GCC Code Coverage Report

Directory: ./
File: src/eps/impls/subspace/subspace.c
Date: 2026-10-22 02:08:06
Exec Total Coverage
Lines: 214 242 88.4%
Functions: 8 8 100.0%
Branches: 479 814 58.8%
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: "subspace"
12
13 Method: Subspace Iteration
14
15 Algorithm:
16
17 Subspace iteration with Rayleigh-Ritz projection and locking,
18 based on the SRRIT implementation.
19
20 References:
21
22 [1] "Subspace Iteration in SLEPc", SLEPc Technical Report STR-3,
23 available at https://slepc.upv.es.
24 */
25
26 #include <slepc/private/epsimpl.h>
27
28 typedef struct {
29 PetscBool estimatedrange; /* the filter range was not set by the user */
30 } EPS_SUBSPACE;
31
32 28 static PetscErrorCode EPSSetUp_Subspace_Filter(EPS eps)
33 {
34 28 EPS_SUBSPACE *ctx = (EPS_SUBSPACE*)eps->data;
35 28 PetscBool estimaterange=PETSC_TRUE;
36 28 PetscReal rleft,rright;
37 28 Mat A;
38
39
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 28 PetscFunctionBegin;
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 28 EPSCheckHermitianCondition(eps,PETSC_TRUE," with polynomial filter");
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 28 EPSCheckStandardCondition(eps,PETSC_TRUE," with polynomial filter");
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 28 PetscCheck(eps->intb<PETSC_MAX_REAL || eps->inta>PETSC_MIN_REAL,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The defined computational interval should have at least one of their sides bounded");
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 28 EPSCheckUnsupportedCondition(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_REGION | EPS_FEATURE_EXTRACTION,PETSC_TRUE," with polynomial filter");
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 28 PetscCall(STFilterSetInterval(eps->st,eps->inta,eps->intb));
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 28 if (!ctx->estimatedrange) {
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 28 PetscCall(STFilterGetRange(eps->st,&rleft,&rright));
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 28 estimaterange = (!rleft && !rright)? PETSC_TRUE: PETSC_FALSE;
48 }
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 2 if (estimaterange) { /* user did not set a range */
50
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 28 PetscCall(STGetMatrix(eps->st,0,&A));
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 28 PetscCall(MatEstimateSpectralRange_EPS(A,&rleft,&rright));
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 28 PetscCall(PetscInfo(eps,"Setting eigenvalue range to [%g,%g]\n",(double)rleft,(double)rright));
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 28 PetscCall(STFilterSetRange(eps->st,rleft,rright));
54 28 ctx->estimatedrange = PETSC_TRUE;
55 }
56
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 28 PetscCall(EPSSetStoppingTest(eps,EPS_STOP_THRESHOLD));
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 28 PetscCall(EPSSetDimensions_Default(eps,&eps->nev,&eps->ncv,&eps->mpd));
58
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 28 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");
59
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 4 PetscFunctionReturn(PETSC_SUCCESS);
60 }
61
62 222 static PetscErrorCode EPSSetUp_Subspace(EPS eps)
63 {
64 222 PetscBool isfilt;
65
66
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 222 PetscFunctionBegin;
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 222 EPSCheckDefinite(eps);
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 222 EPSCheckNotStructured(eps);
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 222 if (eps->max_it==PETSC_DETERMINE) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);
70
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 222 if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps));
71
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 222 if (eps->which==EPS_ALL) {
72
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 28 PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilt));
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 28 PetscCheck(isfilt,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"Spectrum slicing not supported in this solver");
74
