| 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 | SLEPc eigensolver: "arnoldi" | ||
| 12 | |||
| 13 | Method: Explicitly Restarted Arnoldi | ||
| 14 | |||
| 15 | Algorithm: | ||
| 16 | |||
| 17 | Arnoldi method with explicit restart and deflation. | ||
| 18 | |||
| 19 | References: | ||
| 20 | |||
| 21 | [1] "Arnoldi Methods in SLEPc", SLEPc Technical Report STR-4, | ||
| 22 | available at https://slepc.upv.es. | ||
| 23 | */ | ||
| 24 | |||
| 25 | #include <slepc/private/epsimpl.h> /*I "slepceps.h" I*/ | ||
| 26 | |||
| 27 | typedef struct { | ||
| 28 | PetscBool delayed; | ||
| 29 | } EPS_ARNOLDI; | ||
| 30 | |||
| 31 | 297 | static PetscErrorCode EPSSetUp_Arnoldi(EPS eps) | |
| 32 | { | ||
| 33 |
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297 | PetscFunctionBegin; |
| 34 |
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297 | EPSCheckDefinite(eps); |
| 35 |
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297 | EPSCheckNotStructured(eps); |
| 36 |
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297 | PetscCall(EPSSetDimensions_Default(eps,&eps->nev,&eps->ncv,&eps->mpd)); |
| 37 |
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297 | PetscCheck(eps->ncv<=eps->nev+eps->mpd,PetscObjectComm((PetscObject)eps),PETSC_ERR_USER_INPUT,"The value of ncv must not be larger than nev+mpd"); |
| 38 |
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297 | if (eps->max_it==PETSC_DETERMINE) eps->max_it = PetscMax(100,2*eps->n/eps->ncv); |
| 39 |
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297 | if (!eps->which) PetscCall(EPSSetWhichEigenpairs_Default(eps)); |
| 40 |
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297 | PetscCheck(eps->which!=EPS_ALL,PetscObjectComm((PetscObject)eps),PETSC_ERR_SUP,"This solver does not support computing all eigenvalues"); |
| 41 |
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297 | EPSCheckUnsupported(eps,EPS_FEATURE_ARBITRARY | EPS_FEATURE_THRESHOLD | EPS_FEATURE_TWOSIDED); |
| 42 | |||
| 43 |
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297 | PetscCall(EPSAllocateSolution(eps,1)); |
| 44 |
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297 | PetscCall(EPS_SetInnerProduct(eps)); |
| 45 |
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297 | PetscCall(DSSetType(eps->ds,DSNHEP)); |
| 46 |
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297 | if (eps->extraction==EPS_REFINED || eps->extraction==EPS_REFINED_HARMONIC) PetscCall(DSSetRefined(eps->ds,PETSC_TRUE)); |
| 47 |
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297 | PetscCall(DSSetExtraRow(eps->ds,PETSC_TRUE)); |
| 48 |
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297 | PetscCall(DSAllocate(eps->ds,eps->ncv+1)); |
| 49 |
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57 | PetscFunctionReturn(PETSC_SUCCESS); |
| 50 | } | ||
| 51 | |||
| 52 | 297 | static PetscErrorCode EPSSolve_Arnoldi(EPS eps) | |
| 53 | { | ||
| 54 | 297 | PetscInt k,nv,ld; | |
| 55 | 297 | Mat U,Op,H; | |
| 56 | 297 | PetscScalar *Harray; | |
| 57 | 297 | PetscReal beta,gamma=1.0; | |
| 58 | 297 | PetscBool breakdown,harmonic,refined; | |
| 59 | 297 | BVOrthogRefineType orthog_ref; | |
| 60 | 297 | EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data; | |
| 61 | |||
| 62 |
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297 | PetscFunctionBegin; |
| 63 |
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297 | PetscCall(DSGetLeadingDimension(eps->ds,&ld)); |
| 64 |
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297 | PetscCall(DSGetRefined(eps->ds,&refined)); |
| 65 | 297 | harmonic = (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC)?PETSC_TRUE:PETSC_FALSE; | |
| 66 |
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297 | PetscCall(BVGetOrthogonalization(eps->V,NULL,&orthog_ref,NULL,NULL)); |
| 67 | |||
| 68 | /* Get the starting Arnoldi vector */ | ||
| 69 |
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297 | PetscCall(EPSGetStartVector(eps,0,NULL)); |
| 70 | |||
| 71 | /* Restart loop */ | ||
| 72 | 8831 | while (eps->reason == EPS_CONVERGED_ITERATING) { | |
| 73 | 8534 | eps->its++; | |
| 74 | |||
| 75 | /* Compute an nv-step Arnoldi factorization */ | ||
| 76 | 8534 | nv = PetscMin(eps->nconv+eps->mpd,eps->ncv); | |
| 77 |
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8534 | PetscCall(DSSetDimensions(eps->ds,nv,eps->nconv,0)); |
