/*  -- translated by f2c (version 20191129).

   You must link the resulting object file with libf2c:

  on Microsoft Windows system, link with libf2c.lib;

  on Linux or Unix systems, link with .../path/to/libf2c.a -lm

  or, if you install libf2c.a in a standard place, with -lf2c -lm

  -- in that order, at the end of the command line, as in

    cc *.o -lf2c -lm

  Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

    http://www.netlib.org/f2c/libf2c.zip

*/

#include "f2c.h"

/* Table of constant values */

static integer c__1 = 1;

/* > \brief \b DLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using th

e double-shift/single-shift QR algorithm.   

    =========== DOCUMENTATION ===========   

   Online html documentation available at   

              http://www.netlib.org/lapack/explore-html/   

   > \htmlonly   

   > Download DLAHQR + dependencies   

   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlahqr.

f">   

   > [TGZ]</a>   

   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlahqr.

f">   

   > [ZIP]</a>   

   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlahqr.

f">   

   > [TXT]</a>   

   > \endhtmlonly   

    Definition:   

    ===========   

         SUBROUTINE DLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,   

                            ILOZ, IHIZ, Z, LDZ, INFO )   

         INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N   

         LOGICAL            WANTT, WANTZ   

         DOUBLE PRECISION   H( LDH, * ), WI( * ), WR( * ), Z( LDZ, * )   

   > \par Purpose:   

    =============   

   >   

   > \verbatim   

   >   

   >    DLAHQR is an auxiliary routine called by DHSEQR to update the   

   >    eigenvalues and Schur decomposition already computed by DHSEQR, by   

   >    dealing with the Hessenberg submatrix in rows and columns ILO to   

   >    IHI.   

   > \endverbatim   

    Arguments:   

    ==========   

   > \param[in] WANTT   

   > \verbatim   

   >          WANTT is LOGICAL   

   >          = .TRUE. : the full Schur form T is required;   

   >          = .FALSE.: only eigenvalues are required.   

   > \endverbatim   

   >   

   > \param[in] WANTZ   

   > \verbatim   

   >          WANTZ is LOGICAL   

   >          = .TRUE. : the matrix of Schur vectors Z is required;   

   >          = .FALSE.: Schur vectors are not required.   

   > \endverbatim   

   >   

   > \param[in] N   

   > \verbatim   

   >          N is INTEGER   

   >          The order of the matrix H.  N >= 0.   

   > \endverbatim   

   >   

   > \param[in] ILO   

   > \verbatim   

   >          ILO is INTEGER   

   > \endverbatim   

   >   

   > \param[in] IHI   

   > \verbatim   

   >          IHI is INTEGER   

   >          It is assumed that H is already upper quasi-triangular in   

   >          rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless   

   >          ILO = 1). DLAHQR works primarily with the Hessenberg   

   >          submatrix in rows and columns ILO to IHI, but applies   

   >          transformations to all of H if WANTT is .TRUE..   

   >          1 <= ILO <= max(1,IHI); IHI <= N.   

   > \endverbatim   

   >   

   > \param[in,out] H   

   > \verbatim   

   >          H is DOUBLE PRECISION array, dimension (LDH,N)   

   >          On entry, the upper Hessenberg matrix H.   

   >          On exit, if INFO is zero and if WANTT is .TRUE., H is upper   

   >          quasi-triangular in rows and columns ILO:IHI, with any   

   >          2-by-2 diagonal blocks in standard form. If INFO is zero   

   >          and WANTT is .FALSE., the contents of H are unspecified on   

   >          exit.  The output state of H if INFO is nonzero is given   

   >          below under the description of INFO.   

   > \endverbatim   

   >   

   > \param[in] LDH   

   > \verbatim   

   >          LDH is INTEGER   

   >          The leading dimension of the array H. LDH >= max(1,N).   

   > \endverbatim   

   >   

   > \param[out] WR   

   > \verbatim   

   >          WR is DOUBLE PRECISION array, dimension (N)   

   > \endverbatim   

   >   

   > \param[out] WI   

   > \verbatim   

   >          WI is DOUBLE PRECISION array, dimension (N)   

   >          The real and imaginary parts, respectively, of the computed   

   >          eigenvalues ILO to IHI are stored in the corresponding   

   >          elements of WR and WI. If two eigenvalues are computed as a   

   >          complex conjugate pair, they are stored in consecutive   

   >          elements of WR and WI, say the i-th and (i+1)th, with   

   >          WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the   

   >          eigenvalues are stored in the same order as on the diagonal   

   >          of the Schur form returned in H, with WR(i) = H(i,i), and, if   

   >          H(i:i+1,i:i+1) is a 2-by-2 diagonal block,   

   >          WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).   

