Actual source code: pepopts.c

      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    PEP routines related to options that can be set via the command-line
     12:    or procedurally
     13: */

     15: #include <slepc/private/pepimpl.h>
     16: #include <petscdraw.h>

     18: /*@C
     19:    PEPMonitorSetFromOptions - Sets a monitor function and viewer appropriate for the type
     20:    indicated by the user.

     22:    Collective

     24:    Input Parameters:
     25: +  pep      - the polynomial eigensolver context
     26: .  opt      - the command line option for this monitor
     27: .  name     - the monitor type one is seeking
     28: .  ctx      - an optional user context for the monitor, or `NULL`
     29: -  trackall - whether this monitor tracks all eigenvalues or not

     31:    Level: developer

     33: .seealso: [](ch:pep), `PEPMonitorSet()`, `PEPSetTrackAll()`
     34: @*/
     35: PetscErrorCode PEPMonitorSetFromOptions(PEP pep,const char opt[],const char name[],PetscCtx ctx,PetscBool trackall)
     36: {
     37:   PetscErrorCode       (*mfunc)(PEP,PetscInt,PetscInt,PetscScalar*,PetscScalar*,PetscReal*,PetscInt,void*);
     38:   PetscErrorCode       (*cfunc)(PetscViewer,PetscViewerFormat,void*,PetscViewerAndFormat**);
     39:   PetscErrorCode       (*dfunc)(PetscViewerAndFormat**);
     40:   PetscViewerAndFormat *vf;
     41:   PetscViewer          viewer;
     42:   PetscViewerFormat    format;
     43:   PetscViewerType      vtype;
     44:   char                 key[PETSC_MAX_PATH_LEN];
     45:   PetscBool            flg;

     47:   PetscFunctionBegin;
     48:   PetscCall(PetscOptionsCreateViewer(PetscObjectComm((PetscObject)pep),((PetscObject)pep)->options,((PetscObject)pep)->prefix,opt,&viewer,&format,&flg));
     49:   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);

     51:   PetscCall(PetscViewerGetType(viewer,&vtype));
     52:   PetscCall(SlepcMonitorMakeKey_Internal(name,vtype,format,key));
     53:   PetscCall(PetscFunctionListFind(PEPMonitorList,key,&mfunc));
     54:   PetscCheck(mfunc,PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"Specified viewer and format not supported");
     55:   PetscCall(PetscFunctionListFind(PEPMonitorCreateList,key,&cfunc));
     56:   PetscCall(PetscFunctionListFind(PEPMonitorDestroyList,key,&dfunc));
     57:   if (!cfunc) cfunc = PetscViewerAndFormatCreate_Internal;
     58:   if (!dfunc) dfunc = PetscViewerAndFormatDestroy;

     60:   PetscCall((*cfunc)(viewer,format,ctx,&vf));
     61:   PetscCall(PetscViewerDestroy(&viewer));
     62:   PetscCall(PEPMonitorSet(pep,mfunc,vf,(PetscCtxDestroyFn*)dfunc));
     63:   if (trackall) PetscCall(PEPSetTrackAll(pep,PETSC_TRUE));
     64:   PetscFunctionReturn(PETSC_SUCCESS);
     65: }

     67: /*@
     68:    PEPSetFromOptions - Sets `PEP` options from the options database.
     69:    This routine must be called before `PEPSetUp()` if the user is to be
     70:    allowed to configure the solver.

     72:    Collective

     74:    Input Parameter:
     75: .  pep - the polynomial eigensolver context

     77:    Note:
     78:    To see all options, run your program with the `-help` option.

     80:    Level: beginner

     82: .seealso: [](ch:pep), `PEPSetOptionsPrefix()`
     83: @*/
     84: PetscErrorCode PEPSetFromOptions(PEP pep)
     85: {
     86:   char            type[256];
     87:   PetscBool       set,flg,flg1,flg2,flg3,flg4,flg5;
     88:   PetscReal       r,t,array[2]={0,0};
     89:   PetscScalar     s;
     90:   PetscInt        i,j,k;
     91:   PEPScale        scale;
     92:   PEPRefine       refine;
     93:   PEPRefineScheme scheme;

     95:   PetscFunctionBegin;
     97:   PetscCall(PEPRegisterAll());
     98:   PetscObjectOptionsBegin((PetscObject)pep);
     99:     PetscCall(PetscOptionsFList("-pep_type","Polynomial eigensolver method","PEPSetType",PEPList,(char*)(((PetscObject)pep)->type_name?((PetscObject)pep)->type_name:PEPTOAR),type,sizeof(type),&flg));
    100:     if (flg) PetscCall(PEPSetType(pep,type));
    101:     else if (!((PetscObject)pep)->type_name) PetscCall(PEPSetType(pep,PEPTOAR));

    103:     PetscCall(PetscOptionsBoolGroupBegin("-pep_general","General polynomial eigenvalue problem","PEPSetProblemType",&flg));
    104:     if (flg) PetscCall(PEPSetProblemType(pep,PEP_GENERAL));
    105:     PetscCall(PetscOptionsBoolGroup("-pep_hermitian","Hermitian polynomial eigenvalue problem","PEPSetProblemType",&flg));
    106:     if (flg) PetscCall(PEPSetProblemType(pep,PEP_HERMITIAN));
    107:     PetscCall(PetscOptionsBoolGroup("-pep_hyperbolic","Hyperbolic polynomial eigenvalue problem","PEPSetProblemType",&flg));
    108:     if (flg) PetscCall(PEPSetProblemType(pep,PEP_HYPERBOLIC));
    109:     PetscCall(PetscOptionsBoolGroupEnd("-pep_gyroscopic","Gyroscopic polynomial eigenvalue problem","PEPSetProblemType",&flg));
    110:     if (flg) PetscCall(PEPSetProblemType(pep,PEP_GYROSCOPIC));

    112:     scale = pep->scale;
    113:     PetscCall(PetscOptionsEnum("-pep_scale","Scaling strategy","PEPSetScale",PEPScaleTypes,(PetscEnum)scale,(PetscEnum*)&scale,&flg1));
    114:     r = pep->sfactor;
    115:     PetscCall(PetscOptionsReal("-pep_scale_factor","Scale factor","PEPSetScale",pep->sfactor,&r,&flg2));
    116:     if (!flg2 && r==1.0) r = PETSC_DETERMINE;
    117:     j = pep->sits;
    118:     PetscCall(PetscOptionsInt("-pep_scale_its","Number of iterations in diagonal scaling","PEPSetScale",pep->sits,&j,&flg3));
    119:     t = pep->slambda;
    120:     PetscCall(PetscOptionsReal("-pep_scale_lambda","Estimate of eigenvalue (modulus) for diagonal scaling","PEPSetScale",pep->slambda,&t,&flg4));
    121:     if (flg1 || flg2 || flg3 || flg4) PetscCall(PEPSetScale(pep,scale,r,NULL,NULL,j,t));

    123:     PetscCall(PetscOptionsEnum("-pep_extract","Extraction method","PEPSetExtract",PEPExtractTypes,(PetscEnum)pep->extract,(PetscEnum*)&pep->extract,NULL));

    125:     refine = pep->refine;
    126:     PetscCall(PetscOptionsEnum("-pep_refine","Iterative refinement method","PEPSetRefine",PEPRefineTypes,(PetscEnum)refine,(PetscEnum*)&refine,&flg1));
    127:     i = pep->npart;
    128:     PetscCall(PetscOptionsInt("-pep_refine_partitions","Number of partitions of the communicator for iterative refinement","PEPSetRefine",pep->npart,&i,&flg2));
    129:     r = pep->rtol;
    130:     PetscCall(PetscOptionsReal("-pep_refine_tol","Tolerance for iterative refinement","PEPSetRefine",pep->rtol==(PetscReal)PETSC_DETERMINE?SLEPC_DEFAULT_TOL/1000:pep->rtol,&r,&flg3));
    131:     j = pep->rits;
    132:     PetscCall(PetscOptionsInt("-pep_refine_its","Maximum number of iterations for iterative refinement","PEPSetRefine",pep->rits,&j,&flg4));
    133:     scheme = pep->scheme;
    134:     PetscCall(PetscOptionsEnum("-pep_refine_scheme","Scheme used for linear systems within iterative refinement","PEPSetRefine",PEPRefineSchemes,(PetscEnum)scheme,(PetscEnum*)&scheme,&flg5));
    135:     if (flg1 || flg2 || flg3 || flg4 || flg5) PetscCall(PEPSetRefine(pep,refine,i,r,j,scheme));

