Date: 2026-03-31T13:22:57+00:00

Actual source code: slepceps.h

      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:    User interface for the SLEPc linear eigenvalue solvers
     12: */

     14: #pragma once

     16: #include <slepcst.h>
     17: #include <slepcbv.h>
     18: #include <slepcds.h>
     19: #include <slepcrg.h>
     20: #include <slepclme.h>
     21: #include <petscsnes.h>

     23: /* SUBMANSEC = EPS */

     25: SLEPC_EXTERN PetscErrorCode EPSInitializePackage(void);
     26: SLEPC_EXTERN PetscErrorCode EPSFinalizePackage(void);

     28: /*S
     29:    EPS - SLEPc object that manages all the linear eigenvalue problem solvers.

     31:    Level: beginner

     33: .seealso: [](ch:eps), `EPSCreate()`, `ST`
     34: S*/
     35: typedef struct _p_EPS* EPS;

     37: /*J
     38:    EPSType - String with the name of a linear eigensolver.

     40:    Level: beginner

     42: .seealso: [](ch:eps), `EPSSetType()`, `EPS`
     43: J*/
     44: typedef const char *EPSType;
     45: #define EPSPOWER       "power"
     46: #define EPSSUBSPACE    "subspace"
     47: #define EPSARNOLDI     "arnoldi"
     48: #define EPSLANCZOS     "lanczos"
     49: #define EPSKRYLOVSCHUR "krylovschur"
     50: #define EPSGD          "gd"
     51: #define EPSJD          "jd"
     52: #define EPSRQCG        "rqcg"
     53: #define EPSLOBPCG      "lobpcg"
     54: #define EPSCISS        "ciss"
     55: #define EPSLYAPII      "lyapii"
     56: #define EPSLAPACK      "lapack"
     57: #define EPSARPACK      "arpack"
     58: #define EPSBLOPEX      "blopex"
     59: #define EPSPRIMME      "primme"
     60: #define EPSFEAST       "feast"
     61: #define EPSSCALAPACK   "scalapack"
     62: #define EPSELPA        "elpa"
     63: #define EPSELEMENTAL   "elemental"
     64: #define EPSEVSL        "evsl"
     65: #define EPSCHASE       "chase"

     67: /* Logging support */
     68: SLEPC_EXTERN PetscClassId EPS_CLASSID;

     70: /*E
     71:    EPSProblemType - Determines the type of eigenvalue problem.

     73:    Values:
     74: +  `EPS_HEP`    - Hermitian
     75: .  `EPS_GHEP`   - generalized Hermitian
     76: .  `EPS_NHEP`   - non-Hermitian
     77: .  `EPS_GNHEP`  - generalized non-Hermitian
     78: .  `EPS_PGNHEP` - generalized non-Hermitian with positive (semi-)definite $B$
     79: .  `EPS_GHIEP`  - generalized Hermitian-indefinite
     80: .  `EPS_BSE`    - structured Bethe-Salpeter
     81: .  `EPS_HAMILT` - structured Hamiltonian
     82: -  `EPS_LREP`   - structured Linear Response

     84:    Note:
     85:    In real scalars, one should read the term Hermitian as symmetric.

     87:    Level: intermediate

     89: .seealso: [](ch:eps), `EPSSetProblemType()`, `EPSGetProblemType()`
     90: E*/
     91: typedef enum { EPS_HEP    = 1,
     92:                EPS_GHEP   = 2,
     93:                EPS_NHEP   = 3,
     94:                EPS_GNHEP  = 4,
     95:                EPS_PGNHEP = 5,
     96:                EPS_GHIEP  = 6,
     97:                EPS_BSE    = 7,
     98:                EPS_HAMILT = 8,
     99:                EPS_LREP   = 9 } EPSProblemType;

    101: /*MC
    102:    EPS_HEP - A Hermitian eigenvalue problem.

    104:    Note:
    105:    The problem is formulated as $Ax=\lambda x$, where $A$ is real symmetric
    106:    or complex Hermitian.

    108:    Level: intermediate

    110: .seealso: [](ch:eps), `EPSProblemType`, `EPSSetProblemType()`
    111: M*/

    113: /*MC
    114:    EPS_GHEP - A generalized Hermitian eigenvalue problem.

    116:    Note:
    117:    The problem is formulated as $Ax=\lambda Bx$, where $A$ and $B$ are real
    118:    symmetric or complex Hermitian, and $B$ is positive (semi-)definite.

    120:    Level: intermediate

    122: .seealso: [](ch:eps), `EPSProblemType`, `EPSSetProblemType()`
    123: M*/

    125: /*MC
    126:    EPS_NHEP - A non-Hermitian eigenvalue problem.

    128:    Note:
    129:    The problem is formulated as $Ax=\lambda x$, where $A$ is non-symmetric
    130:    (or non-Hermitian).

    132:    Level: intermediate

    134: .seealso: [](ch:eps), `EPSProblemType`, `EPSSetProblemType()`
    135: M*/

    137: /*MC
    138:    EPS_GNHEP - A generalized non-Hermitian eigenvalue problem.

    140:    Note:
    141:    The problem is formulated as $Ax=\lambda Bx$, where $A$ or $B$ are
    142:    non-symmetric (or non-Hermitian).

    144:    Level: intermediate

    146: .seealso: [](ch:eps), `EPSProblemType`, `EPSSetProblemType()`
    147: M*/

    149: /*MC
    150:    EPS_PGNHEP - A generalized non-Hermitian eigenvalue problem with positive
    151:    (semi-)definite $B$.

    153:    Notes:
    154:    The problem is formulated as $Ax=\lambda Bx$, where $A$ is non-symmetric
    155:    (or non-Hermitian), but $B$ is symmetric (or Hermitian) and positive
    156:    (semi-)definite.

    158:    The problem will be solved with a non-Hermitian solver, but using an
    159:    inner product induced by matrix $B$.

    161:    Level: intermediate

    163: .seealso: [](ch:eps), `EPSProblemType`, `EPSSetProblemType()`
    164: M*/

    166: /*MC
    167:    EPS_GHIEP - A generalized Hermitian-indefinite eigenvalue problem.

    169:    Notes:
    170:    The problem is formulated as $Ax=\lambda Bx$, where both $A$ and $B$ are
    171:    real symmetric or complex Hermitian, but $B$ is indefinite.

    173:    The solver will try to exploit the symmetry by using an indefinite
    174:    inner product, which may turn the computation numerically unstable.
    175:    To avoid this, solve the problem as non-Hermitian.

    177:    Level: intermediate

    179: .seealso: [](ch:eps), `EPSProblemType`, `EPSSetProblemType()`
    180: M*/

    182: /*MC
    183:    EPS_BSE - A structured Bethe-Salpeter eigenvalue problem.

    185:    Notes:
    186:    The problem is formulated as $Hx=\lambda x$, where $H$ has a Bethe-Salpeter
    187:    structure,
    188:      $$H = \begin{bmatrix}
    189:         R & C \\
    190:         -C^* & -R^T
    191:         \end{bmatrix},$$
    192:    where $R$ is Hermitian and $C$ is complex symmetric. Can also be used in
    193:    the case of real matrices.

    195:    A description of the properties of this problem can be found in {cite:p}`Alv25`
    196:    and references therein.

    198:    Level: intermediate

    200: .seealso: [](ch:eps), [](sec:structured), `EPSProblemType`, `EPSSetProblemType()`
    201: M*/

    203: /*MC
    204:    EPS_HAMILT - A structured Hamiltonian eigenvalue problem.

    206:    Note:
    207:    The problem is formulated as $Hx=\lambda x$, where $H$ has a Hamiltonian
    208:    structure,
    209:      $$H = \begin{bmatrix}
    210:         A & B \\
    211:         C & -A^*
    212:         \end{bmatrix},$$
    213:    where $A$, $B$ and $C$ are either real with $B=B^T$, $C=C^T$, or complex with
    214:    $B=B^*$, $C=C^*$.

    216:    Level: intermediate

    218: .seealso: [](ch:eps), [](sec:structured), `EPSProblemType`, `EPSSetProblemType()`
    219: M*/

    221: /*MC
    222:    EPS_LREP - A structured Linear Response eigenvalue problem.

    224:    Note:
    225:    The problem is formulated as $Hx=\lambda x$, where $H$ has the form
    226:      $$H_1 = \begin{bmatrix}
    227:         A & B \\
    228:        -B & -A
    229:         \end{bmatrix},$$
    230:    where $A$ and $B$ are real symmetric. An alternative form is
    231:      $$H_2 = \begin{bmatrix}
    232:         0 & K \\
    233:         M & 0
    234:         \end{bmatrix},$$
    235:    where $K=A-B$ and $M=A+B$.

