| 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 | 85048 | PetscErrorCode EPSComputeVectors(EPS eps) | |
| 19 | { | ||
| 20 |
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85048 | PetscFunctionBegin; |
| 21 |
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85048 | EPSCheckSolved(eps,1); |
| 22 |
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85048 | if (eps->state==EPS_STATE_SOLVED) PetscTryTypeMethod(eps,computevectors); |
| 23 | 85048 | eps->state = EPS_STATE_EIGENVECTORS; | |
| 24 |
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85048 | PetscFunctionReturn(PETSC_SUCCESS); |
| 25 | } | ||
| 26 | |||
| 27 | 9545 | static PetscErrorCode EPSComputeValues(EPS eps) | |
| 28 | { | ||
| 29 | 9545 | PetscBool injective,iscomp,isfilter; | |
| 30 | 9545 | PetscInt i,n,aux,nconv0; | |
| 31 | 9545 | Mat A,B=NULL,G,Z; | |
| 32 | |||
| 33 |
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9545 | PetscFunctionBegin; |
| 34 |
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9545 | switch (eps->categ) { |
| 35 | 7425 | case EPS_CATEGORY_KRYLOV: | |
| 36 | case EPS_CATEGORY_OTHER: | ||
| 37 |
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7425 | PetscCall(STIsInjective(eps->st,&injective)); |
| 38 |
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7425 | if (injective) { |
| 39 | /* one-to-one mapping: backtransform eigenvalues */ | ||
| 40 |
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7209 | 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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1896 | for (i=0;i<eps->nconv;i++) { |
| 72 |
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1690 | if (PetscRealPart(eps->eigr[eps->perm[i]])<eps->inta || PetscRealPart(eps->eigr[eps->perm[i]])>eps->intb) { |
| 73 | ✗ | eps->nconv--; | |
| 74 | ✗ | 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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1840 | PetscFunctionReturn(PETSC_SUCCESS); |
| 87 | } | ||
| 88 | |||
| 89 | /*@ | ||
| 90 | EPSSolve - Solves the eigensystem. | ||
| 91 | |||
| 92 | Collective | ||
| 93 | |||
| 94 | Input Parameter: | ||
| 95 | . eps - eigensolver context obtained from EPSCreate() | ||
| 96 | |||
| 97 | Options Database Keys: | ||
| 98 | + -eps_view - print information about the solver used | ||
| 99 | . -eps_view_mat0 - view the first matrix (A) | ||
| 100 | . -eps_view_mat1 - view the second matrix (B) | ||
| 101 | . -eps_view_vectors - view the computed eigenvectors | ||
| 102 | . -eps_view_values - view the computed eigenvalues | ||
| 103 | . -eps_converged_reason - print reason for convergence, and number of iterations | ||
| 104 | . -eps_error_absolute - print absolute errors of each eigenpair | ||
| 105 | . -eps_error_relative - print relative errors of each eigenpair | ||
| 106 | - -eps_error_backward - print backward errors of each eigenpair | ||
| 107 | |||
| 108 | Notes: | ||
| 109 | All the command-line options listed above admit an optional argument specifying | ||
| 110 | the viewer type and options. For instance, use '-eps_view_mat0 binary:amatrix.bin' | ||
| 111 | to save the A matrix to a binary file, '-eps_view_values draw' to draw the computed | ||
| 112 | eigenvalues graphically, or '-eps_error_relative :myerr.m:ascii_matlab' to save | ||
| 113 | the errors in a file that can be executed in Matlab. | ||
| 114 | |||
| 115 | Level: beginner | ||
| 116 | |||
| 117 | .seealso: EPSCreate(), EPSSetUp(), EPSDestroy(), EPSSetTolerances() | ||
| 118 | @*/ | ||
| 119 | 9545 | PetscErrorCode EPSSolve(EPS eps) | |
| 120 | { | ||
| 121 | 9545 | PetscInt i; | |
| 122 | 9545 | PetscBool hasname; | |
| 123 | 9545 | STMatMode matmode; | |
| 124 | 9545 | Mat A,B; | |
| 125 | |||
| 126 |
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9545 | PetscFunctionBegin; |
| 127 |
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9545 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 128 |
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9545 | if (eps->state>=EPS_STATE_SOLVED) PetscFunctionReturn(PETSC_SUCCESS); |
| 129 |
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9545 | PetscCall(PetscLogEventBegin(EPS_Solve,eps,0,0,0)); |
| 130 | |||
| 131 | /* Call setup */ | ||
| 132 |
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9545 | PetscCall(EPSSetUp(eps)); |
| 133 | |||
| 134 | /* Safeguard for matrices of size 0 */ | ||
| 135 |
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9545 | if (eps->n == 0) { |
| 136 | ✗ | eps->nconv = 0; | |
| 137 | ✗ | eps->reason = EPS_CONVERGED_TOL; | |
| 138 | ✗ | eps->state = EPS_STATE_SOLVED; | |
| 139 | ✗ | PetscFunctionReturn(PETSC_SUCCESS); | |
| 140 | } | ||
| 141 | |||
| 142 | 9545 | eps->nconv = 0; | |
| 143 | 9545 | eps->its = 0; | |
| 144 |
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302334 | for (i=0;i<eps->ncv;i++) { |
| 145 | 292789 | eps->eigr[i] = 0.0; | |
| 146 | 292789 | eps->eigi[i] = 0.0; | |
| 147 | 292789 | eps->errest[i] = 0.0; | |
| 148 | 292789 | eps->perm[i] = i; | |
| 149 | } | ||
| 150 |
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9545 | PetscCall(EPSViewFromOptions(eps,NULL,"-eps_view_pre")); |
| 151 |
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9545 | PetscCall(RGViewFromOptions(eps->rg,NULL,"-rg_view")); |
| 152 | |||
| 153 | /* Call solver */ | ||
| 154 |
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9545 | PetscUseTypeMethod(eps,solve); |
| 155 |
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9545 | PetscCheck(eps->reason,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Internal error, solver returned without setting converged reason"); |
| 156 | 9545 | eps->state = EPS_STATE_SOLVED; | |
| 157 | |||
| 158 | /* Only the first nconv columns contain useful information (except in CISS) */ | ||
| 159 |
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9545 | PetscCall(BVSetActiveColumns(eps->V,0,eps->nconv)); |
| 160 |
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9545 | if (eps->twosided) PetscCall(BVSetActiveColumns(eps->W,0,eps->nconv)); |
| 161 | |||
| 162 | /* If inplace, purify eigenvectors before reverting operator */ | ||
| 163 |
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9545 | PetscCall(STGetMatMode(eps->st,&matmode)); |
| 164 |
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9545 | if (matmode == ST_MATMODE_INPLACE && eps->ispositive) PetscCall(EPSComputeVectors(eps)); |
| 165 |
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9545 | PetscCall(STPostSolve(eps->st)); |
| 166 | |||
| 167 | /* Map eigenvalues back to the original problem if appropriate */ | ||
| 168 |
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9545 | PetscCall(EPSComputeValues(eps)); |
| 169 | |||
| 170 | #if !defined(PETSC_USE_COMPLEX) | ||
| 171 | /* Reorder conjugate eigenvalues (positive imaginary first) */ | ||
