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/*                      

   SLEPc eigensolver: "arnoldi"

   Method: Explicitly Restarted Arnoldi

   Algorithm:

       Arnoldi method with explicit restart and deflation.

   References:

       [1] "Arnoldi Methods in SLEPc", SLEPc Technical Report STR-4,

           available at http://www.grycap.upv.es/slepc.

   Last update: Feb 2009

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

   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 <private/epsimpl.h>                /*I "slepceps.h" I*/

#include <slepcblaslapack.h>

PetscErrorCode EPSSolve_Arnoldi(EPS);

typedef struct {

  PetscBool delayed;

} EPS_ARNOLDI;

#undef __FUNCT__  

#define __FUNCT__ "EPSSetUp_Arnoldi"

PetscErrorCode EPSSetUp_Arnoldi(EPS eps)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  if (eps->ncv) { /* ncv set */

    if (eps->ncv<eps->nev) SETERRQ(((PetscObject)eps)->comm,1,"The value of ncv must be at least nev");

  }

  else if (eps->mpd) { /* mpd set */

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

  }

  else { /* neither set: defaults depend on nev being small or large */

    if (eps->nev<500) eps->ncv = PetscMin(eps->n,PetscMax(2*eps->nev,eps->nev+15));

    else { eps->mpd = 500; eps->ncv = PetscMin(eps->n,eps->nev+eps->mpd); }

  }

  if (!eps->mpd) eps->mpd = eps->ncv;

  if (eps->ncv>eps->nev+eps->mpd) SETERRQ(((PetscObject)eps)->comm,1,"The value of ncv must not be larger than nev+mpd");

  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,1,"Wrong value of eps->which");

  if (!eps->extraction) {

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

  }

  ierr = EPSAllocateSolution(eps);CHKERRQ(ierr);

  ierr = PetscFree(eps->T);CHKERRQ(ierr);

  ierr = PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&eps->T);CHKERRQ(ierr);

  if (eps->leftvecs) {

    ierr = PetscFree(eps->Tl);CHKERRQ(ierr);

    ierr = PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&eps->Tl);CHKERRQ(ierr);

    ierr = PetscInfo(eps,"Warning: parameter mpd ignored\n");CHKERRQ(ierr);

    ierr = EPSDefaultGetWork(eps,2);CHKERRQ(ierr);

  } else {

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

  }

  /* dispatch solve method */

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

  eps->ops->solve = EPSSolve_Arnoldi;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDelayedArnoldi"

/*

   EPSDelayedArnoldi - This function is equivalent to EPSBasicArnoldi but

   performs the computation in a different way. The main idea is that

   reorthogonalization is delayed to the next Arnoldi step. This version is

   more scalable but in some cases convergence may stagnate.

*/

PetscErrorCode EPSDelayedArnoldi(EPS eps,PetscScalar *H,PetscInt ldh,Vec *V,PetscInt k,PetscInt *M,Vec f,PetscReal *beta,PetscBool *breakdown)

{

  PetscErrorCode ierr;

  PetscInt       i,j,m=*M;

  Vec            u,t;

  PetscScalar    shh[100],*lhh,dot,dot2;

  PetscReal      norm1=0.0,norm2;

  PetscFunctionBegin;

  if (m<=100) lhh = shh;

  else { ierr = PetscMalloc(m*sizeof(PetscScalar),&lhh);CHKERRQ(ierr); }

  ierr = VecDuplicate(f,&u);CHKERRQ(ierr);

  ierr = VecDuplicate(f,&t);CHKERRQ(ierr);

  for (j=k;j<m;j++) {

    ierr = STApply(eps->OP,V[j],f);CHKERRQ(ierr);

    ierr = IPOrthogonalize(eps->ip,0,PETSC_NULL,eps->nds,PETSC_NULL,eps->DS,f,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

    ierr = IPMInnerProductBegin(eps->ip,f,j+1,V,H+ldh*j);CHKERRQ(ierr);

    if (j>k) {

      ierr = IPMInnerProductBegin(eps->ip,V[j],j,V,lhh);CHKERRQ(ierr);

      ierr = IPInnerProductBegin(eps->ip,V[j],V[j],&dot);CHKERRQ(ierr);

    }

    if (j>k+1) {

      ierr = IPNormBegin(eps->ip,u,&norm2);CHKERRQ(ierr);

      ierr = VecDotBegin(u,V[j-2],&dot2);CHKERRQ(ierr);

