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/*                      

   SLEPc eigensolver: "krylovschur"

   Method: Krylov-Schur with spectrum slicing for symmetric eigenproblems

   References:

       [1] R.G. Grimes et al., "A shifted block Lanczos algorithm for solving

           sparse symmetric generalized eigenproblems", SIAM J. Matrix Analysis

           and App., 15(1), pp. 228–272, 1994.

       [2] C. Campos and J. E. Roman, "Spectrum slicing strategies based on

           restarted Lanczos methods", Numer. Algor., 2012.

           DOI: 10.1007/s11075-012-9564-z

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

   SLEPc - Scalable Library for Eigenvalue Problem Computations

   Copyright (c) 2002-2011, Universitat 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 <slepc-private/epsimpl.h>                /*I "slepceps.h" I*/

#include <slepcblaslapack.h>

#include <slepc-private/psimpl.h>

/* Type of data characterizing a shift (place from where an eps is applied) */

typedef struct _n_shift *shift;

struct _n_shift{

  PetscReal     value;

  PetscInt      inertia;

  PetscBool     comp[2]; /* Shows completion of subintervals (left and right) */

  shift         neighb[2];/* Adjacent shifts */

  PetscInt      index;/* Index in eig where found values are stored */

  PetscInt      neigs; /* Number of values found */

  PetscReal     ext[2];   /* Limits for accepted values */

  PetscInt      nsch[2];  /* Number of missing values for each subinterval */

  PetscInt      nconv[2]; /* Converged on each side (accepted or not)*/

  PetscBool     expf;

};

/* Type of data  for storing the state of spectrum slicing*/

struct _n_SR{

  PetscReal       int0,int1; /* Extremes of the interval */

  PetscInt        dir; /* Determines the order of values in eig (+1 incr, -1 decr) */

  PetscBool       hasEnd; /* Tells whether the interval has an end */

  PetscInt        inertia0,inertia1;

  Vec             *V;

  PetscScalar     *eig,*eigi,*monit,*back;

  PetscReal       *errest;

  PetscInt        *perm;/* Permutation for keeping the eigenvalues in order */

  PetscInt        numEigs; /* Number of eigenvalues in the interval */

  PetscInt        indexEig;

  shift           sPres; /* Present shift */

  shift           *pending;/* Pending shifts array */

  PetscInt        nPend;/* Number of pending shifts */

  PetscInt        maxPend;/* Size of "pending" array */

  Vec             *VDef; /* Vector for deflation */

  PetscInt        *idxDef;/* For deflation */

  PetscInt        nMAXCompl;

  PetscInt        iterCompl;

  PetscInt        itsKs; /* Krylovschur restarts */

  PetscInt        nleap;

  shift           s0;/* Initial shift */

  PetscScalar     *S;/* Matrix for projected problem */

  PetscInt        nS;

  PetscReal       beta;

  shift           sPrev;

};

typedef struct _n_SR  *SR;

/*

   Fills the fields of a shift structure

*/

#undef __FUNCT__

#define __FUNCT__ "EPSCreateShift"

static PetscErrorCode EPSCreateShift(EPS eps,PetscReal val, shift neighb0,shift neighb1)

{

  PetscErrorCode   ierr;

  shift            s,*pending2;

  PetscInt         i;

  SR               sr;

  PetscFunctionBegin;

  sr = (SR)(eps->data);

  ierr = PetscMalloc(sizeof(struct _n_shift),&s);CHKERRQ(ierr);

  s->value = val;

  s->neighb[0] = neighb0;

  if(neighb0) neighb0->neighb[1] = s;

  s->neighb[1] = neighb1;

  if(neighb1) neighb1->neighb[0] = s;

  s->comp[0] = PETSC_FALSE;

  s->comp[1] = PETSC_FALSE;

  s->index = -1;

  s->neigs = 0;

  s->nconv[0] = s->nconv[1] = 0;

  s->nsch[0] = s->nsch[1]=0;

