| 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 | PEP routines related to the solution process | ||
| 12 | |||
| 13 | References: | ||
| 14 | |||
| 15 | [1] C. Campos and J.E. Roman, "Parallel iterative refinement in | ||
| 16 | polynomial eigenvalue problems", Numer. Linear Algebra Appl. | ||
| 17 | 23(4):730-745, 2016. | ||
| 18 | */ | ||
| 19 | |||
| 20 | #include <slepc/private/pepimpl.h> /*I "slepcpep.h" I*/ | ||
| 21 | #include <slepc/private/bvimpl.h> | ||
| 22 | #include <petscdraw.h> | ||
| 23 | |||
| 24 | static PetscBool cited = PETSC_FALSE; | ||
| 25 | static const char citation[] = | ||
| 26 | "@Article{slepc-pep-refine,\n" | ||
| 27 | " author = \"C. Campos and J. E. Roman\",\n" | ||
| 28 | " title = \"Parallel iterative refinement in polynomial eigenvalue problems\",\n" | ||
| 29 | " journal = \"Numer. Linear Algebra Appl.\",\n" | ||
| 30 | " volume = \"23\",\n" | ||
| 31 | " number = \"4\",\n" | ||
| 32 | " pages = \"730--745\",\n" | ||
| 33 | " year = \"2016,\"\n" | ||
| 34 | " doi = \"https://doi.org/10.1002/nla.2052\"\n" | ||
| 35 | "}\n"; | ||
| 36 | |||
| 37 | 16952 | PetscErrorCode PEPComputeVectors(PEP pep) | |
| 38 | { | ||
| 39 |
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16952 | PetscFunctionBegin; |
| 40 |
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16952 | PEPCheckSolved(pep,1); |
| 41 |
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16952 | if (pep->state==PEP_STATE_SOLVED) PetscTryTypeMethod(pep,computevectors); |
| 42 | 16952 | pep->state = PEP_STATE_EIGENVECTORS; | |
| 43 |
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16952 | PetscFunctionReturn(PETSC_SUCCESS); |
| 44 | } | ||
| 45 | |||
| 46 | 1780 | PetscErrorCode PEPExtractVectors(PEP pep) | |
| 47 | { | ||
| 48 |
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1780 | PetscFunctionBegin; |
| 49 |
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1780 | PEPCheckSolved(pep,1); |
| 50 |
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1780 | if (pep->state==PEP_STATE_SOLVED) PetscTryTypeMethod(pep,extractvectors); |
| 51 |
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348 | PetscFunctionReturn(PETSC_SUCCESS); |
| 52 | } | ||
| 53 | |||
| 54 | /*@ | ||
| 55 | PEPSolve - Solves the polynomial eigenproblem. | ||
| 56 | |||
| 57 | Collective | ||
| 58 | |||
| 59 | Input Parameter: | ||
| 60 | . pep - the polynomial eigensolver context | ||
| 61 | |||
| 62 | Options Database Keys: | ||
| 63 | + -pep_view - print information about the solver once the solve is complete | ||
| 64 | . -pep_view_pre - print information about the solver before the solve starts | ||
| 65 | . -pep_view_matk - view the coefficient matrix $A_k$ (replace `k` by an integer from 0 to `nmat`-1) | ||
| 66 | . -pep_view_vectors - view the computed eigenvectors | ||
| 67 | . -pep_view_values - view the computed eigenvalues | ||
| 68 | . -pep_converged_reason - print reason for convergence/divergence, and number of iterations | ||
| 69 | . -pep_error_absolute - print absolute errors of each eigenpair | ||
| 70 | . -pep_error_relative - print relative errors of each eigenpair | ||
| 71 | - -pep_error_backward - print backward errors of each eigenpair | ||
| 72 | |||
| 73 | Notes: | ||
| 74 | The problem matrices are specified with `PEPSetOperators()`. | ||
| 75 | |||
| 76 | `PEPSolve()` will return without generating an error regardless of whether | ||
| 77 | all requested solutions were computed or not. Call `PEPGetConverged()` to get the | ||
| 78 | actual number of computed solutions, and `PEPGetConvergedReason()` to determine if | ||