    }

    ierr = IPMInnerProductEnd(eps->ip,f,j+1,V,H+ldh*j);CHKERRQ(ierr);

    if (j>k) {

      ierr = IPMInnerProductEnd(eps->ip,V[j],j,V,lhh);CHKERRQ(ierr);

      ierr = IPInnerProductEnd(eps->ip,V[j],V[j],&dot);CHKERRQ(ierr);

    }

    if (j>k+1) {

      ierr = IPNormEnd(eps->ip,u,&norm2);CHKERRQ(ierr);

      ierr = VecDotEnd(u,V[j-2],&dot2);CHKERRQ(ierr);

      if (PetscAbsScalar(dot2/norm2) > PETSC_MACHINE_EPSILON) {

        *breakdown = PETSC_TRUE;

        *M = j-1;

        *beta = norm2;

        if (m>100) { ierr = PetscFree(lhh);CHKERRQ(ierr); }

        ierr = VecDestroy(&u);CHKERRQ(ierr);

        ierr = VecDestroy(&t);CHKERRQ(ierr);

        PetscFunctionReturn(0);

      }

    }

    if (j>k) {      

      norm1 = PetscSqrtReal(PetscRealPart(dot));

      for (i=0;i<j;i++)

        H[ldh*j+i] = H[ldh*j+i]/norm1;

      H[ldh*j+j] = H[ldh*j+j]/dot;

      ierr = VecCopy(V[j],t);CHKERRQ(ierr);

      ierr = VecScale(V[j],1.0/norm1);CHKERRQ(ierr);

      ierr = VecScale(f,1.0/norm1);CHKERRQ(ierr);

    }

    ierr = SlepcVecMAXPBY(f,1.0,-1.0,j+1,H+ldh*j,V);CHKERRQ(ierr);

    if (j>k) {

      ierr = SlepcVecMAXPBY(t,1.0,-1.0,j,lhh,V);CHKERRQ(ierr);

      for (i=0;i<j;i++)

        H[ldh*(j-1)+i] += lhh[i];

    }

    if (j>k+1) {

      ierr = VecCopy(u,V[j-1]);CHKERRQ(ierr);

      ierr = VecScale(V[j-1],1.0/norm2);CHKERRQ(ierr);

      H[ldh*(j-2)+j-1] = norm2;

    }

    if (j<m-1) {

      ierr = VecCopy(f,V[j+1]);CHKERRQ(ierr);

      ierr = VecCopy(t,u);CHKERRQ(ierr);

    }

  }

  ierr = IPNorm(eps->ip,t,&norm2);CHKERRQ(ierr);

  ierr = VecScale(t,1.0/norm2);CHKERRQ(ierr);

  ierr = VecCopy(t,V[m-1]);CHKERRQ(ierr);

  H[ldh*(m-2)+m-1] = norm2;

  ierr = IPMInnerProduct(eps->ip,f,m,V,lhh);CHKERRQ(ierr);

  ierr = SlepcVecMAXPBY(f,1.0,-1.0,m,lhh,V);CHKERRQ(ierr);

  for (i=0;i<m;i++)

    H[ldh*(m-1)+i] += lhh[i];

  ierr = IPNorm(eps->ip,f,beta);CHKERRQ(ierr);

  ierr = VecScale(f,1.0 / *beta);CHKERRQ(ierr);

  *breakdown = PETSC_FALSE;

  if (m>100) { ierr = PetscFree(lhh);CHKERRQ(ierr); }

  ierr = VecDestroy(&u);CHKERRQ(ierr);

  ierr = VecDestroy(&t);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDelayedArnoldi1"

/*

   EPSDelayedArnoldi1 - This function is similar to EPSDelayedArnoldi1,

   but without reorthogonalization (only delayed normalization).