  /* Inserts in the stack of pending shifts */

  /* If needed, the array is resized */

  if(sr->nPend >= sr->maxPend){

    sr->maxPend *= 2;

    ierr = PetscMalloc((sr->maxPend)*sizeof(shift),&pending2);CHKERRQ(ierr);

    for(i=0;i < sr->nPend; i++)pending2[i] = sr->pending[i];

    ierr = PetscFree(sr->pending);CHKERRQ(ierr);

    sr->pending = pending2;

  }

  sr->pending[sr->nPend++]=s;

  PetscFunctionReturn(0);

}

/* Provides next shift to be computed */

#undef __FUNCT__

#define __FUNCT__ "EPSExtractShift"

static PetscErrorCode EPSExtractShift(EPS eps){

  PetscErrorCode   ierr;

  PetscInt         iner,dir,i,k,ld;

  PetscScalar      *A;

  Mat              F;

  PC               pc;

  KSP              ksp;

  SR               sr;

  PetscFunctionBegin;  

  sr = (SR)(eps->data);

  if(sr->nPend > 0){

    sr->sPrev = sr->sPres;

    sr->sPres = sr->pending[--sr->nPend];

    ierr = STSetShift(eps->OP, sr->sPres->value);CHKERRQ(ierr);

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

    ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);

    ierr = PCFactorGetMatrix(pc,&F);CHKERRQ(ierr);

    ierr = MatGetInertia(F,&iner,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

    sr->sPres->inertia = iner;

    eps->target = sr->sPres->value;

    eps->reason = EPS_CONVERGED_ITERATING;

    eps->its = 0;

    sr->sPres->expf = PETSC_FALSE;

    /* For rational Krylov */

    if(sr->nS >0 && (sr->sPrev == sr->sPres->neighb[0] || sr->sPrev == sr->sPres->neighb[1]) ){

      ierr = PSGetLeadingDimension(eps->ps,&ld);CHKERRQ(ierr);

      dir = (sr->sPres->neighb[0] == sr->sPrev)?1:-1;

      dir*=sr->dir;

      k = 0;

      for(i=0;i<sr->nS;i++){

        if(dir*PetscRealPart(sr->S[i])>0.0){

          sr->S[k] = sr->S[i];

          sr->S[sr->nS+k] = sr->S[sr->nS+i];

          ierr = VecCopy(eps->V[eps->nconv+i],eps->V[k++]);CHKERRQ(ierr);

          if(k>=sr->nS/2)break;

        }

      }

      /* Copy to PS */

      ierr = PSGetArray(eps->ps,PS_MAT_A,&A);CHKERRQ(ierr);

      ierr = PetscMemzero(A,ld*ld*sizeof(PetscScalar));

      for(i=0;i<k;i++){

        A[i*(1+ld)] = sr->S[i];

        A[k+i*ld] = sr->S[sr->nS+i];

      }

      sr->nS = k;

      ierr = PSRestoreArray(eps->ps,PS_MAT_A,&A);CHKERRQ(ierr);

      ierr = PSSetDimensions(eps->ps,ld,0,k);CHKERRQ(ierr);

      /* Normalize u and append it to V */      

      ierr = VecAXPBY(eps->V[sr->nS],1.0/sr->beta,0.0,eps->work[0]);CHKERRQ(ierr);

    }

    eps->nconv = 0;

  }else sr->sPres = PETSC_NULL;

  PetscFunctionReturn(0);

}

/*

   Symmetric KrylovSchur adapted to spectrum slicing:

   Allows searching an specific amount of eigenvalues in the subintervals left and right.