    137:     i = pep->max_it;
    138:     PetscCall(PetscOptionsInt("-pep_max_it","Maximum number of iterations","PEPSetTolerances",pep->max_it,&i,&flg1));
    139:     r = pep->tol;
    140:     PetscCall(PetscOptionsReal("-pep_tol","Tolerance","PEPSetTolerances",SlepcDefaultTol(pep->tol),&r,&flg2));
    141:     if (flg1 || flg2) PetscCall(PEPSetTolerances(pep,r,i));

    143:     PetscCall(PetscOptionsBoolGroupBegin("-pep_conv_rel","Relative error convergence test","PEPSetConvergenceTest",&flg));
    144:     if (flg) PetscCall(PEPSetConvergenceTest(pep,PEP_CONV_REL));
    145:     PetscCall(PetscOptionsBoolGroup("-pep_conv_norm","Convergence test relative to the matrix norms","PEPSetConvergenceTest",&flg));
    146:     if (flg) PetscCall(PEPSetConvergenceTest(pep,PEP_CONV_NORM));
    147:     PetscCall(PetscOptionsBoolGroup("-pep_conv_abs","Absolute error convergence test","PEPSetConvergenceTest",&flg));
    148:     if (flg) PetscCall(PEPSetConvergenceTest(pep,PEP_CONV_ABS));
    149:     PetscCall(PetscOptionsBoolGroupEnd("-pep_conv_user","User-defined convergence test","PEPSetConvergenceTest",&flg));
    150:     if (flg) PetscCall(PEPSetConvergenceTest(pep,PEP_CONV_USER));

    152:     PetscCall(PetscOptionsBoolGroupBegin("-pep_stop_basic","Stop iteration if all eigenvalues converged or max_it reached","PEPSetStoppingTest",&flg));
    153:     if (flg) PetscCall(PEPSetStoppingTest(pep,PEP_STOP_BASIC));
    154:     PetscCall(PetscOptionsBoolGroupEnd("-pep_stop_user","User-defined stopping test","PEPSetStoppingTest",&flg));
    155:     if (flg) PetscCall(PEPSetStoppingTest(pep,PEP_STOP_USER));

    157:     i = pep->nev;
    158:     PetscCall(PetscOptionsInt("-pep_nev","Number of eigenvalues to compute","PEPSetDimensions",pep->nev,&i,&flg1));
    159:     j = pep->ncv;
    160:     PetscCall(PetscOptionsInt("-pep_ncv","Number of basis vectors","PEPSetDimensions",pep->ncv,&j,&flg2));
    161:     k = pep->mpd;
    162:     PetscCall(PetscOptionsInt("-pep_mpd","Maximum dimension of projected problem","PEPSetDimensions",pep->mpd,&k,&flg3));
    163:     if (flg1 || flg2 || flg3) PetscCall(PEPSetDimensions(pep,i,j,k));

    165:     PetscCall(PetscOptionsEnum("-pep_basis","Polynomial basis","PEPSetBasis",PEPBasisTypes,(PetscEnum)pep->basis,(PetscEnum*)&pep->basis,NULL));

    167:     PetscCall(PetscOptionsBoolGroupBegin("-pep_largest_magnitude","Compute largest eigenvalues in magnitude","PEPSetWhichEigenpairs",&flg));
    168:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_LARGEST_MAGNITUDE));
    169:     PetscCall(PetscOptionsBoolGroup("-pep_smallest_magnitude","Compute smallest eigenvalues in magnitude","PEPSetWhichEigenpairs",&flg));
    170:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_SMALLEST_MAGNITUDE));
    171:     PetscCall(PetscOptionsBoolGroup("-pep_largest_real","Compute eigenvalues with largest real parts","PEPSetWhichEigenpairs",&flg));
    172:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_LARGEST_REAL));
    173:     PetscCall(PetscOptionsBoolGroup("-pep_smallest_real","Compute eigenvalues with smallest real parts","PEPSetWhichEigenpairs",&flg));
    174:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_SMALLEST_REAL));
    175:     PetscCall(PetscOptionsBoolGroup("-pep_largest_imaginary","Compute eigenvalues with largest imaginary parts","PEPSetWhichEigenpairs",&flg));
    176:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_LARGEST_IMAGINARY));
    177:     PetscCall(PetscOptionsBoolGroup("-pep_smallest_imaginary","Compute eigenvalues with smallest imaginary parts","PEPSetWhichEigenpairs",&flg));
    178:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_SMALLEST_IMAGINARY));
    179:     PetscCall(PetscOptionsBoolGroup("-pep_target_magnitude","Compute eigenvalues closest to target","PEPSetWhichEigenpairs",&flg));
    180:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_TARGET_MAGNITUDE));
    181:     PetscCall(PetscOptionsBoolGroup("-pep_target_real","Compute eigenvalues with real parts closest to target","PEPSetWhichEigenpairs",&flg));
    182:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_TARGET_REAL));
    183:     PetscCall(PetscOptionsBoolGroup("-pep_target_imaginary","Compute eigenvalues with imaginary parts closest to target","PEPSetWhichEigenpairs",&flg));
    184:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_TARGET_IMAGINARY));
    185:     PetscCall(PetscOptionsBoolGroup("-pep_all","Compute all eigenvalues in an interval or a region","PEPSetWhichEigenpairs",&flg));
    186:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_ALL));
    187:     PetscCall(PetscOptionsBoolGroupEnd("-pep_which_user","Select the user-defined selection criterion","PEPSetWhichEigenpairs",&flg));
    188:     if (flg) PetscCall(PEPSetWhichEigenpairs(pep,PEP_WHICH_USER));

    190:     PetscCall(PetscOptionsScalar("-pep_target","Value of the target","PEPSetTarget",pep->target,&s,&flg));
    191:     if (flg) {
    192:       if (pep->which!=PEP_TARGET_REAL && pep->which!=PEP_TARGET_IMAGINARY) PetscCall(PEPSetWhichEigenpairs(pep,PEP_TARGET_MAGNITUDE));
    193:       PetscCall(PEPSetTarget(pep,s));
    194:     }

    196:     k = 2;
    197:     PetscCall(PetscOptionsRealArray("-pep_interval","Computational interval (two real values separated with a comma without spaces)","PEPSetInterval",array,&k,&flg));
    198:     if (flg) {
    199:       PetscCheck(k>1,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_SIZ,"Must pass two values in -pep_interval (comma-separated without spaces)");
    200:       PetscCall(PEPSetWhichEigenpairs(pep,PEP_ALL));
    201:       PetscCall(PEPSetInterval(pep,array[0],array[1]));
    202:     }

    204:     /* -----------------------------------------------------------------------*/
    205:     /*
    206:       Cancels all monitors hardwired into code before call to PEPSetFromOptions()
    207:     */
    208:     PetscCall(PetscOptionsBool("-pep_monitor_cancel","Remove any hardwired monitor routines","PEPMonitorCancel",PETSC_FALSE,&flg,&set));
    209:     if (set && flg) PetscCall(PEPMonitorCancel(pep));
    210:     PetscCall(PEPMonitorSetFromOptions(pep,"-pep_monitor","first_approximation",NULL,PETSC_FALSE));
    211:     PetscCall(PEPMonitorSetFromOptions(pep,"-pep_monitor_all","all_approximations",NULL,PETSC_TRUE));
    212:     PetscCall(PEPMonitorSetFromOptions(pep,"-pep_monitor_conv","convergence_history",NULL,PETSC_FALSE));

