| 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 | 16727 | PetscErrorCode PEPComputeVectors(PEP pep) | |
| 38 | { | ||
| 39 |
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16727 | PetscFunctionBegin; |
| 40 |
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16727 | PEPCheckSolved(pep,1); |
| 41 |
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16727 | if (pep->state==PEP_STATE_SOLVED) PetscTryTypeMethod(pep,computevectors); |
| 42 | 16727 | pep->state = PEP_STATE_EIGENVECTORS; | |
| 43 |
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16727 | PetscFunctionReturn(PETSC_SUCCESS); |
| 44 | } | ||
| 45 | |||
| 46 | 1756 | PetscErrorCode PEPExtractVectors(PEP pep) | |
| 47 | { | ||
| 48 |
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1756 | PetscFunctionBegin; |
| 49 |
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1756 | PEPCheckSolved(pep,1); |
| 50 |
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1756 | if (pep->state==PEP_STATE_SOLVED) PetscTryTypeMethod(pep,extractvectors); |
| 51 |
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342 | PetscFunctionReturn(PETSC_SUCCESS); |
| 52 | } | ||
| 53 | |||
| 54 | /*@ | ||
| 55 | PEPSolve - Solves the polynomial eigensystem. | ||
| 56 | |||
| 57 | Collective | ||
| 58 | |||
| 59 | Input Parameter: | ||
| 60 | . pep - eigensolver context obtained from PEPCreate() | ||
| 61 | |||
| 62 | Options Database Keys: | ||
| 63 | + -pep_view - print information about the solver used | ||
| 64 | . -pep_view_matk - view the coefficient matrix Ak (replace k by an integer from 0 to nmat-1) | ||
| 65 | . -pep_view_vectors - view the computed eigenvectors | ||
| 66 | . -pep_view_values - view the computed eigenvalues | ||
| 67 | . -pep_converged_reason - print reason for convergence, and number of iterations | ||
| 68 | . -pep_error_absolute - print absolute errors of each eigenpair | ||
| 69 | . -pep_error_relative - print relative errors of each eigenpair | ||
| 70 | - -pep_error_backward - print backward errors of each eigenpair | ||
| 71 | |||
| 72 | Notes: | ||
| 73 | All the command-line options listed above admit an optional argument specifying | ||
| 74 | the viewer type and options. For instance, use '-pep_view_mat0 binary:amatrix.bin' | ||
| 75 | to save the A matrix to a binary file, '-pep_view_values draw' to draw the computed | ||
| 76 | eigenvalues graphically, or '-pep_error_relative :myerr.m:ascii_matlab' to save | ||
| 77 | the errors in a file that can be executed in Matlab. | ||
| 78 | |||
| 79 | Level: beginner | ||
| 80 | |||
| 81 | .seealso: PEPCreate(), PEPSetUp(), PEPDestroy(), PEPSetTolerances() | ||
| 82 | @*/ | ||
| 83 | 1956 | PetscErrorCode PEPSolve(PEP pep) | |
| 84 | { | ||
| 85 | 1956 | PetscInt i,k; | |
| 86 | 1956 | PetscBool flg,islinear; | |
| 87 | 1956 | char str[16]; | |
| 88 | |||
| 89 |
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1956 | PetscFunctionBegin; |
| 90 |
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1956 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 91 |
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1956 | if (pep->state>=PEP_STATE_SOLVED) PetscFunctionReturn(PETSC_SUCCESS); |
| 92 |
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1956 | PetscCall(PetscLogEventBegin(PEP_Solve,pep,0,0,0)); |
| 93 | |||
| 94 | /* call setup */ | ||
| 95 |
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1956 | PetscCall(PEPSetUp(pep)); |
| 96 | 1956 | pep->nconv = 0; | |
| 97 | 1956 | pep->its = 0; | |
| 98 |
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1956 | k = pep->lineariz? pep->ncv: pep->ncv*(pep->nmat-1); |
| 99 |
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133657 | for (i=0;i<k;i++) { |
| 100 | 131701 | pep->eigr[i] = 0.0; | |
| 101 | 131701 | pep->eigi[i] = 0.0; | |
| 102 | 131701 | pep->errest[i] = 0.0; | |
| 103 | 131701 | pep->perm[i] = i; | |
