Actual source code: ks-twosided.c
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: 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,PetscReal beta,PetscReal betat)
28: {
29: PetscScalar *T,*S,*A,*w;
30: const PetscScalar *pM;
31: Vec u;
32: PetscInt ld,ncv=eps->ncv,i,l,nnv;
33: PetscBLASInt n_,ncv_,*p,one=1;
35: PetscFunctionBegin;
36: PetscCall(DSGetLeadingDimension(eps->ds,&ld));
37: PetscCall(PetscMalloc3(nv,&p,ncv*ncv,&A,ncv,&w));
38: PetscCall(BVGetActiveColumns(eps->V,&l,&nnv));
39: PetscCall(BVSetActiveColumns(eps->V,0,nv));
40: PetscCall(BVSetActiveColumns(eps->W,0,nv));
41: PetscCall(BVGetColumn(eps->V,nv,&u));
42: PetscCall(BVDotVec(eps->W,u,w));
43: PetscCall(BVRestoreColumn(eps->V,nv,&u));
44: PetscCall(MatDenseGetArrayRead(M,&pM));
45: PetscCall(PetscArraycpy(A,pM,ncv*ncv));
46: PetscCall(MatDenseRestoreArrayRead(M,&pM));
47: PetscCall(PetscBLASIntCast(nv,&n_));
48: PetscCall(PetscBLASIntCast(ncv,&ncv_));
49: PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
50: PetscCallLAPACKInfo("LAPACKgetrf",LAPACKgetrf_(&n_,&n_,A,&ncv_,p,&info));
51: PetscCall(PetscLogFlops(2.0*n_*n_*n_/3.0));
52: PetscCallLAPACKInfo("LAPACKgetrs",LAPACKgetrs_("N",&n_,&one,A,&ncv_,p,w,&ncv_,&info));
53: PetscCall(PetscLogFlops(2.0*n_*n_-n_));
54: PetscCall(BVMultColumn(eps->V,-1.0,1.0,nv,w));
55: PetscCall(DSGetArray(eps->ds,DS_MAT_A,&S));
56: for (i=0;i<nv;i++) S[(nv-1)*ld+i] += beta*w[i];
57: PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&S));
58: PetscCall(BVGetColumn(eps->W,nv,&u));
59: PetscCall(BVDotVec(eps->V,u,w));
60: PetscCall(BVRestoreColumn(eps->W,nv,&u));
61: PetscCallLAPACKInfo("LAPACKgetrs",LAPACKgetrs_("C",&n_,&one,A,&ncv_,p,w,&ncv_,&info));
62: PetscCall(PetscFPTrapPop());
63: PetscCall(BVMultColumn(eps->W,-1.0,1.0,nv,w));
64: PetscCall(DSGetArray(eps->ds,DS_MAT_B,&T));
65: for (i=0;i<nv;i++) T[(nv-1)*ld+i] += betat*w[i];
66: PetscCall(DSRestoreArray(eps->ds,DS_MAT_B,&T));
67: PetscCall(PetscFree3(p,A,w));
68: PetscCall(BVSetActiveColumns(eps->V,l,nnv));
69: PetscCall(BVSetActiveColumns(eps->W,l,nnv));
70: PetscFunctionReturn(PETSC_SUCCESS);
71: }
73: static PetscErrorCode EPSTwoSidedRQUpdate2(EPS eps,Mat M,PetscInt k)
74: {
75: PetscScalar *Q,*pM,*w,zero=0.0,sone=1.0,*c,*A;
76: PetscBLASInt n_,ncv_,ld_;
77: PetscReal norm;
78: PetscInt l,nv,ncv=eps->ncv,ld,i,j;
80: PetscFunctionBegin;
81: PetscCall(DSGetLeadingDimension(eps->ds,&ld));
82: PetscCall(BVGetActiveColumns(eps->V,&l,&nv));
83: PetscCall(BVSetActiveColumns(eps->V,0,nv));
84: PetscCall(BVSetActiveColumns(eps->W,0,nv));
85: PetscCall(PetscMalloc2(ncv*ncv,&w,ncv,&c));
86: /* u = u - V*V'*u */
87: PetscCall(BVOrthogonalizeColumn(eps->V,k,c,&norm,NULL));
88: PetscCall(BVScaleColumn(eps->V,k,1.0/norm));
89: PetscCall(DSGetArray(eps->ds,DS_MAT_A,&A));
90: /* H = H + V'*u*b' */
91: for (j=l;j<k;j++) {
92: for (i=0;i<k;i++) A[i+j*ld] += c[i]*A[k+j*ld];
93: A[k+j*ld] *= norm;
94: }
95: PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&A));
96: PetscCall(BVOrthogonalizeColumn(eps->W,k,c,&norm,NULL));