| 79 | the solver converged or failed and why. | ||
| 80 | |||
| 81 | All the command-line options listed above admit an optional argument specifying | ||
| 82 | the viewer type and options. For instance, use `-pep_view_mat0 binary:matrix0.bin` | ||
| 83 | to save the $A_0$ matrix to a binary file, `-pep_view_values draw` to draw the computed | ||
| 84 | eigenvalues graphically, or `-pep_error_relative :myerr.m:ascii_matlab` to save | ||
| 85 | the errors in a file that can be executed in Matlab. | ||
| 86 | See `PetscObjectViewFromOptions()` for more details. | ||
| 87 | |||
| 88 | Level: beginner | ||
| 89 | |||
| 90 | .seealso: [](ch:pep), `PEPCreate()`, `PEPSetUp()`, `PEPDestroy()`, `PEPSetTolerances()`, `PEPGetConverged()`, `PEPGetConvergedReason()` | ||
| 91 | @*/ | ||
| 92 | 1980 | PetscErrorCode PEPSolve(PEP pep) | |
| 93 | { | ||
| 94 | 1980 | PetscInt i,k; | |
| 95 | 1980 | PetscBool flg,islinear; | |
| 96 | 1980 | char str[16]; | |
| 97 | |||
| 98 |
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1980 | PetscFunctionBegin; |
| 99 |
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1980 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 100 |
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1980 | if (pep->state>=PEP_STATE_SOLVED) PetscFunctionReturn(PETSC_SUCCESS); |
| 101 |
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1980 | PetscCall(PetscLogEventBegin(PEP_Solve,pep,0,0,0)); |
| 102 | |||
| 103 | /* call setup */ | ||
| 104 |
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1980 | PetscCall(PEPSetUp(pep)); |
| 105 | 1980 | pep->nconv = 0; | |
| 106 | 1980 | pep->its = 0; | |
| 107 |
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1980 | k = pep->lineariz? pep->ncv: pep->ncv*(pep->nmat-1); |
| 108 |
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134517 | for (i=0;i<k;i++) { |
| 109 | 132537 | pep->eigr[i] = 0.0; | |
| 110 | 132537 | pep->eigi[i] = 0.0; | |
| 111 | 132537 | pep->errest[i] = 0.0; | |
| 112 | 132537 | pep->perm[i] = i; | |
| 113 | } | ||
| 114 |
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1980 | PetscCall(PEPViewFromOptions(pep,NULL,"-pep_view_pre")); |
| 115 |
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1980 | PetscCall(RGViewFromOptions(pep->rg,NULL,"-rg_view")); |
| 116 | |||
| 117 | /* Call solver */ | ||
| 118 |
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1980 | PetscUseTypeMethod(pep,solve); |
| 119 |
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1980 | PetscCheck(pep->reason,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason"); |
| 120 | 1980 | pep->state = PEP_STATE_SOLVED; | |
| 121 | |||
| 122 | /* Only the first nconv columns contain useful information */ | ||
| 123 |
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1980 | PetscCall(BVSetActiveColumns(pep->V,0,pep->nconv)); |
| 124 | |||
| 125 |
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1980 | PetscCall(PetscObjectTypeCompare((PetscObject)pep,PEPLINEAR,&islinear)); |
| 126 |
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1980 | if (!islinear) { |
| 127 |
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1567 | PetscCall(STPostSolve(pep->st)); |
| 128 | /* Map eigenvalues back to the original problem */ | ||
| 129 |
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1567 | PetscCall(STGetTransform(pep->st,&flg)); |
| 130 |
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1567 | if (flg) PetscTryTypeMethod(pep,backtransform); |
| 131 | } | ||
| 132 | |||
| 133 | #if !defined(PETSC_USE_COMPLEX) | ||
| 134 | /* reorder conjugate eigenvalues (positive imaginary first) */ | ||
| 135 |