    214:     /* -----------------------------------------------------------------------*/
    215:     PetscCall(PetscOptionsName("-pep_view","Print detailed information on solver used","PEPView",&set));
    216:     PetscCall(PetscOptionsName("-pep_view_vectors","View computed eigenvectors","PEPVectorsView",&set));
    217:     PetscCall(PetscOptionsName("-pep_view_values","View computed eigenvalues","PEPValuesView",&set));
    218:     PetscCall(PetscOptionsName("-pep_converged_reason","Print reason for convergence, and number of iterations","PEPConvergedReasonView",&set));
    219:     PetscCall(PetscOptionsName("-pep_error_absolute","Print absolute errors of each eigenpair","PEPErrorView",&set));
    220:     PetscCall(PetscOptionsName("-pep_error_relative","Print relative errors of each eigenpair","PEPErrorView",&set));
    221:     PetscCall(PetscOptionsName("-pep_error_backward","Print backward errors of each eigenpair","PEPErrorView",&set));

    223:     PetscTryTypeMethod(pep,setfromoptions,PetscOptionsObject);
    224:     PetscCall(PetscObjectProcessOptionsHandlers((PetscObject)pep,PetscOptionsObject));
    225:   PetscOptionsEnd();

    227:   if (!pep->V) PetscCall(PEPGetBV(pep,&pep->V));
    228:   PetscCall(BVSetFromOptions(pep->V));
    229:   if (!pep->rg) PetscCall(PEPGetRG(pep,&pep->rg));
    230:   PetscCall(RGSetFromOptions(pep->rg));
    231:   if (!pep->ds) PetscCall(PEPGetDS(pep,&pep->ds));
    232:   PetscCall(PEPSetDSType(pep));
    233:   PetscCall(DSSetFromOptions(pep->ds));
    234:   if (!pep->st) PetscCall(PEPGetST(pep,&pep->st));
    235:   PetscCall(PEPSetDefaultST(pep));
    236:   PetscCall(STSetFromOptions(pep->st));
    237:   if (!pep->refineksp) PetscCall(PEPRefineGetKSP(pep,&pep->refineksp));
    238:   PetscCall(KSPSetFromOptions(pep->refineksp));
    239:   PetscFunctionReturn(PETSC_SUCCESS);
    240: }

    242: /*@
    243:    PEPGetTolerances - Gets the tolerance and maximum iteration count used
    244:    by the `PEP` convergence tests.

    246:    Not Collective

    248:    Input Parameter:
    249: .  pep - the polynomial eigensolver context

    251:    Output Parameters:
    252: +  tol - the convergence tolerance
    253: -  maxits - maximum number of iterations

    255:    Note:
    256:    The user can specify `NULL` for any parameter that is not needed.

    258:    Level: intermediate

    260: .seealso: [](ch:pep), `PEPSetTolerances()`
    261: @*/
    262: PetscErrorCode PEPGetTolerances(PEP pep,PetscReal *tol,PetscInt *maxits)
    263: {
    264:   PetscFunctionBegin;
    266:   if (tol)    *tol    = pep->tol;
    267:   if (maxits) *maxits = pep->max_it;
    268:   PetscFunctionReturn(PETSC_SUCCESS);
    269: }

    271: /*@
    272:    PEPSetTolerances - Sets the tolerance and maximum iteration count used
    273:    by the `PEP` convergence tests.

    275:    Logically Collective

    277:    Input Parameters:
    278: +  pep    - the polynomial eigensolver context
    279: .  tol    - the convergence tolerance
    280: -  maxits - maximum number of iterations to use

    282:    Options Database Keys:
    283: +  -pep_tol tol       - sets the convergence tolerance
    284: -  -pep_max_it maxits - sets the maximum number of iterations allowed

    286:    Note:
    287:    Use `PETSC_CURRENT` to retain the current value of any of the parameters.
    288:    Use `PETSC_DETERMINE` for either argument to assign a default value computed
    289:    internally (may be different in each solver).
    290:    For `maxits` use `PETSC_UNLIMITED` to indicate there is no upper bound on this value.

    292:    Level: intermediate

    294: .seealso: [](ch:pep), `PEPGetTolerances()`
    295: @*/
    296: PetscErrorCode PEPSetTolerances(PEP pep,PetscReal tol,PetscInt maxits)
    297: {
    298:   PetscFunctionBegin;
    302:   if (tol == (PetscReal)PETSC_DETERMINE) {
    303:     pep->tol   = PETSC_DETERMINE;
    304:     pep->state = PEP_STATE_INITIAL;
    305:   } else if (tol != (PetscReal)PETSC_CURRENT) {
    306:     PetscCheck(tol>0.0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of tol. Must be > 0");
    307:     pep->tol = tol;
    308:   }
    309:   if (maxits == PETSC_DETERMINE) {
    310:     pep->max_it = PETSC_DETERMINE;
    311:     pep->state  = PEP_STATE_INITIAL;
    312:   } else if (maxits == PETSC_UNLIMITED) {
    313:     pep->max_it = PETSC_INT_MAX;
    314:   } else if (maxits != PETSC_CURRENT) {
    315:     PetscCheck(maxits>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of maxits. Must be > 0");
    316:     pep->max_it = maxits;
    317:   }
    318:   PetscFunctionReturn(PETSC_SUCCESS);
    319: }

    321: /*@
    322:    PEPGetDimensions - Gets the number of eigenvalues to compute
    323:    and the dimension of the subspace.

    325:    Not Collective

    327:    Input Parameter:
    328: .  pep - the polynomial eigensolver context

    330:    Output Parameters:
    331: +  nev - number of eigenvalues to compute
    332: .  ncv - the maximum dimension of the subspace to be used by the solver
    333: -  mpd - the maximum dimension allowed for the projected problem

    335:    Notes:
    336:    The user can specify `NULL` for any parameter that is not needed.

    338:    Level: intermediate

    340: .seealso: [](ch:pep), `PEPSetDimensions()`
    341: @*/
    342: PetscErrorCode PEPGetDimensions(PEP pep,PetscInt *nev,PetscInt *ncv,PetscInt *mpd)
    343: {
    344:   PetscFunctionBegin;
    346:   if (nev) *nev = pep->nev;
    347:   if (ncv) *ncv = pep->ncv;
    348:   if (mpd) *mpd = pep->mpd;
    349:   PetscFunctionReturn(PETSC_SUCCESS);
    350: }

    352: /*@
    353:    PEPSetDimensions - Sets the number of eigenvalues to compute
    354:    and the dimension of the subspace.

    356:    Logically Collective

    358:    Input Parameters:
    359: +  pep - the polynomial eigensolver context
    360: .  nev - number of eigenvalues to compute
    361: .  ncv - the maximum dimension of the subspace to be used by the solver
    362: -  mpd - the maximum dimension allowed for the projected problem

    364:    Options Database Keys:
    365: +  -pep_nev nev - sets the number of eigenvalues
    366: .  -pep_ncv ncv - sets the dimension of the subspace
    367: -  -pep_mpd mpd - sets the maximum projected dimension

    369:    Notes:
    370:    Use `PETSC_DETERMINE` for `ncv` and `mpd` to assign a reasonably good value, which is
    371:    dependent on the solution method. For any of the arguments, use `PETSC_CURRENT`
    372:    to preserve the current value.

    374:    The parameters `ncv` and `mpd` are intimately related, so that the user is advised
    375:    to set one of them at most. Normal usage is\:

    377:     1. in cases where `nev` is small, the user sets `ncv` (a reasonable default is `2*nev`).
    378:     2. in cases where `nev` is large, the user sets `mpd`.

    380:    The value of `ncv` should always be between `nev` and `(nev+mpd)`, typically
    381:    `ncv=nev+mpd`. If `nev` is not too large, `mpd=nev` is a reasonable choice, otherwise
    382:    a smaller value should be used.

    384:    When computing all eigenvalues in an interval, see `PEPSetInterval()`, these
    385:    parameters lose relevance, and tuning must be done with
    386:    `PEPSTOARSetDimensions()`.

