/*  -- 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 logical c_false = FALSE_;

static integer c__1 = 1;

static doublereal c_b22 = 1.;

static doublereal c_b25 = 0.;

static integer c__2 = 2;

static logical c_true = TRUE_;

/* > \brief \b DTREVC   

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

   Online html documentation available at   

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

   > \htmlonly   

   > Download DTREVC + dependencies   

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

f">   

   > [TGZ]</a>   

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

f">   

   > [ZIP]</a>   

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

f">   

   > [TXT]</a>   

   > \endhtmlonly   

    Definition:   

    ===========   

         SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,   

                            LDVR, MM, M, WORK, INFO )   

         CHARACTER          HOWMNY, SIDE   

         INTEGER            INFO, LDT, LDVL, LDVR, M, MM, N   

         LOGICAL            SELECT( * )   

         DOUBLE PRECISION   T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ),   

        $                   WORK( * )   

   > \par Purpose:   

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

   >   

   > \verbatim   

   >   

   > DTREVC computes some or all of the right and/or left eigenvectors of   

   > a real upper quasi-triangular matrix T.   

   > Matrices of this type are produced by the Schur factorization of   

   > a real general matrix:  A = Q*T*Q**T, as computed by DHSEQR.   

   >   

   > The right eigenvector x and the left eigenvector y of T corresponding   

   > to an eigenvalue w are defined by:   

   >   

   >    T*x = w*x,     (y**T)*T = w*(y**T)   

   >   

   > where y**T denotes the transpose of y.   

   > The eigenvalues are not input to this routine, but are read directly   

   > from the diagonal blocks of T.   

   >   

   > This routine returns the matrices X and/or Y of right and left   

   > eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an   

   > input matrix.  If Q is the orthogonal factor that reduces a matrix   

   > A to Schur form T, then Q*X and Q*Y are the matrices of right and   

   > left eigenvectors of A.   

   > \endverbatim   

    Arguments:   

    ==========   

   > \param[in] SIDE   

   > \verbatim   

   >          SIDE is CHARACTER*1   

   >          = 'R':  compute right eigenvectors only;   

   >          = 'L':  compute left eigenvectors only;   

   >          = 'B':  compute both right and left eigenvectors.   

   > \endverbatim   

   >   

   > \param[in] HOWMNY   

   > \verbatim   

   >          HOWMNY is CHARACTER*1   

   >          = 'A':  compute all right and/or left eigenvectors;   

   >          = 'B':  compute all right and/or left eigenvectors,   

   >                  backtransformed by the matrices in VR and/or VL;   

   >          = 'S':  compute selected right and/or left eigenvectors,   

   >                  as indicated by the logical array SELECT.   

   > \endverbatim   

   >   

   > \param[in,out] SELECT   

   > \verbatim   

   >          SELECT is LOGICAL array, dimension (N)   

   >          If HOWMNY = 'S', SELECT specifies the eigenvectors to be   

   >          computed.   

   >          If w(j) is a real eigenvalue, the corresponding real   

   >          eigenvector is computed if SELECT(j) is .TRUE..   

   >          If w(j) and w(j+1) are the real and imaginary parts of a   

   >          complex eigenvalue, the corresponding complex eigenvector is   

   >          computed if either SELECT(j) or SELECT(j+1) is .TRUE., and   

   >          on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to   

   >          .FALSE..   

   >          Not referenced if HOWMNY = 'A' or 'B'.   

   > \endverbatim   

   >   

   > \param[in] N   

   > \verbatim   

   >          N is INTEGER   

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

   > \endverbatim   

   >   

   > \param[in] T   

   > \verbatim   

   >          T is DOUBLE PRECISION array, dimension (LDT,N)   

   >          The upper quasi-triangular matrix T in Schur canonical form.   

   > \endverbatim   

   >   

   > \param[in] LDT   

   > \verbatim   

   >          LDT is INTEGER   

   >          The leading dimension of the array T. LDT >= max(1,N).   

