Actual source code: linear.c
slepc-3.14.2 2021-02-01
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2020, 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: 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,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_NA, MatCreateExplicit_Linear_NB },
260: { MatCreateExplicit_Linear_SA, MatCreateExplicit_Linear_SB },
261: { MatCreateExplicit_Linear_HA, MatCreateExplicit_Linear_HB },
262: };
265: PEPCheckShiftSinvert(pep);
266: PEPCheckUnsupported(pep,PEP_FEATURE_STOPPING);
267: PEPCheckIgnored(pep,PEP_FEATURE_CONVERGENCE);
268: STGetTransform(pep->st,&transf);
269: PetscObjectTypeCompare((PetscObject)pep->st,STSINVERT,&sinv);
270: if (!pep->which) { PEPSetWhichEigenpairs_Default(pep); }
271: if (pep->which==PEP_ALL) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues");
272: STSetUp(pep->st);
273: if (!ctx->eps) { PEPLinearGetEPS(pep,&ctx->eps); }
274: EPSGetST(ctx->eps,&st);
275: if (!transf && !ctx->usereps) { EPSSetTarget(ctx->eps,pep->target); }
276: if (sinv && !transf && !ctx->usereps) { STSetDefaultShift(st,pep->target); }
277: /* compute scale factor if not set by user */
278: PEPComputeScaleFactor(pep);
280: if (ctx->explicitmatrix) {
281: PEPCheckQuadraticCondition(pep,PETSC_TRUE," (with explicit matrix)");
282: PEPCheckUnsupportedCondition(pep,PEP_FEATURE_NONMONOMIAL,PETSC_TRUE," (with explicit matrix)");
283: if (transf) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Explicit matrix option is not implemented with st-transform flag active");
284: 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");
285: if (sinv && !transf) { STSetType(st,STSINVERT); }
286: RGPushScale(pep->rg,1.0/pep->sfactor);
287: STGetMatrixTransformed(pep->st,0,&ctx->K);
288: STGetMatrixTransformed(pep->st,1,&ctx->C);
289: STGetMatrixTransformed(pep->st,2,&ctx->M);
290: ctx->sfactor = pep->sfactor;
291: ctx->dsfactor = pep->dsfactor;
293: MatDestroy(&ctx->A);
294: MatDestroy(&ctx->B);
295: VecDestroy(&ctx->w[0]);
296: VecDestroy(&ctx->w[1]);
297: VecDestroy(&ctx->w[2]);
298: VecDestroy(&ctx->w[3]);
300: switch (pep->problem_type) {
301: case PEP_GENERAL: i = 0; break;
302: case PEP_HERMITIAN:
303: case PEP_HYPERBOLIC: i = 1; break;
304: case PEP_GYROSCOPIC: i = 2; break;
305: }
307: (*fcreate[i][0])(PetscObjectComm((PetscObject)pep),ctx,&ctx->A);
308: (*fcreate[i][1])(PetscObjectComm((PetscObject)pep),ctx,&ctx->B);
309: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->A);
310: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->B);
312: } else { /* implicit matrix */
313: 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");
314: if (!((PetscObject)(ctx->eps))->type_name) {
315: EPSSetType(ctx->eps,EPSKRYLOVSCHUR);
316: } else {
317: PetscObjectTypeCompare((PetscObject)ctx->eps,EPSKRYLOVSCHUR,&ks);
318: if (!ks) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Implicit matrix option only implemented for Krylov-Schur");
319: }
320: if (ctx->alpha!=1.0 || ctx->beta!=0.0) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Implicit matrix option does not support changing alpha,beta parameters of the linearization");
