Actual source code: power.c
1: /*
3: SLEPc eigensolver: "power"
5: Method: Power Iteration
7: Algorithm:
9: This solver implements the power iteration for finding dominant
10: eigenpairs. It also includes the following well-known methods:
11: - Inverse Iteration: when used in combination with shift-and-invert
12: spectral transformation.
13: - Rayleigh Quotient Iteration (RQI): also with shift-and-invert plus
14: a variable shift.
16: References:
18: [1] "Single Vector Iteration Methods in SLEPc", SLEPc Technical Report STR-2,
19: available at http://www.grycap.upv.es/slepc.
21: Last update: Feb 2009
23: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
24: SLEPc - Scalable Library for Eigenvalue Problem Computations
25: Copyright (c) 2002-2011, Universitat Politecnica de Valencia, Spain
27: This file is part of SLEPc.
28:
29: SLEPc is free software: you can redistribute it and/or modify it under the
30: terms of version 3 of the GNU Lesser General Public License as published by
31: the Free Software Foundation.
33: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
34: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
35: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
36: more details.
38: You should have received a copy of the GNU Lesser General Public License
39: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
40: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
41: */
43: #include <private/epsimpl.h> /*I "slepceps.h" I*/
44: #include <slepcblaslapack.h>
46: PetscErrorCode EPSSolve_Power(EPS);
47: PetscErrorCode EPSSolve_TS_Power(EPS);
49: typedef struct {
50: EPSPowerShiftType shift_type;
51: } EPS_POWER;
55: PetscErrorCode EPSSetUp_Power(EPS eps)
56: {
58: EPS_POWER *power = (EPS_POWER *)eps->data;
59: PetscBool flg;
60: STMatMode mode;
63: if (eps->ncv) {
64: if (eps->ncv<eps->nev) SETERRQ(((PetscObject)eps)->comm,1,"The value of ncv must be at least nev");
65: }
66: else eps->ncv = eps->nev;
67: if (eps->mpd) { PetscInfo(eps,"Warning: parameter mpd ignored\n"); }
68: if (!eps->max_it) eps->max_it = PetscMax(2000,100*eps->n);
69: if (!eps->which) { EPSDefaultSetWhich(eps); }
70: if (eps->which!=EPS_LARGEST_MAGNITUDE && eps->which !=EPS_TARGET_MAGNITUDE)
71: SETERRQ(((PetscObject)eps)->comm,1,"Wrong value of eps->which");
72: if (power->shift_type != EPS_POWER_SHIFT_CONSTANT) {
73: PetscTypeCompareAny((PetscObject)eps->OP,&flg,STSINVERT,STCAYLEY,"");
74: if (!flg)
75: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Variable shifts only allowed in shift-and-invert or Cayley ST");
76: STGetMatMode(eps->OP,&mode);
77: if (mode == ST_MATMODE_INPLACE)
78: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"ST matrix mode inplace does not work with variable shifts");
79: }
80: if (eps->extraction) { PetscInfo(eps,"Warning: extraction type ignored\n"); }
81: if (eps->balance!=EPS_BALANCE_NONE)
82: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Balancing not supported in this solver");
83: EPSAllocateSolution(eps);
84: if (eps->leftvecs) {
85: EPSDefaultGetWork(eps,3);
86: } else {
87: EPSDefaultGetWork(eps,2);
88: }
90: /* dispatch solve method */
91: if (eps->leftvecs) eps->ops->solve = EPSSolve_TS_Power;
92: else eps->ops->solve = EPSSolve_Power;
93: return(0);
94: }
98: PetscErrorCode EPSSolve_Power(EPS eps)
99: {
101: EPS_POWER *power = (EPS_POWER *)eps->data;
102: PetscInt i;
103: Vec v,y,e;
104: Mat A;