*/

PetscErrorCode EPSDelayedArnoldi1(EPS eps,PetscScalar *H,PetscInt ldh,Vec *V,PetscInt k,PetscInt *M,Vec f,PetscReal *beta,PetscBool *breakdown)

{

  PetscErrorCode ierr;

  PetscInt       i,j,m=*M;

  PetscScalar    dot;

  PetscReal      norm=0.0;

  PetscFunctionBegin;

  for (j=k;j<m;j++) {

    ierr = STApply(eps->OP,V[j],f);CHKERRQ(ierr);

    ierr = IPOrthogonalize(eps->ip,0,PETSC_NULL,eps->nds,PETSC_NULL,eps->DS,f,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

    ierr = IPMInnerProductBegin(eps->ip,f,j+1,V,H+ldh*j);CHKERRQ(ierr);

    if (j>k) {

      ierr = IPInnerProductBegin(eps->ip,V[j],V[j],&dot);CHKERRQ(ierr);

    }

    ierr = IPMInnerProductEnd(eps->ip,f,j+1,V,H+ldh*j);CHKERRQ(ierr);

    if (j>k) {

      ierr = IPInnerProductEnd(eps->ip,V[j],V[j],&dot);CHKERRQ(ierr);

    }

    if (j>k) {      

      norm = PetscSqrtReal(PetscRealPart(dot));

      ierr = VecScale(V[j],1.0/norm);CHKERRQ(ierr);

      H[ldh*(j-1)+j] = norm;

      for (i=0;i<j;i++)

        H[ldh*j+i] = H[ldh*j+i]/norm;

      H[ldh*j+j] = H[ldh*j+j]/dot;      

      ierr = VecScale(f,1.0/norm);CHKERRQ(ierr);

    }

    ierr = SlepcVecMAXPBY(f,1.0,-1.0,j+1,H+ldh*j,V);CHKERRQ(ierr);

    if (j<m-1) {

      ierr = VecCopy(f,V[j+1]);CHKERRQ(ierr);

    }

  }

  ierr = IPNorm(eps->ip,f,beta);CHKERRQ(ierr);

  ierr = VecScale(f,1.0 / *beta);CHKERRQ(ierr);

  *breakdown = PETSC_FALSE;

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSProjectedArnoldi"

/*

   EPSProjectedArnoldi - Solves the projected eigenproblem.

   On input:

     S is the projected matrix (leading dimension is lds)

   On output:

     S has (real) Schur form with diagonal blocks sorted appropriately

     Q contains the corresponding Schur vectors (order n, leading dimension n)

*/

PetscErrorCode EPSProjectedArnoldi(EPS eps,PetscScalar *S,PetscInt lds,PetscScalar *Q,PetscInt n)

{

  PetscErrorCode ierr;

  PetscInt       i;

  PetscFunctionBegin;

  /* Initialize orthogonal matrix */

  ierr = PetscMemzero(Q,n*n*sizeof(PetscScalar));CHKERRQ(ierr);

  for (i=0;i<n;i++)

    Q[i*(n+1)] = 1.0;

  /* Reduce S to (quasi-)triangular form, S <- Q S Q' */

  ierr = EPSDenseSchur(n,eps->nconv,S,lds,Q,eps->eigr,eps->eigi);CHKERRQ(ierr);

  /* Sort the remaining columns of the Schur form */

  ierr = EPSSortDenseSchur(eps,n,eps->nconv,S,lds,Q,eps->eigr,eps->eigi);CHKERRQ(ierr);    

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSUpdateVectors"

/*

   EPSUpdateVectors - Computes approximate Schur vectors (or eigenvectors) by

   either Ritz extraction (U=U*Q) or refined Ritz extraction

   On input:

     n is the size of U

     U is the orthogonal basis of the subspace used for projecting

     s is the index of the first vector computed

     e+1 is the index of the last vector computed

     Q contains the corresponding Schur vectors of the projected matrix (size n x n, leading dimension ldq)

     H is the (extended) projected matrix (size n+1 x n, leading dimension ldh)

   On output:

     v is the resulting vector

*/

PetscErrorCode EPSUpdateVectors(EPS eps,PetscInt n_,Vec *U,PetscInt s,PetscInt e,PetscScalar *Q,PetscInt ldq,PetscScalar *H,PetscInt ldh_)

{

#if defined(PETSC_MISSING_LAPACK_GESVD) 

  SETERRQ(((PetscObject)eps)->comm,PETSC_ERR_SUP,"GESVD - Lapack routine is unavailable.");

#else

  PetscErrorCode ierr;

  PetscBool      isrefined;

  PetscInt       i,j,k;

  PetscBLASInt   n1,lwork,idummy=1,info,n=n_,ldh=ldh_;

  PetscScalar    *B,sdummy,*work;

  PetscReal      *sigma;