321: STSetType(st,STSHELL);
322: STShellSetContext(st,(PetscObject)ctx);
323: if (!transf) { STShellSetBackTransform(st,BackTransform_Linear); }
324: else { STShellSetBackTransform(st,BackTransform_Skip); }
325: MatCreateVecsEmpty(pep->A[0],&ctx->w[0],&ctx->w[1]);
326: MatCreateVecsEmpty(pep->A[0],&ctx->w[2],&ctx->w[3]);
327: MatCreateVecs(pep->A[0],&ctx->w[4],&ctx->w[5]);
328: PetscLogObjectParents(pep,6,ctx->w);
329: MatCreateShell(PetscObjectComm((PetscObject)pep),deg*pep->nloc,deg*pep->nloc,deg*pep->n,deg*pep->n,ctx,&ctx->A);
330: if (sinv && !transf) {
331: MatShellSetOperation(ctx->A,MATOP_MULT,(void(*)(void))MatMult_Linear_Sinvert);
332: } else {
333: MatShellSetOperation(ctx->A,MATOP_MULT,(void(*)(void))MatMult_Linear_Shift);
334: }
335: STShellSetApply(st,Apply_Linear);
336: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->A);
337: ctx->pep = pep;
339: PEPBasisCoefficients(pep,pep->pbc);
340: if (!transf) {
341: PetscMalloc1(pep->nmat,&pep->solvematcoeffs);
342: PetscLogObjectMemory((PetscObject)pep,pep->nmat*sizeof(PetscScalar));
343: if (sinv) {
344: PEPEvaluateBasis(pep,pep->target,0,pep->solvematcoeffs,NULL);
345: } else {
346: for (i=0;i<deg;i++) pep->solvematcoeffs[i] = 0.0;
347: pep->solvematcoeffs[deg] = 1.0;
348: }
349: STScaleShift(pep->st,1.0/pep->sfactor);
350: RGPushScale(pep->rg,1.0/pep->sfactor);
351: }
352: if (pep->sfactor!=1.0) {
353: for (i=0;i<pep->nmat;i++) {
354: pep->pbc[pep->nmat+i] /= pep->sfactor;
355: pep->pbc[2*pep->nmat+i] /= pep->sfactor*pep->sfactor;
356: }
357: }
358: }
360: EPSSetOperators(ctx->eps,ctx->A,ctx->B);
361: EPSGetProblemType(ctx->eps,&ptype);
362: if (!ptype) {
363: if (ctx->explicitmatrix) {
364: EPSSetProblemType(ctx->eps,EPS_GNHEP);
365: } else {
366: EPSSetProblemType(ctx->eps,EPS_NHEP);
367: }
368: }
369: if (!ctx->usereps) {
370: if (transf) which = EPS_LARGEST_MAGNITUDE;
371: else {
372: switch (pep->which) {
373: case PEP_LARGEST_MAGNITUDE: which = EPS_LARGEST_MAGNITUDE; break;
374: case PEP_SMALLEST_MAGNITUDE: which = EPS_SMALLEST_MAGNITUDE; break;
375: case PEP_LARGEST_REAL: which = EPS_LARGEST_REAL; break;
376: case PEP_SMALLEST_REAL: which = EPS_SMALLEST_REAL; break;
377: case PEP_LARGEST_IMAGINARY: which = EPS_LARGEST_IMAGINARY; break;
378: case PEP_SMALLEST_IMAGINARY: which = EPS_SMALLEST_IMAGINARY; break;
379: case PEP_TARGET_MAGNITUDE: which = EPS_TARGET_MAGNITUDE; break;
380: case PEP_TARGET_REAL: which = EPS_TARGET_REAL; break;
381: case PEP_TARGET_IMAGINARY: which = EPS_TARGET_IMAGINARY; break;
382: case PEP_ALL: which = EPS_ALL; break;
383: case PEP_WHICH_USER: which = EPS_WHICH_USER;
384: EPSSetEigenvalueComparison(ctx->eps,pep->sc->comparison,pep->sc->comparisonctx);
385: break;
386: }
387: }
388: EPSSetWhichEigenpairs(ctx->eps,which);
390: EPSSetDimensions(ctx->eps,pep->nev,pep->ncv,pep->mpd);
391: EPSSetTolerances(ctx->eps,pep->tol==PETSC_DEFAULT?SLEPC_DEFAULT_TOL:pep->tol,pep->max_it);
392: }
393: RGIsTrivial(pep->rg,&istrivial);
