GCC Code Coverage Report

Directory: ./
File: src/eps/impls/krylov/lanczos/lanczos.c
Date: 2025-10-03 04:28:47
Exec Total Coverage
Lines: 462 493 93.7%
Functions: 17 18 94.4%
Branches: 926 1596 58.0%
Line Branch Exec Source
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: "lanczos"
12
13 Method: Explicitly Restarted Symmetric/Hermitian Lanczos
14
15 Algorithm:
16
17 Lanczos method for symmetric (Hermitian) problems, with explicit
18 restart and deflation. Several reorthogonalization strategies can
19 be selected.
20
21 References:
22
23 [1] "Lanczos Methods in SLEPc", SLEPc Technical Report STR-5,
24 available at https://slepc.upv.es.
25 */
26
27 #include <slepc/private/epsimpl.h> /*I "slepceps.h" I*/
28 #include <slepcblaslapack.h>
29
30 typedef struct {
31 EPSLanczosReorthogType reorthog; /* user-provided reorthogonalization parameter */
32 PetscInt allocsize; /* number of columns of work BV's allocated at setup */
33 BV AV; /* work BV used in selective reorthogonalization */
34 } EPS_LANCZOS;
35
36 364 static PetscErrorCode EPSSetUp_Lanczos(EPS eps)
37 {
38 364 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
39 364 BVOrthogRefineType refine;
40 364 BVOrthogBlockType btype;
41 364 PetscReal eta;
42
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 364 PetscFunctionBegin;
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 364 EPSCheckHermitianDefinite(eps);
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 364 EPSCheckNotStructured(eps);
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 364 PetscCall(EPSSetDimensions_Default(eps,&eps->nev,&eps->ncv,&eps->mpd));
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 364 PetscCheck(eps->ncv<=eps->nev+eps->mpd,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must not be larger than nev+mpd");
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 364 if (eps->max_it==PETSC_DETERMINE) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
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 364 if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps));
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 364 PetscCheck(eps->which!=EPS_ALL,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues");
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 364 EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION | EPS_FEATURE_THRESHOLD);
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 364 EPSCheckIgnored(eps,EPS_FEATURE_BALANCE);
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 364 PetscCheck(lanczos->reorthog!=(EPSLanczosReorthogType)-1,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"You should explicitly provide the reorthogonalization type, e.g., -eps_lanczos_reorthog local. Note that the EPSLANCZOS solver is *NOT RECOMMENDED* for general use, because it uses explicit restart which typically has slow convergence. The recommended solver is EPSKRYLOVSCHUR (the default), which implements Lanczos with thick restart in the case of symmetric/Hermitian problems");
55
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 364 PetscCall(EPSAllocateSolution(eps,1));
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 364 PetscCall(EPS_SetInnerProduct(eps));
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 364 if (lanczos->reorthog != EPS_LANCZOS_REORTHOG_FULL) {
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 290 PetscCall(BVGetOrthogonalization(eps->V,NULL,&refine,&eta,&btype));
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 290 PetscCall(BVSetOrthogonalization(eps->V,BV_ORTHOG_MGS,refine,eta,btype));
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 290 PetscCall(PetscInfo(eps,"Switching to MGS orthogonalization\n"));
62 }
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 364 if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_SELECTIVE) {
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 30 if (!lanczos->allocsize) {
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 10 PetscCall(BVDuplicate(eps->V,&lanczos->AV));
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 10 PetscCall(BVGetSizes(lanczos->AV,NULL,NULL,&lanczos->allocsize));
67 } else { /* make sure V and AV have the same size */
68
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 20 PetscCall(BVGetSizes(eps->V,NULL,NULL,&lanczos->allocsize));
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 20 PetscCall(BVResize(lanczos->AV,lanczos->allocsize,PETSC_FALSE));
70 }
71 }
72
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 364 PetscCall(DSSetType(eps->ds,DSHEP));
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 364 PetscCall(DSSetCompact(eps->ds,PETSC_TRUE));
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 364 PetscCall(DSAllocate(eps->ds,eps->ncv+1));
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 364 if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL) PetscCall(EPSSetWorkVecs(eps,1));
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 72 PetscFunctionReturn(PETSC_SUCCESS);
78 }
79
80 /*
81 EPSLocalLanczos - Local reorthogonalization.
82
83 This is the simplest variant. At each Lanczos step, the corresponding Lanczos vector
84 is orthogonalized with respect to the two previous Lanczos vectors, according to
85 the three term Lanczos recurrence. WARNING: This variant does not track the loss of
86 orthogonality that occurs in finite-precision arithmetic and, therefore, the
87 generated vectors are not guaranteed to be (semi-)orthogonal.
88 */
89 5204 static PetscErrorCode EPSLocalLanczos(EPS eps,PetscReal *alpha,PetscReal *beta,PetscInt k,PetscInt *M,PetscBool *breakdown)
90 {
91 5204 PetscInt i,j,m = *M;
92 5204 Mat Op;
93 5204 PetscBool *which,lwhich[100];
94 5204 PetscScalar *hwork,lhwork[100];
95
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 5204 PetscFunctionBegin;
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 5204 if (m > 100) PetscCall(PetscMalloc2(m,&which,m,&hwork));
98 else {
99 5204 which = lwhich;
100 5204 hwork = lhwork;
101 }
102
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 18198 for (i=0;i<k;i++) which[i] = PETSC_TRUE;
103
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 5204 PetscCall(BVSetActiveColumns(eps->V,0,m));
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 5204 PetscCall(STGetOperator(eps->st,&Op));
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 75639 for (j=k;j<m;j++) {
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 70435 PetscCall(BVMatMultColumn(eps->V,Op,j));
108 70435 which[j] = PETSC_TRUE;
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 70435 if (j-2>=k) which[j-2] = PETSC_FALSE;
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 70435 PetscCall(BVOrthogonalizeSomeColumn(eps->V,j+1,which,hwork,beta+j,breakdown));
111 70435 alpha[j] = PetscRealPart(hwork[j]);
112
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 70435 if (PetscUnlikely(*breakdown)) {
113 ✗ *M = j+1;
114 ✗ break;
115
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 70435 } else PetscCall(BVScaleColumn(eps->V,j+1,1/beta[j]));
116 }
117
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 5204 PetscCall(STRestoreOperator(eps->st,&Op));
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 5204 if (m > 100) PetscCall(PetscFree2(which,hwork));
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 1046 PetscFunctionReturn(PETSC_SUCCESS);