  PetscFunctionBegin;

  isrefined = (eps->extraction==EPS_REFINED || eps->extraction==EPS_REFINED_HARMONIC)?PETSC_TRUE:PETSC_FALSE;

  if (isrefined) {

    /* Refined Ritz extraction */

    n1 = n+1;

    ierr = PetscMalloc(n1*n*sizeof(PetscScalar),&B);CHKERRQ(ierr);

    ierr = PetscMalloc(6*n*sizeof(PetscReal),&sigma);CHKERRQ(ierr);

    lwork = 10*n;

    ierr = PetscMalloc(lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);

    for (k=s;k<e;k++) {

      /* copy H to B */

      for (i=0;i<=n;i++) {

        for (j=0;j<n;j++) {

          B[i+j*n1] = H[i+j*ldh];

        }

      }

      /* subtract ritz value from diagonal of B^ */

      for (i=0;i<n;i++) {

        B[i+i*n1] -= eps->eigr[k];  /* MISSING: complex case */

      }

      /* compute SVD of [H-mu*I] */

  #if !defined(PETSC_USE_COMPLEX)

      LAPACKgesvd_("N","O",&n1,&n,B,&n1,sigma,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,&info);

  #else

      LAPACKgesvd_("N","O",&n1,&n,B,&n1,sigma,&sdummy,&idummy,&sdummy,&idummy,work,&lwork,sigma+n,&info);

  #endif

      if (info) SETERRQ1(((PetscObject)eps)->comm,PETSC_ERR_LIB,"Error in Lapack xGESVD %d",info);

      /* the smallest singular value is the new error estimate */

      eps->errest[k] = sigma[n-1];

      /* update vector with right singular vector associated to smallest singular value */

      for (i=0;i<n;i++)

        Q[k*ldq+i] = B[n-1+i*n1];

    }

    /* free workspace */

    ierr = PetscFree(B);CHKERRQ(ierr);

    ierr = PetscFree(sigma);CHKERRQ(ierr);

    ierr = PetscFree(work);CHKERRQ(ierr);

  }

  /* Ritz extraction: v = U*q */

  ierr = SlepcUpdateVectors(n_,U,s,e,Q,ldq,PETSC_FALSE);CHKERRQ(ierr);

  PetscFunctionReturn(0);

#endif

}

#undef __FUNCT__  

#define __FUNCT__ "EPSSolve_Arnoldi"

PetscErrorCode EPSSolve_Arnoldi(EPS eps)

{

  PetscErrorCode     ierr;

  PetscInt           i,k,lwork,nv;

  Vec                f=eps->work[0];

  PetscScalar        *H=eps->T,*U,*g,*work,*Hcopy;

  PetscReal          beta,gnorm,corrf=1.0;

  PetscBool          breakdown;

  IPOrthogRefineType orthog_ref;

  EPS_ARNOLDI        *arnoldi = (EPS_ARNOLDI *)eps->data;

  PetscFunctionBegin;

  ierr = PetscMemzero(eps->T,eps->ncv*eps->ncv*sizeof(PetscScalar));CHKERRQ(ierr);

  ierr = PetscMalloc(eps->ncv*eps->ncv*sizeof(PetscScalar),&U);CHKERRQ(ierr);

  lwork = PetscMax((eps->ncv+1)*eps->ncv,7*eps->ncv);

  ierr = PetscMalloc(lwork*sizeof(PetscScalar),&work);CHKERRQ(ierr);

  if (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC) {

    ierr = PetscMalloc(eps->ncv*sizeof(PetscScalar),&g);CHKERRQ(ierr);

  }

  if (eps->extraction==EPS_REFINED || eps->extraction==EPS_REFINED_HARMONIC) {

    ierr = PetscMalloc((eps->ncv+1)*eps->ncv*sizeof(PetscScalar),&Hcopy);CHKERRQ(ierr);

  }

  ierr = IPGetOrthogonalization(eps->ip,PETSC_NULL,&orthog_ref,PETSC_NULL);CHKERRQ(ierr);

  /* Get the starting Arnoldi vector */

  ierr = EPSGetStartVector(eps,0,eps->V[0],PETSC_NULL);CHKERRQ(ierr);

  /* Restart loop */

  while (eps->reason == EPS_CONVERGED_ITERATING) {

    eps->its++;

    /* Compute an nv-step Arnoldi factorization */

    nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);

    if (!arnoldi->delayed) {

      ierr = EPSBasicArnoldi(eps,PETSC_FALSE,H,eps->ncv,eps->V,eps->nconv,&nv,f,&beta,&breakdown);CHKERRQ(ierr);

