy(x1,y2);
140: VecAXPY(y2,sigma-cb[1],y1);
141: VecScale(y2,1.0/ca[1]);
142: VecResetArray(x1);
143: VecResetArray(y1);
144: VecResetArray(y2);
145: }
147: /* inner blocks */
148: for (i=2;i<deg-1;i++) {
149: VecPlaceArray(x1,px+i*m);
150: VecPlaceArray(y1,py+(i-1)*m);
151: VecPlaceArray(y2,py+i*m);
152: VecPlaceArray(y3,py+(i+1)*m);
153: VecCopy(x1,y3);
154: VecAXPY(y3,sigma-cb[i],y2);
155: VecAXPY(y3,-cg[i],y1);
156: VecScale(y3,1.0/ca[i]);
157: VecResetArray(x1);
158: VecResetArray(y1);
159: VecResetArray(y2);
160: VecResetArray(y3);
161: }
163: /* last block */
164: VecPlaceArray(y1,py);
165: for (i=0;i<deg-2;i++) {
166: VecPlaceArray(y2,py+(i+1)*m);
167: STMatMult(pep->st,i+1,y2,aux);
168: VecAXPY(y1,a,aux);
169: VecResetArray(y2);
170: a *= pep->sfactor;
171: }
172: i = deg-2;
173: VecPlaceArray(y2,py+(i+1)*m);
174: VecPlaceArray(y3,py+i*m);
175: VecCopy(y2,aux2);
176: VecAXPY(aux2,cg[i+1]/ca[i+1],y3);
177: STMatMult(pep->st,i+1,aux2,aux);
178: VecAXPY(y1,a,aux);
179: VecResetArray(y2);
180: VecResetArray(y3);
181: a *= pep->sfactor;
182: i = deg-1;
183: VecPlaceArray(x1,px+i*m);
184: VecPlaceArray(y3,py+i*m);
185: VecCopy(x1,aux2);
186: VecAXPY(aux2,sigma-cb[i],y3);
187: VecScale(aux2,1.0/ca[i]);
188: STMatMult(pep->st,i+1,aux2,aux);
189: VecAXPY(y1,a,aux);
190: VecResetArray(x1);
191: VecResetArray(y3);
193: VecCopy(y1,aux);
194: STMatSolve(pep->st,aux,y1);
195: VecScale(y1,-1.0);
197: /* final update */
198: for (i=1;i<deg;i++) {
199: VecPlaceArray(y2,py+i*m);
200: tt = t;
201: t = ((sigma-cb[i-1])*t-cg[i-1]*tp)/ca[i-1]; /* i-th basis polynomial */
202: tp = tt;
203: VecAXPY(y2,t,y1);
204: VecResetArray(y2);
205: }
206: VecResetArray(y1);
208: VecRestoreArrayRead(x,&px);
209: VecRestoreArray(y,&py);
210: return(0);
211: }
213: static PetscErrorCode BackTransform_Linear(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
214: {
216: PEP_LINEAR *ctx;
217: ST stctx;
220: STShellGetContext(st,(void**)&ctx);
221: PEPGetST(ctx->pep,&stctx);
222: STBackTransform(stctx,n,eigr,eigi);
223: return(0);
224: }
226: /*
227: Dummy backtransform operation
228: */
229: static PetscErrorCode BackTransform_Skip(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
230: {
232: return(0);
233: }
235: static PetscErrorCode Apply_Linear(ST st,Vec x,Vec y)
236: {
238: PEP_LINEAR *ctx;
241: STShellGetContext(st,(void**)&ctx);
242: MatMult(ctx->A,x,y);
243: return(0);
244: }
246: PetscErrorCode PEPSetUp_Linear(PEP pep)
247: {
249: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
250: ST st;
251: PetscInt i=0,deg=pep->nmat-1;
252: EPSWhich which = EPS_LARGEST_MAGNITUDE;
253: EPSProblemType ptype;
254: PetscBool trackall,istrivial,transf,shift,sinv,ks;
255: PetscScalar sigma,*epsarray,*peparray;
256: Vec veps,w=NULL;
257: /* function tables */
258: PetscErrorCode (*fcreate[][2])(MPI_Comm,PEP_LINEAR*,Mat*) = {
259: { MatCreateExplicit_Linear_N1A, MatCreateExplicit_Linear_N1B }, /* N1 */
260: { MatCreateExplicit_Linear_N2A, MatCreateExplicit_Linear_N2B }, /* N2 */
261: { MatCreateExplicit_Linear_S1A, MatCreateExplicit_Linear_S1B }, /* S1 */
262: { MatCreateExplicit_Linear_S2A, MatCreateExplicit_Linear_S2B }, /* S2 */
263: { MatCreateExplicit_Linear_H1A, MatCreateExplicit_Linear_H1B }, /* H1 */
264: { MatCreateExplicit_Linear_H2A, MatCreateExplicit_Linear_H2B } /* H2 */
265: };
268: if (pep->stopping!=PEPStoppingBasic) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"User-defined stopping test not supported");
269: pep->lineariz = PETSC_TRUE;
270: if (!ctx->cform) ctx->cform = 1;
