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/*

  Method: General Davidson Method (includes GD and JD)

  References:

    - Ernest R. Davidson. Super-matrix methods. Computer Physics Communications,

      53:49–60, May 1989.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2010, Universidad Politecnica de Valencia, Spain

   This file is part of SLEPc.

   SLEPc is free software: you can redistribute it and/or modify it under  the

   terms of version 3 of the GNU Lesser General Public License as published by

   the Free Software Foundation.

   SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY

   WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS

   FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for

   more details.

   You  should have received a copy of the GNU Lesser General  Public  License

   along with SLEPc. If not, see <http://www.gnu.org/licenses/>.

   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*/

#include "davidson.h"

PetscErrorCode EPSView_DAVIDSON(EPS eps,PetscViewer viewer);

typedef struct {

  /**** Solver options ****/

  PetscInt blocksize,     /* block size */

    initialsize,          /* initial size of V */

    minv,                 /* size of V after restarting */

    plusk;                /* keep plusk eigenvectors from the last iteration */

  PetscBool  ipB;         /* true if V'B*V=I */

  PetscInt   method;      /* method for improving the approximate solution */

  PetscReal  fix;         /* the fix parameter */

  PetscBool  krylovstart; /* true if the starting subspace is a Krylov basis */

  /**** Solver data ****/

  dvdDashboard ddb;

  /**** Things to destroy ****/

  PetscScalar *wS;

  Vec         *wV;

  PetscInt    size_wV;

} EPS_DAVIDSON;

#undef __FUNCT__  

#define __FUNCT__ "EPSCreate_DAVIDSON"

PetscErrorCode EPSCreate_DAVIDSON(EPS eps)

{

  PetscErrorCode ierr;

  EPS_DAVIDSON   *data;

  PetscFunctionBegin;

  ierr = STSetType(eps->OP, STPRECOND); CHKERRQ(ierr);

  ierr = STPrecondSetKSPHasMat(eps->OP, PETSC_FALSE); CHKERRQ(ierr);

  eps->OP->ops->getbilinearform  = STGetBilinearForm_Default;

  eps->ops->solve                = EPSSolve_DAVIDSON;

  eps->ops->setup                = EPSSetUp_DAVIDSON;

  eps->ops->destroy              = EPSDestroy_DAVIDSON;

  eps->ops->backtransform        = EPSBackTransform_Default;

  eps->ops->computevectors       = EPSComputeVectors_QZ;

  eps->ops->view                 = EPSView_DAVIDSON;

  ierr = PetscMalloc(sizeof(EPS_DAVIDSON), &data); CHKERRQ(ierr);

  eps->data = data;

  /* Set default values */

  ierr = EPSDAVIDSONSetKrylovStart_DAVIDSON(eps, PETSC_FALSE); CHKERRQ(ierr);

  ierr = EPSDAVIDSONSetBlockSize_DAVIDSON(eps, 1); CHKERRQ(ierr);

  ierr = EPSDAVIDSONSetRestart_DAVIDSON(eps, 6, 0); CHKERRQ(ierr);

  ierr = EPSDAVIDSONSetInitialSize_DAVIDSON(eps, 5); CHKERRQ(ierr);

  ierr = EPSDAVIDSONSetFix_DAVIDSON(eps, 0.01); CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSSetUp_DAVIDSON"

PetscErrorCode EPSSetUp_DAVIDSON(EPS eps)

{

  PetscErrorCode ierr;

  EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;

  dvdDashboard   *dvd = &data->ddb;

  dvdBlackboard  b;

  PetscInt       i,nvecs,nscalars,min_size_V,plusk,bs,initv;

  Mat            A,B;

  KSP            ksp;

  PetscBool      t,ipB,ispositive;

  HarmType_t     harm;

  InitType_t     init;

  PetscReal      fix;

  PetscFunctionBegin;

  /* Setup EPS options and get the problem specification */

  ierr = EPSDAVIDSONGetBlockSize_DAVIDSON(eps, &bs); CHKERRQ(ierr);

  if (bs <= 0) bs = 1;

  if(eps->ncv) {

    if (eps->ncv<eps->nev) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"The value of ncv must be at least nev");

  } else if (eps->mpd) eps->ncv = eps->mpd + eps->nev + bs;

  else if (eps->nev<500)

    eps->ncv = PetscMin(eps->n,PetscMax(2*eps->nev,eps->nev+15))+bs;

  else

    eps->ncv = PetscMin(eps->n,eps->nev+500)+bs;

  if (!eps->mpd) eps->mpd = eps->ncv;

  if (eps->mpd > eps->ncv)

