Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
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: "lyapii"
12 :
13 : Method: Lyapunov inverse iteration
14 :
15 : Algorithm:
16 :
17 : Lyapunov inverse iteration using LME solvers
18 :
19 : References:
20 :
21 : [1] H.C. Elman and M. Wu, "Lyapunov inverse iteration for computing a
22 : few rightmost eigenvalues of large generalized eigenvalue problems",
23 : SIAM J. Matrix Anal. Appl. 34(4):1685-1707, 2013.
24 :
25 : [2] K. Meerbergen and A. Spence, "Inverse iteration for purely imaginary
26 : eigenvalues with application to the detection of Hopf bifurcations in
27 : large-scale problems", SIAM J. Matrix Anal. Appl. 31:1982-1999, 2010.
28 : */
29 :
30 : #include <slepc/private/epsimpl.h> /*I "slepceps.h" I*/
31 : #include <slepcblaslapack.h>
32 :
33 : typedef struct {
34 : LME lme; /* Lyapunov solver */
35 : DS ds; /* used to compute the SVD for compression */
36 : PetscInt rkl; /* prescribed rank for the Lyapunov solver */
37 : PetscInt rkc; /* the compressed rank, cannot be larger than rkl */
38 : } EPS_LYAPII;
39 :
40 : typedef struct {
41 : Mat S; /* the operator matrix, S=A^{-1}*B */
42 : BV Q; /* orthogonal basis of converged eigenvectors */
43 : } EPS_LYAPII_MATSHELL;
44 :
45 : typedef struct {
46 : Mat S; /* the matrix from which the implicit operator is built */
47 : PetscInt n; /* the size of matrix S, the operator is nxn */
48 : LME lme; /* dummy LME object */
49 : #if defined(PETSC_USE_COMPLEX)
50 : Mat A,B,F;
51 : Vec w;
52 : #endif
53 : } EPS_EIG_MATSHELL;
54 :
55 3 : static PetscErrorCode EPSSetUp_LyapII(EPS eps)
56 : {
57 3 : PetscRandom rand;
58 3 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
59 :
60 3 : PetscFunctionBegin;
61 3 : EPSCheckSinvert(eps);
62 3 : EPSCheckNotStructured(eps);
63 3 : if (eps->ncv!=PETSC_DETERMINE) {
64 0 : PetscCheck(eps->ncv>=eps->nev+1,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must be at least nev+1");
65 3 : } else eps->ncv = eps->nev+1;
66 3 : if (eps->mpd!=PETSC_DETERMINE) PetscCall(PetscInfo(eps,"Warning: parameter mpd ignored\n"));
67 3 : if (eps->max_it==PETSC_DETERMINE) eps->max_it = PetscMax(1000*eps->nev,100*eps->n);
68 3 : if (!eps->which) eps->which=EPS_LARGEST_REAL;
69 3 : PetscCheck(eps->which==EPS_LARGEST_REAL,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver supports only largest real eigenvalues");
70 3 : EPSCheckUnsupported(eps,EPS_FEATURE_BALANCE | EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION | EPS_FEATURE_TWOSIDED);
71 :
72 3 : if (!ctx->rkc) ctx->rkc = 10;
73 3 : if (!ctx->rkl) ctx->rkl = 3*ctx->rkc;
74 3 : if (!ctx->lme) PetscCall(EPSLyapIIGetLME(eps,&ctx->lme));
75 3 : PetscCall(LMESetProblemType(ctx->lme,LME_LYAPUNOV));
76 3 : PetscCall(LMESetErrorIfNotConverged(ctx->lme,PETSC_TRUE));
77 :
78 3 : if (!ctx->ds) {
79 3 : PetscCall(DSCreate(PetscObjectComm((PetscObject)eps),&ctx->ds));
80 3 : PetscCall(DSSetType(ctx->ds,DSSVD));
81 : }
82 3 : PetscCall(DSAllocate(ctx->ds,ctx->rkl));
83 :
84 3 : PetscCall(DSSetType(eps->ds,DSNHEP));
85 3 : PetscCall(DSAllocate(eps->ds,eps->ncv));
86 :
87 3 : PetscCall(EPSAllocateSolution(eps,0));
88 3 : PetscCall(BVGetRandomContext(eps->V,&rand)); /* make sure the random context is available when duplicating */
89 3 : PetscCall(EPSSetWorkVecs(eps,3));
90 3 : PetscFunctionReturn(PETSC_SUCCESS);
91 : }
92 :
93 3174 : static PetscErrorCode MatMult_EPSLyapIIOperator(Mat M,Vec x,Vec r)
94 : {
95 3174 : EPS_LYAPII_MATSHELL *matctx;
96 :
97 3174 : PetscFunctionBegin;
98 3174 : PetscCall(MatShellGetContext(M,&matctx));
99 3174 : PetscCall(MatMult(matctx->S,x,r));
100 3174 : PetscCall(BVOrthogonalizeVec(matctx->Q,r,NULL,NULL,NULL));