   Returns whether the search has succeeded

*/

#undef __FUNCT__

#define __FUNCT__ "EPSKrylovSchur_Slice"

static PetscErrorCode EPSKrylovSchur_Slice(EPS eps)

{

  PetscErrorCode ierr;

  PetscInt       i,conv,k,l,ld,nv,*iwork,p,j;

  Vec            u=eps->work[0];

  PetscScalar    *Q,*A,nu,rtmp,alpha;

  PetscReal      *a,*b,beta;

  PetscBool      breakdown;

  PetscInt       count0,count1;

  PetscReal      lambda;

  shift          sPres;

  PetscBool      complIterating,iscayley;

  PetscBool      sch0,sch1;

  PetscInt       iterCompl=0,n0,n1,aux,auxc;

  SR             sr;

  PetscFunctionBegin;

  /* Spectrum slicing data */

  sr = (SR)eps->data;

  sPres = sr->sPres;

  complIterating =PETSC_FALSE;

  sch1 = sch0 = PETSC_TRUE;

  ierr = PSGetLeadingDimension(eps->ps,&ld);CHKERRQ(ierr);

  ierr = PetscMalloc(2*ld*sizeof(PetscInt),&iwork);CHKERRQ(ierr);

  count0=0;count1=0; /* Found on both sides */

  /* filling in values for the monitor */

  if(eps->numbermonitors >0){

    ierr = PetscTypeCompare((PetscObject)eps->OP,STCAYLEY,&iscayley);CHKERRQ(ierr);

    if(iscayley){

      ierr = STCayleyGetAntishift(eps->OP,&nu);CHKERRQ(ierr);    

      for(i=0;i<sr->indexEig;i++){

        sr->monit[i]=(nu + sr->eig[i])/(sr->eig[i] - sPres->value);

      }

    }else{

      for(i=0;i<sr->indexEig;i++){

        sr->monit[i]=1.0/(sr->eig[i] - sPres->value);

      }

    }

  }

  if(sr->nS > 0 && (sPres->neighb[0] == sr->sPrev || sPres->neighb[1] == sr->sPrev) ){

    /* Rational Krylov */

    ierr = PSTranslateRKS(eps->ps,sr->sPrev->value-sPres->value);CHKERRQ(ierr);

    ierr = PSGetArray(eps->ps,PS_MAT_Q,&Q);CHKERRQ(ierr);

    ierr = PSGetDimensions(eps->ps,PETSC_NULL,PETSC_NULL,&l);CHKERRQ(ierr);

    ierr = SlepcUpdateVectors(l+1,eps->V,0,l+1,Q,ld,PETSC_FALSE);CHKERRQ(ierr);

    ierr = PSRestoreArray(eps->ps,PS_MAT_Q,&Q);CHKERRQ(ierr);

  }else{

    /* Get the starting Lanczos vector */

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

    l = 0;

  }

  /* Restart loop */

  while (eps->reason == EPS_CONVERGED_ITERATING) {

    eps->its++; sr->itsKs++;

    /* Compute an nv-step Lanczos factorization */

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

    ierr = PSGetArrayReal(eps->ps,PS_MAT_T,&a);CHKERRQ(ierr);

    b = a + ld;

    ierr = EPSFullLanczos(eps,a,b,eps->V,eps->nconv+l,&nv,u,&breakdown);CHKERRQ(ierr);

    if(breakdown){/* explicit purification*/

      sPres->expf = PETSC_TRUE;    

    }

    beta = b[nv-1];

    ierr = PSRestoreArrayReal(eps->ps,PS_MAT_T,&a);CHKERRQ(ierr);

    ierr = PSSetDimensions(eps->ps,nv,eps->nconv,eps->nconv+l);CHKERRQ(ierr);

    if (l==0) {

      ierr = PSSetState(eps->ps,PS_STATE_INTERMEDIATE);CHKERRQ(ierr);

    } else {

      ierr = PSSetState(eps->ps,PS_STATE_RAW);CHKERRQ(ierr);

    }

    /* Solve projected problem and compute residual norm estimates */

    if(eps->its == 1 && l > 0){/* After rational update */

      ierr = PSGetArray(eps->ps,PS_MAT_A,&A);CHKERRQ(ierr);

      ierr = PSGetArrayReal(eps->ps,PS_MAT_T,&a);CHKERRQ(ierr);

      b = a + ld;

      k = eps->nconv+l;

      A[k*ld+k-1] = A[(k-1)*ld+k];