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"The mpd has to be less or equal than ncv");

  if (eps->mpd < 2)

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"The mpd has to be greater than 2");

  if (!eps->max_it) eps->max_it = PetscMax(100,2*eps->n/eps->ncv);

  if (!eps->which) eps->which = EPS_LARGEST_MAGNITUDE;

  if (eps->ishermitian && (eps->which==EPS_LARGEST_IMAGINARY || eps->which==EPS_SMALLEST_IMAGINARY))

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Wrong value of eps->which");

  if (!(eps->nev + bs <= eps->ncv))

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP, "The ncv has to be greater than nev plus blocksize!");

  ierr = EPSDAVIDSONGetRestart_DAVIDSON(eps, &min_size_V, &plusk);

  CHKERRQ(ierr);

  if (!min_size_V) min_size_V = PetscMin(PetscMax(bs,5), eps->mpd/2);

  if (!(min_size_V+bs <= eps->mpd))

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP, "The value of minv must be less than mpd minus blocksize");

  ierr = EPSDAVIDSONGetInitialSize_DAVIDSON(eps, &initv); CHKERRQ(ierr);

  if (eps->mpd < initv)

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"The initv has to be less or equal than mpd");

  /* Davidson solvers do not support left eigenvectors */

  if (eps->leftvecs) SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Left vectors not supported in this solver");

  /* Change the default sigma to inf if necessary */

  if (eps->which == EPS_LARGEST_MAGNITUDE || eps->which == EPS_LARGEST_REAL ||

      eps->which == EPS_LARGEST_IMAGINARY) {

    ierr = STSetDefaultShift(eps->OP, 3e300); CHKERRQ(ierr);

  }

  /* Davidson solvers only support STPRECOND */

  ierr = STSetUp(eps->OP); CHKERRQ(ierr);

  ierr = PetscTypeCompare((PetscObject)eps->OP, STPRECOND, &t); CHKERRQ(ierr);

  if (!t) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_SUP, "%s only works with precond spectral transformation",

    ((PetscObject)eps)->type_name);

  /* Setup problem specification in dvd */

  ierr = STGetOperators(eps->OP, &A, &B); CHKERRQ(ierr);

  ierr = PetscMemzero(dvd, sizeof(dvdDashboard)); CHKERRQ(ierr);

  dvd->A = A; dvd->B = eps->isgeneralized? B : PETSC_NULL;

  ispositive = eps->ispositive;

  dvd->sA = DVD_MAT_IMPLICIT |

            (eps->ishermitian? DVD_MAT_HERMITIAN : 0) |

            ((ispositive && !eps->isgeneralized) ? DVD_MAT_POS_DEF : 0);

  /* Asume -eps_hermitian means hermitian-definite in generalized problems */

  if (!ispositive && !eps->isgeneralized && eps->ishermitian) ispositive = PETSC_TRUE;

  if (!eps->isgeneralized)

    dvd->sB = DVD_MAT_IMPLICIT | DVD_MAT_HERMITIAN | DVD_MAT_IDENTITY |

              DVD_MAT_UNITARY | DVD_MAT_POS_DEF;

  else

    dvd->sB = DVD_MAT_IMPLICIT |

              (eps->ishermitian? DVD_MAT_HERMITIAN : 0) |

              (ispositive? DVD_MAT_POS_DEF : 0);

  ipB = DVD_IS(dvd->sB, DVD_MAT_POS_DEF)?PETSC_TRUE:PETSC_FALSE;

  dvd->sEP = ((!eps->isgeneralized || (eps->isgeneralized && ipB))? DVD_EP_STD : 0) |

             (ispositive? DVD_EP_HERMITIAN : 0);

  dvd->nev = eps->nev;

  dvd->which = eps->which;

  switch(eps->which) {

  case EPS_TARGET_MAGNITUDE:

  case EPS_TARGET_REAL:

  case EPS_TARGET_IMAGINARY:

    dvd->withTarget = PETSC_TRUE;

    dvd->target[0] = eps->target; dvd->target[1] = 1.0;

    break;

  case EPS_LARGEST_MAGNITUDE:

  case EPS_LARGEST_REAL:

  case EPS_LARGEST_IMAGINARY: //TODO: think about this case

  default:

    dvd->withTarget = PETSC_TRUE;

    dvd->target[0] = 1.0; dvd->target[1] = 0.0;

    break;

  case EPS_SMALLEST_MAGNITUDE:

  case EPS_SMALLEST_REAL:

  case EPS_SMALLEST_IMAGINARY: //TODO: think about this case

    dvd->withTarget = PETSC_TRUE;

    dvd->target[0] = 0.0; dvd->target[1] = 1.0;