| 172 |
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55318 | for (i=0;i<eps->nconv-1;i++) { |
| 173 |
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50350 | if (eps->eigi[i] != 0 && (eps->problem_type!=EPS_HAMILT || eps->eigr[i]!=0)) { |
| 174 | /* conjugate eigenvalues */ | ||
| 175 |
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926 | if (eps->eigi[i] < 0) { |
| 176 | 116 | eps->eigi[i] = -eps->eigi[i]; | |
| 177 | 116 | eps->eigi[i+1] = -eps->eigi[i+1]; | |
| 178 | /* the next correction only works with eigenvectors */ | ||
| 179 |
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116 | PetscCall(EPSComputeVectors(eps)); |
| 180 |
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116 | PetscCall(BVScaleColumn(eps->V,i+1,-1.0)); |
| 181 |
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116 | if (eps->W) PetscCall(BVScaleColumn(eps->W,i+1,-1.0)); |
| 182 | } | ||
| 183 | 926 | i++; | |
| 184 | } | ||
| 185 | } | ||
| 186 | #endif | ||
| 187 | |||
| 188 | /* Sort eigenvalues according to eps->which parameter */ | ||
| 189 |
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9545 | if (eps->problem_type==EPS_HAMILT) PetscCall(SlepcSortEigenvaluesSpecial(eps->sc,eps->nconv,eps->eigr,eps->eigi,eps->perm)); |
| 190 |
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9510 | else PetscCall(SlepcSortEigenvalues(eps->sc,eps->nconv,eps->eigr,eps->eigi,eps->perm)); |
| 191 |
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9545 | PetscCall(PetscLogEventEnd(EPS_Solve,eps,0,0,0)); |
| 192 | |||
| 193 | /* Various viewers */ | ||
| 194 |
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9545 | PetscCall(EPSViewFromOptions(eps,NULL,"-eps_view")); |
| 195 |
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9545 | PetscCall(EPSConvergedReasonViewFromOptions(eps)); |
| 196 |
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9545 | PetscCall(EPSErrorViewFromOptions(eps)); |
| 197 |
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9545 | PetscCall(EPSValuesViewFromOptions(eps)); |
| 198 |
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9545 | PetscCall(EPSVectorsViewFromOptions(eps)); |
| 199 | |||
| 200 |
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9545 | PetscCall(PetscOptionsHasName(((PetscObject)eps)->options,((PetscObject)eps)->prefix,"-eps_view_mat0",&hasname)); |
| 201 |
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9545 | if (hasname) { |
| 202 | ✗ | PetscCall(EPSGetOperators(eps,&A,NULL)); | |
| 203 | ✗ | PetscCall(MatViewFromOptions(A,(PetscObject)eps,"-eps_view_mat0")); | |
| 204 | } | ||
| 205 |
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9545 | if (eps->isgeneralized) { |
| 206 |
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2080 | PetscCall(PetscOptionsHasName(((PetscObject)eps)->options,((PetscObject)eps)->prefix,"-eps_view_mat1",&hasname)); |
| 207 |
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2080 | if (hasname) { |
| 208 | ✗ | PetscCall(EPSGetOperators(eps,NULL,&B)); | |
| 209 | ✗ | PetscCall(MatViewFromOptions(B,(PetscObject)eps,"-eps_view_mat1")); | |
| 210 | } | ||
| 211 | } | ||
| 212 | |||
| 213 | /* Remove deflation and initial subspaces */ | ||
| 214 |
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9545 | if (eps->nds) { |
| 215 |
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148 | PetscCall(BVSetNumConstraints(eps->V,0)); |
| 216 | 148 | eps->nds = 0; | |
| 217 | } | ||
| 218 | 9545 | eps->nini = 0; | |
| 219 |
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9545 | PetscFunctionReturn(PETSC_SUCCESS); |
| 220 | } | ||
| 221 | |||
| 222 | /*@ | ||
| 223 | EPSGetIterationNumber - Gets the current iteration number. If the | ||
| 224 | call to EPSSolve() is complete, then it returns the number of iterations | ||
| 225 | carried out by the solution method. | ||
| 226 | |||
| 227 | Not Collective | ||
| 228 | |||
| 229 | Input Parameter: | ||
| 230 | . eps - the eigensolver context | ||
| 231 | |||
| 232 | Output Parameter: | ||
| 233 | . its - number of iterations | ||
| 234 | |||
| 235 | Note: | ||
| 236 | During the i-th iteration this call returns i-1. If EPSSolve() is | ||
| 237 | complete, then parameter "its" contains either the iteration number at | ||
| 238 | which convergence was successfully reached, or failure was detected. | ||
| 239 | Call EPSGetConvergedReason() to determine if the solver converged or | ||
| 240 | failed and why. | ||
| 241 | |||
| 242 | Level: intermediate | ||
| 243 | |||
| 244 | .seealso: EPSGetConvergedReason(), EPSSetTolerances() | ||
| 245 | @*/ | ||
| 246 | 1550 | PetscErrorCode EPSGetIterationNumber(EPS eps,PetscInt *its) | |
| 247 | { | ||
| 248 |
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1550 | PetscFunctionBegin; |
| 249 |
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1550 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 250 |
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1550 | PetscAssertPointer(its,2); |
| 251 | 1550 | *its = eps->its; | |
| 252 |
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1550 | PetscFunctionReturn(PETSC_SUCCESS); |
| 253 | } | ||
| 254 | |||
| 255 | /*@ | ||
| 256 | EPSGetConverged - Gets the number of converged eigenpairs. | ||
| 257 | |||
| 258 | Not Collective | ||
| 259 | |||
| 260 | Input Parameter: | ||
| 261 | . eps - the eigensolver context | ||
| 262 | |||
| 263 | Output Parameter: | ||
| 264 | . nconv - number of converged eigenpairs | ||
| 265 | |||
| 266 | Note: | ||
| 267 | This function should be called after EPSSolve() has finished. | ||
| 268 | |||
| 269 | Level: beginner | ||
| 270 | |||
| 271 | .seealso: EPSSetDimensions(), EPSSolve(), EPSGetEigenpair() | ||
| 272 | @*/ | ||
| 273 | 5635 | PetscErrorCode EPSGetConverged(EPS eps,PetscInt *nconv) | |
| 274 | { | ||
| 275 |
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5635 | PetscFunctionBegin; |
| 276 |
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5635 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 277 |
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5635 | PetscAssertPointer(nconv,2); |
| 278 |
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5635 | EPSCheckSolved(eps,1); |
| 279 |
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5635 | PetscCall(EPS_GetActualConverged(eps,nconv)); |
| 280 |
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1083 | PetscFunctionReturn(PETSC_SUCCESS); |
| 281 | } | ||
| 282 | |||
| 283 | /*@ | ||
| 284 | EPSGetConvergedReason - Gets the reason why the EPSSolve() iteration was | ||
| 285 | stopped. | ||
| 286 | |||
| 287 | Not Collective | ||
| 288 | |||
| 289 | Input Parameter: | ||
| 290 | . eps - the eigensolver context | ||
| 291 | |||
| 292 | Output Parameter: | ||
| 293 | . reason - negative value indicates diverged, positive value converged | ||