120 }
121
122 /*
123 DenseTridiagonal - Solves a real tridiagonal Hermitian Eigenvalue Problem.
124
125 Input Parameters:
126 + n - dimension of the eigenproblem
127 . D - pointer to the array containing the diagonal elements
128 - E - pointer to the array containing the off-diagonal elements
129
130 Output Parameters:
131 + w - pointer to the array to store the computed eigenvalues
132 - V - pointer to the array to store the eigenvectors
133
134 Notes:
135 If V is NULL then the eigenvectors are not computed.
136
137 This routine use LAPACK routines xSTEVR.
138 */
139 6745 static PetscErrorCode DenseTridiagonal(PetscInt n_,PetscReal *D,PetscReal *E,PetscReal *w,PetscScalar *V)
140 {
141 6745 PetscReal abstol = 0.0,vl,vu,*work;
142 6745 PetscBLASInt il,iu,m,*isuppz,n,lwork,*iwork,liwork,info;
143 6745 const char *jobz;
144 #if defined(PETSC_USE_COMPLEX)
145 3380 PetscInt i,j;
146 3380 PetscReal *VV=NULL;
147 #endif
148
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 6745 PetscFunctionBegin;
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 6745 PetscCall(PetscBLASIntCast(n_,&n));
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 6745 PetscCall(PetscBLASIntCast(20*n_,&lwork));
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 6745 PetscCall(PetscBLASIntCast(10*n_,&liwork));
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 6745 if (V) {
154 3380 jobz = "V";
155 #if defined(PETSC_USE_COMPLEX)
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 3380 PetscCall(PetscMalloc1(n*n,&VV));
157 #endif
158 ✗ } else jobz = "N";
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 6745 PetscCall(PetscMalloc3(2*n,&isuppz,lwork,&work,liwork,&iwork));
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 6745 PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
161 #if defined(PETSC_USE_COMPLEX)
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 3380 PetscCallBLAS("LAPACKstevr",LAPACKstevr_(jobz,"A",&n,D,E,&vl,&vu,&il,&iu,&abstol,&m,w,VV,&n,isuppz,work,&lwork,iwork,&liwork,&info));
163 #else
164
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 3365 PetscCallBLAS("LAPACKstevr",LAPACKstevr_(jobz,"A",&n,D,E,&vl,&vu,&il,&iu,&abstol,&m,w,V,&n,isuppz,work,&lwork,iwork,&liwork,&info));
165 #endif
166
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 6745 PetscCall(PetscFPTrapPop());
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 6745 SlepcCheckLapackInfo("stevr",info);
168 #if defined(PETSC_USE_COMPLEX)
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 3380 if (V) {
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 35265 for (i=0;i<n;i++)
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 423810 for (j=0;j<n;j++)
172 391925 V[i*n+j] = VV[i*n+j];
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 3380 PetscCall(PetscFree(VV));
174 }
175 #endif
176
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 6745 PetscCall(PetscFree3(isuppz,work,iwork));
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 1349 PetscFunctionReturn(PETSC_SUCCESS);
178 }
179
180 /*
181 EPSSelectiveLanczos - Selective reorthogonalization.
182 */
183 380 static PetscErrorCode EPSSelectiveLanczos(EPS eps,PetscReal *alpha,PetscReal *beta,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscReal anorm)
184 {
185 380 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
186 380 PetscInt i,j,m = *M,n,nritz=0,nritzo;
187 380 Vec vj1,av;
188 380 Mat Op;
189 380 PetscReal *d,*e,*ritz,norm;
190 380 PetscScalar *Y,*hwork;
191 380 PetscBool *which;
192
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 380 PetscFunctionBegin;
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 380 PetscCall(PetscCalloc6(m+1,&d,m,&e,m,&ritz,m*m,&Y,m,&which,m,&hwork));
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 855 for (i=0;i<k;i++) which[i] = PETSC_TRUE;
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 380 PetscCall(STGetOperator(eps->st,&Op));
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 7125 for (j=k;j<m;j++) {
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 6745 PetscCall(BVSetActiveColumns(eps->V,0,m));
200
201 /* Lanczos step */
202
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 6745 PetscCall(BVMatMultColumn(eps->V,Op,j));
203 6745 which[j] = PETSC_TRUE;
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 6745 if (j-2>=k) which[j-2] = PETSC_FALSE;
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 6745 PetscCall(BVOrthogonalizeSomeColumn(eps->V,j+1,which,hwork,&norm,breakdown));
206 6745 alpha[j] = PetscRealPart(hwork[j]);
207 6745 beta[j] = norm;
208
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 6745 if (PetscUnlikely(*breakdown)) {
209 ✗ *M = j+1;
210 ✗ break;
211 }
212
213 /* Compute eigenvalues and eigenvectors Y of the tridiagonal block */
214 6745 n = j-k+1;
215
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 70235 for (i=0;i<n;i++) {
216 63490 d[i] = alpha[i+k];
217 63490 e[i] = beta[i+k];
218 }
219
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 6745 PetscCall(DenseTridiagonal(n,d,e,ritz,Y));
220
221 /* Estimate ||A|| */
222
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 70235 for (i=0;i<n;i++)
223
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 63490 if (PetscAbsReal(ritz[i]) > anorm) anorm = PetscAbsReal(ritz[i]);
224
225 /* Compute nearly converged Ritz vectors */
226 nritzo = 0;
227
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 70235 for (i=0;i<n;i++) {