  }

  dvd->tol = eps->tol;

  dvd->eps = eps;

  /* Setup the extraction technique */

  if (!eps->extraction) {

    ierr = EPSSetExtraction(eps,EPS_RITZ);CHKERRQ(ierr);

  }

  switch(eps->extraction) {

  case EPS_RITZ:              harm = DVD_HARM_NONE; break;

  case EPS_HARMONIC:          harm = DVD_HARM_RR; break;

  case EPS_HARMONIC_RELATIVE: harm = DVD_HARM_RRR; break;

  case EPS_HARMONIC_RIGHT:    harm = DVD_HARM_REIGS; break;

  case EPS_HARMONIC_LARGEST:  harm = DVD_HARM_LEIGS; break;

  default: SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"Unsupported extraction type");

  }

  /* Setup the type of starting subspace */

  ierr = EPSDAVIDSONGetKrylovStart_DAVIDSON(eps, &t); CHKERRQ(ierr);

  init = (!t)? DVD_INITV_CLASSIC : DVD_INITV_KRYLOV;

  /* Setup IP */

  if (ipB && dvd->B) {

    ierr = IPSetBilinearForm(eps->ip, dvd->B, IP_INNER_HERMITIAN); CHKERRQ(ierr);

  } else {

    ierr = IPSetBilinearForm(eps->ip, 0, IP_INNER_HERMITIAN); CHKERRQ(ierr);

  }

  /* Get the fix parameter */

  ierr = EPSDAVIDSONGetFix_DAVIDSON(eps, &fix); CHKERRQ(ierr);

  /* Orthonormalize the DS */

  ierr = dvd_orthV(eps->ip, PETSC_NULL, 0, PETSC_NULL, 0, eps->DS, 0,

                   PetscAbs(eps->nds), PETSC_NULL, 0, eps->rand); CHKERRQ(ierr);

  /* Preconfigure dvd */

  ierr = STGetKSP(eps->OP, &ksp); CHKERRQ(ierr);

  ierr = dvd_schm_basic_preconf(dvd, &b, eps->ncv, eps->mpd, min_size_V, bs,

                                initv,

                                PetscAbs(eps->nini),

                                plusk, harm,

                                PETSC_NULL, init, eps->trackall);CHKERRQ(ierr);

  /* Reserve memory */

  nvecs = b.max_size_auxV + b.own_vecs;

  nscalars = b.own_scalars + b.max_size_auxS;

  ierr = PetscMalloc((nvecs*eps->nloc+nscalars)*sizeof(PetscScalar), &data->wS);

  CHKERRQ(ierr);

  ierr = PetscMalloc(nvecs*sizeof(Vec), &data->wV); CHKERRQ(ierr);

  data->size_wV = nvecs;

  for (i=0; i<nvecs; i++) {

    ierr = VecCreateMPIWithArray(((PetscObject)eps)->comm, eps->nloc, PETSC_DECIDE,

                                 data->wS+i*eps->nloc, &data->wV[i]);CHKERRQ(ierr);

  }

  b.free_vecs = data->wV;

  b.free_scalars = data->wS + nvecs*eps->nloc;

  dvd->auxV = data->wV + b.own_vecs;

  dvd->auxS = b.free_scalars + b.own_scalars;

  dvd->size_auxV = b.max_size_auxV;

  dvd->size_auxS = b.max_size_auxS;

  /* Configure dvd for a basic GD */

  ierr = dvd_schm_basic_conf(dvd, &b, eps->ncv, eps->mpd, min_size_V, bs,

                             initv,

                             PetscAbs(eps->nini), plusk,

                             eps->ip, harm, dvd->withTarget,

                             eps->target, ksp,

                             fix, init, eps->trackall);CHKERRQ(ierr);

  /* Associate the eigenvalues to the EPS */

  eps->eigr = dvd->eigr;

  eps->eigi = dvd->eigi;

  eps->errest = dvd->errest;

  eps->V = dvd->V;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSSolve_DAVIDSON"

PetscErrorCode EPSSolve_DAVIDSON(EPS eps)

{

  EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;

  dvdDashboard   *d = &data->ddb;

  PetscErrorCode ierr;

  PetscFunctionBegin;