   > \endverbatim   

   >   

   > \param[in,out] VL   

   > \verbatim   

   >          VL is DOUBLE PRECISION array, dimension (LDVL,MM)   

   >          On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must   

   >          contain an N-by-N matrix Q (usually the orthogonal matrix Q   

   >          of Schur vectors returned by DHSEQR).   

   >          On exit, if SIDE = 'L' or 'B', VL contains:   

   >          if HOWMNY = 'A', the matrix Y of left eigenvectors of T;   

   >          if HOWMNY = 'B', the matrix Q*Y;   

   >          if HOWMNY = 'S', the left eigenvectors of T specified by   

   >                           SELECT, stored consecutively in the columns   

   >                           of VL, in the same order as their   

   >                           eigenvalues.   

   >          A complex eigenvector corresponding to a complex eigenvalue   

   >          is stored in two consecutive columns, the first holding the   

   >          real part, and the second the imaginary part.   

   >          Not referenced if SIDE = 'R'.   

   > \endverbatim   

   >   

   > \param[in] LDVL   

   > \verbatim   

   >          LDVL is INTEGER   

   >          The leading dimension of the array VL.  LDVL >= 1, and if   

   >          SIDE = 'L' or 'B', LDVL >= N.   

   > \endverbatim   

   >   

   > \param[in,out] VR   

   > \verbatim   

   >          VR is DOUBLE PRECISION array, dimension (LDVR,MM)   

   >          On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must   

   >          contain an N-by-N matrix Q (usually the orthogonal matrix Q   

   >          of Schur vectors returned by DHSEQR).   

   >          On exit, if SIDE = 'R' or 'B', VR contains:   

   >          if HOWMNY = 'A', the matrix X of right eigenvectors of T;   

   >          if HOWMNY = 'B', the matrix Q*X;   

   >          if HOWMNY = 'S', the right eigenvectors of T specified by   

   >                           SELECT, stored consecutively in the columns   

   >                           of VR, in the same order as their   

   >                           eigenvalues.   

   >          A complex eigenvector corresponding to a complex eigenvalue   

   >          is stored in two consecutive columns, the first holding the   

   >          real part and the second the imaginary part.   

   >          Not referenced if SIDE = 'L'.   

   > \endverbatim   

   >   

   > \param[in] LDVR   

   > \verbatim   

   >          LDVR is INTEGER   

   >          The leading dimension of the array VR.  LDVR >= 1, and if   

   >          SIDE = 'R' or 'B', LDVR >= N.   

   > \endverbatim   

   >   

   > \param[in] MM   

   > \verbatim   

   >          MM is INTEGER   

   >          The number of columns in the arrays VL and/or VR. MM >= M.   

   > \endverbatim   

   >   

   > \param[out] M   

   > \verbatim   

   >          M is INTEGER   

   >          The number of columns in the arrays VL and/or VR actually   

   >          used to store the eigenvectors.   

   >          If HOWMNY = 'A' or 'B', M is set to N.   

   >          Each selected real eigenvector occupies one column and each   

   >          selected complex eigenvector occupies two columns.   

   > \endverbatim   

   >   

   > \param[out] WORK   

   > \verbatim   

   >          WORK is DOUBLE PRECISION array, dimension (3*N)   

   > \endverbatim   

   >   

   > \param[out] INFO   

   > \verbatim   

   >          INFO is INTEGER   

   >          = 0:  successful exit   

   >          < 0:  if INFO = -i, the i-th argument had an illegal value   

   > \endverbatim   

    Authors:   

    ========   

   > \author Univ. of Tennessee   

   > \author Univ. of California Berkeley   

   > \author Univ. of Colorado Denver   

   > \author NAG Ltd.   

   > \date November 2011   

   > \ingroup doubleOTHERcomputational   

   > \par Further Details:   

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

   >   

   > \verbatim   

   >   

   >  The algorithm used in this program is basically backward (forward)   

   >  substitution, with scaling to make the the code robust against   

   >  possible overflow.   

   >   

   >  Each eigenvector is normalized so that the element of largest   

   >  magnitude has magnitude 1; here the magnitude of a complex number   

   >  (x,y) is taken to be |x| + |y|.   