394: if (!istrivial) {
395: if (transf) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"PEPLINEAR does not support a nontrivial region with st-transform");
396: EPSSetRG(ctx->eps,pep->rg);
397: }
398: /* Transfer the trackall option from pep to eps */
399: PEPGetTrackAll(pep,&trackall);
400: EPSSetTrackAll(ctx->eps,trackall);
402: /* temporary change of target */
403: if (pep->sfactor!=1.0) {
404: EPSGetTarget(ctx->eps,&sigma);
405: EPSSetTarget(ctx->eps,sigma/pep->sfactor);
406: }
408: /* process initial vector */
409: if (pep->nini<0) {
410: VecCreateMPI(PetscObjectComm((PetscObject)ctx->eps),deg*pep->nloc,deg*pep->n,&veps);
411: VecGetArray(veps,&epsarray);
412: for (i=0;i<deg;i++) {
413: if (i<-pep->nini) {
414: VecGetArray(pep->IS[i],&peparray);
415: PetscArraycpy(epsarray+i*pep->nloc,peparray,pep->nloc);
416: VecRestoreArray(pep->IS[i],&peparray);
417: } else {
418: if (!w) { VecDuplicate(pep->IS[0],&w); }
419: VecSetRandom(w,NULL);
420: VecGetArray(w,&peparray);
421: PetscArraycpy(epsarray+i*pep->nloc,peparray,pep->nloc);
422: VecRestoreArray(w,&peparray);
423: }
424: }
425: VecRestoreArray(veps,&epsarray);
426: EPSSetInitialSpace(ctx->eps,1,&veps);
427: VecDestroy(&veps);
428: VecDestroy(&w);
429: SlepcBasisDestroy_Private(&pep->nini,&pep->IS);
430: }
432: EPSSetUp(ctx->eps);
433: EPSGetDimensions(ctx->eps,NULL,&pep->ncv,&pep->mpd);
434: EPSGetTolerances(ctx->eps,NULL,&pep->max_it);
435: PEPAllocateSolution(pep,0);
436: return(0);
437: }
439: /*
440: PEPLinearExtract_Residual - Auxiliary routine that copies the solution of the
441: linear eigenproblem to the PEP object. The eigenvector of the generalized
442: problem is supposed to be
443: z = [ x ]
444: [ l*x ]
445: The eigenvector is taken from z(1:n) or z(n+1:2*n) depending on the explicitly
446: computed residual norm.
447: Finally, x is normalized so that ||x||_2 = 1.
448: */
449: static PetscErrorCode PEPLinearExtract_Residual(PEP pep,EPS eps)
450: {
451: PetscErrorCode ierr;
452: PetscInt i,k;
453: const PetscScalar *px;
454: PetscScalar *er=pep->eigr,*ei=pep->eigi;
455: PetscReal rn1,rn2;
456: Vec xr,xi=NULL,wr;
457: Mat A;
458: #if !defined(PETSC_USE_COMPLEX)
459: Vec wi;
460: const PetscScalar *py;
461: #endif
464: #if defined(PETSC_USE_COMPLEX)
465: PEPSetWorkVecs(pep,2);
466: #else
467: PEPSetWorkVecs(pep,4);
468: #endif
469: EPSGetOperators(eps,&A,NULL);
470: MatCreateVecs(A,&xr,NULL);
471: MatCreateVecsEmpty(pep->A[0],&wr,NULL);
472: #if !defined(PETSC_USE_COMPLEX)
473: VecDuplicate(xr,&xi);
474: VecDuplicateEmpty(wr,&wi);
475: #endif
476: for (i=0;i<pep->nconv;i++) {
477: EPSGetEigenpair(eps,i,NULL,NULL,xr,xi);
478: #if !defined(PETSC_USE_COMPLEX)
479: if (ei[i]!=0.0) { /* complex conjugate pair */
480: VecGetArrayRead(xr,&px);
481: VecGetArrayRead(xi,&py);
482: VecPlaceArray(wr,px);
483: VecPlaceArray(wi,py);
484: VecNormalizeComplex(wr,wi,PETSC_TRUE,NULL);
485: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,wi,pep->work,&rn1);
486: BVInsertVec(pep->V,i,wr);
487: BVInsertVec(pep->V,i+1,wi);
