| 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 | EPS routines related to the solution process | ||
| 12 | */ | ||
| 13 | |||
| 14 | #include <slepc/private/epsimpl.h> /*I "slepceps.h" I*/ | ||
| 15 | #include <slepc/private/bvimpl.h> | ||
| 16 | #include <petscdraw.h> | ||
| 17 | |||
| 18 | 94330 | PetscErrorCode EPSComputeVectors(EPS eps) | |
| 19 | { | ||
| 20 |
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94330 | PetscFunctionBegin; |
| 21 |
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94330 | EPSCheckSolved(eps,1); |
| 22 |
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94330 | if (eps->state==EPS_STATE_SOLVED) PetscTryTypeMethod(eps,computevectors); |
| 23 | 94330 | eps->state = EPS_STATE_EIGENVECTORS; | |
| 24 |
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94330 | PetscFunctionReturn(PETSC_SUCCESS); |
| 25 | } | ||
| 26 | |||
| 27 | 9972 | static PetscErrorCode EPSComputeValues(EPS eps) | |
| 28 | { | ||
| 29 | 9972 | PetscBool injective,iscomp,isfilter; | |
| 30 | 9972 | PetscInt i,n,aux,nconv0; | |
| 31 | 9972 | Mat A,B=NULL,G,Z; | |
| 32 | |||
| 33 |
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9972 | PetscFunctionBegin; |
| 34 |
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9972 | switch (eps->categ) { |
| 35 | 7852 | case EPS_CATEGORY_KRYLOV: | |
| 36 | case EPS_CATEGORY_OTHER: | ||
| 37 |
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7852 | PetscCall(STIsInjective(eps->st,&injective)); |
| 38 |
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7852 | if (injective) { |
| 39 | /* one-to-one mapping: backtransform eigenvalues */ | ||
| 40 |
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7636 | PetscUseTypeMethod(eps,backtransform); |
| 41 | } else { | ||
| 42 | /* compute eigenvalues from Rayleigh quotient */ | ||
| 43 |
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216 | PetscCall(DSGetDimensions(eps->ds,&n,NULL,NULL,NULL)); |
| 44 |
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216 | if (!n) break; |
| 45 |
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216 | PetscCall(EPSGetOperators(eps,&A,&B)); |
| 46 |
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216 | PetscCall(BVSetActiveColumns(eps->V,0,n)); |
| 47 |
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216 | PetscCall(DSGetCompact(eps->ds,&iscomp)); |
| 48 |
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216 | PetscCall(DSSetCompact(eps->ds,PETSC_FALSE)); |
| 49 |
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216 | PetscCall(DSGetMat(eps->ds,DS_MAT_A,&G)); |
| 50 |
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216 | PetscCall(BVMatProject(eps->V,A,eps->V,G)); |
| 51 |
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216 | PetscCall(DSRestoreMat(eps->ds,DS_MAT_A,&G)); |
| 52 |
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216 | if (B) { |
| 53 | ✗ | PetscCall(DSGetMat(eps->ds,DS_MAT_B,&G)); | |
| 54 | ✗ | PetscCall(BVMatProject(eps->V,B,eps->V,G)); | |
| 55 | ✗ | PetscCall(DSRestoreMat(eps->ds,DS_MAT_B,&G)); | |
| 56 | } | ||
| 57 |
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216 | PetscCall(DSSolve(eps->ds,eps->eigr,eps->eigi)); |
| 58 |
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216 | PetscCall(DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL)); |
| 59 |
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216 | PetscCall(DSSynchronize(eps->ds,eps->eigr,eps->eigi)); |
| 60 |
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216 | PetscCall(DSSetCompact(eps->ds,iscomp)); |
| 61 |
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216 | if (eps->ishermitian && (!eps->isgeneralized || eps->ispositive)) { /* V = V * Z */ |
| 62 |
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216 | PetscCall(DSVectors(eps->ds,DS_MAT_X,NULL,NULL)); |
| 63 |
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216 | PetscCall(DSGetMat(eps->ds,DS_MAT_X,&Z)); |
| 64 |
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216 | PetscCall(BVMultInPlace(eps->V,Z,0,n)); |
| 65 |
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216 | PetscCall(DSRestoreMat(eps->ds,DS_MAT_X,&Z)); |
| 66 | } | ||
| 67 | /* in case of STFILTER discard computed eigenvalues that lie outside the wanted interval */ | ||
| 68 |
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216 | PetscCall(PetscObjectTypeCompare((PetscObject)eps->st,STFILTER,&isfilter)); |
| 69 |
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216 | if (isfilter) { |
| 70 | 206 | nconv0 = eps->nconv; | |
| 71 |
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2308 | for (i=0;i<eps->nconv;i++) { |
| 72 |
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2102 | if (PetscRealPart(eps->eigr[eps->perm[i]])<eps->inta || PetscRealPart(eps->eigr[eps->perm[i]])>eps->intb) { |
| 73 | 412 | eps->nconv--; | |
| 74 |
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412 | if (i<eps->nconv) { SlepcSwap(eps->perm[i],eps->perm[eps->nconv],aux); i--; } |
| 75 | } | ||
| 76 | } | ||
| 77 |
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206 | if (nconv0>eps->nconv) PetscCall(PetscInfo(eps,"Discarded %" PetscInt_FMT " computed eigenvalues lying outside the interval\n",nconv0-eps->nconv)); |
| 78 | } | ||
| 79 | } | ||
| 80 | break; | ||
| 81 | case EPS_CATEGORY_PRECOND: | ||
| 82 | case EPS_CATEGORY_CONTOUR: | ||
| 83 | /* eigenvalues already available as an output of the solver */ | ||
| 84 | break; | ||
| 85 | } | ||
| 86 |
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1920 | PetscFunctionReturn(PETSC_SUCCESS); |
| 87 | } | ||
| 88 | |||
| 89 | /*@ | ||
| 90 | EPSSolve - Solves the eigensystem. | ||
| 91 | |||
| 92 | Collective | ||
| 93 | |||
| 94 | Input Parameter: | ||
| 95 | . eps - the linear eigensolver context | ||
| 96 | |||
| 97 | Options Database Keys: | ||
| 98 | + -eps_view - print information about the solver once the solve is complete | ||
| 99 | . -eps_view_pre - print information about the solver before the solve starts | ||
| 100 | . -eps_view_mat0 - view the first matrix ($A$) | ||
| 101 | . -eps_view_mat1 - view the second matrix ($B$) | ||
| 102 | . -eps_view_vectors - view the computed eigenvectors | ||
| 103 | . -eps_view_values - view the computed eigenvalues | ||
| 104 | . -eps_converged_reason - print reason for convergence/divergence, and number of iterations | ||
| 105 | . -eps_error_absolute - print absolute errors of each eigenpair | ||
| 106 | . -eps_error_relative - print relative errors of each eigenpair | ||
| 107 | - -eps_error_backward - print backward errors of each eigenpair | ||
| 108 | |||
| 109 | Notes: | ||
| 110 | The problem matrices are specified with `EPSSetOperators()`. | ||
| 111 | |||
| 112 | `EPSSolve()` will return without generating an error regardless of whether | ||
| 113 | all requested solutions were computed or not. Call `EPSGetConverged()` to get the | ||
| 114 | actual number of computed solutions, and `EPSGetConvergedReason()` to determine if | ||
| 115 | the solver converged or failed and why. | ||
| 116 | |||
| 117 | All the command-line options listed above admit an optional argument specifying | ||
| 118 | the viewer type and options. For instance, use `-eps_view_mat0 binary:amatrix.bin` | ||
| 119 | to save the $A$ matrix to a binary file, `-eps_view_values draw` to draw the computed | ||
| 120 | eigenvalues graphically, or `-eps_error_relative :myerr.m:ascii_matlab` to save | ||
| 121 | the errors in a file that can be executed in Matlab. | ||
| 122 | |||
| 123 | Level: beginner | ||
| 124 | |||
| 125 | .seealso: [](ch:eps), `EPSCreate()`, `EPSSetUp()`, `EPSDestroy()`, `EPSSetOperators()`, `EPSGetConverged()`, `EPSGetConvergedReason()` | ||
| 126 | @*/ | ||