  /* Call the starting routines */

  DVD_FL_CALL(d->startList, d);

  for(eps->its=0; eps->its < eps->max_it; eps->its++) {

    /* Initialize V, if it is needed */

    if (d->size_V == 0) { ierr = d->initV(d); CHKERRQ(ierr); }

    /* Find the best approximated eigenpairs in V, X */

    ierr = d->calcPairs(d); CHKERRQ(ierr);

    /* Expand the subspace */

    ierr = d->updateV(d); CHKERRQ(ierr);

    /* Monitor progress */

    eps->nconv = d->nconv;

    ierr = EPSMonitor(eps, eps->its+1, eps->nconv, eps->eigr, eps->eigi, eps->errest, d->size_H+d->nconv);CHKERRQ(ierr);

    /* Test for convergence */

    if (eps->nconv >= eps->nev) break;

  }

  /* Call the ending routines */

  DVD_FL_CALL(d->endList, d);

  if( eps->nconv >= eps->nev ) eps->reason = EPS_CONVERGED_TOL;

  else eps->reason = EPS_DIVERGED_ITS;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDestroy_DAVIDSON"

PetscErrorCode EPSDestroy_DAVIDSON(EPS eps)

{

  EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;

  dvdDashboard   *dvd = &data->ddb;

  PetscErrorCode ierr;

  PetscInt       i;

  PetscFunctionBegin;

  /* Call step destructors and destroys the list */

  DVD_FL_CALL(dvd->destroyList, dvd);

  DVD_FL_DEL(dvd->destroyList);

  DVD_FL_DEL(dvd->startList);

  DVD_FL_DEL(dvd->endList);

  for(i=0; i<data->size_wV; i++) {

    ierr = VecDestroy(&data->wV[i]); CHKERRQ(ierr);

  }

  ierr = PetscFree(data->wV);CHKERRQ(ierr);

  ierr = PetscFree(data->wS);CHKERRQ(ierr);

  ierr = PetscFree(data);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSView_DAVIDSON"

PetscErrorCode EPSView_DAVIDSON(EPS eps,PetscViewer viewer)

{

  PetscErrorCode ierr;

  PetscBool      isascii, opb;

  PetscInt       opi, opi0;

  const char*    name;

  PetscFunctionBegin;

  name = ((PetscObject)eps)->type_name;

  ierr = PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);CHKERRQ(ierr);

  if (!isascii) {

    SETERRQ2(((PetscObject)eps)->comm,1,"Viewer type %s not supported for %s",((PetscObject)viewer)->type_name,name);

  }

  ierr = EPSDAVIDSONGetBlockSize_DAVIDSON(eps, &opi); CHKERRQ(ierr);

  ierr = PetscViewerASCIIPrintf(viewer,"block size: %d\n", opi);CHKERRQ(ierr);

  ierr = EPSDAVIDSONGetKrylovStart_DAVIDSON(eps, &opb); CHKERRQ(ierr);

  if(!opb) {

    ierr = PetscViewerASCIIPrintf(viewer,"type of the initial subspace: non-Krylov\n");CHKERRQ(ierr);

  } else {

    ierr = PetscViewerASCIIPrintf(viewer,"type of the initial subspace: Krylov\n");CHKERRQ(ierr);

  }

  ierr = EPSDAVIDSONGetRestart_DAVIDSON(eps, &opi, &opi0); CHKERRQ(ierr);

  ierr = PetscViewerASCIIPrintf(viewer,"size of the subspace after restarting: %d\n", opi);CHKERRQ(ierr);

  ierr = PetscViewerASCIIPrintf(viewer,"number of vectors after restarting from the previous iteration: %d\n", opi0);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "SLEPcNotImplemented"

PetscErrorCode SLEPcNotImplemented()

{

  SETERRQ(PETSC_COMM_WORLD,1, "Do not call this function!");

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONSetKrylovStart_DAVIDSON"

PetscErrorCode EPSDAVIDSONSetKrylovStart_DAVIDSON(EPS eps,PetscBool krylovstart)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  data->krylovstart = krylovstart;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONGetKrylovStart_DAVIDSON"

PetscErrorCode EPSDAVIDSONGetKrylovStart_DAVIDSON(EPS eps,PetscBool *krylovstart)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  *krylovstart = data->krylovstart;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONSetBlockSize_DAVIDSON"

PetscErrorCode EPSDAVIDSONSetBlockSize_DAVIDSON(EPS eps,PetscInt blocksize)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  if(blocksize == PETSC_DEFAULT || blocksize == PETSC_DECIDE) blocksize = 1;

  if(blocksize <= 0)

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid blocksize value");

  data->blocksize = blocksize;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONGetBlockSize_DAVIDSON"