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5727 | for (i=0;i<pep->nconv-1;i++) { |
| 136 |
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4774 | if (pep->eigi[i] != 0) { |
| 137 |
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715 | if (pep->eigi[i] < 0) { |
| 138 | 175 | pep->eigi[i] = -pep->eigi[i]; | |
| 139 | 175 | pep->eigi[i+1] = -pep->eigi[i+1]; | |
| 140 | /* the next correction only works with eigenvectors */ | ||
| 141 |
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175 | PetscCall(PEPComputeVectors(pep)); |
| 142 |
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175 | PetscCall(BVScaleColumn(pep->V,i+1,-1.0)); |
| 143 | } | ||
| 144 | 715 | i++; | |
| 145 | } | ||
| 146 | } | ||
| 147 | #endif | ||
| 148 | |||
| 149 |
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1980 | if (pep->refine!=PEP_REFINE_NONE) PetscCall(PetscCitationsRegister(citation,&cited)); |
| 150 | |||
| 151 |
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1980 | if (pep->refine==PEP_REFINE_SIMPLE && pep->rits>0 && pep->nconv>0) { |
| 152 |
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156 | PetscCall(PEPComputeVectors(pep)); |
| 153 |
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156 | PetscCall(PEPNewtonRefinementSimple(pep,&pep->rits,pep->rtol,pep->nconv)); |
| 154 | } | ||
| 155 | |||
| 156 | /* sort eigenvalues according to pep->which parameter */ | ||
| 157 |
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1980 | PetscCall(SlepcSortEigenvalues(pep->sc,pep->nconv,pep->eigr,pep->eigi,pep->perm)); |
| 158 |
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1980 | PetscCall(PetscLogEventEnd(PEP_Solve,pep,0,0,0)); |
| 159 | |||
| 160 | /* various viewers */ | ||
| 161 |
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1980 | PetscCall(PEPViewFromOptions(pep,NULL,"-pep_view")); |
| 162 |
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1980 | PetscCall(PEPConvergedReasonViewFromOptions(pep)); |
| 163 |
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1980 | PetscCall(PEPErrorViewFromOptions(pep)); |
| 164 |
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1980 | PetscCall(PEPValuesViewFromOptions(pep)); |
| 165 |
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1980 | PetscCall(PEPVectorsViewFromOptions(pep)); |
| 166 |
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9400 | for (i=0;i<pep->nmat;i++) { |
| 167 |
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7420 | PetscCall(PetscSNPrintf(str,sizeof(str),"-pep_view_mat%" PetscInt_FMT,i)); |
| 168 |
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7420 | PetscCall(MatViewFromOptions(pep->A[i],(PetscObject)pep,str)); |
| 169 | } | ||
| 170 | |||
| 171 | /* Remove the initial subspace */ | ||
| 172 | 1980 | pep->nini = 0; | |
| 173 |
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1980 | PetscFunctionReturn(PETSC_SUCCESS); |
| 174 | } | ||
| 175 | |||
| 176 | /*@ | ||
| 177 | PEPGetIterationNumber - Gets the current iteration number. If the | ||
| 178 | call to `PEPSolve()` is complete, then it returns the number of iterations | ||
| 179 | carried out by the solution method. | ||
| 180 | |||
| 181 | Not Collective | ||
| 182 | |||
| 183 | Input Parameter: | ||
| 184 | . pep - the polynomial eigensolver context | ||
| 185 | |||
| 186 | Output Parameter: | ||
| 187 | . its - number of iterations | ||
| 188 | |||
| 189 | Note: | ||
| 190 | During the $i$-th iteration this call returns $i-1$. If `PEPSolve()` is | ||
| 191 | complete, then parameter `its` contains either the iteration number at | ||
| 192 | which convergence was successfully reached, or failure was detected. | ||