    388:    Level: intermediate

    390: .seealso: [](ch:pep), `PEPGetDimensions()`, `PEPSetInterval()`, `PEPSTOARSetDimensions()`
    391: @*/
    392: PetscErrorCode PEPSetDimensions(PEP pep,PetscInt nev,PetscInt ncv,PetscInt mpd)
    393: {
    394:   PetscFunctionBegin;
    399:   if (nev != PETSC_CURRENT) {
    400:     PetscCheck(nev>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of nev. Must be > 0");
    401:     pep->nev = nev;
    402:   }
    403:   if (ncv == PETSC_DETERMINE) {
    404:     pep->ncv = PETSC_DETERMINE;
    405:   } else if (ncv != PETSC_CURRENT) {
    406:     PetscCheck(ncv>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of ncv. Must be > 0");
    407:     pep->ncv = ncv;
    408:   }
    409:   if (mpd == PETSC_DETERMINE) {
    410:     pep->mpd = PETSC_DETERMINE;
    411:   } else if (mpd != PETSC_CURRENT) {
    412:     PetscCheck(mpd>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of mpd. Must be > 0");
    413:     pep->mpd = mpd;
    414:   }
    415:   pep->state = PEP_STATE_INITIAL;
    416:   PetscFunctionReturn(PETSC_SUCCESS);
    417: }

    419: /*@
    420:    PEPSetWhichEigenpairs - Specifies which portion of the spectrum is
    421:    to be sought.

    423:    Logically Collective

    425:    Input Parameters:
    426: +  pep   - the polynomial eigensolver context
    427: -  which - the portion of the spectrum to be sought, see `PEPWhich` for possible values

    429:    Options Database Keys:
    430: +  -pep_largest_magnitude  - sets largest eigenvalues in magnitude
    431: .  -pep_smallest_magnitude - sets smallest eigenvalues in magnitude
    432: .  -pep_largest_real       - sets largest real parts
    433: .  -pep_smallest_real      - sets smallest real parts
    434: .  -pep_largest_imaginary  - sets largest imaginary parts
    435: .  -pep_smallest_imaginary - sets smallest imaginary parts
    436: .  -pep_target_magnitude   - sets eigenvalues closest to target
    437: .  -pep_target_real        - sets real parts closest to target
    438: .  -pep_target_imaginary   - sets imaginary parts closest to target
    439: .  -pep_all                - sets all eigenvalues in an interval or region
    440: -  -pep_which_user         - select the user-defined selection criterion

    442:    Notes:
    443:    Not all eigensolvers implemented in `PEP` account for all the possible values
    444:    of `which`. Also, some values make sense only for certain types of
    445:    problems. If SLEPc is compiled for real numbers `PEP_LARGEST_IMAGINARY`
    446:    and `PEP_SMALLEST_IMAGINARY` use the absolute value of the imaginary part
    447:    for eigenvalue selection.

    449:    The target is a scalar value provided with `PEPSetTarget()`.

    451:    The criterion `PEP_TARGET_IMAGINARY` is available only in case PETSc and
    452:    SLEPc have been built with complex scalars.

    454:    `PEP_ALL` is intended for use in combination with an interval (see
    455:    `PEPSetInterval()`), when all eigenvalues within the interval are requested,
    456:    and also for computing all eigenvalues in a region with the `PEPCISS` solver.

    458:    Level: intermediate

    460: .seealso: [](ch:pep), `PEPGetWhichEigenpairs()`, `PEPSetTarget()`, `PEPSetInterval()`, `PEPSetDimensions()`, `PEPSetEigenvalueComparison()`, `PEPWhich`
    461: @*/
    462: PetscErrorCode PEPSetWhichEigenpairs(PEP pep,PEPWhich which)
    463: {
    464:   PetscFunctionBegin;
    467:   switch (which) {
    468:     case PEP_LARGEST_MAGNITUDE:
    469:     case PEP_SMALLEST_MAGNITUDE:
    470:     case PEP_LARGEST_REAL:
    471:     case PEP_SMALLEST_REAL:
    472:     case PEP_LARGEST_IMAGINARY:
    473:     case PEP_SMALLEST_IMAGINARY:
    474:     case PEP_TARGET_MAGNITUDE:
    475:     case PEP_TARGET_REAL:
    476: #if defined(PETSC_USE_COMPLEX)
    477:     case PEP_TARGET_IMAGINARY:
    478: #endif
    479:     case PEP_ALL:
    480:     case PEP_WHICH_USER:
    481:       if (pep->which != which) {
    482:         pep->state = PEP_STATE_INITIAL;
    483:         pep->which = which;
    484:       }
    485:       break;
    486: #if !defined(PETSC_USE_COMPLEX)
    487:     case PEP_TARGET_IMAGINARY:
    488:       SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_SUP,"PEP_TARGET_IMAGINARY can be used only with complex scalars");
    489: #endif
    490:     default:
    491:       SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid 'which' value");
    492:   }
    493:   PetscFunctionReturn(PETSC_SUCCESS);
    494: }

    496: /*@
    497:     PEPGetWhichEigenpairs - Returns which portion of the spectrum is to be
    498:     sought.

    500:     Not Collective

    502:     Input Parameter:
    503: .   pep - the polynomial eigensolver context

    505:     Output Parameter:
    506: .   which - the portion of the spectrum to be sought

    508:     Level: intermediate

    510: .seealso: [](ch:pep), `PEPSetWhichEigenpairs()`, `PEPWhich`
    511: @*/
    512: PetscErrorCode PEPGetWhichEigenpairs(PEP pep,PEPWhich *which)
    513: {
    514:   PetscFunctionBegin;
    516:   PetscAssertPointer(which,2);
    517:   *which = pep->which;
    518:   PetscFunctionReturn(PETSC_SUCCESS);
    519: }

    521: /*@C
    522:    PEPSetEigenvalueComparison - Specifies the eigenvalue comparison function
    523:    when `PEPSetWhichEigenpairs()` is set to `PEP_WHICH_USER`.

    525:    Logically Collective

    527:    Input Parameters:
    528: +  pep  - the polynomial eigensolver context
    529: .  comp - the comparison function, see `SlepcEigenvalueComparisonFn` for the calling sequence
    530: -  ctx  - a context pointer (the last parameter to the comparison function)

    532:    Level: advanced

    534: .seealso: [](ch:pep), `PEPSetWhichEigenpairs()`, `PEPWhich`
    535: @*/
    536: PetscErrorCode PEPSetEigenvalueComparison(PEP pep,SlepcEigenvalueComparisonFn *comp,PetscCtx ctx)
    537: {
    538:   PetscFunctionBegin;
    540:   pep->sc->comparison    = comp;
    541:   pep->sc->comparisonctx = ctx;
    542:   pep->which             = PEP_WHICH_USER;
    543:   PetscFunctionReturn(PETSC_SUCCESS);
    544: }

    546: /*@
    547:    PEPSetProblemType - Specifies the type of the polynomial eigenvalue problem.

    549:    Logically Collective

    551:    Input Parameters:
    552: +  pep  - the polynomial eigensolver context
    553: -  type - a known type of polynomial eigenvalue problem

    555:    Options Database Keys:
    556: +  -pep_general    - general problem with no particular structure
    557: .  -pep_hermitian  - problem whose coefficient matrices are Hermitian
    558: .  -pep_hyperbolic - Hermitian problem that satisfies the definition of hyperbolic
    559: -  -pep_gyroscopic - problem with gyroscopic structure

    561:    Notes:
    562:    See `PEPProblemType` for possible problem types.

    564:    This function is used to instruct SLEPc to exploit certain structure in
    565:    the polynomial eigenproblem. By default, no particular structure is assumed.

    567:    If the problem matrices are Hermitian (symmetric in the real case) or
    568:    Hermitian/skew-Hermitian then the solver can exploit this fact to perform
    569:    less operations or provide better stability. Hyperbolic problems are a
    570:    particular case of Hermitian problems, some solvers may treat them simply as
    571:    Hermitian.

    573:    Level: intermediate

    575: .seealso: [](ch:pep), `PEPSetOperators()`, `PEPSetType()`, `PEPGetProblemType()`, `PEPProblemType`
    576: @*/
    577: PetscErrorCode PEPSetProblemType(PEP pep,PEPProblemType type)
    578: {
    579:   PetscFunctionBegin;
    582:   PetscCheck(type==PEP_GENERAL || type==PEP_HERMITIAN || type==PEP_HYPERBOLIC || type==PEP_GYROSCOPIC,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_WRONG,"Unknown eigenvalue problem type");
    583:   if (type != pep->problem_type) {
    584:     pep->problem_type = type;
    585:     pep->state = PEP_STATE_INITIAL;
    586:   }
    587:   PetscFunctionReturn(PETSC_SUCCESS);
    588: }

    590: /*@
    591:    PEPGetProblemType - Gets the problem type from the `PEP` object.