   > \endverbatim   

   >   

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

   Subroutine */ int igraphdtrevc_(char *side, char *howmny, logical *select, 

  integer *n, doublereal *t, integer *ldt, doublereal *vl, integer *

  ldvl, doublereal *vr, integer *ldvr, integer *mm, integer *m, 

  doublereal *work, integer *info)

{

    /* System generated locals */

    integer t_dim1, t_offset, vl_dim1, vl_offset, vr_dim1, vr_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;

    doublereal x[4] /* was [2][2] */;

    integer j1, j2, n2, ii, ki, ip, is;

    doublereal wi, wr, rec, ulp, beta, emax;

    logical pair;

    extern doublereal igraphddot_(integer *, doublereal *, integer *, doublereal *, 

      integer *);

    logical allv;

    integer ierr;

    doublereal unfl, ovfl, smin;

    logical over;

    doublereal vmax;

    integer jnxt;

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

      integer *);

    doublereal scale;

    extern logical igraphlsame_(char *, char *);

    extern /* Subroutine */ int igraphdgemv_(char *, integer *, integer *, 

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

      doublereal *, doublereal *, integer *);

    doublereal remax;

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

      doublereal *, integer *);

    logical leftv, bothv;

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

      integer *, doublereal *, integer *);

    doublereal vcrit;

    logical somev;

    doublereal xnorm;

    extern /* Subroutine */ int igraphdlaln2_(logical *, integer *, integer *, 

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

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

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

       igraphdlabad_(doublereal *, doublereal *);

    extern doublereal igraphdlamch_(char *);

    extern integer igraphidamax_(integer *, doublereal *, integer *);

    extern /* Subroutine */ int igraphxerbla_(char *, integer *, ftnlen);

    doublereal bignum;

    logical rightv;

    doublereal smlnum;

/*  -- LAPACK computational routine (version 3.4.0) --   

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

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

       November 2011   

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

       Decode and test the input parameters   

       Parameter adjustments */

    --select;

    t_dim1 = *ldt;

    t_offset = 1 + t_dim1;

    t -= t_offset;

    vl_dim1 = *ldvl;

    vl_offset = 1 + vl_dim1;

    vl -= vl_offset;

    vr_dim1 = *ldvr;

    vr_offset = 1 + vr_dim1;

    vr -= vr_offset;

    --work;

    /* Function Body */

    bothv = igraphlsame_(side, "B");

    rightv = igraphlsame_(side, "R") || bothv;

    leftv = igraphlsame_(side, "L") || bothv;

    allv = igraphlsame_(howmny, "A");

    over = igraphlsame_(howmny, "B");

    somev = igraphlsame_(howmny, "S");

    *info = 0;

    if (! rightv && ! leftv) {

  *info = -1;

    } else if (! allv && ! over && ! somev) {

  *info = -2;

    } else if (*n < 0) {

  *info = -4;

    } else if (*ldt < max(1,*n)) {

  *info = -6;

    } else if (*ldvl < 1 || leftv && *ldvl < *n) {

  *info = -8;

    } else if (*ldvr < 1 || rightv && *ldvr < *n) {

  *info = -10;

    } else {

/*        Set M to the number of columns required to store the selected   

          eigenvectors, standardize the array SELECT if necessary, and   

          test MM. */

  if (somev) {

      *m = 0;

      pair = FALSE_;

      i__1 = *n;

      for (j = 1; j <= i__1; ++j) {

    if (pair) {

        pair = FALSE_;

        select[j] = FALSE_;

    } else {

        if (j < *n) {

      if (t[j + 1 + j * t_dim1] == 0.) {

          if (select[j]) {

        ++(*m);

          }

      } else {

          pair = TRUE_;

          if (select[j] || select[j + 1]) {

        select[j] = TRUE_;

        *m += 2;

          }

      }

        } else {

      if (select[*n]) {

          ++(*m);

      }

        }

    }

/* L10: */

      }

  } else {

      *m = *n;

  }

  if (*mm < *m) {

      *info = -11;

  }

    }

    if (*info != 0) {

  i__1 = -(*info);

  igraphxerbla_("DTREVC", &i__1, (ftnlen)6);

  return 0;