    237:    Level: intermediate

    239: .seealso: [](ch:eps), [](sec:structured), `EPSProblemType`, `EPSSetProblemType()`, `MatCreateLREP()`
    240: M*/

    242: /*E
    243:    EPSExtraction - Determines the type of extraction technique employed
    244:    by the eigensolver.

    246:    Values:
    247: +  `EPS_RITZ`              - Rayleigh-Ritz extraction
    248: .  `EPS_HARMONIC`          - harmonic Ritz extraction
    249: .  `EPS_HARMONIC_RELATIVE` - harmonic Ritz extraction relative to the eigenvalue
    250: .  `EPS_HARMONIC_RIGHT`    - harmonic Ritz extraction for rightmost eigenvalues
    251: .  `EPS_HARMONIC_LARGEST`  - harmonic Ritz extraction for largest magnitude (without target)
    252: .  `EPS_REFINED`           - refined Ritz extraction
    253: -  `EPS_REFINED_HARMONIC`  - refined harmonic Ritz extraction

    255:    Level: advanced

    257: .seealso: [](ch:eps), `EPSSetExtraction()`, `EPSGetExtraction()`
    258: E*/
    259: typedef enum { EPS_RITZ,
    260:                EPS_HARMONIC,
    261:                EPS_HARMONIC_RELATIVE,
    262:                EPS_HARMONIC_RIGHT,
    263:                EPS_HARMONIC_LARGEST,
    264:                EPS_REFINED,
    265:                EPS_REFINED_HARMONIC } EPSExtraction;

    267: /*MC
    268:    EPS_RITZ - The standard Rayleigh-Ritz extraction.

    270:    Note:
    271:    This is the default way of computing eigenpair approximations from a
    272:    given subspace.

    274:    Level: advanced

    276: .seealso: [](ch:eps), `EPSExtraction`, `EPSSetExtraction()`
    277: M*/

    279: /*MC
    280:    EPS_HARMONIC - The harmonic Ritz extraction.

    282:    Notes:
    283:    This extraction method may provide better convergence when computing
    284:    interior eigenvalues close to a given target.

    286:    For the particular case of Krylov-Schur, a detailed description can
    287:    be found in {cite:p}`Rom09`.

    289:    Level: advanced

    291: .seealso: [](ch:eps), `EPSExtraction`, `EPSSetExtraction()`, `EPSSetTarget()`
    292: M*/

    294: /*MC
    295:    EPS_HARMONIC_RELATIVE - The harmonic Ritz extraction relative to the eigenvalue.

    297:    Note:
    298:    This is a variation of `EPS_HARMONIC`, used in Davidson methods only.

    300:    Level: advanced

    302: .seealso: [](ch:eps), `EPSExtraction`, `EPSSetExtraction()`, `EPSSetTarget()`
    303: M*/

    305: /*MC
    306:    EPS_HARMONIC_RIGHT - The harmonic Ritz extraction for rightmost eigenvalues.

    308:    Note:
    309:    This is a variation of `EPS_HARMONIC`, used in Davidson methods only.

    311:    Level: advanced

    313: .seealso: [](ch:eps), `EPSExtraction`, `EPSSetExtraction()`, `EPSSetTarget()`
    314: M*/

    316: /*MC
    317:    EPS_HARMONIC_LARGEST - The harmonic Ritz extraction for largest magnitude
    318:    eigenvalues (without target).

    320:    Note:
    321:    This is a variation of `EPS_HARMONIC`, used in Davidson methods only.

    323:    Level: advanced

    325: .seealso: [](ch:eps), `EPSExtraction`, `EPSSetExtraction()`
    326: M*/

    328: /*MC
    329:    EPS_REFINED - The refined Ritz extraction method {cite:p}`Jia97`.

    331:    Note:
    332:    Currently implemented only in `EPSARNOLDI`.

    334:    Level: advanced

    336: .seealso: [](ch:eps), `EPSExtraction`, `EPSSetExtraction()`
    337: M*/

    339: /*MC
    340:    EPS_REFINED_HARMONIC - The refined harmonic Ritz extraction.

    342:    Note:
    343:    This is a combination of `EPS_HARMONIC` and `EPS_REFINED`.

    345:    Developer Note:
    346:    Currently not implemented, reserved for future use.

    348:    Level: advanced

    350: .seealso: [](ch:eps), `EPSExtraction`, `EPSSetExtraction()`
    351: M*/

    353: /*E
    354:    EPSWhich - Determines which part of the spectrum is requested.

    356:    Values:
    357: +  `EPS_LARGEST_MAGNITUDE`  - largest $|\lambda|$
    358: .  `EPS_SMALLEST_MAGNITUDE` - smallest $|\lambda|$
    359: .  `EPS_LARGEST_REAL`       - largest $\mathrm{Re}(\lambda)$
    360: .  `EPS_SMALLEST_REAL`      - smallest $\mathrm{Re}(\lambda)$
    361: .  `EPS_LARGEST_IMAGINARY`  - largest $\mathrm{Im}(\lambda)$
    362: .  `EPS_SMALLEST_IMAGINARY` - smallest $\mathrm{Im}(\lambda)$
    363: .  `EPS_TARGET_MAGNITUDE`   - smallest $|\lambda-\tau|$
    364: .  `EPS_TARGET_REAL`        - smallest $|\mathrm{Re}(\lambda-\tau)|$
    365: .  `EPS_TARGET_IMAGINARY`   - smallest $|\mathrm{Im}(\lambda-\tau)|$
    366: .  `EPS_ALL`                - all $\lambda\in[a,b]$ or $\lambda\in\Omega$
    367: -  `EPS_WHICH_USER`         - user-defined sorting criterion

    369:    Notes:
    370:    If SLEPc is compiled for real scalars `EPS_LARGEST_IMAGINARY` and
    371:    `EPS_SMALLEST_IMAGINARY` use the absolute value of the imaginary part
    372:    for eigenvalue selection.

    374:    The target $\tau$ is a scalar value provided with `EPSSetTarget()`.

    376:    The case `EPS_ALL` needs an interval $[a,b]$ given with `EPSSetInterval()`
    377:    or a region $\Omega$ specified with an `RG` object.

    379:    Level: intermediate

    381: .seealso: [](ch:eps), `EPSSetWhichEigenpairs()`, `EPSSetTarget()`, `EPSSetInterval()`
    382: E*/
    383: typedef enum { EPS_LARGEST_MAGNITUDE  = 1,
    384:                EPS_SMALLEST_MAGNITUDE = 2,
    385:                EPS_LARGEST_REAL       = 3,
    386:                EPS_SMALLEST_REAL      = 4,
    387:                EPS_LARGEST_IMAGINARY  = 5,
    388:                EPS_SMALLEST_IMAGINARY = 6,
    389:                EPS_TARGET_MAGNITUDE   = 7,
    390:                EPS_TARGET_REAL        = 8,
    391:                EPS_TARGET_IMAGINARY   = 9,
    392:                EPS_ALL                = 10,
    393:                EPS_WHICH_USER         = 11 } EPSWhich;

    395: /*E
    396:    EPSBalance - The type of balancing used for non-Hermitian problems.

    398:    Values:
    399: +  `EPS_BALANCE_NONE`    - no balancing matrix is used
    400: .  `EPS_BALANCE_ONESIDE` - balancing matrix $D$ is computed with a one-sided Krylov method
    401: .  `EPS_BALANCE_TWOSIDE` - balancing matrix $D$ is computed with a two-sided Krylov method
    402: -  `EPS_BALANCE_USER`    - use a balancing matrix $D$ provided by the user

    404:    Level: intermediate

    406: .seealso: [](ch:eps), [](sec:balancing), `EPSSetBalance()`
    407: E*/
    408: typedef enum { EPS_BALANCE_NONE,
    409:                EPS_BALANCE_ONESIDE,
    410:                EPS_BALANCE_TWOSIDE,
    411:                EPS_BALANCE_USER } EPSBalance;
    412: SLEPC_EXTERN const char *EPSBalanceTypes[];

    414: /*E
    415:    EPSErrorType - The error type used to assess the accuracy of computed solutions.

    417:    Values:
    418: +  `EPS_ERROR_ABSOLUTE` - compute error bound as $\|r\|$
    419: .  `EPS_ERROR_RELATIVE` - compute error bound as $\|r\|/|\lambda|$
    420: -  `EPS_ERROR_BACKWARD` - compute error bound as $\|r\|/(\|A\|+|\lambda|\|B\|)$

    422:    Level: intermediate

    424: .seealso: [](ch:eps), `EPSComputeError()`
    425: E*/
    426: typedef enum { EPS_ERROR_ABSOLUTE,
    427:                EPS_ERROR_RELATIVE,
    428:                EPS_ERROR_BACKWARD } EPSErrorType;
    429: SLEPC_EXTERN const char *EPSErrorTypes[];

    431: /*E
    432:    EPSConv - The convergence criterion to be used by the solver.