   > \endverbatim   

   >   

   > \param[in] ILOZ   

   > \verbatim   

   >          ILOZ is INTEGER   

   > \endverbatim   

   >   

   > \param[in] IHIZ   

   > \verbatim   

   >          IHIZ is INTEGER   

   >          Specify the rows of Z to which transformations must be   

   >          applied if WANTZ is .TRUE..   

   >          1 <= ILOZ <= ILO; IHI <= IHIZ <= N.   

   > \endverbatim   

   >   

   > \param[in,out] Z   

   > \verbatim   

   >          Z is DOUBLE PRECISION array, dimension (LDZ,N)   

   >          If WANTZ is .TRUE., on entry Z must contain the current   

   >          matrix Z of transformations accumulated by DHSEQR, and on   

   >          exit Z has been updated; transformations are applied only to   

   >          the submatrix Z(ILOZ:IHIZ,ILO:IHI).   

   >          If WANTZ is .FALSE., Z is not referenced.   

   > \endverbatim   

   >   

   > \param[in] LDZ   

   > \verbatim   

   >          LDZ is INTEGER   

   >          The leading dimension of the array Z. LDZ >= max(1,N).   

   > \endverbatim   

   >   

   > \param[out] INFO   

   > \verbatim   

   >          INFO is INTEGER   

   >           =   0: successful exit   

   >          .GT. 0: If INFO = i, DLAHQR failed to compute all the   

   >                  eigenvalues ILO to IHI in a total of 30 iterations   

   >                  per eigenvalue; elements i+1:ihi of WR and WI   

   >                  contain those eigenvalues which have been   

   >                  successfully computed.   

   >   

   >                  If INFO .GT. 0 and WANTT is .FALSE., then on exit,   

   >                  the remaining unconverged eigenvalues are the   

   >                  eigenvalues of the upper Hessenberg matrix rows   

   >                  and columns ILO thorugh INFO of the final, output   

   >                  value of H.   

   >   

   >                  If INFO .GT. 0 and WANTT is .TRUE., then on exit   

   >          (*)       (initial value of H)*U  = U*(final value of H)   

   >                  where U is an orthognal matrix.    The final   

   >                  value of H is upper Hessenberg and triangular in   

   >                  rows and columns INFO+1 through IHI.   

   >   

   >                  If INFO .GT. 0 and WANTZ is .TRUE., then on exit   

   >                      (final value of Z)  = (initial value of Z)*U   

   >                  where U is the orthogonal matrix in (*)   

   >                  (regardless of the value of WANTT.)   

   > \endverbatim   

    Authors:   

    ========   

   > \author Univ. of Tennessee   

   > \author Univ. of California Berkeley   

   > \author Univ. of Colorado Denver   

   > \author NAG Ltd.   

   > \date September 2012   

   > \ingroup doubleOTHERauxiliary   

   > \par Further Details:   

    =====================   

   >   

   > \verbatim   

   >   

   >     02-96 Based on modifications by   

   >     David Day, Sandia National Laboratory, USA   

   >   

   >     12-04 Further modifications by   

   >     Ralph Byers, University of Kansas, USA   

   >     This is a modified version of DLAHQR from LAPACK version 3.0.   

   >     It is (1) more robust against overflow and underflow and   

   >     (2) adopts the more conservative Ahues & Tisseur stopping   

   >     criterion (LAWN 122, 1997).   