105: PetscReal relerr,norm,rt1,rt2,cs1,anorm;
106: PetscScalar theta,rho,delta,sigma,alpha2,beta1,sn1;
107: PetscBool breakdown,*select = PETSC_NULL,hasnorm;
110: v = eps->V[0];
111: y = eps->work[1];
112: e = eps->work[0];
114: /* prepare for selective orthogonalization of converged vectors */
115: if (power->shift_type != EPS_POWER_SHIFT_CONSTANT && eps->nev>1) {
116: STGetOperators(eps->OP,&A,PETSC_NULL);
117: MatHasOperation(A,MATOP_NORM,&hasnorm);
118: if (hasnorm) {
119: MatNorm(A,NORM_INFINITY,&anorm);
120: PetscMalloc(eps->nev*sizeof(PetscBool),&select);
121: }
122: }
124: EPSGetStartVector(eps,0,v,PETSC_NULL);
125: STGetShift(eps->OP,&sigma); /* original shift */
126: rho = sigma;
128: while (eps->reason == EPS_CONVERGED_ITERATING) {
129: eps->its = eps->its + 1;
131: /* y = OP v */
132: STApply(eps->OP,v,y);
134: /* theta = (v,y)_B */
135: IPInnerProduct(eps->ip,v,y,&theta);
137: if (power->shift_type == EPS_POWER_SHIFT_CONSTANT) { /* direct & inverse iteration */
139: /* approximate eigenvalue is the Rayleigh quotient */
140: eps->eigr[eps->nconv] = theta;
142: /* compute relative error as ||y-theta v||_2/|theta| */
143: VecCopy(y,e);
144: VecAXPY(e,-theta,v);
145: VecNorm(e,NORM_2,&norm);
146: relerr = norm / PetscAbsScalar(theta);
148: } else { /* RQI */
150: /* delta = ||y||_B */
151: IPNorm(eps->ip,y,&norm);
152: delta = norm;
154: /* compute relative error */
155: if (rho == 0.0) relerr = PETSC_MAX_REAL;
156: else relerr = 1.0 / (norm*PetscAbsScalar(rho));
158: /* approximate eigenvalue is the shift */
159: eps->eigr[eps->nconv] = rho;
161: /* compute new shift */
162: if (relerr<eps->tol) {
163: rho = sigma; /* if converged, restore original shift */
164: STSetShift(eps->OP,rho);
165: } else {
166: rho = rho + theta/(delta*delta); /* Rayleigh quotient R(v) */
167: if (power->shift_type == EPS_POWER_SHIFT_WILKINSON) {
168: #if defined(SLEPC_MISSING_LAPACK_LAEV2)
169: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"LAEV2 - Lapack routine is unavailable.");
170: #else
171: /* beta1 is the norm of the residual associated to R(v) */
172: VecAXPY(v,-theta/(delta*delta),y);
173: VecScale(v,1.0/delta);
174: IPNorm(eps->ip,v,&norm);
175: beta1 = norm;
176:
177: /* alpha2 = (e'*A*e)/(beta1*beta1), where e is the residual */
178: STGetOperators(eps->OP,&A,PETSC_NULL);
179: MatMult(A,v,e);
180: VecDot(v,e,&alpha2);
181: alpha2 = alpha2 / (beta1 * beta1);
183: /* choose the eigenvalue of [rho beta1; beta1 alpha2] closest to rho */
184: LAPACKlaev2_(&rho,&beta1,&alpha2,&rt1,&rt2,&cs1,&sn1);
185: if (PetscAbsScalar(rt1-rho) < PetscAbsScalar(rt2-rho)) rho = rt1;
186: else rho = rt2;
187: #endif
188: }
189: /* update operator according to new shift */
190: PetscPushErrorHandler(PetscIgnoreErrorHandler,PETSC_NULL);
191: STSetShift(eps->OP,rho);
192: PetscPopErrorHandler();
193: if (ierr) {
194: eps->eigr[eps->nconv] = rho;
195: relerr = PETSC_MACHINE_EPSILON;
196: rho = sigma;
197: STSetShift(eps->OP,rho);
198: }
199: }
200: }
202: eps->errest[eps->nconv] = relerr;
203: EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,eps->nconv+1);
205: /* purge previously converged eigenvectors */
206: if (select) {
207: for (i=0;i<eps->nconv;i++) {
208: if(PetscAbsScalar(rho-eps->eigr[i])>eps->its*anorm/1000) select[i] = PETSC_TRUE;
209: else select[i] = PETSC_FALSE;
210: }
211: IPOrthogonalize(eps->ip,eps->nds,eps->DS,eps->nconv,select,eps->V,y,PETSC_NULL,&norm,PETSC_NULL);