    434:    Values:
    435: +  `EPS_CONV_ABS`  - absolute convergence criterion, $\|r\|$
    436: .  `EPS_CONV_REL`  - convergence criterion relative to eigenvalue, $\|r\|/|\lambda|$
    437: .  `EPS_CONV_NORM` - convergence criterion relative to matrix norms, $\|r\|/(\|A\|+|\lambda|\|B\|)$
    438: -  `EPS_CONV_USER` - convergence dictated by user-provided function

    440:    Level: intermediate

    442: .seealso: [](ch:eps), `EPSSetConvergenceTest()`, `EPSSetConvergenceTestFunction()`
    443: E*/
    444: typedef enum { EPS_CONV_ABS,
    445:                EPS_CONV_REL,
    446:                EPS_CONV_NORM,
    447:                EPS_CONV_USER } EPSConv;

    449: /*E
    450:    EPSStop - The stopping test to decide the termination of the outer loop
    451:    of the eigensolver.

    453:    Values:
    454: +  `EPS_STOP_BASIC`     - default stopping test
    455: .  `EPS_STOP_USER`      - user-provided stopping test
    456: -  `EPS_STOP_THRESHOLD` - threshold stopping test

    458:    Level: advanced

    460: .seealso: [](ch:eps), `EPSSetStoppingTest()`, `EPSSetStoppingTestFunction()`
    461: E*/
    462: typedef enum { EPS_STOP_BASIC,
    463:                EPS_STOP_USER,
    464:                EPS_STOP_THRESHOLD } EPSStop;

    466: /*MC
    467:    EPS_STOP_BASIC - The default stopping test.

    469:    Note:
    470:    By default, the termination of the outer loop is decided by calling
    471:    `EPSStoppingBasic()`, which will stop if all requested eigenvalues are converged,
    472:    or if the maximum number of iterations has been reached.

    474:    Level: advanced

    476: .seealso: [](ch:eps), `EPSStop`, `EPSSetStoppingTest()`, `EPSStoppingBasic()`
    477: M*/

    479: /*MC
    480:    EPS_STOP_USER - The user-provided stopping test.

    482:    Note:
    483:    Customized stopping test using the user-provided function given with
    484:    `EPSSetStoppingTestFunction()`.

    486:    Level: advanced

    488: .seealso: [](ch:eps), `EPSStop`, `EPSSetStoppingTest()`, `EPSSetStoppingTestFunction()`
    489: M*/

    491: /*MC
    492:    EPS_STOP_THRESHOLD - The threshold stopping test.

    494:    Note:
    495:    When a threshold has been provided with `EPSSetThreshold()`, the termination
    496:    of the outer loop is decided by calling `EPSStoppingThreshold()`, which will
    497:    stop when one of the computed eigenvalues is not above/below the threshold.
    498:    If a number of wanted eigenvalues has been specified via `EPSSetDimensions()`
    499:    then it is also taken into account, and the solver will stop when one of the
    500:    two conditions (threshold or number of converged values) is met.

    502:    Level: advanced

    504: .seealso: [](ch:eps), `EPSStop`, `EPSSetStoppingTest()`, `EPSStoppingThreshold()`, `EPSSetThreshold()`, `EPSSetDimensions()`
    505: M*/

    507: /*E
    508:    EPSConvergedReason - Reason an eigensolver was determined to have converged
    509:    or diverged.

    511:    Values:
    512: +  `EPS_CONVERGED_TOL`          - converged up to tolerance
    513: .  `EPS_CONVERGED_USER`         - converged due to a user-defined condition
    514: .  `EPS_DIVERGED_ITS`           - exceeded the maximum number of allowed iterations
    515: .  `EPS_DIVERGED_BREAKDOWN`     - generic breakdown in method
    516: .  `EPS_DIVERGED_SYMMETRY_LOST` - pseudo-Lanczos was not able to keep symmetry
    517: -  `EPS_CONVERGED_ITERATING`    - the solver is still running

    519:    Level: intermediate

    521: .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConvergedReason()`, `EPSSetTolerances()`
    522: E*/
    523: typedef enum {/* converged */
    524:               EPS_CONVERGED_TOL                =  1,
    525:               EPS_CONVERGED_USER               =  2,
    526:               /* diverged */
    527:               EPS_DIVERGED_ITS                 = -1,
    528:               EPS_DIVERGED_BREAKDOWN           = -2,
    529:               EPS_DIVERGED_SYMMETRY_LOST       = -3,
    530:               EPS_CONVERGED_ITERATING          =  0} EPSConvergedReason;
    531: SLEPC_EXTERN const char *const*EPSConvergedReasons;

    533: /*MC
    534:    EPS_CONVERGED_TOL - The computed error estimates, based on residual norms,
    535:    for all requested eigenvalues are below the tolerance.

    537:    Level: intermediate

    539: .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConvergedReason()`, `EPSConvergedReason`
    540: M*/

    542: /*MC
    543:    EPS_CONVERGED_USER - The solver was declared converged due to a user-defined condition.

    545:    Note:
    546:    This happens only when a user-defined stopping test has been set with
    547:    `EPSSetStoppingTestFunction()`.

    549:    Level: intermediate

    551: .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConvergedReason()`, `EPSConvergedReason`, `EPSSetStoppingTestFunction()`
    552: M*/

    554: /*MC
    555:    EPS_DIVERGED_ITS - Exceeded the maximum number of allowed iterations
    556:    before the convergence criterion was satisfied.

    558:    Level: intermediate

    560: .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConvergedReason()`, `EPSConvergedReason`
    561: M*/

    563: /*MC
    564:    EPS_DIVERGED_BREAKDOWN - A breakdown in the solver was detected so the
    565:    method could not continue.

    567:    Level: intermediate

    569: .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConvergedReason()`, `EPSConvergedReason`
    570: M*/

    572: /*MC
    573:    EPS_DIVERGED_SYMMETRY_LOST - The selected solver uses a pseudo-Lanczos recurrence,
    574:    which is numerically unstable, and a symmetry test revealed that instability
    575:    had appeared so the solver could not continue.

    577:    Level: intermediate

    579: .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConvergedReason()`, `EPSConvergedReason`
    580: M*/

    582: /*MC
    583:    EPS_CONVERGED_ITERATING - This value is returned if `EPSGetConvergedReason()` is called
    584:    while `EPSSolve()` is still running.

    586:    Level: intermediate

    588: .seealso: [](ch:eps), `EPSSolve()`, `EPSGetConvergedReason()`, `EPSConvergedReason`
    589: M*/

    591: /*S
    592:    EPSStoppingCtx - Data structure (C struct) to hold additional information to
    593:    be used in some stopping test functions.

    595:    Level: advanced

    597: .seealso: [](ch:eps), `EPSSetStoppingTestFunction()`
    598: S*/
    599: struct _n_EPSStoppingCtx {
    600:   PetscReal firstev;    /* the (absolute) value of the first converged eigenvalue */
    601:   PetscReal lastev;     /* the (absolute) value of the last converged eigenvalue */
    602:   PetscReal firstnc;    /* the (absolute) value of the first non-converged eigenvalue */
    603:   PetscReal errest;     /* the error estimate of the first non-converged eigenvalue */
    604:   PetscReal thres;      /* threshold set with EPSSetThreshold() */
    605:   PetscBool threlative; /* threshold is relative */
    606:   PetscInt  its;        /* iteration at which condition is met */
    607:   PetscInt  napprox;    /* number of available approximations */
    608:   EPSWhich  which;      /* which eigenvalues are being computed */
    609: };
    610: typedef struct _n_EPSStoppingCtx* EPSStoppingCtx;