97: PetscCall(BVScaleColumn(eps->W,k,1.0/norm));
98: PetscCall(DSGetArray(eps->ds,DS_MAT_B,&A));
99: /* H = H + V'*u*b' */
100: for (j=l;j<k;j++) {
101: for (i=0;i<k;i++) A[i+j*ld] += c[i]*A[k+j*ld];
102: A[k+j*ld] *= norm;
103: }
104: PetscCall(DSRestoreArray(eps->ds,DS_MAT_B,&A));
106: /* M = Q'*M*Q */
107: PetscCall(MatDenseGetArray(M,&pM));
108: PetscCall(PetscBLASIntCast(ncv,&ncv_));
109: PetscCall(PetscBLASIntCast(nv,&n_));
110: PetscCall(PetscBLASIntCast(ld,&ld_));
111: PetscCall(DSGetArray(eps->ds,DS_MAT_Q,&Q));
112: PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&sone,pM,&ncv_,Q,&ld_,&zero,w,&ncv_));
113: PetscCall(DSRestoreArray(eps->ds,DS_MAT_Q,&Q));
114: PetscCall(DSGetArray(eps->ds,DS_MAT_Z,&Q));
115: PetscCallBLAS("BLASgemm",BLASgemm_("C","N",&n_,&n_,&n_,&sone,Q,&ld_,w,&ncv_,&zero,pM,&ncv_));
116: PetscCall(DSRestoreArray(eps->ds,DS_MAT_Z,&Q));
117: PetscCall(MatDenseRestoreArray(M,&pM));
118: PetscCall(PetscFree2(w,c));
119: PetscCall(BVSetActiveColumns(eps->V,l,nv));
120: PetscCall(BVSetActiveColumns(eps->W,l,nv));
121: PetscFunctionReturn(PETSC_SUCCESS);
122: }
124: PetscErrorCode EPSSolve_KrylovSchur_TwoSided(EPS eps)
125: {
126: EPS_KRYLOVSCHUR *ctx = (EPS_KRYLOVSCHUR*)eps->data;
127: Mat M,U,Op,OpHT,S,T;
128: PetscReal norm,norm2,beta,betat;
129: PetscInt ld,l,nv,nvt,k,nconv,dsn,dsk;
130: PetscBool breakdownt,breakdown,breakdownl;
132: PetscFunctionBegin;
133: PetscCall(DSGetLeadingDimension(eps->ds,&ld));
134: PetscCall(EPSGetStartVector(eps,0,NULL));
135: PetscCall(EPSGetLeftStartVector(eps,0,NULL));
136: l = 0;
137: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,eps->ncv,eps->ncv,NULL,&M));
139: PetscCall(STGetOperator(eps->st,&Op));
140: PetscCall(MatCreateHermitianTranspose(Op,&OpHT));
142: /* Restart loop */
143: while (eps->reason == EPS_CONVERGED_ITERATING) {
144: eps->its++;
146: /* Compute an nv-step Arnoldi factorization for Op */
147: nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
148: PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l));
149: PetscCall(DSGetMat(eps->ds,DS_MAT_A,&S));
150: PetscCall(BVMatArnoldi(eps->V,Op,S,eps->nconv+l,&nv,&beta,&breakdown));
151: PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&S));
153: /* Compute an nv-step Arnoldi factorization for Op' */
154: nvt = nv;
155: PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l));
156: PetscCall(DSGetMat(eps->ds,DS_MAT_B,&T));
157: PetscCall(BVMatArnoldi(eps->W,OpHT,T,eps->nconv+l,&nvt,&betat,&breakdownt));
158: PetscCall(DSRestoreMat(eps->ds,DS_MAT_B,&T));
160: /* Make sure both factorizations have the same length */
161: nv = PetscMin(nv,nvt);
162: PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,eps->nconv+l));
163: if (l==0) PetscCall(DSSetState(eps->ds,DS_STATE_INTERMEDIATE));
164: else PetscCall(DSSetState(eps->ds,DS_STATE_RAW));
165: breakdown = (breakdown || breakdownt)? PETSC_TRUE: PETSC_FALSE;
167: /* Update M, modify Rayleigh quotients S and T */
168: PetscCall(BVSetActiveColumns(eps->V,eps->nconv+l,nv));