    593:    Not Collective

    595:    Input Parameter:
    596: .  pep - the polynomial eigensolver context

    598:    Output Parameter:
    599: .  type - the problem type

    601:    Level: intermediate

    603: .seealso: [](ch:pep), `PEPSetProblemType()`, `PEPProblemType`
    604: @*/
    605: PetscErrorCode PEPGetProblemType(PEP pep,PEPProblemType *type)
    606: {
    607:   PetscFunctionBegin;
    609:   PetscAssertPointer(type,2);
    610:   *type = pep->problem_type;
    611:   PetscFunctionReturn(PETSC_SUCCESS);
    612: }

    614: /*@
    615:    PEPSetBasis - Specifies the type of polynomial basis used to describe the
    616:    polynomial eigenvalue problem.

    618:    Logically Collective

    620:    Input Parameters:
    621: +  pep   - the polynomial eigensolver context
    622: -  basis - the type of polynomial basis, see `PEPBasis` for possible values

    624:    Options Database Key:
    625: .  -pep_basis (monomial|chebyshev1|chebyshev2|legendre|laguerre|hermite) - select the basis type

    627:    Note:
    628:    By default, the coefficient matrices passed via `PEPSetOperators()` are
    629:    expressed in the monomial basis, i.e.
    630:    $P(\lambda) = A_0 + \lambda A_1 + \lambda^2 A_2 + \dots + \lambda^d A_d$.
    631:    Other polynomial bases may have better numerical behavior, but the user
    632:    must then pass the coefficient matrices accordingly.

    634:    Level: intermediate

    636: .seealso: [](ch:pep), `PEPSetOperators()`, `PEPGetBasis()`, `PEPBasis`
    637: @*/
    638: PetscErrorCode PEPSetBasis(PEP pep,PEPBasis basis)
    639: {
    640:   PetscFunctionBegin;
    643:   pep->basis = basis;
    644:   PetscFunctionReturn(PETSC_SUCCESS);
    645: }

    647: /*@
    648:    PEPGetBasis - Gets the type of polynomial basis from the `PEP` object.

    650:    Not Collective

    652:    Input Parameter:
    653: .  pep - the polynomial eigensolver context

    655:    Output Parameter:
    656: .  basis - the polynomial basis

    658:    Level: intermediate

    660: .seealso: [](ch:pep), `PEPSetBasis()`, `PEPBasis`
    661: @*/
    662: PetscErrorCode PEPGetBasis(PEP pep,PEPBasis *basis)
    663: {
    664:   PetscFunctionBegin;
    666:   PetscAssertPointer(basis,2);
    667:   *basis = pep->basis;
    668:   PetscFunctionReturn(PETSC_SUCCESS);
    669: }

    671: /*@
    672:    PEPSetTrackAll - Specifies if the solver must compute the residual of all
    673:    approximate eigenpairs or not.

    675:    Logically Collective

    677:    Input Parameters:
    678: +  pep      - the polynomial eigensolver context
    679: -  trackall - whether compute all residuals or not

    681:    Notes:
    682:    If the user sets `trackall`=`PETSC_TRUE` then the solver explicitly computes
    683:    the residual for each eigenpair approximation. Computing the residual is
    684:    usually an expensive operation and solvers commonly compute the associated
    685:    residual to the first unconverged eigenpair.

    687:    The option `-pep_monitor_all` automatically activates this option.

    689:    Level: developer

    691: .seealso: [](ch:pep), `PEPGetTrackAll()`
    692: @*/
    693: PetscErrorCode PEPSetTrackAll(PEP pep,PetscBool trackall)
    694: {
    695:   PetscFunctionBegin;
    698:   pep->trackall = trackall;
    699:   PetscFunctionReturn(PETSC_SUCCESS);
    700: }

    702: /*@
    703:    PEPGetTrackAll - Returns the flag indicating whether all residual norms must
    704:    be computed or not.

    706:    Not Collective

    708:    Input Parameter:
    709: .  pep - the polynomial eigensolver context

    711:    Output Parameter:
    712: .  trackall - the returned flag

    714:    Level: developer

    716: .seealso: [](ch:pep), `PEPSetTrackAll()`
    717: @*/
    718: PetscErrorCode PEPGetTrackAll(PEP pep,PetscBool *trackall)
    719: {
    720:   PetscFunctionBegin;
    722:   PetscAssertPointer(trackall,2);
    723:   *trackall = pep->trackall;
    724:   PetscFunctionReturn(PETSC_SUCCESS);
    725: }

    727: /*@C
    728:    PEPSetConvergenceTestFunction - Sets a function to compute the error estimate
    729:    used in the convergence test.

    731:    Logically Collective

    733:    Input Parameters:
    734: +  pep     - the polynomial eigensolver context
    735: .  conv    - convergence test function, see `PEPConvergenceTestFn` for the calling sequence
    736: .  ctx     - context for private data for the convergence routine (may be `NULL`)
    737: -  destroy - a routine for destroying the context (may be `NULL`), see `PetscCtxDestroyFn`
    738:              for the calling sequence

    740:    Notes:
    741:    When this is called with a user-defined function, then the convergence
    742:    criterion is set to `PEP_CONV_USER`, see `PEPSetConvergenceTest()`.

    744:    If the error estimate returned by the convergence test function is less than
    745:    the tolerance, then the eigenvalue is accepted as converged.

    747:    Level: advanced

    749: .seealso: [](ch:pep), `PEPSetConvergenceTest()`, `PEPSetTolerances()`
    750: @*/
    751: PetscErrorCode PEPSetConvergenceTestFunction(PEP pep,PEPConvergenceTestFn *conv,PetscCtx ctx,PetscCtxDestroyFn *destroy)
    752: {
    753:   PetscFunctionBegin;
    755:   if (pep->convergeddestroy) PetscCall((*pep->convergeddestroy)(&pep->convergedctx));
    756:   pep->convergeduser    = conv;
    757:   pep->convergeddestroy = destroy;
    758:   pep->convergedctx     = ctx;
    759:   if (conv == PEPConvergedRelative) pep->conv = PEP_CONV_REL;
    760:   else if (conv == PEPConvergedNorm) pep->conv = PEP_CONV_NORM;
    761:   else if (conv == PEPConvergedAbsolute) pep->conv = PEP_CONV_ABS;
    762:   else {
    763:     pep->conv      = PEP_CONV_USER;
    764:     pep->converged = pep->convergeduser;
    765:   }
    766:   PetscFunctionReturn(PETSC_SUCCESS);
    767: }

    769: /*@
    770:    PEPSetConvergenceTest - Specifies how to compute the error estimate
    771:    used in the convergence test.

    773:    Logically Collective

    775:    Input Parameters:
    776: +  pep  - the polynomial eigensolver context
    777: -  conv - the type of convergence test, see `PEPConv` for possible values

    779:    Options Database Keys:
    780: +  -pep_conv_abs  - sets the absolute convergence test
    781: .  -pep_conv_rel  - sets the convergence test relative to the eigenvalue
    782: .  -pep_conv_norm - sets the convergence test relative to the matrix norms
    783: -  -pep_conv_user - selects the user-defined convergence test

    785:    Level: intermediate

    787: .seealso: [](ch:pep), `PEPGetConvergenceTest()`, `PEPSetConvergenceTestFunction()`, `PEPSetStoppingTest()`, `PEPConv`
    788: @*/
    789: PetscErrorCode PEPSetConvergenceTest(PEP pep,PEPConv conv)
    790: {
    791:   PetscFunctionBegin;
    794:   switch (conv) {
    795:     case PEP_CONV_ABS:  pep->converged = PEPConvergedAbsolute; break;
    796:     case PEP_CONV_REL:  pep->converged = PEPConvergedRelative; break;
    797:     case PEP_CONV_NORM: pep->converged = PEPConvergedNorm; break;
    798:     case PEP_CONV_USER:
    799:       PetscCheck(pep->convergeduser,PetscObjectComm((PetscObject)pep),PETSC_ERR_ORDER,"Must call PEPSetConvergenceTestFunction() first");
    800:       pep->converged = pep->convergeduser;
    801:       break;
    802:     default:
    803:       SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid 'conv' value");
    804:   }
    805:   pep->conv = conv;
    806:   PetscFunctionReturn(PETSC_SUCCESS);
    807: }

    809: /*@
    810:    PEPGetConvergenceTest - Gets the method used to compute the error estimate
    811:    used in the convergence test.