    612: SLEPC_EXTERN PetscErrorCode EPSCreate(MPI_Comm,EPS*);
    613: SLEPC_EXTERN PetscErrorCode EPSDestroy(EPS*);
    614: SLEPC_EXTERN PetscErrorCode EPSReset(EPS);
    615: SLEPC_EXTERN PetscErrorCode EPSSetType(EPS,EPSType);
    616: SLEPC_EXTERN PetscErrorCode EPSGetType(EPS,EPSType*);
    617: SLEPC_EXTERN PetscErrorCode EPSSetProblemType(EPS,EPSProblemType);
    618: SLEPC_EXTERN PetscErrorCode EPSGetProblemType(EPS,EPSProblemType*);
    619: SLEPC_EXTERN PetscErrorCode EPSSetExtraction(EPS,EPSExtraction);
    620: SLEPC_EXTERN PetscErrorCode EPSGetExtraction(EPS,EPSExtraction*);
    621: SLEPC_EXTERN PetscErrorCode EPSSetBalance(EPS,EPSBalance,PetscInt,PetscReal);
    622: SLEPC_EXTERN PetscErrorCode EPSGetBalance(EPS,EPSBalance*,PetscInt*,PetscReal*);
    623: SLEPC_EXTERN PetscErrorCode EPSSetOperators(EPS,Mat,Mat);
    624: SLEPC_EXTERN PetscErrorCode EPSGetOperators(EPS,Mat*,Mat*);
    625: SLEPC_EXTERN PetscErrorCode EPSSetFromOptions(EPS);
    626: SLEPC_EXTERN PetscErrorCode EPSSetDSType(EPS);
    627: SLEPC_EXTERN PetscErrorCode EPSSetUp(EPS);
    628: SLEPC_EXTERN PetscErrorCode EPSSolve(EPS);
    629: SLEPC_EXTERN PetscErrorCode EPSView(EPS,PetscViewer);
    630: SLEPC_EXTERN PetscErrorCode EPSViewFromOptions(EPS,PetscObject,const char[]);
    631: SLEPC_EXTERN PetscErrorCode EPSErrorView(EPS,EPSErrorType,PetscViewer);
    632: PETSC_DEPRECATED_FUNCTION(3, 6, 0, "EPSErrorView()", ) static inline PetscErrorCode EPSPrintSolution(EPS eps,PetscViewer v) {return EPSErrorView(eps,EPS_ERROR_RELATIVE,v);}
    633: SLEPC_EXTERN PetscErrorCode EPSErrorViewFromOptions(EPS);
    634: SLEPC_EXTERN PetscErrorCode EPSConvergedReasonView(EPS,PetscViewer);
    635: SLEPC_EXTERN PetscErrorCode EPSConvergedReasonViewFromOptions(EPS);
    636: PETSC_DEPRECATED_FUNCTION(3, 14, 0, "EPSConvergedReasonView()", ) static inline PetscErrorCode EPSReasonView(EPS eps,PetscViewer v) {return EPSConvergedReasonView(eps,v);}
    637: PETSC_DEPRECATED_FUNCTION(3, 14, 0, "EPSConvergedReasonViewFromOptions()", ) static inline PetscErrorCode EPSReasonViewFromOptions(EPS eps) {return EPSConvergedReasonViewFromOptions(eps);}
    638: SLEPC_EXTERN PetscErrorCode EPSValuesView(EPS,PetscViewer);
    639: SLEPC_EXTERN PetscErrorCode EPSValuesViewFromOptions(EPS);
    640: SLEPC_EXTERN PetscErrorCode EPSVectorsView(EPS,PetscViewer);
    641: SLEPC_EXTERN PetscErrorCode EPSVectorsViewFromOptions(EPS);

    643: SLEPC_EXTERN PetscErrorCode EPSSetTarget(EPS,PetscScalar);
    644: SLEPC_EXTERN PetscErrorCode EPSGetTarget(EPS,PetscScalar*);
    645: SLEPC_EXTERN PetscErrorCode EPSSetInterval(EPS,PetscReal,PetscReal);
    646: SLEPC_EXTERN PetscErrorCode EPSGetInterval(EPS,PetscReal*,PetscReal*);
    647: SLEPC_EXTERN PetscErrorCode EPSSetST(EPS,ST);
    648: SLEPC_EXTERN PetscErrorCode EPSGetST(EPS,ST*);
    649: SLEPC_EXTERN PetscErrorCode EPSSetBV(EPS,BV);
    650: SLEPC_EXTERN PetscErrorCode EPSGetBV(EPS,BV*);
    651: SLEPC_EXTERN PetscErrorCode EPSSetRG(EPS,RG);
    652: SLEPC_EXTERN PetscErrorCode EPSGetRG(EPS,RG*);
    653: SLEPC_EXTERN PetscErrorCode EPSSetDS(EPS,DS);
    654: SLEPC_EXTERN PetscErrorCode EPSGetDS(EPS,DS*);
    655: SLEPC_EXTERN PetscErrorCode EPSSetTolerances(EPS,PetscReal,PetscInt);
    656: SLEPC_EXTERN PetscErrorCode EPSGetTolerances(EPS,PetscReal*,PetscInt*);
    657: SLEPC_EXTERN PetscErrorCode EPSSetDimensions(EPS,PetscInt,PetscInt,PetscInt);
    658: SLEPC_EXTERN PetscErrorCode EPSGetDimensions(EPS,PetscInt*,PetscInt*,PetscInt*);

    660: SLEPC_EXTERN PetscErrorCode EPSGetConvergedReason(EPS,EPSConvergedReason*);

    662: SLEPC_EXTERN PetscErrorCode EPSGetConverged(EPS,PetscInt*);
    663: SLEPC_EXTERN PetscErrorCode EPSGetEigenpair(EPS,PetscInt,PetscScalar*,PetscScalar*,Vec,Vec);
    664: SLEPC_EXTERN PetscErrorCode EPSGetEigenvalue(EPS,PetscInt,PetscScalar*,PetscScalar*);
    665: SLEPC_EXTERN PetscErrorCode EPSGetEigenvector(EPS,PetscInt,Vec,Vec);
    666: SLEPC_EXTERN PetscErrorCode EPSGetLeftEigenvector(EPS,PetscInt,Vec,Vec);

    668: SLEPC_EXTERN PetscErrorCode EPSComputeError(EPS,PetscInt,EPSErrorType,PetscReal*);
    669: PETSC_DEPRECATED_FUNCTION(3, 6, 0, "EPSComputeError()", ) static inline PetscErrorCode EPSComputeRelativeError(EPS eps,PetscInt i,PetscReal *r) {return EPSComputeError(eps,i,EPS_ERROR_RELATIVE,r);}
    670: PETSC_DEPRECATED_FUNCTION(3, 6, 0, "EPSComputeError() with EPS_ERROR_ABSOLUTE", ) static inline PetscErrorCode EPSComputeResidualNorm(EPS eps,PetscInt i,PetscReal *r) {return EPSComputeError(eps,i,EPS_ERROR_ABSOLUTE,r);}
    671: SLEPC_EXTERN PetscErrorCode EPSGetInvariantSubspace(EPS,Vec[]);
    672: SLEPC_EXTERN PetscErrorCode EPSGetErrorEstimate(EPS,PetscInt,PetscReal*);
    673: SLEPC_EXTERN PetscErrorCode EPSGetIterationNumber(EPS,PetscInt*);

    675: SLEPC_EXTERN PetscErrorCode EPSSetWhichEigenpairs(EPS,EPSWhich);
    676: SLEPC_EXTERN PetscErrorCode EPSGetWhichEigenpairs(EPS,EPSWhich*);
    677: SLEPC_EXTERN PetscErrorCode EPSSetThreshold(EPS,PetscReal,PetscBool);
    678: SLEPC_EXTERN PetscErrorCode EPSGetThreshold(EPS,PetscReal*,PetscBool*);
    679: SLEPC_EXTERN PetscErrorCode EPSSetTwoSided(EPS,PetscBool);
    680: SLEPC_EXTERN PetscErrorCode EPSGetTwoSided(EPS,PetscBool*);
    681: SLEPC_EXTERN PetscErrorCode EPSSetTrueResidual(EPS,PetscBool);
    682: SLEPC_EXTERN PetscErrorCode EPSGetTrueResidual(EPS,PetscBool*);
    683: SLEPC_EXTERN PetscErrorCode EPSSetPurify(EPS,PetscBool);
    684: SLEPC_EXTERN PetscErrorCode EPSGetPurify(EPS,PetscBool*);
    685: SLEPC_EXTERN PetscErrorCode EPSIsGeneralized(EPS,PetscBool*);
    686: SLEPC_EXTERN PetscErrorCode EPSIsHermitian(EPS,PetscBool*);
    687: SLEPC_EXTERN PetscErrorCode EPSIsPositive(EPS,PetscBool*);
    688: SLEPC_EXTERN PetscErrorCode EPSIsStructured(EPS,PetscBool*);

    690: SLEPC_EXTERN PetscErrorCode EPSSetTrackAll(EPS,PetscBool);
    691: SLEPC_EXTERN PetscErrorCode EPSGetTrackAll(EPS,PetscBool*);

    693: SLEPC_EXTERN PetscErrorCode EPSSetDeflationSpace(EPS,PetscInt,Vec[]);
    694: SLEPC_EXTERN PetscErrorCode EPSSetInitialSpace(EPS,PetscInt,Vec[]);
    695: SLEPC_EXTERN PetscErrorCode EPSSetLeftInitialSpace(EPS,PetscInt,Vec[]);

    697: /*S
    698:    EPSMonitorFn - A function prototype for functions provided to `EPSMonitorSet()`.

