Actual source code: epsdefault.c
slepc-3.21.0 2024-03-30
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: This file contains some simple default routines for common operations
12: */
14: #include <slepc/private/epsimpl.h>
15: #include <slepcvec.h>
17: PetscErrorCode EPSBackTransform_Default(EPS eps)
18: {
19: PetscFunctionBegin;
20: PetscCall(STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi));
21: PetscFunctionReturn(PETSC_SUCCESS);
22: }
24: /*
25: EPSComputeVectors_Hermitian - Copies the Lanczos vectors as eigenvectors
26: using purification for generalized eigenproblems.
27: */
28: PetscErrorCode EPSComputeVectors_Hermitian(EPS eps)
29: {
30: PetscBool iscayley,indef;
31: Mat B,C;
33: PetscFunctionBegin;
34: if (eps->purify) {
35: PetscCall(EPS_Purify(eps,eps->nconv));
36: PetscCall(BVNormalize(eps->V,NULL));
37: } else {
38: /* In the case of Cayley transform, eigenvectors need to be B-normalized */
39: PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley));
40: if (iscayley && eps->isgeneralized) {
41: PetscCall(STGetMatrix(eps->st,1,&B));
42: PetscCall(BVGetMatrix(eps->V,&C,&indef));
43: PetscCheck(!indef,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"The inner product should not be indefinite");
44: PetscCall(BVSetMatrix(eps->V,B,PETSC_FALSE));
45: PetscCall(BVNormalize(eps->V,NULL));
46: PetscCall(BVSetMatrix(eps->V,C,PETSC_FALSE)); /* restore original matrix */
47: }
48: }
49: PetscFunctionReturn(PETSC_SUCCESS);
50: }
52: /*
53: EPSComputeVectors_Indefinite - similar to the Schur version but
54: for indefinite problems
55: */
56: PetscErrorCode EPSComputeVectors_Indefinite(EPS eps)
57: {
58: PetscInt n;
59: Mat X;
61: PetscFunctionBegin;
62: PetscCall(DSGetDimensions(eps->ds,&n,NULL,NULL,NULL));
63: PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL));
64: PetscCall(DSGetMat(eps->ds,DS_MAT_X,&X));
65: PetscCall(BVMultInPlace(eps->V,X,0,n));
66: PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&X));
68: /* purification */
69: if (eps->purify) PetscCall(EPS_Purify(eps,eps->nconv));
71: /* normalization */
72: PetscCall(BVNormalize(eps->V,eps->eigi));
73: PetscFunctionReturn(PETSC_SUCCESS);
74: }
76: /*
77: EPSComputeVectors_Twosided - Adjust left eigenvectors in generalized problems: y = B^-* y.
78: */
79: PetscErrorCode EPSComputeVectors_Twosided(EPS eps)
80: {
81: PetscInt i;
82: Vec w,y;
84: PetscFunctionBegin;
85: if (!eps->twosided || !eps->isgeneralized) PetscFunctionReturn(PETSC_SUCCESS);
86: PetscCall(EPSSetWorkVecs(eps,1));
87: w = eps->work[0];
88: for (i=0;i<eps->nconv;i++) {
89: PetscCall(BVCopyVec(eps->W,i,w));
90: PetscCall(BVGetColumn(eps->W,i,&y));
91: PetscCall(STMatSolveHermitianTranspose(eps->st,w,y));
92: PetscCall(BVRestoreColumn(eps->W,i,&y));
93: }
94: PetscFunctionReturn(PETSC_SUCCESS);
95: }
97: /*
98: EPSComputeVectors_Schur - Compute eigenvectors from the vectors
99: provided by the eigensolver. This version is intended for solvers
100: that provide Schur vectors. Given the partial Schur decomposition
101: OP*V=V*T, the following steps are performed:
102: 1) compute eigenvectors of T: T*Z=Z*D
103: 2) compute eigenvectors of OP: X=V*Z
104: */
105: PetscErrorCode EPSComputeVectors_Schur(EPS eps)
106: {
107: PetscInt i;
108: Mat Z;
109: Vec z;
111: PetscFunctionBegin;
112: if (eps->ishermitian) {
113: if (eps->isgeneralized && !eps->ispositive) PetscCall(EPSComputeVectors_Indefinite(eps));