| 104 | } | ||
| 105 |
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1956 | PetscCall(PEPViewFromOptions(pep,NULL,"-pep_view_pre")); |
| 106 |
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1956 | PetscCall(RGViewFromOptions(pep->rg,NULL,"-rg_view")); |
| 107 | |||
| 108 | /* Call solver */ | ||
| 109 |
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1956 | PetscUseTypeMethod(pep,solve); |
| 110 |
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1956 | PetscCheck(pep->reason,PetscObjectComm((PetscObject)pep),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason"); |
| 111 | 1956 | pep->state = PEP_STATE_SOLVED; | |
| 112 | |||
| 113 | /* Only the first nconv columns contain useful information */ | ||
| 114 |
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1956 | PetscCall(BVSetActiveColumns(pep->V,0,pep->nconv)); |
| 115 | |||
| 116 |
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1956 | PetscCall(PetscObjectTypeCompare((PetscObject)pep,PEPLINEAR,&islinear)); |
| 117 |
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1956 | if (!islinear) { |
| 118 |
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1543 | PetscCall(STPostSolve(pep->st)); |
| 119 | /* Map eigenvalues back to the original problem */ | ||
| 120 |
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1543 | PetscCall(STGetTransform(pep->st,&flg)); |
| 121 |
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1543 | if (flg) PetscTryTypeMethod(pep,backtransform); |
| 122 | } | ||
| 123 | |||
| 124 | #if !defined(PETSC_USE_COMPLEX) | ||
| 125 | /* reorder conjugate eigenvalues (positive imaginary first) */ | ||
| 126 |
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5606 | for (i=0;i<pep->nconv-1;i++) { |
| 127 |
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4664 | if (pep->eigi[i] != 0) { |
| 128 |
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704 | if (pep->eigi[i] < 0) { |
| 129 | 175 | pep->eigi[i] = -pep->eigi[i]; | |
| 130 | 175 | pep->eigi[i+1] = -pep->eigi[i+1]; | |
| 131 | /* the next correction only works with eigenvectors */ | ||
| 132 |
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175 | PetscCall(PEPComputeVectors(pep)); |
| 133 |
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175 | PetscCall(BVScaleColumn(pep->V,i+1,-1.0)); |
| 134 | } | ||
| 135 | 704 | i++; | |
| 136 | } | ||
| 137 | } | ||
| 138 | #endif | ||
| 139 | |||
| 140 |
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1956 | if (pep->refine!=PEP_REFINE_NONE) PetscCall(PetscCitationsRegister(citation,&cited)); |
| 141 | |||
| 142 |
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1956 | if (pep->refine==PEP_REFINE_SIMPLE && pep->rits>0 && pep->nconv>0) { |
| 143 |
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156 | PetscCall(PEPComputeVectors(pep)); |
| 144 |
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156 | PetscCall(PEPNewtonRefinementSimple(pep,&pep->rits,pep->rtol,pep->nconv)); |
| 145 | } | ||
| 146 | |||
| 147 | /* sort eigenvalues according to pep->which parameter */ | ||
| 148 |
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1956 | PetscCall(SlepcSortEigenvalues(pep->sc,pep->nconv,pep->eigr,pep->eigi,pep->perm)); |
| 149 |
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1956 | PetscCall(PetscLogEventEnd(PEP_Solve,pep,0,0,0)); |
| 150 | |||
| 151 | /* various viewers */ | ||
| 152 |
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1956 | PetscCall(PEPViewFromOptions(pep,NULL,"-pep_view")); |
| 153 |
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1956 | PetscCall(PEPConvergedReasonViewFromOptions(pep)); |
| 154 |
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1956 | PetscCall(PEPErrorViewFromOptions(pep)); |
| 155 |
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1956 | PetscCall(PEPValuesViewFromOptions(pep)); |
| 156 |
