Actual source code: pepdefault.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: Simple default routines for common PEP operations
12: */
14: #include <slepc/private/pepimpl.h> /*I "slepcpep.h" I*/
16: /*@
17: PEPSetWorkVecs - Sets a number of work vectors into a PEP object.
19: Collective on PEP
21: Input Parameters:
22: + pep - polynomial eigensolver context
23: - nw - number of work vectors to allocate
25: Developers Note:
26: This is SLEPC_EXTERN because it may be required by user plugin PEP
27: implementations.
29: Level: developer
30: @*/
31: PetscErrorCode PEPSetWorkVecs(PEP pep,PetscInt nw)
32: {
34: Vec t;
37: if (pep->nwork < nw) {
38: VecDestroyVecs(pep->nwork,&pep->work);
39: pep->nwork = nw;
40: BVGetColumn(pep->V,0,&t);
41: VecDuplicateVecs(t,nw,&pep->work);
42: BVRestoreColumn(pep->V,0,&t);
43: PetscLogObjectParents(pep,nw,pep->work);
44: }
45: return(0);
46: }
48: /*
49: PEPConvergedRelative - Checks convergence relative to the eigenvalue.
50: */
51: PetscErrorCode PEPConvergedRelative(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
52: {
53: PetscReal w;
56: w = SlepcAbsEigenvalue(eigr,eigi);
57: *errest = res/w;
58: return(0);
59: }
61: /*
62: PEPConvergedNorm - Checks convergence relative to the matrix norms.
63: */
64: PetscErrorCode PEPConvergedNorm(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
65: {
66: PetscReal w=0.0,t;
67: PetscInt j;
68: PetscBool flg;
72: /* initialization of matrix norms */
73: if (!pep->nrma[pep->nmat-1]) {
74: for (j=0;j<pep->nmat;j++) {
75: MatHasOperation(pep->A[j],MATOP_NORM,&flg);
76: if (!flg) SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The convergence test related to the matrix norms requires a matrix norm operation");
77: MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j]);
78: }
79: }
80: t = SlepcAbsEigenvalue(eigr,eigi);
81: for (j=pep->nmat-1;j>=0;j--) {
82: w = w*t+pep->nrma[j];
83: }
84: *errest = res/w;
85: return(0);
86: }
88: /*
89: PEPConvergedAbsolute - Checks convergence absolutely.
90: */
91: PetscErrorCode PEPConvergedAbsolute(PEP pep,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
92: {
94: *errest = res;
95: return(0);
96: }
98: /*@C
99: PEPStoppingBasic - Default routine to determine whether the outer eigensolver
100: iteration must be stopped.
102: Collective on PEP
104: Input Parameters:
105: + pep - eigensolver context obtained from PEPCreate()
106: . its - current number of iterations
107: . max_it - maximum number of iterations
108: . nconv - number of currently converged eigenpairs
109: . nev - number of requested eigenpairs
110: - ctx - context (not used here)
112: Output Parameter:
113: . reason - result of the stopping test
115: Notes:
116: A positive value of reason indicates that the iteration has finished successfully
117: (converged), and a negative value indicates an error condition (diverged). If
118: the iteration needs to be continued, reason must be set to PEP_CONVERGED_ITERATING
119: (zero).
121: PEPStoppingBasic() will stop if all requested eigenvalues are converged, or if
122: the maximum number of iterations has been reached.
124: Use PEPSetStoppingTest() to provide your own test instead of using this one.