    }

/*     Quick return if possible. */

    if (*n == 0) {

  return 0;

    }

/*     Set the constants to control overflow. */

    unfl = igraphdlamch_("Safe minimum");

    ovfl = 1. / unfl;

    igraphdlabad_(&unfl, &ovfl);

    ulp = igraphdlamch_("Precision");

    smlnum = unfl * (*n / ulp);

    bignum = (1. - ulp) / smlnum;

/*     Compute 1-norm of each column of strictly upper triangular   

       part of T to control overflow in triangular solver. */

    work[1] = 0.;

    i__1 = *n;

    for (j = 2; j <= i__1; ++j) {

  work[j] = 0.;

  i__2 = j - 1;

  for (i__ = 1; i__ <= i__2; ++i__) {

      work[j] += (d__1 = t[i__ + j * t_dim1], abs(d__1));

/* L20: */

  }

/* L30: */

    }

/*     Index IP is used to specify the real or complex eigenvalue:   

         IP = 0, real eigenvalue,   

              1, first of conjugate complex pair: (wr,wi)   

             -1, second of conjugate complex pair: (wr,wi) */

    n2 = *n << 1;

    if (rightv) {

/*        Compute right eigenvectors. */

  ip = 0;

  is = *m;

  for (ki = *n; ki >= 1; --ki) {

      if (ip == 1) {

    goto L130;

      }

      if (ki == 1) {

    goto L40;

      }

      if (t[ki + (ki - 1) * t_dim1] == 0.) {

    goto L40;

      }

      ip = -1;

L40:

      if (somev) {

    if (ip == 0) {

        if (! select[ki]) {

      goto L130;

        }

    } else {

        if (! select[ki - 1]) {

      goto L130;

        }

    }

      }

/*           Compute the KI-th eigenvalue (WR,WI). */

      wr = t[ki + ki * t_dim1];

      wi = 0.;

      if (ip != 0) {

    wi = sqrt((d__1 = t[ki + (ki - 1) * t_dim1], abs(d__1))) * 

      sqrt((d__2 = t[ki - 1 + ki * t_dim1], abs(d__2)));

      }

/* Computing MAX */

      d__1 = ulp * (abs(wr) + abs(wi));

      smin = max(d__1,smlnum);

      if (ip == 0) {

/*              Real right eigenvector */

    work[ki + *n] = 1.;

/*              Form right-hand side */

    i__1 = ki - 1;

    for (k = 1; k <= i__1; ++k) {

        work[k + *n] = -t[k + ki * t_dim1];

/* L50: */

    }

/*              Solve the upper quasi-triangular system:   

                   (T(1:KI-1,1:KI-1) - WR)*X = SCALE*WORK. */

    jnxt = ki - 1;

    for (j = ki - 1; j >= 1; --j) {

        if (j > jnxt) {

      goto L60;

        }

        j1 = j;

        j2 = j;

        jnxt = j - 1;

        if (j > 1) {

      if (t[j + (j - 1) * t_dim1] != 0.) {

          j1 = j - 1;

          jnxt = j - 2;

      }

        }

        if (j1 == j2) {

/*                    1-by-1 diagonal block */

      igraphdlaln2_(&c_false, &c__1, &c__1, &smin, &c_b22, &t[j + 

        j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *

        n], n, &wr, &c_b25, x, &c__2, &scale, &xnorm, 

        &ierr);

/*                    Scale X(1,1) to avoid overflow when updating   

                      the right-hand side. */

      if (xnorm > 1.) {

          if (work[j] > bignum / xnorm) {

        x[0] /= xnorm;

        scale /= xnorm;

          }

      }

/*                    Scale if necessary */

      if (scale != 1.) {

          igraphdscal_(&ki, &scale, &work[*n + 1], &c__1);

      }

      work[j + *n] = x[0];

/*                    Update right-hand side */

      i__1 = j - 1;

      d__1 = -x[0];

      igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[

        *n + 1], &c__1);