| 193 | Call `PEPGetConvergedReason()` to determine if the solver converged or | ||
| 194 | failed and why. | ||
| 195 | |||
| 196 | Level: intermediate | ||
| 197 | |||
| 198 | .seealso: [](ch:pep), `PEPGetConvergedReason()`, `PEPSetTolerances()` | ||
| 199 | @*/ | ||
| 200 | 316 | PetscErrorCode PEPGetIterationNumber(PEP pep,PetscInt *its) | |
| 201 | { | ||
| 202 |
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316 | PetscFunctionBegin; |
| 203 |
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316 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 204 |
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316 | PetscAssertPointer(its,2); |
| 205 | 316 | *its = pep->its; | |
| 206 |
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316 | PetscFunctionReturn(PETSC_SUCCESS); |
| 207 | } | ||
| 208 | |||
| 209 | /*@ | ||
| 210 | PEPGetConverged - Gets the number of converged eigenpairs. | ||
| 211 | |||
| 212 | Not Collective | ||
| 213 | |||
| 214 | Input Parameter: | ||
| 215 | . pep - the polynomial eigensolver context | ||
| 216 | |||
| 217 | Output Parameter: | ||
| 218 | . nconv - number of converged eigenpairs | ||
| 219 | |||
| 220 | Notes: | ||
| 221 | This function should be called after `PEPSolve()` has finished. | ||
| 222 | |||
| 223 | The value `nconv` may be different from the number of requested solutions | ||
| 224 | `nev`, but not larger than `ncv`, see `PEPSetDimensions()`. | ||
| 225 | |||
| 226 | Level: beginner | ||
| 227 | |||
| 228 | .seealso: [](ch:pep), `PEPSetDimensions()`, `PEPSolve()`, `PEPGetEigenpair()` | ||
| 229 | @*/ | ||
| 230 | 942 | PetscErrorCode PEPGetConverged(PEP pep,PetscInt *nconv) | |
| 231 | { | ||
| 232 |
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942 | PetscFunctionBegin; |
| 233 |
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942 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 234 |
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942 | PetscAssertPointer(nconv,2); |
| 235 |
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942 | PEPCheckSolved(pep,1); |
| 236 | 942 | *nconv = pep->nconv; | |
| 237 |
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942 | PetscFunctionReturn(PETSC_SUCCESS); |
| 238 | } | ||
| 239 | |||
| 240 | /*@ | ||
| 241 | PEPGetConvergedReason - Gets the reason why the `PEPSolve()` iteration was | ||
| 242 | stopped. | ||
| 243 | |||
| 244 | Not Collective | ||
| 245 | |||
| 246 | Input Parameter: | ||
| 247 | . pep - the polynomial eigensolver context | ||
| 248 | |||
| 249 | Output Parameter: | ||
| 250 | . reason - negative value indicates diverged, positive value converged, see | ||
| 251 | `PEPConvergedReason` for the possible values | ||
| 252 | |||
| 253 | Options Database Key: | ||
| 254 | . -pep_converged_reason - print reason for convergence/divergence, and number of iterations | ||
| 255 | |||
| 256 | Note: | ||
| 257 | If this routine is called before or doing the `PEPSolve()` the value of | ||
| 258 | `PEP_CONVERGED_ITERATING` is returned. | ||
| 259 | |||
| 260 | Level: intermediate | ||
| 261 | |||
| 262 | .seealso: [](ch:pep), `PEPSetTolerances()`, `PEPSolve()`, `PEPConvergedReason` | ||
| 263 | @*/ | ||
| 264 | 270 | PetscErrorCode PEPGetConvergedReason(PEP pep,PEPConvergedReason *reason) | |
| 265 | { | ||
| 266 |
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270 | PetscFunctionBegin; |
| 267 |
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270 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 268 |
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270 | PetscAssertPointer(reason,2); |