114: else PetscCall(EPSComputeVectors_Hermitian(eps));
115: PetscFunctionReturn(PETSC_SUCCESS);
116: }
118: /* right eigenvectors */
119: PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL));
121: /* V = V * Z */
122: PetscCall(DSGetMat(eps->ds,DS_MAT_X,&Z));
123: PetscCall(BVMultInPlace(eps->V,Z,0,eps->nconv));
124: PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&Z));
126: /* Purify eigenvectors */
127: if (eps->purify) PetscCall(EPS_Purify(eps,eps->nconv));
129: /* Fix eigenvectors if balancing was used */
130: if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
131: for (i=0;i<eps->nconv;i++) {
132: PetscCall(BVGetColumn(eps->V,i,&z));
133: PetscCall(VecPointwiseDivide(z,z,eps->D));
134: PetscCall(BVRestoreColumn(eps->V,i,&z));
135: }
136: }
138: /* normalize eigenvectors (when using purification or balancing) */
139: if (eps->purify || (eps->balance!=EPS_BALANCE_NONE && eps->D)) PetscCall(BVNormalize(eps->V,eps->eigi));
141: /* left eigenvectors */
142: if (eps->twosided) {
143: PetscCall(DSVectors(eps->ds,DS_MAT_Y,NULL,NULL));
144: /* W = W * Z */
145: PetscCall(DSGetMat(eps->ds,DS_MAT_Y,&Z));
146: PetscCall(BVMultInPlace(eps->W,Z,0,eps->nconv));
147: PetscCall(DSRestoreMat(eps->ds,DS_MAT_Y,&Z));
148: /* Fix left eigenvectors if balancing was used */
149: if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
150: for (i=0;i<eps->nconv;i++) {
151: PetscCall(BVGetColumn(eps->W,i,&z));
152: PetscCall(VecPointwiseMult(z,z,eps->D));
153: PetscCall(BVRestoreColumn(eps->W,i,&z));
154: }
155: }
156: PetscCall(EPSComputeVectors_Twosided(eps));
157: /* normalize */
158: PetscCall(BVNormalize(eps->W,eps->eigi));
159: #if !defined(PETSC_USE_COMPLEX)
160: for (i=0;i<eps->nconv-1;i++) {
161: if (eps->eigi[i] != 0.0) {
162: if (eps->eigi[i] > 0.0) PetscCall(BVScaleColumn(eps->W,i+1,-1.0));
163: i++;
164: }
165: }
166: #endif
167: }
168: PetscFunctionReturn(PETSC_SUCCESS);
169: }
171: /*@
172: EPSSetWorkVecs - Sets a number of work vectors into an EPS object.
174: Collective
176: Input Parameters:
177: + eps - eigensolver context
178: - nw - number of work vectors to allocate
180: Developer Notes:
181: This is SLEPC_EXTERN because it may be required by user plugin EPS
182: implementations.
184: Level: developer
186: .seealso: EPSSetUp()
187: @*/
188: PetscErrorCode EPSSetWorkVecs(EPS eps,PetscInt nw)
189: {
190: Vec t;
192: PetscFunctionBegin;
195: PetscCheck(nw>0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"nw must be > 0: nw = %" PetscInt_FMT,nw);
196: if (eps->nwork < nw) {
197: PetscCall(VecDestroyVecs(eps->nwork,&eps->work));
198: eps->nwork = nw;
199: PetscCall(BVGetColumn(eps->V,0,&t));
200: PetscCall(VecDuplicateVecs(t,nw,&eps->work));
201: PetscCall(BVRestoreColumn(eps->V,0,&t));
202: }
203: PetscFunctionReturn(PETSC_SUCCESS);
204: }
206: /*
207: EPSSetWhichEigenpairs_Default - Sets the default value for which,
208: depending on the ST.
209: */
210: PetscErrorCode EPSSetWhichEigenpairs_Default(EPS eps)
211: {
212: PetscBool target;
214: PetscFunctionBegin;
215: PetscCall(PetscObjectTypeCompareAny((PetscObject)eps->st,&target,STSINVERT,STCAYLEY,""));
216: if (target) eps->which = EPS_TARGET_MAGNITUDE;
217: else eps->which = EPS_LARGEST_MAGNITUDE;
218: PetscFunctionReturn(PETSC_SUCCESS);
219: }
221: /*
222: EPSConvergedRelative - Checks convergence relative to the eigenvalue.
