/*  -- translated by f2c (version 20240504).
   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__13 = 13;
static integer c__15 = 15;
static integer c_n1 = -1;
static integer c__12 = 12;
static integer c__14 = 14;
static integer c__16 = 16;
static logical c_false = FALSE_;
static integer c__1 = 1;
static integer c__3 = 3;

/* > \brief \b DLAQR4 computes the eigenvalues of a Hessenberg matrix, and optionally the matrices from the Sc
hur decomposition.   

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

   Online html documentation available at   
              http://www.netlib.org/lapack/explore-html/   

   > \htmlonly   
   > Download DLAQR4 + dependencies   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqr4.
f">   
   > [TGZ]</a>   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqr4.
f">   
   > [ZIP]</a>   
   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqr4.
f">   
   > [TXT]</a>   
   > \endhtmlonly   

    Definition:   
    ===========   

         SUBROUTINE DLAQR4( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR, WI,   
                            ILOZ, IHIZ, Z, LDZ, WORK, LWORK, INFO )   

         INTEGER            IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, LWORK, N   
         LOGICAL            WANTT, WANTZ   
         DOUBLE PRECISION   H( LDH, * ), WI( * ), WORK( * ), WR( * ),   
        $                   Z( LDZ, * )   


   > \par Purpose:   
    =============   
   >   
   > \verbatim   
   >   
   >    DLAQR4 implements one level of recursion for DLAQR0.   
   >    It is a complete implementation of the small bulge multi-shift   
   >    QR algorithm.  It may be called by DLAQR0 and, for large enough   
   >    deflation window size, it may be called by DLAQR3.  This   
   >    subroutine is identical to DLAQR0 except that it calls DLAQR2   
   >    instead of DLAQR3.   
   >   
   >    DLAQR4 computes the eigenvalues of a Hessenberg matrix H   
   >    and, optionally, the matrices T and Z from the Schur decomposition   
   >    H = Z T Z**T, where T is an upper quasi-triangular matrix (the   
   >    Schur form), and Z is the orthogonal matrix of Schur vectors.   
   >   
   >    Optionally Z may be postmultiplied into an input orthogonal   
   >    matrix Q so that this routine can give the Schur factorization   
   >    of a matrix A which has been reduced to the Hessenberg form H   
   >    by the orthogonal matrix Q:  A = Q*H*Q**T = (QZ)*T*(QZ)**T.   
   > \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 .GE. 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 triangular in rows   
   >           and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1,   
   >           H(ILO,ILO-1) is zero. ILO and IHI are normally set by a   
   >           previous call to DGEBAL, and then passed to DGEHRD when the   
   >           matrix output by DGEBAL is reduced to Hessenberg form.   
   >           Otherwise, ILO and IHI should be set to 1 and N,   
   >           respectively.  If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.   
   >           If N = 0, then ILO = 1 and IHI = 0.   
   > \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 = 0 and WANTT is .TRUE., then H contains   
   >           the upper quasi-triangular matrix T from the Schur   
   >           decomposition (the Schur form); 2-by-2 diagonal blocks   
   >           (corresponding to complex conjugate pairs of eigenvalues)   
   >           are returned in standard form, with H(i,i) = H(i+1,i+1)   
   >           and H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and WANTT is   
   >           .FALSE., then the contents of H are unspecified on exit.   
   >           (The output value of H when INFO.GT.0 is given under the   
   >           description of INFO below.)   
   >   
   >           This subroutine may explicitly set H(i,j) = 0 for i.GT.j and   
   >           j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N.   
   > \endverbatim   
   >   
   > \param[in] LDH   
   > \verbatim   
   >          LDH is INTEGER   
   >           The leading dimension of the array H. LDH .GE. max(1,N).   
   > \endverbatim   
   >   
   > \param[out] WR   
   > \verbatim   
   >          WR is DOUBLE PRECISION array, dimension (IHI)   
   > \endverbatim   
   >   
   > \param[out] WI   
   > \verbatim   
   >          WI is DOUBLE PRECISION array, dimension (IHI)   
   >           The real and imaginary parts, respectively, of the computed   
   >           eigenvalues of H(ILO:IHI,ILO:IHI) are stored in WR(ILO:IHI)   
   >           and WI(ILO:IHI). 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) .GT. 0 and WI(i+1) .LT. 0. If WANTT is .TRUE., then   
   >           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 .LE. ILOZ .LE. ILO; IHI .LE. IHIZ .LE. N.   
   > \endverbatim   
   >   
   > \param[in,out] Z   
   > \verbatim   
   >          Z is DOUBLE PRECISION array, dimension (LDZ,IHI)   
   >           If WANTZ is .FALSE., then Z is not referenced.   
   >           If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is   
   >           replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the   
   >           orthogonal Schur factor of H(ILO:IHI,ILO:IHI).   
   >           (The output value of Z when INFO.GT.0 is given under   
   >           the description of INFO below.)   
   > \endverbatim   
   >   
   > \param[in] LDZ   
   > \verbatim   
   >          LDZ is INTEGER   
   >           The leading dimension of the array Z.  if WANTZ is .TRUE.   
   >           then LDZ.GE.MAX(1,IHIZ).  Otherwize, LDZ.GE.1.   
   > \endverbatim   
   >   
   > \param[out] WORK   
   > \verbatim   
   >          WORK is DOUBLE PRECISION array, dimension LWORK   
   >           On exit, if LWORK = -1, WORK(1) returns an estimate of   
   >           the optimal value for LWORK.   
   > \endverbatim   
   >   
   > \param[in] LWORK   
   > \verbatim   
   >          LWORK is INTEGER   
   >           The dimension of the array WORK.  LWORK .GE. max(1,N)   
   >           is sufficient, but LWORK typically as large as 6*N may   
   >           be required for optimal performance.  A workspace query   
   >           to determine the optimal workspace size is recommended.   
   >   
   >           If LWORK = -1, then DLAQR4 does a workspace query.   
   >           In this case, DLAQR4 checks the input parameters and   
   >           estimates the optimal workspace size for the given   
   >           values of N, ILO and IHI.  The estimate is returned   
   >           in WORK(1).  No error message related to LWORK is   
   >           issued by XERBLA.  Neither H nor Z are accessed.   
   > \endverbatim   
   >   
   > \param[out] INFO   
   > \verbatim   
   >          INFO is INTEGER   
   >             =  0:  successful exit   
   >           .GT. 0:  if INFO = i, DLAQR4 failed to compute all of   
   >                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR   
   >                and WI contain those eigenvalues which have been   
   >                successfully computed.  (Failures are rare.)   
   >   
   >                If INFO .GT. 0 and WANT is .FALSE., then on exit,   
   >                the remaining unconverged eigenvalues are the eigen-   
   >                values of the upper Hessenberg matrix rows and   
   >                columns ILO through 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 a orthogonal 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(ILO:IHI,ILOZ:IHIZ)   
   >                   =  (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U   
   >   
   >                where U is the orthogonal matrix in (*) (regard-   
   >                less of the value of WANTT.)   
   >   
   >                If INFO .GT. 0 and WANTZ is .FALSE., then Z is not   
   >                accessed.   
   > \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 Contributors:   
    ==================   
   >   
   >       Karen Braman and Ralph Byers, Department of Mathematics,   
   >       University of Kansas, USA   

