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1 | /* | ||
2 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
3 | SLEPc - Scalable Library for Eigenvalue Problem Computations | ||
4 | Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain | ||
5 | |||
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 | */ | ||
13 | |||
14 | #include <slepc/private/nepimpl.h> /*I "slepcnep.h" I*/ | ||
15 | |||
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; | ||
27 | |||
28 | 40 | static PetscErrorCode MatMult_Resolvent(Mat M,Vec v,Vec r) | |
29 | { | ||
30 | 40 | NEP_RESOLVENT_MATSHELL *ctx; | |
31 | 40 | NEP nep; | |
32 | 40 | PetscInt i,inside=1; | |
33 | 40 | PetscScalar alpha; | |
34 | 40 | Vec x,y,z,w; | |
35 | |||
36 |
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40 | PetscFunctionBegin; |
37 |
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40 | PetscCall(MatShellGetContext(M,&ctx)); |
38 | 40 | nep = ctx->nep; | |
39 | 40 | w = nep->work[0]; | |
40 | 40 | z = nep->work[1]; | |
41 |
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40 | if (((PetscObject)v)->id != ctx->vid || ((PetscObject)v)->state != ctx->vstate) { |
42 |
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20 | PetscCall(PetscArrayzero(ctx->dots_avail,ctx->nep->nconv)); |
43 |
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20 | PetscCall(PetscObjectGetId((PetscObject)v,&ctx->vid)); |
44 |
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20 | PetscCall(VecGetState(v,&ctx->vstate)); |
45 | } | ||
46 |
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40 | PetscCall(VecSet(r,0.0)); |
47 |
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360 | for (i=0;i<nep->nconv;i++) { |
48 |
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320 | if (ctx->rg) PetscCall(RGCheckInside(ctx->rg,1,&nep->eigr[i],&nep->eigi[i],&inside)); |
49 |
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320 | if (inside>=0) { |
50 |
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320 | PetscCall(BVGetColumn(nep->V,i,&x)); |
51 |
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320 | PetscCall(BVGetColumn(nep->W,i,&y)); |
52 |
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320 | PetscCall(NEPApplyJacobian(nep,nep->eigr[i],x,z,w,NULL)); |
53 |
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320 | if (!ctx->dots_avail[i]) { |
54 |
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160 | PetscCall(VecDot(v,y,&ctx->dots[i])); |
55 | 160 | ctx->dots_avail[i] = PETSC_TRUE; | |
56 | } | ||
57 |
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320 | if (!ctx->nfactor_avail[i]) { |
58 |
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80 | PetscCall(VecDot(w,y,&ctx->nfactor[i])); |
59 | 80 | ctx->nfactor_avail[i] = PETSC_TRUE; | |
60 | } | ||
61 | 320 | alpha = ctx->dots[i]/(ctx->nfactor[i]*(ctx->omega-nep->eigr[i])); | |
62 |
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320 | PetscCall(VecAXPY(r,alpha,x)); |
63 |
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320 | PetscCall(BVRestoreColumn(nep->V,i,&x)); |
64 |
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320 | PetscCall(BVRestoreColumn(nep->W,i,&y)); |
65 | } | ||
66 | } | ||
67 |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
68 | } | ||
69 | |||
70 | 10 | static PetscErrorCode MatDestroy_Resolvent(Mat M) | |
71 | { | ||
72 | 10 | NEP_RESOLVENT_MATSHELL *ctx; | |
73 | |||
74 |
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10 | PetscFunctionBegin; |
75 |
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10 | if (M) { |
76 |
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10 | PetscCall(MatShellGetContext(M,&ctx)); |
77 |
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10 | PetscCall(PetscFree4(ctx->nfactor,ctx->nfactor_avail,ctx->dots,ctx->dots_avail)); |
78 |
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10 | PetscCall(PetscFree(ctx)); |
79 | } | ||
80 |
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2 | PetscFunctionReturn(PETSC_SUCCESS); |
81 | } | ||
82 | |||
83 | /*@ | ||
84 | NEPApplyResolvent - Applies the resolvent T^{-1}(z) to a given vector. | ||
85 | |||
86 | Collective | ||
87 | |||
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 | ||
93 | |||
94 | Output Parameter: | ||
95 | . r - result vector | ||
96 | |||
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. | ||
104 | |||
105 | Level: intermediate | ||
106 | |||
107 | .seealso: NEPGetLeftEigenvector(), NEPSolve() | ||
108 | @*/ | ||
109 | 40 | PetscErrorCode NEPApplyResolvent(NEP nep,RG rg,PetscScalar omega,Vec v,Vec r) | |
110 | { | ||
111 | 40 | NEP_RESOLVENT_MATSHELL *ctx; | |
112 | |||
113 |
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40 | PetscFunctionBegin; |
114 |
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40 | PetscValidHeaderSpecific(nep,NEP_CLASSID,1); |
115 |
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40 | PetscValidLogicalCollectiveScalar(nep,omega,3); |
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40 | PetscValidHeaderSpecific(v,VEC_CLASSID,4); |
117 |
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40 | PetscValidHeaderSpecific(r,VEC_CLASSID,5); |
118 |
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40 | NEPCheckSolved(nep,1); |
119 | |||
120 |
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40 | PetscCall(PetscLogEventBegin(NEP_Resolvent,nep,0,0,0)); |
121 |
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40 | if (!nep->resolvent) { |
122 |
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10 | PetscCall(PetscNew(&ctx)); |
123 | 10 | ctx->nep = nep; | |
124 |
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10 | PetscCall(PetscCalloc4(nep->nconv,&ctx->nfactor,nep->nconv,&ctx->nfactor_avail,nep->nconv,&ctx->dots,nep->nconv,&ctx->dots_avail)); |
125 |
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10 | PetscCall(MatCreateShell(PetscObjectComm((PetscObject)nep),nep->nloc,nep->nloc,nep->n,nep->n,ctx,&nep->resolvent)); |
126 |
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10 | PetscCall(MatShellSetOperation(nep->resolvent,MATOP_MULT,(PetscErrorCodeFn*)MatMult_Resolvent)); |
127 |
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10 | PetscCall(MatShellSetOperation(nep->resolvent,MATOP_DESTROY,(PetscErrorCodeFn*)MatDestroy_Resolvent)); |
128 |
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30 | } else PetscCall(MatShellGetContext(nep->resolvent,&ctx)); |
129 |
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40 | PetscCall(NEPComputeVectors(nep)); |
130 |
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40 | PetscCall(NEPSetWorkVecs(nep,2)); |
131 | 40 | ctx->rg = rg; | |
132 | 40 | ctx->omega = omega; | |
133 |
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40 | PetscCall(MatMult(nep->resolvent,v,r)); |
134 |
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40 | PetscCall(PetscLogEventEnd(NEP_Resolvent,nep,0,0,0)); |
135 |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
136 | } | ||
137 |