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1956 | PetscCall(PEPVectorsViewFromOptions(pep)); |
| 157 |
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9302 | for (i=0;i<pep->nmat;i++) { |
| 158 |
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7346 | PetscCall(PetscSNPrintf(str,sizeof(str),"-pep_view_mat%" PetscInt_FMT,i)); |
| 159 |
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7346 | PetscCall(MatViewFromOptions(pep->A[i],(PetscObject)pep,str)); |
| 160 | } | ||
| 161 | |||
| 162 | /* Remove the initial subspace */ | ||
| 163 | 1956 | pep->nini = 0; | |
| 164 |
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1956 | PetscFunctionReturn(PETSC_SUCCESS); |
| 165 | } | ||
| 166 | |||
| 167 | /*@ | ||
| 168 | PEPGetIterationNumber - Gets the current iteration number. If the | ||
| 169 | call to PEPSolve() is complete, then it returns the number of iterations | ||
| 170 | carried out by the solution method. | ||
| 171 | |||
| 172 | Not Collective | ||
| 173 | |||
| 174 | Input Parameter: | ||
| 175 | . pep - the polynomial eigensolver context | ||
| 176 | |||
| 177 | Output Parameter: | ||
| 178 | . its - number of iterations | ||
| 179 | |||
| 180 | Note: | ||
| 181 | During the i-th iteration this call returns i-1. If PEPSolve() is | ||
| 182 | complete, then parameter "its" contains either the iteration number at | ||
| 183 | which convergence was successfully reached, or failure was detected. | ||
| 184 | Call PEPGetConvergedReason() to determine if the solver converged or | ||
| 185 | failed and why. | ||
| 186 | |||
| 187 | Level: intermediate | ||
| 188 | |||
| 189 | .seealso: PEPGetConvergedReason(), PEPSetTolerances() | ||
| 190 | @*/ | ||
| 191 | 310 | PetscErrorCode PEPGetIterationNumber(PEP pep,PetscInt *its) | |
| 192 | { | ||
| 193 |
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310 | PetscFunctionBegin; |
| 194 |
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310 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 195 |
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310 | PetscAssertPointer(its,2); |
| 196 | 310 | *its = pep->its; | |
| 197 |
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310 | PetscFunctionReturn(PETSC_SUCCESS); |
| 198 | } | ||
| 199 | |||
| 200 | /*@ | ||
| 201 | PEPGetConverged - Gets the number of converged eigenpairs. | ||
| 202 | |||
| 203 | Not Collective | ||
| 204 | |||
| 205 | Input Parameter: | ||
| 206 | . pep - the polynomial eigensolver context | ||
| 207 | |||
| 208 | Output Parameter: | ||
| 209 | . nconv - number of converged eigenpairs | ||
| 210 | |||
| 211 | Note: | ||
| 212 | This function should be called after PEPSolve() has finished. | ||
| 213 | |||
| 214 | Level: beginner | ||
| 215 | |||
| 216 | .seealso: PEPSetDimensions(), PEPSolve(), PEPGetEigenpair() | ||
| 217 | @*/ | ||
| 218 | 924 | PetscErrorCode PEPGetConverged(PEP pep,PetscInt *nconv) | |
| 219 | { | ||
| 220 |
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924 | PetscFunctionBegin; |
| 221 |
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924 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 222 |
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924 | PetscAssertPointer(nconv,2); |
| 223 |
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924 | PEPCheckSolved(pep,1); |
| 224 | 924 | *nconv = pep->nconv; | |
| 225 |
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924 | PetscFunctionReturn(PETSC_SUCCESS); |
| 226 | } | ||
| 227 | |||
| 228 | /*@ | ||
| 229 | PEPGetConvergedReason - Gets the reason why the PEPSolve() iteration was | ||
| 230 | stopped. | ||
| 231 | |||
| 232 | Not Collective | ||
| 233 | |||
| 234 | Input Parameter: | ||
| 235 | . pep - the polynomial eigensolver context | ||
| 236 | |||
| 237 | Output Parameter: | ||
| 238 | . reason - negative value indicates diverged, positive value converged | ||
| 239 | |||
| 240 | Options Database Key: | ||