| 294 | |||
| 295 | Options Database Key: | ||
| 296 | . -eps_converged_reason - print the reason to a viewer | ||
| 297 | |||
| 298 | Notes: | ||
| 299 | Possible values for reason are | ||
| 300 | + EPS_CONVERGED_TOL - converged up to tolerance | ||
| 301 | . EPS_CONVERGED_USER - converged due to a user-defined condition | ||
| 302 | . EPS_DIVERGED_ITS - required more than max_it iterations to reach convergence | ||
| 303 | . EPS_DIVERGED_BREAKDOWN - generic breakdown in method | ||
| 304 | - EPS_DIVERGED_SYMMETRY_LOST - pseudo-Lanczos was not able to keep symmetry | ||
| 305 | |||
| 306 | Can only be called after the call to EPSSolve() is complete. | ||
| 307 | |||
| 308 | Level: intermediate | ||
| 309 | |||
| 310 | .seealso: EPSSetTolerances(), EPSSolve(), EPSConvergedReason | ||
| 311 | @*/ | ||
| 312 | 1509 | PetscErrorCode EPSGetConvergedReason(EPS eps,EPSConvergedReason *reason) | |
| 313 | { | ||
| 314 |
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1509 | PetscFunctionBegin; |
| 315 |
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1509 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 316 |
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1509 | PetscAssertPointer(reason,2); |
| 317 |
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1509 | EPSCheckSolved(eps,1); |
| 318 | 1509 | *reason = eps->reason; | |
| 319 |
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1509 | PetscFunctionReturn(PETSC_SUCCESS); |
| 320 | } | ||
| 321 | |||
| 322 | /*@ | ||
| 323 | EPSGetInvariantSubspace - Gets an orthonormal basis of the computed invariant | ||
| 324 | subspace. | ||
| 325 | |||
| 326 | Collective | ||
| 327 | |||
| 328 | Input Parameter: | ||
| 329 | . eps - the eigensolver context | ||
| 330 | |||
| 331 | Output Parameter: | ||
| 332 | . v - an array of vectors | ||
| 333 | |||
| 334 | Notes: | ||
| 335 | This function should be called after EPSSolve() has finished. | ||
| 336 | |||
| 337 | The user should provide in v an array of nconv vectors, where nconv is | ||
| 338 | the value returned by EPSGetConverged(). | ||
| 339 | |||
| 340 | The first k vectors returned in v span an invariant subspace associated | ||
| 341 | with the first k computed eigenvalues (note that this is not true if the | ||
| 342 | k-th eigenvalue is complex and matrix A is real; in this case the first | ||
| 343 | k+1 vectors should be used). An invariant subspace X of A satisfies Ax | ||
| 344 | in X for all x in X (a similar definition applies for generalized | ||
| 345 | eigenproblems). | ||
| 346 | |||
| 347 | Level: intermediate | ||
| 348 | |||
| 349 | .seealso: EPSGetEigenpair(), EPSGetConverged(), EPSSolve() | ||
| 350 | @*/ | ||
| 351 | 80 | PetscErrorCode EPSGetInvariantSubspace(EPS eps,Vec v[]) | |
| 352 | { | ||
| 353 | 80 | PetscInt i; | |
| 354 | 80 | BV V=eps->V; | |
| 355 | 80 | Vec w; | |
| 356 | |||
| 357 |
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80 | PetscFunctionBegin; |
| 358 |
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80 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 359 |
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80 | PetscAssertPointer(v,2); |
| 360 |
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80 | PetscValidHeaderSpecific(*v,VEC_CLASSID,2); |
| 361 |
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80 | EPSCheckSolved(eps,1); |
| 362 |
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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"); |
| 363 |
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80 | if (eps->balance!=EPS_BALANCE_NONE && eps->D) { |
| 364 |
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10 | PetscCall(BVDuplicateResize(eps->V,eps->nconv,&V)); |
| 365 |
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10 | PetscCall(BVSetActiveColumns(eps->V,0,eps->nconv)); |
| 366 |
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10 | PetscCall(BVCopy(eps->V,V)); |
| 367 |
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55 | for (i=0;i<eps->nconv;i++) { |
| 368 |
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45 | PetscCall(BVGetColumn(V,i,&w)); |
| 369 |
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45 | PetscCall(VecPointwiseDivide(w,w,eps->D)); |
| 370 |
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45 | PetscCall(BVRestoreColumn(V,i,&w)); |
| 371 | } | ||
| 372 |
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10 | PetscCall(BVOrthogonalize(V,NULL)); |
| 373 | } | ||
| 374 |
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625 | for (i=0;i<eps->nconv;i++) PetscCall(BVCopyVec(V,i,v[i])); |
| 375 |
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80 | if (eps->balance!=EPS_BALANCE_NONE && eps->D) PetscCall(BVDestroy(&V)); |
| 376 |
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16 | PetscFunctionReturn(PETSC_SUCCESS); |
| 377 | } | ||
| 378 | |||
| 379 | /*@ | ||
| 380 | EPSGetEigenpair - Gets the i-th solution of the eigenproblem as computed by | ||
| 381 | EPSSolve(). The solution consists in both the eigenvalue and the eigenvector. | ||
| 382 | |||
| 383 | Collective | ||
| 384 | |||
| 385 | Input Parameters: | ||
| 386 | + eps - eigensolver context | ||
| 387 | - i - index of the solution | ||
| 388 | |||
| 389 | Output Parameters: | ||
| 390 | + eigr - real part of eigenvalue | ||
| 391 | . eigi - imaginary part of eigenvalue | ||
| 392 | . Vr - real part of eigenvector | ||
| 393 | - Vi - imaginary part of eigenvector | ||
| 394 | |||
| 395 | Notes: | ||
| 396 | It is allowed to pass NULL for Vr and Vi, if the eigenvector is not | ||
| 397 | required. Otherwise, the caller must provide valid Vec objects, i.e., | ||
| 398 | they must be created by the calling program with e.g. MatCreateVecs(). | ||
| 399 | |||
| 400 | If the eigenvalue is real, then eigi and Vi are set to zero. If PETSc is | ||
| 401 | configured with complex scalars the eigenvalue is stored | ||
| 402 | directly in eigr (eigi is set to zero) and the eigenvector in Vr (Vi is | ||
| 403 | set to zero). In both cases, the user can pass NULL in eigi and Vi. | ||
| 404 | |||
| 405 | The index i should be a value between 0 and nconv-1 (see EPSGetConverged()). | ||
| 406 | Eigenpairs are indexed according to the ordering criterion established | ||
| 407 | with EPSSetWhichEigenpairs(). | ||
| 408 | |||
| 409 | The 2-norm of the eigenvector is one unless the problem is generalized | ||
| 410 | Hermitian. In this case the eigenvector is normalized with respect to the | ||
| 411 | norm defined by the B matrix. | ||
| 412 | |||
| 413 | Level: beginner | ||
| 414 | |||
| 415 | .seealso: EPSGetEigenvalue(), EPSGetEigenvector(), EPSGetLeftEigenvector(), EPSSolve(), | ||
| 416 | EPSGetConverged(), EPSSetWhichEigenpairs(), EPSGetInvariantSubspace() | ||