    813:    Not Collective

    815:    Input Parameter:
    816: .  pep   - the polynomial eigensolver context

    818:    Output Parameter:
    819: .  conv  - the type of convergence test

    821:    Level: intermediate

    823: .seealso: [](ch:pep), `PEPSetConvergenceTest()`, `PEPConv`
    824: @*/
    825: PetscErrorCode PEPGetConvergenceTest(PEP pep,PEPConv *conv)
    826: {
    827:   PetscFunctionBegin;
    829:   PetscAssertPointer(conv,2);
    830:   *conv = pep->conv;
    831:   PetscFunctionReturn(PETSC_SUCCESS);
    832: }

    834: /*@C
    835:    PEPSetStoppingTestFunction - Sets a function to decide when to stop the outer
    836:    iteration of the eigensolver.

    838:    Logically Collective

    840:    Input Parameters:
    841: +  pep     - the polynomial eigensolver context
    842: .  stop    - stopping test function, see `PEPStoppingTestFn` for the calling sequence
    843: .  ctx     - context for private data for the stopping routine (may be `NULL`)
    844: -  destroy - a routine for destroying the context (may be `NULL`), see `PetscCtxDestroyFn`
    845:              for the calling sequence

    847:    Note:
    848:    When implementing a function for this, normal usage is to first call the
    849:    default routine `PEPStoppingBasic()` and then set `reason` to `PEP_CONVERGED_USER`
    850:    if some user-defined conditions have been met. To let the eigensolver continue
    851:    iterating, the result must be left as `PEP_CONVERGED_ITERATING`.

    853:    Level: advanced

    855: .seealso: [](ch:pep), `PEPSetStoppingTest()`, `PEPStoppingBasic()`
    856: @*/
    857: PetscErrorCode PEPSetStoppingTestFunction(PEP pep,PEPStoppingTestFn *stop,PetscCtx ctx,PetscCtxDestroyFn *destroy)
    858: {
    859:   PetscFunctionBegin;
    861:   if (pep->stoppingdestroy) PetscCall((*pep->stoppingdestroy)(&pep->stoppingctx));
    862:   pep->stoppinguser    = stop;
    863:   pep->stoppingdestroy = destroy;
    864:   pep->stoppingctx     = ctx;
    865:   if (stop == PEPStoppingBasic) pep->stop = PEP_STOP_BASIC;
    866:   else {
    867:     pep->stop     = PEP_STOP_USER;
    868:     pep->stopping = pep->stoppinguser;
    869:   }
    870:   PetscFunctionReturn(PETSC_SUCCESS);
    871: }

    873: /*@
    874:    PEPSetStoppingTest - Specifies how to decide the termination of the outer
    875:    loop of the eigensolver.

    877:    Logically Collective

    879:    Input Parameters:
    880: +  pep  - the polynomial eigensolver context
    881: -  stop - the type of stopping test, see `PEPStop`

    883:    Options Database Keys:
    884: +  -pep_stop_basic - sets the default stopping test
    885: -  -pep_stop_user  - selects the user-defined stopping test

    887:    Level: advanced

    889: .seealso: [](ch:pep), `PEPGetStoppingTest()`, `PEPSetStoppingTestFunction()`, `PEPSetConvergenceTest()`, `PEPStop`
    890: @*/
    891: PetscErrorCode PEPSetStoppingTest(PEP pep,PEPStop stop)
    892: {
    893:   PetscFunctionBegin;
    896:   switch (stop) {
    897:     case PEP_STOP_BASIC: pep->stopping = PEPStoppingBasic; break;
    898:     case PEP_STOP_USER:
    899:       PetscCheck(pep->stoppinguser,PetscObjectComm((PetscObject)pep),PETSC_ERR_ORDER,"Must call PEPSetStoppingTestFunction() first");
    900:       pep->stopping = pep->stoppinguser;
    901:       break;
    902:     default:
    903:       SETERRQ(PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Invalid 'stop' value");
    904:   }
    905:   pep->stop = stop;
    906:   PetscFunctionReturn(PETSC_SUCCESS);
    907: }

    909: /*@
    910:    PEPGetStoppingTest - Gets the method used to decide the termination of the outer
    911:    loop of the eigensolver.

    913:    Not Collective

    915:    Input Parameter:
    916: .  pep   - the polynomial eigensolver context

    918:    Output Parameter:
    919: .  stop  - the type of stopping test

    921:    Level: advanced

    923: .seealso: [](ch:pep), `PEPSetStoppingTest()`, `PEPStop`
    924: @*/
    925: PetscErrorCode PEPGetStoppingTest(PEP pep,PEPStop *stop)
    926: {
    927:   PetscFunctionBegin;
    929:   PetscAssertPointer(stop,2);
    930:   *stop = pep->stop;
    931:   PetscFunctionReturn(PETSC_SUCCESS);
    932: }

    934: /*@
    935:    PEPSetScale - Specifies the scaling strategy to be used.

    937:    Collective

    939:    Input Parameters:
    940: +  pep    - the polynomial eigensolver context
    941: .  scale  - scaling strategy, see `PEPScale` for possible values
    942: .  alpha  - the scaling factor used in the scalar strategy
    943: .  Dl     - the left diagonal matrix of the diagonal scaling algorithm
    944: .  Dr     - the right diagonal matrix of the diagonal scaling algorithm
    945: .  its    - number of iterations of the diagonal scaling algorithm
    946: -  lambda - approximation to wanted eigenvalues (modulus)

    948:    Options Database Keys:
    949: +  -pep_scale (none|scalar|diagonal|both) - set the scaling type
    950: .  -pep_scale_factor alpha                - set the scaling factor
    951: .  -pep_scale_its its                     - set the number of iterations
    952: -  -pep_scale_lambda lambda               - set the approximation to eigenvalues

    954:    Notes:
    955:    There are two non-exclusive scaling strategies, scalar and diagonal.
    956:    See discussion in section [](#sec:scaling).

    958:    In the scalar strategy, scaling is applied to the eigenvalue, that is,
    959:    $\mu = \lambda/\alpha$ is the new eigenvalue and all matrices are scaled
    960:    accordingly. After solving the scaled problem, the original $\lambda$ is
    961:    recovered. Parameter `alpha` must be positive. Use `PETSC_DETERMINE` to let
    962:    the solver compute a reasonable scaling factor, and `PETSC_CURRENT` to
    963:    retain a previously set value.

    965:    In the diagonal strategy, the solver works implicitly with matrix $D_\ell P(\lambda)D_r$,
    966:    where $D_\ell$ and $D_r$ are appropriate diagonal matrices. This improves the accuracy
    967:    of the computed results in some cases. The user may provide the `Dl` and `Dr`
    968:    matrices represented as `Vec` objects storing diagonal elements. If not
    969:    provided, these matrices are computed internally. This option requires
    970:    that the polynomial coefficient matrices are of `MATAIJ` type.
    971:    The parameter `its` is the number of iterations performed by the method.
    972:    Parameter `lambda` must be positive. Use `PETSC_DETERMINE` or set `lambda` = 1.0
    973:    if no information about eigenvalues is available. `PETSC_CURRENT` can also
    974:    be used to leave `its` and `lambda` unchanged.