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 28 PetscCall(EPSSetUp_Subspace_Filter(eps));
75 } else {
76
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 194 PetscCheck(eps->which==EPS_LARGEST_MAGNITUDE || eps->which==EPS_TARGET_MAGNITUDE,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver supports only largest magnitude or target magnitude eigenvalues");
77
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 194 PetscCall(EPSSetDimensions_Default(eps,&eps->nev,&eps->ncv,&eps->mpd));
78 }
79
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 222 EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_EXTRACTION | EPS_FEATURE_TWOSIDED);
80
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 222 PetscCheck(eps->converged==EPSConvergedRelative,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver only supports relative convergence test");
81
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 222 PetscCall(EPSAllocateSolution(eps,0));
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 222 PetscCall(EPS_SetInnerProduct(eps));
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 222 if (eps->ishermitian) PetscCall(DSSetType(eps->ds,DSHEP));
85
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 61 else PetscCall(DSSetType(eps->ds,DSNHEP));
86
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 222 PetscCall(DSAllocate(eps->ds,eps->ncv));
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 42 PetscFunctionReturn(PETSC_SUCCESS);
88 }
89
90 222 static PetscErrorCode EPSSetUpSort_Subspace(EPS eps)
91 {
92 222 SlepcSC sc;
93
94
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 222 PetscFunctionBegin;
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 222 PetscCall(EPSSetUpSort_Default(eps));
96
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 222 if (eps->which==EPS_ALL) {
97
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 28 PetscCall(DSGetSlepcSC(eps->ds,&sc));
98 28 sc->rg = NULL;
99 28 sc->comparison = SlepcCompareLargestReal;
100 28 sc->comparisonctx = NULL;
101 28 sc->map = NULL;
102 28 sc->mapobj = NULL;
103 }
104
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 42 PetscFunctionReturn(PETSC_SUCCESS);
105 }
106
107 /*
108 EPSSubspaceFindGroup - Find a group of nearly equimodular eigenvalues, provided
109 in arrays wr and wi, according to the tolerance grptol. Also the 2-norms
110 of the residuals must be passed in (rsd). Arrays are processed from index
111 l to index m only. The output information is:
112
113 ngrp - number of entries of the group
114 ctr - (w(l)+w(l+ngrp-1))/2
115 ae - average of wr(l),...,wr(l+ngrp-1)
116 arsd - average of rsd(l),...,rsd(l+ngrp-1)
117 */
118 7036 static PetscErrorCode EPSSubspaceFindGroup(PetscInt l,PetscInt m,PetscScalar *wr,PetscScalar *wi,PetscReal *rsd,PetscReal grptol,PetscInt *ngrp,PetscReal *ctr,PetscReal *ae,PetscReal *arsd)
119 {
120 7036 PetscInt i;
121 7036 PetscReal rmod,rmod1;
122
123
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 7036 PetscFunctionBegin;
124 7036 *ngrp = 0;
125 7036 *ctr = 0;
126 7036 rmod = SlepcAbsEigenvalue(wr[l],wi[l]);
127
128
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 21212 for (i=l;i<m;) {
129 17540 rmod1 = SlepcAbsEigenvalue(wr[i],wi[i]);
130
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 17540 if (PetscAbsReal(rmod-rmod1) > grptol*(rmod+rmod1)) break;
131 10738 *ctr = (rmod+rmod1)/2.0;
132
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 10738 if (wi[i] == 0.0) {
133 10738 (*ngrp)++;
134 10738 i++;
135 } else {
136 ✗ (*ngrp)+=2;
137 ✗ i+=2;
138 }
139 }
140
141 7036 *ae = 0;
142 7036 *arsd = 0;
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 7036 if (*ngrp) {
144
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 17774 for (i=l;i<l+*ngrp;i++) {
145 10738 (*ae) += PetscRealPart(wr[i]);
146 10738 (*arsd) += rsd[i]*rsd[i];
147 }
148 7036 *ae = *ae / *ngrp;
149 7036 *arsd = PetscSqrtReal(*arsd / *ngrp);
150 }
151
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 7036 PetscFunctionReturn(PETSC_SUCCESS);
152 }
153
154 /*
155 EPSSubspaceResidualNorms - Computes the column norms of residual vectors
156 OP*V(1:n,l:m) - V*T(1:m,l:m), where, on entry, OP*V has been computed and
157 stored in R. On exit, rsd(l) to rsd(m) contain the computed norms.