    700:    Calling Sequence:
    701: +  eps    - the linear eigensolver context
    702: .  its    - iteration number
    703: .  nconv  - number of converged eigenpairs
    704: .  eigr   - real part of the eigenvalues
    705: .  eigi   - imaginary part of the eigenvalues
    706: .  errest - relative error estimates for each eigenpair
    707: .  nest   - number of error estimates
    708: -  ctx    - optional monitoring context, as provided with `EPSMonitorSet()`

    710:    Level: intermediate

    712: .seealso: [](ch:eps), `EPSMonitorSet()`
    713: S*/
    714: PETSC_EXTERN_TYPEDEF typedef PetscErrorCode EPSMonitorFn(EPS eps,PetscInt its,PetscInt nconv,PetscScalar eigr[],PetscScalar eigi[],PetscReal errest[],PetscInt nest,PetscCtx ctx);

    716: /*S
    717:    EPSMonitorRegisterFn - A function prototype for functions provided to `EPSMonitorRegister()`.

    719:    Calling Sequence:
    720: +  eps    - the linear eigensolver context
    721: .  its    - iteration number
    722: .  nconv  - number of converged eigenpairs
    723: .  eigr   - real part of the eigenvalues
    724: .  eigi   - imaginary part of the eigenvalues
    725: .  errest - relative error estimates for each eigenpair
    726: .  nest   - number of error estimates
    727: -  ctx    - `PetscViewerAndFormat` object

    729:    Level: advanced

    731:    Note:
    732:    This is an `EPSMonitorFn` specialized for a context of `PetscViewerAndFormat`.

    734: .seealso: [](ch:eps), `EPSMonitorSet()`, `EPSMonitorRegister()`, `EPSMonitorFn`, `EPSMonitorRegisterCreateFn`, `EPSMonitorRegisterDestroyFn`
    735: S*/
    736: PETSC_EXTERN_TYPEDEF typedef PetscErrorCode EPSMonitorRegisterFn(EPS eps,PetscInt its,PetscInt nconv,PetscScalar eigr[],PetscScalar eigi[],PetscReal errest[],PetscInt nest,PetscViewerAndFormat *ctx);

    738: /*S
    739:    EPSMonitorRegisterCreateFn - A function prototype for functions that do the
    740:    creation when provided to `EPSMonitorRegister()`.

    742:    Calling Sequence:
    743: +  viewer - the viewer to be used with the `EPSMonitorRegisterFn`
    744: .  format - the format of the viewer
    745: .  ctx    - a context for the monitor
    746: -  result - a `PetscViewerAndFormat` object

    748:    Level: advanced

    750: .seealso: [](ch:eps), `EPSMonitorRegisterFn`, `EPSMonitorSet()`, `EPSMonitorRegister()`, `EPSMonitorFn`, `EPSMonitorRegisterDestroyFn`
    751: S*/
    752: PETSC_EXTERN_TYPEDEF typedef PetscErrorCode EPSMonitorRegisterCreateFn(PetscViewer viewer,PetscViewerFormat format,PetscCtx ctx,PetscViewerAndFormat **result);

    754: /*S
    755:    EPSMonitorRegisterDestroyFn - A function prototype for functions that do the after
    756:    use destruction when provided to `EPSMonitorRegister()`.

    758:    Calling Sequence:
    759: .  vf - a `PetscViewerAndFormat` object to be destroyed, including any context

    761:    Level: advanced

    763: .seealso: [](ch:eps), `EPSMonitorRegisterFn`, `EPSMonitorSet()`, `EPSMonitorRegister()`, `EPSMonitorFn`, `EPSMonitorRegisterCreateFn`
    764: S*/
    765: PETSC_EXTERN_TYPEDEF typedef PetscErrorCode EPSMonitorRegisterDestroyFn(PetscViewerAndFormat **result);

    767: SLEPC_EXTERN PetscErrorCode EPSMonitor(EPS,PetscInt,PetscInt,PetscScalar[],PetscScalar[],PetscReal[],PetscInt);
    768: SLEPC_EXTERN PetscErrorCode EPSMonitorSet(EPS,EPSMonitorFn,PetscCtx,PetscCtxDestroyFn*);
    769: SLEPC_EXTERN PetscErrorCode EPSMonitorCancel(EPS);
    770: SLEPC_EXTERN PetscErrorCode EPSGetMonitorContext(EPS,PetscCtxRt);

    772: SLEPC_EXTERN PetscErrorCode EPSMonitorSetFromOptions(EPS,const char[],const char[],PetscCtx,PetscBool);
    773: SLEPC_EXTERN EPSMonitorRegisterFn        EPSMonitorFirst;
    774: SLEPC_EXTERN EPSMonitorRegisterFn        EPSMonitorFirstDrawLG;
    775: SLEPC_EXTERN EPSMonitorRegisterCreateFn  EPSMonitorFirstDrawLGCreate;
    776: SLEPC_EXTERN EPSMonitorRegisterFn        EPSMonitorAll;
    777: SLEPC_EXTERN EPSMonitorRegisterFn        EPSMonitorAllDrawLG;
    778: SLEPC_EXTERN EPSMonitorRegisterCreateFn  EPSMonitorAllDrawLGCreate;
    779: SLEPC_EXTERN EPSMonitorRegisterFn        EPSMonitorConverged;
    780: SLEPC_EXTERN EPSMonitorRegisterCreateFn  EPSMonitorConvergedCreate;
    781: SLEPC_EXTERN EPSMonitorRegisterFn        EPSMonitorConvergedDrawLG;
    782: SLEPC_EXTERN EPSMonitorRegisterCreateFn  EPSMonitorConvergedDrawLGCreate;

    784: SLEPC_EXTERN PetscErrorCode EPSSetOptionsPrefix(EPS,const char[]);
    785: SLEPC_EXTERN PetscErrorCode EPSAppendOptionsPrefix(EPS,const char[]);
    786: SLEPC_EXTERN PetscErrorCode EPSGetOptionsPrefix(EPS,const char*[]);

    788: SLEPC_EXTERN PetscFunctionList EPSList;
    789: SLEPC_EXTERN PetscFunctionList EPSMonitorList;
    790: SLEPC_EXTERN PetscFunctionList EPSMonitorCreateList;
    791: SLEPC_EXTERN PetscFunctionList EPSMonitorDestroyList;
    792: SLEPC_EXTERN PetscErrorCode EPSRegister(const char[],PetscErrorCode(*)(EPS));
    793: SLEPC_EXTERN PetscErrorCode EPSMonitorRegister(const char[],PetscViewerType,PetscViewerFormat,EPSMonitorRegisterFn*,EPSMonitorRegisterCreateFn*,EPSMonitorRegisterDestroyFn*);

    795: SLEPC_EXTERN PetscErrorCode EPSSetWorkVecs(EPS,PetscInt);
    796: SLEPC_EXTERN PetscErrorCode EPSAllocateSolution(EPS,PetscInt);
    797: SLEPC_EXTERN PetscErrorCode EPSReallocateSolution(EPS,PetscInt);

    799: /*S
    800:    EPSConvergenceTestFn - A prototype of an `EPS` convergence test function that
    801:    would be passed to `EPSSetConvergenceTestFunction()`.

    803:    Calling Sequence:
    804: +  eps    - the linear eigensolver context
    805: .  eigr   - real part of the eigenvalue
    806: .  eigi   - imaginary part of the eigenvalue
    807: .  res    - residual norm associated to the eigenpair
    808: .  errest - [output] computed error estimate
    809: -  ctx    - optional convergence context, as set by `EPSSetConvergenceTestFunction()`

    811:    Level: advanced

    813: .seealso: [](ch:eps), `EPSSetConvergenceTest()`, `EPSSetConvergenceTestFunction()`
    814: S*/
    815: PETSC_EXTERN_TYPEDEF typedef PetscErrorCode EPSConvergenceTestFn(EPS eps,PetscScalar eigr,PetscScalar eigi,PetscReal res,PetscReal *errest,PetscCtx ctx);

    817: SLEPC_EXTERN PetscErrorCode EPSSetConvergenceTest(EPS,EPSConv);
    818: SLEPC_EXTERN PetscErrorCode EPSGetConvergenceTest(EPS,EPSConv*);
    819: SLEPC_EXTERN EPSConvergenceTestFn EPSConvergedAbsolute;
    820: SLEPC_EXTERN EPSConvergenceTestFn EPSConvergedRelative;
    821: SLEPC_EXTERN EPSConvergenceTestFn EPSConvergedNorm;
    822: SLEPC_EXTERN PetscErrorCode EPSSetConvergenceTestFunction(EPS,EPSConvergenceTestFn*,PetscCtx,PetscCtxDestroyFn*);

    824: /*S
    825:    EPSStoppingTestFn - A prototype of an `EPS` stopping test function that would
    826:    be passed to `EPSSetStoppingTestFunction()`.

    828:    Calling Sequence:
    829: +  eps    - the linear eigensolver context
    830: .  its    - current number of iterations
    831: .  max_it - maximum number of iterations
    832: .  nconv  - number of currently converged eigenpairs
    833: .  nev    - number of requested eigenpairs
    834: .  reason - [output] result of the stopping test
    835: -  ctx    - optional stopping context, as set by `EPSSetStoppingTestFunction()`

    837:    Note:
    838:    A positive value of `reason` indicates that the iteration has finished successfully
    839:    (converged), and a negative value indicates an error condition (diverged). If
    840:    the iteration needs to be continued, `reason` must be set to `EPS_CONVERGED_ITERATING`
    841:    (zero).

