Actual source code: epsdefault.c
slepc-3.18.2 2023-01-26
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: STBackTransform(eps->st,eps->nconv,eps->eigr,eps->eigi);
20: return 0;
21: }
23: /*
24: EPSComputeVectors_Hermitian - Copies the Lanczos vectors as eigenvectors
25: using purification for generalized eigenproblems.
26: */
27: PetscErrorCode EPSComputeVectors_Hermitian(EPS eps)
28: {
29: PetscBool iscayley,indef;
30: Mat B,C;
32: if (eps->purify) {
33: EPS_Purify(eps,eps->nconv);
34: BVNormalize(eps->V,NULL);
35: } else {
36: /* In the case of Cayley transform, eigenvectors need to be B-normalized */
37: PetscObjectTypeCompare((PetscObject)eps->st,STCAYLEY,&iscayley);
38: if (iscayley && eps->isgeneralized) {
39: STGetMatrix(eps->st,1,&B);
40: BVGetMatrix(eps->V,&C,&indef);
42: BVSetMatrix(eps->V,B,PETSC_FALSE);
43: BVNormalize(eps->V,NULL);
44: BVSetMatrix(eps->V,C,PETSC_FALSE); /* restore original matrix */
45: }
46: }
47: return 0;
48: }
50: /*
51: EPSComputeVectors_Indefinite - similar to the Schur version but
52: for indefinite problems
53: */
54: PetscErrorCode EPSComputeVectors_Indefinite(EPS eps)
55: {
56: PetscInt n;
57: Mat X;
59: DSGetDimensions(eps->ds,&n,NULL,NULL,NULL);
60: DSVectors(eps->ds,DS_MAT_X,NULL,NULL);
61: DSGetMat(eps->ds,DS_MAT_X,&X);
62: BVMultInPlace(eps->V,X,0,n);
63: DSRestoreMat(eps->ds,DS_MAT_X,&X);
65: /* purification */
66: if (eps->purify) EPS_Purify(eps,eps->nconv);
68: /* normalization */
69: BVNormalize(eps->V,eps->eigi);
70: return 0;
71: }
73: /*
74: EPSComputeVectors_Twosided - Adjust left eigenvectors in generalized problems: y = B^-* y.
75: */
76: PetscErrorCode EPSComputeVectors_Twosided(EPS eps)
77: {
78: PetscInt i;
79: Vec w,y;
81: if (!eps->twosided || !eps->isgeneralized) return 0;
82: EPSSetWorkVecs(eps,1);
83: w = eps->work[0];
84: for (i=0;i<eps->nconv;i++) {
85: BVCopyVec(eps->W,i,w);
86: VecConjugate(w);
87: BVGetColumn(eps->W,i,&y);
88: STMatSolveTranspose(eps->st,w,y);
89: VecConjugate(y);
90: BVRestoreColumn(eps->W,i,&y);
91: }
92: return 0;
93: }
95: /*
96: EPSComputeVectors_Schur - Compute eigenvectors from the vectors
97: provided by the eigensolver. This version is intended for solvers
98: that provide Schur vectors. Given the partial Schur decomposition
99: OP*V=V*T, the following steps are performed:
100: 1) compute eigenvectors of T: T*Z=Z*D
101: 2) compute eigenvectors of OP: X=V*Z
102: */
103: PetscErrorCode EPSComputeVectors_Schur(EPS eps)
104: {
105: PetscInt i;
106: Mat Z;
107: Vec z;
109: if (eps->ishermitian) {
110: if (eps->isgeneralized && !eps->ispositive) EPSComputeVectors_Indefinite(eps);
111: else EPSComputeVectors_Hermitian(eps);
112: return 0;
113: }
115: /* right eigenvectors */
116: DSVectors(eps->ds,DS_MAT_X,NULL,NULL);
118: /* V = V * Z */
119: DSGetMat(eps->ds,DS_MAT_X,&Z);
120: BVMultInPlace(eps->V,Z,0,eps->nconv);
121: DSRestoreMat(eps->ds,DS_MAT_X,&Z);
123: /* Purify eigenvectors */
124: if (eps->purify) EPS_Purify(eps,eps->nconv);
126: /* Fix eigenvectors if balancing was used */
127: if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
128: for (i=0;i<eps->nconv;i++) {
129: BVGetColumn(eps->V,i,&z);
130: VecPointwiseDivide(z,z,eps->D);
131: BVRestoreColumn(eps->V,i,&z);
132: }
133: }
135: /* normalize eigenvectors (when using purification or balancing) */
136: if (eps->purify || (eps->balance!=EPS_BALANCE_NONE && eps->D)) BVNormalize(eps->V,eps->eigi);
138: /* left eigenvectors */
139: if (eps->twosided) {
140: DSVectors(eps->ds,DS_MAT_Y,NULL,NULL);
141: /* W = W * Z */
142: DSGetMat(eps->ds,DS_MAT_Y,&Z);
143: BVMultInPlace(eps->W,Z,0,eps->nconv);
144: DSRestoreMat(eps->ds,DS_MAT_Y,&Z);
145: /* Fix left eigenvectors if balancing was used */
146: if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
147: for (i=0;i<eps->nconv;i++) {
148: BVGetColumn(eps->W,i,&z);
149: VecPointwiseMult(z,z,eps->D);
150: BVRestoreColumn(eps->W,i,&z);
151: }
152: }
153: EPSComputeVectors_Twosided(eps);
154: /* normalize */
155: BVNormalize(eps->W,eps->eigi);
156: #if !defined(PETSC_USE_COMPLEX)
157: for (i=0;i<eps->nconv-1;i++) {
158: if (eps->eigi[i] != 0.0) {
159: if (eps->eigi[i] > 0.0) BVScaleColumn(eps->W,i+1,-1.0);
160: i++;
161: }
162: }
163: #endif
164: }
165: return 0;
166: }
168: /*@
169: EPSSetWorkVecs - Sets a number of work vectors into an EPS object.