| 269 |
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270 | PEPCheckSolved(pep,1); |
| 270 | 270 | *reason = pep->reason; | |
| 271 |
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270 | PetscFunctionReturn(PETSC_SUCCESS); |
| 272 | } | ||
| 273 | |||
| 274 | /*@ | ||
| 275 | PEPGetEigenpair - Gets the `i`-th solution of the eigenproblem as computed by | ||
| 276 | `PEPSolve()`. The solution consists in both the eigenvalue and the eigenvector. | ||
| 277 | |||
| 278 | Collective | ||
| 279 | |||
| 280 | Input Parameters: | ||
| 281 | + pep - the polynomial eigensolver context | ||
| 282 | - i - index of the solution | ||
| 283 | |||
| 284 | Output Parameters: | ||
| 285 | + eigr - real part of eigenvalue | ||
| 286 | . eigi - imaginary part of eigenvalue | ||
| 287 | . Vr - real part of eigenvector | ||
| 288 | - Vi - imaginary part of eigenvector | ||
| 289 | |||
| 290 | Notes: | ||
| 291 | It is allowed to pass `NULL` for `Vr` and `Vi`, if the eigenvector is not | ||
| 292 | required. Otherwise, the caller must provide valid `Vec` objects, i.e., | ||
| 293 | they must be created by the calling program with e.g. `MatCreateVecs()`. | ||
| 294 | |||
| 295 | If the eigenvalue is real, then `eigi` and `Vi` are set to zero. If PETSc is | ||
| 296 | configured with complex scalars the eigenvalue is stored | ||
| 297 | directly in `eigr` (`eigi` is set to zero) and the eigenvector in `Vr` (`Vi` is | ||
| 298 | set to zero). In any case, the user can pass `NULL` in `Vr` or `Vi` if one of | ||
| 299 | them is not required. | ||
| 300 | |||
| 301 | The index `i` should be a value between 0 and `nconv`-1 (see `PEPGetConverged()`). | ||
| 302 | Eigenpairs are indexed according to the ordering criterion established | ||
| 303 | with `PEPSetWhichEigenpairs()`. | ||
| 304 | |||
| 305 | The eigenvector is normalized to have unit norm. | ||
| 306 | |||
| 307 | Level: beginner | ||
| 308 | |||
| 309 | .seealso: [](ch:pep), `PEPSolve()`, `PEPGetConverged()`, `PEPSetWhichEigenpairs()` | ||
| 310 | @*/ | ||
| 311 | 16611 | PetscErrorCode PEPGetEigenpair(PEP pep,PetscInt i,PetscScalar *eigr,PetscScalar *eigi,Vec Vr,Vec Vi) | |
| 312 | { | ||
| 313 | 16611 | PetscInt k; | |
| 314 | |||
| 315 |
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16611 | PetscFunctionBegin; |
| 316 |
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16611 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 317 |
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16611 | PetscValidLogicalCollectiveInt(pep,i,2); |
| 318 |
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16611 | if (Vr) { PetscValidHeaderSpecific(Vr,VEC_CLASSID,5); PetscCheckSameComm(pep,1,Vr,5); } |
| 319 |
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16611 | if (Vi) { PetscValidHeaderSpecific(Vi,VEC_CLASSID,6); PetscCheckSameComm(pep,1,Vi,6); } |
| 320 |
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16611 | PEPCheckSolved(pep,1); |
| 321 |
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16611 | PetscCheck(i>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 322 |
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16611 | PetscCheck(i<pep->nconv,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see PEPGetConverged()"); |
| 323 | |||
| 324 |
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16611 | PetscCall(PEPComputeVectors(pep)); |
| 325 | 16611 | k = pep->perm[i]; | |
| 326 | |||
| 327 | /* eigenvalue */ | ||
| 328 | #if defined(PETSC_USE_COMPLEX) | ||
| 329 |
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8413 | if (eigr) *eigr = pep->eigr[k]; |
| 330 |