223: */
224: PetscErrorCode EPSConvergedRelative(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
225: {
226: PetscReal w;
228: PetscFunctionBegin;
229: w = SlepcAbsEigenvalue(eigr,eigi);
230: *errest = res/w;
231: PetscFunctionReturn(PETSC_SUCCESS);
232: }
234: /*
235: EPSConvergedAbsolute - Checks convergence absolutely.
236: */
237: PetscErrorCode EPSConvergedAbsolute(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
238: {
239: PetscFunctionBegin;
240: *errest = res;
241: PetscFunctionReturn(PETSC_SUCCESS);
242: }
244: /*
245: EPSConvergedNorm - Checks convergence relative to the eigenvalue and
246: the matrix norms.
247: */
248: PetscErrorCode EPSConvergedNorm(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
249: {
250: PetscReal w;
252: PetscFunctionBegin;
253: w = SlepcAbsEigenvalue(eigr,eigi);
254: *errest = res / (eps->nrma + w*eps->nrmb);
255: PetscFunctionReturn(PETSC_SUCCESS);
256: }
258: /*@C
259: EPSStoppingBasic - Default routine to determine whether the outer eigensolver
260: iteration must be stopped.
262: Collective
264: Input Parameters:
265: + eps - eigensolver context obtained from EPSCreate()
266: . its - current number of iterations
267: . max_it - maximum number of iterations
268: . nconv - number of currently converged eigenpairs
269: . nev - number of requested eigenpairs
270: - ctx - context (not used here)
272: Output Parameter:
273: . reason - result of the stopping test
275: Notes:
276: A positive value of reason indicates that the iteration has finished successfully
277: (converged), and a negative value indicates an error condition (diverged). If
278: the iteration needs to be continued, reason must be set to EPS_CONVERGED_ITERATING
279: (zero).
281: EPSStoppingBasic() will stop if all requested eigenvalues are converged, or if
282: the maximum number of iterations has been reached.
284: Use EPSSetStoppingTest() to provide your own test instead of using this one.
286: Level: advanced
288: .seealso: EPSSetStoppingTest(), EPSConvergedReason, EPSGetConvergedReason()
289: @*/
290: PetscErrorCode EPSStoppingBasic(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
291: {
292: PetscFunctionBegin;
293: *reason = EPS_CONVERGED_ITERATING;
294: if (nconv >= nev) {
295: PetscCall(PetscInfo(eps,"Linear eigensolver finished successfully: %" PetscInt_FMT " eigenpairs converged at iteration %" PetscInt_FMT "\n",nconv,its));
296: *reason = EPS_CONVERGED_TOL;
297: } else if (its >= max_it) {
298: *reason = EPS_DIVERGED_ITS;
299: PetscCall(PetscInfo(eps,"Linear eigensolver iteration reached maximum number of iterations (%" PetscInt_FMT ")\n",its));
300: }
301: PetscFunctionReturn(PETSC_SUCCESS);
302: }
304: /*
305: EPSComputeRitzVector - Computes the current Ritz vector.
307: Simple case (complex scalars or real scalars with Zi=NULL):
308: x = V*Zr (V is a basis of nv vectors, Zr has length nv)
310: Split case:
311: x = V*Zr y = V*Zi (Zr and Zi have length nv)
312: */
313: PetscErrorCode EPSComputeRitzVector(EPS eps,PetscScalar *Zr,PetscScalar *Zi,BV V,Vec x,Vec y)
314: {
315: PetscInt l,k;
316: PetscReal norm;
317: #if !defined(PETSC_USE_COMPLEX)
318: Vec z;
319: #endif
321: PetscFunctionBegin;
322: /* compute eigenvector */
323: PetscCall(BVGetActiveColumns(V,&l,&k));
324: PetscCall(BVSetActiveColumns(V,0,k));
325: PetscCall(BVMultVec(V,1.0,0.0,x,Zr));
327: /* purify eigenvector if necessary */