| 417 | @*/ | ||
| 418 | 55066 | PetscErrorCode EPSGetEigenpair(EPS eps,PetscInt i,PetscScalar *eigr,PetscScalar *eigi,Vec Vr,Vec Vi) | |
| 419 | { | ||
| 420 | 55066 | PetscInt nconv; | |
| 421 | |||
| 422 |
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55066 | PetscFunctionBegin; |
| 423 |
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55066 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 424 |
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55066 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 425 |
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55066 | EPSCheckSolved(eps,1); |
| 426 |
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55066 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 427 |
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55066 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 428 |
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55066 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 429 |
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55066 | PetscCall(EPSGetEigenvalue(eps,i,eigr,eigi)); |
| 430 |
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55066 | if (Vr || Vi) PetscCall(EPSGetEigenvector(eps,i,Vr,Vi)); |
| 431 |
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11090 | PetscFunctionReturn(PETSC_SUCCESS); |
| 432 | } | ||
| 433 | |||
| 434 | /*@ | ||
| 435 | EPSGetEigenvalue - Gets the i-th eigenvalue as computed by EPSSolve(). | ||
| 436 | |||
| 437 | Not Collective | ||
| 438 | |||
| 439 | Input Parameters: | ||
| 440 | + eps - eigensolver context | ||
| 441 | - i - index of the solution | ||
| 442 | |||
| 443 | Output Parameters: | ||
| 444 | + eigr - real part of eigenvalue | ||
| 445 | - eigi - imaginary part of eigenvalue | ||
| 446 | |||
| 447 | Notes: | ||
| 448 | If the eigenvalue is real, then eigi is set to zero. If PETSc is | ||
| 449 | configured with complex scalars the eigenvalue is stored | ||
| 450 | directly in eigr (eigi is set to zero). | ||
| 451 | |||
| 452 | The index i should be a value between 0 and nconv-1 (see EPSGetConverged()). | ||
| 453 | Eigenpairs are indexed according to the ordering criterion established | ||
| 454 | with EPSSetWhichEigenpairs(). | ||
| 455 | |||
| 456 | Level: beginner | ||
| 457 | |||
| 458 | .seealso: EPSSolve(), EPSGetConverged(), EPSSetWhichEigenpairs(), EPSGetEigenpair() | ||
| 459 | @*/ | ||
| 460 | 107963 | PetscErrorCode EPSGetEigenvalue(EPS eps,PetscInt i,PetscScalar *eigr,PetscScalar *eigi) | |
| 461 | { | ||
| 462 | 107963 | PetscInt k,nconv; | |
| 463 | #if !defined(PETSC_USE_COMPLEX) | ||
| 464 | 55729 | PetscInt k2, iquad; | |
| 465 | #endif | ||
| 466 | |||
| 467 |
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107963 | PetscFunctionBegin; |
| 468 |
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107963 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 469 |
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107963 | EPSCheckSolved(eps,1); |
| 470 |
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107963 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 471 |
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107963 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 472 |
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107963 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 473 |
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107963 | if (nconv==eps->nconv) { |
| 474 | 101771 | k = eps->perm[i]; | |
| 475 | #if defined(PETSC_USE_COMPLEX) | ||
| 476 |
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49274 | if (eigr) *eigr = eps->eigr[k]; |
| 477 |
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49274 | if (eigi) *eigi = 0; |
| 478 | #else | ||
| 479 |
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52497 | if (eigr) *eigr = eps->eigr[k]; |
| 480 |
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52497 | if (eigi) *eigi = eps->eigi[k]; |
| 481 | #endif | ||
| 482 | } else { | ||
| 483 |
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6192 | PetscCheck(eps->problem_type==EPS_BSE || eps->problem_type==EPS_HAMILT,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Problem type should be BSE or Hamiltonian"); |
| 484 |
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6192 | if (eps->problem_type==EPS_BSE) { |
| 485 | /* BSE problem, even index is +lambda, odd index is -lambda */ | ||
| 486 | 5672 | k = eps->perm[i/2]; | |
| 487 | #if defined(PETSC_USE_COMPLEX) | ||
| 488 |
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2960 | if (eigr) *eigr = (i%2)? -eps->eigr[k]: eps->eigr[k]; |
| 489 |
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2960 | if (eigi) *eigi = 0; |
| 490 | #else | ||
| 491 |
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2712 | if (eigr) *eigr = (i%2)? -eps->eigr[k]: eps->eigr[k]; |
| 492 |
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2712 | if (eigi) *eigi = eps->eigi[k]; |
| 493 | #endif | ||
| 494 |
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520 | } else if (eps->problem_type==EPS_HAMILT) { |
| 495 | /* Hamiltonian eigenproblem */ | ||
| 496 | 520 | k = eps->perm[i/2]; | |
| 497 | #if defined(PETSC_USE_COMPLEX) | ||
| 498 | ✗ | if (eigr) *eigr = (i%2)? -eps->eigr[k]: eps->eigr[k]; | |
| 499 | ✗ | if (eigi) *eigi = 0; | |
| 500 | #else | ||
| 501 |
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520 | if (eps->eigi[k]==0.0) { /* real eigenvalue */ |
| 502 | ✗ | if (eigr) *eigr = (i%2)? -eps->eigr[k]: eps->eigr[k]; | |
| 503 | ✗ | if (eigi) *eigi = 0.0; | |
| 504 |
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520 | } else if (eps->eigr[k]==0.0) { /* purely imaginary eigenvalue */ |
| 505 |
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120 | if (eigr) *eigr = 0.0; |
| 506 |
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120 | if (eigi) *eigi = (i%2)? -eps->eigi[k]: eps->eigi[k]; |
| 507 | } else { /* quadruple eigenvalue (-conj(lambda),-lambda,lambda,conj(lambda)) */ | ||
| 508 | 400 | iquad = i%2; /* index within the 4 values */ | |
| 509 |
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400 | if (i>1) { |
| 510 | 320 | k2 = eps->perm[(i-2)/2]; | |
| 511 |
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320 | if (eps->eigr[k]==eps->eigr[k2] && eps->eigi[k]==-eps->eigi[k2]) iquad += 2; |
| 512 | } | ||
| 513 |
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400 | if (eigr) *eigr = (iquad<2)? -eps->eigr[k]: eps->eigr[k]; |
| 514 |
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400 | if (eigi) *eigi = (iquad%3)? -eps->eigi[k]: eps->eigi[k]; |
| 515 | } | ||
| 516 | #endif | ||
| 517 | } | ||
| 518 | } | ||
| 519 |
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22063 | PetscFunctionReturn(PETSC_SUCCESS); |
| 520 | } | ||
| 521 | |||
| 522 | /*@ | ||