    976:    Level: intermediate

    978: .seealso: [](ch:pep), [](#sec:scaling), `PEPGetScale()`
    979: @*/
    980: PetscErrorCode PEPSetScale(PEP pep,PEPScale scale,PetscReal alpha,Vec Dl,Vec Dr,PetscInt its,PetscReal lambda)
    981: {
    982:   PetscFunctionBegin;
    985:   pep->scale = scale;
    986:   if (scale==PEP_SCALE_SCALAR || scale==PEP_SCALE_BOTH) {
    988:     if (alpha == (PetscReal)PETSC_DETERMINE) {
    989:       pep->sfactor = 0.0;
    990:       pep->sfactor_set = PETSC_FALSE;
    991:     } else if (alpha != (PetscReal)PETSC_CURRENT) {
    992:       PetscCheck(alpha>0.0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of alpha. Must be > 0");
    993:       pep->sfactor = alpha;
    994:       pep->sfactor_set = PETSC_TRUE;
    995:     }
    996:   }
    997:   if (scale==PEP_SCALE_DIAGONAL || scale==PEP_SCALE_BOTH) {
    998:     if (Dl) {
    1000:       PetscCheckSameComm(pep,1,Dl,4);
    1001:       PetscCall(PetscObjectReference((PetscObject)Dl));
    1002:       PetscCall(VecDestroy(&pep->Dl));
    1003:       pep->Dl = Dl;
    1004:     }
    1005:     if (Dr) {
    1007:       PetscCheckSameComm(pep,1,Dr,5);
    1008:       PetscCall(PetscObjectReference((PetscObject)Dr));
    1009:       PetscCall(VecDestroy(&pep->Dr));
    1010:       pep->Dr = Dr;
    1011:     }
    1014:     if (its==PETSC_DETERMINE) pep->sits = 5;
    1015:     else if (its!=PETSC_CURRENT) {
    1016:       PetscCheck(its>0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of its. Must be > 0");
    1017:       pep->sits = its;
    1018:     }
    1019:     if (lambda == (PetscReal)PETSC_DETERMINE) pep->slambda = 1.0;
    1020:     else if (lambda != (PetscReal)PETSC_CURRENT) {
    1021:       PetscCheck(lambda>0.0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of lambda. Must be > 0");
    1022:       pep->slambda = lambda;
    1023:     }
    1024:   }
    1025:   pep->state = PEP_STATE_INITIAL;
    1026:   PetscFunctionReturn(PETSC_SUCCESS);
    1027: }

    1029: /*@
    1030:    PEPGetScale - Gets the scaling strategy used by the `PEP` object, and the
    1031:    associated parameters.

    1033:    Not Collective

    1035:    Input Parameter:
    1036: .  pep - the polynomial eigensolver context

    1038:    Output Parameters:
    1039: +  scale  - scaling strategy
    1040: .  alpha  - the scaling factor used in the scalar strategy
    1041: .  Dl     - the left diagonal matrix of the diagonal scaling algorithm
    1042: .  Dr     - the right diagonal matrix of the diagonal scaling algorithm
    1043: .  its    - number of iterations of the diagonal scaling algorithm
    1044: -  lambda - approximation to wanted eigenvalues (modulus)

    1046:    Notes:
    1047:    The user can specify `NULL` for any parameter that is not needed.

    1049:    If `Dl` or `Dr` were not set by the user, then the ones computed internally are
    1050:    returned (or a `NULL` pointer if called before `PEPSetUp()`).

    1052:    Level: intermediate

    1054: .seealso: [](ch:pep), `PEPSetScale()`, `PEPSetUp()`
    1055: @*/
    1056: PetscErrorCode PEPGetScale(PEP pep,PEPScale *scale,PetscReal *alpha,Vec *Dl,Vec *Dr,PetscInt *its,PetscReal *lambda)
    1057: {
    1058:   PetscFunctionBegin;
    1060:   if (scale)  *scale  = pep->scale;
    1061:   if (alpha)  *alpha  = pep->sfactor;
    1062:   if (Dl)     *Dl     = pep->Dl;
    1063:   if (Dr)     *Dr     = pep->Dr;
    1064:   if (its)    *its    = pep->sits;
    1065:   if (lambda) *lambda = pep->slambda;
    1066:   PetscFunctionReturn(PETSC_SUCCESS);
    1067: }

    1069: /*@
    1070:    PEPSetExtract - Specifies the extraction strategy to be used.

    1072:    Logically Collective

    1074:    Input Parameters:
    1075: +  pep     - the polynomial eigensolver context
    1076: -  extract - extraction strategy, see `PEPExtract` for possible values

    1078:    Options Database Key:
    1079: .  -pep_extract (none|norm|residual|structured) - set the extraction type

    1081:    Note:
    1082:    This is relevant for solvers based on linearization. Once the solver has
    1083:    converged, the polynomial eigenvectors can be extracted from the
    1084:    eigenvectors of the linearized problem in different ways. See the
    1085:    discussion in section [](#sec:pepextr).

    1087:    Level: intermediate

    1089: .seealso: [](ch:pep), [](#sec:pepextr), `PEPExtract`, `PEPGetExtract()`
    1090: @*/
    1091: PetscErrorCode PEPSetExtract(PEP pep,PEPExtract extract)
    1092: {
    1093:   PetscFunctionBegin;
    1096:   pep->extract = extract;
    1097:   PetscFunctionReturn(PETSC_SUCCESS);
    1098: }

    1100: /*@
    1101:    PEPGetExtract - Gets the extraction strategy used by the `PEP` object.

    1103:    Not Collective

    1105:    Input Parameter:
    1106: .  pep - the polynomial eigensolver context

    1108:    Output Parameter:
    1109: .  extract - extraction strategy

    1111:    Level: intermediate

    1113: .seealso: [](ch:pep), `PEPSetExtract()`, `PEPExtract`
    1114: @*/
    1115: PetscErrorCode PEPGetExtract(PEP pep,PEPExtract *extract)
    1116: {
    1117:   PetscFunctionBegin;
    1119:   PetscAssertPointer(extract,2);
    1120:   *extract = pep->extract;
    1121:   PetscFunctionReturn(PETSC_SUCCESS);
    1122: }

    1124: /*@
    1125:    PEPSetRefine - Specifies the refinement type (and options) to be used
    1126:    after the solve.

    1128:    Logically Collective

    1130:    Input Parameters:
    1131: +  pep    - the polynomial eigensolver context
    1132: .  refine - refinement type, see `PEPRefine` for possible values
    1133: .  npart  - number of partitions of the communicator
    1134: .  tol    - the convergence tolerance
    1135: .  its    - maximum number of refinement iterations
    1136: -  scheme - the scheme for solving the involved linear systems, see `PEPRefineScheme`
    1137:             for possible values

    1139:    Options Database Keys:
    1140: +  -pep_refine (none|simple|multiple)      - set the refinement type
    1141: .  -pep_refine_partitions npart            - set the number of partitions
    1142: .  -pep_refine_tol tol                     - set the tolerance
    1143: .  -pep_refine_its its                     - set the number of iterations
    1144: -  -pep_refine_scheme (schur|mbe|explicit) - set the scheme for the linear solves

    1146:    Notes:
    1147:    This function configures the parameters of Newton iterative refinement,
    1148:    see section [](#sec:refine) for a discussion of the different strategies.

    1150:    By default, iterative refinement is disabled, since it may be very
    1151:    costly. There are two possible refinement strategies, simple and multiple.
    1152:    The simple approach performs iterative refinement on each of the
    1153:    converged eigenpairs individually, whereas the multiple strategy works
    1154:    with the invariant pair as a whole, refining all eigenpairs simultaneously.
    1155:    The latter may be required for the case of multiple eigenvalues.

    1157:    In some cases, especially when using direct solvers within the
    1158:    iterative refinement method, it may be helpful for improved scalability
    1159:    to split the communicator in several partitions. The `npart` parameter
    1160:    indicates how many partitions to use (defaults to 1).

    1162:    The `tol` and `its` parameters specify the stopping criterion. In the simple
    1163:    method, refinement continues until the residual of each eigenpair is
    1164:    below the tolerance (`tol` defaults to the `PEP` tolerance, but may be set to a
    1165:    different value). In contrast, the multiple method simply performs its
    1166:    refinement iterations (just one by default).

    1168:    The `scheme` argument is used to change the way in which linear systems are
    1169:    solved. Possible choices are explicit, mixed block elimination (MBE),
    1170:    and Schur complement.

