Actual source code: nepresolv.c

slepc-3.18.3 2023-03-24
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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:   return 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:   return 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:   return 0;
133: }