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8413 | if (eigi) *eigi = 0; |
| 331 | #else | ||
| 332 |
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8198 | if (eigr) *eigr = pep->eigr[k]; |
| 333 |
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8198 | if (eigi) *eigi = pep->eigi[k]; |
| 334 | #endif | ||
| 335 | |||
| 336 | /* eigenvector */ | ||
| 337 |
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16611 | PetscCall(BV_GetEigenvector(pep->V,k,pep->eigi[k],Vr,Vi)); |
| 338 |
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3240 | PetscFunctionReturn(PETSC_SUCCESS); |
| 339 | } | ||
| 340 | |||
| 341 | /*@ | ||
| 342 | PEPGetErrorEstimate - Returns the error estimate associated to the `i`-th | ||
| 343 | computed eigenpair. | ||
| 344 | |||
| 345 | Not Collective | ||
| 346 | |||
| 347 | Input Parameters: | ||
| 348 | + pep - the polynomial eigensolver context | ||
| 349 | - i - index of eigenpair | ||
| 350 | |||
| 351 | Output Parameter: | ||
| 352 | . errest - the error estimate | ||
| 353 | |||
| 354 | Note: | ||
| 355 | This is the error estimate used internally by the eigensolver. The actual | ||
| 356 | error bound can be computed with `PEPComputeError()`. | ||
| 357 | |||
| 358 | Level: advanced | ||
| 359 | |||
| 360 | .seealso: [](ch:pep), `PEPComputeError()` | ||
| 361 | @*/ | ||
| 362 | 45 | PetscErrorCode PEPGetErrorEstimate(PEP pep,PetscInt i,PetscReal *errest) | |
| 363 | { | ||
| 364 |
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45 | PetscFunctionBegin; |
| 365 |
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45 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 366 |
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45 | PetscAssertPointer(errest,3); |
| 367 |
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45 | PEPCheckSolved(pep,1); |
| 368 |
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45 | PetscCheck(i>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 369 |
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45 | PetscCheck(i<pep->nconv,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see PEPGetConverged()"); |
| 370 | 45 | *errest = pep->errest[pep->perm[i]]; | |
| 371 |
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45 | PetscFunctionReturn(PETSC_SUCCESS); |
| 372 | } | ||
| 373 | |||
| 374 | /* | ||
| 375 | PEPComputeResidualNorm_Private - Computes the norm of the residual vector | ||
| 376 | associated with an eigenpair. | ||
| 377 | |||
| 378 | Input Parameters: | ||
| 379 | kr,ki - eigenvalue | ||
| 380 | xr,xi - eigenvector | ||
| 381 | z - array of 4 work vectors (z[2],z[3] not referenced in complex scalars) | ||
| 382 | */ | ||
| 383 | 12003 | PetscErrorCode PEPComputeResidualNorm_Private(PEP pep,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm) | |
| 384 | { | ||
| 385 | 12003 | Mat *A=pep->A; | |
| 386 | 12003 | PetscInt i,nmat=pep->nmat; | |
| 387 | 12003 | PetscScalar t[20],*vals=t,*ivals=NULL; | |
| 388 | 12003 | Vec u,w; | |
| 389 | #if !defined(PETSC_USE_COMPLEX) | ||
| 390 | 5559 | Vec ui,wi; | |
| 391 | 5559 | PetscReal ni; | |
| 392 | 5559 | PetscBool imag; | |
| 393 | 5559 | PetscScalar it[20]; | |
| 394 | #endif | ||
| 395 | |||
| 396 |
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12003 | PetscFunctionBegin; |
| 397 | 12003 | u = z[0]; w = z[1]; | |
| 398 |
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12003 | PetscCall(VecSet(u,0.0)); |
| 399 | #if !defined(PETSC_USE_COMPLEX) | ||
| 400 | 5559 | ui = z[2]; wi = z[3]; | |
| 401 | 5559 | ivals = it; | |
| 402 | #endif | ||
| 403 |
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12003 | if (nmat>20) { |
