Actual source code: ks-twosided.c
slepc-3.15.1 2021-05-28
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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: PetscErrorCode ierr;
30: PetscScalar *T,*S,*A,*w,beta;
31: const PetscScalar *pM;
32: Vec u;
33: PetscInt ld,ncv=eps->ncv,i,l,nnv;
34: PetscBLASInt info,n_,ncv_,*p,one=1;
37: DSGetLeadingDimension(eps->ds,&ld);
38: PetscMalloc3(nv,&p,ncv*ncv,&A,ncv,&w);
39: BVGetActiveColumns(eps->V,&l,&nnv);
40: BVSetActiveColumns(eps->V,0,nv);
41: BVSetActiveColumns(eps->W,0,nv);
42: BVGetColumn(eps->V,nv,&u);
43: BVDotVec(eps->W,u,w);
44: BVRestoreColumn(eps->V,nv,&u);
45: MatDenseGetArrayRead(M,&pM);
46: PetscArraycpy(A,pM,ncv*ncv);
47: MatDenseRestoreArrayRead(M,&pM);
48: PetscBLASIntCast(nv,&n_);
49: PetscBLASIntCast(ncv,&ncv_);
50: PetscFPTrapPush(PETSC_FP_TRAP_OFF);
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: PetscFPTrapPop();
67: BVMultColumn(eps->W,-1.0,1.0,nv,w);
68: DSGetArray(eps->ds,DS_MAT_B,&T);
69: beta = T[(nv-1)*ld+nv];
70: for (i=0;i<nv;i++) T[(nv-1)*ld+i] += beta*w[i];
71: DSRestoreArray(eps->ds,DS_MAT_B,&T);
72: PetscFree3(p,A,w);
73: BVSetActiveColumns(eps->V,l,nnv);
74: BVSetActiveColumns(eps->W,l,nnv);
75: return(0);
76: }
78: static PetscErrorCode EPSTwoSidedRQUpdate2(EPS eps,Mat M,PetscInt k)
79: {
81: PetscScalar *Q,*pM,*w,zero=0.0,sone=1.0,*c,*A;
82: PetscBLASInt n_,ncv_,ld_;
83: PetscReal norm;
84: PetscInt l,nv,ncv=eps->ncv,ld,i,j;
87: DSGetLeadingDimension(eps->ds,&ld);
88: BVGetActiveColumns(eps->V,&l,&nv);
89: BVSetActiveColumns(eps->V,0,nv);
90: BVSetActiveColumns(eps->W,0,nv);
91: PetscMalloc2(ncv*ncv,&w,ncv,&c);
92: /* u = u - V*V'*u */
93: BVOrthogonalizeColumn(eps->V,k,c,&norm,NULL);
94: BVScaleColumn(eps->V,k,1.0/norm);
95: DSGetArray(eps->ds,DS_MAT_A,&A);
96: /* H = H + V'*u*b' */
97: for (j=l;j<k;j++) {
98: for (i=0;i<k;i++) A[i+j*ld] += c[i]*A[k+j*ld];
99: A[k+j*ld] *= norm;
100: }
101: DSRestoreArray(eps->ds,DS_MAT_A,&A);
102: BVOrthogonalizeColumn(eps->W,k,c,&norm,NULL);
103: BVScaleColumn(eps->W,k,1.0/norm);
104: DSGetArray(eps->ds,DS_MAT_B,&A);
105: /* H = H + V'*u*b' */
106: for (j=l;j<k;j++) {
107: for (i=0;i<k;i++) A[i+j*ld] += c[i]*A[k+j*ld];
108: A[k+j*ld] *= norm;
109: }
110: DSRestoreArray(eps->ds,DS_MAT_B,&A);
112: /* M = Q'*M*Q */
113: MatDenseGetArray(M,&pM);
114: PetscBLASIntCast(ncv,&ncv_);
115: PetscBLASIntCast(nv,&n_);
116: PetscBLASIntCast(ld,&ld_);
117: DSGetArray(eps->ds,DS_MAT_Q,&Q);
118: PetscStackCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,pM,&ncv_,Q,&ld_,&zero,w,&ncv_));
119: DSRestoreArray(eps->ds,DS_MAT_Q,&Q);
120: DSGetArray(eps->ds,DS_MAT_Z,&Q);
121: PetscStackCallBLAS("BLASgemm",BLASgemm_("C","N",&n_,&n_,&n_,&sone,Q,&ld_,w,&ncv_,&zero,pM,&ncv_));
122: DSRestoreArray(eps->ds,DS_MAT_Z,&Q);
123: MatDenseRestoreArray(M,&pM);
124: PetscFree2(w,c);
125: BVSetActiveColumns(eps->V,l,nv);
126: BVSetActiveColumns(eps->W,l,nv);
127: return(0);
128: }
130: PetscErrorCode EPSSolve_KrylovSchur_TwoSided(EPS eps)
131: {
132: PetscErrorCode ierr;
133: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
134: Mat M,U,Op,OpHT;
135: PetscReal norm,norm2,beta,betat;
136: PetscScalar *S,*T;
137: PetscInt ld,l,nv,nvt,k,nconv,dsn,dsk;
138: PetscBool breakdownt,breakdown,breakdownl;
141: DSGetLeadingDimension(eps->ds,&ld);
142: EPSGetStartVector(eps,0,NULL);
143: EPSGetLeftStartVector(eps,0,NULL);
144: l = 0;
145: MatCreateSeqDense(PETSC_COMM_SELF,eps->ncv,eps->ncv,NULL,&M);
147: STGetOperator(eps->st,&Op);