        } else {

/*                    2-by-2 diagonal block */

      igraphdlaln2_(&c_false, &c__2, &c__1, &smin, &c_b22, &t[j - 

        1 + (j - 1) * t_dim1], ldt, &c_b22, &c_b22, &

        work[j - 1 + *n], n, &wr, &c_b25, x, &c__2, &

        scale, &xnorm, &ierr);

/*                    Scale X(1,1) and X(2,1) to avoid overflow when   

                      updating the right-hand side. */

      if (xnorm > 1.) {

/* Computing MAX */

          d__1 = work[j - 1], d__2 = work[j];

          beta = max(d__1,d__2);

          if (beta > bignum / xnorm) {

        x[0] /= xnorm;

        x[1] /= xnorm;

        scale /= xnorm;

          }

      }

/*                    Scale if necessary */

      if (scale != 1.) {

          igraphdscal_(&ki, &scale, &work[*n + 1], &c__1);

      }

      work[j - 1 + *n] = x[0];

      work[j + *n] = x[1];

/*                    Update right-hand side */

      i__1 = j - 2;

      d__1 = -x[0];

      igraphdaxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1, 

        &work[*n + 1], &c__1);

      i__1 = j - 2;

      d__1 = -x[1];

      igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[

        *n + 1], &c__1);

        }

L60:

        ;

    }

/*              Copy the vector x or Q*x to VR and normalize. */

    if (! over) {

        igraphdcopy_(&ki, &work[*n + 1], &c__1, &vr[is * vr_dim1 + 1], &

          c__1);

        ii = igraphidamax_(&ki, &vr[is * vr_dim1 + 1], &c__1);

        remax = 1. / (d__1 = vr[ii + is * vr_dim1], abs(d__1));

        igraphdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);

        i__1 = *n;

        for (k = ki + 1; k <= i__1; ++k) {

      vr[k + is * vr_dim1] = 0.;

/* L70: */

        }

    } else {

        if (ki > 1) {

      i__1 = ki - 1;

      igraphdgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &

        work[*n + 1], &c__1, &work[ki + *n], &vr[ki * 

        vr_dim1 + 1], &c__1);

        }

        ii = igraphidamax_(n, &vr[ki * vr_dim1 + 1], &c__1);

        remax = 1. / (d__1 = vr[ii + ki * vr_dim1], abs(d__1));

        igraphdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);

    }

      } else {

/*              Complex right eigenvector.   

                Initial solve   

                  [ (T(KI-1,KI-1) T(KI-1,KI) ) - (WR + I* WI)]*X = 0.   

                  [ (T(KI,KI-1)   T(KI,KI)   )               ] */

    if ((d__1 = t[ki - 1 + ki * t_dim1], abs(d__1)) >= (d__2 = t[

      ki + (ki - 1) * t_dim1], abs(d__2))) {

        work[ki - 1 + *n] = 1.;

        work[ki + n2] = wi / t[ki - 1 + ki * t_dim1];

    } else {

        work[ki - 1 + *n] = -wi / t[ki + (ki - 1) * t_dim1];

        work[ki + n2] = 1.;

    }

    work[ki + *n] = 0.;

    work[ki - 1 + n2] = 0.;

/*              Form right-hand side */

    i__1 = ki - 2;

    for (k = 1; k <= i__1; ++k) {

        work[k + *n] = -work[ki - 1 + *n] * t[k + (ki - 1) * 

          t_dim1];

        work[k + n2] = -work[ki + n2] * t[k + ki * t_dim1];

/* L80: */

    }

/*              Solve upper quasi-triangular system:   

                (T(1:KI-2,1:KI-2) - (WR+i*WI))*X = SCALE*(WORK+i*WORK2) */

    jnxt = ki - 2;

    for (j = ki - 2; j >= 1; --j) {

        if (j > jnxt) {

      goto L90;

        }

        j1 = j;

        j2 = j;

        jnxt = j - 1;

        if (j > 1) {

      if (t[j + (j - 1) * t_dim1] != 0.) {

          j1 = j - 1;

          jnxt = j - 2;

      }

        }

        if (j1 == j2) {

/*                    1-by-1 diagonal block */

      igraphdlaln2_(&c_false, &c__1, &c__2, &smin, &c_b22, &t[j + 

        j * t_dim1], ldt, &c_b22, &c_b22, &work[j + *

        n], n, &wr, &wi, x, &c__2, &scale, &xnorm, &

        ierr);