271: STGetTransform(pep->st,&transf);
272: PetscObjectTypeCompare((PetscObject)pep->st,STSHIFT,&shift);
273: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
274: if (!shift && !sinv) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Only STSHIFT and STSINVERT spectral transformations can be used");
275: if (!pep->which) {
276: if (sinv) pep->which = PEP_TARGET_MAGNITUDE;
277: else pep->which = PEP_LARGEST_MAGNITUDE;
278: }
279: STSetUp(pep->st);
280: if (!ctx->eps) { PEPLinearGetEPS(pep,&ctx->eps); }
281: EPSGetST(ctx->eps,&st);
282: if (!transf && !ctx->usereps) { EPSSetTarget(ctx->eps,pep->target); }
283: if (sinv && !transf && !ctx->usereps) { STSetDefaultShift(st,pep->target); }
284: /* compute scale factor if not set by user */
285: PEPComputeScaleFactor(pep);
287: if (ctx->explicitmatrix) {
288: if (transf) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Explicit matrix option is not implemented with st-transform flag active");
289: if (pep->nmat!=3) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Explicit matrix option only available for quadratic problems");
290: if (pep->basis!=PEP_BASIS_MONOMIAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Explicit matrix option not implemented for non-monomial bases");
291: if (pep->scale==PEP_SCALE_DIAGONAL || pep->scale==PEP_SCALE_BOTH) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Diagonal scaling not allowed in PEPLINEAR with explicit matrices");
292: if (sinv && !transf) { STSetType(st,STSINVERT); }
293: RGPushScale(pep->rg,1.0/pep->sfactor);
294: STGetMatrixTransformed(pep->st,0,&ctx->K);
295: STGetMatrixTransformed(pep->st,1,&ctx->C);
296: STGetMatrixTransformed(pep->st,2,&ctx->M);
297: ctx->sfactor = pep->sfactor;
298: ctx->dsfactor = pep->dsfactor;
300: MatDestroy(&ctx->A);
301: MatDestroy(&ctx->B);
302: VecDestroy(&ctx->w[0]);
303: VecDestroy(&ctx->w[1]);
304: VecDestroy(&ctx->w[2]);
305: VecDestroy(&ctx->w[3]);
307: switch (pep->problem_type) {
308: case PEP_GENERAL: i = 0; break;
309: case PEP_HERMITIAN: i = 2; break;
310: case PEP_GYROSCOPIC: i = 4; break;
311: }
312: i += ctx->cform-1;
314: (*fcreate[i][0])(PetscObjectComm((PetscObject)pep),ctx,&ctx->A);
315: (*fcreate[i][1])(PetscObjectComm((PetscObject)pep),ctx,&ctx->B);
316: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->A);
317: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->B);
319: } else { /* implicit matrix */
320: if (pep->problem_type!=PEP_GENERAL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Must use the explicit matrix option if problem type is not general");
321: if (!((PetscObject)(ctx->eps))->type_name) {
322: EPSSetType(ctx->eps,EPSKRYLOVSCHUR);
323: } else {
324: PetscObjectTypeCompare((PetscObject)ctx->eps,EPSKRYLOVSCHUR,&ks);
325: if (!ks) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Implicit matrix option only implemented for Krylov-Schur");
326: }
327: if (ctx->cform!=1) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Implicit matrix option not available for 2nd companion form");
328: STSetType(st,STSHELL);
329: STShellSetContext(st,(PetscObject)ctx);
330: if (!transf) { STShellSetBackTransform(st,BackTransform_Linear); }
331: else { STShellSetBackTransform(st,BackTransform_Skip); }
332: MatCreateVecsEmpty(pep->A[0],&ctx->w[0],&ctx->w[1]);
333: MatCreateVecsEmpty(pep->A[0],&ctx->w[2],&ctx->w[3]);
334: MatCreateVecs(pep->A[0],&ctx->w[4],&ctx->w[5]);
335: PetscLogObjectParents(pep,6,ctx->w);
336: MatCreateShell(PetscObjectComm((PetscObject)pep),deg*pep->nloc,deg*pep->nloc,deg*pep->n,deg*pep->n,ctx,&ctx->A);