| 127 | 9972 | PetscErrorCode EPSSolve(EPS eps) | |
| 128 | { | ||
| 129 | 9972 | PetscInt i; | |
| 130 | 9972 | PetscBool hasname; | |
| 131 | 9972 | STMatMode matmode; | |
| 132 | 9972 | Mat A,B; | |
| 133 | |||
| 134 |
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9972 | PetscFunctionBegin; |
| 135 |
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9972 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 136 |
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9972 | if (eps->state>=EPS_STATE_SOLVED) PetscFunctionReturn(PETSC_SUCCESS); |
| 137 |
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9972 | PetscCall(PetscLogEventBegin(EPS_Solve,eps,0,0,0)); |
| 138 | |||
| 139 | /* Call setup */ | ||
| 140 |
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9972 | PetscCall(EPSSetUp(eps)); |
| 141 | |||
| 142 | /* Safeguard for matrices of size 0 */ | ||
| 143 |
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9972 | if (eps->n == 0) { |
| 144 | ✗ | eps->nconv = 0; | |
| 145 | ✗ | eps->reason = EPS_CONVERGED_TOL; | |
| 146 | ✗ | eps->state = EPS_STATE_SOLVED; | |
| 147 | ✗ | PetscFunctionReturn(PETSC_SUCCESS); | |
| 148 | } | ||
| 149 | |||
| 150 | 9972 | eps->nconv = 0; | |
| 151 | 9972 | eps->its = 0; | |
| 152 |
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302172 | for (i=0;i<eps->ncv;i++) { |
| 153 | 292200 | eps->eigr[i] = 0.0; | |
| 154 | 292200 | eps->eigi[i] = 0.0; | |
| 155 | 292200 | eps->errest[i] = 0.0; | |
| 156 | 292200 | eps->perm[i] = i; | |
| 157 | } | ||
| 158 |
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9972 | PetscCall(EPSViewFromOptions(eps,NULL,"-eps_view_pre")); |
| 159 |
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9972 | PetscCall(RGViewFromOptions(eps->rg,NULL,"-rg_view")); |
| 160 | |||
| 161 | /* Call solver */ | ||
| 162 |
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9972 | PetscUseTypeMethod(eps,solve); |
| 163 |
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9972 | PetscCheck(eps->reason,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason"); |
| 164 | 9972 | eps->state = EPS_STATE_SOLVED; | |
| 165 | |||
| 166 | /* Only the first nconv columns contain useful information (except in CISS) */ | ||
| 167 |
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9972 | PetscCall(BVSetActiveColumns(eps->V,0,eps->nconv)); |
| 168 |
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9972 | if (eps->twosided) PetscCall(BVSetActiveColumns(eps->W,0,eps->nconv)); |
| 169 | |||
| 170 | /* If inplace, purify eigenvectors before reverting operator */ | ||
| 171 |
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9972 | PetscCall(STGetMatMode(eps->st,&matmode)); |
| 172 |
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9972 | if (matmode == ST_MATMODE_INPLACE && eps->ispositive) PetscCall(EPSComputeVectors(eps)); |
| 173 |
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9972 | PetscCall(STPostSolve(eps->st)); |
| 174 | |||
| 175 | /* Map eigenvalues back to the original problem if appropriate */ | ||
| 176 |
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9972 | PetscCall(EPSComputeValues(eps)); |
| 177 | |||
| 178 | #if !defined(PETSC_USE_COMPLEX) | ||
| 179 | /* Reorder conjugate eigenvalues (positive imaginary first) */ | ||
| 180 |
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56949 | for (i=0;i<eps->nconv-1;i++) { |
| 181 |
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51717 | if (eps->eigi[i] != 0 && (eps->problem_type!=EPS_HAMILT || eps->eigr[i]!=0)) { |
| 182 | /* conjugate eigenvalues */ | ||
| 183 |
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925 | if (eps->eigi[i] < 0) { |
| 184 | 116 | eps->eigi[i] = -eps->eigi[i]; | |
| 185 | 116 | eps->eigi[i+1] = -eps->eigi[i+1]; | |
| 186 | /* the next correction only works with eigenvectors */ | ||
| 187 |
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116 | PetscCall(EPSComputeVectors(eps)); |
| 188 |
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116 | PetscCall(BVScaleColumn(eps->V,i+1,-1.0)); |
| 189 |
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116 | if (eps->W) PetscCall(BVScaleColumn(eps->W,i+1,-1.0)); |
| 190 | } | ||
| 191 | 925 | i++; | |
| 192 | } | ||
| 193 | } | ||
| 194 | #endif | ||
| 195 | |||
| 196 | /* Sort eigenvalues according to eps->which parameter */ | ||
| 197 |
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9972 | if (eps->problem_type==EPS_HAMILT) PetscCall(SlepcSortEigenvaluesSpecial(eps->sc,eps->nconv,eps->eigr,eps->eigi,eps->perm)); |
| 198 |
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9937 | else PetscCall(SlepcSortEigenvalues(eps->sc,eps->nconv,eps->eigr,eps->eigi,eps->perm)); |
| 199 |
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9972 | PetscCall(PetscLogEventEnd(EPS_Solve,eps,0,0,0)); |
| 200 | |||
| 201 | /* Various viewers */ | ||
| 202 |
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9972 | PetscCall(EPSViewFromOptions(eps,NULL,"-eps_view")); |
| 203 |
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9972 | PetscCall(EPSConvergedReasonViewFromOptions(eps)); |
| 204 |
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9972 | PetscCall(EPSErrorViewFromOptions(eps)); |
| 205 |
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9972 | PetscCall(EPSValuesViewFromOptions(eps)); |
| 206 |
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9972 | PetscCall(EPSVectorsViewFromOptions(eps)); |
| 207 | |||
| 208 |
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9972 | PetscCall(PetscOptionsHasName(((PetscObject)eps)->options,((PetscObject)eps)->prefix,"-eps_view_mat0",&hasname)); |
| 209 |
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9972 | if (hasname) { |
| 210 | ✗ | PetscCall(EPSGetOperators(eps,&A,NULL)); | |
| 211 | ✗ | PetscCall(MatViewFromOptions(A,(PetscObject)eps,"-eps_view_mat0")); | |
| 212 | } | ||
| 213 |
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9972 | if (eps->isgeneralized) { |
| 214 |
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2080 | PetscCall(PetscOptionsHasName(((PetscObject)eps)->options,((PetscObject)eps)->prefix,"-eps_view_mat1",&hasname)); |
| 215 |
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2080 | if (hasname) { |
| 216 | ✗ | PetscCall(EPSGetOperators(eps,NULL,&B)); | |
| 217 | ✗ | PetscCall(MatViewFromOptions(B,(PetscObject)eps,"-eps_view_mat1")); | |
| 218 | } | ||
| 219 | } | ||
| 220 | |||
| 221 | /* Remove deflation and initial subspaces */ | ||
| 222 |
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9972 | if (eps->nds) { |
| 223 |
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153 | PetscCall(BVSetNumConstraints(eps->V,0)); |
| 224 | 153 | eps->nds = 0; | |
| 225 | } | ||
| 226 | 9972 | eps->nini = 0; | |
| 227 |
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9972 | PetscFunctionReturn(PETSC_SUCCESS); |
| 228 | } | ||
| 229 | |||
| 230 | /*@ | ||
| 231 | EPSGetIterationNumber - Gets the current iteration number. If the | ||
| 232 | call to `EPSSolve()` is complete, then it returns the number of iterations | ||
| 233 | carried out by the solution method. | ||
| 234 | |||
| 235 | Not Collective | ||
| 236 | |||
| 237 | Input Parameter: | ||
| 238 | . eps - the linear eigensolver context | ||
| 239 | |||
| 240 | Output Parameter: | ||
| 241 | . its - number of iterations | ||
| 242 | |||
| 243 | Note: | ||
| 244 | During the $i$-th iteration this call returns $i-1$. If `EPSSolve()` is | ||
| 245 | complete, then parameter `its` contains either the iteration number at | ||
| 246 | which convergence was successfully reached, or failure was detected. | ||
| 247 | Call `EPSGetConvergedReason()` to determine if the solver converged or | ||
| 248 | failed and why. | ||
| 249 | |||