169: PetscCall(BVSetActiveColumns(eps->W,eps->nconv+l,nv));
170: PetscCall(BVMatProject(eps->V,NULL,eps->W,M));
172: PetscCall(EPSTwoSidedRQUpdate1(eps,M,nv,beta,betat));
174: /* Solve projected problem */
175: PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi));
176: PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL));
177: PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));
178: PetscCall(DSUpdateExtraRow(eps->ds));
180: /* Check convergence */
181: PetscCall(BVNormColumn(eps->V,nv,NORM_2,&norm));
182: PetscCall(BVNormColumn(eps->W,nv,NORM_2,&norm2));
183: PetscCall(EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta*norm,betat*norm2,1.0,&k));
184: PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx));
185: nconv = k;
187: /* Update l */
188: if (eps->reason != EPS_CONVERGED_ITERATING || breakdown || k==nv) l = 0;
189: else {
190: l = PetscMax(1,(PetscInt)((nv-k)*ctx->keep));
191: PetscCall(DSGetTruncateSize(eps->ds,k,nv,&l));
192: }
193: if (!ctx->lock && l>0) { l += k; k = 0; } /* non-locking variant: reset no. of converged pairs */
194: if (l) PetscCall(PetscInfo(eps,"Preparing to restart keeping l=%" PetscInt_FMT " vectors\n",l));
196: /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */
197: PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv));
198: PetscCall(BVSetActiveColumns(eps->W,eps->nconv,nv));
199: PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&U));
200: PetscCall(BVMultInPlace(eps->V,U,eps->nconv,k+l));
201: PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&U));
202: PetscCall(DSGetMat(eps->ds,DS_MAT_Z,&U));
203: PetscCall(BVMultInPlace(eps->W,U,eps->nconv,k+l));
204: PetscCall(DSRestoreMat(eps->ds,DS_MAT_Z,&U));
205: if (eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {
206: PetscCall(BVCopyColumn(eps->V,nv,k+l));
207: PetscCall(BVCopyColumn(eps->W,nv,k+l));
208: }
210: if (eps->reason == EPS_CONVERGED_ITERATING) {
211: if (breakdown || k==nv) {
212: /* Start a new Arnoldi factorization */
213: PetscCall(PetscInfo(eps,"Breakdown in Krylov-Schur method (it=%" PetscInt_FMT " norm=%g)\n",eps->its,(double)beta));
214: if (k<eps->nev) {
215: PetscCall(EPSGetStartVector(eps,k,&breakdown));
216: PetscCall(EPSGetLeftStartVector(eps,k,&breakdownl));
217: if (breakdown || breakdownl) {
218: eps->reason = EPS_DIVERGED_BREAKDOWN;
219: PetscCall(PetscInfo(eps,"Unable to generate more start vectors\n"));
220: }
221: }
222: } else {
223: PetscCall(DSGetDimensions(eps->ds,&dsn,NULL,&dsk,NULL));
224: PetscCall(DSSetDimensions(eps->ds,dsn,k,dsk));
225: PetscCall(DSTruncate(eps->ds,k+l,PETSC_FALSE));
226: }
227: PetscCall(EPSTwoSidedRQUpdate2(eps,M,k+l));
228: }
229: eps->nconv = k;
230: PetscCall(EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,nv));
231: }
233: PetscCall(STRestoreOperator(eps->st,&Op));
234: PetscCall(MatDestroy(&OpHT));
236: PetscCall(DSTruncate(eps->ds,eps->nconv,PETSC_TRUE));
237: PetscCall(MatDestroy(&M));
238: PetscFunctionReturn(PETSC_SUCCESS);
239: }