337: if (sinv && !transf) {
338: MatShellSetOperation(ctx->A,MATOP_MULT,(void(*)(void))MatMult_Linear_Sinvert);
339: } else {
340: MatShellSetOperation(ctx->A,MATOP_MULT,(void(*)(void))MatMult_Linear_Shift);
341: }
342: STShellSetApply(st,Apply_Linear);
343: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->A);
344: ctx->pep = pep;
346: PEPBasisCoefficients(pep,pep->pbc);
347: if (!transf) {
348: PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
349: PetscLogObjectMemory((PetscObject)pep,pep->nmat*sizeof(PetscScalar));
350: if (sinv) {
351: PEPEvaluateBasis(pep,pep->target,0,pep->solvematcoeffs,NULL);
352: } else {
353: for (i=0;i<deg;i++) pep->solvematcoeffs[i] = 0.0;
354: pep->solvematcoeffs[deg] = 1.0;
355: }
356: STScaleShift(pep->st,1.0/pep->sfactor);
357: RGPushScale(pep->rg,1.0/pep->sfactor);
358: }
359: if (pep->sfactor!=1.0) {
360: for (i=0;i<pep->nmat;i++) {
361: pep->pbc[pep->nmat+i] /= pep->sfactor;
362: pep->pbc[2*pep->nmat+i] /= pep->sfactor*pep->sfactor;
363: }
364: }
365: }
367: EPSSetOperators(ctx->eps,ctx->A,ctx->B);
368: EPSGetProblemType(ctx->eps,&ptype);
369: if (!ptype) {
370: if (ctx->explicitmatrix) {
371: EPSSetProblemType(ctx->eps,EPS_GNHEP);
372: } else {
373: EPSSetProblemType(ctx->eps,EPS_NHEP);
374: }
375: }
376: if (!ctx->usereps) {
377: if (transf) which = EPS_LARGEST_MAGNITUDE;
378: else {
379: switch (pep->which) {
380: case PEP_LARGEST_MAGNITUDE: which = EPS_LARGEST_MAGNITUDE; break;
381: case PEP_SMALLEST_MAGNITUDE: which = EPS_SMALLEST_MAGNITUDE; break;
382: case PEP_LARGEST_REAL: which = EPS_LARGEST_REAL; break;
383: case PEP_SMALLEST_REAL: which = EPS_SMALLEST_REAL; break;
384: case PEP_LARGEST_IMAGINARY: which = EPS_LARGEST_IMAGINARY; break;
385: case PEP_SMALLEST_IMAGINARY: which = EPS_SMALLEST_IMAGINARY; break;
386: case PEP_TARGET_MAGNITUDE: which = EPS_TARGET_MAGNITUDE; break;
387: case PEP_TARGET_REAL: which = EPS_TARGET_REAL; break;
388: case PEP_TARGET_IMAGINARY: which = EPS_TARGET_IMAGINARY; break;
389: case PEP_WHICH_USER: which = EPS_WHICH_USER;
390: EPSSetEigenvalueComparison(ctx->eps,pep->sc->comparison,pep->sc->comparisonctx);
391: break;
392: }
393: }
394: EPSSetWhichEigenpairs(ctx->eps,which);
396: EPSSetDimensions(ctx->eps,pep->nev,pep->ncv?pep->ncv:PETSC_DEFAULT,pep->mpd?pep->mpd:PETSC_DEFAULT);
397: EPSSetTolerances(ctx->eps,pep->tol==PETSC_DEFAULT?SLEPC_DEFAULT_TOL:pep->tol,pep->max_it?pep->max_it:PETSC_DEFAULT);
398: }
399: RGIsTrivial(pep->rg,&istrivial);
400: if (!istrivial) {
401: if (transf) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"PEPLINEAR does not support a nontrivial region with st-transform");
402: EPSSetRG(ctx->eps,pep->rg);
403: }
404: /* Transfer the trackall option from pep to eps */
405: PEPGetTrackAll(pep,&trackall);
406: EPSSetTrackAll(ctx->eps,trackall);
408: /* temporary change of target */
409: if (pep->sfactor!=1.0) {
410: EPSGetTarget(ctx->eps,&sigma);
411: EPSSetTarget(ctx->eps,sigma/pep->sfactor);
412: }
414: /* process initial vector */
415: if (pep->nini<0) {
416: VecCreateMPI(PetscObjectComm((PetscObject)ctx->eps),deg*pep->nloc,deg*pep->n,&veps);
417: VecGetArray(veps,&epsarray);
418: for (i=0;i<deg;i++) {
419: if (i<-pep->nini) {
420: VecGetArray(pep->IS[i],&peparray);
421: PetscMemcpy(epsarray+i*pep->nloc,peparray,pep->nloc*sizeof(PetscScalar));
422: VecRestoreArray(pep->IS[i],&peparray);
423: } else {
424: if (!w) { VecDuplicate(pep->IS[0],&w); }
425: VecSetRandom(w,NULL);
426: VecGetArray(w,&peparray);
