Actual source code: sinvert.c
slepc-3.16.2 2022-02-01
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2021, 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: PetscErrorCode STBackTransform_Sinvert(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
17: {
18: PetscInt j;
19: #if !defined(PETSC_USE_COMPLEX)
20: PetscScalar t;
21: #endif
24: #if !defined(PETSC_USE_COMPLEX)
25: for (j=0;j<n;j++) {
26: if (eigi[j] == 0) eigr[j] = 1.0 / eigr[j] + st->sigma;
27: else {
28: t = eigr[j] * eigr[j] + eigi[j] * eigi[j];
29: eigr[j] = eigr[j] / t + st->sigma;
30: eigi[j] = - eigi[j] / t;
31: }
32: }
33: #else
34: for (j=0;j<n;j++) {
35: eigr[j] = 1.0 / eigr[j] + st->sigma;
36: }
37: #endif
38: return(0);
39: }
41: PetscErrorCode STPostSolve_Sinvert(ST st)
42: {
46: if (st->matmode == ST_MATMODE_INPLACE) {
47: if (st->nmat>1) {
48: MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
49: } else {
50: MatShift(st->A[0],st->sigma);
51: }
52: st->Astate[0] = ((PetscObject)st->A[0])->state;
53: st->state = ST_STATE_INITIAL;
54: st->opready = PETSC_FALSE;
55: }
56: return(0);
57: }
59: /*
60: Operator (sinvert):
61: Op P M
62: if nmat=1: (A-sI)^-1 A-sI NULL
63: if nmat=2: (A-sB)^-1 B A-sB B
64: */
65: PetscErrorCode STComputeOperator_Sinvert(ST st)
66: {
70: /* if the user did not set the shift, use the target value */
71: if (!st->sigma_set) st->sigma = st->defsigma;
72: PetscObjectReference((PetscObject)st->A[1]);
73: MatDestroy(&st->T[0]);
74: st->T[0] = st->A[1];
75: STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),&st->T[1]);
76: PetscObjectReference((PetscObject)st->T[1]);
77: MatDestroy(&st->P);
78: st->P = st->T[1];
79: st->M = (st->nmat>1)? st->T[0]: NULL;
80: return(0);
81: }
83: PetscErrorCode STSetUp_Sinvert(ST st)
84: {
86: PetscInt k,nc,nmat=st->nmat;
87: PetscScalar *coeffs=NULL;
90: if (nmat>1) {
91: STSetWorkVecs(st,1);
92: }
93: /* if the user did not set the shift, use the target value */
94: if (!st->sigma_set) st->sigma = st->defsigma;
95: if (nmat>2) { /* set-up matrices for polynomial eigenproblems */
96: if (st->transform) {
97: nc = (nmat*(nmat+1))/2;
98: PetscMalloc1(nc,&coeffs);
99: /* Compute coeffs */
100: STCoeffs_Monomial(st,coeffs);
101: /* T[0] = A_n */
102: k = nmat-1;
103: PetscObjectReference((PetscObject)st->A[k]);
104: MatDestroy(&st->T[0]);
105: st->T[0] = st->A[k];
106: for (k=1;k<nmat;k++) {
107: 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),&st->T[k]);
108: }
109: PetscFree(coeffs);
110: PetscObjectReference((PetscObject)st->T[nmat-1]);
111: MatDestroy(&st->P);
112: st->P = st->T[nmat-1];
113: STKSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P);
114: } else {
115: for (k=0;k<nmat;k++) {
116: PetscObjectReference((PetscObject)st->A[k]);
117: MatDestroy(&st->T[k]);
118: st->T[k] = st->A[k];
119: }
120: }
121: }
122: if (st->P) {
123: KSPSetUp(st->ksp);
124: }
125: return(0);
126: }
128: PetscErrorCode STSetShift_Sinvert(ST st,PetscScalar newshift)
129: {
131: PetscInt nmat=PetscMax(st->nmat,2),k,nc;
132: PetscScalar *coeffs=NULL;
135: if (st->transform) {
136: if (st->matmode == ST_MATMODE_COPY && nmat>2) {
137: nc = (nmat*(nmat+1))/2;
138: PetscMalloc1(nc,&coeffs);
139: /* Compute coeffs */
140: STCoeffs_Monomial(st,coeffs);
141: }
142: for (k=1;k<nmat;k++) {
143: 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,&st->T[k]);
144: }
145: if (st->matmode == ST_MATMODE_COPY && nmat>2) {
146: PetscFree(coeffs);
147: }
148: if (st->P!=st->T[nmat-1]) {
149: PetscObjectReference((PetscObject)st->T[nmat-1]);
150: MatDestroy(&st->P);
151: st->P = st->T[nmat-1];
152: }
153: }
154: if (st->P) {
155: STKSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P);
156: KSPSetUp(st->ksp);
157: }
158: return(0);
159: }
161: SLEPC_EXTERN PetscErrorCode STCreate_Sinvert(ST st)
162: {
164: st->usesksp = PETSC_TRUE;
166: st->ops->apply = STApply_Generic;
167: st->ops->applytrans = STApplyTranspose_Generic;
168: st->ops->backtransform = STBackTransform_Sinvert;
169: st->ops->setshift = STSetShift_Sinvert;
170: st->ops->getbilinearform = STGetBilinearForm_Default;
171: st->ops->setup = STSetUp_Sinvert;
172: st->ops->computeoperator = STComputeOperator_Sinvert;
173: st->ops->postsolve = STPostSolve_Sinvert;
174: st->ops->checknullspace = STCheckNullSpace_Default;
175: st->ops->setdefaultksp = STSetDefaultKSP_Default;
176: return(0);
177: }