101 3174 : PetscFunctionReturn(PETSC_SUCCESS);
102 : }
103 :
104 3 : static PetscErrorCode MatDestroy_EPSLyapIIOperator(Mat M)
105 : {
106 3 : EPS_LYAPII_MATSHELL *matctx;
107 :
108 3 : PetscFunctionBegin;
109 3 : PetscCall(MatShellGetContext(M,&matctx));
110 3 : PetscCall(MatDestroy(&matctx->S));
111 3 : PetscCall(PetscFree(matctx));
112 3 : PetscFunctionReturn(PETSC_SUCCESS);
113 : }
114 :
115 704 : static PetscErrorCode MatMult_EigOperator(Mat M,Vec x,Vec y)
116 : {
117 704 : EPS_EIG_MATSHELL *matctx;
118 : #if !defined(PETSC_USE_COMPLEX)
119 : PetscInt n,lds;
120 : PetscScalar *Y,*C,zero=0.0,done=1.0,dtwo=2.0;
121 : const PetscScalar *S,*X;
122 : PetscBLASInt n_,lds_;
123 : #endif
124 :
125 704 : PetscFunctionBegin;
126 704 : PetscCall(MatShellGetContext(M,&matctx));
127 :
128 : #if defined(PETSC_USE_COMPLEX)
129 704 : PetscCall(MatMult(matctx->B,x,matctx->w));
130 704 : PetscCall(MatSolve(matctx->F,matctx->w,y));
131 : #else
132 : PetscCall(VecGetArrayRead(x,&X));
133 : PetscCall(VecGetArray(y,&Y));
134 : PetscCall(MatDenseGetArrayRead(matctx->S,&S));
135 : PetscCall(MatDenseGetLDA(matctx->S,&lds));
136 :
137 : n = matctx->n;
138 : PetscCall(PetscCalloc1(n*n,&C));
139 : PetscCall(PetscBLASIntCast(n,&n_));
140 : PetscCall(PetscBLASIntCast(lds,&lds_));
141 :
142 : /* C = 2*S*X*S.' */
143 : PetscCallBLAS("BLASgemm",BLASgemm_("N","N",&n_,&n_,&n_,&dtwo,S,&lds_,X,&n_,&zero,Y,&n_));
144 : PetscCallBLAS("BLASgemm",BLASgemm_("N","T",&n_,&n_,&n_,&done,Y,&n_,S,&lds_,&zero,C,&n_));
145 :
146 : /* Solve S*Y + Y*S' = -C */
147 : PetscCall(LMEDenseLyapunov(matctx->lme,n,(PetscScalar*)S,lds,C,n,Y,n));
148 :
149 : PetscCall(PetscFree(C));
150 : PetscCall(VecRestoreArrayRead(x,&X));
151 : PetscCall(VecRestoreArray(y,&Y));
152 : PetscCall(MatDenseRestoreArrayRead(matctx->S,&S));
153 : #endif
154 704 : PetscFunctionReturn(PETSC_SUCCESS);
155 : }
156 :
157 3 : static PetscErrorCode MatDestroy_EigOperator(Mat M)
158 : {
159 3 : EPS_EIG_MATSHELL *matctx;
160 :
161 3 : PetscFunctionBegin;
162 3 : PetscCall(MatShellGetContext(M,&matctx));
163 : #if defined(PETSC_USE_COMPLEX)
164 3 : PetscCall(MatDestroy(&matctx->A));
165 3 : PetscCall(MatDestroy(&matctx->B));
166 3 : PetscCall(MatDestroy(&matctx->F));
167 3 : PetscCall(VecDestroy(&matctx->w));
168 : #else
169 : PetscCall(MatDestroy(&matctx->S));
170 : #endif
171 3 : PetscCall(PetscFree(matctx));
172 3 : PetscFunctionReturn(PETSC_SUCCESS);
173 : }
174 :
175 : /*
176 : EV2x2: solve the eigenproblem for a 2x2 matrix M
177 : */
178 25 : static PetscErrorCode EV2x2(PetscScalar *M,PetscInt ld,PetscScalar *wr,PetscScalar *wi,PetscScalar *vec)
179 : {
180 25 : PetscBLASInt lwork=10,ld_;
181 25 : PetscScalar work[10];
182 25 : PetscBLASInt two=2,info;
183 : #if defined(PETSC_USE_COMPLEX)
184 25 : PetscReal rwork[6];
185 : #endif
186 :
187 25 : PetscFunctionBegin;
188 25 : PetscCall(PetscBLASIntCast(ld,&ld_));
189 25 : PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
190 : #if !defined(PETSC_USE_COMPLEX)
191 : PetscCallBLAS("LAPACKgeev",LAPACKgeev_("N","V",&two,M,&ld_,wr,wi,NULL,&ld_,vec,&ld_,work,&lwork,&info));
192 : #else
193 25 : PetscCallBLAS("LAPACKgeev",LAPACKgeev_("N","V",&two,M,&ld_,wr,NULL,&ld_,vec,&ld_,work,&lwork,rwork,&info));
194 : #endif
195 25 : SlepcCheckLapackInfo("geev",info);
196 25 : PetscCall(PetscFPTrapPop());
197 25 : PetscFunctionReturn(PETSC_SUCCESS);
198 : }
199 :
200 : /*
201 : LyapIIBuildRHS: prepare the right-hand side of the Lyapunov equation SY + YS' = -2*S*Z*S'
202 : in factored form:
203 : if (V) U=sqrt(2)*S*V (uses 1 work vector)
204 : else U=sqrt(2)*S*U (uses 2 work vectors)
205 : where U,V are assumed to have rk columns.