212: } else {
213: IPOrthogonalize(eps->ip,eps->nds,eps->DS,eps->nconv,PETSC_NULL,eps->V,y,PETSC_NULL,&norm,PETSC_NULL);
214: }
216: /* v = y/||y||_B */
217: VecCopy(y,v);
218: VecScale(v,1.0/norm);
220: /* if relerr<tol, accept eigenpair */
221: if (relerr<eps->tol) {
222: eps->nconv = eps->nconv + 1;
223: if (eps->nconv==eps->nev) eps->reason = EPS_CONVERGED_TOL;
224: else {
225: v = eps->V[eps->nconv];
226: EPSGetStartVector(eps,eps->nconv,v,&breakdown);
227: if (breakdown) {
228: eps->reason = EPS_DIVERGED_BREAKDOWN;
229: PetscInfo(eps,"Unable to generate more start vectors\n");
230: }
231: }
232: }
233: if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
234: }
235: PetscFree(select);
236: return(0);
237: }
241: PetscErrorCode EPSSolve_TS_Power(EPS eps)
242: {
244: EPS_POWER *power = (EPS_POWER *)eps->data;
245: Vec v,w,y,z,e;
246: Mat A;
247: PetscReal relerr,norm,rt1,rt2,cs1;
248: PetscScalar theta,alpha,beta,rho,delta,sigma,alpha2,beta1,sn1;
251: v = eps->V[0];
252: y = eps->work[1];
253: e = eps->work[0];
254: w = eps->W[0];
255: z = eps->work[2];
257: EPSGetStartVector(eps,0,v,PETSC_NULL);
258: EPSGetStartVectorLeft(eps,0,w,PETSC_NULL);
259: STGetShift(eps->OP,&sigma); /* original shift */
260: rho = sigma;
262: while (eps->its<eps->max_it) {
263: eps->its++;
264:
265: /* y = OP v, z = OP' w */
266: STApply(eps->OP,v,y);
267: STApplyTranspose(eps->OP,w,z);
269: /* theta = (v,z)_B */
270: IPInnerProduct(eps->ip,v,z,&theta);
272: if (power->shift_type == EPS_POWER_SHIFT_CONSTANT) { /* direct & inverse iteration */
274: /* approximate eigenvalue is the Rayleigh quotient */
275: eps->eigr[eps->nconv] = theta;
277: /* compute relative errors (right and left) */
278: VecCopy(y,e);
279: VecAXPY(e,-theta,v);
280: VecNorm(e,NORM_2,&norm);
281: relerr = norm / PetscAbsScalar(theta);
282: eps->errest[eps->nconv] = relerr;
283: VecCopy(z,e);
284: VecAXPY(e,-theta,w);
285: VecNorm(e,NORM_2,&norm);
286: relerr = norm / PetscAbsScalar(theta);
287: eps->errest_left[eps->nconv] = relerr;
289: } else { /* RQI */
291: /* delta = sqrt(y,z)_B */
292: IPInnerProduct(eps->ip,y,z,&alpha);
293: if (alpha==0.0) SETERRQ(((PetscObject)eps)->comm,1,"Breakdown in two-sided Power/RQI");
294: delta = PetscSqrtScalar(alpha);
296: /* compute relative error */
297: if (rho == 0.0) relerr = PETSC_MAX_REAL;
298: else relerr = 1.0 / (PetscAbsScalar(delta*rho));
299: eps->errest[eps->nconv] = relerr;
300: eps->errest_left[eps->nconv] = relerr;
302: /* approximate eigenvalue is the shift */
303: eps->eigr[eps->nconv] = rho;
305: /* compute new shift */
306: if (eps->errest[eps->nconv]<eps->tol && eps->errest_left[eps->nconv]<eps->tol) {
307: rho = sigma; /* if converged, restore original shift */
308: STSetShift(eps->OP,rho);
309: } else {
310: rho = rho + theta/(delta*delta); /* Rayleigh quotient R(v,w) */
311: if (power->shift_type == EPS_POWER_SHIFT_WILKINSON) {
312: #if defined(SLEPC_MISSING_LAPACK_LAEV2)
313: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"LAEV2 - Lapack routine is unavailable.");
314: #else
315: /* beta1 is the norm of the residual associated to R(v,w) */
316: VecAXPY(v,-theta/(delta*delta),y);
317: VecScale(v,1.0/delta);
318: IPNorm(eps->ip,v,&norm);
319: beta1 = norm;
320:
321: /* alpha2 = (e'*A*e)/(beta1*beta1), where e is the residual */
322: STGetOperators(eps->OP,&A,PETSC_NULL);
323: MatMult(A,v,e);
324: VecDot(v,e,&alpha2);