      A[k*ld+k] = a[k];

      for(j=k+1; j< nv; j++){

        A[j*ld+j] = a[j];

        A[j*ld+j-1] = b[j-1] ;

        A[(j-1)*ld+j] = b[j-1];

      }

      ierr = PSRestoreArray(eps->ps,PS_MAT_A,&A);CHKERRQ(ierr);

      ierr = PSRestoreArrayReal(eps->ps,PS_MAT_T,&a);CHKERRQ(ierr);

      ierr = PSSolve(eps->ps,eps->eigr,PETSC_NULL);CHKERRQ(ierr);

      ierr = PSSetCompact(eps->ps,PETSC_TRUE);

    }else{/* Restart */

      ierr = PSSolve(eps->ps,eps->eigr,PETSC_NULL);CHKERRQ(ierr);

    }

    ierr = PSSort(eps->ps,eps->eigr,PETSC_NULL,eps->which_func,eps->which_ctx);CHKERRQ(ierr);

    /* Residual */

    ierr = EPSKrylovConvergence(eps,PETSC_TRUE,eps->nconv,nv-eps->nconv,eps->V,nv,beta,1.0,&k);CHKERRQ(ierr);

    /* Check convergence */

    ierr = PSGetArrayReal(eps->ps,PS_MAT_T,&a);CHKERRQ(ierr);

    b = a + ld;

    conv = 0;

    j = k = eps->nconv;

    for(i=eps->nconv;i<nv;i++)if(eps->errest[i] < eps->tol)conv++;

    for(i=eps->nconv;i<nv;i++){

      if(eps->errest[i] < eps->tol){

        iwork[j++]=i;

      }else iwork[conv+k++]=i;

    }

    for(i=eps->nconv;i<nv;i++){

      a[i]=PetscRealPart(eps->eigr[i]);

      b[i]=eps->errest[i];

    }

    for(i=eps->nconv;i<nv;i++){

      eps->eigr[i] = a[iwork[i]];

      eps->errest[i] = b[iwork[i]];

    }

    for(i=eps->nconv;i<nv;i++){

      a[i]=PetscRealPart(eps->eigr[i]);

      b[i]=eps->errest[i];

    }

    k=eps->nconv+conv;

    ierr = PSPermuteColumns_Private(eps->ps,eps->nconv,nv,PS_MAT_Q,iwork);CHKERRQ(ierr);

    ierr = PSRestoreArrayReal(eps->ps,PS_MAT_T,&a);CHKERRQ(ierr);

    /* Checking values obtained for completing */

    for(i=0;i<k;i++){

      sr->back[i]=eps->eigr[i];

    }

    ierr = STBackTransform(eps->OP,k,sr->back,eps->eigi);CHKERRQ(ierr);

    count0=count1=0;

    for(i=0;i<k;i++){

      lambda = PetscRealPart(sr->back[i]);

      if( ((sr->dir)*(sPres->value - lambda) > 0) && ((sr->dir)*(lambda - sPres->ext[0]) > 0))count0++;

      if( ((sr->dir)*(lambda - sPres->value) > 0) && ((sr->dir)*(sPres->ext[1] - lambda) > 0))count1++;

    }

    /* Checks completion */

    if( (!sch0||count0 >= sPres->nsch[0]) && (!sch1 ||count1 >= sPres->nsch[1]) ) {

      eps->reason = EPS_CONVERGED_TOL;

    }else {

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

      if(complIterating){

        if(--iterCompl <= 0) eps->reason = EPS_DIVERGED_ITS;

      }else if (k >= eps->nev) {

        n0 = sPres->nsch[0]-count0;

        n1 = sPres->nsch[1]-count1;

        if( sr->iterCompl>0 && ( (n0>0 && n0<= sr->nMAXCompl)||(n1>0&&n1<=sr->nMAXCompl) )){

          /* Iterating for completion*/

          complIterating = PETSC_TRUE;

          if(n0 >sr->nMAXCompl)sch0 = PETSC_FALSE;

          if(n1 >sr->nMAXCompl)sch1 = PETSC_FALSE;

          iterCompl = sr->iterCompl;

