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:    Shift spectral transformation, applies (A + sigma I) as operator, or
 12:    inv(B)(A + sigma B) for generalized problems
 13: */

 15: #include <slepc/private/stimpl.h>

 17: static PetscErrorCode STBackTransform_Shift(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
 18: {
 19:   PetscInt j;

 21:   PetscFunctionBegin;
 22:   for (j=0;j<n;j++) {
 23:     eigr[j] += st->sigma;
 24:   }
 25:   PetscFunctionReturn(PETSC_SUCCESS);
 26: }

 28: static PetscErrorCode STPostSolve_Shift(ST st)
 29: {
 30:   PetscFunctionBegin;
 31:   if (st->matmode == ST_MATMODE_INPLACE) {
 32:     if (st->nmat>1) PetscCall(MatAXPY(st->A[0],st->sigma,st->A[1],st->str));
 33:     else PetscCall(MatShift(st->A[0],st->sigma));
 34:     st->Astate[0] = ((PetscObject)st->A[0])->state;
 35:     st->state   = ST_STATE_INITIAL;
 36:     st->opready = PETSC_FALSE;
 37:   }
 38:   PetscFunctionReturn(PETSC_SUCCESS);
 39: }

 41: /*
 42:    Operator (shift):
 43:                Op               P         M
 44:    if nmat=1:  A-sI             NULL      A-sI
 45:    if nmat=2:  B^-1 (A-sB)      B         A-sB
 46: */
 47: static PetscErrorCode STComputeOperator_Shift(ST st)
 48: {
 49:   PetscFunctionBegin;
 50:   st->usesksp = (st->nmat>1)? PETSC_TRUE: PETSC_FALSE;
 51:   PetscCall(PetscObjectReference((PetscObject)st->A[1]));
 52:   PetscCall(MatDestroy(&st->T[1]));
 53:   st->T[1] = st->A[1];
 54:   PetscCall(STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[0]));
 55:   if (st->nmat>1) PetscCall(PetscObjectReference((PetscObject)st->T[1]));
 56:   PetscCall(MatDestroy(&st->P));
 57:   st->P = (st->nmat>1)? st->T[1]: NULL;
 58:   st->M = st->T[0];
 59:   if (st->nmat>1 && st->Psplit) {  /* build custom preconditioner from the split matrices */
 60:     PetscCall(MatDestroy(&st->Pmat));
 61:     PetscCall(PetscObjectReference((PetscObject)st->Psplit[1]));
 62:     st->Pmat = st->Psplit[1];
 63:   }
 64:   PetscFunctionReturn(PETSC_SUCCESS);
 65: }

 67: static PetscErrorCode STSetUp_Shift(ST st)
 68: {
 69:   PetscInt       k,nc,nmat=st->nmat;
 70:   PetscScalar    *coeffs=NULL;

 72:   PetscFunctionBegin;
 73:   if (nmat>1) PetscCall(STSetWorkVecs(st,1));
 74:   if (nmat>2) {  /* set-up matrices for polynomial eigenproblems */
 75:     if (st->transform) {
 76:       nc = (nmat*(nmat+1))/2;
 77:       PetscCall(PetscMalloc1(nc,&coeffs));
 78:       /* Compute coeffs */
 79:       PetscCall(STCoeffs_Monomial(st,coeffs));
 80:       /* T[n] = A_n */
 81:       k = nmat-1;
 82:       PetscCall(PetscObjectReference((PetscObject)st->A[k]));
 83:       PetscCall(MatDestroy(&st->T[k]));
 84:       st->T[k] = st->A[k];
 85:       for (k=0;k<nmat-1;k++) PetscCall(STMatMAXPY_Private(st,nmat>2?st->sigma:-st->sigma,0.0,k,coeffs?coeffs+((nmat-k)*(nmat-k-1))/2:NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[k]));
 86:       PetscCall(PetscFree(coeffs));
 87:       PetscCall(PetscObjectReference((PetscObject)st->T[nmat-1]));
 88:       PetscCall(MatDestroy(&st->P));
 89:       st->P = st->T[nmat-1];
 90:       if (st->Psplit) {  /* build custom preconditioner from the split matrices */
 91:         PetscCall(STMatMAXPY_Private(st,st->sigma,0.0,nmat-1,coeffs?coeffs:NULL,PETSC_TRUE,PETSC_TRUE,&st->Pmat));
 92:       }
 93:       PetscCall(ST_KSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P));
 94:     } else {
 95:       for (k=0;k<nmat;k++) {
 96:         PetscCall(PetscObjectReference((PetscObject)st->A[k]));
 97:         PetscCall(MatDestroy(&st->T[k]));
 98:         st->T[k] = st->A[k];
 99:       }
100:     }
101:   }
102:   if (st->P) PetscCall(KSPSetUp(st->ksp));
103:   PetscFunctionReturn(PETSC_SUCCESS);
104: }

106: static PetscErrorCode STSetShift_Shift(ST st,PetscScalar newshift)
107: {
108:   PetscInt       k,nc,nmat=PetscMax(st->nmat,2);
109:   PetscScalar    *coeffs=NULL;

111:   PetscFunctionBegin;
112:   if (st->transform) {
113:     if (st->matmode == ST_MATMODE_COPY && nmat>2) {
114:       nc = (nmat*(nmat+1))/2;
115:       PetscCall(PetscMalloc1(nc,&coeffs));
116:       /* Compute coeffs */
117:       PetscCall(STCoeffs_Monomial(st,coeffs));
118:     }
119:     for (k=0;k<nmat-1;k++) PetscCall(STMatMAXPY_Private(st,nmat>2?newshift:-newshift,nmat>2?st->sigma:-st->sigma,k,coeffs?coeffs+((nmat-k)*(nmat-k-1))/2:NULL,PETSC_FALSE,PETSC_FALSE,&st->T[k]));
120:     if (st->matmode == ST_MATMODE_COPY && nmat>2) PetscCall(PetscFree(coeffs));
121:     if (st->nmat<=2) st->M = st->T[0];
122:   }
123:   PetscFunctionReturn(PETSC_SUCCESS);
124: }

126: SLEPC_EXTERN PetscErrorCode STCreate_Shift(ST st)
127: {
128:   PetscFunctionBegin;
129:   st->usesksp = PETSC_TRUE;

131:   st->ops->apply           = STApply_Generic;
132:   st->ops->applytrans      = STApplyTranspose_Generic;
133:   st->ops->applyhermtrans  = STApplyHermitianTranspose_Generic;
134:   st->ops->backtransform   = STBackTransform_Shift;
135:   st->ops->setshift        = STSetShift_Shift;
136:   st->ops->getbilinearform = STGetBilinearForm_Default;
137:   st->ops->setup           = STSetUp_Shift;
138:   st->ops->computeoperator = STComputeOperator_Shift;
139:   st->ops->postsolve       = STPostSolve_Shift;
140:   st->ops->setdefaultksp   = STSetDefaultKSP_Default;
141:   PetscFunctionReturn(PETSC_SUCCESS);
142: }