427: PetscMemcpy(epsarray+i*pep->nloc,peparray,pep->nloc*sizeof(PetscScalar));
428: VecRestoreArray(w,&peparray);
429: }
430: }
431: VecRestoreArray(veps,&epsarray);
432: EPSSetInitialSpace(ctx->eps,1,&veps);
433: VecDestroy(&veps);
434: VecDestroy(&w);
435: SlepcBasisDestroy_Private(&pep->nini,&pep->IS);
436: }
438: EPSSetUp(ctx->eps);
439: EPSGetDimensions(ctx->eps,NULL,&pep->ncv,&pep->mpd);
440: EPSGetTolerances(ctx->eps,NULL,&pep->max_it);
441: PEPAllocateSolution(pep,0);
442: return(0);
443: }
445: /*
446: PEPLinearExtract_Residual - Auxiliary routine that copies the solution of the
447: linear eigenproblem to the PEP object. The eigenvector of the generalized
448: problem is supposed to be
449: z = [ x ]
450: [ l*x ]
451: The eigenvector is taken from z(1:n) or z(n+1:2*n) depending on the explicitly
452: computed residual norm.
453: Finally, x is normalized so that ||x||_2 = 1.
454: */
455: static PetscErrorCode PEPLinearExtract_Residual(PEP pep,EPS eps)
456: {
457: PetscErrorCode ierr;
458: PetscInt i,k;
459: const PetscScalar *px;
460: PetscScalar *er=pep->eigr,*ei=pep->eigi;
461: PetscReal rn1,rn2;
462: Vec xr,xi=NULL,wr;
463: Mat A;
464: #if !defined(PETSC_USE_COMPLEX)
465: Vec wi;
466: const PetscScalar *py;
467: #endif
470: #if defined(PETSC_USE_COMPLEX)
471: PEPSetWorkVecs(pep,2);
472: #else
473: PEPSetWorkVecs(pep,4);
474: #endif
475: EPSGetOperators(eps,&A,NULL);
476: MatCreateVecs(A,&xr,NULL);
477: MatCreateVecsEmpty(pep->A[0],&wr,NULL);
478: #if !defined(PETSC_USE_COMPLEX)
479: VecDuplicate(xr,&xi);
480: VecDuplicateEmpty(wr,&wi);
481: #endif
482: for (i=0;i<pep->nconv;i++) {
483: EPSGetEigenpair(eps,i,NULL,NULL,xr,xi);
484: #if !defined(PETSC_USE_COMPLEX)
485: if (ei[i]!=0.0) { /* complex conjugate pair */
486: VecGetArrayRead(xr,&px);
487: VecGetArrayRead(xi,&py);
488: VecPlaceArray(wr,px);
489: VecPlaceArray(wi,py);
490: VecNormalizeComplex(wr,wi,PETSC_TRUE,NULL);
491: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,wi,pep->work,&rn1);
492: BVInsertVec(pep->V,i,wr);
493: BVInsertVec(pep->V,i+1,wi);
494: for (k=1;k<pep->nmat-1;k++) {
495: VecResetArray(wr);
496: VecResetArray(wi);
497: VecPlaceArray(wr,px+k*pep->nloc);
498: VecPlaceArray(wi,py+k*pep->nloc);
499: VecNormalizeComplex(wr,wi,PETSC_TRUE,NULL);
500: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,wi,pep->work,&rn2);
501: if (rn1>rn2) {
502: BVInsertVec(pep->V,i,wr);
503: BVInsertVec(pep->V,i+1,wi);
504: rn1 = rn2;
505: }
506: }
507: VecResetArray(wr);
508: VecResetArray(wi);
509: VecRestoreArrayRead(xr,&px);
510: VecRestoreArrayRead(xi,&py);
511: i++;
512: } else /* real eigenvalue */
513: #endif
514: {
515: VecGetArrayRead(xr,&px);
516: VecPlaceArray(wr,px);
517: VecNormalizeComplex(wr,NULL,PETSC_FALSE,NULL);
518: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,NULL,pep->work,&rn1);
519: BVInsertVec(pep->V,i,wr);
520: for (k=1;k<pep->nmat-1;k++) {
521: VecResetArray(wr);
522: VecPlaceArray(wr,px+k*pep->nloc);
523: VecNormalizeComplex(wr,NULL,PETSC_FALSE,NULL);
524: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,NULL,pep->work,&rn2);
525: if (rn1>rn2) {
526: BVInsertVec(pep->V,i,wr);
527: rn1 = rn2;
528: }
529: }
530: VecResetArray(wr);
531: VecRestoreArrayRead(xr,&px);
532: }
533: }
534: VecDestroy(&wr);
535: VecDestroy(&xr);
536: #if !defined(PETSC_USE_COMPLEX)
537: VecDestroy(&wi);
538: VecDestroy(&xi);
539: #endif
540: return(0);
541: }
543: /*
544: PEPLinearExtract_None - Same as PEPLinearExtract_Norm but always takes
545: the first block.
