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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] G.W. Stewart, "A Krylov-Schur Algorithm for Large Eigenproblems",

           SIAM J. Matrix Analysis and App., 23(3), pp. 601-614, 2001.

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

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

#include <slepcblaslapack.h>

extern PetscErrorCode EPSProjectedKSSym(EPS,PetscInt,PetscInt,PetscReal*,PetscReal*,PetscScalar*,PetscScalar*,PetscReal*,PetscInt*);

/* 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)*/

};

/* 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;

  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 */

};

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;

  Mat              F;

  PC               pc;

  KSP              ksp;

  SR               sr;

  PetscFunctionBegin;  

  sr = (SR)(eps->data);

  if(sr->nPend > 0){

    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->nconv = 0;

    eps->reason = EPS_CONVERGED_ITERATING;

    eps->its = 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,lds,lt,nv,m,*iwork,p,j;

  Vec            u=eps->work[0];

  PetscScalar    *Q;

  PetscReal      *a,*b,*work,beta,rtmp;

  PetscBool      breakdown;

  PetscInt       count0,count1;

  PetscReal      theta,lambda;

  shift          sPres;

  PetscBool      complIterating;/* Shows whether iterations are made for completion */

  PetscBool      sch0,sch1;/* Shows whether values are looked after on each side */

  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;

  lds = PetscMin(eps->mpd,eps->ncv);

  ierr = PetscMalloc(lds*lds*sizeof(PetscReal),&work);CHKERRQ(ierr);

  ierr = PetscMalloc(lds*lds*sizeof(PetscScalar),&Q);CHKERRQ(ierr);

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

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

  ierr = PetscMalloc(lt*sizeof(PetscReal),&a);CHKERRQ(ierr);

  ierr = PetscMalloc(lt*sizeof(PetscReal),&b);CHKERRQ(ierr);

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

   /* filling in values for the monitor */

  for(i=0;i<sr->indexEig;i++){

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

    }

  /* 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 */

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

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

    nv = m - eps->nconv;

    beta = b[nv-1];

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

    ierr = EPSProjectedKSSym(eps,nv,l,a,b,eps->eigr+eps->nconv,Q,work,iwork);CHKERRQ(ierr);

    /* Residual */

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

    /* Check convergence */

    conv=k=j=0;

    for(i=0;i<nv;i++)if(eps->errest[eps->nconv+i] < eps->tol)conv++;

    for(i=0;i<nv;i++){

      if(eps->errest[eps->nconv+i] < eps->tol){

        iwork[j++]=i;

      }else iwork[conv+k++]=i;

    }

    for(i=0;i<nv;i++){

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

      b[i]=eps->errest[eps->nconv+i];

    }

    for(i=0;i<nv;i++){

      eps->eigr[eps->nconv+i] = a[iwork[i]];

      eps->errest[eps->nconv+i] = b[iwork[i]];

    }

    for( i=0;i<nv;i++){

      p=iwork[i];

      if(p!=i){

        j=i+1;

        while(iwork[j]!=i)j++;

        iwork[j]=p;iwork[i]=i;

        for(k=0;k<nv;k++){

          rtmp=Q[k+p*nv];Q[k+p*nv]=Q[k+i*nv];Q[k+i*nv]=rtmp;

        }

      }

    }

    k=eps->nconv+conv;

    /* Checking values obtained for completing */

    count0=count1=0;

    for(i=0;i<k;i++){      

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

      lambda = sPres->value + 1/theta;

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

      if( ((sr->dir)*theta > 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 || breakdown) l = 0;

    else l = (eps->nconv+nv-k)/2;

    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 */

        for (i=0;i<l;i++) {

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

          b[i] = PetscRealPart(Q[nv-1+(i+k-eps->nconv)*nv]*beta);

        }

      }

    }

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

    ierr = SlepcUpdateVectors(nv,eps->V+eps->nconv,0,k+l-eps->nconv,Q,nv,PETSC_FALSE);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);

    }

    aux = auxc = 0;

    for(i=0;i<nv+eps->nconv;i++){

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

      lambda = sPres->value + 1/theta;

      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;

  }

  /* 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;

  ierr = PetscFree(Q);CHKERRQ(ierr);

  ierr = PetscFree(a);CHKERRQ(ierr);

  ierr = PetscFree(b);CHKERRQ(ierr);

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

  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;

  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 */

      shift 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      cond;

  SR             sr;

  shift          sPres;

  PetscFunctionBegin;

  sr = (SR)(eps->data);

  sPres = sr->sPres;

  sPres->index = sr->indexEig;

  count = sr->indexEig;

  /* Backtransform */

  for(i=0;i < eps->nconv; i++) eps->eigr[i] =  sPres->value + 1.0/(eps->eigr[i]);

  /* Sort eigenvalues */

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

  /* Values stored in global array */

  /* Condition for avoiding comparing with a non-existing end */

  cond = (!sPres->neighb[1] && !sr->hasEnd)?PETSC_TRUE:PETSC_FALSE;

  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;

      /* Purification */

      if (eps->isgeneralized){

        ierr = STApply(eps->OP,eps->V[eps->perm[i]],sr->V[count]);CHKERRQ(ierr);

        ierr = IPNorm(eps->ip,sr->V[count],&norm);CHKERRQ(ierr);

        ierr = VecScale(sr->V[count],1.0/norm);CHKERRQ(ierr);