488: for (k=1;k<pep->nmat-1;k++) {
489: VecResetArray(wr);
490: VecResetArray(wi);
491: VecPlaceArray(wr,px+k*pep->nloc);
492: VecPlaceArray(wi,py+k*pep->nloc);
493: VecNormalizeComplex(wr,wi,PETSC_TRUE,NULL);
494: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,wi,pep->work,&rn2);
495: if (rn1>rn2) {
496: BVInsertVec(pep->V,i,wr);
497: BVInsertVec(pep->V,i+1,wi);
498: rn1 = rn2;
499: }
500: }
501: VecResetArray(wr);
502: VecResetArray(wi);
503: VecRestoreArrayRead(xr,&px);
504: VecRestoreArrayRead(xi,&py);
505: i++;
506: } else /* real eigenvalue */
507: #endif
508: {
509: VecGetArrayRead(xr,&px);
510: VecPlaceArray(wr,px);
511: VecNormalizeComplex(wr,NULL,PETSC_FALSE,NULL);
512: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,NULL,pep->work,&rn1);
513: BVInsertVec(pep->V,i,wr);
514: for (k=1;k<pep->nmat-1;k++) {
515: VecResetArray(wr);
516: VecPlaceArray(wr,px+k*pep->nloc);
517: VecNormalizeComplex(wr,NULL,PETSC_FALSE,NULL);
518: PEPComputeResidualNorm_Private(pep,er[i],ei[i],wr,NULL,pep->work,&rn2);
519: if (rn1>rn2) {
520: BVInsertVec(pep->V,i,wr);
521: rn1 = rn2;
522: }
523: }
524: VecResetArray(wr);
525: VecRestoreArrayRead(xr,&px);
526: }
527: }
528: VecDestroy(&wr);
529: VecDestroy(&xr);
530: #if !defined(PETSC_USE_COMPLEX)
531: VecDestroy(&wi);
532: VecDestroy(&xi);
533: #endif
534: return(0);
535: }
537: /*
538: PEPLinearExtract_None - Same as PEPLinearExtract_Norm but always takes
539: the first block.
540: */
541: static PetscErrorCode PEPLinearExtract_None(PEP pep,EPS eps)
542: {
543: PetscErrorCode ierr;
544: PetscInt i;
545: const PetscScalar *px;
546: Mat A;
547: Vec xr,xi=NULL,w;
548: #if !defined(PETSC_USE_COMPLEX)
549: PetscScalar *ei=pep->eigi;
550: #endif
553: EPSGetOperators(eps,&A,NULL);
554: MatCreateVecs(A,&xr,NULL);
555: #if !defined(PETSC_USE_COMPLEX)
556: VecDuplicate(xr,&xi);
557: #endif
558: MatCreateVecsEmpty(pep->A[0],&w,NULL);
559: for (i=0;i<pep->nconv;i++) {
560: EPSGetEigenvector(eps,i,xr,xi);
561: #if !defined(PETSC_USE_COMPLEX)
562: if (ei[i]!=0.0) { /* complex conjugate pair */
563: VecGetArrayRead(xr,&px);
564: VecPlaceArray(w,px);
565: BVInsertVec(pep->V,i,w);
566: VecResetArray(w);
567: VecRestoreArrayRead(xr,&px);
568: VecGetArrayRead(xi,&px);
569: VecPlaceArray(w,px);
570: BVInsertVec(pep->V,i+1,w);
571: VecResetArray(w);
572: VecRestoreArrayRead(xi,&px);
573: i++;
574: } else /* real eigenvalue */
575: #endif
576: {
577: VecGetArrayRead(xr,&px);
578: VecPlaceArray(w,px);
579: BVInsertVec(pep->V,i,w);
580: VecResetArray(w);
581: VecRestoreArrayRead(xr,&px);
582: }
583: }
584: VecDestroy(&w);
585: VecDestroy(&xr);
586: #if !defined(PETSC_USE_COMPLEX)
587: VecDestroy(&xi);
588: #endif
589: return(0);
590: }
592: /*
593: PEPLinearExtract_Norm - Auxiliary routine that copies the solution of the
594: linear eigenproblem to the PEP object. The eigenvector of the generalized
595: problem is supposed to be
596: z = [ x ]
597: [ l*x ]
598: If |l|<1.0, the eigenvector is taken from z(1:n), otherwise from z(n+1:2*n).
599: Finally, x is normalized so that ||x||_2 = 1.