228
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 63490 if (norm*PetscAbsScalar(Y[i*n+n-1]) < PETSC_SQRT_MACHINE_EPSILON*anorm) nritzo++;
229 }
230
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 6745 if (nritzo>nritz) {
231 nritz = 0;
232
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 1780 for (i=0;i<n;i++) {
233
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 1555 if (norm*PetscAbsScalar(Y[i*n+n-1]) < PETSC_SQRT_MACHINE_EPSILON*anorm) {
234
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 345 PetscCall(BVSetActiveColumns(eps->V,k,k+n));
235
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 345 PetscCall(BVGetColumn(lanczos->AV,nritz,&av));
236
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 345 PetscCall(BVMultVec(eps->V,1.0,0.0,av,Y+i*n));
237
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 345 PetscCall(BVRestoreColumn(lanczos->AV,nritz,&av));
238 345 nritz++;
239 }
240 }
241 }
242
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 6745 if (nritz > 0) {
243
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 2510 PetscCall(BVGetColumn(eps->V,j+1,&vj1));
244
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 2510 PetscCall(BVSetActiveColumns(lanczos->AV,0,nritz));
245
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 2510 PetscCall(BVOrthogonalizeVec(lanczos->AV,vj1,hwork,&norm,breakdown));
246
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 2510 PetscCall(BVRestoreColumn(eps->V,j+1,&vj1));
247
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 2510 if (PetscUnlikely(*breakdown)) {
248 ✗ *M = j+1;
249 ✗ break;
250 }
251 }
252
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 6745 PetscCall(BVScaleColumn(eps->V,j+1,1.0/norm));
253 }
254
255
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 380 PetscCall(STRestoreOperator(eps->st,&Op));
256
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 380 PetscCall(PetscFree6(d,e,ritz,Y,which,hwork));
257
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 76 PetscFunctionReturn(PETSC_SUCCESS);
258 }
259
260 8050 static void update_omega(PetscReal *omega,PetscReal *omega_old,PetscInt j,PetscReal *alpha,PetscReal *beta,PetscReal eps1,PetscReal anorm)
261 {
262 8050 PetscInt k;
263 8050 PetscReal T,binv;
264
265
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 8050 PetscFunctionBegin;
266 /* Estimate of contribution to roundoff errors from A*v
267 fl(A*v) = A*v + f,
268 where ||f|| \approx eps1*||A||.
269 For a full matrix A, a rule-of-thumb estimate is eps1 = sqrt(n)*eps */
270 8050 T = eps1*anorm;
271 8050 binv = 1.0/beta[j+1];
272
273 /* Update omega(1) using omega(0)==0 */
274 8050 omega_old[0]= beta[1]*omega[1] + (alpha[0]-alpha[j])*omega[0] - beta[j]*omega_old[0];
275
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 8050 if (omega_old[0] > 0) omega_old[0] = binv*(omega_old[0] + T);
276 4835 else omega_old[0] = binv*(omega_old[0] - T);
277
278 /* Update remaining components */
279
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 73230 for (k=1;k<j-1;k++) {
280 65180 omega_old[k] = beta[k+1]*omega[k+1] + (alpha[k]-alpha[j])*omega[k] + beta[k]*omega[k-1] - beta[j]*omega_old[k];
281
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 65180 if (omega_old[k] > 0) omega_old[k] = binv*(omega_old[k] + T);
282 33928 else omega_old[k] = binv*(omega_old[k] - T);
283 }
284 8050 omega_old[j-1] = binv*T;
285
286 /* Swap omega and omega_old */
287
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 89150 for (k=0;k<j;k++) {
288 81100 omega[k] = omega_old[k];
289 81100 omega_old[k] = omega[k];
290 }
291 8050 omega[j] = eps1;
292
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 8050 PetscFunctionReturnVoid();
293 }
294
295 505 static void compute_int(PetscBool *which,PetscReal *mu,PetscInt j,PetscReal delta,PetscReal eta)
296 {
297 505 PetscInt i,k,maxpos;
298 505 PetscReal max;
299 505 PetscBool found;
300
301
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 505 PetscFunctionBegin;
302 /* initialize which */
303 505 found = PETSC_FALSE;
304 505 maxpos = 0;
305 505 max = 0.0;
306
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 7990 for (i=0;i<j;i++) {
307
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 7485 if (PetscAbsReal(mu[i]) >= delta) {
308 1820 which[i] = PETSC_TRUE;
309 1820 found = PETSC_TRUE;
310 5665 } else which[i] = PETSC_FALSE;
311
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 7485 if (PetscAbsReal(mu[i]) > max) {
312 830 maxpos = i;
313 830 max = PetscAbsReal(mu[i]);
314 }
315 }
316
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 505 if (!found) which[maxpos] = PETSC_TRUE;
317
318
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 7990 for (i=0;i<j;i++) {
319
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 7485 if (which[i]) {
320 /* find left interval */
321
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 6560 for (k=i;k>=0;k--) {
322
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 6560 if (PetscAbsReal(mu[k])<eta || which[k]) break;
323 ✗ else which[k] = PETSC_TRUE;
324 }
325 /* find right interval */
326
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 11300 for (k=i+1;k<j;k++) {
327
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 10980 if (PetscAbsReal(mu[k])<eta || which[k]) break;
328 4740 else which[k] = PETSC_TRUE;
329 }
330 }
331 }
332
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 505 PetscFunctionReturnVoid();