        }else eps->reason = EPS_CONVERGED_TOL;

      }      

    }

    /* Update l */

    if(eps->reason == EPS_CONVERGED_ITERATING )l = (nv-k)/2;

    else l=nv-k;

    if(breakdown)l=0;

    if (eps->reason == EPS_CONVERGED_ITERATING) {

      if (breakdown) {

        /* Start a new Lanczos factorization */

        ierr = PetscInfo2(eps,"Breakdown in Krylov-Schur 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);

        }

      } else {

        /* Prepare the Rayleigh quotient for restart */

        ierr = PSGetArrayReal(eps->ps,PS_MAT_T,&a);CHKERRQ(ierr);

        ierr = PSGetArray(eps->ps,PS_MAT_Q,&Q);CHKERRQ(ierr);

        b = a + ld;

        for (i=k;i<k+l;i++) {

          a[i] = PetscRealPart(eps->eigr[i]);

          b[i] = PetscRealPart(Q[nv-1+i*ld]*beta);

        }

        ierr = PSRestoreArrayReal(eps->ps,PS_MAT_T,&a);CHKERRQ(ierr);

        ierr = PSRestoreArray(eps->ps,PS_MAT_Q,&Q);CHKERRQ(ierr);

      }

    }

    /* Update the corresponding vectors V(:,idx) = V*Q(:,idx) */

    ierr = PSGetArray(eps->ps,PS_MAT_Q,&Q);CHKERRQ(ierr);

    ierr = SlepcUpdateVectors(nv,eps->V,eps->nconv,k+l,Q,ld,PETSC_FALSE);CHKERRQ(ierr);

    /* Purification */

    if(!sPres->expf){/* u not saved if breakdown */

      for(i=eps->nconv; i<k;i++){

        alpha = (Q[nv-1+i*ld])/PetscRealPart(eps->eigr[i]);

        ierr = VecAXPY(eps->V[i], alpha, u);CHKERRQ(ierr);

      }

    }

    ierr = PSRestoreArray(eps->ps,PS_MAT_Q,&Q);CHKERRQ(ierr);

    /* Normalize u and append it to V */

    if ( eps->reason == EPS_CONVERGED_ITERATING && !breakdown) {

      ierr = VecAXPBY(eps->V[k+l],1.0/beta,0.0,u);CHKERRQ(ierr);

    }

    /* Monitor */

    if(eps->numbermonitors >0){

      aux = auxc = 0;

      for(i=0;i<nv;i++){

        sr->back[i]=eps->eigr[i];

      }

      ierr = STBackTransform(eps->OP,nv,sr->back,eps->eigi);CHKERRQ(ierr);

      for(i=0;i<nv;i++){

        lambda = PetscRealPart(sr->back[i]);

        if( ((sr->dir)*(lambda - sPres->ext[0]) > 0)&& ((sr->dir)*(sPres->ext[1] - lambda) > 0)){

          sr->monit[sr->indexEig+aux]=eps->eigr[i];

          sr->errest[sr->indexEig+aux]=eps->errest[i];

          aux++;

          if(eps->errest[i] < eps->tol)auxc++;

        }

      }

      ierr = EPSMonitor(eps,eps->its,auxc+sr->indexEig,sr->monit,sr->eigi,sr->errest,sr->indexEig+aux);CHKERRQ(ierr);

    }

    eps->nconv = k;

    if(eps->reason != EPS_CONVERGED_ITERATING){

      /* Store approximated values for next shift */

      ierr = PSGetArray(eps->ps,PS_MAT_Q,&Q);CHKERRQ(ierr);

      sr->nS = l;

      for (i=0;i<l;i++) {

        sr->S[i] = eps->eigr[i+k];/* Diagonal elements */

        sr->S[i+l] = Q[nv-1+(i+k)*ld]*beta; /* Out of diagonal elements */

      }

      sr->beta = beta;

      ierr = PSRestoreArray(eps->ps,PS_MAT_Q,&Q);CHKERRQ(ierr);