158 */
159 2067 static PetscErrorCode EPSSubspaceResidualNorms(BV R,BV V,Mat T,PetscInt l,PetscInt m,PetscScalar *eigi,PetscReal *rsd)
160 {
161 2067 PetscInt i;
162
163
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 2067 PetscFunctionBegin;
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 2067 PetscCall(BVMult(R,-1.0,1.0,V,T));
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 35961 for (i=l;i<m;i++) PetscCall(BVNormColumnBegin(R,i,NORM_2,rsd+i));
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 35961 for (i=l;i<m;i++) PetscCall(BVNormColumnEnd(R,i,NORM_2,rsd+i));
167 #if !PetscDefined(USE_COMPLEX)
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 16476 for (i=l;i<m-1;i++) {
169
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 15466 if (eigi[i]!=0.0) {
170 ✗ rsd[i] = SlepcAbs(rsd[i],rsd[i+1]);
171 ✗ rsd[i+1] = rsd[i];
172 ✗ i++;
173 }
174 }
175 #endif
176
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 382 PetscFunctionReturn(PETSC_SUCCESS);
177 }
178
179 222 static PetscErrorCode EPSSolve_Subspace(EPS eps)
180 {
181 222 Mat H,Q,S,T,B;
182 222 BV AV,R;
183 222 PetscBool indef;
184 222 PetscInt i,k,ngrp,nogrp,*itrsd,*itrsdold,*p_itrsd,*p_itrsdold;
185 222 PetscInt nxtsrr,idsrr,idort,nxtort,nv,its;
186 222 PetscReal arsd,oarsd,ctr,octr,ae,oae,*rsd,*orsd,*p_rsd,*p_orsd,tcond=1.0;
187 222 PetscScalar *oeigr,*oeigi,*p_oeigr,*p_oeigi;
188 /* Parameters */
189 222 PetscInt init = 5; /* Number of initial iterations */
190 222 PetscReal stpfac = 1.5; /* Max num of iter before next SRR step */
191 222 PetscReal alpha = 1.0; /* Used to predict convergence of next residual */
192 222 PetscReal beta = 1.1; /* Used to predict convergence of next residual */
193 222 PetscReal grptol = SLEPC_DEFAULT_TOL; /* Tolerance for EPSSubspaceFindGroup */
194 222 PetscReal cnvtol = 1e-6; /* Convergence criterion for cnv */
195 222 PetscInt orttol = 2; /* Number of decimal digits whose loss
196 can be tolerated in orthogonalization */
197
198
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 222 PetscFunctionBegin;
199 222 its = 0;
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 222 PetscCall(PetscMalloc6(eps->ncv,&rsd,eps->ncv,&orsd,eps->ncv,&oeigr,eps->ncv,&oeigi,eps->ncv,&itrsd,eps->ncv,&itrsdold));
201
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 222 PetscCall(BVDuplicate(eps->V,&AV));
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 222 PetscCall(BVDuplicate(eps->V,&R));
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 222 PetscCall(STGetOperator(eps->st,&S));
204
205
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 4206 for (i=0;i<eps->ncv;i++) {
206 3984 rsd[i] = 0.0;
207 3984 itrsd[i] = -1;
208 }
209
210 /* Complete the initial basis with random vectors and orthonormalize them */
211
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 4176 for (k=eps->nini;k<eps->ncv;k++) {
212
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 3954 PetscCall(BVSetRandomColumn(eps->V,k));
213
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 3954 PetscCall(BVOrthonormalizeColumn(eps->V,k,PETSC_TRUE,NULL,NULL));
214 }
215
216 2067 while (eps->reason == EPS_CONVERGED_ITERATING) {
217 2067 eps->its++;
218 2067 nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
219
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 2067 PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,0));
220
221
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 35961 for (i=eps->nconv;i<nv;i++) {
222 33894 oeigr[i] = eps->eigr[i];
223 33894 oeigi[i] = eps->eigi[i];
224 33894 orsd[i] = rsd[i];
225 }
226
227 /* AV(:,idx) = OP * V(:,idx) */
228
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 2067 PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv));
229
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 2067 PetscCall(BVSetActiveColumns(AV,eps->nconv,nv));
230
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 2067 PetscCall(BVMatMult(eps->V,S,AV));
231
232 /* T(:,idx) = V' * AV(:,idx) */
233
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 2067 PetscCall(BVSetActiveColumns(eps->V,0,nv));
234
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 2067 PetscCall(DSGetMat(eps->ds,DS_MAT_A,&H));
235
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 2067 PetscCall(BVDot(AV,eps->V,H));
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 2067 PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&H));
237
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 2067 PetscCall(DSSetState(eps->ds,DS_STATE_RAW));
238
239 /* Solve projected problem */
240