333 }
334
335 /*
336 EPSPartialLanczos - Partial reorthogonalization.
337 */
338 760 static PetscErrorCode EPSPartialLanczos(EPS eps,PetscReal *alpha,PetscReal *beta,PetscInt k,PetscInt *M,PetscBool *breakdown,PetscReal anorm)
339 {
340 760 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
341 760 PetscInt i,j,m = *M;
342 760 Mat Op;
343 760 PetscReal norm,*omega,lomega[100],*omega_old,lomega_old[100],eps1,delta,eta;
344 760 PetscBool *which,lwhich[100],*which2,lwhich2[100];
345 760 PetscBool reorth = PETSC_FALSE,force_reorth = PETSC_FALSE;
346 760 PetscBool fro = PETSC_FALSE,estimate_anorm = PETSC_FALSE;
347 760 PetscScalar *hwork,lhwork[100];
348
349
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 760 PetscFunctionBegin;
350
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 760 if (m>100) PetscCall(PetscMalloc5(m,&omega,m,&omega_old,m,&which,m,&which2,m,&hwork));
351 else {
352 760 omega = lomega;
353 760 omega_old = lomega_old;
354 760 which = lwhich;
355 760 which2 = lwhich2;
356 760 hwork = lhwork;
357 }
358
359 760 eps1 = PetscSqrtReal((PetscReal)eps->n)*PETSC_MACHINE_EPSILON/2;
360 760 delta = PETSC_SQRT_MACHINE_EPSILON/PetscSqrtReal((PetscReal)eps->ncv);
361 760 eta = PetscPowReal(PETSC_MACHINE_EPSILON,3.0/4.0)/PetscSqrtReal((PetscReal)eps->ncv);
362
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 760 if (anorm < 0.0) {
363 60 anorm = 1.0;
364 60 estimate_anorm = PETSC_TRUE;
365 }
366
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 76760 for (i=0;i<PetscMax(100,m);i++) omega[i] = omega_old[i] = 0.0;
367
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 1710 for (i=0;i<k;i++) which[i] = PETSC_TRUE;
368
369
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 760 PetscCall(BVSetActiveColumns(eps->V,0,m));
370
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 760 PetscCall(STGetOperator(eps->st,&Op));
371
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 14250 for (j=k;j<m;j++) {
372
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 13490 PetscCall(BVMatMultColumn(eps->V,Op,j));
373
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 13490 if (fro) {
374 /* Lanczos step with full reorthogonalization */
375
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 4680 PetscCall(BVOrthogonalizeColumn(eps->V,j+1,hwork,&norm,breakdown));
376 4680 alpha[j] = PetscRealPart(hwork[j]);
377 } else {
378 /* Lanczos step */
379 8810 which[j] = PETSC_TRUE;
380
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 8810 if (j-2>=k) which[j-2] = PETSC_FALSE;
381
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 8810 PetscCall(BVOrthogonalizeSomeColumn(eps->V,j+1,which,hwork,&norm,breakdown));
382 8810 alpha[j] = PetscRealPart(hwork[j]);
383 8810 beta[j] = norm;
384
385 /* Estimate ||A|| if needed */
386
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 8810 if (estimate_anorm) {
387
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 1140 if (j>k) anorm = PetscMax(anorm,PetscAbsReal(alpha[j])+norm+beta[j-1]);
388
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 60 else anorm = PetscMax(anorm,PetscAbsReal(alpha[j])+norm);
389 }
390
391 /* Check if reorthogonalization is needed */
392 8810 reorth = PETSC_FALSE;
393
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 8810 if (j>k) {
394 8050 update_omega(omega,omega_old,j,alpha,beta-1,eps1,anorm);
395
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 87950 for (i=0;i<j-k;i++) {
396
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 71850 if (PetscAbsReal(omega[i]) > delta) reorth = PETSC_TRUE;
397 }
398 }
399
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 8810 if (reorth || force_reorth) {
400
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 2940 for (i=0;i<k;i++) which2[i] = PETSC_FALSE;
401
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 27790 for (i=k;i<=j;i++) which2[i] = PETSC_TRUE;
402
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 1660 if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_PERIODIC) {
403 /* Periodic reorthogonalization */
404
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 820 if (force_reorth) force_reorth = PETSC_FALSE;
405 485 else force_reorth = PETSC_TRUE;
406
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 12880 for (i=0;i<j-k;i++) omega[i] = eps1;
407 } else {
408 /* Partial reorthogonalization */
409
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 840 if (force_reorth) force_reorth = PETSC_FALSE;
410 else {
411 505 force_reorth = PETSC_TRUE;
412 505 compute_int(which2+k,omega,j-k,delta,eta);
413
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 8495 for (i=0;i<j-k;i++) {
414
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 7485 if (which2[i+k]) omega[i] = eps1;
415 }
416 }
417 }
418
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 1660 PetscCall(BVOrthogonalizeSomeColumn(eps->V,j+1,which2,hwork,&norm,breakdown));
419 }
420 }
421
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 13490 if (PetscUnlikely(*breakdown || norm < eps->n*anorm*PETSC_MACHINE_EPSILON)) {
423 ✗ *M = j+1;
424 ✗ break;
425 }
426
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 13490 if (!fro && norm*delta < anorm*eps1) {
427 280 fro = PETSC_TRUE;
428
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 280 PetscCall(PetscInfo(eps,"Switching to full reorthogonalization at iteration %" PetscInt_FMT "\n",eps->its));
429 }
430 13490 beta[j] = norm;
431
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 13490 PetscCall(BVScaleColumn(eps->V,j+1,1.0/norm));
432 }
433
434
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 760 PetscCall(STRestoreOperator(eps->st,&Op));
435
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 760 if (m>100) PetscCall(PetscFree5(omega,omega_old,which,which2,hwork));
436
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 152 PetscFunctionReturn(PETSC_SUCCESS);
437 }
438
439 /*
440 EPSBasicLanczos - Computes an m-step Lanczos factorization. The first k
441 columns are assumed to be locked and therefore they are not modified. On
442 exit, the following relation is satisfied:
443
444 OP * V - V * T = f * e_m^T
445
446 where the columns of V are the Lanczos vectors, T is a tridiagonal matrix,
447 f is the residual vector and e_m is the m-th vector of the canonical basis.