| 523 | EPSGetEigenvector - Gets the i-th right eigenvector as computed by EPSSolve(). | ||
| 524 | |||
| 525 | Collective | ||
| 526 | |||
| 527 | Input Parameters: | ||
| 528 | + eps - eigensolver context | ||
| 529 | - i - index of the solution | ||
| 530 | |||
| 531 | Output Parameters: | ||
| 532 | + Vr - real part of eigenvector | ||
| 533 | - Vi - imaginary part of eigenvector | ||
| 534 | |||
| 535 | Notes: | ||
| 536 | The caller must provide valid Vec objects, i.e., they must be created | ||
| 537 | by the calling program with e.g. MatCreateVecs(). | ||
| 538 | |||
| 539 | If the corresponding eigenvalue is real, then Vi is set to zero. If PETSc is | ||
| 540 | configured with complex scalars the eigenvector is stored | ||
| 541 | directly in Vr (Vi is set to zero). In any case, the user can pass NULL in Vr | ||
| 542 | or Vi if one of them is not required. | ||
| 543 | |||
| 544 | The index i should be a value between 0 and nconv-1 (see EPSGetConverged()). | ||
| 545 | Eigenpairs are indexed according to the ordering criterion established | ||
| 546 | with EPSSetWhichEigenpairs(). | ||
| 547 | |||
| 548 | The 2-norm of the eigenvector is one unless the problem is generalized | ||
| 549 | Hermitian. In this case the eigenvector is normalized with respect to the | ||
| 550 | norm defined by the B matrix. | ||
| 551 | |||
| 552 | Level: beginner | ||
| 553 | |||
| 554 | .seealso: EPSSolve(), EPSGetConverged(), EPSSetWhichEigenpairs(), EPSGetEigenpair(), EPSGetLeftEigenvector() | ||
| 555 | @*/ | ||
| 556 | 79915 | PetscErrorCode EPSGetEigenvector(EPS eps,PetscInt i,Vec Vr,Vec Vi) | |
| 557 | { | ||
| 558 | 79915 | PetscInt nconv; | |
| 559 | |||
| 560 |
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79915 | PetscFunctionBegin; |
| 561 |
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79915 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 562 |
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79915 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 563 |
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79915 | if (Vr) { PetscValidHeaderSpecific(Vr,VEC_CLASSID,3); PetscCheckSameComm(eps,1,Vr,3); } |
| 564 |
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79915 | if (Vi) { PetscValidHeaderSpecific(Vi,VEC_CLASSID,4); PetscCheckSameComm(eps,1,Vi,4); } |
| 565 |
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79915 | EPSCheckSolved(eps,1); |
| 566 |
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79915 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 567 |
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79915 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 568 |
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79915 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 569 |
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79915 | PetscCall(EPSComputeVectors(eps)); |
| 570 |
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79915 | PetscCall(EPS_GetEigenvector(eps,eps->V,i,Vr,Vi)); |
| 571 |
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14325 | PetscFunctionReturn(PETSC_SUCCESS); |
| 572 | } | ||
| 573 | |||
| 574 | /*@ | ||
| 575 | EPSGetLeftEigenvector - Gets the i-th left eigenvector as computed by EPSSolve(). | ||
| 576 | |||
| 577 | Collective | ||
| 578 | |||
| 579 | Input Parameters: | ||
| 580 | + eps - eigensolver context | ||
| 581 | - i - index of the solution | ||
| 582 | |||
| 583 | Output Parameters: | ||
| 584 | + Wr - real part of left eigenvector | ||
| 585 | - Wi - imaginary part of left eigenvector | ||
| 586 | |||
| 587 | Notes: | ||
| 588 | The caller must provide valid Vec objects, i.e., they must be created | ||
| 589 | by the calling program with e.g. MatCreateVecs(). | ||
| 590 | |||
| 591 | If the corresponding eigenvalue is real, then Wi is set to zero. If PETSc is | ||
| 592 | configured with complex scalars the eigenvector is stored directly in Wr | ||
| 593 | (Wi is set to zero). In any case, the user can pass NULL in Wr or Wi if | ||
| 594 | one of them is not required. | ||
| 595 | |||
| 596 | The index i should be a value between 0 and nconv-1 (see EPSGetConverged()). | ||
| 597 | Eigensolutions are indexed according to the ordering criterion established | ||
| 598 | with EPSSetWhichEigenpairs(). | ||
| 599 | |||
| 600 | Left eigenvectors are available only if the twosided flag was set, see | ||
| 601 | EPSSetTwoSided(). | ||
| 602 | |||
| 603 | Level: intermediate | ||
| 604 | |||
| 605 | .seealso: EPSGetEigenvector(), EPSGetConverged(), EPSSetWhichEigenpairs(), EPSSetTwoSided() | ||
| 606 | @*/ | ||
| 607 | 4505 | PetscErrorCode EPSGetLeftEigenvector(EPS eps,PetscInt i,Vec Wr,Vec Wi) | |
| 608 | { | ||
| 609 | 4505 | PetscInt nconv; | |
| 610 | 4505 | PetscBool trivial; | |
| 611 | 4505 | Mat H; | |
| 612 | 4505 | IS is[2]; | |
| 613 | 4505 | Vec v; | |
| 614 | |||
| 615 |
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4505 | PetscFunctionBegin; |
| 616 |
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4505 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 617 |
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4505 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 618 |
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4505 | if (Wr) { PetscValidHeaderSpecific(Wr,VEC_CLASSID,3); PetscCheckSameComm(eps,1,Wr,3); } |
| 619 |
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4505 | if (Wi) { PetscValidHeaderSpecific(Wi,VEC_CLASSID,4); PetscCheckSameComm(eps,1,Wi,4); } |
| 620 |
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4505 | EPSCheckSolved(eps,1); |
| 621 |
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4505 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 622 |
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4505 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 623 |
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4505 | PetscCheck(i<nconv,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index can be nconv-1 at most, see EPSGetConverged()"); |
| 624 | |||
| 625 | 4505 | trivial = (eps->problem_type==EPS_HEP || eps->problem_type==EPS_GHEP || eps->problem_type==EPS_BSE)? PETSC_TRUE: PETSC_FALSE; | |
| 626 |
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4505 | if (!trivial) PetscCheck(eps->twosided,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONGSTATE,"Must request left vectors with EPSSetTwoSided"); |
| 627 | |||
| 628 |
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4505 | PetscCall(EPSComputeVectors(eps)); |
| 629 |
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4505 | if (trivial) { |
| 630 |
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3612 | PetscCall(EPS_GetEigenvector(eps,eps->V,i,Wr,Wi)); |
| 631 |
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3612 | if (eps->problem_type==EPS_BSE) { /* change sign of bottom part of the vector */ |