| 241 | . -pep_converged_reason - print the reason to a viewer | ||
| 242 | |||
| 243 | Notes: | ||
| 244 | Possible values for reason are | ||
| 245 | + PEP_CONVERGED_TOL - converged up to tolerance | ||
| 246 | . PEP_CONVERGED_USER - converged due to a user-defined condition | ||
| 247 | . PEP_DIVERGED_ITS - required more than max_it iterations to reach convergence | ||
| 248 | . PEP_DIVERGED_BREAKDOWN - generic breakdown in method | ||
| 249 | - PEP_DIVERGED_SYMMETRY_LOST - pseudo-Lanczos was not able to keep symmetry | ||
| 250 | |||
| 251 | Can only be called after the call to PEPSolve() is complete. | ||
| 252 | |||
| 253 | Level: intermediate | ||
| 254 | |||
| 255 | .seealso: PEPSetTolerances(), PEPSolve(), PEPConvergedReason | ||
| 256 | @*/ | ||
| 257 | 266 | PetscErrorCode PEPGetConvergedReason(PEP pep,PEPConvergedReason *reason) | |
| 258 | { | ||
| 259 |
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266 | PetscFunctionBegin; |
| 260 |
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266 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 261 |
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266 | PetscAssertPointer(reason,2); |
| 262 |
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266 | PEPCheckSolved(pep,1); |
| 263 | 266 | *reason = pep->reason; | |
| 264 |
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266 | PetscFunctionReturn(PETSC_SUCCESS); |
| 265 | } | ||
| 266 | |||
| 267 | /*@ | ||
| 268 | PEPGetEigenpair - Gets the i-th solution of the eigenproblem as computed by | ||
| 269 | PEPSolve(). The solution consists in both the eigenvalue and the eigenvector. | ||
| 270 | |||
| 271 | Collective | ||
| 272 | |||
| 273 | Input Parameters: | ||
| 274 | + pep - polynomial eigensolver context | ||
| 275 | - i - index of the solution | ||
| 276 | |||
| 277 | Output Parameters: | ||
| 278 | + eigr - real part of eigenvalue | ||
| 279 | . eigi - imaginary part of eigenvalue | ||
| 280 | . Vr - real part of eigenvector | ||
| 281 | - Vi - imaginary part of eigenvector | ||
| 282 | |||
| 283 | Notes: | ||
| 284 | It is allowed to pass NULL for Vr and Vi, if the eigenvector is not | ||
| 285 | required. Otherwise, the caller must provide valid Vec objects, i.e., | ||
| 286 | they must be created by the calling program with e.g. MatCreateVecs(). | ||
| 287 | |||
| 288 | If the eigenvalue is real, then eigi and Vi are set to zero. If PETSc is | ||
| 289 | configured with complex scalars the eigenvalue is stored | ||
| 290 | directly in eigr (eigi is set to zero) and the eigenvector in Vr (Vi is | ||
| 291 | set to zero). In any case, the user can pass NULL in Vr or Vi if one of | ||
| 292 | them is not required. | ||
| 293 | |||
| 294 | The index i should be a value between 0 and nconv-1 (see PEPGetConverged()). | ||
| 295 | Eigenpairs are indexed according to the ordering criterion established | ||
| 296 | with PEPSetWhichEigenpairs(). | ||
| 297 | |||
| 298 | Level: beginner | ||
| 299 | |||
| 300 | .seealso: PEPSolve(), PEPGetConverged(), PEPSetWhichEigenpairs() | ||
| 301 | @*/ | ||
| 302 | 16386 | PetscErrorCode PEPGetEigenpair(PEP pep,PetscInt i,PetscScalar *eigr,PetscScalar *eigi,Vec Vr,Vec Vi) | |
| 303 | { | ||
| 304 | 16386 | PetscInt k; | |
| 305 | |||
| 306 |
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16386 | PetscFunctionBegin; |
| 307 |
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16386 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 308 |
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16386 | PetscValidLogicalCollectiveInt(pep,i,2); |
| 309 |
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16386 | if (Vr) { PetscValidHeaderSpecific(Vr,VEC_CLASSID,5); PetscCheckSameComm(pep,1,Vr,5); } |
| 310 |
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16386 | if (Vi) { PetscValidHeaderSpecific(Vi,VEC_CLASSID,6); PetscCheckSameComm(pep,1,Vi,6); } |