   > \endverbatim   

   >   

    =====================================================================   

   Subroutine */ int igraphdlahqr_(logical *wantt, logical *wantz, integer *n, 

  integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal 

  *wr, doublereal *wi, integer *iloz, integer *ihiz, doublereal *z__, 

  integer *ldz, integer *info)

{

    /* System generated locals */

    integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3;

    doublereal d__1, d__2, d__3, d__4;

    /* Builtin functions */

    double sqrt(doublereal);

    /* Local variables */

    integer i__, j, k, l, m;

    doublereal s, v[3];

    integer i1, i2;

    doublereal t1, t2, t3, v2, v3, aa, ab, ba, bb, h11, h12, h21, h22, cs;

    integer nh;

    doublereal sn;

    integer nr;

    doublereal tr;

    integer nz;

    doublereal det, h21s;

    integer its;

    doublereal ulp, sum, tst, rt1i, rt2i, rt1r, rt2r;

    extern /* Subroutine */ int igraphdrot_(integer *, doublereal *, integer *, 

      doublereal *, integer *, doublereal *, doublereal *), igraphdcopy_(

      integer *, doublereal *, integer *, doublereal *, integer *), 

      igraphdlanv2_(doublereal *, doublereal *, doublereal *, doublereal *, 

      doublereal *, doublereal *, doublereal *, doublereal *, 

      doublereal *, doublereal *), igraphdlabad_(doublereal *, doublereal *);

    extern doublereal igraphdlamch_(char *);

    extern /* Subroutine */ int igraphdlarfg_(integer *, doublereal *, doublereal *,

       integer *, doublereal *);

    doublereal safmin, safmax, rtdisc, smlnum;

/*  -- LAPACK auxiliary routine (version 3.4.2) --   

    -- LAPACK is a software package provided by Univ. of Tennessee,    --   

    -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--   

       September 2012   

    =========================================================   

       Parameter adjustments */

    h_dim1 = *ldh;

    h_offset = 1 + h_dim1;

    h__ -= h_offset;

    --wr;

    --wi;

    z_dim1 = *ldz;

    z_offset = 1 + z_dim1;

    z__ -= z_offset;

    /* Function Body */

    *info = 0;

/*     Quick return if possible */

    if (*n == 0) {

  return 0;

    }

    if (*ilo == *ihi) {

  wr[*ilo] = h__[*ilo + *ilo * h_dim1];

  wi[*ilo] = 0.;

  return 0;

    }

/*     ==== clear out the trash ==== */

    i__1 = *ihi - 3;

    for (j = *ilo; j <= i__1; ++j) {

  h__[j + 2 + j * h_dim1] = 0.;

  h__[j + 3 + j * h_dim1] = 0.;

/* L10: */

    }

    if (*ilo <= *ihi - 2) {

  h__[*ihi + (*ihi - 2) * h_dim1] = 0.;

    }

    nh = *ihi - *ilo + 1;

    nz = *ihiz - *iloz + 1;

/*     Set machine-dependent constants for the stopping criterion. */

    safmin = igraphdlamch_("SAFE MINIMUM");

    safmax = 1. / safmin;

    igraphdlabad_(&safmin, &safmax);

    ulp = igraphdlamch_("PRECISION");

    smlnum = safmin * ((doublereal) nh / ulp);

/*     I1 and I2 are the indices of the first row and last column of H   

       to which transformations must be applied. If eigenvalues only are   

       being computed, I1 and I2 are set inside the main loop. */

    if (*wantt) {

  i1 = 1;

  i2 = *n;

    }

/*     The main loop begins here. I is the loop index and decreases from   

       IHI to ILO in steps of 1 or 2. Each iteration of the loop works   

       with the active submatrix in rows and columns L to I.   

       Eigenvalues I+1 to IHI have already converged. Either L = ILO or   

       H(L,L-1) is negligible so that the matrix splits. */

    i__ = *ihi;

L20:

    l = *ilo;

    if (i__ < *ilo) {

  goto L160;

    }

/*     Perform QR iterations on rows and columns ILO to I until a   

       submatrix of order 1 or 2 splits off at the bottom because a   

       subdiagonal element has become negligible. */

    for (its = 0; its <= 30; ++its) {

/*        Look for a single small subdiagonal element. */

  i__1 = l + 1;

  for (k = i__; k >= i__1; --k) {

      if ((d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)) <= smlnum) {

    goto L40;

      }

      tst = (d__1 = h__[k - 1 + (k - 1) * h_dim1], abs(d__1)) + (d__2 = 

        h__[k + k * h_dim1], abs(d__2));

      if (tst == 0.) {

    if (k - 2 >= *ilo) {

        tst += (d__1 = h__[k - 1 + (k - 2) * h_dim1], abs(d__1));

    }

    if (k + 1 <= *ihi) {

        tst += (d__1 = h__[k + 1 + k * h_dim1], abs(d__1));