600: */
601: static PetscErrorCode PEPLinearExtract_Norm(PEP pep,EPS eps)
602: {
603: PetscErrorCode ierr;
604: PetscInt i,offset;
605: const PetscScalar *px;
606: PetscScalar *er=pep->eigr;
607: Mat A;
608: Vec xr,xi=NULL,w;
609: #if !defined(PETSC_USE_COMPLEX)
610: PetscScalar *ei=pep->eigi;
611: #endif
614: EPSGetOperators(eps,&A,NULL);
615: MatCreateVecs(A,&xr,NULL);
616: #if !defined(PETSC_USE_COMPLEX)
617: VecDuplicate(xr,&xi);
618: #endif
619: MatCreateVecsEmpty(pep->A[0],&w,NULL);
620: for (i=0;i<pep->nconv;i++) {
621: EPSGetEigenpair(eps,i,NULL,NULL,xr,xi);
622: if (SlepcAbsEigenvalue(er[i],ei[i])>1.0) offset = (pep->nmat-2)*pep->nloc;
623: else offset = 0;
624: #if !defined(PETSC_USE_COMPLEX)
625: if (ei[i]!=0.0) { /* complex conjugate pair */
626: VecGetArrayRead(xr,&px);
627: VecPlaceArray(w,px+offset);
628: BVInsertVec(pep->V,i,w);
629: VecResetArray(w);
630: VecRestoreArrayRead(xr,&px);
631: VecGetArrayRead(xi,&px);
632: VecPlaceArray(w,px+offset);
633: BVInsertVec(pep->V,i+1,w);
634: VecResetArray(w);
635: VecRestoreArrayRead(xi,&px);
636: i++;
637: } else /* real eigenvalue */
638: #endif
639: {
640: VecGetArrayRead(xr,&px);
641: VecPlaceArray(w,px+offset);
642: BVInsertVec(pep->V,i,w);
643: VecResetArray(w);
644: VecRestoreArrayRead(xr,&px);
645: }
646: }
647: VecDestroy(&w);
648: VecDestroy(&xr);
649: #if !defined(PETSC_USE_COMPLEX)
650: VecDestroy(&xi);
651: #endif
652: return(0);
653: }
655: PetscErrorCode PEPExtractVectors_Linear(PEP pep)
656: {
658: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
661: switch (pep->extract) {
662: case PEP_EXTRACT_NONE:
663: PEPLinearExtract_None(pep,ctx->eps);
664: break;
665: case PEP_EXTRACT_NORM:
666: PEPLinearExtract_Norm(pep,ctx->eps);
667: break;
668: case PEP_EXTRACT_RESIDUAL:
669: PEPLinearExtract_Residual(pep,ctx->eps);
670: break;
671: case PEP_EXTRACT_STRUCTURED:
672: SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Extraction not implemented in this solver");
673: }
674: return(0);
675: }
677: PetscErrorCode PEPSolve_Linear(PEP pep)
678: {
680: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
681: PetscScalar sigma;
682: PetscBool flg;
683: PetscInt i;
686: EPSSolve(ctx->eps);
687: EPSGetConverged(ctx->eps,&pep->nconv);
688: EPSGetIterationNumber(ctx->eps,&pep->its);
689: EPSGetConvergedReason(ctx->eps,(EPSConvergedReason*)&pep->reason);
691: /* recover eigenvalues */
692: for (i=0;i<pep->nconv;i++) {
693: EPSGetEigenpair(ctx->eps,i,&pep->eigr[i],&pep->eigi[i],NULL,NULL);
694: pep->eigr[i] *= pep->sfactor;
695: pep->eigi[i] *= pep->sfactor;
696: }
698: /* restore target */
699: EPSGetTarget(ctx->eps,&sigma);
700: EPSSetTarget(ctx->eps,sigma*pep->sfactor);
702: STGetTransform(pep->st,&flg);
703: if (flg && pep->ops->backtransform) {
704: (*pep->ops->backtransform)(pep);
705: }
706: if (pep->sfactor!=1.0) {
707: /* Restore original values */
708: for (i=0;i<pep->nmat;i++){
709: pep->pbc[pep->nmat+i] *= pep->sfactor;
710: pep->pbc[2*pep->nmat+i] *= pep->sfactor*pep->sfactor;
711: }
712: if (!flg && !ctx->explicitmatrix) {
713: STScaleShift(pep->st,pep->sfactor);
714: }
715: }
716: if (ctx->explicitmatrix || !flg) {
717: RGPopScale(pep->rg);
718: }
719: return(0);
720: }
722: static PetscErrorCode EPSMonitor_Linear(EPS eps,PetscInt its,PetscInt nconv,PetscScalar *eigr,PetscScalar *eigi,PetscReal *errest,PetscInt nest,void *ctx)
723: {
724: PEP pep = (PEP)ctx;
728: PEPMonitor(pep,its,nconv,eigr,eigi,errest,nest);
729: return(0);