206 : */
207 28 : static PetscErrorCode LyapIIBuildRHS(Mat S,PetscInt rk,Mat U,BV V,Vec *work)
208 : {
209 28 : PetscScalar *array,*uu;
210 28 : PetscInt i,nloc;
211 28 : Vec v,u=work[0];
212 :
213 28 : PetscFunctionBegin;
214 28 : PetscCall(MatGetLocalSize(U,&nloc,NULL));
215 75 : for (i=0;i<rk;i++) {
216 47 : PetscCall(MatDenseGetColumn(U,i,&array));
217 47 : if (V) PetscCall(BVGetColumn(V,i,&v));
218 : else {
219 40 : v = work[1];
220 40 : PetscCall(VecPlaceArray(v,array));
221 : }
222 47 : PetscCall(MatMult(S,v,u));
223 47 : if (V) PetscCall(BVRestoreColumn(V,i,&v));
224 40 : else PetscCall(VecResetArray(v));
225 47 : PetscCall(VecScale(u,PETSC_SQRT2));
226 47 : PetscCall(VecGetArray(u,&uu));
227 47 : PetscCall(PetscArraycpy(array,uu,nloc));
228 47 : PetscCall(VecRestoreArray(u,&uu));
229 47 : PetscCall(MatDenseRestoreColumn(U,&array));
230 : }
231 28 : PetscFunctionReturn(PETSC_SUCCESS);
232 : }
233 :
234 : /*
235 : LyapIIBuildEigenMat: create shell matrix Op=A\B with A = kron(I,S)+kron(S,I), B = -2*kron(S,S)
236 : where S is a sequential square dense matrix of order n.
237 : v0 is the initial vector, should have the form v0 = w*w' (for instance 1*1')
238 : */
239 28 : static PetscErrorCode LyapIIBuildEigenMat(LME lme,Mat S,Mat *Op,Vec *v0)
240 : {
241 28 : PetscInt n,m;
242 28 : PetscBool create=PETSC_FALSE;
243 28 : EPS_EIG_MATSHELL *matctx;
244 : #if defined(PETSC_USE_COMPLEX)
245 28 : PetscScalar theta,*aa,*bb;
246 28 : const PetscScalar *ss;
247 28 : PetscInt i,j,f,c,off,ld,lds;
248 28 : IS perm;
249 : #endif
250 :
251 28 : PetscFunctionBegin;
252 28 : PetscCall(MatGetSize(S,&n,NULL));
253 28 : if (!*Op) create=PETSC_TRUE;
254 : else {
255 25 : PetscCall(MatGetSize(*Op,&m,NULL));
256 25 : if (m!=n*n) create=PETSC_TRUE;
257 : }
258 25 : if (create) {
259 3 : PetscCall(MatDestroy(Op));
260 3 : PetscCall(VecDestroy(v0));
261 3 : PetscCall(PetscNew(&matctx));
262 : #if defined(PETSC_USE_COMPLEX)
263 3 : PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n*n,n*n,NULL,&matctx->A));
264 3 : PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n*n,n*n,NULL,&matctx->B));
265 3 : PetscCall(MatCreateVecs(matctx->A,NULL,&matctx->w));
266 : #else
267 : PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&matctx->S));
268 : #endif
269 3 : PetscCall(MatCreateShell(PETSC_COMM_SELF,n*n,n*n,PETSC_DETERMINE,PETSC_DETERMINE,matctx,Op));
270 3 : PetscCall(MatShellSetOperation(*Op,MATOP_MULT,(void(*)(void))MatMult_EigOperator));
271 3 : PetscCall(MatShellSetOperation(*Op,MATOP_DESTROY,(void(*)(void))MatDestroy_EigOperator));
272 3 : PetscCall(MatCreateVecs(*Op,NULL,v0));
273 : } else {
274 25 : PetscCall(MatShellGetContext(*Op,&matctx));
275 : #if defined(PETSC_USE_COMPLEX)
276 25 : PetscCall(MatZeroEntries(matctx->A));
277 : #endif
278 : }
279 : #if defined(PETSC_USE_COMPLEX)
280 28 : PetscCall(MatDenseGetArray(matctx->A,&aa));
281 28 : PetscCall(MatDenseGetArray(matctx->B,&bb));
282 28 : PetscCall(MatDenseGetArrayRead(S,&ss));
283 28 : PetscCall(MatDenseGetLDA(S,&lds));
284 28 : ld = n*n;
285 282 : for (f=0;f<n;f++) {
286 254 : off = f*n+f*n*ld;
287 24242 : for (i=0;i<n;i++) for (j=0;j<n;j++) aa[off+i+j*ld] = ss[i+j*lds];
288 2586 : for (c=0;c<n;c++) {
289 2332 : off = f*n+c*n*ld;
290 2332 : theta = ss[f+c*lds];
291 23988 : for (i=0;i<n;i++) aa[off+i+i*ld] += theta;
292 227236 : for (i=0;i<n;i++) for (j=0;j<n;j++) bb[off+i+j*ld] = -2*theta*ss[i+j*lds];
293 : }
294 : }
295 28 : PetscCall(MatDenseRestoreArray(matctx->A,&aa));
296 28 : PetscCall(MatDenseRestoreArray(matctx->B,&bb));
297 28 : PetscCall(MatDenseRestoreArrayRead(S,&ss));
298 28 : PetscCall(ISCreateStride(PETSC_COMM_SELF,n*n,0,1,&perm));
299 28 : PetscCall(MatDestroy(&matctx->F));
300 28 : PetscCall(MatDuplicate(matctx->A,MAT_COPY_VALUES,&matctx->F));
301 28 : PetscCall(MatLUFactor(matctx->F,perm,perm,NULL));
302 28 : PetscCall(ISDestroy(&perm));
303 : #else
304 : PetscCall(MatCopy(S,matctx->S,SAME_NONZERO_PATTERN));