448 The Lanczos vectors (together with vector f) are B-orthogonal (to working
449 accuracy) if full reorthogonalization is being used, otherwise they are
450 (B-)semi-orthogonal. On exit, beta contains the B-norm of f and the next
451 Lanczos vector can be computed as v_{m+1} = f / beta.
452
453 This function simply calls another function which depends on the selected
454 reorthogonalization strategy.
455 */
456 9504 static PetscErrorCode EPSBasicLanczos(EPS eps,PetscInt k,PetscInt *m,PetscReal *betam,PetscBool *breakdown,PetscReal anorm)
457 {
458 9504 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
459 9504 PetscScalar *T;
460 9504 PetscInt i,n=*m,ld;
461 9504 PetscReal *alpha,*beta;
462 9504 BVOrthogRefineType orthog_ref;
463 9504 Mat Op,M;
464
465
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 9504 PetscFunctionBegin;
466
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 9504 PetscCall(DSGetLeadingDimension(eps->ds,&ld));
467
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 9504 switch (lanczos->reorthog) {
468 5204 case EPS_LANCZOS_REORTHOG_LOCAL:
469
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 5204 PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&alpha));
470 5204 beta = alpha + ld;
471
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 5204 PetscCall(EPSLocalLanczos(eps,alpha,beta,k,m,breakdown));
472 5204 *betam = beta[*m-1];
473
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 5204 PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&alpha));
474 break;
475 2910 case EPS_LANCZOS_REORTHOG_FULL:
476
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 2910 PetscCall(STGetOperator(eps->st,&Op));
477
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 2910 PetscCall(DSGetMat(eps->ds,DS_MAT_T,&M));
478
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 2910 PetscCall(BVMatLanczos(eps->V,Op,M,k,m,betam,breakdown));
479
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 2910 PetscCall(DSRestoreMat(eps->ds,DS_MAT_T,&M));
480
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 2910 PetscCall(STRestoreOperator(eps->st,&Op));
481 break;
482 380 case EPS_LANCZOS_REORTHOG_SELECTIVE:
483
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 380 PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&alpha));
484 380 beta = alpha + ld;
485
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 380 PetscCall(EPSSelectiveLanczos(eps,alpha,beta,k,m,breakdown,anorm));
486 380 *betam = beta[*m-1];
487
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 380 PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&alpha));
488 break;
489 760 case EPS_LANCZOS_REORTHOG_PERIODIC:
490 case EPS_LANCZOS_REORTHOG_PARTIAL:
491
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 760 PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&alpha));
492 760 beta = alpha + ld;
493
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 760 PetscCall(EPSPartialLanczos(eps,alpha,beta,k,m,breakdown,anorm));
494 760 *betam = beta[*m-1];
495
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 760 PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&alpha));
496 break;
497 250 case EPS_LANCZOS_REORTHOG_DELAYED:
498
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 250 PetscCall(PetscMalloc1(n*n,&T));
499
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 250 PetscCall(BVGetOrthogonalization(eps->V,NULL,&orthog_ref,NULL,NULL));
500
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 250 if (orthog_ref == BV_ORTHOG_REFINE_NEVER) PetscCall(EPSDelayedArnoldi1(eps,T,n,k,m,betam,breakdown));
501
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 250 else PetscCall(EPSDelayedArnoldi(eps,T,n,k,m,betam,breakdown));
502 250 n = *m;
503
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 250 PetscCall(DSGetArrayReal(eps->ds,DS_MAT_T,&alpha));
504 250 beta = alpha + ld;
505
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 4375 for (i=k;i<n-1;i++) {
506 4125 alpha[i] = PetscRealPart(T[n*i+i]);
507 4125 beta[i] = PetscRealPart(T[n*i+i+1]);
508 }
509 250 alpha[n-1] = PetscRealPart(T[n*(n-1)+n-1]);
510 250 beta[n-1] = *betam;
511
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 250 PetscCall(DSRestoreArrayReal(eps->ds,DS_MAT_T,&alpha));
512
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 250 PetscCall(PetscFree(T));
513 break;
514 }
515
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 1877 PetscFunctionReturn(PETSC_SUCCESS);
516 }
517
518 364 static PetscErrorCode EPSSolve_Lanczos(EPS eps)
519 {
520 364 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
521 364 PetscInt nconv,i,j,k,l,x,n,*perm,restart,ncv=eps->ncv,r,ld;
522 364 Vec vi,vj,w;
523 364 Mat U;
524 364 PetscScalar *Y,*ritz,stmp;
525 364 PetscReal *bnd,anorm,beta,norm,rtmp,resnorm;
526 364 PetscBool breakdown;
527 364 char *conv,ctmp;
528
529
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 364 PetscFunctionBegin;
530
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 364 PetscCall(DSGetLeadingDimension(eps->ds,&ld));
531
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 364 PetscCall(PetscMalloc4(ncv,&ritz,ncv,&bnd,ncv,&perm,ncv,&conv));
532
533 /* The first Lanczos vector is the normalized initial vector */
534
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 364 PetscCall(EPSGetStartVector(eps,0,NULL));
535
536 anorm = -1.0;
537 nconv = 0;
538
539 /* Restart loop */
540 9868 while (eps->reason == EPS_CONVERGED_ITERATING) {
541 9504 eps->its++;
542
543 /* Compute an ncv-step Lanczos factorization */
544 9504 n = PetscMin(nconv+eps->mpd,ncv);
545
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 9504 PetscCall(DSSetDimensions(eps->ds,n,nconv,PETSC_DETERMINE));
546
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 9504 PetscCall(EPSBasicLanczos(eps,nconv,&n,&beta,&breakdown,anorm));
547