    843:    Level: advanced

    845: .seealso: [](ch:eps), `EPSSetStoppingTest()`, `EPSSetStoppingTestFunction()`
    846: S*/
    847: PETSC_EXTERN_TYPEDEF typedef PetscErrorCode EPSStoppingTestFn(EPS eps,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,EPSConvergedReason *reason,PetscCtx ctx);

    849: SLEPC_EXTERN PetscErrorCode EPSSetStoppingTest(EPS,EPSStop);
    850: SLEPC_EXTERN PetscErrorCode EPSGetStoppingTest(EPS,EPSStop*);
    851: SLEPC_EXTERN EPSStoppingTestFn EPSStoppingBasic;
    852: SLEPC_EXTERN EPSStoppingTestFn EPSStoppingThreshold;
    853: SLEPC_EXTERN PetscErrorCode EPSSetStoppingTestFunction(EPS,EPSStoppingTestFn*,PetscCtx,PetscCtxDestroyFn*);

    855: SLEPC_EXTERN PetscErrorCode EPSSetEigenvalueComparison(EPS,SlepcEigenvalueComparisonFn*,PetscCtx);
    856: SLEPC_EXTERN PetscErrorCode EPSSetArbitrarySelection(EPS,SlepcArbitrarySelectionFn*,PetscCtx);
    857: SLEPC_EXTERN PetscErrorCode EPSSetArbitrarySelectionContextDestroy(EPS,PetscCtxDestroyFn*);

    859: /* --------- options specific to particular eigensolvers -------- */

    861: /*E
    862:    EPSPowerShiftType - The type of shift used in the Power iteration solver.

    864:    Values:
    865: +  `EPS_POWER_SHIFT_CONSTANT`  - constant shift
    866: .  `EPS_POWER_SHIFT_RAYLEIGH`  - variable shift using Rayleigh quotient
    867: -  `EPS_POWER_SHIFT_WILKINSON` - variable shift using Wilkinson's approach

    869:    Note:
    870:    Details of the three variants can be found in {cite:p}`Her05`.

    872:    Level: advanced

    874: .seealso: [](ch:eps), `EPSPowerSetShiftType()`, `EPSPowerGetShiftType()`
    875: E*/
    876: typedef enum { EPS_POWER_SHIFT_CONSTANT,
    877:                EPS_POWER_SHIFT_RAYLEIGH,
    878:                EPS_POWER_SHIFT_WILKINSON } EPSPowerShiftType;
    879: SLEPC_EXTERN const char *EPSPowerShiftTypes[];

    881: /*MC
    882:    EPS_POWER_SHIFT_CONSTANT - The power iteration will use a constant shift.

    884:    Note:
    885:    Together with `STSINVERT`, the `EPSPOWER` solver implements the inverse iteration
    886:    method, i.e., it will apply $(A-\sigma I)^{-1}$ at each iteration, by solving
    887:    a linear system. By default, the shift $\sigma$ is constant and given by the
    888:    user with `EPSSetTarget()`.

    890:    Details of the three variants can be found in {cite:p}`Her05`.

    892:    Level: advanced

    894: .seealso: [](ch:eps), `EPSPowerShiftType`, `EPSPowerSetShiftType()`, `STSetShift()`, `EPSSetTarget()`, `EPS_POWER_SHIFT_RAYLEIGH`, `EPS_POWER_SHIFT_WILKINSON`
    895: M*/

    897: /*MC
    898:    EPS_POWER_SHIFT_RAYLEIGH - The power iteration will use a variable shift
    899:    computed with the Rayleigh quotient.

    901:    Notes:
    902:    Together with `STSINVERT`, the `EPSPOWER` solver implements the inverse iteration
    903:    method, i.e., it will apply $(A-\sigma I)^{-1}$ at each iteration, by solving
    904:    a linear system. With this strategy, the value of the shift will be updated at
    905:    each iteration as $\sigma=\frac{x^*Ax}{x^*x}$, where $x$ is the current eigenvector
    906:    approximation. The resulting iteration is the RQI method.

    908:    Updating the shift may involve a high computational cost if the linear solve
    909:    is done via a factorization.

    911:    Details of the three variants can be found in {cite:p}`Her05`.

    913:    Level: advanced

    915: .seealso: [](ch:eps), `EPSPowerShiftType`, `EPSPowerSetShiftType()`, `STSetShift()`, `EPSSetTarget()`, `EPS_POWER_SHIFT_CONSTANT`, `EPS_POWER_SHIFT_WILKINSON`
    916: M*/

    918: /*MC
    919:    EPS_POWER_SHIFT_WILKINSON - The power iteration will use a variable shift
    920:    computed with Wilkinson's approach.

    922:    Note:
    923:    Together with `STSINVERT`, the `EPSPOWER` solver implements the inverse iteration
    924:    method, i.e., it will apply $(A-\sigma I)^{-1}$ at each iteration, by solving
    925:    a linear system. With this strategy, the value of the shift will be updated at
    926:    each iteration as proposed by Wilkinson, see {cite:p}`Par80{8.10}`.

    928:    Updating the shift may involve a high computational cost if the linear solve
    929:    is done via a factorization.

    931:    Details of the three variants can be found in {cite:p}`Her05`.

    933:    Level: advanced

    935: .seealso: [](ch:eps), `EPSPowerShiftType`, `EPSPowerSetShiftType()`, `STSetShift()`, `EPSSetTarget()`, `EPS_POWER_SHIFT_CONSTANT`, `EPS_POWER_SHIFT_RAYLEIGH`
    936: M*/

    938: SLEPC_EXTERN PetscErrorCode EPSPowerSetShiftType(EPS,EPSPowerShiftType);
    939: SLEPC_EXTERN PetscErrorCode EPSPowerGetShiftType(EPS,EPSPowerShiftType*);
    940: SLEPC_EXTERN PetscErrorCode EPSPowerSetNonlinear(EPS,PetscBool);
    941: SLEPC_EXTERN PetscErrorCode EPSPowerGetNonlinear(EPS,PetscBool*);
    942: SLEPC_EXTERN PetscErrorCode EPSPowerSetUpdate(EPS,PetscBool);
    943: SLEPC_EXTERN PetscErrorCode EPSPowerGetUpdate(EPS,PetscBool*);
    944: SLEPC_EXTERN PetscErrorCode EPSPowerSetSignNormalization(EPS,PetscBool);
    945: SLEPC_EXTERN PetscErrorCode EPSPowerGetSignNormalization(EPS,PetscBool*);
    946: SLEPC_EXTERN PetscErrorCode EPSPowerSetSNES(EPS,SNES);
    947: SLEPC_EXTERN PetscErrorCode EPSPowerGetSNES(EPS,SNES*);

    949: SLEPC_EXTERN PetscErrorCode EPSArnoldiSetDelayed(EPS,PetscBool);
    950: SLEPC_EXTERN PetscErrorCode EPSArnoldiGetDelayed(EPS,PetscBool*);

    952: /*E
    953:    EPSKrylovSchurBSEType - The method to be used in the Krylov-Schur solver
    954:    for the case of BSE structured eigenproblems.

    956:    Values:
    957: +  `EPS_KRYLOVSCHUR_BSE_SHAO`         - a Lanczos method proposed by Shao and coauthors
    958: .  `EPS_KRYLOVSCHUR_BSE_GRUNING`      - a Lanczos method proposed by Gruning and coauthors
    959: -  `EPS_KRYLOVSCHUR_BSE_PROJECTEDBSE` - a Lanczos method resulting is a projected problem with BSE structure

    961:    Note:
    962:    All variants are implemented in combination with a thick restart, see
    963:    the details in {cite:p}`Alv25`.