| 404 | ✗ | PetscCall(PetscMalloc1(nmat,&vals)); | |
| 405 | #if !defined(PETSC_USE_COMPLEX) | ||
| 406 | ✗ | PetscCall(PetscMalloc1(nmat,&ivals)); | |
| 407 | #endif | ||
| 408 | } | ||
| 409 |
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12003 | PetscCall(PEPEvaluateBasis(pep,kr,ki,vals,ivals)); |
| 410 | #if !defined(PETSC_USE_COMPLEX) | ||
| 411 |
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5559 | if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON)) |
| 412 | imag = PETSC_FALSE; | ||
| 413 | else { | ||
| 414 | 1157 | imag = PETSC_TRUE; | |
| 415 |
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1157 | PetscCall(VecSet(ui,0.0)); |
| 416 | } | ||
| 417 | #endif | ||
| 418 |
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50382 | for (i=0;i<nmat;i++) { |
| 419 |
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38379 | if (vals[i]!=0.0) { |
| 420 |
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38379 | PetscCall(MatMult(A[i],xr,w)); |
| 421 |
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38379 | PetscCall(VecAXPY(u,vals[i],w)); |
| 422 | } | ||
| 423 | #if !defined(PETSC_USE_COMPLEX) | ||
| 424 |
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17002 | if (imag) { |
| 425 |
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3751 | if (ivals[i]!=0 || vals[i]!=0) { |
| 426 |
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3751 | PetscCall(MatMult(A[i],xi,wi)); |
| 427 |
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3751 | if (vals[i]==0) PetscCall(MatMult(A[i],xr,w)); |
| 428 | } | ||
| 429 |
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3751 | if (ivals[i]!=0) { |
| 430 |
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2594 | PetscCall(VecAXPY(u,-ivals[i],wi)); |
| 431 |
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2594 | PetscCall(VecAXPY(ui,ivals[i],w)); |
| 432 | } | ||
| 433 |
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17002 | if (vals[i]!=0) PetscCall(VecAXPY(ui,vals[i],wi)); |
| 434 | } | ||
| 435 | #endif | ||
| 436 | } | ||
| 437 |
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12003 | PetscCall(VecNorm(u,NORM_2,norm)); |
| 438 | #if !defined(PETSC_USE_COMPLEX) | ||
| 439 |
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5559 | if (imag) { |
| 440 |
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1157 | PetscCall(VecNorm(ui,NORM_2,&ni)); |
| 441 | 1157 | *norm = SlepcAbsEigenvalue(*norm,ni); | |
| 442 | } | ||
| 443 | #endif | ||
| 444 |
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12003 | if (nmat>20) { |
| 445 | ✗ | PetscCall(PetscFree(vals)); | |
| 446 | #if !defined(PETSC_USE_COMPLEX) | ||
| 447 | ✗ | PetscCall(PetscFree(ivals)); | |
| 448 | #endif | ||
| 449 | } | ||
| 450 |
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2344 | PetscFunctionReturn(PETSC_SUCCESS); |
| 451 | } | ||
| 452 | |||
| 453 | /*@ | ||
| 454 | PEPComputeError - Computes the error (based on the residual norm) associated | ||
| 455 | with the `i`-th computed eigenpair. | ||
| 456 | |||
| 457 | Collective | ||
| 458 | |||
| 459 | Input Parameters: | ||
| 460 | + pep - the polynomial eigensolver context | ||
| 461 | . i - the solution index | ||
| 462 | - type - the type of error to compute, see `PEPErrorType` | ||
| 463 | |||
| 464 | Output Parameter: | ||
| 465 | . error - the error | ||
| 466 | |||
| 467 | Note: | ||
| 468 | The error can be computed in various ways, all of them based on the residual | ||
| 469 | norm $\|P(\lambda)x\|_2$ where $(\lambda,x)$ is the approximate eigenpair. | ||
| 470 | |||
| 471 | Level: beginner | ||