    } else if (orthog_ref == IP_ORTHOG_REFINE_NEVER) {

      ierr = EPSDelayedArnoldi1(eps,H,eps->ncv,eps->V,eps->nconv,&nv,f,&beta,&breakdown);CHKERRQ(ierr);

    } else {

      ierr = EPSDelayedArnoldi(eps,H,eps->ncv,eps->V,eps->nconv,&nv,f,&beta,&breakdown);CHKERRQ(ierr);

    }

    if (eps->extraction==EPS_REFINED || eps->extraction==EPS_REFINED_HARMONIC) {

      ierr = PetscMemcpy(Hcopy,H,eps->ncv*eps->ncv*sizeof(PetscScalar));CHKERRQ(ierr);

      for (i=0;i<nv-1;i++) Hcopy[nv+i*eps->ncv] = 0.0;

      Hcopy[nv+(nv-1)*eps->ncv] = beta;

    }

    /* Compute translation of Krylov decomposition if harmonic extraction used */

    if (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC) {

      ierr = EPSTranslateHarmonic(nv,H,eps->ncv,eps->target,(PetscScalar)beta,g,work);CHKERRQ(ierr);

      gnorm = 0.0;

      for (i=0;i<nv;i++)

        gnorm = gnorm + PetscRealPart(g[i]*PetscConj(g[i]));

      corrf = PetscSqrtReal(1.0+gnorm);

    }

    /* Solve projected problem */

    ierr = EPSProjectedArnoldi(eps,H,eps->ncv,U,nv);CHKERRQ(ierr);

    /* Check convergence */

    ierr = EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,H,eps->ncv,U,eps->V,nv,beta,corrf,&k,work);CHKERRQ(ierr);

    ierr = EPSUpdateVectors(eps,nv,eps->V,eps->nconv,PetscMin(k+1,nv),U,nv,Hcopy,eps->ncv);CHKERRQ(ierr);

    eps->nconv = k;

    ierr = EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);CHKERRQ(ierr);

    if (breakdown) {

      ierr = PetscInfo2(eps,"Breakdown in Arnoldi method (it=%D norm=%G)\n",eps->its,beta);CHKERRQ(ierr);

      ierr = EPSGetStartVector(eps,k,eps->V[k],&breakdown);CHKERRQ(ierr);

      if (breakdown) {

        eps->reason = EPS_DIVERGED_BREAKDOWN;

        ierr = PetscInfo(eps,"Unable to generate more start vectors\n");CHKERRQ(ierr);

      }

    }

    if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;

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

  }

  ierr = PetscFree(U);CHKERRQ(ierr);

  ierr = PetscFree(work);CHKERRQ(ierr);

  if (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC) {

    ierr = PetscFree(g);CHKERRQ(ierr);

  }

  if (eps->extraction==EPS_REFINED || eps->extraction==EPS_REFINED_HARMONIC) {

    ierr = PetscFree(Hcopy);CHKERRQ(ierr);

  }

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSSetFromOptions_Arnoldi"

PetscErrorCode EPSSetFromOptions_Arnoldi(EPS eps)

{

  PetscErrorCode ierr;

  PetscBool      set,val;

  EPS_ARNOLDI    *arnoldi = (EPS_ARNOLDI *)eps->data;

  PetscFunctionBegin;

  ierr = PetscOptionsHead("EPS Arnoldi Options");CHKERRQ(ierr);

  ierr = PetscOptionsBool("-eps_arnoldi_delayed","Arnoldi with delayed reorthogonalization","EPSArnoldiSetDelayed",arnoldi->delayed,&val,&set);CHKERRQ(ierr);

  if (set) {

    ierr = EPSArnoldiSetDelayed(eps,val);CHKERRQ(ierr);

  }

  ierr = PetscOptionsTail();CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "EPSArnoldiSetDelayed_Arnoldi"

PetscErrorCode EPSArnoldiSetDelayed_Arnoldi(EPS eps,PetscBool delayed)

{

  EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI *)eps->data;

  PetscFunctionBegin;

  arnoldi->delayed = delayed;

  PetscFunctionReturn(0);

}

EXTERN_C_END

#undef __FUNCT__  

#define __FUNCT__ "EPSArnoldiSetDelayed"

/*@

   EPSArnoldiSetDelayed - Activates or deactivates delayed reorthogonalization

   in the Arnoldi iteration.

