| Line | Branch | Exec | Source |
|---|---|---|---|
| 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)); |
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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)); |
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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)); |
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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 - the nonlinear eigensolver context | ||
| 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 | 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. | ||
| 104 | |||
| 105 | Level: intermediate | ||
| 106 | |||
| 107 | .seealso: [](ch:nep), `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); |
| 116 |
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40 | PetscValidHeaderSpecific(v,VEC_CLASSID,4); |
| 117 |
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40 | PetscValidHeaderSpecific(r,VEC_CLASSID,5); |
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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)); |
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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)); |
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40 | PetscCall(PetscLogEventEnd(NEP_Resolvent,nep,0,0,0)); |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
| 136 | } | ||
| 137 |