    965:    Level: advanced

    967: .seealso: [](ch:eps), `EPSKrylovSchurSetBSEType()`, `EPSKrylovSchurGetBSEType()`
    968: E*/
    969: typedef enum { EPS_KRYLOVSCHUR_BSE_SHAO,
    970:                EPS_KRYLOVSCHUR_BSE_GRUNING,
    971:                EPS_KRYLOVSCHUR_BSE_PROJECTEDBSE } EPSKrylovSchurBSEType;
    972: SLEPC_EXTERN const char *EPSKrylovSchurBSETypes[];

    974: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurSetBSEType(EPS,EPSKrylovSchurBSEType);
    975: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetBSEType(EPS,EPSKrylovSchurBSEType*);
    976: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurSetRestart(EPS,PetscReal);
    977: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetRestart(EPS,PetscReal*);
    978: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurSetLocking(EPS,PetscBool);
    979: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetLocking(EPS,PetscBool*);
    980: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurSetPartitions(EPS,PetscInt);
    981: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetPartitions(EPS,PetscInt*);
    982: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurSetDetectZeros(EPS,PetscBool);
    983: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetDetectZeros(EPS,PetscBool*);
    984: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurSetDimensions(EPS,PetscInt,PetscInt,PetscInt);
    985: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetDimensions(EPS,PetscInt*,PetscInt*,PetscInt*);
    986: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurSetSubintervals(EPS,PetscReal[]);
    987: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetSubintervals(EPS,PetscReal*[]);
    988: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetInertias(EPS,PetscInt*,PetscReal*[],PetscInt*[]);
    989: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetSubcommInfo(EPS,PetscInt*,PetscInt*,Vec*);
    990: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetSubcommPairs(EPS,PetscInt,PetscScalar*,Vec);
    991: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetSubcommMats(EPS,Mat*,Mat*);
    992: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurUpdateSubcommMats(EPS,PetscScalar,PetscScalar,Mat,PetscScalar,PetscScalar, Mat,MatStructure,PetscBool);
    993: SLEPC_EXTERN PetscErrorCode EPSKrylovSchurGetKSP(EPS,KSP*);

    995: /*E
    996:    EPSLanczosReorthogType - The type of reorthogonalization used in `EPSLANCZOS`.

    998:    Values:
    999: +  `EPS_LANCZOS_REORTHOG_LOCAL`     - local orthogonalization, only involves previous two vectors
    1000: .  `EPS_LANCZOS_REORTHOG_FULL`      - full orthogonalization against all previous vectors
    1001: .  `EPS_LANCZOS_REORTHOG_SELECTIVE` - selective reorthogonalization against nearly converged Ritz vectors
    1002: .  `EPS_LANCZOS_REORTHOG_PERIODIC`  - periodic reorthogonalization against all previous vectors
    1003: .  `EPS_LANCZOS_REORTHOG_PARTIAL`   - partial reorthogonalization against as subset of previous vectors
    1004: -  `EPS_LANCZOS_REORTHOG_DELAYED`   - full orthogonalization with delayed reorthogonalization

    1006:    Note:
    1007:    Details of the different reorthogonalization strategies can be found in
    1008:    {cite:p}`Her06`.

    1010:    Level: advanced

    1012: .seealso: [](ch:eps), `EPSLanczosSetReorthog()`, `EPSLanczosGetReorthog()`
    1013: E*/
    1014: typedef enum { EPS_LANCZOS_REORTHOG_LOCAL,
    1015:                EPS_LANCZOS_REORTHOG_FULL,
    1016:                EPS_LANCZOS_REORTHOG_SELECTIVE,
    1017:                EPS_LANCZOS_REORTHOG_PERIODIC,
    1018:                EPS_LANCZOS_REORTHOG_PARTIAL,
    1019:                EPS_LANCZOS_REORTHOG_DELAYED } EPSLanczosReorthogType;
    1020: SLEPC_EXTERN const char *EPSLanczosReorthogTypes[];

    1022: SLEPC_EXTERN PetscErrorCode EPSLanczosSetReorthog(EPS,EPSLanczosReorthogType);
    1023: SLEPC_EXTERN PetscErrorCode EPSLanczosGetReorthog(EPS,EPSLanczosReorthogType*);

    1025: /*E
    1026:    EPSPRIMMEMethod - The method selected in the PRIMME library.

    1028:    Note:
    1029:    See the documentation of PRIMME {cite:p}`Sta10` for a description of the methods.

    1031:    Level: advanced

    1033: .seealso: [](ch:eps), `EPSPRIMMESetMethod()`, `EPSPRIMMEGetMethod()`
    1034: E*/
    1035: typedef enum { EPS_PRIMME_DYNAMIC             = 1,
    1036:                EPS_PRIMME_DEFAULT_MIN_TIME    = 2,
    1037:                EPS_PRIMME_DEFAULT_MIN_MATVECS = 3,
    1038:                EPS_PRIMME_ARNOLDI             = 4,
    1039:                EPS_PRIMME_GD                  = 5,
    1040:                EPS_PRIMME_GD_PLUSK            = 6,
    1041:                EPS_PRIMME_GD_OLSEN_PLUSK      = 7,
    1042:                EPS_PRIMME_JD_OLSEN_PLUSK      = 8,
    1043:                EPS_PRIMME_RQI                 = 9,
    1044:                EPS_PRIMME_JDQR                = 10,
    1045:                EPS_PRIMME_JDQMR               = 11,
    1046:                EPS_PRIMME_JDQMR_ETOL          = 12,
    1047:                EPS_PRIMME_SUBSPACE_ITERATION  = 13,
    1048:                EPS_PRIMME_LOBPCG_ORTHOBASIS   = 14,
    1049:                EPS_PRIMME_LOBPCG_ORTHOBASISW  = 15 } EPSPRIMMEMethod;
    1050: SLEPC_EXTERN const char *EPSPRIMMEMethods[];

    1052: SLEPC_EXTERN PetscErrorCode EPSPRIMMESetBlockSize(EPS,PetscInt);
    1053: SLEPC_EXTERN PetscErrorCode EPSPRIMMEGetBlockSize(EPS,PetscInt*);
    1054: SLEPC_EXTERN PetscErrorCode EPSPRIMMESetMethod(EPS,EPSPRIMMEMethod);
    1055: SLEPC_EXTERN PetscErrorCode EPSPRIMMEGetMethod(EPS,EPSPRIMMEMethod*);

    1057: SLEPC_EXTERN PetscErrorCode EPSGDSetKrylovStart(EPS,PetscBool);
    1058: SLEPC_EXTERN PetscErrorCode EPSGDGetKrylovStart(EPS,PetscBool*);
    1059: SLEPC_EXTERN PetscErrorCode EPSGDSetBlockSize(EPS,PetscInt);
    1060: SLEPC_EXTERN PetscErrorCode EPSGDGetBlockSize(EPS,PetscInt*);
    1061: SLEPC_EXTERN PetscErrorCode EPSGDSetRestart(EPS,PetscInt,PetscInt);
    1062: SLEPC_EXTERN PetscErrorCode EPSGDGetRestart(EPS,PetscInt*,PetscInt*);
    1063: SLEPC_EXTERN PetscErrorCode EPSGDSetInitialSize(EPS,PetscInt);
    1064: SLEPC_EXTERN PetscErrorCode EPSGDGetInitialSize(EPS,PetscInt*);
    1065: SLEPC_EXTERN PetscErrorCode EPSGDSetBOrth(EPS,PetscBool);
    1066: SLEPC_EXTERN PetscErrorCode EPSGDGetBOrth(EPS,PetscBool*);
    1067: SLEPC_EXTERN PetscErrorCode EPSGDSetDoubleExpansion(EPS,PetscBool);
    1068: SLEPC_EXTERN PetscErrorCode EPSGDGetDoubleExpansion(EPS,PetscBool*);

    1070: SLEPC_EXTERN PetscErrorCode EPSJDSetKrylovStart(EPS,PetscBool);
    1071: SLEPC_EXTERN PetscErrorCode EPSJDGetKrylovStart(EPS,PetscBool*);
    1072: SLEPC_EXTERN PetscErrorCode EPSJDSetBlockSize(EPS,PetscInt);
    1073: SLEPC_EXTERN PetscErrorCode EPSJDGetBlockSize(EPS,PetscInt*);
    1074: SLEPC_EXTERN PetscErrorCode EPSJDSetRestart(EPS,PetscInt,PetscInt);
    1075: SLEPC_EXTERN PetscErrorCode EPSJDGetRestart(EPS,PetscInt*,PetscInt*);
    1076: SLEPC_EXTERN PetscErrorCode EPSJDSetInitialSize(EPS,PetscInt);
    1077: SLEPC_EXTERN PetscErrorCode EPSJDGetInitialSize(EPS,PetscInt*);
    1078: SLEPC_EXTERN PetscErrorCode EPSJDSetFix(EPS,PetscReal);
    1079: SLEPC_EXTERN PetscErrorCode EPSJDGetFix(EPS,PetscReal*);
    1080: SLEPC_EXTERN PetscErrorCode EPSJDSetConstCorrectionTol(EPS,PetscBool);
    1081: SLEPC_EXTERN PetscErrorCode EPSJDGetConstCorrectionTol(EPS,PetscBool*);
    1082: SLEPC_EXTERN PetscErrorCode EPSJDSetBOrth(EPS,PetscBool);
    1083: SLEPC_EXTERN PetscErrorCode EPSJDGetBOrth(EPS,PetscBool*);

    1085: SLEPC_EXTERN PetscErrorCode EPSRQCGSetReset(EPS,PetscInt);
    1086: SLEPC_EXTERN PetscErrorCode EPSRQCGGetReset(EPS,PetscInt*);

    1088: SLEPC_EXTERN PetscErrorCode EPSLOBPCGSetBlockSize(EPS,PetscInt);
    1089: SLEPC_EXTERN PetscErrorCode EPSLOBPCGGetBlockSize(EPS,PetscInt*);
    1090: SLEPC_EXTERN PetscErrorCode EPSLOBPCGSetRestart(EPS,PetscReal);
    1091: SLEPC_EXTERN PetscErrorCode EPSLOBPCGGetRestart(EPS,PetscReal*);
    1092: SLEPC_EXTERN PetscErrorCode EPSLOBPCGSetLocking(EPS,PetscBool);
    1093: SLEPC_EXTERN PetscErrorCode EPSLOBPCGGetLocking(EPS,PetscBool*);

    1095: /*E
    1096:    EPSCISSQuadRule - The quadrature rule used in the `EPSCISS` solver.