126: Level: advanced
128: .seealso: PEPSetStoppingTest(), PEPConvergedReason, PEPGetConvergedReason()
129: @*/
130: PetscErrorCode PEPStoppingBasic(PEP pep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,PEPConvergedReason *reason,void *ctx)
131: {
135: *reason = PEP_CONVERGED_ITERATING;
136: if (nconv >= nev) {
137: PetscInfo2(pep,"Polynomial eigensolver finished successfully: %D eigenpairs converged at iteration %D\n",nconv,its);
138: *reason = PEP_CONVERGED_TOL;
139: } else if (its >= max_it) {
140: *reason = PEP_DIVERGED_ITS;
141: PetscInfo1(pep,"Polynomial eigensolver iteration reached maximum number of iterations (%D)\n",its);
142: }
143: return(0);
144: }
146: PetscErrorCode PEPBackTransform_Default(PEP pep)
147: {
151: STBackTransform(pep->st,pep->nconv,pep->eigr,pep->eigi);
152: return(0);
153: }
155: PetscErrorCode PEPComputeVectors_Default(PEP pep)
156: {
158: PetscInt i;
159: Vec v;
160: #if !defined(PETSC_USE_COMPLEX)
161: Vec v1;
162: #endif
165: PEPExtractVectors(pep);
167: /* Fix eigenvectors if balancing was used */
168: if ((pep->scale==PEP_SCALE_DIAGONAL || pep->scale==PEP_SCALE_BOTH) && pep->Dr && (pep->refine!=PEP_REFINE_MULTIPLE)) {
169: for (i=0;i<pep->nconv;i++) {
170: BVGetColumn(pep->V,i,&v);
171: VecPointwiseMult(v,v,pep->Dr);
172: BVRestoreColumn(pep->V,i,&v);
173: }
174: }
176: /* normalization */
177: for (i=0;i<pep->nconv;i++) {
178: #if !defined(PETSC_USE_COMPLEX)
179: if (pep->eigi[i]!=0.0) { /* first eigenvalue of a complex conjugate pair */
180: BVGetColumn(pep->V,i,&v);
181: BVGetColumn(pep->V,i+1,&v1);
182: VecNormalizeComplex(v,v1,PETSC_TRUE,NULL);
183: BVRestoreColumn(pep->V,i,&v);
184: BVRestoreColumn(pep->V,i+1,&v1);
185: i++;
186: } else /* real eigenvalue */
187: #endif
188: {
189: BVGetColumn(pep->V,i,&v);
190: VecNormalizeComplex(v,NULL,PETSC_FALSE,NULL);
191: BVRestoreColumn(pep->V,i,&v);
192: }
193: }
194: return(0);
195: }
197: /*
198: PEPBuildDiagonalScaling - compute two diagonal matrices to be applied for balancing
199: in polynomial eigenproblems.
200: */
201: PetscErrorCode PEPBuildDiagonalScaling(PEP pep)
202: {
204: PetscInt it,i,j,k,nmat,nr,e,nz,lst,lend,nc=0,*cols,emax,emin,emaxl,eminl;
205: const PetscInt *cidx,*ridx;
206: Mat M,*T,A;
207: PetscMPIInt n;
208: PetscBool cont=PETSC_TRUE,flg=PETSC_FALSE;
209: PetscScalar *array,*Dr,*Dl,t;
210: PetscReal l2,d,*rsum,*aux,*csum,w=1.0;
211: MatStructure str;
212: MatInfo info;
215: l2 = 2*PetscLogReal(2.0);
216: nmat = pep->nmat;
217: PetscMPIIntCast(pep->n,&n);
218: STGetMatStructure(pep->st,&str);
219: PetscMalloc1(nmat,&T);
220: for (k=0;k<nmat;k++) {
221: STGetMatrixTransformed(pep->st,k,&T[k]);
222: }
223: /* Form local auxiliar matrix M */
224: PetscObjectTypeCompareAny((PetscObject)T[0],&cont,MATMPIAIJ,MATSEQAIJ,"");
225: if (!cont) SETERRQ(PetscObjectComm((PetscObject)T[0]),PETSC_ERR_SUP,"Only for MPIAIJ or SEQAIJ matrix types");
226: PetscObjectTypeCompare((PetscObject)T[0],MATMPIAIJ,&cont);
227: if (cont) {
228: MatMPIAIJGetLocalMat(T[0],MAT_INITIAL_MATRIX,&M);
229: flg = PETSC_TRUE;
230: } else {
231: MatDuplicate(T[0],MAT_COPY_VALUES,&M);
232: }
233: MatGetInfo(M,MAT_LOCAL,&info);
234: nz = (PetscInt)info.nz_used;
235: MatSeqAIJGetArray(M,&array);
236: for (i=0;i<nz;i++) {
237: t = PetscAbsScalar(array[i]);
238: array[i] = t*t;
239: }
240: MatSeqAIJRestoreArray(M,&array);
241: for (k=1;k<nmat;k++) {
242: if (flg) {
243: MatMPIAIJGetLocalMat(T[k],MAT_INITIAL_MATRIX,&A);
244: } else {
245: if (str==SAME_NONZERO_PATTERN) {
246: MatCopy(T[k],A,SAME_NONZERO_PATTERN);