305 : #endif
306 28 : matctx->lme = lme;
307 28 : matctx->n = n;
308 28 : PetscCall(VecSet(*v0,1.0));
309 28 : PetscFunctionReturn(PETSC_SUCCESS);
310 : }
311 :
312 3 : static PetscErrorCode EPSSolve_LyapII(EPS eps)
313 : {
314 3 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
315 3 : PetscInt i,ldds,rk,nloc,mloc,nv,idx,k;
316 3 : Vec v,w,z=eps->work[0],v0=NULL;
317 3 : Mat S,C,Ux[2],Y,Y1,R,U,W,X,Op=NULL;
318 3 : BV V;
319 3 : BVOrthogType type;
320 3 : BVOrthogRefineType refine;
321 3 : PetscScalar eigr[2],eigi[2],*array,er,ei,*uu,*s,*xx,*aa,pM[4],vec[4];
322 3 : PetscReal eta;
323 3 : EPS epsrr;
324 3 : PetscReal norm;
325 3 : EPS_LYAPII_MATSHELL *matctx;
326 :
327 3 : PetscFunctionBegin;
328 3 : PetscCall(DSGetLeadingDimension(ctx->ds,&ldds));
329 :
330 : /* Operator for the Lyapunov equation */
331 3 : PetscCall(PetscNew(&matctx));
332 3 : PetscCall(STGetOperator(eps->st,&matctx->S));
333 3 : PetscCall(MatGetLocalSize(matctx->S,&mloc,&nloc));
334 3 : PetscCall(MatCreateShell(PetscObjectComm((PetscObject)eps),mloc,nloc,PETSC_DETERMINE,PETSC_DETERMINE,matctx,&S));
335 3 : matctx->Q = eps->V;
336 3 : PetscCall(MatShellSetOperation(S,MATOP_MULT,(void(*)(void))MatMult_EPSLyapIIOperator));
337 3 : PetscCall(MatShellSetOperation(S,MATOP_DESTROY,(void(*)(void))MatDestroy_EPSLyapIIOperator));
338 3 : PetscCall(LMESetCoefficients(ctx->lme,S,NULL,NULL,NULL));
339 :
340 : /* Right-hand side */
341 3 : PetscCall(BVDuplicateResize(eps->V,ctx->rkl,&V));
342 3 : PetscCall(BVGetOrthogonalization(V,&type,&refine,&eta,NULL));
343 3 : PetscCall(BVSetOrthogonalization(V,type,refine,eta,BV_ORTHOG_BLOCK_TSQR));
344 3 : PetscCall(MatCreateDense(PetscObjectComm((PetscObject)eps),eps->nloc,PETSC_DECIDE,PETSC_DECIDE,1,NULL,&Ux[0]));
345 3 : PetscCall(MatCreateDense(PetscObjectComm((PetscObject)eps),eps->nloc,PETSC_DECIDE,PETSC_DECIDE,2,NULL,&Ux[1]));
346 3 : nv = ctx->rkl;
347 3 : PetscCall(PetscMalloc1(nv,&s));
348 :
349 : /* Initialize first column */
350 3 : PetscCall(EPSGetStartVector(eps,0,NULL));
351 3 : PetscCall(BVGetColumn(eps->V,0,&v));
352 3 : PetscCall(BVInsertVec(V,0,v));
353 3 : PetscCall(BVRestoreColumn(eps->V,0,&v));
354 3 : PetscCall(BVSetActiveColumns(eps->V,0,0)); /* no deflation at the beginning */
355 3 : PetscCall(LyapIIBuildRHS(S,1,Ux[0],V,eps->work));
356 3 : idx = 0;
357 :
358 : /* EPS for rank reduction */
359 3 : PetscCall(EPSCreate(PETSC_COMM_SELF,&epsrr));
360 3 : PetscCall(EPSSetOptionsPrefix(epsrr,((PetscObject)eps)->prefix));
361 3 : PetscCall(EPSAppendOptionsPrefix(epsrr,"eps_lyapii_"));
362 3 : PetscCall(EPSSetDimensions(epsrr,1,PETSC_CURRENT,PETSC_CURRENT));
363 3 : PetscCall(EPSSetTolerances(epsrr,PETSC_MACHINE_EPSILON*100,PETSC_CURRENT));
364 :
365 31 : while (eps->reason == EPS_CONVERGED_ITERATING) {
366 28 : eps->its++;
367 :
368 : /* Matrix for placing the solution of the Lyapunov equation (an alias of V) */
369 28 : PetscCall(BVSetActiveColumns(V,0,nv));
370 28 : PetscCall(BVGetMat(V,&Y1));
371 28 : PetscCall(MatZeroEntries(Y1));
372 28 : PetscCall(MatCreateLRC(NULL,Y1,NULL,NULL,&Y));
373 28 : PetscCall(LMESetSolution(ctx->lme,Y));
374 :
375 : /* Solve the Lyapunov equation SY + YS' = -2*S*Z*S' */
376 28 : PetscCall(MatCreateLRC(NULL,Ux[idx],NULL,NULL,&C));
377 28 : PetscCall(LMESetRHS(ctx->lme,C));
378 28 : PetscCall(MatDestroy(&C));
379 28 : PetscCall(LMESolve(ctx->lme));
380 28 : PetscCall(BVRestoreMat(V,&Y1));
381 28 : PetscCall(MatDestroy(&Y));
382 :
383 : /* SVD of the solution: [Q,R]=qr(V); [U,Sigma,~]=svd(R) */
384 28 : PetscCall(DSSetDimensions(ctx->ds,nv,0,0));
385 28 : PetscCall(DSSVDSetDimensions(ctx->ds,nv));
386 28 : PetscCall(DSGetMat(ctx->ds,DS_MAT_A,&R));
387 28 : PetscCall(BVOrthogonalize(V,R));
388 28 : PetscCall(DSRestoreMat(ctx->ds,DS_MAT_A,&R));
389 28 : PetscCall(DSSetState(ctx->ds,DS_STATE_RAW));
390 28 : PetscCall(DSSolve(ctx->ds,s,NULL));
391 :
392 : /* Determine rank */
393 519 : rk = nv;