    }

      }

/*           ==== The following is a conservative small subdiagonal   

             .    deflation  criterion due to Ahues & Tisseur (LAWN 122,   

             .    1997). It has better mathematical foundation and   

             .    improves accuracy in some cases.  ==== */

      if ((d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)) <= ulp * tst) {

/* Computing MAX */

    d__3 = (d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)), d__4 = (

      d__2 = h__[k - 1 + k * h_dim1], abs(d__2));

    ab = max(d__3,d__4);

/* Computing MIN */

    d__3 = (d__1 = h__[k + (k - 1) * h_dim1], abs(d__1)), d__4 = (

      d__2 = h__[k - 1 + k * h_dim1], abs(d__2));

    ba = min(d__3,d__4);

/* Computing MAX */

    d__3 = (d__1 = h__[k + k * h_dim1], abs(d__1)), d__4 = (d__2 =

       h__[k - 1 + (k - 1) * h_dim1] - h__[k + k * h_dim1], 

      abs(d__2));

    aa = max(d__3,d__4);

/* Computing MIN */

    d__3 = (d__1 = h__[k + k * h_dim1], abs(d__1)), d__4 = (d__2 =

       h__[k - 1 + (k - 1) * h_dim1] - h__[k + k * h_dim1], 

      abs(d__2));

    bb = min(d__3,d__4);

    s = aa + ab;

/* Computing MAX */

    d__1 = smlnum, d__2 = ulp * (bb * (aa / s));

    if (ba * (ab / s) <= max(d__1,d__2)) {

        goto L40;

    }

      }

/* L30: */

  }

L40:

  l = k;

  if (l > *ilo) {

/*           H(L,L-1) is negligible */

      h__[l + (l - 1) * h_dim1] = 0.;

  }

/*        Exit from loop if a submatrix of order 1 or 2 has split off. */

  if (l >= i__ - 1) {

      goto L150;

  }

/*        Now the active submatrix is in rows and columns L to I. If   

          eigenvalues only are being computed, only the active submatrix   

          need be transformed. */

  if (! (*wantt)) {

      i1 = l;

      i2 = i__;

  }

  if (its == 10) {

/*           Exceptional shift. */

      s = (d__1 = h__[l + 1 + l * h_dim1], abs(d__1)) + (d__2 = h__[l + 

        2 + (l + 1) * h_dim1], abs(d__2));

      h11 = s * .75 + h__[l + l * h_dim1];

      h12 = s * -.4375;

      h21 = s;

      h22 = h11;

  } else if (its == 20) {

/*           Exceptional shift. */

      s = (d__1 = h__[i__ + (i__ - 1) * h_dim1], abs(d__1)) + (d__2 = 

        h__[i__ - 1 + (i__ - 2) * h_dim1], abs(d__2));

      h11 = s * .75 + h__[i__ + i__ * h_dim1];

      h12 = s * -.4375;

      h21 = s;

      h22 = h11;

  } else {

/*           Prepare to use Francis' double shift   

             (i.e. 2nd degree generalized Rayleigh quotient) */

      h11 = h__[i__ - 1 + (i__ - 1) * h_dim1];

      h21 = h__[i__ + (i__ - 1) * h_dim1];

      h12 = h__[i__ - 1 + i__ * h_dim1];

      h22 = h__[i__ + i__ * h_dim1];

  }

  s = abs(h11) + abs(h12) + abs(h21) + abs(h22);

  if (s == 0.) {

      rt1r = 0.;

      rt1i = 0.;

      rt2r = 0.;

      rt2i = 0.;

  } else {

      h11 /= s;

      h21 /= s;

      h12 /= s;

      h22 /= s;

      tr = (h11 + h22) / 2.;

      det = (h11 - tr) * (h22 - tr) - h12 * h21;

      rtdisc = sqrt((abs(det)));

      if (det >= 0.) {

/*              ==== complex conjugate shifts ==== */

    rt1r = tr * s;

    rt2r = rt1r;

    rt1i = rtdisc * s;

    rt2i = -rt1i;

      } else {

/*              ==== real shifts (use only one of them)  ==== */

    rt1r = tr + rtdisc;

    rt2r = tr - rtdisc;

    if ((d__1 = rt1r - h22, abs(d__1)) <= (d__2 = rt2r - h22, abs(

      d__2))) {

        rt1r *= s;

        rt2r = rt1r;

