Actual source code: ks-twosided.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: SLEPc eigensolver: "krylovschur"
13: Method: Two-sided Arnoldi with Krylov-Schur restart (for left eigenvectors)
15: References:
17: [1] I.N. Zwaan and M.E. Hochstenbach, "Krylov-Schur-type restarts
18: for the two-sided Arnoldi method", SIAM J. Matrix Anal. Appl.
19: 38(2):297-321, 2017.
21: */
23: #include <slepc/private/epsimpl.h>
24: #include "krylovschur.h"
25: #include <slepcblaslapack.h>
27: static PetscErrorCode EPSTwoSidedRQUpdate1(EPS eps,Mat M,PetscInt nv)
28: {
29: #if defined(PETSC_MISSING_LAPACK_GETRF) || defined(PETSC_MISSING_LAPACK_GETRS)
31: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"GETRF/GETRS - Lapack routines are unavailable");
32: #else
34: PetscScalar *T,*S,*A,*w,*pM,beta;
35: Vec u;
36: PetscInt ld,ncv=eps->ncv,i;
37: PetscBLASInt info,n_,ncv_,*p,one=1;
40: DSGetLeadingDimension(eps->ds,&ld);
41: PetscMalloc3(nv,&p,ncv*ncv,&A,ncv,&w);
42: BVSetActiveColumns(eps->V,0,nv);
43: BVSetActiveColumns(eps->W,0,nv);
44: BVGetColumn(eps->V,nv,&u);
45: BVDotVec(eps->W,u,w);
46: BVRestoreColumn(eps->V,nv,&u);
47: MatDenseGetArray(M,&pM);
48: PetscMemcpy(A,pM,ncv*ncv*sizeof(PetscScalar));
49: PetscBLASIntCast(nv,&n_);
50: PetscBLASIntCast(ncv,&ncv_);
51: PetscStackCallBLAS("LAPACKgetrf",LAPACKgetrf_(&n_,&n_,A,&ncv_,p,&info));
52: SlepcCheckLapackInfo("getrf",info);
53: PetscLogFlops(2.0*n_*n_*n_/3.0);
54: PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("N",&n_,&one,A,&ncv_,p,w,&ncv_,&info));
55: SlepcCheckLapackInfo("getrs",info);
56: PetscLogFlops(2.0*n_*n_-n_);
57: BVMultColumn(eps->V,-1.0,1.0,nv,w);
58: DSGetArray(eps->ds,DS_MAT_A,&S);
59: beta = S[(nv-1)*ld+nv];
60: for (i=0;i<nv;i++) S[(nv-1)*ld+i] += beta*w[i];
61: DSRestoreArray(eps->ds,DS_MAT_A,&S);
62: BVGetColumn(eps->W,nv,&u);
63: BVDotVec(eps->V,u,w);
64: BVRestoreColumn(eps->W,nv,&u);
65: PetscStackCallBLAS("LAPACKgetrs",LAPACKgetrs_("C",&n_,&one,A,&ncv_,p,w,&ncv_,&info));
66: BVMultColumn(eps->W,-1.0,1.0,nv,w);
67: DSGetArray(eps->dsts,DS_MAT_A,&T);
68: beta = T[(nv-1)*ld+nv];
69: for (i=0;i<nv;i++) T[(nv-1)*ld+i] += beta*w[i];
70: DSRestoreArray(eps->dsts,DS_MAT_A,&T);
71: PetscFree3(p,A,w);
72: return(0);
73: #endif
74: }
76: static PetscErrorCode EPSTwoSidedRQUpdate2(EPS eps,Mat M,PetscInt k)
77: {
79: PetscScalar *Q,*pM,*w,zero=0.0,sone=1.0,*c,*A;
80: PetscBLASInt n_,ncv_,ld_;
81: PetscReal norm;
82: PetscInt l,nv,ncv=eps->ncv,ld,i,j;
85: DSGetLeadingDimension(eps->ds,&ld);
86: BVGetActiveColumns(eps->V,&l,&nv);
87: PetscMalloc2(ncv*ncv,&w,ncv,&c);
88: /* u = u - V*V'*u */
89: BVOrthogonalizeColumn(eps->V,k,c,&norm,NULL);
90: BVScaleColumn(eps->V,k,1.0/norm);
91: DSGetArray(eps->ds,DS_MAT_A,&A);
92: /* H = H + V'*u*b' */
93: for (j=l;j<k;j++) {
94: for (i=0;i<k;i++) A[i+j*ld] += c[i]*A[k+j*ld];
95: A[k+j*ld] *= norm;
96: }
97: DSRestoreArray(eps->ds,DS_MAT_A,&A);
98: BVOrthogonalizeColumn(eps->W,k,c,&norm,NULL);
99: BVScaleColumn(eps->W,k,1.0/norm);
100: DSGetArray(eps->dsts,DS_MAT_A,&A);
101: /* H = H + V'*u*b' */
102: for (j=l;j<k;j++) {
103: for (i=0;i<k;i++) A[i+j*ld] += c[i]*A[k+j*ld];
104: A[k+j*ld] *= norm;
105: }
106: DSRestoreArray(eps->dsts,DS_MAT_A,&A);
108: /* M = Q'*M*Q */
109: MatDenseGetArray(M,&pM);
110: PetscBLASIntCast(ncv,&ncv_);
111: PetscBLASIntCast(nv,&n_);