394 519 : for (i=1;i<nv;i++) if (PetscAbsScalar(s[i]/s[0])<PETSC_SQRT_MACHINE_EPSILON) {rk=i; break;}
395 28 : PetscCall(PetscInfo(eps,"The computed solution of the Lyapunov equation has rank %" PetscInt_FMT "\n",rk));
396 28 : rk = PetscMin(rk,ctx->rkc);
397 28 : PetscCall(DSGetMat(ctx->ds,DS_MAT_U,&U));
398 28 : PetscCall(BVMultInPlace(V,U,0,rk));
399 28 : PetscCall(DSRestoreMat(ctx->ds,DS_MAT_U,&U));
400 28 : PetscCall(BVSetActiveColumns(V,0,rk));
401 :
402 : /* Rank reduction */
403 28 : PetscCall(DSSetDimensions(ctx->ds,rk,0,0));
404 28 : PetscCall(DSSVDSetDimensions(ctx->ds,rk));
405 28 : PetscCall(DSGetMat(ctx->ds,DS_MAT_A,&W));
406 28 : PetscCall(BVMatProject(V,S,V,W));
407 28 : PetscCall(LyapIIBuildEigenMat(ctx->lme,W,&Op,&v0)); /* Op=A\B, A=kron(I,S)+kron(S,I), B=-2*kron(S,S) */
408 28 : PetscCall(DSRestoreMat(ctx->ds,DS_MAT_A,&W));
409 28 : PetscCall(EPSSetOperators(epsrr,Op,NULL));
410 28 : PetscCall(EPSSetInitialSpace(epsrr,1,&v0));
411 28 : PetscCall(EPSSolve(epsrr));
412 28 : PetscCall(EPSComputeVectors(epsrr));
413 : /* Copy first eigenvector, vec(A)=x */
414 28 : PetscCall(BVGetArray(epsrr->V,&xx));
415 28 : PetscCall(DSGetArray(ctx->ds,DS_MAT_A,&aa));
416 282 : for (i=0;i<rk;i++) PetscCall(PetscArraycpy(aa+i*ldds,xx+i*rk,rk));
417 28 : PetscCall(DSRestoreArray(ctx->ds,DS_MAT_A,&aa));
418 28 : PetscCall(BVRestoreArray(epsrr->V,&xx));
419 28 : PetscCall(DSSetState(ctx->ds,DS_STATE_RAW));
420 : /* Compute [U,Sigma,~] = svd(A), its rank should be 1 or 2 */
421 28 : PetscCall(DSSolve(ctx->ds,s,NULL));
422 28 : if (PetscAbsScalar(s[1]/s[0])<PETSC_SQRT_MACHINE_EPSILON) rk=1;
423 25 : else rk = 2;
424 28 : PetscCall(PetscInfo(eps,"The eigenvector has rank %" PetscInt_FMT "\n",rk));
425 28 : PetscCall(DSGetMat(ctx->ds,DS_MAT_U,&U));
426 28 : PetscCall(BVMultInPlace(V,U,0,rk));
427 28 : PetscCall(DSRestoreMat(ctx->ds,DS_MAT_U,&U));
428 :
429 : /* Save V in Ux */
430 28 : idx = (rk==2)?1:0;
431 81 : for (i=0;i<rk;i++) {
432 53 : PetscCall(BVGetColumn(V,i,&v));
433 53 : PetscCall(VecGetArray(v,&uu));
434 53 : PetscCall(MatDenseGetColumn(Ux[idx],i,&array));
435 53 : PetscCall(PetscArraycpy(array,uu,eps->nloc));
436 53 : PetscCall(MatDenseRestoreColumn(Ux[idx],&array));
437 53 : PetscCall(VecRestoreArray(v,&uu));
438 53 : PetscCall(BVRestoreColumn(V,i,&v));
439 : }
440 :
441 : /* Eigenpair approximation */
442 28 : PetscCall(BVGetColumn(V,0,&v));
443 28 : PetscCall(MatMult(S,v,z));
444 28 : PetscCall(VecDot(z,v,pM));
445 28 : PetscCall(BVRestoreColumn(V,0,&v));
446 28 : if (rk>1) {
447 25 : PetscCall(BVGetColumn(V,1,&w));
448 25 : PetscCall(VecDot(z,w,pM+1));
449 25 : PetscCall(MatMult(S,w,z));
450 25 : PetscCall(VecDot(z,w,pM+3));
451 25 : PetscCall(BVGetColumn(V,0,&v));
452 25 : PetscCall(VecDot(z,v,pM+2));
453 25 : PetscCall(BVRestoreColumn(V,0,&v));
454 25 : PetscCall(BVRestoreColumn(V,1,&w));
455 25 : PetscCall(EV2x2(pM,2,eigr,eigi,vec));
456 25 : PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,2,2,vec,&X));
457 25 : PetscCall(BVSetActiveColumns(V,0,rk));
458 25 : PetscCall(BVMultInPlace(V,X,0,rk));
459 25 : PetscCall(MatDestroy(&X));
460 : #if !defined(PETSC_USE_COMPLEX)
461 : norm = eigr[0]*eigr[0]+eigi[0]*eigi[0];
462 : er = eigr[0]/norm; ei = -eigi[0]/norm;
463 : #else
464 25 : er =1.0/eigr[0]; ei = 0.0;
465 : #endif
466 : } else {
467 3 : eigr[0] = pM[0]; eigi[0] = 0.0;
468 3 : er = 1.0/eigr[0]; ei = 0.0;
469 : }
470 28 : PetscCall(BVGetColumn(V,0,&v));
471 28 : if (eigi[0]!=0.0) PetscCall(BVGetColumn(V,1,&w));
472 28 : else w = NULL;
473 28 : eps->eigr[eps->nconv] = eigr[0]; eps->eigi[eps->nconv] = eigi[0];
474 28 : PetscCall(EPSComputeResidualNorm_Private(eps,PETSC_FALSE,er,ei,v,w,eps->work,&norm));
475 28 : PetscCall(BVRestoreColumn(V,0,&v));
476 28 : if (w) PetscCall(BVRestoreColumn(V,1,&w));
477 28 : PetscCall((*eps->converged)(eps,er,ei,norm,&eps->errest[eps->nconv],eps->convergedctx));
478 28 : k = 0;
479 28 : if (eps->errest[eps->nconv]<eps->tol) {