546: */
547: static PetscErrorCode PEPLinearExtract_None(PEP pep,EPS eps)
548: {
549: PetscErrorCode ierr;
550: PetscInt i;
551: const PetscScalar *px;
552: Mat A;
553: Vec xr,xi,w;
554: #if !defined(PETSC_USE_COMPLEX)
555: PetscScalar *ei=pep->eigi;
556: #endif
559: EPSGetOperators(eps,&A,NULL);
560: MatCreateVecs(A,&xr,NULL);
561: VecDuplicate(xr,&xi);
562: MatCreateVecsEmpty(pep->A[0],&w,NULL);
563: for (i=0;i<pep->nconv;i++) {
564: EPSGetEigenpair(eps,i,NULL,NULL,xr,xi);
565: #if !defined(PETSC_USE_COMPLEX)
566: if (ei[i]!=0.0) { /* complex conjugate pair */
567: VecGetArrayRead(xr,&px);
568: VecPlaceArray(w,px);
569: BVInsertVec(pep->V,i,w);
570: VecResetArray(w);
571: VecRestoreArrayRead(xr,&px);
572: VecGetArrayRead(xi,&px);
573: VecPlaceArray(w,px);
574: BVInsertVec(pep->V,i+1,w);
575: VecResetArray(w);
576: VecRestoreArrayRead(xi,&px);
577: i++;
578: } else /* real eigenvalue */
579: #endif
580: {
581: VecGetArrayRead(xr,&px);
582: VecPlaceArray(w,px);
583: BVInsertVec(pep->V,i,w);
584: VecResetArray(w);
585: VecRestoreArrayRead(xr,&px);
586: }
587: }
588: VecDestroy(&w);
589: VecDestroy(&xr);
590: VecDestroy(&xi);
591: return(0);
592: }
594: /*
595: PEPLinearExtract_Norm - Auxiliary routine that copies the solution of the
596: linear eigenproblem to the PEP object. The eigenvector of the generalized
597: problem is supposed to be
598: z = [ x ]
599: [ l*x ]
600: If |l|<1.0, the eigenvector is taken from z(1:n), otherwise from z(n+1:2*n).
601: Finally, x is normalized so that ||x||_2 = 1.
602: */
603: static PetscErrorCode PEPLinearExtract_Norm(PEP pep,EPS eps)
604: {
605: PetscErrorCode ierr;
606: PetscInt i,offset;
607: const PetscScalar *px;
608: PetscScalar *er=pep->eigr;
609: Mat A;
610: Vec xr,xi=NULL,w;
611: #if !defined(PETSC_USE_COMPLEX)
612: PetscScalar *ei=pep->eigi;
613: #endif
616: EPSGetOperators(eps,&A,NULL);
617: MatCreateVecs(A,&xr,NULL);
618: #if !defined(PETSC_USE_COMPLEX)
619: VecDuplicate(xr,&xi);
620: #endif
621: MatCreateVecsEmpty(pep->A[0],&w,NULL);
622: for (i=0;i<pep->nconv;i++) {
623: EPSGetEigenpair(eps,i,NULL,NULL,xr,xi);
624: if (SlepcAbsEigenvalue(er[i],ei[i])>1.0) offset = (pep->nmat-2)*pep->nloc;
625: else offset = 0;
626: #if !defined(PETSC_USE_COMPLEX)
627: if (ei[i]!=0.0) { /* complex conjugate pair */
628: VecGetArrayRead(xr,&px);
629: VecPlaceArray(w,px+offset);
630: BVInsertVec(pep->V,i,w);
631: VecResetArray(w);
632: VecRestoreArrayRead(xr,&px);
633: VecGetArrayRead(xi,&px);
634: VecPlaceArray(w,px+offset);
635: BVInsertVec(pep->V,i+1,w);
636: VecResetArray(w);
637: VecRestoreArrayRead(xi,&px);
638: i++;
639: } else /* real eigenvalue */
640: #endif
641: {
642: VecGetArrayRead(xr,&px);
643: VecPlaceArray(w,px+offset);
644: BVInsertVec(pep->V,i,w);
645: VecResetArray(w);
646: VecRestoreArrayRead(xr,&px);
647: }
648: }
649: VecDestroy(&w);
650: VecDestroy(&xr);
651: #if !defined(PETSC_USE_COMPLEX)
652: VecDestroy(&xi);
653: #endif
654: return(0);
655: }
657: PetscErrorCode PEPExtractVectors_Linear(PEP pep)
658: {
660: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
663: switch (pep->extract) {
664: case PEP_EXTRACT_NONE:
665: PEPLinearExtract_None(pep,ctx->eps);
666: break;