328: if (eps->purify) {
329: PetscCall(STApply(eps->st,x,y));
330: if (eps->ishermitian) PetscCall(BVNormVec(eps->V,y,NORM_2,&norm));
331: else PetscCall(VecNorm(y,NORM_2,&norm));
332: PetscCall(VecScale(y,1.0/norm));
333: PetscCall(VecCopy(y,x));
334: }
335: /* fix eigenvector if balancing is used */
336: if (!eps->ishermitian && eps->balance!=EPS_BALANCE_NONE && eps->D) PetscCall(VecPointwiseDivide(x,x,eps->D));
337: #if !defined(PETSC_USE_COMPLEX)
338: /* compute imaginary part of eigenvector */
339: if (Zi) {
340: PetscCall(BVMultVec(V,1.0,0.0,y,Zi));
341: if (eps->ispositive) {
342: PetscCall(BVCreateVec(V,&z));
343: PetscCall(STApply(eps->st,y,z));
344: PetscCall(VecNorm(z,NORM_2,&norm));
345: PetscCall(VecScale(z,1.0/norm));
346: PetscCall(VecCopy(z,y));
347: PetscCall(VecDestroy(&z));
348: }
349: if (eps->balance!=EPS_BALANCE_NONE && eps->D) PetscCall(VecPointwiseDivide(y,y,eps->D));
350: } else
351: #endif
352: PetscCall(VecSet(y,0.0));
354: /* normalize eigenvectors (when using balancing) */
355: if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
356: #if !defined(PETSC_USE_COMPLEX)
357: if (Zi) PetscCall(VecNormalizeComplex(x,y,PETSC_TRUE,NULL));
358: else
359: #endif
360: PetscCall(VecNormalize(x,NULL));
361: }
362: PetscCall(BVSetActiveColumns(V,l,k));
363: PetscFunctionReturn(PETSC_SUCCESS);
364: }
366: /*
367: EPSBuildBalance_Krylov - uses a Krylov subspace method to compute the
368: diagonal matrix to be applied for balancing in non-Hermitian problems.
369: */
370: PetscErrorCode EPSBuildBalance_Krylov(EPS eps)
371: {
372: Vec z,p,r;
373: PetscInt i,j;
374: PetscReal norma;
375: PetscScalar *pz,*pD;
376: const PetscScalar *pr,*pp;
377: PetscRandom rand;
379: PetscFunctionBegin;
380: PetscCall(EPSSetWorkVecs(eps,3));
381: PetscCall(BVGetRandomContext(eps->V,&rand));
382: r = eps->work[0];
383: p = eps->work[1];
384: z = eps->work[2];
385: PetscCall(VecSet(eps->D,1.0));
387: for (j=0;j<eps->balance_its;j++) {
389: /* Build a random vector of +-1's */
390: PetscCall(VecSetRandom(z,rand));
391: PetscCall(VecGetArray(z,&pz));
392: for (i=0;i<eps->nloc;i++) {
393: if (PetscRealPart(pz[i])<0.5) pz[i]=-1.0;
394: else pz[i]=1.0;
395: }
396: PetscCall(VecRestoreArray(z,&pz));
398: /* Compute p=DA(D\z) */
399: PetscCall(VecPointwiseDivide(r,z,eps->D));
400: PetscCall(STApply(eps->st,r,p));
401: PetscCall(VecPointwiseMult(p,p,eps->D));
402: if (eps->balance == EPS_BALANCE_TWOSIDE) {
403: if (j==0) {
404: /* Estimate the matrix inf-norm */
405: PetscCall(VecAbs(p));
406: PetscCall(VecMax(p,NULL,&norma));
407: }
408: /* Compute r=D\(A'Dz) */
409: PetscCall(VecPointwiseMult(z,z,eps->D));
410: PetscCall(STApplyHermitianTranspose(eps->st,z,r));
411: PetscCall(VecPointwiseDivide(r,r,eps->D));
412: }
414: /* Adjust values of D */
415: PetscCall(VecGetArrayRead(r,&pr));
416: PetscCall(VecGetArrayRead(p,&pp));
417: PetscCall(VecGetArray(eps->D,&pD));
418: for (i=0;i<eps->nloc;i++) {
419: if (eps->balance == EPS_BALANCE_TWOSIDE) {
420: if (PetscAbsScalar(pp[i])>eps->balance_cutoff*norma && pr[i]!=0.0)
421: pD[i] *= PetscSqrtReal(PetscAbsScalar(pr[i]/pp[i]));
422: } else {
423: if (pp[i]!=0.0) pD[i] /= PetscAbsScalar(pp[i]);
424: }
425: }
426: PetscCall(VecRestoreArrayRead(r,&pr));
427: PetscCall(VecRestoreArrayRead(p,&pp));
428: PetscCall(VecRestoreArray(eps->D,&pD));
429: }
430: PetscFunctionReturn(PETSC_SUCCESS);
431: }