Date: 2026-03-09T09:12:17+00:00

Actual source code: shift.c

      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>
     16: #include <petsc/private/matimpl.h>  /* Mat_MPIDense */

     18: /*
     19:    Special STApply() for the BSE structured matrix

     21:        H = [ R  C; -C^H -R^T ].

     23:    Assumes that H is a MATNEST and x,y are VECNEST.

     25:    Only the upper part of the product y=H*x is computed.

     27:        y1 = R*x1+C*x2

     29:    The bottom part of the input vector x2 is computed as
     30:    either conj(x1) or -conj(x1), where the sign is given by
     31:    s in the context SlepcMatStruct.
     32:    The bottom part of the output vector y2 is not referenced.
     33: */
     34: static PetscErrorCode STApply_Shift_BSE(ST st,Vec x,Vec y)
     35: {
     36:   Mat            H,R,C;
     37:   Vec            x1,x2,y1;
     38:   PetscContainer container;
     39:   SlepcMatStruct mctx;

     41:   PetscFunctionBegin;
     42:   H = st->T[0];
     43:   PetscCall(PetscObjectQuery((PetscObject)H,"SlepcMatStruct",(PetscObject*)&container));
     44:   PetscCall(PetscContainerGetPointer(container,(void**)&mctx));
     45:   PetscCall(MatNestGetSubMat(H,0,0,&R));
     46:   PetscCall(MatNestGetSubMat(H,0,1,&C));
     47:   PetscCall(VecNestGetSubVec(x,0,&x1));
     48:   PetscCall(VecNestGetSubVec(x,1,&x2));
     49:   PetscCall(VecNestGetSubVec(y,0,&y1));

     51:   /* x2 = +/-conj(x1) */
     52:   PetscCall(VecCopy(x1,x2));
     53:   PetscCall(VecConjugate(x2));
     54:   if (mctx->s==-1.0) PetscCall(VecScale(x2,-1.0));

     56:   PetscCall(MatMult(C,x2,y1));
     57:   PetscCall(MatMultAdd(R,x1,y1,y1));
     58:   PetscFunctionReturn(PETSC_SUCCESS);
     59: }

     61: /*
     62:    Specialized version that avoids communication for multiplication by R.
     63:    It needs to access internal data structures of MATMPIDENSE.
     64: */
     65: static PetscErrorCode STApply_Shift_BSE_Dense(ST st,Vec x,Vec y)
     66: {
     67:   Mat            H,R,C;
     68:   Vec            x1,x2,y1;
     69:   Mat_MPIDense   *mdnR,*mdnC;
     70:   PetscContainer container;
     71:   SlepcMatStruct mctx;

     73:   PetscFunctionBegin;
     74:   H = st->T[0];
     75:   PetscCall(PetscObjectQuery((PetscObject)H,"SlepcMatStruct",(PetscObject*)&container));
     76:   PetscCall(PetscContainerGetPointer(container,(void**)&mctx));
     77:   PetscCall(MatNestGetSubMat(H,0,0,&R));
     78:   PetscCall(MatNestGetSubMat(H,0,1,&C));
     79:   mdnR = (Mat_MPIDense*)R->data;
     80:   mdnC = (Mat_MPIDense*)C->data;
     81:   PetscCall(VecNestGetSubVec(x,0,&x1));
     82:   PetscCall(VecNestGetSubVec(x,1,&x2));
     83:   PetscCall(VecNestGetSubVec(y,0,&y1));

     85:   /* x2 = +/-conj(x1) */
     86:   PetscCall(VecCopy(x1,x2));
     87:   PetscCall(VecConjugate(x2));
     88:   if (mctx->s==-1.0) PetscCall(VecScale(x2,-1.0));

     90:   PetscCall(MatMult(C,x2,y1));
     91:   /* PetscCall(MatMultAdd(R,x1,y1,y1)); */
     92:   PetscCall(VecConjugate(mdnC->lvec));
     93:   if (mctx->s==-1.0) PetscCall(VecScale(mdnC->lvec,-1.0));
     94:   PetscCall(PetscLogEventBegin(MAT_MultAdd,R,mdnC->lvec,y1,y1));
     95:   PetscCall(VecLockReadPush(mdnC->lvec));
     96:   PetscCall((*mdnR->A->ops->multadd)(mdnR->A,mdnC->lvec,y1,y1));
     97:   PetscCall(VecLockReadPop(mdnC->lvec));
     98:   PetscCall(PetscLogEventEnd(MAT_MultAdd,R,mdnC->lvec,y1,y1));
     99:   PetscCall(PetscObjectStateIncrease((PetscObject)y1));
    100:   PetscFunctionReturn(PETSC_SUCCESS);
    101: }