| 632 |
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3612 | PetscCall(STGetMatrix(eps->st,0,&H)); |
| 633 |
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3612 | PetscCall(MatNestGetISs(H,is,NULL)); |
| 634 |
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3612 | if (Wr) { |
| 635 |
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3612 | PetscCall(VecGetSubVector(Wr,is[1],&v)); |
| 636 |
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3612 | PetscCall(VecScale(v,-1.0)); |
| 637 |
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3612 | PetscCall(VecRestoreSubVector(Wr,is[1],&v)); |
| 638 | } | ||
| 639 | #if !defined(PETSC_USE_COMPLEX) | ||
| 640 |
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1768 | if (Wi) { |
| 641 | ✗ | PetscCall(VecGetSubVector(Wi,is[1],&v)); | |
| 642 | ✗ | PetscCall(VecScale(v,-1.0)); | |
| 643 | ✗ | PetscCall(VecRestoreSubVector(Wi,is[1],&v)); | |
| 644 | } | ||
| 645 | #endif | ||
| 646 | } | ||
| 647 | } else { | ||
| 648 |
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893 | PetscCall(EPS_GetEigenvector(eps,eps->W,i,Wr,Wi)); |
| 649 | } | ||
| 650 |
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817 | PetscFunctionReturn(PETSC_SUCCESS); |
| 651 | } | ||
| 652 | |||
| 653 | /*@ | ||
| 654 | EPSGetErrorEstimate - Returns the error estimate associated to the i-th | ||
| 655 | computed eigenpair. | ||
| 656 | |||
| 657 | Not Collective | ||
| 658 | |||
| 659 | Input Parameters: | ||
| 660 | + eps - eigensolver context | ||
| 661 | - i - index of eigenpair | ||
| 662 | |||
| 663 | Output Parameter: | ||
| 664 | . errest - the error estimate | ||
| 665 | |||
| 666 | Notes: | ||
| 667 | This is the error estimate used internally by the eigensolver. The actual | ||
| 668 | error bound can be computed with EPSComputeError(). See also the users | ||
| 669 | manual for details. | ||
| 670 | |||
| 671 | Level: advanced | ||
| 672 | |||
| 673 | .seealso: EPSComputeError() | ||
| 674 | @*/ | ||
| 675 | 612 | PetscErrorCode EPSGetErrorEstimate(EPS eps,PetscInt i,PetscReal *errest) | |
| 676 | { | ||
| 677 | 612 | PetscInt nconv; | |
| 678 | |||
| 679 |
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612 | PetscFunctionBegin; |
| 680 |
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612 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 681 |
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612 | PetscAssertPointer(errest,3); |
| 682 |
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612 | EPSCheckSolved(eps,1); |
| 683 |
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612 | PetscCheck(i>=0,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"The index cannot be negative"); |
| 684 |
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612 | PetscCall(EPS_GetActualConverged(eps,&nconv)); |
| 685 |
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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()"); |
| 686 |
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612 | if (nconv==eps->nconv) { |
| 687 | 612 | *errest = eps->errest[eps->perm[i]]; | |
| 688 | } else { | ||
| 689 | ✗ | PetscCheck(eps->problem_type==EPS_BSE,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Problem type should be BSE"); | |
| 690 | /* BSE problem, even index is +lambda, odd index is -lambda, assume both have same error */ | ||
| 691 | ✗ | *errest = eps->errest[eps->perm[i/2]]; | |
| 692 | } | ||
| 693 |
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116 | PetscFunctionReturn(PETSC_SUCCESS); |
| 694 | } | ||
| 695 | |||
| 696 | /* | ||
| 697 | EPSComputeResidualNorm_Private - Computes the norm of the residual vector | ||
| 698 | associated with an eigenpair. | ||
| 699 | |||
| 700 | Input Parameters: | ||
| 701 | trans - whether A' must be used instead of A | ||
| 702 | kr,ki - eigenvalue | ||
| 703 | xr,xi - eigenvector | ||
| 704 | z - three work vectors (the second one not referenced in complex scalars) | ||
| 705 | */ | ||
| 706 | 44419 | PetscErrorCode EPSComputeResidualNorm_Private(EPS eps,PetscBool trans,PetscScalar kr,PetscScalar ki,Vec xr,Vec xi,Vec *z,PetscReal *norm) | |
| 707 | { | ||
| 708 | 44419 | PetscInt nmat; | |
| 709 | 44419 | Mat A,B; | |
| 710 | 44419 | Vec u,w; | |
| 711 | 44419 | PetscScalar alpha; | |
| 712 | #if !defined(PETSC_USE_COMPLEX) | ||
| 713 | 22558 | Vec v; | |
| 714 | 22558 | PetscReal ni,nr; | |
| 715 | #endif | ||
| 716 |
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44419 | PetscErrorCode (*matmult)(Mat,Vec,Vec) = trans? MatMultHermitianTranspose: MatMult; |
| 717 | |||
| 718 |
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44419 | PetscFunctionBegin; |
| 719 | 44419 | u = z[0]; w = z[2]; | |
| 720 |
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44419 | PetscCall(STGetNumMatrices(eps->st,&nmat)); |
| 721 |
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44419 | PetscCall(STGetMatrix(eps->st,0,&A)); |
| 722 |
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44419 | if (nmat>1) PetscCall(STGetMatrix(eps->st,1,&B)); |
| 723 | |||
| 724 | #if !defined(PETSC_USE_COMPLEX) | ||
| 725 | 22558 | v = z[1]; | |
| 726 |
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22558 | if (ki == 0 || PetscAbsScalar(ki) < PetscAbsScalar(kr*PETSC_MACHINE_EPSILON)) { |
| 727 | #endif | ||
| 728 |
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43247 | PetscCall((*matmult)(A,xr,u)); /* u=A*x */ |
| 729 |
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43247 | if (PetscAbsScalar(kr) > PETSC_MACHINE_EPSILON) { |
| 730 |
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43247 | if (nmat>1) PetscCall((*matmult)(B,xr,w)); |
| 731 |
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21478 | else PetscCall(VecCopy(xr,w)); /* w=B*x */ |
| 732 |
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43247 | alpha = trans? -PetscConj(kr): -kr; |
| 733 |
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43247 | PetscCall(VecAXPY(u,alpha,w)); /* u=A*x-k*B*x */ |
| 734 | } | ||
| 735 |
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43247 | PetscCall(VecNorm(u,NORM_2,norm)); |
| 736 | #if !defined(PETSC_USE_COMPLEX) | ||
| 737 | } else { | ||
| 738 |
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1172 | PetscCall((*matmult)(A,xr,u)); /* u=A*xr */ |
| 739 |
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1172 | if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) { |
| 740 |
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1172 | if (nmat>1) PetscCall((*matmult)(B,xr,v)); |
| 741 |
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1156 | else PetscCall(VecCopy(xr,v)); /* v=B*xr */ |
| 742 |
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1172 | PetscCall(VecAXPY(u,-kr,v)); /* u=A*xr-kr*B*xr */ |