| 250 | Level: intermediate | ||
| 251 | |||
| 252 | .seealso: [](ch:eps), `EPSGetConvergedReason()`, `EPSSetTolerances()` | ||
| 253 | @*/ | ||
| 254 | 1564 | PetscErrorCode EPSGetIterationNumber(EPS eps,PetscInt *its) | |
| 255 | { | ||
| 256 |
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1564 | PetscFunctionBegin; |
| 257 |
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1564 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 258 |
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1564 | PetscAssertPointer(its,2); |
| 259 | 1564 | *its = eps->its; | |
| 260 |
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1564 | PetscFunctionReturn(PETSC_SUCCESS); |
| 261 | } | ||
| 262 | |||
| 263 | /*@ | ||
| 264 | EPSGetConverged - Gets the number of converged eigenpairs. | ||
| 265 | |||
| 266 | Not Collective | ||
| 267 | |||
| 268 | Input Parameter: | ||
| 269 | . eps - the linear eigensolver context | ||
| 270 | |||
| 271 | Output Parameter: | ||
| 272 | . nconv - number of converged eigenpairs | ||
| 273 | |||
| 274 | Notes: | ||
| 275 | This function should be called after `EPSSolve()` has finished. | ||
| 276 | |||
| 277 | The value `nconv` may be different from the number of requested solutions | ||
| 278 | `nev`, but not larger than `ncv`, see `EPSSetDimensions()`. | ||
| 279 | |||
| 280 | Level: beginner | ||
| 281 | |||
| 282 | .seealso: [](ch:eps), `EPSSetDimensions()`, `EPSSolve()`, `EPSGetEigenpair()` | ||
| 283 | @*/ | ||
| 284 | 6066 | PetscErrorCode EPSGetConverged(EPS eps,PetscInt *nconv) | |
| 285 | { | ||
| 286 |
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6066 | PetscFunctionBegin; |
| 287 |
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6066 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 288 |
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6066 | PetscAssertPointer(nconv,2); |
| 289 |
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6066 | EPSCheckSolved(eps,1); |
| 290 |
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6066 | PetscCall(EPS_GetActualConverged(eps,nconv)); |
| 291 |
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1165 | PetscFunctionReturn(PETSC_SUCCESS); |
| 292 | } | ||
| 293 | |||
| 294 | /*@ | ||
| 295 | EPSGetConvergedReason - Gets the reason why the `EPSSolve()` iteration was | ||
| 296 | stopped. | ||
| 297 | |||
| 298 | Not Collective | ||
| 299 | |||
| 300 | Input Parameter: | ||
| 301 | . eps - the linear eigensolver context | ||
| 302 | |||
| 303 | Output Parameter: | ||
| 304 | . reason - negative value indicates diverged, positive value converged, see | ||
| 305 | `EPSConvergedReason` for the possible values | ||
| 306 | |||
| 307 | Options Database Key: | ||
| 308 | . -eps_converged_reason - print reason for convergence/divergence, and number of iterations | ||
| 309 | |||
| 310 | Note: | ||
| 311 | If this routine is called before or doing the `EPSSolve()` the value of | ||
| 312 | `EPS_CONVERGED_ITERATING` is returned. | ||
| 313 | |||
| 314 | Level: intermediate | ||
| 315 | |||
| 316 | .seealso: [](ch:eps), `EPSSetTolerances()`, `EPSSolve()`, `EPSConvergedReason` | ||
| 317 | @*/ | ||
| 318 | 1513 | PetscErrorCode EPSGetConvergedReason(EPS eps,EPSConvergedReason *reason) | |
| 319 | { | ||
| 320 |
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1513 | PetscFunctionBegin; |
| 321 |
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1513 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 322 |
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1513 | PetscAssertPointer(reason,2); |
| 323 |
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1513 | EPSCheckSolved(eps,1); |
| 324 | 1513 | *reason = eps->reason; | |
| 325 |
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1513 | PetscFunctionReturn(PETSC_SUCCESS); |
| 326 | } | ||
| 327 | |||
| 328 | /*@ | ||
| 329 | EPSGetInvariantSubspace - Gets an orthonormal basis of the computed invariant | ||
| 330 | subspace. | ||
| 331 | |||
| 332 | Collective | ||
| 333 | |||
| 334 | Input Parameter: | ||
| 335 | . eps - the linear eigensolver context | ||
| 336 | |||
| 337 | Output Parameter: | ||
| 338 | . v - an array of vectors | ||
| 339 | |||
| 340 | Notes: | ||
| 341 | This function should be called after `EPSSolve()` has finished. | ||
| 342 | |||
| 343 | The user should provide in `v` an array of `nconv` vectors, where `nconv` | ||
| 344 | is the value returned by `EPSGetConverged()`. | ||
| 345 | |||
| 346 | The first $k$ vectors returned in `v` span an invariant subspace associated | ||
| 347 | with the first $k$ computed eigenvalues (note that this is not true if the | ||
| 348 | $k$-th eigenvalue is complex and matrix $A$ is real; in this case the first | ||
| 349 | $k+1$ vectors should be used). An invariant subspace $X$ of $A$ satisfies | ||
| 350 | $Ax\in X, \forall x\in X$ (a similar definition applies for generalized | ||
| 351 | eigenproblems). | ||
| 352 | |||
| 353 | Level: intermediate | ||
| 354 | |||
| 355 | .seealso: [](ch:eps), `EPSGetEigenpair()`, `EPSGetConverged()`, `EPSSolve()` | ||
| 356 | @*/ | ||
| 357 | 80 | PetscErrorCode EPSGetInvariantSubspace(EPS eps,Vec v[]) | |
| 358 | { | ||
| 359 | 80 | PetscInt i; | |
| 360 | 80 | BV V=eps->V; | |
| 361 | 80 | Vec w; | |
| 362 | |||
| 363 |
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80 | PetscFunctionBegin; |
| 364 |
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80 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 365 |
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80 | PetscAssertPointer(v,2); |
| 366 |
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80 | PetscValidHeaderSpecific(*v,VEC_CLASSID,2); |
| 367 |
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80 | EPSCheckSolved(eps,1); |
| 368 |
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80 | PetscCheck(eps->ishermitian || eps->state!=EPS_STATE_EIGENVECTORS,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"EPSGetInvariantSubspace must be called before EPSGetEigenpair,EPSGetEigenvector or EPSComputeError"); |
| 369 |
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80 | if (eps->balance!=EPS_BALANCE_NONE && eps->D) { |
| 370 |
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10 | PetscCall(BVDuplicateResize(eps->V,eps->nconv,&V)); |
| 371 |
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10 | PetscCall(BVSetActiveColumns(eps->V,0,eps->nconv)); |
| 372 |
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10 | PetscCall(BVCopy(eps->V,V)); |
| 373 |
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55 | for (i=0;i<eps->nconv;i++) { |
| 374 |
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45 | PetscCall(BVGetColumn(V,i,&w)); |
| 375 |
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45 | PetscCall(VecPointwiseDivide(w,w,eps->D)); |
| 376 |
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45 | PetscCall(BVRestoreColumn(V,i,&w)); |
| 377 | } | ||
| 378 |
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10 | PetscCall(BVOrthogonalize(V,NULL)); |
| 379 | } | ||
| 380 |
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625 | for (i=0;i<eps->nconv;i++) PetscCall(BVCopyVec(V,i,v[i])); |
| 381 |
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80 | if (eps->balance!=EPS_BALANCE_NONE && eps->D) PetscCall(BVDestroy(&V)); |
| 382 |
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16 | PetscFunctionReturn(PETSC_SUCCESS); |
| 383 | } | ||
| 384 | |||
| 385 | /*@ | ||
| 386 | EPSGetEigenpair - Gets the `i`-th solution of the eigenproblem as computed by | ||
| 387 | `EPSSolve()`. The solution consists in both the eigenvalue and the eigenvector. | ||
| 388 | |||
| 389 | Collective | ||
| 390 | |||
| 391 | Input Parameters: | ||