247: } else {
248: MatDuplicate(T[k],MAT_COPY_VALUES,&A);
249: }
250: }
251: MatGetInfo(A,MAT_LOCAL,&info);
252: nz = (PetscInt)info.nz_used;
253: MatSeqAIJGetArray(A,&array);
254: for (i=0;i<nz;i++) {
255: t = PetscAbsScalar(array[i]);
256: array[i] = t*t;
257: }
258: MatSeqAIJRestoreArray(A,&array);
259: w *= pep->slambda*pep->slambda*pep->sfactor;
260: MatAXPY(M,w,A,str);
261: if (flg || str!=SAME_NONZERO_PATTERN || k==nmat-2) {
262: MatDestroy(&A);
263: }
264: }
265: MatGetRowIJ(M,0,PETSC_FALSE,PETSC_FALSE,&nr,&ridx,&cidx,&cont);
266: if (!cont) SETERRQ(PetscObjectComm((PetscObject)T[0]),PETSC_ERR_SUP,"It is not possible to compute scaling diagonals for these PEP matrices");
267: MatGetInfo(M,MAT_LOCAL,&info);
268: nz = (PetscInt)info.nz_used;
269: VecGetOwnershipRange(pep->Dl,&lst,&lend);
270: PetscMalloc4(nr,&rsum,pep->n,&csum,pep->n,&aux,PetscMin(pep->n-lend+lst,nz),&cols);
271: VecSet(pep->Dr,1.0);
272: VecSet(pep->Dl,1.0);
273: VecGetArray(pep->Dl,&Dl);
274: VecGetArray(pep->Dr,&Dr);
275: MatSeqAIJGetArray(M,&array);
276: PetscMemzero(aux,pep->n*sizeof(PetscReal));
277: for (j=0;j<nz;j++) {
278: /* Search non-zero columns outsize lst-lend */
279: if (aux[cidx[j]]==0 && (cidx[j]<lst || lend<=cidx[j])) cols[nc++] = cidx[j];
280: /* Local column sums */
281: aux[cidx[j]] += PetscAbsScalar(array[j]);
282: }
283: for (it=0;it<pep->sits && cont;it++) {
284: emaxl = 0; eminl = 0;
285: /* Column sum */
286: if (it>0) { /* it=0 has been already done*/
287: MatSeqAIJGetArray(M,&array);
288: PetscMemzero(aux,pep->n*sizeof(PetscReal));
289: for (j=0;j<nz;j++) aux[cidx[j]] += PetscAbsScalar(array[j]);
290: MatSeqAIJRestoreArray(M,&array);
291: }
292: MPI_Allreduce(aux,csum,n,MPIU_REAL,MPIU_SUM,PetscObjectComm((PetscObject)pep->Dr));
293: /* Update Dr */
294: for (j=lst;j<lend;j++) {
295: d = PetscLogReal(csum[j])/l2;
296: e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
297: d = PetscPowReal(2.0,e);
298: Dr[j-lst] *= d;
299: aux[j] = d*d;
300: emaxl = PetscMax(emaxl,e);
301: eminl = PetscMin(eminl,e);
302: }
303: for (j=0;j<nc;j++) {
304: d = PetscLogReal(csum[cols[j]])/l2;
305: e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
306: d = PetscPowReal(2.0,e);
307: aux[cols[j]] = d*d;
308: emaxl = PetscMax(emaxl,e);
309: eminl = PetscMin(eminl,e);
310: }
311: /* Scale M */
312: MatSeqAIJGetArray(M,&array);
313: for (j=0;j<nz;j++) {
314: array[j] *= aux[cidx[j]];
315: }
316: MatSeqAIJRestoreArray(M,&array);
317: /* Row sum */
318: PetscMemzero(rsum,nr*sizeof(PetscReal));
319: MatSeqAIJGetArray(M,&array);
320: for (i=0;i<nr;i++) {
321: for (j=ridx[i];j<ridx[i+1];j++) rsum[i] += PetscAbsScalar(array[j]);
322: /* Update Dl */
323: d = PetscLogReal(rsum[i])/l2;
324: e = -(PetscInt)((d < 0)?(d-0.5):(d+0.5));
325: d = PetscPowReal(2.0,e);
326: Dl[i] *= d;
327: /* Scale M */
328: for (j=ridx[i];j<ridx[i+1];j++) array[j] *= d*d;
329: emaxl = PetscMax(emaxl,e);
330: eminl = PetscMin(eminl,e);
331: }
332: MatSeqAIJRestoreArray(M,&array);
333: /* Compute global max and min */
334: MPI_Allreduce(&emaxl,&emax,1,MPIU_INT,MPI_MAX,PetscObjectComm((PetscObject)pep->Dl));
335: MPI_Allreduce(&eminl,&emin,1,MPIU_INT,MPI_MIN,PetscObjectComm((PetscObject)pep->Dl));
336: if (emax<=emin+2) cont = PETSC_FALSE;
337: }
338: VecRestoreArray(pep->Dr,&Dr);
339: VecRestoreArray(pep->Dl,&Dl);
340: /* Free memory*/
341: MatDestroy(&M);
342: PetscFree4(rsum,csum,aux,cols);
343: PetscFree(T);
344: return(0);
345: }
347: /*
348: PEPComputeScaleFactor - compute sfactor as described in [Betcke 2008].