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 2067 PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi));
241
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 2067 PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL));
242
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 2067 PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi));
243
244 /* Update vectors V(:,idx) = V * U(:,idx) */
245
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 2067 PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&Q));
246
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 2067 PetscCall(BVSetActiveColumns(AV,0,nv));
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 2067 PetscCall(BVSetActiveColumns(R,0,nv));
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 2067 PetscCall(BVMultInPlace(eps->V,Q,eps->nconv,nv));
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 2067 PetscCall(BVMultInPlace(AV,Q,eps->nconv,nv));
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 2067 PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&Q));
251
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 2067 PetscCall(BVCopy(AV,R));
252
253 /* Convergence check */
254
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 2067 PetscCall(DSGetMat(eps->ds,DS_MAT_A,&T));
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 2067 PetscCall(EPSSubspaceResidualNorms(R,eps->V,T,eps->nconv,nv,eps->eigi,rsd));
256
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 2067 PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&T));
257
258
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 35961 for (i=eps->nconv;i<nv;i++) {
259 33894 itrsdold[i] = itrsd[i];
260 33894 itrsd[i] = its;
261 33894 eps->errest[i] = rsd[i];
262 }
263
264 3518 for (;;) {
265 /* Find clusters of computed eigenvalues */
266
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 3518 PetscCall(EPSSubspaceFindGroup(eps->nconv,nv,eps->eigr,eps->eigi,eps->errest,grptol,&ngrp,&ctr,&ae,&arsd));
267
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 3518 PetscCall(EPSSubspaceFindGroup(eps->nconv,nv,oeigr,oeigi,orsd,grptol,&nogrp,&octr,&oae,&oarsd));
268
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 3518 if (ngrp!=nogrp) break;
269
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 3296 if (ngrp==0) break;
270
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 3296 if (PetscAbsReal(ae-oae)>ctr*cnvtol*(itrsd[eps->nconv]-itrsdold[eps->nconv])) break;
271
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 2479 if (arsd>ctr*eps->tol) break;
272 1457 eps->nconv = eps->nconv + ngrp;
273
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 1457 if (eps->nconv>=nv) break;
274 }
275
276
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 2067 PetscCall(EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv));
277
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 2067 EPSSetCtxThreshold(eps,eps->eigr,eps->eigi,eps->errest,eps->nconv,nv);
278
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 2067 PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,eps->nconv,eps->nev,&eps->reason,eps->stoppingctx));
279
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 2067 if (eps->reason != EPS_CONVERGED_ITERATING) break;
280
281 /* Compute nxtsrr (iteration of next projection step) */
282 1845 nxtsrr = PetscMax((PetscInt)PetscFloorReal(stpfac*its),init);
283
284
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 1845 if (ngrp!=nogrp || ngrp==0 || arsd>=oarsd) {
285 252 idsrr = nxtsrr - its;
286 } else {
287 1593 idsrr = (PetscInt)PetscFloorReal(alpha+beta*(itrsdold[eps->nconv]-itrsd[eps->nconv])*PetscLogReal(arsd/eps->tol)/PetscLogReal(arsd/oarsd));
288 1593 idsrr = PetscMax(1,idsrr);
289 }
290 1845 nxtsrr = PetscMin(nxtsrr,its+idsrr);
291
292 /* Compute nxtort (iteration of next orthogonalization step) */
293
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 1845 PetscCall(DSCond(eps->ds,&tcond));
294
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 1845 idort = PetscMax(1,(PetscInt)PetscFloorReal(orttol/PetscMax(1,PetscLog10Real(tcond))));
295 1845 nxtort = PetscMin(its+idort,nxtsrr);
296
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 1845 PetscCall(PetscInfo(eps,"Updated iteration counts: nxtort=%" PetscInt_FMT ", nxtsrr=%" PetscInt_FMT "\n",nxtort,nxtsrr));
297
298 /* V(:,idx) = AV(:,idx) */
299
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 1845 PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv));
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 1845 PetscCall(BVSetActiveColumns(AV,eps->nconv,nv));
301
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 1845 PetscCall(BVCopy(AV,eps->V));
