Actual source code: sinvert.c
slepc-3.23.1 2025-05-01
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
6: This file is part of SLEPc.
7: SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9: */
10: /*
11: Implements the shift-and-invert technique for eigenvalue problems
12: */
14: #include <slepc/private/stimpl.h>
16: /*
17: Special STApply() for the BSE structured matrix
19: H = [ R C; -C^H -R^T ].
21: Assumes that H is a MATNEST and x,y are VECNEST.
23: The bottom part of the input vector x2 is computed as
24: either conj(x1) or -conj(x1), where the sign is given by
25: s in the context SlepcMatStruct.
26: */
27: static PetscErrorCode STApply_Sinvert_BSE(ST st,Vec x,Vec y)
28: {
29: Vec x1,x2;
30: PetscContainer container;
31: SlepcMatStruct mctx;
33: PetscFunctionBegin;
34: PetscCall(PetscObjectQuery((PetscObject)st->A[0],"SlepcMatStruct",(PetscObject*)&container));
35: PetscCall(PetscContainerGetPointer(container,(void**)&mctx));
36: PetscCall(VecNestGetSubVec(x,0,&x1));
37: PetscCall(VecNestGetSubVec(x,1,&x2));
39: /* x2 = +/-conj(x1) */
40: PetscCall(VecCopy(x1,x2));
41: PetscCall(VecConjugate(x2));
42: if (mctx->s==-1.0) PetscCall(VecScale(x2,-1.0));
44: PetscCall(STApply_Generic(st,x,y));
45: PetscFunctionReturn(PETSC_SUCCESS);
46: }
48: static PetscErrorCode STBackTransform_Sinvert(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
49: {
50: PetscInt j;
51: #if !defined(PETSC_USE_COMPLEX)
52: PetscScalar t;
53: #endif
55: PetscFunctionBegin;
56: #if !defined(PETSC_USE_COMPLEX)
57: for (j=0;j<n;j++) {
58: if (eigi[j] == 0) eigr[j] = 1.0 / eigr[j] + st->sigma;
59: else {
60: t = eigr[j] * eigr[j] + eigi[j] * eigi[j];
61: eigr[j] = eigr[j] / t + st->sigma;
62: eigi[j] = - eigi[j] / t;
63: }
64: }
65: #else
66: for (j=0;j<n;j++) {
67: eigr[j] = 1.0 / eigr[j] + st->sigma;
68: }
69: #endif
70: PetscFunctionReturn(PETSC_SUCCESS);
71: }
73: static PetscErrorCode STPostSolve_Sinvert(ST st)
74: {
75: PetscFunctionBegin;
76: if (st->matmode == ST_MATMODE_INPLACE) {
77: if (st->nmat>1) PetscCall(MatAXPY(st->A[0],st->sigma,st->A[1],st->str));
78: else PetscCall(MatShift(st->A[0],st->sigma));
79: st->Astate[0] = ((PetscObject)st->A[0])->state;
80: st->state = ST_STATE_INITIAL;
81: st->opready = PETSC_FALSE;
82: }
83: PetscFunctionReturn(PETSC_SUCCESS);
84: }
86: /*
87: Operator (sinvert):
88: Op P M
89: if nmat=1: (A-sI)^-1 A-sI NULL
90: if nmat=2: (A-sB)^-1 B A-sB B
91: */
92: static PetscErrorCode STComputeOperator_Sinvert(ST st)
93: {
94: PetscFunctionBegin;
95: /* if the user did not set the shift, use the target value */
96: if (!st->sigma_set) st->sigma = st->defsigma;
97: PetscCall(PetscObjectReference((PetscObject)st->A[1]));
98: PetscCall(MatDestroy(&st->T[0]));
99: st->T[0] = st->A[1];
100: PetscCall(STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[1]));
101: PetscCall(PetscObjectReference((PetscObject)st->T[1]));
102: PetscCall(MatDestroy(&st->P));
103: st->P = st->T[1];
104: st->M = (st->nmat>1)? st->T[0]: NULL;