| 743 |
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1172 | if (nmat>1) PetscCall((*matmult)(B,xi,w)); |
| 744 |
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1156 | else PetscCall(VecCopy(xi,w)); /* w=B*xi */ |
| 745 |
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1172 | PetscCall(VecAXPY(u,trans?-ki:ki,w)); /* u=A*xr-kr*B*xr+ki*B*xi */ |
| 746 | } | ||
| 747 |
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1172 | PetscCall(VecNorm(u,NORM_2,&nr)); |
| 748 |
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1172 | PetscCall((*matmult)(A,xi,u)); /* u=A*xi */ |
| 749 |
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1172 | if (SlepcAbsEigenvalue(kr,ki) > PETSC_MACHINE_EPSILON) { |
| 750 |
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1172 | PetscCall(VecAXPY(u,-kr,w)); /* u=A*xi-kr*B*xi */ |
| 751 |
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1172 | PetscCall(VecAXPY(u,trans?ki:-ki,v)); /* u=A*xi-kr*B*xi-ki*B*xr */ |
| 752 | } | ||
| 753 |
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1172 | PetscCall(VecNorm(u,NORM_2,&ni)); |
| 754 | 1172 | *norm = SlepcAbsEigenvalue(nr,ni); | |
| 755 | } | ||
| 756 | #endif | ||
| 757 |
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8816 | PetscFunctionReturn(PETSC_SUCCESS); |
| 758 | } | ||
| 759 | |||
| 760 | /*@ | ||
| 761 | EPSComputeError - Computes the error (based on the residual norm) associated | ||
| 762 | with the i-th computed eigenpair. | ||
| 763 | |||
| 764 | Collective | ||
| 765 | |||
| 766 | Input Parameters: | ||
| 767 | + eps - the eigensolver context | ||
| 768 | . i - the solution index | ||
| 769 | - type - the type of error to compute | ||
| 770 | |||
| 771 | Output Parameter: | ||
| 772 | . error - the error | ||
| 773 | |||
| 774 | Notes: | ||
| 775 | The error can be computed in various ways, all of them based on the residual | ||
| 776 | norm ||Ax-kBx||_2 where k is the eigenvalue and x is the eigenvector. | ||
| 777 | |||
| 778 | Level: beginner | ||
| 779 | |||
| 780 | .seealso: EPSErrorType, EPSSolve(), EPSGetErrorEstimate() | ||
| 781 | @*/ | ||
| 782 | 41034 | PetscErrorCode EPSComputeError(EPS eps,PetscInt i,EPSErrorType type,PetscReal *error) | |
| 783 | { | ||
| 784 | 41034 | Mat A,B; | |
| 785 | 41034 | Vec xr,xi,w[3]; | |
| 786 | 41034 | PetscReal t,vecnorm=1.0,errorl; | |
| 787 | 41034 | PetscScalar kr,ki; | |
| 788 | 41034 | PetscBool flg; | |
| 789 | |||
| 790 |
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41034 | PetscFunctionBegin; |
| 791 |
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41034 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 792 |
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41034 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 793 |
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41034 | PetscValidLogicalCollectiveEnum(eps,type,3); |
| 794 |
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41034 | PetscAssertPointer(error,4); |
| 795 |
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41034 | EPSCheckSolved(eps,1); |
| 796 | |||
| 797 | /* allocate work vectors */ | ||
| 798 | #if defined(PETSC_USE_COMPLEX) | ||
| 799 |
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|
20106 | PetscCall(EPSSetWorkVecs(eps,3)); |
| 800 | 20106 | xi = NULL; | |
| 801 | 20106 | w[1] = NULL; | |
| 802 | #else | ||
| 803 |
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20928 | PetscCall(EPSSetWorkVecs(eps,5)); |
| 804 | 20928 | xi = eps->work[3]; | |
| 805 | 20928 | w[1] = eps->work[4]; | |
| 806 | #endif | ||
| 807 | 41034 | xr = eps->work[0]; | |
| 808 | 41034 | w[0] = eps->work[1]; | |
| 809 | 41034 | w[2] = eps->work[2]; | |
| 810 | |||
| 811 | /* compute residual norm */ | ||
| 812 |
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41034 | PetscCall(EPSGetEigenpair(eps,i,&kr,&ki,xr,xi)); |
| 813 |
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41034 | PetscCall(EPSComputeResidualNorm_Private(eps,PETSC_FALSE,kr,ki,xr,xi,w,error)); |
| 814 | |||
| 815 | /* compute 2-norm of eigenvector */ | ||
| 816 |
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41034 | if (eps->problem_type==EPS_GHEP) PetscCall(VecNorm(xr,NORM_2,&vecnorm)); |
| 817 | |||
| 818 | /* if two-sided, compute left residual norm and take the maximum */ | ||
| 819 |
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41034 | if (eps->twosided) { |
| 820 |
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450 | PetscCall(EPSGetLeftEigenvector(eps,i,xr,xi)); |
| 821 |
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450 | PetscCall(EPSComputeResidualNorm_Private(eps,PETSC_TRUE,kr,ki,xr,xi,w,&errorl)); |
| 822 |
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673 | *error = PetscMax(*error,errorl); |
| 823 | } | ||
| 824 | |||
| 825 | /* compute error */ | ||
| 826 |
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41034 | switch (type) { |
| 827 | case EPS_ERROR_ABSOLUTE: | ||
| 828 | break; | ||
| 829 | 23584 | case EPS_ERROR_RELATIVE: | |
| 830 | 23584 | *error /= SlepcAbsEigenvalue(kr,ki)*vecnorm; | |
| 831 | 23584 | break; | |
| 832 | 17198 | case EPS_ERROR_BACKWARD: | |
| 833 | /* initialization of matrix norms */ | ||
| 834 |
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17198 | if (!eps->nrma) { |
| 835 |
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395 | PetscCall(STGetMatrix(eps->st,0,&A)); |
| 836 |
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395 | PetscCall(MatHasOperation(A,MATOP_NORM,&flg)); |
| 837 |
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395 | PetscCheck(flg,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation"); |
| 838 |
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395 | PetscCall(MatNorm(A,NORM_INFINITY,&eps->nrma)); |
| 839 | } | ||
| 840 |
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17198 | if (eps->isgeneralized) { |
| 841 |
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16945 | if (!eps->nrmb) { |
| 842 |
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336 | PetscCall(STGetMatrix(eps->st,1,&B)); |
| 843 |
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336 | PetscCall(MatHasOperation(B,MATOP_NORM,&flg)); |
| 844 |
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336 | PetscCheck(flg,PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_WRONG,"The computation of backward errors requires a matrix norm operation"); |
| 845 |
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336 | PetscCall(MatNorm(B,NORM_INFINITY,&eps->nrmb)); |
| 846 | } | ||
| 847 | 253 | } else eps->nrmb = 1.0; | |
| 848 | 17198 | t = SlepcAbsEigenvalue(kr,ki); | |
| 849 | 17198 | *error /= (eps->nrma+t*eps->nrmb)*vecnorm; | |
| 850 | 17198 | break; | |
| 851 | ✗ | default: | |
| 852 | ✗ | SETERRQ(PetscObjectComm((PetscObject)eps),PETSC_ERR_ARG_OUTOFRANGE,"Invalid error type"); | |