667: case PEP_EXTRACT_NORM:
668: PEPLinearExtract_Norm(pep,ctx->eps);
669: break;
670: case PEP_EXTRACT_RESIDUAL:
671: PEPLinearExtract_Residual(pep,ctx->eps);
672: break;
673: case PEP_EXTRACT_STRUCTURED:
674: SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Extraction not implemented in this solver");
675: }
676: return(0);
677: }
679: PetscErrorCode PEPSolve_Linear(PEP pep)
680: {
682: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
683: PetscScalar sigma;
684: PetscBool flg;
685: PetscInt i;
688: EPSSolve(ctx->eps);
689: EPSGetConverged(ctx->eps,&pep->nconv);
690: EPSGetIterationNumber(ctx->eps,&pep->its);
691: EPSGetConvergedReason(ctx->eps,(EPSConvergedReason*)&pep->reason);
693: /* recover eigenvalues */
694: for (i=0;i<pep->nconv;i++) {
695: EPSGetEigenpair(ctx->eps,i,&pep->eigr[i],&pep->eigi[i],NULL,NULL);
696: pep->eigr[i] *= pep->sfactor;
697: pep->eigi[i] *= pep->sfactor;
698: }
700: /* restore target */
701: EPSGetTarget(ctx->eps,&sigma);
702: EPSSetTarget(ctx->eps,sigma*pep->sfactor);
704: STGetTransform(pep->st,&flg);
705: if (flg && pep->ops->backtransform) {
706: (*pep->ops->backtransform)(pep);
707: }
708: if (pep->sfactor!=1.0) {
709: /* Restore original values */
710: for (i=0;i<pep->nmat;i++){
711: pep->pbc[pep->nmat+i] *= pep->sfactor;
712: pep->pbc[2*pep->nmat+i] *= pep->sfactor*pep->sfactor;
713: }
714: if (!flg && !ctx->explicitmatrix) {
715: STScaleShift(pep->st,pep->sfactor);
716: }
717: }
718: if (ctx->explicitmatrix || !flg) {
719: RGPopScale(pep->rg);
720: }
721: return(0);
722: }
724: static PetscErrorCode EPSMonitor_Linear(EPS eps,PetscInt its,PetscInt nconv,PetscScalar *eigr,PetscScalar *eigi,PetscReal *errest,PetscInt nest,void *ctx)
725: {
726: PEP pep = (PEP)ctx;
730: PEPMonitor(pep,its,nconv,eigr,eigi,errest,nest);
731: return(0);
732: }
734: PetscErrorCode PEPSetFromOptions_Linear(PetscOptionItems *PetscOptionsObject,PEP pep)
735: {
737: PetscBool set,val;
738: PetscInt i;
739: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
742: PetscOptionsHead(PetscOptionsObject,"PEP Linear Options");
744: PetscOptionsInt("-pep_linear_cform","Number of the companion form (1 or 2)","PEPLinearSetCompanionForm",ctx->cform,&i,&set);
745: if (set) { PEPLinearSetCompanionForm(pep,i); }
747: PetscOptionsBool("-pep_linear_explicitmatrix","Use explicit matrix in linearization","PEPLinearSetExplicitMatrix",ctx->explicitmatrix,&val,&set);
748: if (set) { PEPLinearSetExplicitMatrix(pep,val); }
750: PetscOptionsTail();
752: if (!ctx->eps) { PEPLinearGetEPS(pep,&ctx->eps); }
753: EPSSetFromOptions(ctx->eps);
754: return(0);
755: }
757: static PetscErrorCode PEPLinearSetCompanionForm_Linear(PEP pep,PetscInt cform)
758: {
759: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
762: if (!cform) return(0);
763: if (cform==PETSC_DECIDE || cform==PETSC_DEFAULT) ctx->cform = 1;
764: else {
765: if (cform!=1 && cform!=2) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid value of argument 'cform'");
766: ctx->cform = cform;
767: }
768: return(0);
769: }
771: /*@
772: PEPLinearSetCompanionForm - Choose between the two companion forms available
773: for the linearization of a quadratic eigenproblem.