    103: static PetscErrorCode STBackTransform_Shift(ST st,PetscInt n,PetscScalar *eigr,PetscScalar *eigi)
    104: {
    105:   PetscInt j;

    107:   PetscFunctionBegin;
    108:   for (j=0;j<n;j++) {
    109:     eigr[j] += st->sigma;
    110:   }
    111:   PetscFunctionReturn(PETSC_SUCCESS);
    112: }

    114: static PetscErrorCode STPostSolve_Shift(ST st)
    115: {
    116:   PetscFunctionBegin;
    117:   if (st->matmode == ST_MATMODE_INPLACE) {
    118:     if (st->nmat>1) PetscCall(MatAXPY(st->A[0],st->sigma,st->A[1],st->str));
    119:     else PetscCall(MatShift(st->A[0],st->sigma));
    120:     st->Astate[0] = ((PetscObject)st->A[0])->state;
    121:     st->state   = ST_STATE_INITIAL;
    122:     st->opready = PETSC_FALSE;
    123:   }
    124:   PetscFunctionReturn(PETSC_SUCCESS);
    125: }

    127: /*
    128:    Operator (shift):
    129:                Op               P         M
    130:    if nmat=1:  A-sI             NULL      A-sI
    131:    if nmat=2:  B^-1 (A-sB)      B         A-sB
    132: */
    133: static PetscErrorCode STComputeOperator_Shift(ST st)
    134: {
    135:   PetscFunctionBegin;
    136:   st->usesksp = (st->nmat>1)? PETSC_TRUE: PETSC_FALSE;
    137:   PetscCall(PetscObjectReference((PetscObject)st->A[1]));
    138:   PetscCall(MatDestroy(&st->T[1]));
    139:   st->T[1] = st->A[1];
    140:   PetscCall(STMatMAXPY_Private(st,-st->sigma,0.0,0,NULL,PetscNot(st->state==ST_STATE_UPDATED),PETSC_FALSE,&st->T[0]));
    141:   if (st->nmat>1) PetscCall(PetscObjectReference((PetscObject)st->T[1]));
    142:   PetscCall(MatDestroy(&st->P));
    143:   st->P = (st->nmat>1)? st->T[1]: NULL;
    144:   st->M = st->T[0];
    145:   if (st->nmat>1 && st->Psplit) {  /* build custom preconditioner from the split matrices */
    146:     PetscCall(MatDestroy(&st->Pmat));
    147:     PetscCall(PetscObjectReference((PetscObject)st->Psplit[1]));
    148:     st->Pmat = st->Psplit[1];
    149:   }
    150:   PetscFunctionReturn(PETSC_SUCCESS);
    151: }

    153: static PetscErrorCode STSetUp_Shift(ST st)
    154: {
    155:   PetscInt       k,nc,nmat=st->nmat;
    156:   PetscScalar    *coeffs=NULL;
    157:   PetscBool      denseR,denseC;
    158:   Mat            H,R,C;