    } else {

        rt2r *= s;

        rt1r = rt2r;

    }

    rt1i = 0.;

    rt2i = 0.;

      }

  }

/*        Look for two consecutive small subdiagonal elements. */

  i__1 = l;

  for (m = i__ - 2; m >= i__1; --m) {

/*           Determine the effect of starting the double-shift QR   

             iteration at row M, and see if this would make H(M,M-1)   

             negligible.  (The following uses scaling to avoid   

             overflows and most underflows.) */

      h21s = h__[m + 1 + m * h_dim1];

      s = (d__1 = h__[m + m * h_dim1] - rt2r, abs(d__1)) + abs(rt2i) + 

        abs(h21s);

      h21s = h__[m + 1 + m * h_dim1] / s;

      v[0] = h21s * h__[m + (m + 1) * h_dim1] + (h__[m + m * h_dim1] - 

        rt1r) * ((h__[m + m * h_dim1] - rt2r) / s) - rt1i * (rt2i 

        / s);

      v[1] = h21s * (h__[m + m * h_dim1] + h__[m + 1 + (m + 1) * h_dim1]

         - rt1r - rt2r);

      v[2] = h21s * h__[m + 2 + (m + 1) * h_dim1];

      s = abs(v[0]) + abs(v[1]) + abs(v[2]);

      v[0] /= s;

      v[1] /= s;

      v[2] /= s;

      if (m == l) {

    goto L60;

      }

      if ((d__1 = h__[m + (m - 1) * h_dim1], abs(d__1)) * (abs(v[1]) + 

        abs(v[2])) <= ulp * abs(v[0]) * ((d__2 = h__[m - 1 + (m - 

        1) * h_dim1], abs(d__2)) + (d__3 = h__[m + m * h_dim1], 

        abs(d__3)) + (d__4 = h__[m + 1 + (m + 1) * h_dim1], abs(

        d__4)))) {

    goto L60;

      }

/* L50: */

  }

L60:

/*        Double-shift QR step */

  i__1 = i__ - 1;

  for (k = m; k <= i__1; ++k) {

/*           The first iteration of this loop determines a reflection G   

             from the vector V and applies it from left and right to H,   

             thus creating a nonzero bulge below the subdiagonal.   

             Each subsequent iteration determines a reflection G to   

             restore the Hessenberg form in the (K-1)th column, and thus   

             chases the bulge one step toward the bottom of the active   

             submatrix. NR is the order of G.   

   Computing MIN */

      i__2 = 3, i__3 = i__ - k + 1;

      nr = min(i__2,i__3);

      if (k > m) {

    igraphdcopy_(&nr, &h__[k + (k - 1) * h_dim1], &c__1, v, &c__1);

      }

      igraphdlarfg_(&nr, v, &v[1], &c__1, &t1);

      if (k > m) {

    h__[k + (k - 1) * h_dim1] = v[0];

    h__[k + 1 + (k - 1) * h_dim1] = 0.;

    if (k < i__ - 1) {

        h__[k + 2 + (k - 1) * h_dim1] = 0.;

    }

      } else if (m > l) {

/*               ==== Use the following instead of   

                 .    H( K, K-1 ) = -H( K, K-1 ) to   

                 .    avoid a bug when v(2) and v(3)   

                 .    underflow. ==== */

    h__[k + (k - 1) * h_dim1] *= 1. - t1;

      }

      v2 = v[1];

      t2 = t1 * v2;

      if (nr == 3) {

    v3 = v[2];

    t3 = t1 * v3;

/*              Apply G from the left to transform the rows of the matrix   

                in columns K to I2. */

    i__2 = i2;

    for (j = k; j <= i__2; ++j) {

        sum = h__[k + j * h_dim1] + v2 * h__[k + 1 + j * h_dim1] 

          + v3 * h__[k + 2 + j * h_dim1];

        h__[k + j * h_dim1] -= sum * t1;

        h__[k + 1 + j * h_dim1] -= sum * t2;

        h__[k + 2 + j * h_dim1] -= sum * t3;

/* L70: */

    }

/*              Apply G from the right to transform the columns of the   

                matrix in rows I1 to min(K+3,I).   