    1098:    Values:
    1099: +  `EPS_CISS_QUADRULE_TRAPEZOIDAL` - trapezoidal rule
    1100: -  `EPS_CISS_QUADRULE_CHEBYSHEV`   - Gauss quadrature on Chebyshev points

    1102:    Note:
    1103:    For a detailed description see {cite:p}`Mae16`.

    1105:    Level: advanced

    1107: .seealso: [](ch:eps), `EPSCISSSetQuadRule()`, `EPSCISSGetQuadRule()`
    1108: E*/
    1109: typedef enum { EPS_CISS_QUADRULE_TRAPEZOIDAL = 1,
    1110:                EPS_CISS_QUADRULE_CHEBYSHEV   = 2 } EPSCISSQuadRule;
    1111: SLEPC_EXTERN const char *EPSCISSQuadRules[];

    1113: /*E
    1114:    EPSCISSExtraction - The extraction technique used in the `EPSCISS` solver.

    1116:    Values:
    1117: +  `EPS_CISS_EXTRACTION_RITZ`   - Ritz approximations from Rayleigh-Ritz projection
    1118: -  `EPS_CISS_EXTRACTION_HANKEL` - use Hankel pencil as in the original Sakurai-Sugiura method

    1120:    Note:
    1121:    For a detailed description see {cite:p}`Mae16`.

    1123:    Level: advanced

    1125: .seealso: [](ch:eps), `EPSCISSSetExtraction()`, `EPSCISSGetExtraction()`
    1126: E*/
    1127: typedef enum { EPS_CISS_EXTRACTION_RITZ,
    1128:                EPS_CISS_EXTRACTION_HANKEL } EPSCISSExtraction;
    1129: SLEPC_EXTERN const char *EPSCISSExtractions[];

    1131: SLEPC_EXTERN PetscErrorCode EPSCISSSetExtraction(EPS,EPSCISSExtraction);
    1132: SLEPC_EXTERN PetscErrorCode EPSCISSGetExtraction(EPS,EPSCISSExtraction*);
    1133: SLEPC_EXTERN PetscErrorCode EPSCISSSetQuadRule(EPS,EPSCISSQuadRule);
    1134: SLEPC_EXTERN PetscErrorCode EPSCISSGetQuadRule(EPS,EPSCISSQuadRule*);
    1135: SLEPC_EXTERN PetscErrorCode EPSCISSSetSizes(EPS,PetscInt,PetscInt,PetscInt,PetscInt,PetscInt,PetscBool);
    1136: SLEPC_EXTERN PetscErrorCode EPSCISSGetSizes(EPS,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscInt*,PetscBool*);
    1137: SLEPC_EXTERN PetscErrorCode EPSCISSSetThreshold(EPS,PetscReal,PetscReal);
    1138: SLEPC_EXTERN PetscErrorCode EPSCISSGetThreshold(EPS,PetscReal*,PetscReal*);
    1139: SLEPC_EXTERN PetscErrorCode EPSCISSSetRefinement(EPS,PetscInt,PetscInt);
    1140: SLEPC_EXTERN PetscErrorCode EPSCISSGetRefinement(EPS,PetscInt*,PetscInt*);
    1141: SLEPC_EXTERN PetscErrorCode EPSCISSSetUseST(EPS,PetscBool);
    1142: SLEPC_EXTERN PetscErrorCode EPSCISSGetUseST(EPS,PetscBool*);
    1143: SLEPC_EXTERN PetscErrorCode EPSCISSGetKSPs(EPS,PetscInt*,KSP*[]);

    1145: SLEPC_EXTERN PetscErrorCode EPSLyapIISetLME(EPS,LME);
    1146: SLEPC_EXTERN PetscErrorCode EPSLyapIIGetLME(EPS,LME*);
    1147: SLEPC_EXTERN PetscErrorCode EPSLyapIISetRanks(EPS,PetscInt,PetscInt);
    1148: SLEPC_EXTERN PetscErrorCode EPSLyapIIGetRanks(EPS,PetscInt*,PetscInt*);

    1150: SLEPC_EXTERN PetscErrorCode EPSBLOPEXSetBlockSize(EPS,PetscInt);
    1151: SLEPC_EXTERN PetscErrorCode EPSBLOPEXGetBlockSize(EPS,PetscInt*);

    1153: /*E
    1154:    EPSEVSLDOSMethod - The method to approximate the density of states (DOS)
    1155:    in the `EPSEVSL` solver.

    1157:    Values:
    1158: +  `EPS_EVSL_DOS_KPM`     - Kernel Polynomial Method
    1159: -  `EPS_EVSL_DOS_LANCZOS` - Lanczos method

    1161:    Note:
    1162:    See the documentation of EVSL {cite:p}`Li19` for an explanation.

    1164:    Level: advanced

    1166: .seealso: [](ch:eps), `EPSEVSLSetDOSParameters()`, `EPSEVSLGetDOSParameters()`
    1167: E*/
    1168: typedef enum { EPS_EVSL_DOS_KPM,
    1169:                EPS_EVSL_DOS_LANCZOS } EPSEVSLDOSMethod;
    1170: SLEPC_EXTERN const char *EPSEVSLDOSMethods[];

    1172: /*E
    1173:    EPSEVSLDamping - The damping type used in the `EPSEVSL` solver.

    1175:    Values:
    1176: +  `EPS_EVSL_DAMPING_NONE`    - no damping
    1177: .  `EPS_EVSL_DAMPING_JACKSON` - Jackson damping
    1178: -  `EPS_EVSL_DAMPING_SIGMA`   - Lanczos damping

    1180:    Note:
    1181:    See the documentation of EVSL {cite:p}`Li19` for an explanation.

    1183:    Level: advanced

    1185: .seealso: [](ch:eps), `EPSEVSLSetDOSParameters()`, `EPSEVSLGetDOSParameters()`
    1186: E*/
    1187: typedef enum { EPS_EVSL_DAMPING_NONE,
    1188:                EPS_EVSL_DAMPING_JACKSON,
    1189:                EPS_EVSL_DAMPING_SIGMA } EPSEVSLDamping;
    1190: SLEPC_EXTERN const char *EPSEVSLDampings[];

    1192: SLEPC_EXTERN PetscErrorCode EPSEVSLSetRange(EPS,PetscReal,PetscReal);
    1193: SLEPC_EXTERN PetscErrorCode EPSEVSLGetRange(EPS,PetscReal*,PetscReal*);
    1194: SLEPC_EXTERN PetscErrorCode EPSEVSLSetSlices(EPS,PetscInt);
    1195: SLEPC_EXTERN PetscErrorCode EPSEVSLGetSlices(EPS,PetscInt*);
    1196: SLEPC_EXTERN PetscErrorCode EPSEVSLSetDOSParameters(EPS,EPSEVSLDOSMethod,PetscInt,PetscInt,PetscInt,PetscInt);
    1197: SLEPC_EXTERN PetscErrorCode EPSEVSLGetDOSParameters(EPS,EPSEVSLDOSMethod*,PetscInt*,PetscInt*,PetscInt*,PetscInt*);
    1198: SLEPC_EXTERN PetscErrorCode EPSEVSLSetPolParameters(EPS,PetscInt,PetscReal);
    1199: SLEPC_EXTERN PetscErrorCode EPSEVSLGetPolParameters(EPS,PetscInt*,PetscReal*);
    1200: SLEPC_EXTERN PetscErrorCode EPSEVSLSetDamping(EPS,EPSEVSLDamping);
    1201: SLEPC_EXTERN PetscErrorCode EPSEVSLGetDamping(EPS,EPSEVSLDamping*);

    1203: SLEPC_EXTERN PetscErrorCode EPSFEASTSetNumPoints(EPS,PetscInt);
    1204: SLEPC_EXTERN PetscErrorCode EPSFEASTGetNumPoints(EPS,PetscInt*);

    1206: SLEPC_EXTERN PetscErrorCode EPSCHASESetDegree(EPS,PetscInt,PetscBool);
    1207: SLEPC_EXTERN PetscErrorCode EPSCHASEGetDegree(EPS,PetscInt*,PetscBool*);