| 78 |
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8534 | if (!arnoldi->delayed) { |
| 79 |
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8174 | PetscCall(STGetOperator(eps->st,&Op)); |
| 80 |
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8174 | PetscCall(DSGetMat(eps->ds,DS_MAT_A,&H)); |
| 81 |
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8174 | PetscCall(BVMatArnoldi(eps->V,Op,H,eps->nconv,&nv,&beta,&breakdown)); |
| 82 |
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8174 | PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&H)); |
| 83 |
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8174 | PetscCall(STRestoreOperator(eps->st,&Op)); |
| 84 |
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360 | } else if (orthog_ref == BV_ORTHOG_REFINE_NEVER) { |
| 85 |
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180 | PetscCall(DSGetArray(eps->ds,DS_MAT_A,&Harray)); |
| 86 |
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180 | PetscCall(EPSDelayedArnoldi1(eps,Harray,ld,eps->nconv,&nv,&beta,&breakdown)); |
| 87 |
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180 | PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&Harray)); |
| 88 | } else { | ||
| 89 |
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180 | PetscCall(DSGetArray(eps->ds,DS_MAT_A,&Harray)); |
| 90 |
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180 | PetscCall(EPSDelayedArnoldi(eps,Harray,ld,eps->nconv,&nv,&beta,&breakdown)); |
| 91 |
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180 | PetscCall(DSRestoreArray(eps->ds,DS_MAT_A,&Harray)); |
| 92 | } | ||
| 93 |
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8534 | PetscCall(DSSetState(eps->ds,DS_STATE_INTERMEDIATE)); |
| 94 |
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8534 | PetscCall(BVSetActiveColumns(eps->V,eps->nconv,nv)); |
| 95 | |||
| 96 | /* Compute translation of Krylov decomposition if harmonic extraction used */ | ||
| 97 |
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8534 | if (harmonic) PetscCall(DSTranslateHarmonic(eps->ds,eps->target,beta,PETSC_FALSE,NULL,&gamma)); |
| 98 | |||
| 99 | /* Solve projected problem */ | ||
| 100 |
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8534 | PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi)); |
| 101 |
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8534 | PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL)); |
| 102 |
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8534 | PetscCall(DSUpdateExtraRow(eps->ds)); |
| 103 |
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8534 | PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi)); |
| 104 | |||
| 105 | /* Check convergence */ | ||
| 106 |
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8534 | PetscCall(EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta,0.0,gamma,&k)); |
| 107 |
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8534 | if (refined) { |
| 108 |
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943 | PetscCall(DSGetMat(eps->ds,DS_MAT_X,&U)); |
| 109 |
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943 | PetscCall(BVMultInPlace(eps->V,U,eps->nconv,k+1)); |
| 110 |
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943 | PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&U)); |
| 111 |
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943 | PetscCall(BVOrthonormalizeColumn(eps->V,k,PETSC_FALSE,NULL,NULL)); |
| 112 | } else { | ||
| 113 |
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7591 | PetscCall(DSGetMat(eps->ds,DS_MAT_Q,&U)); |
| 114 |
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7591 | PetscCall(BVMultInPlace(eps->V,U,eps->nconv,PetscMin(k+1,nv))); |
| 115 |
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7591 | PetscCall(DSRestoreMat(eps->ds,DS_MAT_Q,&U)); |
| 116 | } | ||
| 117 |
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8534 | PetscCall((*eps->stopping)(eps,eps->its,eps->max_it,k,eps->nev,&eps->reason,eps->stoppingctx)); |
| 118 |
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8534 | if (eps->reason == EPS_CONVERGED_ITERATING && breakdown) { |
| 119 | ✗ | PetscCall(PetscInfo(eps,"Breakdown in Arnoldi method (it=%" PetscInt_FMT " norm=%g)\n",eps->its,(double)beta)); | |
| 120 | ✗ | PetscCall(EPSGetStartVector(eps,k,&breakdown)); | |
| 121 | ✗ | if (breakdown) { | |