325: alpha2 = alpha2 / (beta1 * beta1);
327: /* choose the eigenvalue of [rho beta1; beta1 alpha2] closest to rho */
328: LAPACKlaev2_(&rho,&beta1,&alpha2,&rt1,&rt2,&cs1,&sn1);
329: if (PetscAbsScalar(rt1-rho) < PetscAbsScalar(rt2-rho)) rho = rt1;
330: else rho = rt2;
331: #endif
332: }
333: /* update operator according to new shift */
334: PetscPushErrorHandler(PetscIgnoreErrorHandler,PETSC_NULL);
335: STSetShift(eps->OP,rho);
336: PetscPopErrorHandler();
337: if (ierr) {
338: eps->eigr[eps->nconv] = rho;
339: eps->errest[eps->nconv] = PETSC_MACHINE_EPSILON;
340: eps->errest_left[eps->nconv] = PETSC_MACHINE_EPSILON;
341: rho = sigma;
342: STSetShift(eps->OP,rho);
343: }
344: }
345: }
347: EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,eps->nconv+1);
348: EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest_left,eps->nconv+1);
350: /* purge previously converged eigenvectors */
351: IPBiOrthogonalize(eps->ip,eps->nconv,eps->V,eps->W,z,PETSC_NULL,PETSC_NULL);
352: IPBiOrthogonalize(eps->ip,eps->nconv,eps->W,eps->V,y,PETSC_NULL,PETSC_NULL);
354: /* normalize so that (y,z)_B=1 */
355: VecCopy(y,v);
356: VecCopy(z,w);
357: IPInnerProduct(eps->ip,y,z,&alpha);
358: if (alpha==0.0) SETERRQ(((PetscObject)eps)->comm,1,"Breakdown in two-sided Power/RQI");
359: delta = PetscSqrtScalar(PetscAbsScalar(alpha));
360: beta = 1.0/PetscConj(alpha/delta);
361: delta = 1.0/delta;
362: VecScale(w,beta);
363: VecScale(v,delta);
365: /* if relerr<tol (both right and left), accept eigenpair */
366: if (eps->errest[eps->nconv]<eps->tol && eps->errest_left[eps->nconv]<eps->tol) {
367: eps->nconv = eps->nconv + 1;
368: if (eps->nconv==eps->nev) break;
369: v = eps->V[eps->nconv];
370: EPSGetStartVector(eps,eps->nconv,v,PETSC_NULL);
371: w = eps->W[eps->nconv];
372: EPSGetStartVectorLeft(eps,eps->nconv,w,PETSC_NULL);
373: }
374: }
375: if (eps->nconv == eps->nev) eps->reason = EPS_CONVERGED_TOL;
376: else eps->reason = EPS_DIVERGED_ITS;
377: return(0);
378: }
382: PetscErrorCode EPSBackTransform_Power(EPS eps)
383: {
385: EPS_POWER *power = (EPS_POWER *)eps->data;
388: if (power->shift_type == EPS_POWER_SHIFT_CONSTANT) {
389: EPSBackTransform_Default(eps);
390: }
391: return(0);
392: }
396: PetscErrorCode EPSSetFromOptions_Power(EPS eps)
397: {
398: PetscErrorCode ierr;
399: EPS_POWER *power = (EPS_POWER *)eps->data;
400: PetscBool flg;
401: EPSPowerShiftType shift;
404: PetscOptionsHead("EPS Power Options");
405: PetscOptionsEnum("-eps_power_shift_type","Shift type","EPSPowerSetShiftType",EPSPowerShiftTypes,(PetscEnum)power->shift_type,(PetscEnum*)&shift,&flg);
406: if (flg) { EPSPowerSetShiftType(eps,shift); }
407: if (power->shift_type != EPS_POWER_SHIFT_CONSTANT) {
408: STSetType(eps->OP,STSINVERT);
409: }
410: PetscOptionsTail();
411: return(0);
412: }
417: PetscErrorCode EPSPowerSetShiftType_Power(EPS eps,EPSPowerShiftType shift)
418: {
419: EPS_POWER *power = (EPS_POWER *)eps->data;
422: switch (shift) {
423: case EPS_POWER_SHIFT_CONSTANT:
424: case EPS_POWER_SHIFT_RAYLEIGH:
425: case EPS_POWER_SHIFT_WILKINSON:
426: power->shift_type = shift;
427: break;
428: default:
429: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid shift type");
430: }
431: return(0);
432: }
437: /*@
438: EPSPowerSetShiftType - Sets the type of shifts used during the power
439: iteration. This can be used to emulate the Rayleigh Quotient Iteration
440: (RQI) method.