349: */
350: PetscErrorCode PEPComputeScaleFactor(PEP pep)
351: {
353: PetscBool has0,has1,flg;
354: PetscReal norm0,norm1;
355: Mat T[2];
356: PEPBasis basis;
357: PetscInt i;
360: if (pep->scale==PEP_SCALE_NONE || pep->scale==PEP_SCALE_DIAGONAL) { /* no scalar scaling */
361: pep->sfactor = 1.0;
362: pep->dsfactor = 1.0;
363: return(0);
364: }
365: if (pep->sfactor_set) return(0); /* user provided value */
366: pep->sfactor = 1.0;
367: pep->dsfactor = 1.0;
368: PEPGetBasis(pep,&basis);
369: if (basis==PEP_BASIS_MONOMIAL) {
370: STGetTransform(pep->st,&flg);
371: if (flg) {
372: STGetMatrixTransformed(pep->st,0,&T[0]);
373: STGetMatrixTransformed(pep->st,pep->nmat-1,&T[1]);
374: } else {
375: T[0] = pep->A[0];
376: T[1] = pep->A[pep->nmat-1];
377: }
378: if (pep->nmat>2) {
379: MatHasOperation(T[0],MATOP_NORM,&has0);
380: MatHasOperation(T[1],MATOP_NORM,&has1);
381: if (has0 && has1) {
382: MatNorm(T[0],NORM_INFINITY,&norm0);
383: MatNorm(T[1],NORM_INFINITY,&norm1);
384: pep->sfactor = PetscPowReal(norm0/norm1,1.0/(pep->nmat-1));
385: pep->dsfactor = norm1;
386: for (i=pep->nmat-2;i>0;i--) {
387: STGetMatrixTransformed(pep->st,i,&T[1]);
388: MatHasOperation(T[1],MATOP_NORM,&has1);
389: if (has1) {
390: MatNorm(T[1],NORM_INFINITY,&norm1);
391: pep->dsfactor = pep->dsfactor*pep->sfactor+norm1;
392: } else break;
393: }
394: if (has1) {
395: pep->dsfactor = pep->dsfactor*pep->sfactor+norm0;
396: pep->dsfactor = pep->nmat/pep->dsfactor;
397: } else pep->dsfactor = 1.0;
398: }
399: }
400: }
401: return(0);
402: }
404: /*
405: PEPBasisCoefficients - compute polynomial basis coefficients
406: */
407: PetscErrorCode PEPBasisCoefficients(PEP pep,PetscReal *pbc)
408: {
409: PetscReal *ca,*cb,*cg;
410: PetscInt k,nmat=pep->nmat;
413: ca = pbc;
414: cb = pbc+nmat;
415: cg = pbc+2*nmat;
416: switch (pep->basis) {
417: case PEP_BASIS_MONOMIAL:
418: for (k=0;k<nmat;k++) {
419: ca[k] = 1.0; cb[k] = 0.0; cg[k] = 0.0;
420: }
421: break;
422: case PEP_BASIS_CHEBYSHEV1:
423: ca[0] = 1.0; cb[0] = 0.0; cg[0] = 0.0;
424: for (k=1;k<nmat;k++) {
425: ca[k] = .5; cb[k] = 0.0; cg[k] = .5;
426: }
427: break;
428: case PEP_BASIS_CHEBYSHEV2:
429: ca[0] = .5; cb[0] = 0.0; cg[0] = 0.0;
430: for (k=1;k<nmat;k++) {
431: ca[k] = .5; cb[k] = 0.0; cg[k] = .5;
432: }
433: break;
434: case PEP_BASIS_LEGENDRE:
435: ca[0] = 1.0; cb[0] = 0.0; cg[0] = 0.0;
436: for (k=1;k<nmat;k++) {
437: ca[k] = k+1; cb[k] = -2*k; cg[k] = k;
438: }
439: break;
440: case PEP_BASIS_LAGUERRE:
441: ca[0] = -1.0; cb[0] = 0.0; cg[0] = 0.0;
442: for (k=1;k<nmat;k++) {
443: ca[k] = -(k+1); cb[k] = 2*k+1; cg[k] = -k;
444: }
445: break;
446: case PEP_BASIS_HERMITE:
447: ca[0] = .5; cb[0] = 0.0; cg[0] = 0.0;
448: for (k=1;k<nmat;k++) {
449: ca[k] = .5; cb[k] = 0.0; cg[k] = -k;
450: }
451: break;
452: }
453: return(0);
454: }