      }else{

        ierr = VecCopy(eps->V[eps->perm[i]], sr->V[count]);CHKERRQ(ierr);

      }

      count++;

    }

  }

  sPres->neigs = count - sr->indexEig;

  sr->indexEig = count;

  /* Global ordering array updating */

  ierr = sortRealEigenvalues(sr->eig,sr->perm,count,PETSC_TRUE,sr->dir);CHKERRQ(ierr);

  PetscFunctionReturn(0);

}

#undef __FUNCT__

#define __FUNCT__ "EPSLookForDeflation"

PetscErrorCode EPSLookForDeflation(EPS eps)

{

  PetscReal       val;

  PetscInt        i,count0=0,count1=0;

  shift           sPres;

  PetscInt        ini,fin,k,idx0,idx1;

  SR              sr;

  PetscFunctionBegin;

  sr = (SR)(eps->data);

  sPres = sr->sPres;

  if(sPres->neighb[0]) ini = (sr->dir)*(sPres->neighb[0]->inertia - sr->inertia0);

  else ini = 0;

  fin = sr->indexEig;

  /* Selection of ends for searching new values */

  if(!sPres->neighb[0]) sPres->ext[0] = sr->int0;/* First shift */

  else sPres->ext[0] = sPres->neighb[0]->value;

  if(!sPres->neighb[1]) {

    if(sr->hasEnd) sPres->ext[1] = sr->int1;

    else sPres->ext[1] = (sr->dir > 0)?PETSC_MAX_REAL:PETSC_MIN_REAL;

  }else sPres->ext[1] = sPres->neighb[1]->value;

  /* Selection of values between right and left ends */

  for(i=ini;i<fin;i++){

    val=PetscRealPart(sr->eig[sr->perm[i]]);

    /* Values to the right of left shift */

    if( (sr->dir)*(val - sPres->ext[1]) < 0 ){

      if((sr->dir)*(val - sPres->value) < 0)count0++;

      else count1++;

    }else break;

  }

  /* The number of values on each side are found */

  if(sPres->neighb[0])

     sPres->nsch[0] = (sr->dir)*(sPres->inertia - sPres->neighb[0]->inertia)-count0;

  else sPres->nsch[0] = 0;

  if(sPres->neighb[1])

    sPres->nsch[1] = (sr->dir)*(sPres->neighb[1]->inertia - sPres->inertia) - count1;

  else sPres->nsch[1] = (sr->dir)*(sr->inertia1 - sPres->inertia);

  /* Completing vector of indexes for deflation */

  idx0 = ini;

  idx1 = ini+count0+count1;

  k=0;

  for(i=idx0;i<idx1;i++)sr->idxDef[k++]=sr->perm[i];

  for(i=0;i<k;i++)sr->VDef[i]=sr->V[sr->idxDef[i]];

  eps->DS = sr->VDef;

  eps->nds = k;

  PetscFunctionReturn(0);

}

#undef __FUNCT__

#define __FUNCT__ "EPSSolve_KrylovSchur_Slice"

PetscErrorCode EPSSolve_KrylovSchur_Slice(EPS eps)

{

  PetscErrorCode ierr;

  PetscInt       i;

  PetscReal      newS;

  KSP            ksp;

  PC             pc;

  Mat            F;  

  PetscReal      *errest_left;

  Vec            t;

  SR             sr;

  PetscFunctionBegin;

  ierr = PetscMalloc(sizeof(struct _n_SR),&sr);CHKERRQ(ierr);

  eps->data = sr;

  sr->itsKs = 0;

  sr->nleap = 0;

  sr->nMAXCompl = eps->nev/4;

  sr->iterCompl = eps->max_it/4;

  /* Checking presence of ends and finding direction */

  if( eps->inta > PETSC_MIN_REAL){

    sr->int0 = eps->inta;

    sr->int1 = eps->intb;

    sr->dir = 1;

    if(eps->intb >= PETSC_MAX_REAL){ /* Right-open interval */

      sr->hasEnd = PETSC_FALSE;

      sr->inertia1 = eps->n;

    }else sr->hasEnd = PETSC_TRUE;

  }else{ /* Left-open interval */

    sr->int0 = eps->intb;

    sr->int1 = eps->inta;

    sr->dir = -1;

    sr->hasEnd = PETSC_FALSE;

    sr->inertia1 = 0;

  }

  /* Array of pending shifts */

  sr->maxPend = 100;/* Initial size */

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

  if(sr->hasEnd){

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

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

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

    /* Not looking for values in b (just inertia).*/

    ierr = MatGetInertia(F,&sr->inertia1,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

  }

  sr->nPend = 0;

  ierr = EPSCreateShift(eps,sr->int0,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);

  ierr = EPSExtractShift(eps);

  sr->s0 = sr->sPres;

  sr->inertia0 = sr->s0->inertia;

  sr->numEigs = (sr->dir)*(sr->inertia1 - sr->inertia0);

  sr->indexEig = 0;

  /* Only with eigenvalues present in the interval ...*/

  if(sr->numEigs==0){

    eps->reason = EPS_CONVERGED_TOL;

    ierr = PetscFree(sr->s0);CHKERRQ(ierr);