   > \par References:   
    ================   
   >   
   >       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR   
   >       Algorithm Part I: Maintaining Well Focused Shifts, and Level 3   
   >       Performance, SIAM Journal of Matrix Analysis, volume 23, pages   
   >       929--947, 2002.   
   > \n   
   >       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR   
   >       Algorithm Part II: Aggressive Early Deflation, SIAM Journal   
   >       of Matrix Analysis, volume 23, pages 948--973, 2002.   
   >   
    =====================================================================   
   Subroutine */ int igraphdlaqr4_(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, doublereal *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5;
    doublereal d__1, d__2, d__3, d__4;

    /* Local variables */
    integer i__, k;
    doublereal aa, bb, cc, dd;
    integer ld;
    doublereal cs;
    integer nh, it, ks, kt;
    doublereal sn;
    integer ku, kv, ls, ns;
    doublereal ss;
    integer nw, inf, kdu, nho, nve, kwh, nsr, nwr, kwv, ndec, ndfl, kbot, 
	    nmin;
    doublereal swap;
    integer ktop;
    doublereal zdum[1]	/* was [1][1] */;
    integer kacc22, itmax, nsmax, nwmax, kwtop;
    extern /* Subroutine */ int igraphdlaqr2_(logical *, logical *, integer *, 
	    integer *, integer *, integer *, doublereal *, integer *, integer 
	    *, integer *, doublereal *, integer *, integer *, integer *, 
	    doublereal *, doublereal *, doublereal *, integer *, integer *, 
	    doublereal *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, integer *), igraphdlanv2_(doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *, 
	    doublereal *, doublereal *, doublereal *, doublereal *), igraphdlaqr5_(
	    logical *, logical *, integer *, integer *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, doublereal *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *, doublereal *, integer *);
    integer nibble;
    extern /* Subroutine */ int igraphdlahqr_(logical *, logical *, integer *, 
	    integer *, integer *, doublereal *, integer *, doublereal *, 
	    doublereal *, integer *, integer *, doublereal *, integer *, 
	    integer *), igraphdlacpy_(char *, integer *, integer *, doublereal *, 
	    integer *, doublereal *, integer *);
    extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    char jbcmpz[2];
    integer nwupbd;
    logical sorted;
    integer lwkopt;