| 853 | } | ||
| 854 |
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8100 | PetscFunctionReturn(PETSC_SUCCESS); |
| 855 | } | ||
| 856 | |||
| 857 | /* | ||
| 858 | EPSGetStartVector - Generate a suitable vector to be used as the starting vector | ||
| 859 | for the recurrence that builds the right subspace. | ||
| 860 | |||
| 861 | Collective | ||
| 862 | |||
| 863 | Input Parameters: | ||
| 864 | + eps - the eigensolver context | ||
| 865 | - i - iteration number | ||
| 866 | |||
| 867 | Output Parameters: | ||
| 868 | . breakdown - flag indicating that a breakdown has occurred | ||
| 869 | |||
| 870 | Notes: | ||
| 871 | The start vector is computed from another vector: for the first step (i=0), | ||
| 872 | the first initial vector is used (see EPSSetInitialSpace()); otherwise a random | ||
| 873 | vector is created. Then this vector is forced to be in the range of OP (only | ||
| 874 | for generalized definite problems) and orthonormalized with respect to all | ||
| 875 | V-vectors up to i-1. The resulting vector is placed in V[i]. | ||
| 876 | |||
| 877 | The flag breakdown is set to true if either i=0 and the vector belongs to the | ||
| 878 | deflation space, or i>0 and the vector is linearly dependent with respect | ||
| 879 | to the V-vectors. | ||
| 880 | */ | ||
| 881 | 7002 | PetscErrorCode EPSGetStartVector(EPS eps,PetscInt i,PetscBool *breakdown) | |
| 882 | { | ||
| 883 | 7002 | PetscReal norm; | |
| 884 | 7002 | PetscBool lindep; | |
| 885 | 7002 | Vec w,z; | |
| 886 | |||
| 887 |
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7002 | PetscFunctionBegin; |
| 888 |
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7002 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 889 |
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7002 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 890 | |||
| 891 | /* For the first step, use the first initial vector, otherwise a random one */ | ||
| 892 |
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7002 | if (i>0 || eps->nini==0) PetscCall(BVSetRandomColumn(eps->V,i)); |
| 893 | |||
| 894 | /* Force the vector to be in the range of OP for generalized problems with B-inner product */ | ||
| 895 |
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7002 | if (eps->ispositive || (eps->isgeneralized && eps->ishermitian)) { |
| 896 |
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1033 | PetscCall(BVCreateVec(eps->V,&w)); |
| 897 |
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1033 | PetscCall(BVCopyVec(eps->V,i,w)); |
| 898 |
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1033 | PetscCall(BVGetColumn(eps->V,i,&z)); |
| 899 |
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1033 | PetscCall(STApply(eps->st,w,z)); |
| 900 |
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1033 | PetscCall(BVRestoreColumn(eps->V,i,&z)); |
| 901 |
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1033 | PetscCall(VecDestroy(&w)); |
| 902 | } | ||
| 903 | |||
| 904 | /* Orthonormalize the vector with respect to previous vectors */ | ||
| 905 |
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7002 | PetscCall(BVOrthogonalizeColumn(eps->V,i,NULL,&norm,&lindep)); |
| 906 |
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7002 | if (breakdown) *breakdown = lindep; |
| 907 |
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6645 | else if (lindep || norm == 0.0) { |
| 908 | ✗ | PetscCheck(i,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Initial vector is zero or belongs to the deflation space"); | |
| 909 | ✗ | PetscCheck(!i,PetscObjectComm((PetscObject)eps),PETSC_ERR_CONV_FAILED,"Unable to generate more start vectors"); | |
| 910 | } | ||
| 911 |
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7002 | PetscCall(BVScaleColumn(eps->V,i,1.0/norm)); |
| 912 |
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1346 | PetscFunctionReturn(PETSC_SUCCESS); |
| 913 | } | ||
| 914 | |||
| 915 | /* | ||
| 916 | EPSGetLeftStartVector - Generate a suitable vector to be used as the left starting | ||
| 917 | vector for the recurrence that builds the left subspace. See EPSGetStartVector(). | ||
| 918 | */ | ||
| 919 | 254 | PetscErrorCode EPSGetLeftStartVector(EPS eps,PetscInt i,PetscBool *breakdown) | |
| 920 | { | ||
| 921 | 254 | PetscReal norm; | |
| 922 | 254 | PetscBool lindep; | |
| 923 | 254 | Vec w,z; | |
| 924 | |||
| 925 |
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254 | PetscFunctionBegin; |
| 926 |
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254 | PetscValidHeaderSpecific(eps,EPS_CLASSID,1); |
| 927 |
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254 | PetscValidLogicalCollectiveInt(eps,i,2); |
| 928 | |||
| 929 | /* For the first step, use the first initial vector, otherwise a random one */ | ||
| 930 |
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254 | if (i>0 || eps->ninil==0) PetscCall(BVSetRandomColumn(eps->W,i)); |
| 931 | |||
| 932 | /* Force the vector to be in the range of OP' for generalized problems with B-inner product */ | ||
| 933 |
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254 | if (eps->ispositive || (eps->isgeneralized && eps->ishermitian)) { |
| 934 |
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13 | PetscCall(BVCreateVec(eps->W,&w)); |
| 935 |
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13 | PetscCall(BVCopyVec(eps->W,i,w)); |
| 936 |
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13 | PetscCall(BVGetColumn(eps->W,i,&z)); |
| 937 |
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13 | PetscCall(STApplyHermitianTranspose(eps->st,w,z)); |
| 938 |
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13 | PetscCall(BVRestoreColumn(eps->W,i,&z)); |
| 939 |
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13 | PetscCall(VecDestroy(&w)); |
| 940 | } | ||
| 941 | |||
| 942 | /* Orthonormalize the vector with respect to previous vectors */ | ||
| 943 |
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254 | PetscCall(BVOrthogonalizeColumn(eps->W,i,NULL,&norm,&lindep)); |
| 944 |
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254 | if (breakdown) *breakdown = lindep; |
| 945 |
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199 | else if (lindep || norm == 0.0) { |
| 946 | ✗ | PetscCheck(i,PetscObjectComm((PetscObject)eps),PETSC_ERR_PLIB,"Left initial vector is zero"); | |
| 947 | ✗ | PetscCheck(!i,PetscObjectComm((PetscObject)eps),PETSC_ERR_CONV_FAILED,"Unable to generate more left start vectors"); | |
| 948 | } | ||
| 949 |
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254 | PetscCall(BVScaleColumn(eps->W,i,1.0/norm)); |
| 950 |
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50 | PetscFunctionReturn(PETSC_SUCCESS); |
| 951 | } | ||
| 952 |