| 311 |
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16386 | PEPCheckSolved(pep,1); |
| 312 |
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16386 | PetscCheck(i>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 313 |
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16386 | PetscCheck(i<pep->nconv,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see PEPGetConverged()"); |
| 314 | |||
| 315 |
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16386 | PetscCall(PEPComputeVectors(pep)); |
| 316 | 16386 | k = pep->perm[i]; | |
| 317 | |||
| 318 | /* eigenvalue */ | ||
| 319 | #if defined(PETSC_USE_COMPLEX) | ||
| 320 |
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8320 | if (eigr) *eigr = pep->eigr[k]; |
| 321 |
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8320 | if (eigi) *eigi = 0; |
| 322 | #else | ||
| 323 |
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8066 | if (eigr) *eigr = pep->eigr[k]; |
| 324 |
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8066 | if (eigi) *eigi = pep->eigi[k]; |
| 325 | #endif | ||
| 326 | |||
| 327 | /* eigenvector */ | ||
| 328 |
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16386 | PetscCall(BV_GetEigenvector(pep->V,k,pep->eigi[k],Vr,Vi)); |
| 329 |
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3198 | PetscFunctionReturn(PETSC_SUCCESS); |
| 330 | } | ||
| 331 | |||
| 332 | /*@ | ||
| 333 | PEPGetErrorEstimate - Returns the error estimate associated to the i-th | ||
| 334 | computed eigenpair. | ||
| 335 | |||
| 336 | Not Collective | ||
| 337 | |||
| 338 | Input Parameters: | ||
| 339 | + pep - polynomial eigensolver context | ||
| 340 | - i - index of eigenpair | ||
| 341 | |||
| 342 | Output Parameter: | ||
| 343 | . errest - the error estimate | ||
| 344 | |||
| 345 | Notes: | ||
| 346 | This is the error estimate used internally by the eigensolver. The actual | ||
| 347 | error bound can be computed with PEPComputeError(). See also the users | ||
| 348 | manual for details. | ||
| 349 | |||
| 350 | Level: advanced | ||
| 351 | |||
| 352 | .seealso: PEPComputeError() | ||
| 353 | @*/ | ||
| 354 | 43 | PetscErrorCode PEPGetErrorEstimate(PEP pep,PetscInt i,PetscReal *errest) | |
| 355 | { | ||
| 356 |
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43 | PetscFunctionBegin; |
| 357 |
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43 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 358 |
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43 | PetscAssertPointer(errest,3); |
| 359 |
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43 | PEPCheckSolved(pep,1); |
| 360 |
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43 | PetscCheck(i>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 361 |
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43 | PetscCheck(i<pep->nconv,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see PEPGetConverged()"); |
| 362 | 43 | *errest = pep->errest[pep->perm[i]]; | |
| 363 |
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43 | PetscFunctionReturn(PETSC_SUCCESS); |
| 364 | } | ||
| 365 | |||
| 366 | /* | ||
| 367 | PEPComputeResidualNorm_Private - Computes the norm of the residual vector | ||
| 368 | associated with an eigenpair. | ||
| 369 | |||
| 370 | Input Parameters: | ||
| 371 | kr,ki - eigenvalue | ||
| 372 | xr,xi - eigenvector | ||
| 373 | z - array of 4 work vectors (z[2],z[3] not referenced in complex scalars) | ||
| 374 | */ | ||
| 375 | 11837 | PetscErrorCode PEPComputeResidualNorm_Private(PEP pep,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm) | |
| 376 | { | ||
| 377 | 11837 | Mat *A=pep->A; | |
| 378 | 11837 | PetscInt i,nmat=pep->nmat; | |
| 379 | 11837 | PetscScalar t[20],*vals=t,*ivals=NULL; | |
| 380 | 11837 | Vec u,w; | |
| 381 | #if !defined(PETSC_USE_COMPLEX) | ||
| 382 | 5437 | Vec ui,wi; | |
| 383 | 5437 | PetscReal ni; | |