171: Collective on eps
173: Input Parameters:
174: + eps - eigensolver context
175: - nw - number of work vectors to allocate
177: Developer Notes:
178: This is SLEPC_EXTERN because it may be required by user plugin EPS
179: implementations.
181: Level: developer
183: .seealso: EPSSetUp()
184: @*/
185: PetscErrorCode EPSSetWorkVecs(EPS eps,PetscInt nw)
186: {
187: Vec t;
192: if (eps->nwork < nw) {
193: VecDestroyVecs(eps->nwork,&eps->work);
194: eps->nwork = nw;
195: BVGetColumn(eps->V,0,&t);
196: VecDuplicateVecs(t,nw,&eps->work);
197: BVRestoreColumn(eps->V,0,&t);
198: }
199: return 0;
200: }
202: /*
203: EPSSetWhichEigenpairs_Default - Sets the default value for which,
204: depending on the ST.
205: */
206: PetscErrorCode EPSSetWhichEigenpairs_Default(EPS eps)
207: {
208: PetscBool target;
210: PetscObjectTypeCompareAny((PetscObject)eps->st,&target,STSINVERT,STCAYLEY,"");
211: if (target) eps->which = EPS_TARGET_MAGNITUDE;
212: else eps->which = EPS_LARGEST_MAGNITUDE;
213: return 0;
214: }
216: /*
217: EPSConvergedRelative - Checks convergence relative to the eigenvalue.
218: */
219: PetscErrorCode EPSConvergedRelative(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
220: {
221: PetscReal w;
223: w = SlepcAbsEigenvalue(eigr,eigi);
224: *errest = res/w;
225: return 0;
226: }
228: /*
229: EPSConvergedAbsolute - Checks convergence absolutely.
230: */
231: PetscErrorCode EPSConvergedAbsolute(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
232: {
233: *errest = res;
234: return 0;
235: }
237: /*
238: EPSConvergedNorm - Checks convergence relative to the eigenvalue and
239: the matrix norms.
240: */
241: PetscErrorCode EPSConvergedNorm(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,void *ctx)
242: {
243: PetscReal w;
245: w = SlepcAbsEigenvalue(eigr,eigi);
246: *errest = res / (eps->nrma + w*eps->nrmb);
247: return 0;
248: }
250: /*@C
251: EPSStoppingBasic - Default routine to determine whether the outer eigensolver
252: iteration must be stopped.
254: Collective on eps
256: Input Parameters:
257: + eps - eigensolver context obtained from EPSCreate()
258: . its - current number of iterations
259: . max_it - maximum number of iterations
260: . nconv - number of currently converged eigenpairs
261: . nev - number of requested eigenpairs
262: - ctx - context (not used here)
264: Output Parameter:
265: . reason - result of the stopping test
267: Notes:
268: A positive value of reason indicates that the iteration has finished successfully
269: (converged), and a negative value indicates an error condition (diverged). If
270: the iteration needs to be continued, reason must be set to EPS_CONVERGED_ITERATING
271: (zero).
273: EPSStoppingBasic() will stop if all requested eigenvalues are converged, or if
274: the maximum number of iterations has been reached.
276: Use EPSSetStoppingTest() to provide your own test instead of using this one.
278: Level: advanced
280: .seealso: EPSSetStoppingTest(), EPSConvergedReason, EPSGetConvergedReason()
281: @*/
282: PetscErrorCode EPSStoppingBasic(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,void *ctx)
283: {
284: *reason = EPS_CONVERGED_ITERATING;
285: if (nconv >= nev) {
286: PetscInfo(eps,"Linear eigensolver finished successfully: %" PetscInt_FMT " eigenpairs converged at iteration %" PetscInt_FMT "\n",nconv,its);
287: *reason = EPS_CONVERGED_TOL;
288: } else if (its >= max_it) {
289: *reason = EPS_DIVERGED_ITS;
290: PetscInfo(eps,"Linear eigensolver iteration reached maximum number of iterations (%" PetscInt_FMT ")\n",its);
291: }
292: return 0;
293: }
295: /*
296: EPSComputeRitzVector - Computes the current Ritz vector.