| 122 | ✗ | eps->reason = EPS_DIVERGED_BREAKDOWN; | |
| 123 | ✗ | PetscCall(PetscInfo(eps,"Unable to generate more start vectors\n")); | |
| 124 | } | ||
| 125 | } | ||
| 126 | 8534 | eps->nconv = k; | |
| 127 |
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8831 | PetscCall(EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv)); |
| 128 | } | ||
| 129 |
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297 | PetscCall(DSTruncate(eps->ds,eps->nconv,PETSC_TRUE)); |
| 130 |
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57 | PetscFunctionReturn(PETSC_SUCCESS); |
| 131 | } | ||
| 132 | |||
| 133 | 209 | static PetscErrorCode EPSSetFromOptions_Arnoldi(EPS eps,PetscOptionItems PetscOptionsObject) | |
| 134 | { | ||
| 135 | 209 | PetscBool set,val; | |
| 136 | 209 | EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data; | |
| 137 | |||
| 138 |
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209 | PetscFunctionBegin; |
| 139 |
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209 | PetscOptionsHeadBegin(PetscOptionsObject,"EPS Arnoldi Options"); |
| 140 | |||
| 141 |
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209 | PetscCall(PetscOptionsBool("-eps_arnoldi_delayed","Use delayed reorthogonalization","EPSArnoldiSetDelayed",arnoldi->delayed,&val,&set)); |
| 142 |
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209 | if (set) PetscCall(EPSArnoldiSetDelayed(eps,val)); |
| 143 | |||
| 144 |
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209 | PetscOptionsHeadEnd(); |
| 145 |
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41 | PetscFunctionReturn(PETSC_SUCCESS); |
| 146 | } | ||
| 147 | |||
| 148 | 40 | static PetscErrorCode EPSArnoldiSetDelayed_Arnoldi(EPS eps,PetscBool delayed) | |
| 149 | { | ||
| 150 | 40 | EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data; | |
| 151 | |||
| 152 |
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40 | PetscFunctionBegin; |
| 153 | 40 | arnoldi->delayed = delayed; | |
| 154 |
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40 | PetscFunctionReturn(PETSC_SUCCESS); |
| 155 | } | ||
| 156 | |||
| 157 | /*@ | ||
| 158 | EPSArnoldiSetDelayed - Activates or deactivates delayed reorthogonalization | ||
| 159 | in the Arnoldi iteration. | ||
| 160 | |||
| 161 | Logically Collective | ||
| 162 | |||
| 163 | Input Parameters: | ||
| 164 | + eps - the linear eigensolver context | ||
| 165 | - delayed - boolean flag | ||
| 166 | |||
| 167 | Options Database Key: | ||
| 168 | . -eps_arnoldi_delayed (true|false) - activates delayed reorthogonalization in `EPSARNOLDI` | ||
| 169 | |||
| 170 | Note: | ||
| 171 | Delayed reorthogonalization is an aggressive optimization for the `EPSARNOLDI` | ||
| 172 | eigensolver than may provide better scalability, but sometimes makes the | ||
| 173 | solver converge more slowly compared to the default algorithm. The details | ||
| 174 | can be found in {cite:p}`Her07`. | ||
| 175 | |||
| 176 | Level: advanced | ||
| 177 | |||
| 178 | .seealso: [](ch:eps), `EPSARNOLDI`, `EPSArnoldiGetDelayed()` | ||
| 179 | @*/ | ||
| 180 | 40 | PetscErrorCode EPSArnoldiSetDelayed(EPS eps,PetscBool delayed) | |
| 181 | { | ||
| 182 |
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40 | PetscFunctionBegin; |
| 183 |
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40 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 184 |
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40 | PetscValidLogicalCollectiveBool(eps,delayed,2); |
| 185 |
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40 | PetscTryMethod(eps,"EPSArnoldiSetDelayed_C",(EPS,PetscBool),(eps,delayed)); |
| 186 |
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40 | PetscFunctionReturn(PETSC_SUCCESS); |
| 187 | } | ||
| 188 | |||
| 189 | 50 | static PetscErrorCode EPSArnoldiGetDelayed_Arnoldi(EPS eps,PetscBool *delayed) | |
| 190 | { | ||
| 191 | 50 | EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data; | |
| 192 | |||
| 193 |
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50 | PetscFunctionBegin; |
| 194 | 50 | *delayed = arnoldi->delayed; | |
| 195 |
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50 | PetscFunctionReturn(PETSC_SUCCESS); |
| 196 | } | ||
| 197 | |||
| 198 | /*@ | ||
| 199 | EPSArnoldiGetDelayed - Gets the type of reorthogonalization used during the Arnoldi | ||
| 200 | iteration. | ||
| 201 | |||