730: }
732: PetscErrorCode PEPSetFromOptions_Linear(PetscOptionItems *PetscOptionsObject,PEP pep)
733: {
735: PetscBool set,val;
736: PetscInt k;
737: PetscReal array[2]={0,0};
738: PetscBool flg;
739: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
742: PetscOptionsHead(PetscOptionsObject,"PEP Linear Options");
744: k = 2;
745: PetscOptionsRealArray("-pep_linear_linearization","Parameters of the linearization","PEPLinearSetLinearization",array,&k,&flg);
746: if (flg) {
747: PEPLinearSetLinearization(pep,array[0],array[1]);
748: }
750: PetscOptionsBool("-pep_linear_explicitmatrix","Use explicit matrix in linearization","PEPLinearSetExplicitMatrix",ctx->explicitmatrix,&val,&set);
751: if (set) { PEPLinearSetExplicitMatrix(pep,val); }
753: PetscOptionsTail();
755: if (!ctx->eps) { PEPLinearGetEPS(pep,&ctx->eps); }
756: EPSSetFromOptions(ctx->eps);
757: return(0);
758: }
760: static PetscErrorCode PEPLinearSetLinearization_Linear(PEP pep,PetscReal alpha,PetscReal beta)
761: {
762: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
765: if (beta==0.0 && alpha==0.0) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"Parameters alpha and beta cannot be zero simultaneously");
766: ctx->alpha = alpha;
767: ctx->beta = beta;
768: return(0);
769: }
771: /*@
772: PEPLinearSetLinearization - Set the coefficients that define
773: the linearization of a quadratic eigenproblem.
775: Logically Collective on pep
777: Input Parameters:
778: + pep - polynomial eigenvalue solver
779: . alpha - first parameter of the linearization
780: - beta - second parameter of the linearization
782: Options Database Key:
783: . -pep_linear_linearization <alpha,beta> - Sets the coefficients
785: Notes:
786: Cannot pass zero for both alpha and beta. The default values are
787: alpha=1 and beta=0.
789: Level: advanced
791: .seealso: PEPLinearGetLinearization()
792: @*/
793: PetscErrorCode PEPLinearSetLinearization(PEP pep,PetscReal alpha,PetscReal beta)
794: {
801: PetscTryMethod(pep,"PEPLinearSetLinearization_C",(PEP,PetscReal,PetscReal),(pep,alpha,beta));
802: return(0);
803: }
805: static PetscErrorCode PEPLinearGetLinearization_Linear(PEP pep,PetscReal *alpha,PetscReal *beta)
806: {
807: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
810: if (alpha) *alpha = ctx->alpha;
811: if (beta) *beta = ctx->beta;
812: return(0);
813: }
815: /*@
816: PEPLinearGetLinearization - Returns the coefficients that define
817: the linearization of a quadratic eigenproblem.
819: Not Collective
821: Input Parameter:
822: . pep - polynomial eigenvalue solver
824: Output Parameters:
825: + alpha - the first parameter of the linearization
826: - beta - the second parameter of the linearization
828: Level: advanced
830: .seealso: PEPLinearSetLinearization()
831: @*/
832: PetscErrorCode PEPLinearGetLinearization(PEP pep,PetscReal *alpha,PetscReal *beta)
833: {
838: PetscUseMethod(pep,"PEPLinearGetLinearization_C",(PEP,PetscReal*,PetscReal*),(pep,alpha,beta));
839: return(0);
840: }
842: static PetscErrorCode PEPLinearSetExplicitMatrix_Linear(PEP pep,PetscBool explicitmatrix)
843: {
844: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
847: if (ctx->explicitmatrix != explicitmatrix) {
848: ctx->explicitmatrix = explicitmatrix;
849: pep->state = PEP_STATE_INITIAL;
850: }
851: return(0);
852: }
854: /*@
855: PEPLinearSetExplicitMatrix - Indicate if the matrices A and B for the
856: linearization of the problem must be built explicitly.