| 392 | + eps - the linear eigensolver context | ||
| 393 | - i - index of the solution | ||
| 394 | |||
| 395 | Output Parameters: | ||
| 396 | + eigr - real part of eigenvalue | ||
| 397 | . eigi - imaginary part of eigenvalue | ||
| 398 | . Vr - real part of eigenvector | ||
| 399 | - Vi - imaginary part of eigenvector | ||
| 400 | |||
| 401 | Notes: | ||
| 402 | It is allowed to pass `NULL` for `Vr` and `Vi`, if the eigenvector is not | ||
| 403 | required. Otherwise, the caller must provide valid `Vec` objects, i.e., | ||
| 404 | they must be created by the calling program with e.g. `MatCreateVecs()`. | ||
| 405 | |||
| 406 | If the eigenvalue is real, then `eigi` and `Vi` are set to zero. If PETSc is | ||
| 407 | configured with complex scalars the eigenvalue is stored | ||
| 408 | directly in `eigr` (`eigi` is set to zero) and the eigenvector in `Vr` (`Vi` is | ||
| 409 | set to zero). In both cases, the user can pass `NULL` in `eigi` and `Vi`. | ||
| 410 | |||
| 411 | The index `i` should be a value between 0 and `nconv`-1 (see `EPSGetConverged()`). | ||
| 412 | Eigenpairs are indexed according to the ordering criterion established | ||
| 413 | with `EPSSetWhichEigenpairs()`. | ||
| 414 | |||
| 415 | The 2-norm of the eigenvector is one unless the problem is generalized | ||
| 416 | Hermitian. In this case the eigenvector is normalized with respect to the | ||
| 417 | norm defined by the $B$ matrix. | ||
| 418 | |||
| 419 | In case of structured eigenproblems such as `EPS_BSE`, see the discussion about | ||
| 420 | [](#sec:structured-vectors). | ||
| 421 | |||
| 422 | Level: beginner | ||
| 423 | |||
| 424 | .seealso: [](ch:eps), `EPSGetEigenvalue()`, `EPSGetEigenvector()`, `EPSGetLeftEigenvector()`, `EPSSolve()`, `EPSGetConverged()`, `EPSSetWhichEigenpairs()`, `EPSGetInvariantSubspace()` | ||
| 425 | @*/ | ||
| 426 | 56416 | PetscErrorCode EPSGetEigenpair(EPS eps,PetscInt i,PetscScalar *eigr,PetscScalar *eigi,Vec Vr,Vec Vi) | |
| 427 | { | ||
| 428 | 56416 | PetscInt nconv; | |
| 429 | |||
| 430 |
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56416 | PetscFunctionBegin; |
| 431 |
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56416 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 432 |
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56416 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 433 |
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56416 | EPSCheckSolved(eps,1); |
| 434 |
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56416 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 435 |
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56416 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 436 |
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56416 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 437 |
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56416 | PetscCall(EPSGetEigenvalue(eps,i,eigr,eigi)); |
| 438 |
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56416 | if (Vr || Vi) PetscCall(EPSGetEigenvector(eps,i,Vr,Vi)); |
| 439 |
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11301 | PetscFunctionReturn(PETSC_SUCCESS); |
| 440 | } | ||
| 441 | |||
| 442 | /*@ | ||
| 443 | EPSGetEigenvalue - Gets the `i`-th eigenvalue as computed by `EPSSolve()`. | ||
| 444 | |||
| 445 | Not Collective | ||
| 446 | |||
| 447 | Input Parameters: | ||
| 448 | + eps - the linear eigensolver context | ||
| 449 | - i - index of the solution | ||
| 450 | |||
| 451 | Output Parameters: | ||
| 452 | + eigr - real part of eigenvalue | ||
| 453 | - eigi - imaginary part of eigenvalue | ||
| 454 | |||
| 455 | Notes: | ||
| 456 | If the eigenvalue is real, then `eigi` is set to zero. If PETSc is | ||
| 457 | configured with complex scalars the eigenvalue is stored | ||
| 458 | directly in `eigr` (`eigi` is set to zero). | ||
| 459 | |||
| 460 | The index `i` should be a value between 0 and `nconv`-1 (see `EPSGetConverged()`). | ||
| 461 | Eigenpairs are indexed according to the ordering criterion established | ||
| 462 | with `EPSSetWhichEigenpairs()`. | ||
| 463 | |||
| 464 | Level: beginner | ||
| 465 | |||
| 466 | .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConverged()`, `EPSSetWhichEigenpairs()`, `EPSGetEigenpair()` | ||
| 467 | @*/ | ||
| 468 | 110657 | PetscErrorCode EPSGetEigenvalue(EPS eps,PetscInt i,PetscScalar *eigr,PetscScalar *eigi) | |
| 469 | { | ||
| 470 | 110657 | PetscInt k,nconv; | |
| 471 | #if !defined(PETSC_USE_COMPLEX) | ||
| 472 | 57704 | PetscInt k2, iquad; | |
| 473 | #endif | ||
| 474 | |||
| 475 |
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110657 | PetscFunctionBegin; |
| 476 |
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110657 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 477 |
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110657 | EPSCheckSolved(eps,1); |
| 478 |
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110657 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 479 |
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110657 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 480 |
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110657 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 481 |
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110657 | if (nconv==eps->nconv) { |
| 482 | 101625 | k = eps->perm[i]; | |
| 483 | #if defined(PETSC_USE_COMPLEX) | ||
| 484 |
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49129 | if (eigr) *eigr = eps->eigr[k]; |
| 485 |
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49129 | if (eigi) *eigi = 0; |
| 486 | #else | ||
| 487 |
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52496 | if (eigr) *eigr = eps->eigr[k]; |
| 488 |
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52496 | if (eigi) *eigi = eps->eigi[k]; |
| 489 | #endif | ||
| 490 | } else { | ||
| 491 |
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9032 | PetscCheck(eps->problem_type==EPS_BSE || eps->problem_type==EPS_HAMILT || eps->problem_type==EPS_LREP,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Problem type should be BSE, Hamiltonian, or LREP"); |
| 492 |
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9032 | if (eps->problem_type==EPS_BSE || eps->problem_type==EPS_LREP) { |
| 493 | /* BSE problem, even index is +lambda, odd index is -lambda */ | ||
| 494 | 8512 | k = eps->perm[i/2]; | |
| 495 | #if defined(PETSC_USE_COMPLEX) | ||
| 496 |
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3824 | if (eigr) *eigr = (i%2)? -eps->eigr[k]: eps->eigr[k]; |
| 497 |
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3824 | if (eigi) *eigi = 0; |
| 498 | #else | ||
| 499 |
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4688 | if (eigr) *eigr = (i%2)? -eps->eigr[k]: eps->eigr[k]; |
| 500 |
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4688 | if (eigi) *eigi = eps->eigi[k]; |
| 501 | #endif | ||
| 502 |
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520 | } else if (eps->problem_type==EPS_HAMILT) { |
| 503 | /* Hamiltonian eigenproblem */ | ||
| 504 | 520 | k = eps->perm[i/2]; | |
| 505 | #if defined(PETSC_USE_COMPLEX) | ||
| 506 | ✗ | if (eigr) *eigr = (i%2)? -eps->eigr[k]: eps->eigr[k]; | |
| 507 | ✗ | if (eigi) *eigi = 0; | |
| 508 | #else | ||
| 509 |
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520 | if (eps->eigi[k]==0.0) { /* real eigenvalue */ |
| 510 | ✗ | if (eigr) *eigr = (i%2)? -eps->eigr[k]: eps->eigr[k]; | |
| 511 | ✗ | if (eigi) *eigi = 0.0; | |
| 512 |
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520 | } else if (eps->eigr[k]==0.0) { /* purely imaginary eigenvalue */ |
| 513 |
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120 | if (eigr) *eigr = 0.0; |
| 514 |