298: Simple case (complex scalars or real scalars with Zi=NULL):
299: x = V*Zr (V is a basis of nv vectors, Zr has length nv)
301: Split case:
302: x = V*Zr y = V*Zi (Zr and Zi have length nv)
303: */
304: PetscErrorCode EPSComputeRitzVector(EPS eps,PetscScalar *Zr,PetscScalar *Zi,BV V,Vec x,Vec y)
305: {
306: PetscInt l,k;
307: PetscReal norm;
308: #if !defined(PETSC_USE_COMPLEX)
309: Vec z;
310: #endif
312: /* compute eigenvector */
313: BVGetActiveColumns(V,&l,&k);
314: BVSetActiveColumns(V,0,k);
315: BVMultVec(V,1.0,0.0,x,Zr);
317: /* purify eigenvector if necessary */
318: if (eps->purify) {
319: STApply(eps->st,x,y);
320: if (eps->ishermitian) BVNormVec(eps->V,y,NORM_2,&norm);
321: else VecNorm(y,NORM_2,&norm);
322: VecScale(y,1.0/norm);
323: VecCopy(y,x);
324: }
325: /* fix eigenvector if balancing is used */
326: if (!eps->ishermitian && eps->balance!=EPS_BALANCE_NONE && eps->D) VecPointwiseDivide(x,x,eps->D);
327: #if !defined(PETSC_USE_COMPLEX)
328: /* compute imaginary part of eigenvector */
329: if (Zi) {
330: BVMultVec(V,1.0,0.0,y,Zi);
331: if (eps->ispositive) {
332: BVCreateVec(V,&z);
333: STApply(eps->st,y,z);
334: VecNorm(z,NORM_2,&norm);
335: VecScale(z,1.0/norm);
336: VecCopy(z,y);
337: VecDestroy(&z);
338: }
339: if (eps->balance!=EPS_BALANCE_NONE && eps->D) VecPointwiseDivide(y,y,eps->D);
340: } else
341: #endif
342: VecSet(y,0.0);
344: /* normalize eigenvectors (when using balancing) */
345: if (eps->balance!=EPS_BALANCE_NONE && eps->D) {
346: #if !defined(PETSC_USE_COMPLEX)
347: if (Zi) VecNormalizeComplex(x,y,PETSC_TRUE,NULL);
348: else
349: #endif
350: VecNormalize(x,NULL);
351: }
352: BVSetActiveColumns(V,l,k);
353: return 0;
354: }
356: /*
357: EPSBuildBalance_Krylov - uses a Krylov subspace method to compute the
358: diagonal matrix to be applied for balancing in non-Hermitian problems.
359: */
360: PetscErrorCode EPSBuildBalance_Krylov(EPS eps)
361: {
362: Vec z,p,r;
363: PetscInt i,j;
364: PetscReal norma;
365: PetscScalar *pz,*pD;
366: const PetscScalar *pr,*pp;
367: PetscRandom rand;
369: EPSSetWorkVecs(eps,3);
370: BVGetRandomContext(eps->V,&rand);
371: r = eps->work[0];
372: p = eps->work[1];
373: z = eps->work[2];
374: VecSet(eps->D,1.0);
376: for (j=0;j<eps->balance_its;j++) {
378: /* Build a random vector of +-1's */
379: VecSetRandom(z,rand);
380: VecGetArray(z,&pz);
381: for (i=0;i<eps->nloc;i++) {
382: if (PetscRealPart(pz[i])<0.5) pz[i]=-1.0;
383: else pz[i]=1.0;
384: }
385: VecRestoreArray(z,&pz);
387: /* Compute p=DA(D\z) */
388: VecPointwiseDivide(r,z,eps->D);
389: STApply(eps->st,r,p);
390: VecPointwiseMult(p,p,eps->D);
391: if (eps->balance == EPS_BALANCE_TWOSIDE) {
392: if (j==0) {
393: /* Estimate the matrix inf-norm */
394: VecAbs(p);
395: VecMax(p,NULL,&norma);
396: }
397: /* Compute r=D\(A'Dz) */
398: VecPointwiseMult(z,z,eps->D);
399: STApplyHermitianTranspose(eps->st,z,r);
400: VecPointwiseDivide(r,r,eps->D);
401: }
403: /* Adjust values of D */
404: VecGetArrayRead(r,&pr);
405: VecGetArrayRead(p,&pp);
406: VecGetArray(eps->D,&pD);
407: for (i=0;i<eps->nloc;i++) {
408: if (eps->balance == EPS_BALANCE_TWOSIDE) {
409: if (PetscAbsScalar(pp[i])>eps->balance_cutoff*norma && pr[i]!=0.0)
410: pD[i] *= PetscSqrtReal(PetscAbsScalar(pr[i]/pp[i]));
411: } else {
412: if (pp[i]!=0.0) pD[i] /= PetscAbsScalar(pp[i]);
413: }
414: }
415: VecRestoreArrayRead(r,&pr);
416: VecRestoreArrayRead(p,&pp);
417: VecRestoreArray(eps->D,&pD);
418: }
419: return 0;
420: }