775: Logically Collective on PEP
777: Input Parameters:
778: + pep - polynomial eigenvalue solver
779: - cform - 1 or 2 (first or second companion form)
781: Options Database Key:
782: . -pep_linear_cform <int> - Choose the companion form
784: Level: advanced
786: .seealso: PEPLinearGetCompanionForm()
787: @*/
788: PetscErrorCode PEPLinearSetCompanionForm(PEP pep,PetscInt cform)
789: {
795: PetscTryMethod(pep,"PEPLinearSetCompanionForm_C",(PEP,PetscInt),(pep,cform));
796: return(0);
797: }
799: static PetscErrorCode PEPLinearGetCompanionForm_Linear(PEP pep,PetscInt *cform)
800: {
801: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
804: *cform = ctx->cform;
805: return(0);
806: }
808: /*@
809: PEPLinearGetCompanionForm - Returns the number of the companion form that
810: will be used for the linearization of a quadratic eigenproblem.
812: Not Collective
814: Input Parameter:
815: . pep - polynomial eigenvalue solver
817: Output Parameter:
818: . cform - the companion form number (1 or 2)
820: Level: advanced
822: .seealso: PEPLinearSetCompanionForm()
823: @*/
824: PetscErrorCode PEPLinearGetCompanionForm(PEP pep,PetscInt *cform)
825: {
831: PetscUseMethod(pep,"PEPLinearGetCompanionForm_C",(PEP,PetscInt*),(pep,cform));
832: return(0);
833: }
835: static PetscErrorCode PEPLinearSetExplicitMatrix_Linear(PEP pep,PetscBool explicitmatrix)
836: {
837: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
840: if (ctx->explicitmatrix != explicitmatrix) {
841: ctx->explicitmatrix = explicitmatrix;
842: pep->state = PEP_STATE_INITIAL;
843: }
844: return(0);
845: }
847: /*@
848: PEPLinearSetExplicitMatrix - Indicate if the matrices A and B for the
849: linearization of the problem must be built explicitly.
851: Logically Collective on PEP
853: Input Parameters:
854: + pep - polynomial eigenvalue solver
855: - explicit - boolean flag indicating if the matrices are built explicitly
857: Options Database Key:
858: . -pep_linear_explicitmatrix <boolean> - Indicates the boolean flag
860: Level: advanced
862: .seealso: PEPLinearGetExplicitMatrix()
863: @*/
864: PetscErrorCode PEPLinearSetExplicitMatrix(PEP pep,PetscBool explicitmatrix)
865: {
871: PetscTryMethod(pep,"PEPLinearSetExplicitMatrix_C",(PEP,PetscBool),(pep,explicitmatrix));
872: return(0);
873: }
875: static PetscErrorCode PEPLinearGetExplicitMatrix_Linear(PEP pep,PetscBool *explicitmatrix)
876: {
877: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
880: *explicitmatrix = ctx->explicitmatrix;
881: return(0);
882: }
884: /*@
885: PEPLinearGetExplicitMatrix - Returns the flag indicating if the matrices
886: A and B for the linearization are built explicitly.
888: Not Collective
890: Input Parameter:
891: . pep - polynomial eigenvalue solver
893: Output Parameter:
894: . explicitmatrix - the mode flag
896: Level: advanced
898: .seealso: PEPLinearSetExplicitMatrix()
899: @*/
900: PetscErrorCode PEPLinearGetExplicitMatrix(PEP pep,PetscBool *explicitmatrix)
901: {
907: PetscUseMethod(pep,"PEPLinearGetExplicitMatrix_C",(PEP,PetscBool*),(pep,explicitmatrix));
908: return(0);
909: }
911: static PetscErrorCode PEPLinearSetEPS_Linear(PEP pep,EPS eps)
912: {
914: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
917: PetscObjectReference((PetscObject)eps);
918: EPSDestroy(&ctx->eps);
919: ctx->eps = eps;
920: ctx->usereps = PETSC_TRUE;
921: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->eps);
922: pep->state = PEP_STATE_INITIAL;
923: return(0);
924: }
926: /*@
927: PEPLinearSetEPS - Associate an eigensolver object (EPS) to the
928: polynomial eigenvalue solver.