105: if (st->Psplit) { /* build custom preconditioner from the split matrices */
106: PetscCall(STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PETSC_TRUE,PETSC_TRUE,&st->Pmat));
107: }
108: PetscFunctionReturn(PETSC_SUCCESS);
109: }
111: static PetscErrorCode STSetUp_Sinvert(ST st)
112: {
113: PetscInt k,nc,nmat=st->nmat,nsub;
114: PetscScalar *coeffs=NULL;
115: PetscBool islu;
116: KSP *subksp;
117: PC pc,pcsub;
118: Mat A00;
119: MatType type;
120: PetscBool flg;
121: char str[64];
123: PetscFunctionBegin;
124: if (nmat>1) PetscCall(STSetWorkVecs(st,1));
125: /* if the user did not set the shift, use the target value */
126: if (!st->sigma_set) st->sigma = st->defsigma;
127: if (nmat>2) { /* set-up matrices for polynomial eigenproblems */
128: if (st->transform) {
129: nc = (nmat*(nmat+1))/2;
130: PetscCall(PetscMalloc1(nc,&coeffs));
131: /* Compute coeffs */
132: PetscCall(STCoeffs_Monomial(st,coeffs));
133: /* T[0] = A_n */
134: k = nmat-1;
135: PetscCall(PetscObjectReference((PetscObject)st->A[k]));
136: PetscCall(MatDestroy(&st->T[0]));
137: st->T[0] = st->A[k];
138: for (k=1;k<nmat;k++) PetscCall(STMatMAXPY_Private(st,nmat>2?st->sigma:-st->sigma,0.0,nmat-k-1,coeffs?coeffs+(k*(k+1))/2:NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[k]));
139: PetscCall(PetscFree(coeffs));
140: PetscCall(PetscObjectReference((PetscObject)st->T[nmat-1]));
141: PetscCall(MatDestroy(&st->P));
142: st->P = st->T[nmat-1];
143: if (st->Psplit) { /* build custom preconditioner from the split matrices */
144: PetscCall(STMatMAXPY_Private(st,st->sigma,0.0,0,coeffs?coeffs+((nmat-1)*nmat)/2:NULL,PETSC_TRUE,PETSC_TRUE,&st->Pmat));
145: }
146: PetscCall(ST_KSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P));
147: } else {
148: for (k=0;k<nmat;k++) {
149: PetscCall(PetscObjectReference((PetscObject)st->A[k]));
150: PetscCall(MatDestroy(&st->T[k]));
151: st->T[k] = st->A[k];
152: }
153: }
154: }
155: if (st->structured) {
156: /* ./ex55 -st_type sinvert -eps_target 0 -eps_target_magnitude
157: -st_ksp_type preonly -st_pc_type fieldsplit
158: -st_fieldsplit_0_ksp_type preonly -st_fieldsplit_0_pc_type lu
159: -st_fieldsplit_1_ksp_type preonly -st_fieldsplit_1_pc_type lu
160: -st_pc_fieldsplit_type schur -st_pc_fieldsplit_schur_fact_type full
161: -st_pc_fieldsplit_schur_precondition full */
162: PetscCall(KSPGetPC(st->ksp,&pc));
163: PetscCall(PetscObjectTypeCompare((PetscObject)pc,PCLU,&islu));
164: if (islu) { /* assume PCLU means the user has not set any options */
165: PetscCall(KSPSetType(st->ksp,KSPPREONLY));
166: PetscCall(PCSetType(pc,PCFIELDSPLIT));
167: PetscCall(PCFieldSplitSetType(pc,PC_COMPOSITE_SCHUR));
168: PetscCall(PCFieldSplitSetSchurFactType(pc,PC_FIELDSPLIT_SCHUR_FACT_FULL));
169: PetscCall(PCFieldSplitSetSchurPre(pc,PC_FIELDSPLIT_SCHUR_PRE_FULL,NULL));
170: /* hack to set Mat type of Schur complement equal to A00, assumes default prefixes */
171: PetscCall(PetscOptionsHasName(((PetscObject)st)->options,((PetscObject)st)->prefix,"-st_fieldsplit_1_explicit_operator_mat_type",&flg));