858: Logically Collective on pep
860: Input Parameters:
861: + pep - polynomial eigenvalue solver
862: - explicit - boolean flag indicating if the matrices are built explicitly
864: Options Database Key:
865: . -pep_linear_explicitmatrix <boolean> - Indicates the boolean flag
867: Level: advanced
869: .seealso: PEPLinearGetExplicitMatrix()
870: @*/
871: PetscErrorCode PEPLinearSetExplicitMatrix(PEP pep,PetscBool explicitmatrix)
872: {
878: PetscTryMethod(pep,"PEPLinearSetExplicitMatrix_C",(PEP,PetscBool),(pep,explicitmatrix));
879: return(0);
880: }
882: static PetscErrorCode PEPLinearGetExplicitMatrix_Linear(PEP pep,PetscBool *explicitmatrix)
883: {
884: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
887: *explicitmatrix = ctx->explicitmatrix;
888: return(0);
889: }
891: /*@
892: PEPLinearGetExplicitMatrix - Returns the flag indicating if the matrices
893: A and B for the linearization are built explicitly.
895: Not Collective
897: Input Parameter:
898: . pep - polynomial eigenvalue solver
900: Output Parameter:
901: . explicitmatrix - the mode flag
903: Level: advanced
905: .seealso: PEPLinearSetExplicitMatrix()
906: @*/
907: PetscErrorCode PEPLinearGetExplicitMatrix(PEP pep,PetscBool *explicitmatrix)
908: {
914: PetscUseMethod(pep,"PEPLinearGetExplicitMatrix_C",(PEP,PetscBool*),(pep,explicitmatrix));
915: return(0);
916: }
918: static PetscErrorCode PEPLinearSetEPS_Linear(PEP pep,EPS eps)
919: {
921: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
924: PetscObjectReference((PetscObject)eps);
925: EPSDestroy(&ctx->eps);
926: ctx->eps = eps;
927: ctx->usereps = PETSC_TRUE;
928: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->eps);
929: pep->state = PEP_STATE_INITIAL;
930: return(0);
931: }
933: /*@
934: PEPLinearSetEPS - Associate an eigensolver object (EPS) to the
935: polynomial eigenvalue solver.
937: Collective on pep
939: Input Parameters:
940: + pep - polynomial eigenvalue solver
941: - eps - the eigensolver object
943: Level: advanced
945: .seealso: PEPLinearGetEPS()
946: @*/
947: PetscErrorCode PEPLinearSetEPS(PEP pep,EPS eps)
948: {
955: PetscTryMethod(pep,"PEPLinearSetEPS_C",(PEP,EPS),(pep,eps));
956: return(0);
957: }
959: static PetscErrorCode PEPLinearGetEPS_Linear(PEP pep,EPS *eps)
960: {
962: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
965: if (!ctx->eps) {
966: EPSCreate(PetscObjectComm((PetscObject)pep),&ctx->eps);
967: PetscObjectIncrementTabLevel((PetscObject)ctx->eps,(PetscObject)pep,1);
968: EPSSetOptionsPrefix(ctx->eps,((PetscObject)pep)->prefix);
969: EPSAppendOptionsPrefix(ctx->eps,"pep_linear_");
970: PetscLogObjectParent((PetscObject)pep,(PetscObject)ctx->eps);
971: PetscObjectSetOptions((PetscObject)ctx->eps,((PetscObject)pep)->options);
972: EPSMonitorSet(ctx->eps,EPSMonitor_Linear,pep,NULL);
973: }
974: *eps = ctx->eps;
975: return(0);
976: }
978: /*@
979: PEPLinearGetEPS - Retrieve the eigensolver object (EPS) associated
980: to the polynomial eigenvalue solver.