112: PetscBLASIntCast(ld,&ld_);
113: DSGetArray(eps->ds,DS_MAT_Q,&Q);
114: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,pM,&ncv_,Q,&ld_,&zero,w,&ncv_));
115: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
116: DSGetArray(eps->dsts,DS_MAT_Q,&Q);
117: PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&n_,&n_,&n_,&sone,Q,&ld_,w,&ncv_,&zero,pM,&ncv_));
118: DSRestoreArray(eps->dsts,DS_MAT_Q,&Q);
119: PetscFree2(w,c);
120: return(0);
121: }
123: PetscErrorCode EPSSolve_KrylovSchur_TwoSided(EPS eps)
124: {
125: PetscErrorCode ierr;
126: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
127: Mat M,U;
128: PetscReal norm,norm2,beta,betat,s,t;
129: PetscScalar *pM,*S,*T,*eigr,*eigi,*Q;
130: PetscInt ld,l,nv,ncv=eps->ncv,i,j,k,nconv,*p,cont,*idx,*idx2,id=0;
131: PetscBool breakdownt,breakdown;
132: #if defined(PETSC_USE_COMPLEX)
133: Mat A;
134: #endif
137: ctx->lock = PETSC_FALSE; /* TO DO */
138: DSGetLeadingDimension(eps->ds,&ld);
139: EPSGetStartVector(eps,0,NULL);
140: BVSetRandomColumn(eps->W,0);
141: BVNormColumn(eps->W,0,NORM_2,&norm);
142: BVScaleColumn(eps->W,0,1.0/norm);
143: l = 0;
144: PetscMalloc6(ncv*ncv,&pM,ncv,&eigr,ncv,&eigi,ncv,&idx,ncv,&idx2,ncv,&p);
145: MatCreateSeqDense(PETSC_COMM_SELF,eps->ncv,eps->ncv,pM,&M);
147: /* Restart loop */
148: while (eps->reason == EPS_CONVERGED_ITERATING) {
149: eps->its++;
151: /* Compute an nv-step Arnoldi factorization */
152: nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
153: DSGetArray(eps->ds,DS_MAT_A,&S);
154: EPSBasicArnoldi(eps,PETSC_FALSE,S,ld,eps->nconv+l,&nv,&beta,&breakdown);
155: DSRestoreArray(eps->ds,DS_MAT_A,&S);
156: DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
157: if (l==0) {
158: DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
159: } else {
160: DSSetState(eps->ds,DS_STATE_RAW);
161: }
163: /* Compute an nv-step Arnoldi factorization */
164: DSGetArray(eps->dsts,DS_MAT_A,&T);
165: EPSBasicArnoldi(eps,PETSC_TRUE,T,ld,eps->nconv+l,&nv,&betat,&breakdownt);
166: DSRestoreArray(eps->dsts,DS_MAT_A,&T);
167: DSSetDimensions(eps->dsts,nv,0,eps->nconv,eps->nconv+l);
168: if (l==0) {
169: DSSetState(eps->dsts,DS_STATE_INTERMEDIATE);
170: } else {
171: DSSetState(eps->dsts,DS_STATE_RAW);
172: }
174: /* Update M, modify Rayleigh quotients S and T */
175: BVSetActiveColumns(eps->V,eps->nconv+l,nv);
176: BVSetActiveColumns(eps->W,eps->nconv+l,nv);
177: BVMatProject(eps->V,NULL,eps->W,M);
179: EPSTwoSidedRQUpdate1(eps,M,nv);
181: /* Solve projected problem */
182: DSSolve(eps->ds,eps->eigr,eps->eigi);
183: DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);
184: DSSynchronize(eps->ds,eps->eigr,eps->eigi);
185: DSSolve(eps->dsts,eigr,eigi);
186: #if defined(PETSC_USE_COMPLEX)
187: DSGetMat(eps->dsts,DS_MAT_A,&A);
188: MatConjugate(A);
189: DSRestoreMat(eps->dsts,DS_MAT_A,&A);
190: DSGetMat(eps->dsts,DS_MAT_Q,&U);
191: MatConjugate(U);
192: DSRestoreMat(eps->dsts,DS_MAT_Q,&U);
193: for (i=0;i<nv;i++) eigr[i] = PetscConj(eigr[i]);
194: #endif
195: DSSort(eps->dsts,eigr,eigi,NULL,NULL,NULL);
196: /* check correct eigenvalue correspondence */
197: cont = 0;
198: for (i=0;i<nv;i++) {
199: if (PetscAbsScalar(eigr[i]-eps->eigr[i])+PetscAbsScalar(eigi[i]-eps->eigi[i])>PETSC_SQRT_MACHINE_EPSILON) {idx2[cont] =i; idx[cont++] = i;}
200: p[i] = -1;
201: }
202: if (cont) {
203: for (i=0;i<cont;i++) {