   Computing MIN */

    i__3 = k + 3;

    i__2 = min(i__3,i__);

    for (j = i1; j <= i__2; ++j) {

        sum = h__[j + k * h_dim1] + v2 * h__[j + (k + 1) * h_dim1]

           + v3 * h__[j + (k + 2) * h_dim1];

        h__[j + k * h_dim1] -= sum * t1;

        h__[j + (k + 1) * h_dim1] -= sum * t2;

        h__[j + (k + 2) * h_dim1] -= sum * t3;

/* L80: */

    }

    if (*wantz) {

/*                 Accumulate transformations in the matrix Z */

        i__2 = *ihiz;

        for (j = *iloz; j <= i__2; ++j) {

      sum = z__[j + k * z_dim1] + v2 * z__[j + (k + 1) * 

        z_dim1] + v3 * z__[j + (k + 2) * z_dim1];

      z__[j + k * z_dim1] -= sum * t1;

      z__[j + (k + 1) * z_dim1] -= sum * t2;

      z__[j + (k + 2) * z_dim1] -= sum * t3;

/* L90: */

        }

    }

      } else if (nr == 2) {

/*              Apply G from the left to transform the rows of the matrix   

                in columns K to I2. */

    i__2 = i2;

    for (j = k; j <= i__2; ++j) {

        sum = h__[k + j * h_dim1] + v2 * h__[k + 1 + j * h_dim1];

        h__[k + j * h_dim1] -= sum * t1;

        h__[k + 1 + j * h_dim1] -= sum * t2;

/* L100: */

    }

/*              Apply G from the right to transform the columns of the   

                matrix in rows I1 to min(K+3,I). */

    i__2 = i__;

    for (j = i1; j <= i__2; ++j) {

        sum = h__[j + k * h_dim1] + v2 * h__[j + (k + 1) * h_dim1]

          ;

        h__[j + k * h_dim1] -= sum * t1;

        h__[j + (k + 1) * h_dim1] -= sum * t2;

/* L110: */

    }

    if (*wantz) {

/*                 Accumulate transformations in the matrix Z */

        i__2 = *ihiz;

        for (j = *iloz; j <= i__2; ++j) {

      sum = z__[j + k * z_dim1] + v2 * z__[j + (k + 1) * 

        z_dim1];

      z__[j + k * z_dim1] -= sum * t1;

      z__[j + (k + 1) * z_dim1] -= sum * t2;

/* L120: */

        }

    }

      }

/* L130: */

  }

/* L140: */

    }

/*     Failure to converge in remaining number of iterations */

    *info = i__;

    return 0;

L150:

    if (l == i__) {

/*        H(I,I-1) is negligible: one eigenvalue has converged. */

  wr[i__] = h__[i__ + i__ * h_dim1];

  wi[i__] = 0.;

    } else if (l == i__ - 1) {

/*        H(I-1,I-2) is negligible: a pair of eigenvalues have converged.   

          Transform the 2-by-2 submatrix to standard Schur form,   

          and compute and store the eigenvalues. */

  igraphdlanv2_(&h__[i__ - 1 + (i__ - 1) * h_dim1], &h__[i__ - 1 + i__ * 

    h_dim1], &h__[i__ + (i__ - 1) * h_dim1], &h__[i__ + i__ * 

    h_dim1], &wr[i__ - 1], &wi[i__ - 1], &wr[i__], &wi[i__], &cs, 

    &sn);

  if (*wantt) {

/*           Apply the transformation to the rest of H. */

      if (i2 > i__) {

    i__1 = i2 - i__;

    igraphdrot_(&i__1, &h__[i__ - 1 + (i__ + 1) * h_dim1], ldh, &h__[

      i__ + (i__ + 1) * h_dim1], ldh, &cs, &sn);

      }

      i__1 = i__ - i1 - 1;

      igraphdrot_(&i__1, &h__[i1 + (i__ - 1) * h_dim1], &c__1, &h__[i1 + i__ *

         h_dim1], &c__1, &cs, &sn);

  }

  if (*wantz) {

/*           Apply the transformation to Z. */

      igraphdrot_(&nz, &z__[*iloz + (i__ - 1) * z_dim1], &c__1, &z__[*iloz + 

        i__ * z_dim1], &c__1, &cs, &sn);

  }

    }

/*     return to start of the main loop with new value of I. */

    i__ = l - 1;

    goto L20;

L160:

    return 0;

/*     End of DLAHQR */

} /* igraphdlahqr_ */