982: Not Collective
984: Input Parameter:
985: . pep - polynomial eigenvalue solver
987: Output Parameter:
988: . eps - the eigensolver object
990: Level: advanced
992: .seealso: PEPLinearSetEPS()
993: @*/
994: PetscErrorCode PEPLinearGetEPS(PEP pep,EPS *eps)
995: {
1001: PetscUseMethod(pep,"PEPLinearGetEPS_C",(PEP,EPS*),(pep,eps));
1002: return(0);
1003: }
1005: PetscErrorCode PEPView_Linear(PEP pep,PetscViewer viewer)
1006: {
1008: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
1009: PetscBool isascii;
1012: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
1013: if (isascii) {
1014: if (!ctx->eps) { PEPLinearGetEPS(pep,&ctx->eps); }
1015: PetscViewerASCIIPrintf(viewer," %s matrices\n",ctx->explicitmatrix? "explicit": "implicit");
1016: PetscViewerASCIIPrintf(viewer," linearization parameters: alpha=%g beta=%g\n",(double)ctx->alpha,(double)ctx->beta);
1017: PetscViewerASCIIPushTab(viewer);
1018: EPSView(ctx->eps,viewer);
1019: PetscViewerASCIIPopTab(viewer);
1020: }
1021: return(0);
1022: }
1024: PetscErrorCode PEPReset_Linear(PEP pep)
1025: {
1027: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
1030: if (!ctx->eps) { EPSReset(ctx->eps); }
1031: MatDestroy(&ctx->A);
1032: MatDestroy(&ctx->B);
1033: VecDestroy(&ctx->w[0]);
1034: VecDestroy(&ctx->w[1]);
1035: VecDestroy(&ctx->w[2]);
1036: VecDestroy(&ctx->w[3]);
1037: VecDestroy(&ctx->w[4]);
1038: VecDestroy(&ctx->w[5]);
1039: return(0);
1040: }
1042: PetscErrorCode PEPDestroy_Linear(PEP pep)
1043: {
1045: PEP_LINEAR *ctx = (PEP_LINEAR*)pep->data;
1048: EPSDestroy(&ctx->eps);
1049: PetscFree(pep->data);
1050: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetLinearization_C",NULL);
1051: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetLinearization_C",NULL);
1052: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetEPS_C",NULL);
1053: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetEPS_C",NULL);
1054: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetExplicitMatrix_C",NULL);
1055: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetExplicitMatrix_C",NULL);
1056: return(0);
1057: }
1059: SLEPC_EXTERN PetscErrorCode PEPCreate_Linear(PEP pep)
1060: {
1062: PEP_LINEAR *ctx;
1065: PetscNewLog(pep,&ctx);
1066: pep->data = (void*)ctx;
1068: pep->lineariz = PETSC_TRUE;
1069: ctx->explicitmatrix = PETSC_FALSE;
1070: ctx->alpha = 1.0;
1071: ctx->beta = 0.0;
1073: pep->ops->solve = PEPSolve_Linear;
1074: pep->ops->setup = PEPSetUp_Linear;
1075: pep->ops->setfromoptions = PEPSetFromOptions_Linear;
1076: pep->ops->destroy = PEPDestroy_Linear;
1077: pep->ops->reset = PEPReset_Linear;
1078: pep->ops->view = PEPView_Linear;
1079: pep->ops->backtransform = PEPBackTransform_Default;
1080: pep->ops->computevectors = PEPComputeVectors_Default;
1081: pep->ops->extractvectors = PEPExtractVectors_Linear;
1083: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetLinearization_C",PEPLinearSetLinearization_Linear);
1084: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetLinearization_C",PEPLinearGetLinearization_Linear);
1085: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetEPS_C",PEPLinearSetEPS_Linear);
1086: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetEPS_C",PEPLinearGetEPS_Linear);
1087: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearSetExplicitMatrix_C",PEPLinearSetExplicitMatrix_Linear);
1088: PetscObjectComposeFunction((PetscObject)pep,"PEPLinearGetExplicitMatrix_C",PEPLinearGetExplicitMatrix_Linear);
1089: return(0);
1090: }