| 384 | 5437 | PetscBool imag; | |
| 385 | 5437 | PetscScalar it[20]; | |
| 386 | #endif | ||
| 387 | |||
| 388 |
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11837 | PetscFunctionBegin; |
| 389 | 11837 | u = z[0]; w = z[1]; | |
| 390 |
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11837 | PetscCall(VecSet(u,0.0)); |
| 391 | #if !defined(PETSC_USE_COMPLEX) | ||
| 392 | 5437 | ui = z[2]; wi = z[3]; | |
| 393 | 5437 | ivals = it; | |
| 394 | #endif | ||
| 395 |
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11837 | if (nmat>20) { |
| 396 | ✗ | PetscCall(PetscMalloc1(nmat,&vals)); | |
| 397 | #if !defined(PETSC_USE_COMPLEX) | ||
| 398 | ✗ | PetscCall(PetscMalloc1(nmat,&ivals)); | |
| 399 | #endif | ||
| 400 | } | ||
| 401 |
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11837 | PetscCall(PEPEvaluateBasis(pep,kr,ki,vals,ivals)); |
| 402 | #if !defined(PETSC_USE_COMPLEX) | ||
| 403 |
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5437 | if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON)) |
| 404 | imag = PETSC_FALSE; | ||
| 405 | else { | ||
| 406 | 1139 | imag = PETSC_TRUE; | |
| 407 |
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1139 | PetscCall(VecSet(ui,0.0)); |
| 408 | } | ||
| 409 | #endif | ||
| 410 |
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49718 | for (i=0;i<nmat;i++) { |
| 411 |
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37881 | if (vals[i]!=0.0) { |
| 412 |
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37881 | PetscCall(MatMult(A[i],xr,w)); |
| 413 |
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37881 | PetscCall(VecAXPY(u,vals[i],w)); |
| 414 | } | ||
| 415 | #if !defined(PETSC_USE_COMPLEX) | ||
| 416 |
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16636 | if (imag) { |
| 417 |
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3697 | if (ivals[i]!=0 || vals[i]!=0) { |
| 418 |
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3697 | PetscCall(MatMult(A[i],xi,wi)); |
| 419 |
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3697 | if (vals[i]==0) PetscCall(MatMult(A[i],xr,w)); |
| 420 | } | ||
| 421 |
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3697 | if (ivals[i]!=0) { |
| 422 |
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2558 | PetscCall(VecAXPY(u,-ivals[i],wi)); |
| 423 |
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2558 | PetscCall(VecAXPY(ui,ivals[i],w)); |
| 424 | } | ||
| 425 |
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16636 | if (vals[i]!=0) PetscCall(VecAXPY(ui,vals[i],wi)); |
| 426 | } | ||
| 427 | #endif | ||
| 428 | } | ||
| 429 |
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11837 | PetscCall(VecNorm(u,NORM_2,norm)); |
| 430 | #if !defined(PETSC_USE_COMPLEX) | ||
| 431 |
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5437 | if (imag) { |
| 432 |
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1139 | PetscCall(VecNorm(ui,NORM_2,&ni)); |
| 433 | 1139 | *norm = SlepcAbsEigenvalue(*norm,ni); | |
| 434 | } | ||
| 435 | #endif | ||
| 436 |
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11837 | if (nmat>20) { |
| 437 | ✗ | PetscCall(PetscFree(vals)); | |
| 438 | #if !defined(PETSC_USE_COMPLEX) | ||
| 439 | ✗ | PetscCall(PetscFree(ivals)); | |
| 440 | #endif | ||
| 441 | } | ||
| 442 |
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2326 | PetscFunctionReturn(PETSC_SUCCESS); |
| 443 | } | ||
| 444 | |||
| 445 | /*@ | ||
| 446 | PEPComputeError - Computes the error (based on the residual norm) associated | ||
| 447 | with the i-th computed eigenpair. | ||
| 448 | |||
| 449 | Collective | ||
| 450 | |||
| 451 | Input Parameters: | ||
| 452 | + pep - the polynomial eigensolver context | ||
| 453 | . i - the solution index | ||
| 454 | - type - the type of error to compute | ||
| 455 | |||
| 456 | Output Parameter: | ||
| 457 | . error - the error | ||