172: if (!flg) {
173: PetscCall(MatNestGetSubMat(st->A[0],0,0,&A00));
174: PetscCall(MatGetType(A00,&type));
175: PetscCall(PetscSNPrintf(str,sizeof(str),"-%sst_fieldsplit_1_explicit_operator_mat_type %s",((PetscObject)st)->prefix?((PetscObject)st)->prefix:"",type));
176: PetscCall(PetscOptionsInsertString(((PetscObject)st)->options,str));
177: }
178: /* set preonly+lu on block solvers */
179: PetscCall(KSPSetUp(st->ksp));
180: PetscCall(PCFieldSplitGetSubKSP(pc,&nsub,&subksp));
181: PetscCall(KSPSetType(subksp[0],KSPPREONLY));
182: PetscCall(KSPGetPC(subksp[0],&pcsub));
183: PetscCall(PCSetType(pcsub,PCLU));
184: PetscCall(KSPSetType(subksp[1],KSPPREONLY));
185: PetscCall(KSPGetPC(subksp[1],&pcsub));
186: PetscCall(PCSetType(pcsub,PCLU));
187: PetscCall(PetscFree(subksp));
188: }
189: st->ops->apply = STApply_Sinvert_BSE;
190: } else {
191: if (st->P) PetscCall(KSPSetUp(st->ksp));
192: }
193: PetscFunctionReturn(PETSC_SUCCESS);
194: }
196: static PetscErrorCode STSetShift_Sinvert(ST st,PetscScalar newshift)
197: {
198: PetscInt nmat=PetscMax(st->nmat,2),k,nc;
199: PetscScalar *coeffs=NULL;
201: PetscFunctionBegin;
202: if (st->transform) {
203: if (st->matmode == ST_MATMODE_COPY && nmat>2) {
204: nc = (nmat*(nmat+1))/2;
205: PetscCall(PetscMalloc1(nc,&coeffs));
206: /* Compute coeffs */
207: PetscCall(STCoeffs_Monomial(st,coeffs));
208: }
209: for (k=1;k<nmat;k++) PetscCall(STMatMAXPY_Private(st,nmat>2?newshift:-newshift,nmat>2?st->sigma:-st->sigma,nmat-k-1,coeffs?coeffs+(k*(k+1))/2:NULL,PETSC_FALSE,PETSC_FALSE,&st->T[k]));
210: if (st->matmode == ST_MATMODE_COPY && nmat>2) PetscCall(PetscFree(coeffs));
211: if (st->P!=st->T[nmat-1]) {
212: PetscCall(PetscObjectReference((PetscObject)st->T[nmat-1]));
213: PetscCall(MatDestroy(&st->P));
214: st->P = st->T[nmat-1];
215: }
216: if (st->Psplit) { /* build custom preconditioner from the split matrices */
217: PetscCall(STMatMAXPY_Private(st,nmat>2?newshift:-newshift,nmat>2?st->sigma:-st->sigma,0,coeffs?coeffs+((nmat-1)*nmat)/2:NULL,PETSC_FALSE,PETSC_TRUE,&st->Pmat));
218: }
219: }
220: if (st->P) {
221: PetscCall(ST_KSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P));
222: PetscCall(KSPSetUp(st->ksp));
223: }
224: PetscFunctionReturn(PETSC_SUCCESS);
225: }
227: SLEPC_EXTERN PetscErrorCode STCreate_Sinvert(ST st)
228: {
229: PetscFunctionBegin;
230: st->usesksp = PETSC_TRUE;
232: st->ops->apply = STApply_Generic;
233: st->ops->applytrans = STApplyTranspose_Generic;
234: st->ops->applyhermtrans = STApplyHermitianTranspose_Generic;
235: st->ops->backtransform = STBackTransform_Sinvert;
236: st->ops->setshift = STSetShift_Sinvert;
237: st->ops->getbilinearform = STGetBilinearForm_Default;
238: st->ops->setup = STSetUp_Sinvert;
239: st->ops->computeoperator = STComputeOperator_Sinvert;
240: st->ops->postsolve = STPostSolve_Sinvert;
241: st->ops->checknullspace = STCheckNullSpace_Default;
242: st->ops->setdefaultksp = STSetDefaultKSP_Default;
243: PetscFunctionReturn(PETSC_SUCCESS);
244: }