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120 | if (eigi) *eigi = (i%2)? -eps->eigi[k]: eps->eigi[k]; |
| 515 | } else { /* quadruple eigenvalue (-conj(lambda),-lambda,lambda,conj(lambda)) */ | ||
| 516 | 400 | iquad = i%2; /* index within the 4 values */ | |
| 517 |
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400 | if (i>1) { |
| 518 | 320 | k2 = eps->perm[(i-2)/2]; | |
| 519 |
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320 | if (eps->eigr[k]==eps->eigr[k2] && eps->eigi[k]==-eps->eigi[k2]) iquad += 2; |
| 520 | } | ||
| 521 |
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400 | if (eigr) *eigr = (iquad<2)? -eps->eigr[k]: eps->eigr[k]; |
| 522 |
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400 | if (eigi) *eigi = (iquad%3)? -eps->eigi[k]: eps->eigi[k]; |
| 523 | } | ||
| 524 | #endif | ||
| 525 | } | ||
| 526 | } | ||
| 527 |
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22530 | PetscFunctionReturn(PETSC_SUCCESS); |
| 528 | } | ||
| 529 | |||
| 530 | /*@ | ||
| 531 | EPSGetEigenvector - Gets the `i`-th right eigenvector as computed by `EPSSolve()`. | ||
| 532 | |||
| 533 | Collective | ||
| 534 | |||
| 535 | Input Parameters: | ||
| 536 | + eps - the linear eigensolver context | ||
| 537 | - i - index of the solution | ||
| 538 | |||
| 539 | Output Parameters: | ||
| 540 | + Vr - real part of eigenvector | ||
| 541 | - Vi - imaginary part of eigenvector | ||
| 542 | |||
| 543 | Notes: | ||
| 544 | The caller must provide valid `Vec` objects, i.e., they must be created | ||
| 545 | by the calling program with e.g. `MatCreateVecs()`. | ||
| 546 | |||
| 547 | If the corresponding eigenvalue is real, then `Vi` is set to zero. If PETSc is | ||
| 548 | configured with complex scalars the eigenvector is stored | ||
| 549 | directly in `Vr` (`Vi` is set to zero). In any case, the user can pass `NULL` in `Vr` | ||
| 550 | or `Vi` if one of them is not required. | ||
| 551 | |||
| 552 | The index `i` should be a value between 0 and `nconv`-1 (see `EPSGetConverged()`). | ||
| 553 | Eigenpairs are indexed according to the ordering criterion established | ||
| 554 | with `EPSSetWhichEigenpairs()`. | ||
| 555 | |||
| 556 | The 2-norm of the eigenvector is one unless the problem is generalized | ||
| 557 | Hermitian. In this case the eigenvector is normalized with respect to the | ||
| 558 | norm defined by the $B$ matrix. | ||
| 559 | |||
| 560 | In case of structured eigenproblems such as `EPS_BSE`, see the discussion about | ||
| 561 | [](#sec:structured-vectors). | ||
| 562 | |||
| 563 | Level: beginner | ||
| 564 | |||
| 565 | .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConverged()`, `EPSSetWhichEigenpairs()`, `EPSGetEigenpair()`, `EPSGetLeftEigenvector()` | ||
| 566 | @*/ | ||
| 567 | 85249 | PetscErrorCode EPSGetEigenvector(EPS eps,PetscInt i,Vec Vr,Vec Vi) | |
| 568 | { | ||
| 569 | 85249 | PetscInt nconv; | |
| 570 | |||
| 571 |
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85249 | PetscFunctionBegin; |
| 572 |
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85249 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 573 |
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85249 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 574 |
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85249 | if (Vr) { PetscValidHeaderSpecific(Vr,VEC_CLASSID,3); PetscCheckSameComm(eps,1,Vr,3); } |
| 575 |
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85249 | if (Vi) { PetscValidHeaderSpecific(Vi,VEC_CLASSID,4); PetscCheckSameComm(eps,1,Vi,4); } |
| 576 |
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85249 | EPSCheckSolved(eps,1); |
| 577 |
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85249 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 578 |
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85249 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 579 |
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85249 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 580 |
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85249 | PetscCall(EPSComputeVectors(eps)); |
| 581 |
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85249 | PetscCall(EPS_GetEigenvector(eps,eps->V,i,Vr,Vi)); |
| 582 |
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15200 | PetscFunctionReturn(PETSC_SUCCESS); |
| 583 | } | ||
| 584 | |||
| 585 | /*@ | ||
| 586 | EPSGetLeftEigenvector - Gets the `i`-th left eigenvector as computed by `EPSSolve()`. | ||
| 587 | |||
| 588 | Collective | ||
| 589 | |||
| 590 | Input Parameters: | ||
| 591 | + eps - the linear eigensolver context | ||
| 592 | - i - index of the solution | ||
| 593 | |||
| 594 | Output Parameters: | ||
| 595 | + Wr - real part of left eigenvector | ||
| 596 | - Wi - imaginary part of left eigenvector | ||
| 597 | |||
| 598 | Notes: | ||
| 599 | The caller must provide valid `Vec` objects, i.e., they must be created | ||
| 600 | by the calling program with e.g. `MatCreateVecs()`. | ||
| 601 | |||
| 602 | If the corresponding eigenvalue is real, then `Wi` is set to zero. If PETSc is | ||
| 603 | configured with complex scalars the eigenvector is stored directly in `Wr` | ||
| 604 | (`Wi` is set to zero). In any case, the user can pass `NULL` in `Wr` or `Wi` if | ||
| 605 | one of them is not required. | ||
| 606 | |||
| 607 | The index `i` should be a value between 0 and `nconv`-1 (see `EPSGetConverged()`). | ||
| 608 | Eigensolutions are indexed according to the ordering criterion established | ||
| 609 | with `EPSSetWhichEigenpairs()`. | ||
| 610 | |||
| 611 | Left eigenvectors are available only if the `twosided` flag was set, see | ||
| 612 | `EPSSetTwoSided()`. | ||
| 613 | |||
| 614 | In case of structured eigenproblems such as `EPS_BSE`, see the discussion about | ||
| 615 | [](#sec:structured-vectors). | ||
| 616 | |||
| 617 | Level: intermediate | ||
| 618 | |||
| 619 | .seealso: [](ch:eps), `EPSGetEigenvector()`, `EPSGetConverged()`, `EPSSetWhichEigenpairs()`, `EPSSetTwoSided()` | ||
| 620 | @*/ | ||
| 621 | 8453 | PetscErrorCode EPSGetLeftEigenvector(EPS eps,PetscInt i,Vec Wr,Vec Wi) | |
| 622 | { | ||
| 623 | 8453 | PetscInt nconv; | |
| 624 | 8453 | PetscBool trivial,lrepreduced=PETSC_FALSE; | |
| 625 | 8453 | Mat H; | |
| 626 | 8453 | IS is[2]; | |
| 627 | 8453 | Vec v0,v1,z,z0,z1; | |
| 628 | |||
| 629 |
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8453 | PetscFunctionBegin; |
| 630 |
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8453 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 631 |
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8453 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 632 |
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8453 | if (Wr) { PetscValidHeaderSpecific(Wr,VEC_CLASSID,3); PetscCheckSameComm(eps,1,Wr,3); } |
| 633 |
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8453 | if (Wi) { PetscValidHeaderSpecific(Wi,VEC_CLASSID,4); PetscCheckSameComm(eps,1,Wi,4); } |
| 634 |
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8453 | EPSCheckSolved(eps,1); |
| 635 |
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8453 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 636 |
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|
8453 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 637 |
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8453 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 638 | |||
| 639 |
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|
8453 | trivial = (eps->problem_type==EPS_HEP || eps->problem_type==EPS_GHEP || eps->problem_type==EPS_BSE || eps->problem_type==EPS_LREP)? PETSC_TRUE: PETSC_FALSE; |
| 640 |