PetscErrorCode EPSDAVIDSONGetBlockSize_DAVIDSON(EPS eps,PetscInt *blocksize)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  *blocksize = data->blocksize;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONSetRestart_DAVIDSON"

PetscErrorCode EPSDAVIDSONSetRestart_DAVIDSON(EPS eps,PetscInt minv,PetscInt plusk)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  if(minv == PETSC_DEFAULT || minv == PETSC_DECIDE) minv = 5;

  if(minv <= 0)

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid minv value");

  if(plusk == PETSC_DEFAULT || plusk == PETSC_DECIDE) plusk = 5;

  if(plusk < 0)

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid plusk value");

  data->minv = minv;

  data->plusk = plusk;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONGetRestart_DAVIDSON"

PetscErrorCode EPSDAVIDSONGetRestart_DAVIDSON(EPS eps,PetscInt *minv,PetscInt *plusk)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  *minv = data->minv;

  *plusk = data->plusk;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONGetInitialSize_DAVIDSON"

PetscErrorCode EPSDAVIDSONGetInitialSize_DAVIDSON(EPS eps,PetscInt *initialsize)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  *initialsize = data->initialsize;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONSetInitialSize_DAVIDSON"

PetscErrorCode EPSDAVIDSONSetInitialSize_DAVIDSON(EPS eps,PetscInt initialsize)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  if(initialsize == PETSC_DEFAULT || initialsize == PETSC_DECIDE) initialsize = 5;

  if(initialsize <= 0)

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid initial size value");

  data->initialsize = initialsize;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONGetFix_DAVIDSON"

PetscErrorCode EPSDAVIDSONGetFix_DAVIDSON(EPS eps,PetscReal *fix)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  *fix = data->fix;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDAVIDSONSetFix_DAVIDSON"

PetscErrorCode EPSDAVIDSONSetFix_DAVIDSON(EPS eps,PetscReal fix)

{

  EPS_DAVIDSON *data = (EPS_DAVIDSON*)eps->data;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  if(fix == PETSC_DEFAULT || fix == PETSC_DECIDE) fix = 0.01;

  if(fix < 0.0)

    SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_ARG_OUTOFRANGE,"Invalid fix value");

  data->fix = fix;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSComputeVectors_QZ"

/*

  EPSComputeVectors_QZ - Compute eigenvectors from the vectors

  provided by the eigensolver. This version is intended for solvers

  that provide Schur vectors from the QZ decompositon. Given the partial

  Schur decomposition OP*V=V*T, the following steps are performed:

      1) compute eigenvectors of (S,T): S*Z=T*Z*D

      2) compute eigenvectors of OP: X=V*Z

  If left eigenvectors are required then also do Z'*Tl=D*Z', Y=W*Z

 */

PetscErrorCode EPSComputeVectors_QZ(EPS eps)

{

  PetscErrorCode ierr;

  EPS_DAVIDSON   *data = (EPS_DAVIDSON*)eps->data;

  dvdDashboard   *d = &data->ddb;

  PetscScalar    *pX, *auxS;

  PetscInt       size_auxS;

  PetscFunctionBegin;

  /* Compute the eigenvectors associated to (cS, cT) */

  ierr = PetscMalloc(sizeof(PetscScalar)*d->nconv*d->nconv, &pX); CHKERRQ(ierr);

  size_auxS = 11*d->nconv + 4*d->nconv*d->nconv;

  ierr = PetscMalloc(sizeof(PetscScalar)*size_auxS, &auxS); CHKERRQ(ierr);

  ierr = dvd_compute_eigenvectors(d->nconv, d->cS, d->ldcS, d->cT, d->ldcT,

                                  pX, d->nconv, PETSC_NULL, 0, auxS,

                                  size_auxS, PETSC_FALSE); CHKERRQ(ierr);

  /* pX[i] <- pX[i] / ||pX[i]|| */

  ierr = SlepcDenseNorm(pX, d->nconv, d->nconv, d->nconv, d->ceigi);CHKERRQ(ierr);

  /* V <- cX * pX */

  ierr = SlepcUpdateVectorsZ(eps->V, 0.0, 1.0, d->cX, d->size_cX, pX,

                             d->nconv, d->nconv, d->nconv); CHKERRQ(ierr);

  ierr = PetscFree(pX); CHKERRQ(ierr);

  ierr = PetscFree(auxS); CHKERRQ(ierr);

  eps->evecsavailable = PETSC_TRUE;

  PetscFunctionReturn(0);

}