| 472 | |||
| 473 | .seealso: [](ch:pep), `PEPErrorType`, `PEPSolve()`, `PEPGetErrorEstimate()` | ||
| 474 | @*/ | ||
| 475 | 10738 | PetscErrorCode PEPComputeError(PEP pep,PetscInt i,PEPErrorType type,PetscReal *error) | |
| 476 | { | ||
| 477 | 10738 | Vec xr,xi,w[4]; | |
| 478 | 10738 | PetscScalar kr,ki; | |
| 479 | 10738 | PetscReal t,z=0.0; | |
| 480 | 10738 | PetscInt j; | |
| 481 | 10738 | PetscBool flg; | |
| 482 | |||
| 483 |
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10738 | PetscFunctionBegin; |
| 484 |
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10738 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 485 |
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10738 | PetscValidLogicalCollectiveInt(pep,i,2); |
| 486 |
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10738 | PetscValidLogicalCollectiveEnum(pep,type,3); |
| 487 |
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10738 | PetscAssertPointer(error,4); |
| 488 |
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10738 | PEPCheckSolved(pep,1); |
| 489 | |||
| 490 | /* allocate work vectors */ | ||
| 491 | #if defined(PETSC_USE_COMPLEX) | ||
| 492 |
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5554 | PetscCall(PEPSetWorkVecs(pep,3)); |
| 493 | 5554 | xi = NULL; | |
| 494 | 5554 | w[2] = NULL; | |
| 495 | 5554 | w[3] = NULL; | |
| 496 | #else | ||
| 497 |
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5184 | PetscCall(PEPSetWorkVecs(pep,6)); |
| 498 | 5184 | xi = pep->work[3]; | |
| 499 | 5184 | w[2] = pep->work[4]; | |
| 500 | 5184 | w[3] = pep->work[5]; | |
| 501 | #endif | ||
| 502 | 10738 | xr = pep->work[0]; | |
| 503 | 10738 | w[0] = pep->work[1]; | |
| 504 | 10738 | w[1] = pep->work[2]; | |
| 505 | |||
| 506 | /* compute residual norms */ | ||
| 507 |
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10738 | PetscCall(PEPGetEigenpair(pep,i,&kr,&ki,xr,xi)); |
| 508 |
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10738 | PetscCall(PEPComputeResidualNorm_Private(pep,kr,ki,xr,xi,w,error)); |
| 509 | |||
| 510 | /* compute error */ | ||
| 511 |
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10738 | switch (type) { |
| 512 | case PEP_ERROR_ABSOLUTE: | ||
| 513 | break; | ||
| 514 | 329 | case PEP_ERROR_RELATIVE: | |
| 515 | 329 | *error /= SlepcAbsEigenvalue(kr,ki); | |
| 516 | 329 | break; | |
| 517 | 10289 | case PEP_ERROR_BACKWARD: | |
| 518 | /* initialization of matrix norms */ | ||
| 519 |
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10289 | if (!pep->nrma[pep->nmat-1]) { |
| 520 |
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6504 | for (j=0;j<pep->nmat;j++) { |
| 521 |
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4933 | PetscCall(MatHasOperation(pep->A[j],MATOP_NORM,&flg)); |
| 522 |
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4933 | PetscCheck(flg,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation"); |
| 523 |
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4933 | PetscCall(MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j])); |
| 524 | } | ||
| 525 | } | ||
| 526 | 10289 | t = SlepcAbsEigenvalue(kr,ki); | |
| 527 |
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42576 | for (j=pep->nmat-1;j>=0;j--) { |
| 528 | 32287 | z = z*t+pep->nrma[j]; | |
| 529 | } | ||
| 530 | 10289 | *error /= z; | |
| 531 | 10289 | break; | |
| 532 | ✗ | default: | |
| 533 | − | SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type"); | |
| 534 | } | ||
| 535 |
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2091 | PetscFunctionReturn(PETSC_SUCCESS); |
| 536 | } | ||
| 537 |