| 202 | Not Collective | ||
| 203 | |||
| 204 | Input Parameter: | ||
| 205 | . eps - the linear eigensolver context | ||
| 206 | |||
| 207 | Output Parameter: | ||
| 208 | . delayed - boolean flag indicating if delayed reorthogonalization has been enabled | ||
| 209 | |||
| 210 | Level: advanced | ||
| 211 | |||
| 212 | .seealso: [](ch:eps), `EPSARNOLDI`, `EPSArnoldiSetDelayed()` | ||
| 213 | @*/ | ||
| 214 | 50 | PetscErrorCode EPSArnoldiGetDelayed(EPS eps,PetscBool *delayed) | |
| 215 | { | ||
| 216 |
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50 | PetscFunctionBegin; |
| 217 |
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50 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
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50 | PetscAssertPointer(delayed,2); |
| 219 |
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50 | PetscUseMethod(eps,"EPSArnoldiGetDelayed_C",(EPS,PetscBool*),(eps,delayed)); |
| 220 |
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50 | PetscFunctionReturn(PETSC_SUCCESS); |
| 221 | } | ||
| 222 | |||
| 223 | 219 | static PetscErrorCode EPSDestroy_Arnoldi(EPS eps) | |
| 224 | { | ||
| 225 |
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219 | PetscFunctionBegin; |
| 226 |
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219 | PetscCall(PetscFree(eps->data)); |
| 227 |
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219 | PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiSetDelayed_C",NULL)); |
| 228 |
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219 | PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiGetDelayed_C",NULL)); |
| 229 |
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43 | PetscFunctionReturn(PETSC_SUCCESS); |
| 230 | } | ||
| 231 | |||
| 232 | ✗ | static PetscErrorCode EPSView_Arnoldi(EPS eps,PetscViewer viewer) | |
| 233 | { | ||
| 234 | ✗ | PetscBool isascii; | |
| 235 | ✗ | EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI*)eps->data; | |
| 236 | |||
| 237 | ✗ | PetscFunctionBegin; | |
| 238 | ✗ | PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii)); | |
| 239 | ✗ | if (isascii && arnoldi->delayed) PetscCall(PetscViewerASCIIPrintf(viewer," using delayed reorthogonalization\n")); | |
| 240 | ✗ | PetscFunctionReturn(PETSC_SUCCESS); | |
| 241 | } | ||
| 242 | |||
| 243 | /*MC | ||
| 244 | EPSARNOLDI - EPSARNOLDI = "arnoldi" - A basic Krylov method for non-Hermitian | ||
| 245 | problems, with explicit restart. | ||
| 246 | |||
| 247 | Notes: | ||
| 248 | This solver is very basic and is not recommended in general, since it | ||
| 249 | will not be competitive with respect to other solvers. | ||
| 250 | |||
| 251 | The implemented method is Arnoldi with explicit restart and deflation. | ||
| 252 | Generally, it is much better to use implicit restart as in `EPSKRYLOVSCHUR`. | ||
| 253 | |||
| 254 | Level: beginner | ||
| 255 | |||
| 256 | .seealso: [](ch:eps), `EPS`, `EPSType`, `EPSSetType()` | ||
| 257 | M*/ | ||
| 258 | 219 | SLEPC_EXTERN PetscErrorCode EPSCreate_Arnoldi(EPS eps) | |
| 259 | { | ||
| 260 | 219 | EPS_ARNOLDI *ctx; | |
| 261 | |||
| 262 |
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219 | PetscFunctionBegin; |
| 263 |
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219 | PetscCall(PetscNew(&ctx)); |
| 264 | 219 | eps->data = (void*)ctx; | |
| 265 | |||
| 266 | 219 | eps->useds = PETSC_TRUE; | |
| 267 | |||
| 268 | 219 | eps->ops->solve = EPSSolve_Arnoldi; | |
| 269 | 219 | eps->ops->setup = EPSSetUp_Arnoldi; | |
| 270 | 219 | eps->ops->setupsort = EPSSetUpSort_Default; | |
| 271 | 219 | eps->ops->setfromoptions = EPSSetFromOptions_Arnoldi; | |
| 272 | 219 | eps->ops->destroy = EPSDestroy_Arnoldi; | |
| 273 | 219 | eps->ops->view = EPSView_Arnoldi; | |
| 274 | 219 | eps->ops->backtransform = EPSBackTransform_Default; | |
| 275 | 219 | eps->ops->computevectors = EPSComputeVectors_Schur; | |
| 276 | |||
| 277 |
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219 | PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiSetDelayed_C",EPSArnoldiSetDelayed_Arnoldi)); |
| 278 |
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219 | PetscCall(PetscObjectComposeFunction((PetscObject)eps,"EPSArnoldiGetDelayed_C",EPSArnoldiGetDelayed_Arnoldi)); |
| 279 |
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43 | PetscFunctionReturn(PETSC_SUCCESS); |
| 280 | } | ||
| 281 |