930: Collective on PEP
932: Input Parameters:
933: + pep - polynomial eigenvalue solver
934: - eps - the eigensolver object
936: Level: advanced
938: .seealso: PEPLinearGetEPS()
939: @*/
940: PetscErrorCode PEPLinearSetEPS(PEP pep,EPS eps)
941: {
948: PetscTryMethod(pep,"PEPLinearSetEPS_C",(PEP,EPS),(pep,eps));
949: return(0);
950: }
952: static PetscErrorCode PEPLinearGetEPS_Linear(PEP pep,EPS *eps)
953: {
955: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
958: if (!ctx->eps) {
959: EPSCreate(PetscObjectComm((PetscObject)pep),&ctx->eps);
960: EPSSetOptionsPrefix(ctx->eps,((PetscObject)pep)->prefix);
961: EPSAppendOptionsPrefix(ctx->eps,"pep_linear_");
962: PetscObjectIncrementTabLevel((PetscObject)ctx->eps,(PetscObject)pep,1);
963: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->eps);
964: EPSMonitorSet(ctx->eps,EPSMonitor_Linear,pep,NULL);
965: }
966: *eps = ctx->eps;
967: return(0);
968: }
970: /*@
971: PEPLinearGetEPS - Retrieve the eigensolver object (EPS) associated
972: to the polynomial eigenvalue solver.
974: Not Collective
976: Input Parameter:
977: . pep - polynomial eigenvalue solver
979: Output Parameter:
980: . eps - the eigensolver object
982: Level: advanced
984: .seealso: PEPLinearSetEPS()
985: @*/
986: PetscErrorCode PEPLinearGetEPS(PEP pep,EPS *eps)
987: {
993: PetscUseMethod(pep,"PEPLinearGetEPS_C",(PEP,EPS*),(pep,eps));
994: return(0);
995: }
997: PetscErrorCode PEPView_Linear(PEP pep,PetscViewer viewer)
998: {
1000: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
1001: PetscBool isascii;
1004: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1005: if (isascii) {
1006: if (!ctx->eps) { PEPLinearGetEPS(pep,&ctx->eps); }
1007: PetscViewerASCIIPrintf(viewer," %s matrices\n",ctx->explicitmatrix? "explicit": "implicit");
1008: PetscViewerASCIIPrintf(viewer," %s companion form\n",ctx->cform==1? "1st": "2nd");
1009: PetscViewerASCIIPushTab(viewer);
1010: EPSView(ctx->eps,viewer);
1011: PetscViewerASCIIPopTab(viewer);
1012: }
1013: return(0);
1014: }
1016: PetscErrorCode PEPReset_Linear(PEP pep)
1017: {
1019: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
1022: if (!ctx->eps) { EPSReset(ctx->eps); }
1023: MatDestroy(&ctx->A);
1024: MatDestroy(&ctx->B);
1025: VecDestroy(&ctx->w[0]);
1026: VecDestroy(&ctx->w[1]);
1027: VecDestroy(&ctx->w[2]);
1028: VecDestroy(&ctx->w[3]);
1029: VecDestroy(&ctx->w[4]);
1030: VecDestroy(&ctx->w[5]);
1031: return(0);
1032: }
1034: PetscErrorCode PEPDestroy_Linear(PEP pep)
1035: {
1037: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
1040: EPSDestroy(&ctx->eps);
1041: PetscFree(pep->data);
1042: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetCompanionForm_C",NULL);
1043: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetCompanionForm_C",NULL);
1044: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetEPS_C",NULL);
1045: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetEPS_C",NULL);
1046: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetExplicitMatrix_C",NULL);
1047: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetExplicitMatrix_C",NULL);
1048: return(0);
1049: }
1051: PETSC_EXTERN PetscErrorCode PEPCreate_Linear(PEP pep)
1052: {
1054: PEP_LINEAR *ctx;
1057: PetscNewLog(pep,&ctx);
1058: ctx->explicitmatrix = PETSC_FALSE;
1059: pep->data = (void*)ctx;
1061: pep->ops->solve = PEPSolve_Linear;
1062: pep->ops->setup = PEPSetUp_Linear;
1063: pep->ops->setfromoptions = PEPSetFromOptions_Linear;
1064: pep->ops->destroy = PEPDestroy_Linear;
1065: pep->ops->reset = PEPReset_Linear;
1066: pep->ops->view = PEPView_Linear;
1067: pep->ops->backtransform = PEPBackTransform_Default;
1068: pep->ops->computevectors = PEPComputeVectors_Default;
1069: pep->ops->extractvectors = PEPExtractVectors_Linear;
1071: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetCompanionForm_C",PEPLinearSetCompanionForm_Linear);
1072: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetCompanionForm_C",PEPLinearGetCompanionForm_Linear);
1073: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetEPS_C",PEPLinearSetEPS_Linear);
1074: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetEPS_C",PEPLinearGetEPS_Linear);
1075: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetExplicitMatrix_C",PEPLinearSetExplicitMatrix_Linear);
1076: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetExplicitMatrix_C",PEPLinearGetExplicitMatrix_Linear);
1077: return(0);
1078: }