/*  -- 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   


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

       ==== Matrices of order NTINY or smaller must be processed by   
       .    DLAHQR because of insufficient subdiagonal scratch space.   
       .    (This is a hard limit.) ====   

       ==== Exceptional deflation windows:  try to cure rare   
       .    slow convergence by varying the size of the   
       .    deflation window after KEXNW iterations. ====   

       ==== Exceptional shifts: try to cure rare slow convergence   
       .    with ad-hoc exceptional shifts every KEXSH iterations.   
       .    ====   

       ==== The constants WILK1 and WILK2 are used to form the   
       .    exceptional shifts. ====   
       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;
    --work;

    /* Function Body */
    *info = 0;

/*     ==== Quick return for N = 0: nothing to do. ==== */

    if (*n == 0) {
	work[1] = 1.;
	return 0;
    }

    if (*n <= 11) {

/*        ==== Tiny matrices must use DLAHQR. ==== */

	lwkopt = 1;
	if (*lwork != -1) {
	    igraphdlahqr_(wantt, wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &
		    wi[1], iloz, ihiz, &z__[z_offset], ldz, info);
	}
    } else {

/*        ==== Use small bulge multi-shift QR with aggressive early   
          .    deflation on larger-than-tiny matrices. ====   

          ==== Hope for the best. ==== */

	*info = 0;

/*        ==== Set up job flags for ILAENV. ==== */

	if (*wantt) {
	    *(unsigned char *)jbcmpz = 'S';
	} else {
	    *(unsigned char *)jbcmpz = 'E';
	}
	if (*wantz) {
	    *(unsigned char *)&jbcmpz[1] = 'V';
	} else {
	    *(unsigned char *)&jbcmpz[1] = 'N';
	}

/*        ==== NWR = recommended deflation window size.  At this   
          .    point,  N .GT. NTINY = 11, so there is enough   
          .    subdiagonal workspace for NWR.GE.2 as required.   
          .    (In fact, there is enough subdiagonal space for   
          .    NWR.GE.3.) ==== */

	nwr = igraphilaenv_(&c__13, "DLAQR4", jbcmpz, n, ilo, ihi, lwork, (ftnlen)6,
		 (ftnlen)2);
	nwr = max(2,nwr);
/* Computing MIN */
	i__1 = *ihi - *ilo + 1, i__2 = (*n - 1) / 3, i__1 = min(i__1,i__2);
	nwr = min(i__1,nwr);

/*        ==== NSR = recommended number of simultaneous shifts.   
          .    At this point N .GT. NTINY = 11, so there is at   
          .    enough subdiagonal workspace for NSR to be even   
          .    and greater than or equal to two as required. ==== */

	nsr = igraphilaenv_(&c__15, "DLAQR4", jbcmpz, n, ilo, ihi, lwork, (ftnlen)6,
		 (ftnlen)2);
/* Computing MIN */
	i__1 = nsr, i__2 = (*n + 6) / 9, i__1 = min(i__1,i__2), i__2 = *ihi - 
		*ilo;
	nsr = min(i__1,i__2);
/* Computing MAX */
	i__1 = 2, i__2 = nsr - nsr % 2;
	nsr = max(i__1,i__2);

/*        ==== Estimate optimal workspace ====   

          ==== Workspace query call to DLAQR2 ==== */

	i__1 = nwr + 1;
	igraphdlaqr2_(wantt, wantz, n, ilo, ihi, &i__1, &h__[h_offset], ldh, iloz, 
		ihiz, &z__[z_offset], ldz, &ls, &ld, &wr[1], &wi[1], &h__[
		h_offset], ldh, n, &h__[h_offset], ldh, n, &h__[h_offset], 
		ldh, &work[1], &c_n1);

/*        ==== Optimal workspace = MAX(DLAQR5, DLAQR2) ====   

   Computing MAX */
	i__1 = nsr * 3 / 2, i__2 = (integer) work[1];
	lwkopt = max(i__1,i__2);

/*        ==== Quick return in case of workspace query. ==== */

	if (*lwork == -1) {
	    work[1] = (doublereal) lwkopt;
	    return 0;
	}

/*        ==== DLAHQR/DLAQR0 crossover point ==== */

	nmin = igraphilaenv_(&c__12, "DLAQR4", jbcmpz, n, ilo, ihi, lwork, (ftnlen)
		6, (ftnlen)2);
	nmin = max(11,nmin);