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 9504 PetscCall(DSSetDimensions(eps->ds,n,nconv,0));
548
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 9504 PetscCall(DSSetState(eps->ds,DS_STATE_INTERMEDIATE));
549
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 9504 PetscCall(BVSetActiveColumns(eps->V,nconv,n));
550
551 /* Solve projected problem */
552
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 9504 PetscCall(DSSolve(eps->ds,ritz,NULL));
553
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 9504 PetscCall(DSSort(eps->ds,ritz,NULL,NULL,NULL,NULL));
554
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 9504 PetscCall(DSSynchronize(eps->ds,ritz,NULL));
555
556 /* Estimate ||A|| */
557
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 135454 for (i=nconv;i<n;i++)
558
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 130215 anorm = PetscMax(anorm,PetscAbsReal(PetscRealPart(ritz[i])));
559
560 /* Compute residual norm estimates as beta*abs(Y(m,:)) + eps*||A|| */
561
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 9504 PetscCall(DSGetArray(eps->ds,DS_MAT_Q,&Y));
562
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 135454 for (i=nconv;i<n;i++) {
563 125950 resnorm = beta*PetscAbsScalar(Y[n-1+i*ld]) + PETSC_MACHINE_EPSILON*anorm;
564
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 125950 PetscCall((*eps->converged)(eps,ritz[i],eps->eigi[i],resnorm,&bnd[i],eps->convergedctx));
565
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 125950 if (bnd[i]<eps->tol) conv[i] = 'C';
566 124255 else conv[i] = 'N';
567 }
568
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 9504 PetscCall(DSRestoreArray(eps->ds,DS_MAT_Q,&Y));
569
570 /* purge repeated ritz values */
571
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 9504 if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL) {
572
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 70435 for (i=nconv+1;i<n;i++) {
573
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 65231 if (conv[i] == 'C' && PetscAbsScalar((ritz[i]-ritz[i-1])/ritz[i]) < eps->tol) conv[i] = 'R';
574 }
575 }
576
577 /* Compute restart vector */
578
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 9504 if (breakdown) PetscCall(PetscInfo(eps,"Breakdown in Lanczos method (it=%" PetscInt_FMT " norm=%g)\n",eps->its,(double)beta));
579 else {
580 restart = nconv;
581
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 10975 while (restart<n && conv[restart] != 'N') restart++;
582
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 9494 if (restart >= n) {
583 ✗ breakdown = PETSC_TRUE;
584 } else {
585
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 124289 for (i=restart+1;i<n;i++) {
586
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 114795 if (conv[i] == 'N') {
587
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 114761 PetscCall(SlepcSCCompare(eps->sc,ritz[restart],0.0,ritz[i],0.0,&r));
588
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 114761 if (r>0) restart = i;
589 }
590 }
591
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 9494 PetscCall(DSGetArray(eps->ds,DS_MAT_Q,&Y));
592
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 9494 PetscCall(BVMultColumn(eps->V,1.0,0.0,n,Y+restart*ld+nconv));
593
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 9494 PetscCall(DSRestoreArray(eps->ds,DS_MAT_Q,&Y));
594 }
595 }
596
597 /* Count and put converged eigenvalues first */
598
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 135454 for (i=nconv;i<n;i++) perm[i] = i;
599
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 11175 for (k=nconv;k<n;k++) {
600
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 11165 if (conv[perm[k]] != 'C') {
601 9521 j = k + 1;
602
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 124340 while (j<n && conv[perm[j]] != 'C') j++;
603
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 9521 if (j>=n) break;
604 27 l = perm[k]; perm[k] = perm[j]; perm[j] = l;
605 }
606 }
607
608 /* Sort eigenvectors according to permutation */
609
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 9504 PetscCall(DSGetArray(eps->ds,DS_MAT_Q,&Y));
610
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 11175 for (i=nconv;i<k;i++) {
611 1671 x = perm[i];
612
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 1671 if (x != i) {
613 27 j = i + 1;
614
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 61 while (perm[j] != i) j++;
615 /* swap eigenvalues i and j */
616 27 stmp = ritz[x]; ritz[x] = ritz[i]; ritz[i] = stmp;
617 27 rtmp = bnd[x]; bnd[x] = bnd[i]; bnd[i] = rtmp;
618 27 ctmp = conv[x]; conv[x] = conv[i]; conv[i] = ctmp;
619 27 perm[j] = x; perm[i] = i;
620 /* swap eigenvectors i and j */
621
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 540 for (l=0;l<n;l++) {
622 513 stmp = Y[l+x*ld]; Y[l+x*ld] = Y[l+i*ld]; Y[l+i*ld] = stmp;
623 }
624 }
625 }
626
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 9504 PetscCall(DSRestoreArray(eps->ds,DS_MAT_Q,&Y));
627
628 /* compute converged eigenvectors */
629
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 9504 PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&U));
630
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 9504 PetscCall(BVMultInPlace(eps->V,U,nconv,k));
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 9504 PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&U));
632
633 /* purge spurious ritz values */
634
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 9504 if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL) {
635
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 5949 for (i=nconv;i<k;i++) {
636
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 745 PetscCall(BVGetColumn(eps->V,i,&vi));
637
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 745 PetscCall(VecNorm(vi,NORM_2,&norm));
638