480 7 : k++;
481 7 : if (rk==2) {
482 : #if !defined (PETSC_USE_COMPLEX)
483 : eps->eigr[eps->nconv+k] = eigr[0]; eps->eigi[eps->nconv+k] = -eigi[0];
484 : #else
485 6 : eps->eigr[eps->nconv+k] = PetscConj(eps->eigr[eps->nconv]);
486 : #endif
487 6 : k++;
488 : }
489 : /* Store converged eigenpairs and vectors for deflation */
490 20 : for (i=0;i<k;i++) {
491 13 : PetscCall(BVGetColumn(V,i,&v));
492 13 : PetscCall(BVInsertVec(eps->V,eps->nconv+i,v));
493 13 : PetscCall(BVRestoreColumn(V,i,&v));
494 : }
495 7 : eps->nconv += k;
496 7 : PetscCall(BVSetActiveColumns(eps->V,eps->nconv-rk,eps->nconv));
497 7 : PetscCall(BVOrthogonalize(eps->V,NULL));
498 7 : PetscCall(DSSetDimensions(eps->ds,eps->nconv,0,0));
499 7 : PetscCall(DSGetMat(eps->ds,DS_MAT_A,&W));
500 7 : PetscCall(BVMatProject(eps->V,matctx->S,eps->V,W));
501 7 : PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&W));
502 7 : if (eps->nconv<eps->nev) {
503 4 : idx = 0;
504 4 : PetscCall(BVSetRandomColumn(V,0));
505 4 : PetscCall(BVNormColumn(V,0,NORM_2,&norm));
506 4 : PetscCall(BVScaleColumn(V,0,1.0/norm));
507 4 : PetscCall(LyapIIBuildRHS(S,1,Ux[idx],V,eps->work));
508 : }
509 : } else {
510 : /* Prepare right-hand side */
511 21 : PetscCall(LyapIIBuildRHS(S,rk,Ux[idx],NULL,eps->work));
512 : }
513 28 : PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,eps->nconv,eps->nev,&eps->reason,eps->stoppingctx));
514 31 : PetscCall(EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,eps->nconv+1));
515 : }
516 3 : PetscCall(STRestoreOperator(eps->st,&matctx->S));
517 3 : PetscCall(MatDestroy(&S));
518 3 : PetscCall(MatDestroy(&Ux[0]));
519 3 : PetscCall(MatDestroy(&Ux[1]));
520 3 : PetscCall(MatDestroy(&Op));
521 3 : PetscCall(VecDestroy(&v0));
522 3 : PetscCall(BVDestroy(&V));
523 3 : PetscCall(EPSDestroy(&epsrr));
524 3 : PetscCall(PetscFree(s));
525 3 : PetscFunctionReturn(PETSC_SUCCESS);
526 : }
527 :
528 3 : static PetscErrorCode EPSSetFromOptions_LyapII(EPS eps,PetscOptionItems *PetscOptionsObject)
529 : {
530 3 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
531 3 : PetscInt k,array[2]={PETSC_DETERMINE,PETSC_DETERMINE};
532 3 : PetscBool flg;
533 :
534 3 : PetscFunctionBegin;
535 3 : PetscOptionsHeadBegin(PetscOptionsObject,"EPS Lyapunov Inverse Iteration Options");
536 :
537 3 : k = 2;
538 3 : PetscCall(PetscOptionsIntArray("-eps_lyapii_ranks","Ranks for Lyapunov equation (one or two comma-separated integers)","EPSLyapIISetRanks",array,&k,&flg));
539 3 : if (flg) PetscCall(EPSLyapIISetRanks(eps,array[0],array[1]));
540 :
541 3 : PetscOptionsHeadEnd();
542 :
543 3 : if (!ctx->lme) PetscCall(EPSLyapIIGetLME(eps,&ctx->lme));
544 3 : PetscCall(LMESetFromOptions(ctx->lme));
545 3 : PetscFunctionReturn(PETSC_SUCCESS);
546 : }
547 :
548 1 : static PetscErrorCode EPSLyapIISetRanks_LyapII(EPS eps,PetscInt rkc,PetscInt rkl)
549 : {
550 1 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
551 :
552 1 : PetscFunctionBegin;
553 1 : if (rkc==PETSC_DETERMINE) {
554 0 : if (ctx->rkc != 10) eps->state = EPS_STATE_INITIAL;
555 0 : ctx->rkc = 10;
556 1 : } else if (rkc!=PETSC_CURRENT) {
557 1 : PetscCheck(rkc>1,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The compressed rank %" PetscInt_FMT " must be larger than 1",rkc);
558 1 : if (ctx->rkc != rkc) eps->state = EPS_STATE_INITIAL;
559 1 : ctx->rkc = rkc;
560 : }
561 1 : if (rkl==PETSC_DETERMINE) {
562 0 : if (ctx->rkl != 3*rkc) eps->state = EPS_STATE_INITIAL;
563 0 : ctx->rkl = 3*rkc;
564 1 : } else if (rkl!=PETSC_CURRENT) {
565 1 : PetscCheck(rkl>=rkc,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The Lyapunov rank %" PetscInt_FMT " cannot be smaller than the compressed rank %" PetscInt_FMT,rkl,rkc);
566 1 : if (ctx->rkl != rkl) eps->state = EPS_STATE_INITIAL;
567 1 : ctx->rkl = rkl;
568 : }
569 1 : PetscFunctionReturn(PETSC_SUCCESS);
570 : }
571 :
572 : /*@
573 : EPSLyapIISetRanks - Set the ranks used in the solution of the Lyapunov equation.