| 458 | |||
| 459 | Notes: | ||
| 460 | The error can be computed in various ways, all of them based on the residual | ||
| 461 | norm ||P(l)x||_2 where l is the eigenvalue and x is the eigenvector. | ||
| 462 | See the users guide for additional details. | ||
| 463 | |||
| 464 | Level: beginner | ||
| 465 | |||
| 466 | .seealso: PEPErrorType, PEPSolve(), PEPGetErrorEstimate() | ||
| 467 | @*/ | ||
| 468 | 10572 | PetscErrorCode PEPComputeError(PEP pep,PetscInt i,PEPErrorType type,PetscReal *error) | |
| 469 | { | ||
| 470 | 10572 | Vec xr,xi,w[4]; | |
| 471 | 10572 | PetscScalar kr,ki; | |
| 472 | 10572 | PetscReal t,z=0.0; | |
| 473 | 10572 | PetscInt j; | |
| 474 | 10572 | PetscBool flg; | |
| 475 | |||
| 476 |
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10572 | PetscFunctionBegin; |
| 477 |
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10572 | PetscValidHeaderSpecific(pep,PEP_CLASSID,1); |
| 478 |
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10572 | PetscValidLogicalCollectiveInt(pep,i,2); |
| 479 |
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10572 | PetscValidLogicalCollectiveEnum(pep,type,3); |
| 480 |
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10572 | PetscAssertPointer(error,4); |
| 481 |
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10572 | PEPCheckSolved(pep,1); |
| 482 | |||
| 483 | /* allocate work vectors */ | ||
| 484 | #if defined(PETSC_USE_COMPLEX) | ||
| 485 |
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5510 | PetscCall(PEPSetWorkVecs(pep,3)); |
| 486 | 5510 | xi = NULL; | |
| 487 | 5510 | w[2] = NULL; | |
| 488 | 5510 | w[3] = NULL; | |
| 489 | #else | ||
| 490 |
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5062 | PetscCall(PEPSetWorkVecs(pep,6)); |
| 491 | 5062 | xi = pep->work[3]; | |
| 492 | 5062 | w[2] = pep->work[4]; | |
| 493 | 5062 | w[3] = pep->work[5]; | |
| 494 | #endif | ||
| 495 | 10572 | xr = pep->work[0]; | |
| 496 | 10572 | w[0] = pep->work[1]; | |
| 497 | 10572 | w[1] = pep->work[2]; | |
| 498 | |||
| 499 | /* compute residual norms */ | ||
| 500 |
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10572 | PetscCall(PEPGetEigenpair(pep,i,&kr,&ki,xr,xi)); |
| 501 |
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10572 | PetscCall(PEPComputeResidualNorm_Private(pep,kr,ki,xr,xi,w,error)); |
| 502 | |||
| 503 | /* compute error */ | ||
| 504 |
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10572 | switch (type) { |
| 505 | case PEP_ERROR_ABSOLUTE: | ||
| 506 | break; | ||
| 507 | 327 | case PEP_ERROR_RELATIVE: | |
| 508 | 327 | *error /= SlepcAbsEigenvalue(kr,ki); | |
| 509 | 327 | break; | |
| 510 | 10125 | case PEP_ERROR_BACKWARD: | |
| 511 | /* initialization of matrix norms */ | ||
| 512 |
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10125 | if (!pep->nrma[pep->nmat-1]) { |
| 513 |
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6432 | for (j=0;j<pep->nmat;j++) { |
| 514 |
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4879 | PetscCall(MatHasOperation(pep->A[j],MATOP_NORM,&flg)); |
| 515 |
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4879 | PetscCheck(flg,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation"); |
| 516 |
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4879 | PetscCall(MatNorm(pep->A[j],NORM_INFINITY,&pep->nrma[j])); |
| 517 | } | ||
| 518 | } | ||
| 519 | 10125 | t = SlepcAbsEigenvalue(kr,ki); | |
| 520 |
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41920 | for (j=pep->nmat-1;j>=0;j--) { |
| 521 | 31795 | z = z*t+pep->nrma[j]; | |
| 522 | } | ||
| 523 | 10125 | *error /= z; | |
| 524 | 10125 | break; | |
| 525 | ✗ | default: | |
| 526 | ✗ | SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type"); | |
| 527 | } | ||
| 528 |
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2073 | PetscFunctionReturn(PETSC_SUCCESS); |
| 529 | } | ||
| 530 |