Actual source code: sinvert.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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 STApply_Sinvert(ST st,Vec x,Vec y)
 17: {

 21:   if (st->nmat>1) {
 22:     /* generalized eigenproblem: y = (A - sB)^-1 B x */
 23:     MatMult(st->T[0],x,st->work[0]);
 24:     STMatSolve(st,st->work[0],y);
 25:   } else {
 26:     /* standard eigenproblem: y = (A - sI)^-1 x */
 27:     STMatSolve(st,x,y);
 28:   }
 29:   return(0);
 30: }

 32: PetscErrorCode STApplyTranspose_Sinvert(ST st,Vec x,Vec y)
 33: {

 37:   if (st->nmat>1) {
 38:     /* generalized eigenproblem: y = B^T (A - sB)^-T x */
 39:     STMatSolveTranspose(st,x,st->work[0]);
 40:     MatMultTranspose(st->T[0],st->work[0],y);
 41:   } else {
 42:     /* standard eigenproblem: y = (A - sI)^-T x */
 43:     STMatSolveTranspose(st,x,y);
 44:   }
 45:   return(0);
 46: }

 48: 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

 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:   return(0);
 71: }

 73: PetscErrorCode STPostSolve_Sinvert(ST st)
 74: {

 78:   if (st->shift_matrix == ST_MATMODE_INPLACE) {
 79:     if (st->nmat>1) {
 80:       MatAXPY(st->A[0],st->sigma,st->A[1],st->str);
 81:     } else {
 82:       MatShift(st->A[0],st->sigma);
 83:     }
 84:     st->Astate[0] = ((PetscObject)st->A[0])->state;
 85:     st->state = ST_STATE_INITIAL;
 86:   }
 87:   return(0);
 88: }

 90: PetscErrorCode STSetUp_Sinvert(ST st)
 91: {
 93:   PetscInt       k,nc,nmat=PetscMax(st->nmat,2);
 94:   PetscScalar    *coeffs=NULL;

 97:   if (st->nmat>1) {
 98:     STSetWorkVecs(st,1);
 99:   }
100:   /* if the user did not set the shift, use the target value */
101:   if (!st->sigma_set) st->sigma = st->defsigma;
102:   if (st->transform) {
103:     if (nmat>2) {
104:       nc = (nmat*(nmat+1))/2;
105:       PetscMalloc1(nc,&coeffs);
106:       /* Compute coeffs */
107:       STCoeffs_Monomial(st,coeffs);
108:     }
109:     /* T[0] = A_n */
110:     k = nmat-1;
111:     PetscObjectReference((PetscObject)st->A[k]);
112:     MatDestroy(&st->T[0]);
113:     st->T[0] = st->A[k];
114:     for (k=1;k<nmat;k++) {
115:       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]);
116:     }
117:     if (nmat>2) { PetscFree(coeffs); }
118:     PetscObjectReference((PetscObject)st->T[nmat-1]);
119:     MatDestroy(&st->P);
120:     st->P = st->T[nmat-1];
121:   } else {
122:     for (k=0;k<nmat;k++) {
123:       PetscObjectReference((PetscObject)st->A[k]);
124:       MatDestroy(&st->T[k]);
125:       st->T[k] = st->A[k];
126:     }
127:   }
128:   if (st->P) {
129:     if (!st->ksp) { STGetKSP(st,&st->ksp); }
130:     STCheckFactorPackage(st);
131:     KSPSetOperators(st->ksp,st->P,st->P);
132:     KSPSetUp(st->ksp);
133:   }
134:   return(0);
135: }

137: PetscErrorCode STSetShift_Sinvert(ST st,PetscScalar newshift)
138: {
140:   PetscInt       nmat=PetscMax(st->nmat,2),k,nc;
141:   PetscScalar    *coeffs=NULL;

144:   if (st->transform) {
145:     if (st->shift_matrix == ST_MATMODE_COPY && nmat>2) {
146:       nc = (nmat*(nmat+1))/2;
147:       PetscMalloc1(nc,&coeffs);
148:       /* Compute coeffs */
149:       STCoeffs_Monomial(st,coeffs);
150:     }
151:     for (k=1;k<nmat;k++) {
152:       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]);
153:     }
154:     if (st->shift_matrix == ST_MATMODE_COPY && nmat>2) {
155:       PetscFree(coeffs);
156:     }
157:     if (st->P!=st->T[nmat-1]) {
158:       PetscObjectReference((PetscObject)st->T[nmat-1]);
159:       MatDestroy(&st->P);
160:       st->P = st->T[nmat-1];
161:     }
162:   }
163:   if (st->P) {
164:     if (!st->ksp) { STGetKSP(st,&st->ksp); }
165:     KSPSetOperators(st->ksp,st->P,st->P);
166:     KSPSetUp(st->ksp);
167:   }
168:   return(0);
169: }

171: SLEPC_EXTERN PetscErrorCode STCreate_Sinvert(ST st)
172: {
174:   st->ops->apply           = STApply_Sinvert;
175:   st->ops->getbilinearform = STGetBilinearForm_Default;
176:   st->ops->applytrans      = STApplyTranspose_Sinvert;
177:   st->ops->postsolve       = STPostSolve_Sinvert;
178:   st->ops->backtransform   = STBackTransform_Sinvert;
179:   st->ops->setup           = STSetUp_Sinvert;
180:   st->ops->setshift        = STSetShift_Sinvert;
181:   st->ops->checknullspace  = STCheckNullSpace_Default;
182:   st->ops->setdefaultksp   = STSetDefaultKSP_Default;
183:   return(0);
184: }