574 :
575 : Logically Collective
576 :
577 : Input Parameters:
578 : + eps - the eigenproblem solver context
579 : . rkc - the compressed rank
580 : - rkl - the Lyapunov rank
581 :
582 : Options Database Key:
583 : . -eps_lyapii_ranks <rkc,rkl> - Sets the rank parameters
584 :
585 : Notes:
586 : PETSC_CURRENT can be used to preserve the current value of any of the
587 : arguments, and PETSC_DETERMINE to set them to a default value.
588 :
589 : Lyapunov inverse iteration needs to solve a large-scale Lyapunov equation
590 : at each iteration of the eigensolver. For this, an iterative solver (LME)
591 : is used, which requires to prescribe the rank of the solution matrix X. This
592 : is the meaning of parameter rkl. Later, this matrix is compressed into
593 : another matrix of rank rkc. If not provided, rkl is a small multiple of rkc.
594 :
595 : Level: intermediate
596 :
597 : .seealso: EPSLyapIIGetRanks()
598 : @*/
599 1 : PetscErrorCode EPSLyapIISetRanks(EPS eps,PetscInt rkc,PetscInt rkl)
600 : {
601 1 : PetscFunctionBegin;
602 1 : PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
603 3 : PetscValidLogicalCollectiveInt(eps,rkc,2);
604 3 : PetscValidLogicalCollectiveInt(eps,rkl,3);
605 1 : PetscTryMethod(eps,"EPSLyapIISetRanks_C",(EPS,PetscInt,PetscInt),(eps,rkc,rkl));
606 1 : PetscFunctionReturn(PETSC_SUCCESS);
607 : }
608 :
609 1 : static PetscErrorCode EPSLyapIIGetRanks_LyapII(EPS eps,PetscInt *rkc,PetscInt *rkl)
610 : {
611 1 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
612 :
613 1 : PetscFunctionBegin;
614 1 : if (rkc) *rkc = ctx->rkc;
615 1 : if (rkl) *rkl = ctx->rkl;
616 1 : PetscFunctionReturn(PETSC_SUCCESS);
617 : }
618 :
619 : /*@
620 : EPSLyapIIGetRanks - Return the rank values used for the Lyapunov step.
621 :
622 : Not Collective
623 :
624 : Input Parameter:
625 : . eps - the eigenproblem solver context
626 :
627 : Output Parameters:
628 : + rkc - the compressed rank
629 : - rkl - the Lyapunov rank
630 :
631 : Level: intermediate
632 :
633 : .seealso: EPSLyapIISetRanks()
634 : @*/
635 1 : PetscErrorCode EPSLyapIIGetRanks(EPS eps,PetscInt *rkc,PetscInt *rkl)
636 : {
637 1 : PetscFunctionBegin;
638 1 : PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
639 1 : PetscUseMethod(eps,"EPSLyapIIGetRanks_C",(EPS,PetscInt*,PetscInt*),(eps,rkc,rkl));
640 1 : PetscFunctionReturn(PETSC_SUCCESS);
641 : }
642 :
643 0 : static PetscErrorCode EPSLyapIISetLME_LyapII(EPS eps,LME lme)
644 : {
645 0 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
646 :
647 0 : PetscFunctionBegin;
648 0 : PetscCall(PetscObjectReference((PetscObject)lme));
649 0 : PetscCall(LMEDestroy(&ctx->lme));
650 0 : ctx->lme = lme;
651 0 : eps->state = EPS_STATE_INITIAL;
652 0 : PetscFunctionReturn(PETSC_SUCCESS);
653 : }
654 :
655 : /*@
656 : EPSLyapIISetLME - Associate a linear matrix equation solver object (LME) to the
657 : eigenvalue solver.
658 :
659 : Collective
660 :
661 : Input Parameters:
662 : + eps - the eigenproblem solver context
663 : - lme - the linear matrix equation solver object
664 :
665 : Level: advanced
666 :
667 : .seealso: EPSLyapIIGetLME()
668 : @*/
669 0 : PetscErrorCode EPSLyapIISetLME(EPS eps,LME lme)
670 : {
671 0 : PetscFunctionBegin;
672 0 : PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
673 0 : PetscValidHeaderSpecific(lme,LME_CLASSID,2);
674 0 : PetscCheckSameComm(eps,1,lme,2);
675 0 : PetscTryMethod(eps,"EPSLyapIISetLME_C",(EPS,LME),(eps,lme));
676 0 : PetscFunctionReturn(PETSC_SUCCESS);
677 : }
678 :
679 3 : static PetscErrorCode EPSLyapIIGetLME_LyapII(EPS eps,LME *lme)
680 : {
681 3 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
682 :
683 3 : PetscFunctionBegin;
684 3 : if (!ctx->lme) {
685 3 : PetscCall(LMECreate(PetscObjectComm((PetscObject)eps),&ctx->lme));
686 3 : PetscCall(LMESetOptionsPrefix(ctx->lme,((PetscObject)eps)->prefix));
687 3 : PetscCall(LMEAppendOptionsPrefix(ctx->lme,"eps_lyapii_"));
688 3 : PetscCall(PetscObjectIncrementTabLevel((PetscObject)ctx->lme,(PetscObject)eps,1));
689 : }
690 3 : *lme = ctx->lme;
691 3 : PetscFunctionReturn(PETSC_SUCCESS);
692 : }
693 :
694 : /*@
695 : EPSLyapIIGetLME - Retrieve the linear matrix equation solver object (LME)
696 : associated with the eigenvalue solver.