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 745 PetscCall(VecScale(vi,1.0/norm));
639 745 w = eps->work[0];
640
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 745 PetscCall(STApply(eps->st,vi,w));
641
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 745 PetscCall(VecAXPY(w,-ritz[i],vi));
642
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 745 PetscCall(BVRestoreColumn(eps->V,i,&vi));
643
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 745 PetscCall(VecNorm(w,NORM_2,&norm));
644
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 745 PetscCall((*eps->converged)(eps,ritz[i],eps->eigi[i],norm,&bnd[i],eps->convergedctx));
645
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 745 if (bnd[i]>=eps->tol) conv[i] = 'S';
646 }
647
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 5944 for (i=nconv;i<k;i++) {
648
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 745 if (conv[i] != 'C') {
649 5 j = i + 1;
650
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 5 while (j<k && conv[j] != 'C') j++;
651
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 5 if (j>=k) break;
652 /* swap eigenvalues i and j */
653 ✗ stmp = ritz[j]; ritz[j] = ritz[i]; ritz[i] = stmp;
654 ✗ rtmp = bnd[j]; bnd[j] = bnd[i]; bnd[i] = rtmp;
655 ✗ ctmp = conv[j]; conv[j] = conv[i]; conv[i] = ctmp;
656 /* swap eigenvectors i and j */
657 ✗ PetscCall(BVGetColumn(eps->V,i,&vi));
658 ✗ PetscCall(BVGetColumn(eps->V,j,&vj));
659 ✗ PetscCall(VecSwap(vi,vj));
660 ✗ PetscCall(BVRestoreColumn(eps->V,i,&vi));
661
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 740 PetscCall(BVRestoreColumn(eps->V,j,&vj));
662 }
663 }
664 k = i;
665 }
666
667 /* store ritz values and estimated errors */
668
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 135454 for (i=nconv;i<n;i++) {
669 125950 eps->eigr[i] = ritz[i];
670 125950 eps->errest[i] = bnd[i];
671 }
672 9504 nconv = k;
673
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 9504 PetscCall(EPSMonitor(eps,eps->its,nconv,eps->eigr,eps->eigi,eps->errest,n));
674
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 9504 PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,nconv,eps->nev,&eps->reason,eps->stoppingctx));
675
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 9504 if (eps->reason == EPS_CONVERGED_ITERATING) { /* copy restart vector */
677
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 9140 PetscCall(BVCopyColumn(eps->V,n,nconv));
678
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 9140 if (lanczos->reorthog == EPS_LANCZOS_REORTHOG_LOCAL && !breakdown) {
679 /* Reorthonormalize restart vector */
680
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 5024 PetscCall(BVOrthonormalizeColumn(eps->V,nconv,PETSC_FALSE,NULL,&breakdown));
681 }
682
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 9140 if (breakdown) {
683 /* Use random vector for restarting */
684 ✗ PetscCall(PetscInfo(eps,"Using random vector for restart\n"));
685 ✗ PetscCall(EPSGetStartVector(eps,nconv,&breakdown));
686 }
687
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 9140 if (PetscUnlikely(breakdown)) { /* give up */
688 ✗ eps->reason = EPS_DIVERGED_BREAKDOWN;
689
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 9868 PetscCall(PetscInfo(eps,"Unable to generate more start vectors\n"));
690 }
691 }
692 }
693 364 eps->nconv = nconv;
694
695
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 364 PetscCall(PetscFree4(ritz,bnd,perm,conv));
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 72 PetscFunctionReturn(PETSC_SUCCESS);
697 }
698
699 184 static PetscErrorCode EPSSetFromOptions_Lanczos(EPS eps,PetscOptionItems PetscOptionsObject)
700 {
701 184 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
702 184 PetscBool flg;
703 184 EPSLanczosReorthogType reorthog=EPS_LANCZOS_REORTHOG_LOCAL,curval;
704
705
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 184 PetscFunctionBegin;
706
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 184 PetscOptionsHeadBegin(PetscOptionsObject,"EPS Lanczos Options");
707
708
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 184 curval = (lanczos->reorthog==(EPSLanczosReorthogType)-1)? EPS_LANCZOS_REORTHOG_LOCAL: lanczos->reorthog;
709
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 184 PetscCall(PetscOptionsEnum("-eps_lanczos_reorthog","Lanczos reorthogonalization","EPSLanczosSetReorthog",EPSLanczosReorthogTypes,(PetscEnum)curval,(PetscEnum*)&reorthog,&flg));
710
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 184 if (flg) PetscCall(EPSLanczosSetReorthog(eps,reorthog));
711
712
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 184 PetscOptionsHeadEnd();
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 36 PetscFunctionReturn(PETSC_SUCCESS);
714 }
715
716 194 static PetscErrorCode EPSLanczosSetReorthog_Lanczos(EPS eps,EPSLanczosReorthogType reorthog)
717 {
718 194 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
719
720
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 194 PetscFunctionBegin;
721
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 194 switch (reorthog) {
722 194 case EPS_LANCZOS_REORTHOG_LOCAL:
723 case EPS_LANCZOS_REORTHOG_FULL:
724 case EPS_LANCZOS_REORTHOG_DELAYED:
725 case EPS_LANCZOS_REORTHOG_SELECTIVE:
726 case EPS_LANCZOS_REORTHOG_PERIODIC:
727 case EPS_LANCZOS_REORTHOG_PARTIAL:
728
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 194 if (lanczos->reorthog != reorthog) {
729 194 lanczos->reorthog = reorthog;
730 194 eps->state = EPS_STATE_INITIAL;
731 }
732 38 break;
733 ✗ default:
734 ✗ SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid reorthogonalization type");
735 }
736
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 38 PetscFunctionReturn(PETSC_SUCCESS);
737 }
738
739 /*@
740 EPSLanczosSetReorthog - Sets the type of reorthogonalization used during the Lanczos
741 iteration.