    }

  }

  /* Check for completion */

  for(i=0;i< eps->nconv; i++){

    if( (sr->dir)*PetscRealPart(eps->eigr[i])>0 )sPres->nconv[1]++;

    else sPres->nconv[0]++;

  }

  sPres->comp[0] = (count0 >= sPres->nsch[0])?PETSC_TRUE:PETSC_FALSE;

  sPres->comp[1] = (count1 >= sPres->nsch[1])?PETSC_TRUE:PETSC_FALSE;

  if(count0 > sPres->nsch[0] || count1 > sPres->nsch[1])SETERRQ(((PetscObject)eps)->comm,1,"Unexpected error in Spectrum Slicing!\nMismatch between number of values found and information from inertia");

  ierr = PetscFree(iwork);CHKERRQ(ierr);  

  PetscFunctionReturn(0);

}

/*

  Obtains value of subsequent shift

*/

#undef __FUNCT__

#define __FUNCT__ "EPSGetNewShiftValue"

static PetscErrorCode EPSGetNewShiftValue(EPS eps,PetscInt side,PetscReal *newS)

{

  PetscReal   lambda,d_prev;

  PetscInt    i,idxP;

  SR          sr;

  shift       sPres,s;

  PetscFunctionBegin;  

  sr = (SR)eps->data;

  sPres = sr->sPres;

  if( sPres->neighb[side]){

  /* Completing a previous interval */

    if(!sPres->neighb[side]->neighb[side] && sPres->neighb[side]->nconv[side]==0){ /* One of the ends might be too far from eigenvalues */

      if(side) *newS = (sPres->value + PetscRealPart(sr->eig[sr->perm[sr->indexEig-1]]))/2;

      else *newS = (sPres->value + PetscRealPart(sr->eig[sr->perm[0]]))/2;

    }else *newS=(sPres->value + sPres->neighb[side]->value)/2;

  }else{ /* (Only for side=1). Creating a new interval. */

    if(sPres->neigs==0){/* No value has been accepted*/

      if(sPres->neighb[0]){

        /* Multiplying by 10 the previous distance */

        *newS = sPres->value + 10*(sr->dir)*PetscAbsReal(sPres->value - sPres->neighb[0]->value);

        sr->nleap++;

        /* Stops when the interval is open and no values are found in the last 5 shifts (there might be infinite eigenvalues) */

        if( !sr->hasEnd && sr->nleap > 5)SETERRQ(((PetscObject)eps)->comm,1,"Unable to compute the wanted eigenvalues with open interval");          

      }else {/* First shift */

        if(eps->nconv != 0){

           /* Unaccepted values give information for next shift */

           idxP=0;/* Number of values left from shift */

           for(i=0;i<eps->nconv;i++){

             lambda = PetscRealPart(eps->eigr[i]);

             if( (sr->dir)*(lambda - sPres->value) <0)idxP++;

             else break;

           }

           /* Avoiding subtraction of eigenvalues (might be the same).*/

           if(idxP>0){

             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[0]))/(idxP+0.3);

           }else {

             d_prev = PetscAbsReal(sPres->value - PetscRealPart(eps->eigr[eps->nconv-1]))/(eps->nconv+0.3);

           }

           *newS = sPres->value + ((sr->dir)*d_prev*eps->nev)/2;

        }else{/* No values found, no information for next shift */

          SETERRQ(((PetscObject)eps)->comm,1,"First shift renders no information");

        }

      }

    }else{/* Accepted values found */

      sr->nleap = 0;

      /* Average distance of values in previous subinterval */

      s = sPres->neighb[0];

      while(s && PetscAbs(s->inertia - sPres->inertia)==0){

        s = s->neighb[0];/* Looking for previous shifts with eigenvalues within */

      }

      if(s){

        d_prev = PetscAbsReal( (sPres->value - s->value)/(sPres->inertia - s->inertia));