148: MatCreateHermitianTranspose(Op,&OpHT);
150: /* Restart loop */
151: while (eps->reason == EPS_CONVERGED_ITERATING) {
152: eps->its++;
154: /* Compute an nv-step Arnoldi factorization for Op */
155: nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
156: DSGetArray(eps->ds,DS_MAT_A,&S);
157: BVMatArnoldi(eps->V,Op,S,ld,eps->nconv+l,&nv,&beta,&breakdown);
158: DSRestoreArray(eps->ds,DS_MAT_A,&S);
160: /* Compute an nv-step Arnoldi factorization for Op' */
161: nvt = nv;
162: DSGetArray(eps->ds,DS_MAT_B,&T);
163: BVMatArnoldi(eps->W,OpHT,T,ld,eps->nconv+l,&nvt,&betat,&breakdownt);
164: DSRestoreArray(eps->ds,DS_MAT_B,&T);
166: /* Make sure both factorizations have the same length */
167: nv = PetscMin(nv,nvt);
168: DSSetDimensions(eps->ds,nv,0,eps->nconv,eps->nconv+l);
169: if (l==0) {
170: DSSetState(eps->ds,DS_STATE_INTERMEDIATE);
171: } else {
172: DSSetState(eps->ds,DS_STATE_RAW);
173: }
174: breakdown = (breakdown || breakdownt)? PETSC_TRUE: PETSC_FALSE;
176: /* Update M, modify Rayleigh quotients S and T */
177: BVSetActiveColumns(eps->V,eps->nconv+l,nv);
178: BVSetActiveColumns(eps->W,eps->nconv+l,nv);
179: BVMatProject(eps->V,NULL,eps->W,M);
181: EPSTwoSidedRQUpdate1(eps,M,nv);
183: /* Solve projected problem */
184: DSSolve(eps->ds,eps->eigr,eps->eigi);
185: DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);
186: DSSynchronize(eps->ds,eps->eigr,eps->eigi);
187: DSUpdateExtraRow(eps->ds);
189: /* Check convergence */
190: BVNormColumn(eps->V,nv,NORM_2,&norm);
191: BVNormColumn(eps->W,nv,NORM_2,&norm2);
192: EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta*norm,betat*norm2,1.0,&k);
193: (*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx);
194: nconv = k;
196: /* Update l */
197: if (eps->reason != EPS_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
198: else {
199: l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
200: DSGetTruncateSize(eps->ds,k,nv,&l);
201: }
202: if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
203: if (l) { PetscInfo1(eps,"Preparing to restart keeping l=%D vectors\n",l); }
205: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
206: BVSetActiveColumns(eps->V,eps->nconv,nv);
207: BVSetActiveColumns(eps->W,eps->nconv,nv);
208: DSGetMat(eps->ds,DS_MAT_Q,&U);
209: BVMultInPlace(eps->V,U,eps->nconv,k+l);
210: MatDestroy(&U);
211: DSGetMat(eps->ds,DS_MAT_Z,&U);
212: BVMultInPlace(eps->W,U,eps->nconv,k+l);
213: MatDestroy(&U);
214: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
215: BVCopyColumn(eps->V,nv,k+l);
216: BVCopyColumn(eps->W,nv,k+l);
217: }
219: if (eps->reason == EPS_CONVERGED_ITERATING) {
220: if (breakdown || k==nv) {
221: /* Start a new Arnoldi factorization */
222: PetscInfo2(eps,"Breakdown in Krylov-Schur method (it=%D norm=%g)\n",eps->its,(double)beta);
223: if (k<eps->nev) {
224: EPSGetStartVector(eps,k,&breakdown);
225: EPSGetLeftStartVector(eps,k,&breakdownl);
226: if (breakdown || breakdownl) {
227: eps->reason = EPS_DIVERGED_BREAKDOWN;
228: PetscInfo(eps,"Unable to generate more start vectors\n");
229: }
230: }
231: } else {
232: DSGetDimensions(eps->ds,&dsn,NULL,NULL,&dsk,NULL);
233: DSSetDimensions(eps->ds,dsn,0,k,dsk);
234: DSTruncate(eps->ds,k+l,PETSC_FALSE);
235: }
236: EPSTwoSidedRQUpdate2(eps,M,k+l);
237: }
238: eps->nconv = k;
239: EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,nv);
240: }
242: STRestoreOperator(eps->st,&Op);
243: MatDestroy(&OpHT);
245: DSTruncate(eps->ds,eps->nconv,PETSC_TRUE);
246: MatDestroy(&M);
247: return(0);
248: }