Actual source code: sinvert.c
1: /*
2: Implements the shift-and-invert technique for eigenvalue problems.
4: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
5: SLEPc - Scalable Library for Eigenvalue Problem Computations
6: Copyright (c) 2002-2013, Universitat Politecnica de Valencia, Spain
8: This file is part of SLEPc.
10: SLEPc is free software: you can redistribute it and/or modify it under the
11: terms of version 3 of the GNU Lesser General Public License as published by
12: the Free Software Foundation.
14: SLEPc is distributed in the hope that it will be useful, but WITHOUT ANY
15: WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
16: FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for
17: more details.
19: You should have received a copy of the GNU Lesser General Public License
20: along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
21: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
22: */
24: #include <slepc-private/stimpl.h> /*I "slepcst.h" I*/
28: PetscErrorCode STApply_Sinvert(ST st,Vec x,Vec y)
29: {
33: if (st->nmat>1) {
34: /* generalized eigenproblem: y = (A - sB)^-1 B x */
35: MatMult(st->T[0],x,st->w);
36: STMatSolve(st,1,st->w,y);
37: } else {
38: /* standard eigenproblem: y = (A - sI)^-1 x */
39: STMatSolve(st,1,x,y);
40: }
41: return(0);
42: }
46: PetscErrorCode STApplyTranspose_Sinvert(ST st,Vec x,Vec y)
47: {
51: if (st->nmat>1) {
52: /* generalized eigenproblem: y = B^T (A - sB)^-T x */
53: STMatSolveTranspose(st,1,x,st->w);
54: MatMultTranspose(st->T[0],st->w,y);
55: } else {
56: /* standard eigenproblem: y = (A - sI)^-T x */
57: STMatSolveTranspose(st,1,x,y);
58: }
59: return(0);
60: }
64: PetscErrorCode STBackTransform_Sinvert(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
65: {
66: PetscInt j;
67: #if !defined(PETSC_USE_COMPLEX)
68: PetscScalar t;
69: #endif
72: #if !defined(PETSC_USE_COMPLEX)
73: for (j=0;j<n;j++) {
74: if (eigi[j] == 0) eigr[j] = 1.0 / eigr[j] + st->sigma;
75: else {
76: t = eigr[j] * eigr[j] + eigi[j] * eigi[j];
77: eigr[j] = eigr[j] / t + st->sigma;
78: eigi[j] = - eigi[j] / t;
79: }
80: }
81: #else
82: for (j=0;j<n;j++) {
83: eigr[j] = 1.0 / eigr[j] + st->sigma;
84: }
85: #endif
86: return(0);
87: }
91: PetscErrorCode STPostSolve_Sinvert(ST st)
92: {
94: PetscScalar s;
97: if (st->shift_matrix == ST_MATMODE_INPLACE) {
98: if (st->nmat>1) {
99: if (st->nmat==3) {
100: MatAXPY(st->A[0],-st->sigma*st->sigma,st->A[2],st->str);
101: MatAXPY(st->A[1],-2.0*st->sigma,st->A[2],st->str);
102: s = -st->sigma;
103: } else s = st->sigma;
104: MatAXPY(st->A[0],s,st->A[1],st->str);
105: } else {
106: MatShift(st->A[0],st->sigma);
107: }
108: st->Astate[0] = ((PetscObject)st->A[0])->state;
109: st->setupcalled = 0;
110: }
111: return(0);
112: }
116: PetscErrorCode STSetUp_Sinvert(ST st)
117: {
119: PetscScalar gamma;
122: /* if the user did not set the shift, use the target value */
123: if (!st->sigma_set) st->sigma = st->defsigma;
124: if (st->nmat<3) {
125: /* T[0] = B */
126: if (st->nmat>1) { PetscObjectReference((PetscObject)st->A[1]); }
127: st->T[0] = st->A[1];
128: gamma = -st->sigma;
129: } else {
130: /* T[0] = C */
131: PetscObjectReference((PetscObject)st->A[2]);
132: st->T[0] = st->A[2];
133: /* T[2] = A+sigma*B+sigma*sigma*C */
134: STMatGAXPY_Private(st,st->sigma,0.0,2,2,PETSC_TRUE);
135: gamma = 2.0*st->sigma;
136: }
137: /* T[1] = A-sigma*B or B+2*sigma*C */
138: STMatGAXPY_Private(st,gamma,0.0,1,1,PETSC_TRUE);
139: if (st->nmat<3) {
140: if (!st->ksp) { STGetKSP(st,&st->ksp); }
141: KSPSetOperators(st->ksp,st->T[1],st->T[1],DIFFERENT_NONZERO_PATTERN);
142: KSPSetUp(st->ksp);
143: st->kspidx = 1;
144: }
145: return(0);
146: }
150: PetscErrorCode STSetShift_Sinvert(ST st,PetscScalar newshift)
151: {
153: MatStructure flg;
154: PetscScalar alpha,beta;
157: /* Nothing to be done if STSetUp has not been called yet */
158: if (!st->setupcalled) return(0);
159: if (st->nmat<3) {
160: alpha = -newshift; beta = -st->sigma;
161: } else {
162: STMatGAXPY_Private(st,newshift,st->sigma,2,2,PETSC_FALSE);
163: alpha = 2.0*newshift; beta = 2.0*st->sigma;
164: }
165: STMatGAXPY_Private(st,alpha,beta,1,1,PETSC_FALSE);
166: if (st->kspidx==1 || (st->nmat==3 && st->kspidx==2)) { /* Update KSP operator */
167: /* Check if the new KSP matrix has the same zero structure */
168: if (st->nmat>1 && st->str == DIFFERENT_NONZERO_PATTERN && (st->sigma == 0.0 || newshift == 0.0)) flg = DIFFERENT_NONZERO_PATTERN;
169: else flg = SAME_NONZERO_PATTERN;
170: KSPSetOperators(st->ksp,st->T[st->kspidx],st->T[st->kspidx],flg);
171: KSPSetUp(st->ksp);
172: }
173: return(0);
174: }
178: PetscErrorCode STSetFromOptions_Sinvert(ST st)
179: {
181: PC pc;
182: PCType pctype;
183: KSPType ksptype;
186: if (!st->ksp) { STGetKSP(st,&st->ksp); }
187: KSPGetPC(st->ksp,&pc);
188: KSPGetType(st->ksp,&ksptype);
189: PCGetType(pc,&pctype);
190: if (!pctype && !ksptype) {
191: if (st->shift_matrix == ST_MATMODE_SHELL) {
192: /* in shell mode use GMRES with Jacobi as the default */
193: KSPSetType(st->ksp,KSPGMRES);
194: PCSetType(pc,PCJACOBI);
195: } else {
196: /* use direct solver as default */
197: KSPSetType(st->ksp,KSPPREONLY);
198: PCSetType(pc,PCREDUNDANT);
199: }
200: }
201: return(0);
202: }
206: PETSC_EXTERN PetscErrorCode STCreate_Sinvert(ST st)
207: {
209: st->ops->apply = STApply_Sinvert;
210: st->ops->getbilinearform = STGetBilinearForm_Default;
211: st->ops->applytrans = STApplyTranspose_Sinvert;
212: st->ops->postsolve = STPostSolve_Sinvert;
213: st->ops->backtransform = STBackTransform_Sinvert;
214: st->ops->setup = STSetUp_Sinvert;
215: st->ops->setshift = STSetShift_Sinvert;
216: st->ops->setfromoptions = STSetFromOptions_Sinvert;
217: st->ops->checknullspace = STCheckNullSpace_Default;
218: return(0);
219: }