      }else{/* First shift. Average distance obtained with values in this shift */

        /* first shift might be too far from first wanted eigenvalue (no values found outside the interval)*/

        if( (sr->dir)*(PetscRealPart(sr->eig[0])-sPres->value)>0 && PetscAbsReal( (PetscRealPart(sr->eig[sr->indexEig-1]) - PetscRealPart(sr->eig[0]))/PetscRealPart(sr->eig[0])) > PetscSqrtReal(eps->tol) ){

          d_prev =  PetscAbsReal( (PetscRealPart(sr->eig[sr->indexEig-1]) - PetscRealPart(sr->eig[0])))/(sPres->neigs+0.3);

        }else{

          d_prev = PetscAbsReal( PetscRealPart(sr->eig[sr->indexEig-1]) - sPres->value)/(sPres->neigs+0.3);          

        }

      }

      /* Average distance is used for next shift by adding it to value on the right or to shift */

      if( (sr->dir)*(PetscRealPart(sr->eig[sPres->index + sPres->neigs -1]) - sPres->value) >0){

        *newS = PetscRealPart(sr->eig[sPres->index + sPres->neigs -1])+ ((sr->dir)*d_prev*(eps->nev))/2;  

      }else{/* Last accepted value is on the left of shift. Adding to shift */

        *newS = sPres->value + ((sr->dir)*d_prev*(eps->nev))/2;

      }

    }

    /* End of interval can not be surpassed */

    if((sr->dir)*( sr->int1 - *newS) < 0) *newS = sr->int1;

  }/* of neighb[side]==null */

  PetscFunctionReturn(0);

}

/*

  Function for sorting an array of real values

*/

#undef __FUNCT__

#define __FUNCT__ "sortRealEigenvalues"

static PetscErrorCode sortRealEigenvalues(PetscScalar *r,PetscInt *perm,PetscInt nr,PetscBool prev,PetscInt dir)

{

  PetscReal      re;

  PetscInt       i,j,tmp;

  PetscFunctionBegin;

  if(!prev) for (i=0; i < nr; i++) { perm[i] = i; }

  /* Insertion sort */

  for (i=1; i < nr; i++) {

    re = PetscRealPart(r[perm[i]]);

    j = i-1;

    while ( j>=0 && dir*(re - PetscRealPart(r[perm[j]])) <= 0 ) {

      tmp = perm[j]; perm[j] = perm[j+1]; perm[j+1] = tmp; j--;

    }

  }

  PetscFunctionReturn(0);

}

/* Stores the pairs obtained since the last shift in the global arrays */

#undef __FUNCT__

#define __FUNCT__ "EPSStoreEigenpairs"

PetscErrorCode EPSStoreEigenpairs(EPS eps)

{

  PetscErrorCode ierr;

  PetscReal      lambda,err,norm;

  PetscInt       i,count;

  PetscBool      iscayley;

  SR             sr;

  shift          sPres;

  PetscFunctionBegin;

  sr = (SR)(eps->data);

  sPres = sr->sPres;

  sPres->index = sr->indexEig;

  count = sr->indexEig;

  /* Back-transform */

  ierr = EPSBackTransform_Default(eps);CHKERRQ(ierr);

  ierr = PetscTypeCompare((PetscObject)eps->OP,STCAYLEY,&iscayley);CHKERRQ(ierr);

  /* Sort eigenvalues */

  ierr = sortRealEigenvalues(eps->eigr,eps->perm,eps->nconv,PETSC_FALSE,sr->dir);

  /* Values stored in global array */

  for( i=0; i < eps->nconv ;i++ ){

    lambda = PetscRealPart(eps->eigr[eps->perm[i]]);

    err = eps->errest[eps->perm[i]];

    if(  (sr->dir)*(lambda - sPres->ext[0]) > 0 && (sr->dir)*(sPres->ext[1] - lambda) > 0  ){/* Valid value */

      if(count>=sr->numEigs){/* Error found */

         SETERRQ(((PetscObject)eps)->comm,1,"Unexpected error in Spectrum Slicing!");

      }

      sr->eig[count] = lambda;

      sr->errest[count] = err;