    160:   PetscFunctionBegin;
    161:   if (nmat>1) PetscCall(STSetWorkVecs(st,1));
    162:   if (nmat>2) {  /* set-up matrices for polynomial eigenproblems */
    163:     if (st->transform) {
    164:       nc = (nmat*(nmat+1))/2;
    165:       PetscCall(PetscMalloc1(nc,&coeffs));
    166:       /* Compute coeffs */
    167:       PetscCall(STCoeffs_Monomial(st,coeffs));
    168:       /* T[n] = A_n */
    169:       k = nmat-1;
    170:       PetscCall(PetscObjectReference((PetscObject)st->A[k]));
    171:       PetscCall(MatDestroy(&st->T[k]));
    172:       st->T[k] = st->A[k];
    173:       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]));
    174:       PetscCall(PetscFree(coeffs));
    175:       PetscCall(PetscObjectReference((PetscObject)st->T[nmat-1]));
    176:       PetscCall(MatDestroy(&st->P));
    177:       st->P = st->T[nmat-1];
    178:       if (st->Psplit) {  /* build custom preconditioner from the split matrices */
    179:         PetscCall(STMatMAXPY_Private(st,st->sigma,0.0,nmat-1,coeffs?coeffs:NULL,PETSC_TRUE,PETSC_TRUE,&st->Pmat));
    180:       }
    181:       PetscCall(ST_KSPSetOperators(st,st->P,st->Pmat?st->Pmat:st->P));
    182:     } else {
    183:       for (k=0;k<nmat;k++) {
    184:         PetscCall(PetscObjectReference((PetscObject)st->A[k]));
    185:         PetscCall(MatDestroy(&st->T[k]));
    186:         st->T[k] = st->A[k];
    187:       }
    188:     }
    189:   }
    190:   if (st->P) PetscCall(KSPSetUp(st->ksp));
    191:   if (st->structured) {
    192:     H = st->T[0];
    193:     PetscCall(MatNestGetSubMat(H,0,0,&R));
    194:     PetscCall(MatNestGetSubMat(H,0,1,&C));
    195:     PetscCall(PetscObjectTypeCompareAny((PetscObject)R,&denseR,MATMPIDENSE,MATMPIDENSECUDA,MATMPIDENSEHIP,""));
    196:     PetscCall(PetscObjectTypeCompareAny((PetscObject)C,&denseC,MATMPIDENSE,MATMPIDENSECUDA,MATMPIDENSEHIP,""));
    197:     st->ops->apply = (denseR && denseC)? STApply_Shift_BSE_Dense: STApply_Shift_BSE;
    198:   }
    199:   PetscFunctionReturn(PETSC_SUCCESS);
    200: }

    202: static PetscErrorCode STSetShift_Shift(ST st,PetscScalar newshift)
    203: {
    204:   PetscInt       k,nc,nmat=PetscMax(st->nmat,2);
    205:   PetscScalar    *coeffs=NULL;

    207:   PetscFunctionBegin;
    208:   if (st->transform) {
    209:     if (st->matmode == ST_MATMODE_COPY && nmat>2) {
    210:       nc = (nmat*(nmat+1))/2;
    211:       PetscCall(PetscMalloc1(nc,&coeffs));
    212:       /* Compute coeffs */
    213:       PetscCall(STCoeffs_Monomial(st,coeffs));
    214:     }
    215:     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]));
    216:     if (st->matmode == ST_MATMODE_COPY && nmat>2) PetscCall(PetscFree(coeffs));
    217:     if (st->nmat<=2) st->M = st->T[0];
    218:   }
    219:   PetscFunctionReturn(PETSC_SUCCESS);
    220: }

    222: /*MC
    223:    STSHIFT - STSHIFT = "shift" - A shift of origin, where the spectrum is
    224:    shifted by a constant amount.

    226:    Level: beginner

    228:    Notes:
    229:    The operator in this `ST` is $B^{-1}A-\sigma I$, where $A$ and $B$ are the
    230:    matrices set with `STSetMatrices()` and the shift $\sigma$ is given in
    231:    `STSetShift()`.

    233:    This is the default `ST`. If no shift is given, the default is $\sigma=0$,
    234:    i.e., no transformation.

    236: .seealso: [](ch:st), `ST`, `STType`, `STSetType()`, `STSetMatrices()`, `STSetShift()`
    237: M*/

    239: SLEPC_EXTERN PetscErrorCode STCreate_Shift(ST st)
    240: {
    241:   PetscFunctionBegin;
    242:   st->usesksp = PETSC_TRUE;

    244:   st->ops->apply           = STApply_Generic;
    245:   st->ops->applytrans      = STApplyTranspose_Generic;
    246:   st->ops->applyhermtrans  = STApplyHermitianTranspose_Generic;
    247:   st->ops->backtransform   = STBackTransform_Shift;
    248:   st->ops->setshift        = STSetShift_Shift;
    249:   st->ops->getbilinearform = STGetBilinearForm_Default;
    250:   st->ops->setup           = STSetUp_Shift;
    251:   st->ops->computeoperator = STComputeOperator_Shift;
    252:   st->ops->postsolve       = STPostSolve_Shift;
    253:   st->ops->setdefaultksp   = STSetDefaultKSP_Default;
    254:   PetscFunctionReturn(PETSC_SUCCESS);
    255: }