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8453 | if (!trivial) PetscCheck(eps->twosided,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must request left vectors with EPSSetTwoSided"); |
| 641 | |||
| 642 |
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8453 | PetscCall(EPSComputeVectors(eps)); |
| 643 |
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8453 | if (trivial) { |
| 644 |
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7560 | PetscCall(EPS_GetEigenvector(eps,eps->V,i,Wr,Wi)); |
| 645 |
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|
7560 | PetscCall(STGetMatrix(eps->st,0,&H)); |
| 646 |
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|
7560 | if (eps->problem_type==EPS_LREP) PetscCall(SlepcCheckMatLREPReduced(H,&lrepreduced)); |
| 647 |
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|
7560 | if (eps->problem_type==EPS_BSE || !lrepreduced) { /* change sign of bottom part of the vector */ |
| 648 |
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6472 | PetscCall(MatNestGetISs(H,is,NULL)); |
| 649 |
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6472 | if (Wr) { |
| 650 |
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6472 | PetscCall(VecGetSubVector(Wr,is[1],&v1)); |
| 651 |
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6472 | PetscCall(VecScale(v1,-1.0)); |
| 652 |
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6472 | PetscCall(VecRestoreSubVector(Wr,is[1],&v1)); |
| 653 | } | ||
| 654 | #if !defined(PETSC_USE_COMPLEX) | ||
| 655 |
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|
3764 | if (Wi) { |
| 656 | ✗ | PetscCall(VecGetSubVector(Wi,is[1],&v1)); | |
| 657 | ✗ | PetscCall(VecScale(v1,-1.0)); | |
| 658 | ✗ | PetscCall(VecRestoreSubVector(Wi,is[1],&v1)); | |
| 659 | } | ||
| 660 | #endif | ||
| 661 |
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1088 | } else if (eps->problem_type==EPS_LREP) { /* swap the two parts of the vector */ |
| 662 |
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1088 | if (Wr) { |
| 663 |
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1088 | PetscCall(VecDuplicate(Wr,&z)); |
| 664 |
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1088 | PetscCall(VecCopy(Wr,z)); |
| 665 |
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1088 | PetscCall(MatNestGetISs(H,is,NULL)); |
| 666 |
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1088 | PetscCall(VecGetSubVector(Wr,is[0],&v0)); |
| 667 |
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1088 | PetscCall(VecGetSubVector(Wr,is[1],&v1)); |
| 668 |
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1088 | PetscCall(VecGetSubVector(z,is[0],&z0)); |
| 669 |
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1088 | PetscCall(VecGetSubVector(z,is[1],&z1)); |
| 670 |
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1088 | PetscCall(VecCopy(z0,v1)); |
| 671 |
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1088 | PetscCall(VecCopy(z1,v0)); |
| 672 |
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1088 | PetscCall(VecRestoreSubVector(Wr,is[0],&v0)); |
| 673 |
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1088 | PetscCall(VecRestoreSubVector(Wr,is[1],&v1)); |
| 674 |
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1088 | PetscCall(VecRestoreSubVector(z,is[0],&z0)); |
| 675 |
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1088 | PetscCall(VecRestoreSubVector(z,is[1],&z1)); |
| 676 |
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1088 | PetscCall(VecDestroy(&z)); |
| 677 | } | ||
| 678 | } | ||
| 679 | } else { | ||
| 680 |
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893 | PetscCall(EPS_GetEigenvector(eps,eps->W,i,Wr,Wi)); |
| 681 | } | ||
| 682 |
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|
1459 | PetscFunctionReturn(PETSC_SUCCESS); |
| 683 | } | ||
| 684 | |||
| 685 | /*@ | ||
| 686 | EPSGetErrorEstimate - Returns the error estimate associated to the `i`-th | ||
| 687 | computed eigenpair. | ||
| 688 | |||
| 689 | Not Collective | ||
| 690 | |||
| 691 | Input Parameters: | ||
| 692 | + eps - the linear eigensolver context | ||
| 693 | - i - index of eigenpair | ||
| 694 | |||
| 695 | Output Parameter: | ||
| 696 | . errest - the error estimate | ||
| 697 | |||
| 698 | Note: | ||
| 699 | This is the error estimate used internally by the eigensolver. The actual | ||
| 700 | error bound can be computed with `EPSComputeError()`. See discussion at | ||
| 701 | section [](#sec:errbnd). | ||
| 702 | |||
| 703 | Level: advanced | ||
| 704 | |||
| 705 | .seealso: [](ch:eps), [](#sec:errbnd), `EPSComputeError()` | ||
| 706 | @*/ | ||
| 707 | 612 | PetscErrorCode EPSGetErrorEstimate(EPS eps,PetscInt i,PetscReal *errest) | |
| 708 | { | ||
| 709 | 612 | PetscInt nconv; | |
| 710 | |||
| 711 |
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612 | PetscFunctionBegin; |
| 712 |
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612 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 713 |
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612 | PetscAssertPointer(errest,3); |
| 714 |
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612 | EPSCheckSolved(eps,1); |
| 715 |
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612 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 716 |
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612 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 717 |
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612 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 718 |
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612 | if (nconv==eps->nconv) { |
| 719 | 612 | *errest = eps->errest[eps->perm[i]]; | |
| 720 | } else { | ||
| 721 | ✗ | PetscCheck(eps->problem_type==EPS_BSE,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Problem type should be BSE"); | |
| 722 | /* BSE problem, even index is +lambda, odd index is -lambda, assume both have same error */ | ||
| 723 | ✗ | *errest = eps->errest[eps->perm[i/2]]; | |
| 724 | } | ||
| 725 |
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|
116 | PetscFunctionReturn(PETSC_SUCCESS); |
| 726 | } | ||
| 727 | |||
| 728 | /* | ||
| 729 | EPSComputeResidualNorm_Private - Computes the norm of the residual vector | ||
| 730 | associated with an eigenpair. | ||
| 731 | |||
| 732 | Input Parameters: | ||
| 733 | trans - whether A' must be used instead of A | ||
| 734 | kr,ki - eigenvalue | ||
| 735 | xr,xi - eigenvector | ||
| 736 | z - three work vectors (the second one not referenced in complex scalars) | ||
| 737 | */ | ||
| 738 | 45769 | PetscErrorCode EPSComputeResidualNorm_Private(EPS eps,PetscBool trans,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm) | |
| 739 | { | ||
| 740 | 45769 | PetscInt nmat; | |
| 741 | 45769 | Mat A,B; | |
| 742 | 45769 | Vec u,w; | |
| 743 | 45769 | PetscScalar alpha; | |
| 744 | #if !defined(PETSC_USE_COMPLEX) | ||
| 745 | 23516 | Vec v; | |
| 746 | 23516 | PetscReal ni,nr; | |
| 747 | #endif | ||
| 748 |
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45769 | PetscErrorCode (*matmult)(Mat,Vec,Vec) = trans? MatMultHermitianTranspose: MatMult; |
| 749 | |||
| 750 |
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45769 | PetscFunctionBegin; |
| 751 | 45769 | u = z[0]; w = z[2]; | |
| 752 |
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45769 | PetscCall(STGetNumMatrices(eps->st,&nmat)); |
| 753 |
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45769 | PetscCall(STGetMatrix(eps->st,0,&A)); |
| 754 |
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45769 | if (nmat>1) PetscCall(STGetMatrix(eps->st,1,&B)); |
| 755 | |||
| 756 | #if !defined(PETSC_USE_COMPLEX) | ||
| 757 | 23516 | v = z[1]; | |
| 758 |
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23516 | if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON)) { |
