Date: 2022-08-09T09:05:53+00:00

Actual source code: nepresolv.c
slepc-3.17.2 2022-08-09
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      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:   MatShellGetContext(M,&ctx);
     37:   nep = ctx->nep;
     38:   w = nep->work[0];
     39:   z = nep->work[1];
     40:   if (((PetscObject)v)->id != ctx->vid || ((PetscObject)v)->state != ctx->vstate) {
     41:     PetscArrayzero(ctx->dots_avail,ctx->nep->nconv);
     42:     PetscObjectGetId((PetscObject)v,&ctx->vid);
     43:     PetscObjectStateGet((PetscObject)v,&ctx->vstate);
     44:   }
     45:   VecSet(r,0.0);
     46:   for (i=0;i<nep->nconv;i++) {
     47:     if (ctx->rg) RGCheckInside(ctx->rg,1,&nep->eigr[i],&nep->eigi[i],&inside);
     48:     if (inside>=0) {
     49:       BVGetColumn(nep->V,i,&x);
     50:       BVGetColumn(nep->W,i,&y);
     51:       NEPApplyJacobian(nep,nep->eigr[i],x,z,w,NULL);
     52:       if (!ctx->dots_avail[i]) {
     53:         VecDot(v,y,&ctx->dots[i]);
     54:         ctx->dots_avail[i] = PETSC_TRUE;
     55:       }
     56:       if (!ctx->nfactor_avail[i]) {
     57:         VecDot(w,y,&ctx->nfactor[i]);
     58:         ctx->nfactor_avail[i] = PETSC_TRUE;
     59:       }
     60:       alpha = ctx->dots[i]/(ctx->nfactor[i]*(ctx->omega-nep->eigr[i]));
     61:       VecAXPY(r,alpha,x);
     62:       BVRestoreColumn(nep->V,i,&x);
     63:       BVRestoreColumn(nep->W,i,&y);
     64:     }
     65:   }
     66:   PetscFunctionReturn(0);
     67: }

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

     73:   if (M) {
     74:     MatShellGetContext(M,&ctx);
     75:     PetscFree4(ctx->nfactor,ctx->nfactor_avail,ctx->dots,ctx->dots_avail);
     76:     PetscFree(ctx);
     77:   }
     78:   PetscFunctionReturn(0);
     79: }

     81: /*@
     82:    NEPApplyResolvent - Applies the resolvent T^{-1}(z) to a given vector.

     84:    Collective on nep

     86:    Input Parameters:
     87: +  nep   - eigensolver context obtained from NEPCreate()
     88: .  rg    - optional region
     89: .  omega - value where the resolvent must be evaluated
     90: -  v     - input vector

     92:    Output Parameter:
     93: .  r     - result vector

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

    103:    Level: intermediate

    105: .seealso: NEPGetLeftEigenvector(), NEPSolve()
    106: @*/
    107: PetscErrorCode NEPApplyResolvent(NEP nep,RG rg,PetscScalar omega,Vec v,Vec r)
    108: {
    109:   NEP_RESOLVENT_MATSHELL *ctx;

    115:   NEPCheckSolved(nep,1);

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