    1172:    Use `PETSC_CURRENT` to retain the current value of `npart`, `tol` or `its`. Use
    1173:    `PETSC_DETERMINE` to assign a default value.

    1175:    Level: intermediate

    1177: .seealso: [](ch:pep), [](#sec:refine), `PEPGetRefine()`
    1178: @*/
    1179: PetscErrorCode PEPSetRefine(PEP pep,PEPRefine refine,PetscInt npart,PetscReal tol,PetscInt its,PEPRefineScheme scheme)
    1180: {
    1181:   PetscMPIInt    size;

    1183:   PetscFunctionBegin;
    1190:   pep->refine = refine;
    1191:   if (refine) {  /* process parameters only if not REFINE_NONE */
    1192:     if (npart!=pep->npart) {
    1193:       PetscCall(PetscSubcommDestroy(&pep->refinesubc));
    1194:       PetscCall(KSPDestroy(&pep->refineksp));
    1195:     }
    1196:     if (npart == PETSC_DETERMINE) {
    1197:       pep->npart = 1;
    1198:     } else if (npart != PETSC_CURRENT) {
    1199:       PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)pep),&size));
    1200:       PetscCheck(npart>0 && npart<=size,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of npart");
    1201:       pep->npart = npart;
    1202:     }
    1203:     if (tol == (PetscReal)PETSC_DETERMINE) {
    1204:       pep->rtol = PETSC_DETERMINE;
    1205:     } else if (tol != (PetscReal)PETSC_CURRENT) {
    1206:       PetscCheck(tol>0.0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of tol. Must be > 0");
    1207:       pep->rtol = tol;
    1208:     }
    1209:     if (its==PETSC_DETERMINE) {
    1210:       pep->rits = PETSC_DETERMINE;
    1211:     } else if (its != PETSC_CURRENT) {
    1212:       PetscCheck(its>=0,PetscObjectComm((PetscObject)pep),PETSC_ERR_ARG_OUTOFRANGE,"Illegal value of its. Must be >= 0");
    1213:       pep->rits = its;
    1214:     }
    1215:     pep->scheme = scheme;
    1216:   }
    1217:   pep->state = PEP_STATE_INITIAL;
    1218:   PetscFunctionReturn(PETSC_SUCCESS);
    1219: }

    1221: /*@
    1222:    PEPGetRefine - Gets the refinement strategy used by the `PEP` object, and the
    1223:    associated parameters.

    1225:    Not Collective

    1227:    Input Parameter:
    1228: .  pep - the polynomial eigensolver context

    1230:    Output Parameters:
    1231: +  refine - refinement type
    1232: .  npart  - number of partitions of the communicator
    1233: .  tol    - the convergence tolerance
    1234: .  its    - maximum number of refinement iterations
    1235: -  scheme - the scheme used for solving linear systems

    1237:    Note:
    1238:    The user can specify `NULL` for any parameter that is not needed.

    1240:    Level: intermediate

    1242: .seealso: [](ch:pep), `PEPSetRefine()`
    1243: @*/
    1244: PetscErrorCode PEPGetRefine(PEP pep,PEPRefine *refine,PetscInt *npart,PetscReal *tol,PetscInt *its,PEPRefineScheme *scheme)
    1245: {
    1246:   PetscFunctionBegin;
    1248:   if (refine) *refine = pep->refine;
    1249:   if (npart)  *npart  = pep->npart;
    1250:   if (tol)    *tol    = pep->rtol;
    1251:   if (its)    *its    = pep->rits;
    1252:   if (scheme) *scheme = pep->scheme;
    1253:   PetscFunctionReturn(PETSC_SUCCESS);
    1254: }

    1256: /*@
    1257:    PEPSetOptionsPrefix - Sets the prefix used for searching for all
    1258:    `PEP` options in the database.

    1260:    Logically Collective

    1262:    Input Parameters:
    1263: +  pep    - the polynomial eigensolver context
    1264: -  prefix - the prefix string to prepend to all `PEP` option requests

    1266:    Notes:
    1267:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    1268:    The first character of all runtime options is AUTOMATICALLY the
    1269:    hyphen.

    1271:    For example, to distinguish between the runtime options for two
    1272:    different `PEP` contexts, one could call
    1273: .vb
    1274:    PEPSetOptionsPrefix(pep1,"qeig1_")
    1275:    PEPSetOptionsPrefix(pep2,"qeig2_")
    1276: .ve

    1278:    Level: advanced

    1280: .seealso: [](ch:pep), `PEPAppendOptionsPrefix()`, `PEPGetOptionsPrefix()`
    1281: @*/
    1282: PetscErrorCode PEPSetOptionsPrefix(PEP pep,const char prefix[])
    1283: {
    1284:   PetscFunctionBegin;
    1286:   if (!pep->st) PetscCall(PEPGetST(pep,&pep->st));
    1287:   PetscCall(STSetOptionsPrefix(pep->st,prefix));
    1288:   if (!pep->V) PetscCall(PEPGetBV(pep,&pep->V));
    1289:   PetscCall(BVSetOptionsPrefix(pep->V,prefix));
    1290:   if (!pep->ds) PetscCall(PEPGetDS(pep,&pep->ds));
    1291:   PetscCall(DSSetOptionsPrefix(pep->ds,prefix));
    1292:   if (!pep->rg) PetscCall(PEPGetRG(pep,&pep->rg));
    1293:   PetscCall(RGSetOptionsPrefix(pep->rg,prefix));
    1294:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)pep,prefix));
    1295:   PetscFunctionReturn(PETSC_SUCCESS);
    1296: }

    1298: /*@
    1299:    PEPAppendOptionsPrefix - Appends to the prefix used for searching for all
    1300:    `PEP` options in the database.

    1302:    Logically Collective

    1304:    Input Parameters:
    1305: +  pep    - the polynomial eigensolver context
    1306: -  prefix - the prefix string to prepend to all `PEP` option requests

    1308:    Notes:
    1309:    A hyphen (-) must NOT be given at the beginning of the prefix name.
    1310:    The first character of all runtime options is AUTOMATICALLY the hyphen.

    1312:    Level: advanced

    1314: .seealso: [](ch:pep), `PEPSetOptionsPrefix()`, `PEPGetOptionsPrefix()`
    1315: @*/
    1316: PetscErrorCode PEPAppendOptionsPrefix(PEP pep,const char prefix[])
    1317: {
    1318:   PetscFunctionBegin;
    1320:   if (!pep->st) PetscCall(PEPGetST(pep,&pep->st));
    1321:   PetscCall(STAppendOptionsPrefix(pep->st,prefix));
    1322:   if (!pep->V) PetscCall(PEPGetBV(pep,&pep->V));
    1323:   PetscCall(BVAppendOptionsPrefix(pep->V,prefix));
    1324:   if (!pep->ds) PetscCall(PEPGetDS(pep,&pep->ds));
    1325:   PetscCall(DSAppendOptionsPrefix(pep->ds,prefix));
    1326:   if (!pep->rg) PetscCall(PEPGetRG(pep,&pep->rg));
    1327:   PetscCall(RGAppendOptionsPrefix(pep->rg,prefix));
    1328:   PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)pep,prefix));
    1329:   PetscFunctionReturn(PETSC_SUCCESS);
    1330: }

    1332: /*@
    1333:    PEPGetOptionsPrefix - Gets the prefix used for searching for all
    1334:    `PEP` options in the database.

    1336:    Not Collective

    1338:    Input Parameter:
    1339: .  pep - the polynomial eigensolver context

    1341:    Output Parameter:
    1342: .  prefix - pointer to the prefix string used is returned

    1344:    Level: advanced

    1346: .seealso: [](ch:pep), `PEPSetOptionsPrefix()`, `PEPAppendOptionsPrefix()`
    1347: @*/
    1348: PetscErrorCode PEPGetOptionsPrefix(PEP pep,const char *prefix[])
    1349: {
    1350:   PetscFunctionBegin;
    1352:   PetscAssertPointer(prefix,2);
    1353:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)pep,prefix));
    1354:   PetscFunctionReturn(PETSC_SUCCESS);
    1355: }