Actual source code: nepresolv.c
slepc-main 2024-11-15
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 - eigensolver context obtained from NEPCreate()
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: Notes:
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: 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,(void(*)(void))MatMult_Resolvent));
127: PetscCall(MatShellSetOperation(nep->resolvent,MATOP_DESTROY,(void(*)(void))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: }