742
743 Logically Collective
744
745 Input Parameters:
746 + eps - the eigenproblem solver context
747 - reorthog - the type of reorthogonalization
748
749 Options Database Key:
750 . -eps_lanczos_reorthog - Sets the reorthogonalization type (either 'local', 'selective',
751 'periodic', 'partial', 'full' or 'delayed')
752
753 Level: advanced
754
755 .seealso: EPSLanczosGetReorthog(), EPSLanczosReorthogType
756 @*/
757 194 PetscErrorCode EPSLanczosSetReorthog(EPS eps,EPSLanczosReorthogType reorthog)
758 {
759
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 194 PetscFunctionBegin;
760
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 194 PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
761
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 194 PetscValidLogicalCollectiveEnum(eps,reorthog,2);
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 194 PetscTryMethod(eps,"EPSLanczosSetReorthog_C",(EPS,EPSLanczosReorthogType),(eps,reorthog));
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 194 PetscFunctionReturn(PETSC_SUCCESS);
764 }
765
766 50 static PetscErrorCode EPSLanczosGetReorthog_Lanczos(EPS eps,EPSLanczosReorthogType *reorthog)
767 {
768 50 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
769
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 50 PetscFunctionBegin;
771 50 *reorthog = lanczos->reorthog;
772
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 50 PetscFunctionReturn(PETSC_SUCCESS);
773 }
774
775 /*@
776 EPSLanczosGetReorthog - Gets the type of reorthogonalization used during
777 the Lanczos iteration.
778
779 Not Collective
780
781 Input Parameter:
782 . eps - the eigenproblem solver context
783
784 Output Parameter:
785 . reorthog - the type of reorthogonalization
786
787 Level: advanced
788
789 .seealso: EPSLanczosSetReorthog(), EPSLanczosReorthogType
790 @*/
791 50 PetscErrorCode EPSLanczosGetReorthog(EPS eps,EPSLanczosReorthogType *reorthog)
792 {
793
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 50 PetscFunctionBegin;
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 50 PetscValidHeaderSpecific(eps,EPS_CLASSID,1);
795
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 50 PetscAssertPointer(reorthog,2);
796
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 50 PetscUseMethod(eps,"EPSLanczosGetReorthog_C",(EPS,EPSLanczosReorthogType*),(eps,reorthog));
797
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 50 PetscFunctionReturn(PETSC_SUCCESS);
798 }
799
800 224 static PetscErrorCode EPSReset_Lanczos(EPS eps)
801 {
802 224 EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
803
804
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 224 PetscFunctionBegin;
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 224 PetscCall(BVDestroy(&lanczos->AV));
806 224 lanczos->allocsize = 0;
807
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 224 PetscFunctionReturn(PETSC_SUCCESS);
808 }
809
810 194 static PetscErrorCode EPSDestroy_Lanczos(EPS eps)
811 {
812
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 194 PetscFunctionBegin;
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 194 PetscCall(PetscFree(eps->data));
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 194 PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLanczosSetReorthog_C",NULL));
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 194 PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLanczosGetReorthog_C",NULL));
816
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 38 PetscFunctionReturn(PETSC_SUCCESS);
817 }
818
819 ✗ static PetscErrorCode EPSView_Lanczos(EPS eps,PetscViewer viewer)
820 {
821 ✗ EPS_LANCZOS *lanczos = (EPS_LANCZOS*)eps->data;
822 ✗ PetscBool isascii;
823
824 ✗ PetscFunctionBegin;
825 ✗ PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii));
826 ✗ if (isascii) {
827 ✗ if (lanczos->reorthog != (EPSLanczosReorthogType)-1) PetscCall(PetscViewerASCIIPrintf(viewer," %s reorthogonalization\n",EPSLanczosReorthogTypes[lanczos->reorthog]));
828 }
829 ✗ PetscFunctionReturn(PETSC_SUCCESS);
830 }
831
832 194 SLEPC_EXTERN PetscErrorCode EPSCreate_Lanczos(EPS eps)
833 {
834 194 EPS_LANCZOS *ctx;
835
836
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 194 PetscFunctionBegin;
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 194 PetscCall(PetscNew(&ctx));
838 194 eps->data = (void*)ctx;
839 194 ctx->reorthog = (EPSLanczosReorthogType)-1;
840
841 194 eps->useds = PETSC_TRUE;
842
843 194 eps->ops->solve = EPSSolve_Lanczos;
844 194 eps->ops->setup = EPSSetUp_Lanczos;
845 194 eps->ops->setupsort = EPSSetUpSort_Default;
846 194 eps->ops->setfromoptions = EPSSetFromOptions_Lanczos;
847 194 eps->ops->destroy = EPSDestroy_Lanczos;
848 194 eps->ops->reset = EPSReset_Lanczos;
849 194 eps->ops->view = EPSView_Lanczos;
850 194 eps->ops->backtransform = EPSBackTransform_Default;
851 194 eps->ops->computevectors = EPSComputeVectors_Hermitian;
852
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 194 PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLanczosSetReorthog_C",EPSLanczosSetReorthog_Lanczos));
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 194 PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSLanczosGetReorthog_C",EPSLanczosGetReorthog_Lanczos));
855
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 38 PetscFunctionReturn(PETSC_SUCCESS);
856 }
857