442: Logically Collective on EPS
444: Input Parameters:
445: + eps - the eigenproblem solver context
446: - shift - the type of shift
448: Options Database Key:
449: . -eps_power_shift_type - Sets the shift type (either 'constant' or
450: 'rayleigh' or 'wilkinson')
452: Notes:
453: By default, shifts are constant (EPS_POWER_SHIFT_CONSTANT) and the iteration
454: is the simple power method (or inverse iteration if a shift-and-invert
455: transformation is being used).
457: A variable shift can be specified (EPS_POWER_SHIFT_RAYLEIGH or
458: EPS_POWER_SHIFT_WILKINSON). In this case, the iteration behaves rather like
459: a cubic converging method as RQI. See the users manual for details.
460:
461: Level: advanced
463: .seealso: EPSPowerGetShiftType(), STSetShift(), EPSPowerShiftType
464: @*/
465: PetscErrorCode EPSPowerSetShiftType(EPS eps,EPSPowerShiftType shift)
466: {
472: PetscTryMethod(eps,"EPSPowerSetShiftType_C",(EPS,EPSPowerShiftType),(eps,shift));
473: return(0);
474: }
479: PetscErrorCode EPSPowerGetShiftType_Power(EPS eps,EPSPowerShiftType *shift)
480: {
481: EPS_POWER *power = (EPS_POWER *)eps->data;
484: *shift = power->shift_type;
485: return(0);
486: }
491: /*@C
492: EPSPowerGetShiftType - Gets the type of shifts used during the power
493: iteration.
495: Not Collective
497: Input Parameter:
498: . eps - the eigenproblem solver context
500: Input Parameter:
501: . shift - the type of shift
503: Level: advanced
505: .seealso: EPSPowerSetShiftType(), EPSPowerShiftType
506: @*/
507: PetscErrorCode EPSPowerGetShiftType(EPS eps,EPSPowerShiftType *shift)
508: {
514: PetscTryMethod(eps,"EPSPowerGetShiftType_C",(EPS,EPSPowerShiftType*),(eps,shift));
515: return(0);
516: }
520: PetscErrorCode EPSDestroy_Power(EPS eps)
521: {
525: PetscFree(eps->data);
526: PetscObjectComposeFunctionDynamic((PetscObject)eps,"EPSPowerSetShiftType_C","",PETSC_NULL);
527: PetscObjectComposeFunctionDynamic((PetscObject)eps,"EPSPowerGetShiftType_C","",PETSC_NULL);
528: return(0);
529: }
533: PetscErrorCode EPSView_Power(EPS eps,PetscViewer viewer)
534: {
536: EPS_POWER *power = (EPS_POWER *)eps->data;
537: PetscBool isascii;
540: PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
541: if (!isascii) {
542: SETERRQ1(((PetscObject)eps)->comm,1,"Viewer type %s not supported for EPS Power",((PetscObject)viewer)->type_name);
543: }
544: PetscViewerASCIIPrintf(viewer," Power: %s shifts\n",EPSPowerShiftTypes[power->shift_type]);
545: return(0);
546: }
551: PetscErrorCode EPSCreate_Power(EPS eps)
552: {
556: PetscNewLog(eps,EPS_POWER,&eps->data);
557: eps->ops->setup = EPSSetUp_Power;
558: eps->ops->setfromoptions = EPSSetFromOptions_Power;
559: eps->ops->destroy = EPSDestroy_Power;
560: eps->ops->reset = EPSReset_Default;
561: eps->ops->view = EPSView_Power;
562: eps->ops->backtransform = EPSBackTransform_Power;
563: eps->ops->computevectors = EPSComputeVectors_Default;
564: PetscObjectComposeFunctionDynamic((PetscObject)eps,"EPSPowerSetShiftType_C","EPSPowerSetShiftType_Power",EPSPowerSetShiftType_Power);
565: PetscObjectComposeFunctionDynamic((PetscObject)eps,"EPSPowerGetShiftType_C","EPSPowerGetShiftType_Power",EPSPowerGetShiftType_Power);
566: return(0);
567: }