Date: 2026-03-09T09:12:21+00:00

Actual source code: nepresolv.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:    NEP routines related to resolvent T^{-1}(z) = sum_i (z-lambda_i)^{-1} x_i y_i'
     12: */

     14: #include <slepc/private/nepimpl.h>

     16: typedef struct {
     17:   NEP              nep;
     18:   RG               rg;
     19:   PetscScalar      omega;
     20:   PetscScalar      *nfactor;         /* normalization factors y_i'*T'(lambda_i)*x_i */
     21:   PetscBool        *nfactor_avail;
     22:   PetscScalar      *dots;            /* inner products y_i'*v */
     23:   PetscBool        *dots_avail;
     24:   PetscObjectId    vid;
     25:   PetscObjectState vstate;
     26: } NEP_RESOLVENT_MATSHELL;

     28: static PetscErrorCode MatMult_Resolvent(Mat M,Vec v,Vec r)
     29: {
     30:   NEP_RESOLVENT_MATSHELL *ctx;
     31:   NEP                    nep;
     32:   PetscInt               i,inside=1;
     33:   PetscScalar            alpha;
     34:   Vec                    x,y,z,w;

     36:   PetscFunctionBegin;
     37:   PetscCall(MatShellGetContext(M,&ctx));
     38:   nep = ctx->nep;
     39:   w = nep->work[0];
     40:   z = nep->work[1];
     41:   if (((PetscObject)v)->id != ctx->vid || ((PetscObject)v)->state != ctx->vstate) {
     42:     PetscCall(PetscArrayzero(ctx->dots_avail,ctx->nep->nconv));
     43:     PetscCall(PetscObjectGetId((PetscObject)v,&ctx->vid));
     44:     PetscCall(VecGetState(v,&ctx->vstate));
     45:   }
     46:   PetscCall(VecSet(r,0.0));
     47:   for (i=0;i<nep->nconv;i++) {
     48:     if (ctx->rg) PetscCall(RGCheckInside(ctx->rg,1,&nep->eigr[i],&nep->eigi[i],&inside));
     49:     if (inside>=0) {
     50:       PetscCall(BVGetColumn(nep->V,i,&x));
     51:       PetscCall(BVGetColumn(nep->W,i,&y));
     52:       PetscCall(NEPApplyJacobian(nep,nep->eigr[i],x,z,w,NULL));
     53:       if (!ctx->dots_avail[i]) {
     54:         PetscCall(VecDot(v,y,&ctx->dots[i]));
     55:         ctx->dots_avail[i] = PETSC_TRUE;
     56:       }
     57:       if (!ctx->nfactor_avail[i]) {
     58:         PetscCall(VecDot(w,y,&ctx->nfactor[i]));
     59:         ctx->nfactor_avail[i] = PETSC_TRUE;
     60:       }
     61:       alpha = ctx->dots[i]/(ctx->nfactor[i]*(ctx->omega-nep->eigr[i]));
     62:       PetscCall(VecAXPY(r,alpha,x));
     63:       PetscCall(BVRestoreColumn(nep->V,i,&x));
     64:       PetscCall(BVRestoreColumn(nep->W,i,&y));
     65:     }
     66:   }
     67:   PetscFunctionReturn(PETSC_SUCCESS);
     68: }

     70: static PetscErrorCode MatDestroy_Resolvent(Mat M)
     71: {
     72:   NEP_RESOLVENT_MATSHELL *ctx;

     74:   PetscFunctionBegin;
     75:   if (M) {
     76:     PetscCall(MatShellGetContext(M,&ctx));
     77:     PetscCall(PetscFree4(ctx->nfactor,ctx->nfactor_avail,ctx->dots,ctx->dots_avail));
     78:     PetscCall(PetscFree(ctx));
     79:   }
     80:   PetscFunctionReturn(PETSC_SUCCESS);
     81: }

     83: /*@
     84:    NEPApplyResolvent - Applies the resolvent $T^{-1}(z)$ to a given vector.

     86:    Collective

     88:    Input Parameters:
     89: +  nep   - the nonlinear eigensolver context
     90: .  rg    - optional region
     91: .  omega - value where the resolvent must be evaluated
     92: -  v     - input vector

     94:    Output Parameter:
     95: .  r     - result vector

     97:    Note:
     98:    The resolvent $T^{-1}(z) = \sum_i (z-\lambda_i)^{-1} x_i y_i^*$ is evaluated at
     99:    $z=\omega$ and the matrix-vector multiplication $r = T^{-1}(\omega) v$ is computed.
    100:    Vectors $x_i$ and $y_i$ are right and left eigenvectors, respectively, normalized
    101:    so that $y_i^*T'(\lambda_i)x_i=1$. The sum contains only eigenvectors that have
    102:    been previously computed with `NEPSolve()`, and if a region `rg` is given then only
    103:    those corresponding to eigenvalues inside the region are considered.

    105:    Level: intermediate

    107: .seealso: [](ch:nep), `NEPGetLeftEigenvector()`, `NEPSolve()`
    108: @*/
    109: PetscErrorCode NEPApplyResolvent(NEP nep,RG rg,PetscScalar omega,Vec v,Vec r)
    110: {
    111:   NEP_RESOLVENT_MATSHELL *ctx;

    113:   PetscFunctionBegin;
    118:   NEPCheckSolved(nep,1);

    120:   PetscCall(PetscLogEventBegin(NEP_Resolvent,nep,0,0,0));
    121:   if (!nep->resolvent) {
    122:     PetscCall(PetscNew(&ctx));
    123:     ctx->nep = nep;
    124:     PetscCall(PetscCalloc4(nep->nconv,&ctx->nfactor,nep->nconv,&ctx->nfactor_avail,nep->nconv,&ctx->dots,nep->nconv,&ctx->dots_avail));
    125:     PetscCall(MatCreateShell(PetscObjectComm((PetscObject)nep),nep->nloc,nep->nloc,nep->n,nep->n,ctx,&nep->resolvent));
    126:     PetscCall(MatShellSetOperation(nep->resolvent,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Resolvent));
    127:     PetscCall(MatShellSetOperation(nep->resolvent,MATOP_DESTROY,(PetscErrorCodeFn*)MatDestroy_Resolvent));
    128:   } else PetscCall(MatShellGetContext(nep->resolvent,&ctx));
    129:   PetscCall(NEPComputeVectors(nep));
    130:   PetscCall(NEPSetWorkVecs(nep,2));
    131:   ctx->rg    = rg;
    132:   ctx->omega = omega;
    133:   PetscCall(MatMult(nep->resolvent,v,r));
    134:   PetscCall(PetscLogEventEnd(NEP_Resolvent,nep,0,0,0));
    135:   PetscFunctionReturn(PETSC_SUCCESS);
    136: }