204: t = PETSC_MAX_REAL;
205: for (j=0;j<cont;j++) if (idx2[j]!=-1 && (s=PetscAbsScalar(eigr[idx[j]]-eps->eigr[idx[i]])+PetscAbsScalar(eigi[idx[j]]-eps->eigi[idx[i]]))<t) { id = j; t = s; }
206: p[idx[i]] = idx[id];
207: idx2[id] = -1;
208: }
209: for (i=0;i<nv;i++) if (p[i]==-1) p[i] = i;
210: DSSortWithPermutation(eps->dsts,p,eigr,eigi);
211: }
212: #if defined(PETSC_USE_COMPLEX)
213: DSGetMat(eps->dsts,DS_MAT_A,&A);
214: MatConjugate(A);
215: DSRestoreMat(eps->dsts,DS_MAT_A,&A);
216: DSGetMat(eps->dsts,DS_MAT_Q,&U);
217: MatConjugate(U);
218: DSRestoreMat(eps->dsts,DS_MAT_Q,&U);
219: #endif
220: DSSynchronize(eps->dsts,eigr,eigi);
222: /* Check convergence */
223: BVNormColumn(eps->V,nv,NORM_2,&norm);
224: BVNormColumn(eps->W,nv,NORM_2,&norm2);
225: EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta*norm,betat*norm2,1.0,&k);
226: (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);
227: nconv = k;
229: /* Update l */
230: if (eps->reason != EPS_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
231: else {
232: l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
233: #if !defined(PETSC_USE_COMPLEX)
234: DSGetArray(eps->ds,DS_MAT_A,&S);
235: if (S[k+l+(k+l-1)*ld] != 0.0) {
236: if (k+l<nv-1) l = l+1;
237: else l = l-1;
238: }
239: DSRestoreArray(eps->ds,DS_MAT_A,&S);
240: #endif
241: }
242: if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
244: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
245: BVSetActiveColumns(eps->V,eps->nconv,nv);
246: BVSetActiveColumns(eps->W,eps->nconv,nv);
247: DSGetMat(eps->ds,DS_MAT_Q,&U);
248: BVMultInPlace(eps->V,U,eps->nconv,k+l);
249: MatDestroy(&U);
250: DSGetMat(eps->dsts,DS_MAT_Q,&U);
251: BVMultInPlace(eps->W,U,eps->nconv,k+l);
252: MatDestroy(&U);
253: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
254: BVCopyColumn(eps->V,nv,k+l);
255: BVCopyColumn(eps->W,nv,k+l);
256: }
258: if (eps->reason == EPS_CONVERGED_ITERATING) {
259: if (breakdown || k==nv) {
260: /* Start a new Arnoldi factorization */
261: PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
262: if (k<eps->nev) {
263: EPSGetStartVector(eps,k,&breakdown);
264: if (breakdown) {
265: eps->reason = EPS_DIVERGED_BREAKDOWN;
266: PetscInfo(eps,"Unable to generate more start vectors\n");
267: }
268: }
269: } else {
270: /* Prepare the Rayleigh quotient for restart */
271: DSGetArray(eps->ds,DS_MAT_A,&S);
272: DSGetArray(eps->ds,DS_MAT_Q,&Q);
273: for (i=k;i<k+l;i++) S[k+l+i*ld] = Q[nv-1+i*ld]*beta;
274: DSRestoreArray(eps->ds,DS_MAT_A,&S);
275: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
276: DSGetArray(eps->dsts,DS_MAT_A,&S);
277: DSGetArray(eps->dsts,DS_MAT_Q,&Q);
278: for (i=k;i<k+l;i++) S[k+l+i*ld] = Q[nv-1+i*ld]*betat;
279: DSRestoreArray(eps->dsts,DS_MAT_A,&S);
280: DSRestoreArray(eps->dsts,DS_MAT_Q,&Q);
281: }
282: EPSTwoSidedRQUpdate2(eps,M,k+l);
283: }
284: eps->nconv = k;
285: EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,nv);
286: }
288: /* truncate Schur decomposition and change the state to raw so that
289: DSVectors() computes eigenvectors from scratch */
290: DSSetDimensions(eps->ds,eps->nconv,0,0,0);
291: DSSetState(eps->ds,DS_STATE_RAW);
292: DSSetDimensions(eps->dsts,eps->nconv,0,0,0);
293: DSSetState(eps->dsts,DS_STATE_RAW);
294: PetscFree6(pM,eigr,eigi,idx,idx2,p);
295: MatDestroy(&M);
296: return(0);
297: }