| 759 | #endif | ||
| 760 |
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44599 | PetscCall((*matmult)(A,xr,u)); /* u=A*x */ |
| 761 |
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44599 | if (PetscAbsScalar(kr) > PETSC_MACHINE_EPSILON) { |
| 762 |
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44599 | if (nmat>1) PetscCall((*matmult)(B,xr,w)); |
| 763 |
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22828 | else PetscCall(VecCopy(xr,w)); /* w=B*x */ |
| 764 |
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44599 | alpha = trans? -PetscConj(kr): -kr; |
| 765 |
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44599 | PetscCall(VecAXPY(u,alpha,w)); /* u=A*x-k*B*x */ |
| 766 | } | ||
| 767 |
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|
44599 | PetscCall(VecNorm(u,NORM_2,norm)); |
| 768 | #if !defined(PETSC_USE_COMPLEX) | ||
| 769 | } else { | ||
| 770 |
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1170 | PetscCall((*matmult)(A,xr,u)); /* u=A*xr */ |
| 771 |
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1170 | if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) { |
| 772 |
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1170 | if (nmat>1) PetscCall((*matmult)(B,xr,v)); |
| 773 |
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1156 | else PetscCall(VecCopy(xr,v)); /* v=B*xr */ |
| 774 |
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1170 | PetscCall(VecAXPY(u,-kr,v)); /* u=A*xr-kr*B*xr */ |
| 775 |
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1170 | if (nmat>1) PetscCall((*matmult)(B,xi,w)); |
| 776 |
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1156 | else PetscCall(VecCopy(xi,w)); /* w=B*xi */ |
| 777 |
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1170 | PetscCall(VecAXPY(u,trans?-ki:ki,w)); /* u=A*xr-kr*B*xr+ki*B*xi */ |
| 778 | } | ||
| 779 |
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1170 | PetscCall(VecNorm(u,NORM_2,&nr)); |
| 780 |
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1170 | PetscCall((*matmult)(A,xi,u)); /* u=A*xi */ |
| 781 |
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1170 | if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) { |
| 782 |
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1170 | PetscCall(VecAXPY(u,-kr,w)); /* u=A*xi-kr*B*xi */ |
| 783 |
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1170 | PetscCall(VecAXPY(u,trans?ki:-ki,v)); /* u=A*xi-kr*B*xi-ki*B*xr */ |
| 784 | } | ||
| 785 |
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|
1170 | PetscCall(VecNorm(u,NORM_2,&ni)); |
| 786 | 1170 | *norm = SlepcAbsEigenvalue(nr,ni); | |
| 787 | } | ||
| 788 | #endif | ||
| 789 |
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|
9041 | PetscFunctionReturn(PETSC_SUCCESS); |
| 790 | } | ||
| 791 | |||
| 792 | /*@ | ||
| 793 | EPSComputeError - Computes the error (based on the residual norm) associated | ||
| 794 | with the `i`-th computed eigenpair. | ||
| 795 | |||
| 796 | Collective | ||
| 797 | |||
| 798 | Input Parameters: | ||
| 799 | + eps - the linear eigensolver context | ||
| 800 | . i - the solution index | ||
| 801 | - type - the type of error to compute, see `EPSErrorType` | ||
| 802 | |||
| 803 | Output Parameter: | ||
| 804 | . error - the error | ||
| 805 | |||
| 806 | Notes: | ||
| 807 | The error can be computed in various ways, all of them based on the residual | ||
| 808 | norm $\|Ax-\lambda Bx\|_2$ where $(\lambda,x)$ is the approximate eigenpair. | ||
| 809 | |||
| 810 | If the computation of left eigenvectors was enabled with `EPSSetTwoSided()`, | ||
| 811 | then the error will be computed using the maximum of the value above and | ||
| 812 | the left residual norm $\|y^*A-\lambda y^*B\|_2$, where $y$ is the approximate left | ||
| 813 | eigenvector. | ||
| 814 | |||
| 815 | Level: beginner | ||
| 816 | |||
| 817 | .seealso: [](ch:eps), `EPSErrorType`, `EPSSolve()`, `EPSGetErrorEstimate()`, `EPSSetTwoSided()` | ||
| 818 | @*/ | ||
| 819 | 42384 | PetscErrorCode EPSComputeError(EPS eps,PetscInt i,EPSErrorType type,PetscReal *error) | |
| 820 | { | ||
| 821 | 42384 | Mat A,B; | |
| 822 | 42384 | Vec xr,xi,w[3]; | |
| 823 | 42384 | PetscReal t,vecnorm=1.0,errorl; | |
| 824 | 42384 | PetscScalar kr,ki; | |
| 825 | 42384 | PetscBool flg; | |
| 826 | |||
| 827 |
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42384 | PetscFunctionBegin; |
| 828 |
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42384 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 829 |
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42384 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 830 |
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|
42384 | PetscValidLogicalCollectiveEnum(eps,type,3); |
| 831 |
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42384 | PetscAssertPointer(error,4); |
| 832 |
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42384 | EPSCheckSolved(eps,1); |
| 833 | |||
| 834 | /* allocate work vectors */ | ||
| 835 | #if defined(PETSC_USE_COMPLEX) | ||
| 836 |
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|
20498 | PetscCall(EPSSetWorkVecs(eps,3)); |
| 837 | 20498 | xi = NULL; | |
| 838 | 20498 | w[1] = NULL; | |
| 839 | #else | ||
| 840 |
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21886 | PetscCall(EPSSetWorkVecs(eps,5)); |
| 841 | 21886 | xi = eps->work[3]; | |
| 842 | 21886 | w[1] = eps->work[4]; | |
| 843 | #endif | ||
| 844 | 42384 | xr = eps->work[0]; | |
| 845 | 42384 | w[0] = eps->work[1]; | |
| 846 | 42384 | w[2] = eps->work[2]; | |
| 847 | |||
| 848 | /* compute residual norm */ | ||
| 849 |
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42384 | PetscCall(EPSGetEigenpair(eps,i,&kr,&ki,xr,xi)); |
| 850 |
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42384 | PetscCall(EPSComputeResidualNorm_Private(eps,PETSC_FALSE,kr,ki,xr,xi,w,error)); |
| 851 | |||
| 852 | /* compute 2-norm of eigenvector */ | ||
| 853 |
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|
42384 | if (eps->problem_type==EPS_GHEP) PetscCall(VecNorm(xr,NORM_2,&vecnorm)); |
| 854 | |||
| 855 | /* if two-sided, compute left residual norm and take the maximum */ | ||
| 856 |
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42384 | if (eps->twosided) { |
| 857 |
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450 | PetscCall(EPSGetLeftEigenvector(eps,i,xr,xi)); |
| 858 |
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450 | PetscCall(EPSComputeResidualNorm_Private(eps,PETSC_TRUE,kr,ki,xr,xi,w,&errorl)); |
| 859 |
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|
667 | *error = PetscMax(*error,errorl); |
| 860 | } | ||
| 861 | |||
| 862 | /* compute error */ | ||
| 863 |
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42384 | switch (type) { |
| 864 | case EPS_ERROR_ABSOLUTE: | ||
| 865 | break; | ||
| 866 | 24934 | case EPS_ERROR_RELATIVE: | |
| 867 | 24934 | *error /= SlepcAbsEigenvalue(kr,ki)*vecnorm; | |
| 868 | 24934 | break; | |
| 869 | 17198 | case EPS_ERROR_BACKWARD: | |
| 870 | /* initialization of matrix norms */ | ||
| 871 |
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17198 | if (!eps->nrma) { |
| 872 |
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395 | PetscCall(STGetMatrix(eps->st,0,&A)); |
| 873 |
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395 | PetscCall(MatHasOperation(A,MATOP_NORM,&flg)); |
| 874 |
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395 | PetscCheck(flg,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation"); |
| 875 |
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395 | PetscCall(MatNorm(A,NORM_INFINITY,&eps->nrma)); |
| 876 | } | ||
| 877 |