302 1845 its++;
303
304 /* Orthogonalization loop */
305 19676 do {
306
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 19676 PetscCall(BVGetMatrix(eps->V,&B,&indef));
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 19676 PetscCall(BVSetMatrix(eps->V,NULL,PETSC_FALSE));
308
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 54569 while (its<nxtort) {
309 /* A(:,idx) = OP*V(:,idx) with normalization */
310
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 34893 PetscCall(BVMatMult(eps->V,S,AV));
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 34893 PetscCall(BVCopy(AV,eps->V));
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 34893 PetscCall(BVNormalize(eps->V,NULL));
313 34893 its++;
314 }
315
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 19676 PetscCall(BVSetMatrix(eps->V,B,indef));
316 /* Orthonormalize vectors */
317
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 19676 PetscCall(BVOrthogonalize(eps->V,NULL));
318 19676 nxtort = PetscMin(its+idort,nxtsrr);
319
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 19676 } while (its<nxtsrr);
320
321
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 1845 if (eps->stop==EPS_STOP_THRESHOLD && nv/(PetscReal)eps->nconv<1.3) { /* reallocate */
322 ✗ eps->ncv = 1.3*eps->nconv+1;
323 ✗ PetscCall(EPSReallocateSolution(eps,eps->ncv));
324 ✗ PetscCall(BVResize(AV,eps->ncv,PETSC_TRUE));
325 ✗ PetscCall(BVResize(R,eps->ncv,PETSC_TRUE));
326 ✗ for (i=nv;i<eps->ncv;i++) eps->perm[i] = i;
327 ✗ PetscCall(DSReallocate(eps->ds,eps->ncv));
328 ✗ for (k=nv;k<eps->ncv;k++) {
329 ✗ PetscCall(BVSetRandomColumn(eps->V,k));
330 ✗ PetscCall(BVOrthonormalizeColumn(eps->V,k,PETSC_TRUE,NULL,NULL));
331 }
332 ✗ p_rsd = rsd;
333 ✗ p_orsd = orsd;
334 ✗ p_oeigr = oeigr;
335 ✗ p_oeigi = oeigi;
336 ✗ p_itrsd = itrsd;
337 ✗ p_itrsdold = itrsdold;
338 ✗ PetscCall(PetscMalloc6(eps->ncv,&rsd,eps->ncv,&orsd,eps->ncv,&oeigr,eps->ncv,&oeigi,eps->ncv,&itrsd,eps->ncv,&itrsdold));
339 ✗ for (i=0;i<nv;i++) {
340 ✗ rsd[i] = p_rsd[i];
341 ✗ orsd[i] = p_orsd[i];
342 ✗ oeigr[i] = p_oeigr[i];
343 ✗ oeigi[i] = p_oeigi[i];
344 ✗ itrsd[i] = p_itrsd[i];
345 ✗ itrsdold[i] = p_itrsdold[i];
346 }
347
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 2067 PetscCall(PetscFree6(p_rsd,p_orsd,p_oeigr,p_oeigi,p_itrsd,p_itrsdold));
348 }
349
350 }
351
352
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 222 PetscCall(PetscFree6(rsd,orsd,oeigr,oeigi,itrsd,itrsdold));
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 222 PetscCall(BVDestroy(&AV));
354
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 222 PetscCall(BVDestroy(&R));
355
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 222 PetscCall(STRestoreOperator(eps->st,&S));
356
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 222 PetscCall(DSTruncate(eps->ds,eps->nconv,PETSC_TRUE));
357
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 42 PetscFunctionReturn(PETSC_SUCCESS);
358 }
359
360 202 static PetscErrorCode EPSDestroy_Subspace(EPS eps)
361 {
362
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 202 PetscFunctionBegin;
363
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 202 PetscCall(PetscFree(eps->data));
364
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 38 PetscFunctionReturn(PETSC_SUCCESS);
365 }
366
367 /*MC
368 EPSSUBSPACE - EPSSUBSPACE = "subspace" - The simple subspace iteration method.
369
370 Notes:
371 This solver is very basic and is not recommended in general, since it
372 will not be competitive with respect to other solvers.
373
374 The implemented method is subspace iteration with Rayleigh-Ritz projection and
375 locking, based on the SRRIT code {cite:p}`Bai97`.
376
377 Level: beginner
378
379 .seealso: [](ch:eps), `EPS`, `EPSType`, `EPSSetType()`
380 M*/
381 202 SLEPC_EXTERN PetscErrorCode EPSCreate_Subspace(EPS eps)
382 {
383 202 EPS_SUBSPACE *ctx;
384
385
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 202 PetscFunctionBegin;
386
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 202 PetscCall(PetscNew(&ctx));
387 202 eps->data = (void*)ctx;
388
389 202 eps->useds = PETSC_TRUE;
390 202 eps->categ = EPS_CATEGORY_OTHER;
391
392 202 eps->ops->solve = EPSSolve_Subspace;
393 202 eps->ops->setup = EPSSetUp_Subspace;
394 202 eps->ops->setupsort = EPSSetUpSort_Subspace;
395 202 eps->ops->destroy = EPSDestroy_Subspace;
396 202 eps->ops->backtransform = EPSBackTransform_Default;
397 202 eps->ops->computevectors = EPSComputeVectors_Schur;
398
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 202 PetscFunctionReturn(PETSC_SUCCESS);
399 }
400