/*                    Scale X(1,1) and X(1,2) to avoid overflow when   

                      updating the right-hand side. */

      if (xnorm > 1.) {

          if (work[j] > bignum / xnorm) {

        x[0] /= xnorm;

        x[2] /= xnorm;

        scale /= xnorm;

          }

      }

/*                    Scale if necessary */

      if (scale != 1.) {

          igraphdscal_(&ki, &scale, &work[*n + 1], &c__1);

          igraphdscal_(&ki, &scale, &work[n2 + 1], &c__1);

      }

      work[j + *n] = x[0];

      work[j + n2] = x[2];

/*                    Update the right-hand side */

      i__1 = j - 1;

      d__1 = -x[0];

      igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[

        *n + 1], &c__1);

      i__1 = j - 1;

      d__1 = -x[2];

      igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[

        n2 + 1], &c__1);

        } else {

/*                    2-by-2 diagonal block */

      igraphdlaln2_(&c_false, &c__2, &c__2, &smin, &c_b22, &t[j - 

        1 + (j - 1) * t_dim1], ldt, &c_b22, &c_b22, &

        work[j - 1 + *n], n, &wr, &wi, x, &c__2, &

        scale, &xnorm, &ierr);

/*                    Scale X to avoid overflow when updating   

                      the right-hand side. */

      if (xnorm > 1.) {

/* Computing MAX */

          d__1 = work[j - 1], d__2 = work[j];

          beta = max(d__1,d__2);

          if (beta > bignum / xnorm) {

        rec = 1. / xnorm;

        x[0] *= rec;

        x[2] *= rec;

        x[1] *= rec;

        x[3] *= rec;

        scale *= rec;

          }

      }

/*                    Scale if necessary */

      if (scale != 1.) {

          igraphdscal_(&ki, &scale, &work[*n + 1], &c__1);

          igraphdscal_(&ki, &scale, &work[n2 + 1], &c__1);

      }

      work[j - 1 + *n] = x[0];

      work[j + *n] = x[1];

      work[j - 1 + n2] = x[2];

      work[j + n2] = x[3];

/*                    Update the right-hand side */

      i__1 = j - 2;

      d__1 = -x[0];

      igraphdaxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1, 

        &work[*n + 1], &c__1);

      i__1 = j - 2;

      d__1 = -x[1];

      igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[

        *n + 1], &c__1);

      i__1 = j - 2;

      d__1 = -x[2];

      igraphdaxpy_(&i__1, &d__1, &t[(j - 1) * t_dim1 + 1], &c__1, 

        &work[n2 + 1], &c__1);

      i__1 = j - 2;

      d__1 = -x[3];

      igraphdaxpy_(&i__1, &d__1, &t[j * t_dim1 + 1], &c__1, &work[

        n2 + 1], &c__1);

        }

L90:

        ;

    }

/*              Copy the vector x or Q*x to VR and normalize. */

    if (! over) {

        igraphdcopy_(&ki, &work[*n + 1], &c__1, &vr[(is - 1) * vr_dim1 

          + 1], &c__1);

        igraphdcopy_(&ki, &work[n2 + 1], &c__1, &vr[is * vr_dim1 + 1], &

          c__1);

        emax = 0.;

        i__1 = ki;

        for (k = 1; k <= i__1; ++k) {

/* Computing MAX */

      d__3 = emax, d__4 = (d__1 = vr[k + (is - 1) * vr_dim1]

        , abs(d__1)) + (d__2 = vr[k + is * vr_dim1], 

        abs(d__2));

      emax = max(d__3,d__4);

/* L100: */

        }

        remax = 1. / emax;

        igraphdscal_(&ki, &remax, &vr[(is - 1) * vr_dim1 + 1], &c__1);

        igraphdscal_(&ki, &remax, &vr[is * vr_dim1 + 1], &c__1);

        i__1 = *n;

        for (k = ki + 1; k <= i__1; ++k) {

      vr[k + (is - 1) * vr_dim1] = 0.;

      vr[k + is * vr_dim1] = 0.;