   Logically Collective on EPS

   Input Parameters:

+  eps - the eigenproblem solver context

-  delayed - boolean flag

   Options Database Key:

.  -eps_arnoldi_delayed - Activates delayed reorthogonalization in Arnoldi

   Note:

   Delayed reorthogonalization is an aggressive optimization for the Arnoldi

   eigensolver than may provide better scalability, but sometimes makes the

   solver converge less than the default algorithm.

   Level: advanced

.seealso: EPSArnoldiGetDelayed()

@*/

PetscErrorCode EPSArnoldiSetDelayed(EPS eps,PetscBool delayed)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  PetscValidLogicalCollectiveBool(eps,delayed,2);

  ierr = PetscTryMethod(eps,"EPSArnoldiSetDelayed_C",(EPS,PetscBool),(eps,delayed));CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "EPSArnoldiGetDelayed_Arnoldi"

PetscErrorCode EPSArnoldiGetDelayed_Arnoldi(EPS eps,PetscBool *delayed)

{

  EPS_ARNOLDI *arnoldi = (EPS_ARNOLDI *)eps->data;

  PetscFunctionBegin;

  *delayed = arnoldi->delayed;

  PetscFunctionReturn(0);

}

EXTERN_C_END

#undef __FUNCT__  

#define __FUNCT__ "EPSArnoldiGetDelayed"

/*@C

   EPSArnoldiGetDelayed - Gets the type of reorthogonalization used during the Arnoldi

   iteration.

   Not Collective

   Input Parameter:

.  eps - the eigenproblem solver context

   Input Parameter:

.  delayed - boolean flag indicating if delayed reorthogonalization has been enabled

   Level: advanced

.seealso: EPSArnoldiSetDelayed()

@*/

PetscErrorCode EPSArnoldiGetDelayed(EPS eps,PetscBool *delayed)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  PetscValidHeaderSpecific(eps,EPS_CLASSID,1);

  PetscValidPointer(delayed,2);

  ierr = PetscTryMethod(eps,"EPSArnoldiGetDelayed_C",(EPS,PetscBool*),(eps,delayed));CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSReset_Arnoldi"

PetscErrorCode EPSReset_Arnoldi(EPS eps)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  ierr = PetscFree(eps->T);CHKERRQ(ierr);

  ierr = PetscFree(eps->Tl);CHKERRQ(ierr);

  ierr = EPSReset_Default(eps);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSDestroy_Arnoldi"

PetscErrorCode EPSDestroy_Arnoldi(EPS eps)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

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

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)eps,"EPSArnoldiSetDelayed_C","",PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)eps,"EPSArnoldiGetDelayed_C","",PETSC_NULL);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__  

#define __FUNCT__ "EPSView_Arnoldi"

PetscErrorCode EPSView_Arnoldi(EPS eps,PetscViewer viewer)

{

  PetscErrorCode ierr;

  PetscBool      isascii;

  EPS_ARNOLDI    *arnoldi = (EPS_ARNOLDI *)eps->data;

  PetscFunctionBegin;

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

  if (!isascii) {

    SETERRQ1(((PetscObject)eps)->comm,1,"Viewer type %s not supported for EPS Arnoldi",((PetscObject)viewer)->type_name);

  }

  if (arnoldi->delayed) {

    ierr = PetscViewerASCIIPrintf(viewer,"  Arnoldi: using delayed reorthogonalization\n");CHKERRQ(ierr);

  }  

  PetscFunctionReturn(0);

}

extern PetscErrorCode EPSSolve_TS_Arnoldi(EPS);

EXTERN_C_BEGIN

#undef __FUNCT__  

#define __FUNCT__ "EPSCreate_Arnoldi"

PetscErrorCode EPSCreate_Arnoldi(EPS eps)

{

  PetscErrorCode ierr;

  PetscFunctionBegin;

  ierr = PetscNewLog(eps,EPS_ARNOLDI,&eps->data);CHKERRQ(ierr);

  eps->ops->setup                = EPSSetUp_Arnoldi;

  eps->ops->setfromoptions       = EPSSetFromOptions_Arnoldi;

  eps->ops->destroy              = EPSDestroy_Arnoldi;

  eps->ops->reset                = EPSReset_Arnoldi;

  eps->ops->view                 = EPSView_Arnoldi;