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17198 | if (eps->isgeneralized) { |
| 878 |
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16945 | if (!eps->nrmb) { |
| 879 |
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336 | PetscCall(STGetMatrix(eps->st,1,&B)); |
| 880 |
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336 | PetscCall(MatHasOperation(B,MATOP_NORM,&flg)); |
| 881 |
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336 | PetscCheck(flg,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation"); |
| 882 |
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336 | PetscCall(MatNorm(B,NORM_INFINITY,&eps->nrmb)); |
| 883 | } | ||
| 884 | 253 | } else eps->nrmb = 1.0; | |
| 885 | 17198 | t = SlepcAbsEigenvalue(kr,ki); | |
| 886 | 17198 | *error /= (eps->nrma+t*eps->nrmb)*vecnorm; | |
| 887 | 17198 | break; | |
| 888 | ✗ | default: | |
| 889 | ✗ | SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type"); | |
| 890 | } | ||
| 891 |
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|
8325 | PetscFunctionReturn(PETSC_SUCCESS); |
| 892 | } | ||
| 893 | |||
| 894 | /* | ||
| 895 | EPSGetStartVector - Generate a suitable vector to be used as the starting vector | ||
| 896 | for the recurrence that builds the right subspace. | ||
| 897 | |||
| 898 | Collective | ||
| 899 | |||
| 900 | Input Parameters: | ||
| 901 | + eps - the linear eigensolver context | ||
| 902 | - i - iteration number | ||
| 903 | |||
| 904 | Output Parameter: | ||
| 905 | . breakdown - flag indicating that a breakdown has occurred | ||
| 906 | |||
| 907 | Notes: | ||
| 908 | The start vector is computed from another vector: for the first step (i=0), | ||
| 909 | the first initial vector is used (see EPSSetInitialSpace()); otherwise a random | ||
| 910 | vector is created. Then this vector is forced to be in the range of OP (only | ||
| 911 | for generalized definite problems) and orthonormalized with respect to all | ||
| 912 | V-vectors up to i-1. The resulting vector is placed in V[i]. | ||
| 913 | |||
| 914 | The flag breakdown is set to true if either i=0 and the vector belongs to the | ||
| 915 | deflation space, or i>0 and the vector is linearly dependent with respect | ||
| 916 | to the V-vectors. | ||
| 917 | */ | ||
| 918 | 7089 | PetscErrorCode EPSGetStartVector(EPS eps,PetscInt i,PetscBool *breakdown) | |
| 919 | { | ||
| 920 | 7089 | PetscReal norm; | |
| 921 | 7089 | PetscBool lindep; | |
| 922 | 7089 | Vec w,z; | |
| 923 | |||
| 924 |
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7089 | PetscFunctionBegin; |
| 925 |
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7089 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 926 |
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|
7089 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 927 | |||
| 928 | /* For the first step, use the first initial vector, otherwise a random one */ | ||
| 929 |
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7089 | if (i>0 || eps->nini==0) PetscCall(BVSetRandomColumn(eps->V,i)); |
| 930 | |||
| 931 | /* Force the vector to be in the range of OP for generalized problems with B-inner product */ | ||
| 932 |
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7089 | if (eps->ispositive || (eps->isgeneralized && eps->ishermitian)) { |
| 933 |
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1033 | PetscCall(BVCreateVec(eps->V,&w)); |
| 934 |
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1033 | PetscCall(BVCopyVec(eps->V,i,w)); |
| 935 |
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1033 | PetscCall(BVGetColumn(eps->V,i,&z)); |
| 936 |
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1033 | PetscCall(STApply(eps->st,w,z)); |
| 937 |
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1033 | PetscCall(BVRestoreColumn(eps->V,i,&z)); |
| 938 |
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1033 | PetscCall(VecDestroy(&w)); |
| 939 | } | ||
| 940 | |||
| 941 | /* Orthonormalize the vector with respect to previous vectors */ | ||
| 942 |
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7089 | PetscCall(BVOrthogonalizeColumn(eps->V,i,NULL,&norm,&lindep)); |
| 943 |
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7089 | if (breakdown) *breakdown = lindep; |
| 944 |
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6732 | else if (lindep || norm == 0.0) { |
| 945 | ✗ | PetscCheck(i,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Initial vector is zero or belongs to the deflation space"); | |
| 946 | ✗ | PetscCheck(!i,PetscObjectComm((PetscObject)eps),PETSC_ERR_CONV_FAILED,"Unable to generate more start vectors"); | |
| 947 | } | ||
| 948 |
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7089 | PetscCall(BVScaleColumn(eps->V,i,1.0/norm)); |
| 949 |
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1370 | PetscFunctionReturn(PETSC_SUCCESS); |
| 950 | } | ||
| 951 | |||
| 952 | /* | ||
| 953 | EPSGetLeftStartVector - Generate a suitable vector to be used as the left starting | ||
| 954 | vector for the recurrence that builds the left subspace. See EPSGetStartVector(). | ||
| 955 | */ | ||
| 956 | 254 | PetscErrorCode EPSGetLeftStartVector(EPS eps,PetscInt i,PetscBool *breakdown) | |
| 957 | { | ||
| 958 | 254 | PetscReal norm; | |
| 959 | 254 | PetscBool lindep; | |
| 960 | 254 | Vec w,z; | |
| 961 | |||
| 962 |
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254 | PetscFunctionBegin; |
| 963 |
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254 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 964 |
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254 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 965 | |||
| 966 | /* For the first step, use the first initial vector, otherwise a random one */ | ||
| 967 |
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254 | if (i>0 || eps->ninil==0) PetscCall(BVSetRandomColumn(eps->W,i)); |
| 968 | |||
| 969 | /* Force the vector to be in the range of OP' for generalized problems with B-inner product */ | ||
| 970 |
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254 | if (eps->ispositive || (eps->isgeneralized && eps->ishermitian)) { |
| 971 |
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13 | PetscCall(BVCreateVec(eps->W,&w)); |
| 972 |
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13 | PetscCall(BVCopyVec(eps->W,i,w)); |
| 973 |
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13 | PetscCall(BVGetColumn(eps->W,i,&z)); |
| 974 |
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13 | PetscCall(STApplyHermitianTranspose(eps->st,w,z)); |
| 975 |
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13 | PetscCall(BVRestoreColumn(eps->W,i,&z)); |
| 976 |
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13 | PetscCall(VecDestroy(&w)); |
| 977 | } | ||
| 978 | |||
| 979 | /* Orthonormalize the vector with respect to previous vectors */ | ||
| 980 |
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254 | PetscCall(BVOrthogonalizeColumn(eps->W,i,NULL,&norm,&lindep)); |
| 981 |
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254 | if (breakdown) *breakdown = lindep; |
| 982 |
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|
199 | else if (lindep || norm == 0.0) { |
| 983 | ✗ | PetscCheck(i,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Left initial vector is zero"); | |
| 984 | ✗ | PetscCheck(!i,PetscObjectComm((PetscObject)eps),PETSC_ERR_CONV_FAILED,"Unable to generate more left start vectors"); | |
| 985 | } | ||
| 986 |
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254 | PetscCall(BVScaleColumn(eps->W,i,1.0/norm)); |
| 987 |
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50 | PetscFunctionReturn(PETSC_SUCCESS); |
| 988 | } | ||
| 989 |