/* L110: */

        }

    } else {

        if (ki > 2) {

      i__1 = ki - 2;

      igraphdgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &

        work[*n + 1], &c__1, &work[ki - 1 + *n], &vr[(

        ki - 1) * vr_dim1 + 1], &c__1);

      i__1 = ki - 2;

      igraphdgemv_("N", n, &i__1, &c_b22, &vr[vr_offset], ldvr, &

        work[n2 + 1], &c__1, &work[ki + n2], &vr[ki * 

        vr_dim1 + 1], &c__1);

        } else {

      igraphdscal_(n, &work[ki - 1 + *n], &vr[(ki - 1) * vr_dim1 

        + 1], &c__1);

      igraphdscal_(n, &work[ki + n2], &vr[ki * vr_dim1 + 1], &

        c__1);

        }

        emax = 0.;

        i__1 = *n;

        for (k = 1; k <= i__1; ++k) {

/* Computing MAX */

      d__3 = emax, d__4 = (d__1 = vr[k + (ki - 1) * vr_dim1]

        , abs(d__1)) + (d__2 = vr[k + ki * vr_dim1], 

        abs(d__2));

      emax = max(d__3,d__4);

/* L120: */

        }

        remax = 1. / emax;

        igraphdscal_(n, &remax, &vr[(ki - 1) * vr_dim1 + 1], &c__1);

        igraphdscal_(n, &remax, &vr[ki * vr_dim1 + 1], &c__1);

    }

      }

      --is;

      if (ip != 0) {

    --is;

      }

L130:

      if (ip == 1) {

    ip = 0;

      }

      if (ip == -1) {

    ip = 1;

      }

/* L140: */

  }

    }

    if (leftv) {

/*        Compute left eigenvectors. */

  ip = 0;

  is = 1;

  i__1 = *n;

  for (ki = 1; ki <= i__1; ++ki) {

      if (ip == -1) {

    goto L250;

      }

      if (ki == *n) {

    goto L150;

      }

      if (t[ki + 1 + ki * t_dim1] == 0.) {

    goto L150;

      }

      ip = 1;

L150:

      if (somev) {

    if (! select[ki]) {

        goto L250;

    }

      }

/*           Compute the KI-th eigenvalue (WR,WI). */

      wr = t[ki + ki * t_dim1];

      wi = 0.;

      if (ip != 0) {

    wi = sqrt((d__1 = t[ki + (ki + 1) * t_dim1], abs(d__1))) * 

      sqrt((d__2 = t[ki + 1 + ki * t_dim1], abs(d__2)));

      }

/* Computing MAX */

      d__1 = ulp * (abs(wr) + abs(wi));

      smin = max(d__1,smlnum);

      if (ip == 0) {

/*              Real left eigenvector. */

    work[ki + *n] = 1.;

/*              Form right-hand side */

    i__2 = *n;

    for (k = ki + 1; k <= i__2; ++k) {

        work[k + *n] = -t[ki + k * t_dim1];

/* L160: */

    }

/*              Solve the quasi-triangular system:   

                   (T(KI+1:N,KI+1:N) - WR)**T*X = SCALE*WORK */

    vmax = 1.;

    vcrit = bignum;

    jnxt = ki + 1;

    i__2 = *n;

    for (j = ki + 1; j <= i__2; ++j) {

        if (j < jnxt) {

      goto L170;

        }

        j1 = j;

        j2 = j;

        jnxt = j + 1;

        if (j < *n) {

      if (t[j + 1 + j * t_dim1] != 0.) {

          j2 = j + 1;

          jnxt = j + 2;

      }

        }

        if (j1 == j2) {

/*                    1-by-1 diagonal block   

                      Scale if necessary to avoid overflow when forming   

                      the right-hand side. */

      if (work[j] > vcrit) {

          rec = 1. / vmax;

          i__3 = *n - ki + 1;

          igraphdscal_(&i__3, &rec, &work[ki + *n], &c__1);

          vmax = 1.;

          vcrit = bignum;

      }