697 :
698 : Not Collective
699 :
700 : Input Parameter:
701 : . eps - the eigenproblem solver context
702 :
703 : Output Parameter:
704 : . lme - the linear matrix equation solver object
705 :
706 : Level: advanced
707 :
708 : .seealso: EPSLyapIISetLME()
709 : @*/
710 3 : PetscErrorCode EPSLyapIIGetLME(EPS eps,LME *lme)
711 : {
712 3 : PetscFunctionBegin;
713 3 : PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
714 3 : PetscAssertPointer(lme,2);
715 3 : PetscUseMethod(eps,"EPSLyapIIGetLME_C",(EPS,LME*),(eps,lme));
716 3 : PetscFunctionReturn(PETSC_SUCCESS);
717 : }
718 :
719 1 : static PetscErrorCode EPSView_LyapII(EPS eps,PetscViewer viewer)
720 : {
721 1 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
722 1 : PetscBool isascii;
723 :
724 1 : PetscFunctionBegin;
725 1 : PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
726 1 : if (isascii) {
727 1 : PetscCall(PetscViewerASCIIPrintf(viewer," ranks: for Lyapunov solver=%" PetscInt_FMT ", after compression=%" PetscInt_FMT "\n",ctx->rkl,ctx->rkc));
728 1 : if (!ctx->lme) PetscCall(EPSLyapIIGetLME(eps,&ctx->lme));
729 1 : PetscCall(PetscViewerASCIIPushTab(viewer));
730 1 : PetscCall(LMEView(ctx->lme,viewer));
731 1 : PetscCall(PetscViewerASCIIPopTab(viewer));
732 : }
733 1 : PetscFunctionReturn(PETSC_SUCCESS);
734 : }
735 :
736 3 : static PetscErrorCode EPSReset_LyapII(EPS eps)
737 : {
738 3 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
739 :
740 3 : PetscFunctionBegin;
741 3 : if (!ctx->lme) PetscCall(LMEReset(ctx->lme));
742 3 : PetscFunctionReturn(PETSC_SUCCESS);
743 : }
744 :
745 3 : static PetscErrorCode EPSDestroy_LyapII(EPS eps)
746 : {
747 3 : EPS_LYAPII *ctx = (EPS_LYAPII*)eps->data;
748 :
749 3 : PetscFunctionBegin;
750 3 : PetscCall(LMEDestroy(&ctx->lme));
751 3 : PetscCall(DSDestroy(&ctx->ds));
752 3 : PetscCall(PetscFree(eps->data));
753 3 : PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLyapIISetLME_C",NULL));
754 3 : PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLyapIIGetLME_C",NULL));
755 3 : PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLyapIISetRanks_C",NULL));
756 3 : PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLyapIIGetRanks_C",NULL));
757 3 : PetscFunctionReturn(PETSC_SUCCESS);
758 : }
759 :
760 6 : static PetscErrorCode EPSSetDefaultST_LyapII(EPS eps)
761 : {
762 6 : PetscFunctionBegin;
763 6 : if (!((PetscObject)eps->st)->type_name) PetscCall(STSetType(eps->st,STSINVERT));
764 6 : PetscFunctionReturn(PETSC_SUCCESS);
765 : }
766 :
767 3 : SLEPC_EXTERN PetscErrorCode EPSCreate_LyapII(EPS eps)
768 : {
769 3 : EPS_LYAPII *ctx;
770 :
771 3 : PetscFunctionBegin;
772 3 : PetscCall(PetscNew(&ctx));
773 3 : eps->data = (void*)ctx;
774 :
775 3 : eps->useds = PETSC_TRUE;
776 :
777 3 : eps->ops->solve = EPSSolve_LyapII;
778 3 : eps->ops->setup = EPSSetUp_LyapII;
779 3 : eps->ops->setupsort = EPSSetUpSort_Default;
780 3 : eps->ops->setfromoptions = EPSSetFromOptions_LyapII;
781 3 : eps->ops->reset = EPSReset_LyapII;
782 3 : eps->ops->destroy = EPSDestroy_LyapII;
783 3 : eps->ops->view = EPSView_LyapII;
784 3 : eps->ops->setdefaultst = EPSSetDefaultST_LyapII;
785 3 : eps->ops->backtransform = EPSBackTransform_Default;
786 3 : eps->ops->computevectors = EPSComputeVectors_Schur;
787 :
788 3 : PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLyapIISetLME_C",EPSLyapIISetLME_LyapII));
789 3 : PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLyapIIGetLME_C",EPSLyapIIGetLME_LyapII));
790 3 : PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLyapIISetRanks_C",EPSLyapIISetRanks_LyapII));
791 3 : PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLyapIIGetRanks_C",EPSLyapIIGetRanks_LyapII));
792 3 : PetscFunctionReturn(PETSC_SUCCESS);
793 : }
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