/*        ==== Nibble crossover point ==== */

	nibble = igraphilaenv_(&c__14, "DLAQR4", jbcmpz, n, ilo, ihi, lwork, (
		ftnlen)6, (ftnlen)2);
	nibble = max(0,nibble);

/*        ==== Accumulate reflections during ttswp?  Use block   
          .    2-by-2 structure during matrix-matrix multiply? ==== */

	kacc22 = igraphilaenv_(&c__16, "DLAQR4", jbcmpz, n, ilo, ihi, lwork, (
		ftnlen)6, (ftnlen)2);
	kacc22 = max(0,kacc22);
	kacc22 = min(2,kacc22);

/*        ==== NWMAX = the largest possible deflation window for   
          .    which there is sufficient workspace. ====   

   Computing MIN */
	i__1 = (*n - 1) / 3, i__2 = *lwork / 2;
	nwmax = min(i__1,i__2);
	nw = nwmax;

/*        ==== NSMAX = the Largest number of simultaneous shifts   
          .    for which there is sufficient workspace. ====   

   Computing MIN */
	i__1 = (*n + 6) / 9, i__2 = (*lwork << 1) / 3;
	nsmax = min(i__1,i__2);
	nsmax -= nsmax % 2;

/*        ==== NDFL: an iteration count restarted at deflation. ==== */

	ndfl = 1;

/*        ==== ITMAX = iteration limit ====   

   Computing MAX */
	i__1 = 10, i__2 = *ihi - *ilo + 1;
	itmax = max(i__1,i__2) * 30;

/*        ==== Last row and column in the active block ==== */

	kbot = *ihi;

/*        ==== Main Loop ==== */

	i__1 = itmax;
	for (it = 1; it <= i__1; ++it) {

/*           ==== Done when KBOT falls below ILO ==== */

	    if (kbot < *ilo) {
		goto L90;
	    }

/*           ==== Locate active block ==== */

	    i__2 = *ilo + 1;
	    for (k = kbot; k >= i__2; --k) {
		if (h__[k + (k - 1) * h_dim1] == 0.) {
		    goto L20;
		}
/* L10: */
	    }
	    k = *ilo;
L20:
	    ktop = k;

/*           ==== Select deflation window size:   
             .    Typical Case:   
             .      If possible and advisable, nibble the entire   
             .      active block.  If not, use size MIN(NWR,NWMAX)   
             .      or MIN(NWR+1,NWMAX) depending upon which has   
             .      the smaller corresponding subdiagonal entry   
             .      (a heuristic).   
             .   
             .    Exceptional Case:   
             .      If there have been no deflations in KEXNW or   
             .      more iterations, then vary the deflation window   
             .      size.   At first, because, larger windows are,   
             .      in general, more powerful than smaller ones,   
             .      rapidly increase the window to the maximum possible.   
             .      Then, gradually reduce the window size. ==== */

	    nh = kbot - ktop + 1;
	    nwupbd = min(nh,nwmax);
	    if (ndfl < 5) {
		nw = min(nwupbd,nwr);
	    } else {
/* Computing MIN */
		i__2 = nwupbd, i__3 = nw << 1;
		nw = min(i__2,i__3);
	    }
	    if (nw < nwmax) {
		if (nw >= nh - 1) {
		    nw = nh;
		} else {
		    kwtop = kbot - nw + 1;
		    if ((d__1 = h__[kwtop + (kwtop - 1) * h_dim1], abs(d__1)) 
			    > (d__2 = h__[kwtop - 1 + (kwtop - 2) * h_dim1], 
			    abs(d__2))) {
			++nw;
		    }
		}
	    }
	    if (ndfl < 5) {
		ndec = -1;
	    } else if (ndec >= 0 || nw >= nwupbd) {
		++ndec;
		if (nw - ndec < 2) {
		    ndec = 0;
		}
		nw -= ndec;
	    }

/*           ==== Aggressive early deflation:   
             .    split workspace under the subdiagonal into   
             .      - an nw-by-nw work array V in the lower   
             .        left-hand-corner,   
             .      - an NW-by-at-least-NW-but-more-is-better   
             .        (NW-by-NHO) horizontal work array along   
             .        the bottom edge,   
             .      - an at-least-NW-but-more-is-better (NHV-by-NW)   
             .        vertical work array along the left-hand-edge.   
             .        ==== */

	    kv = *n - nw + 1;
	    kt = nw + 1;
	    nho = *n - nw - 1 - kt + 1;
	    kwv = nw + 2;
	    nve = *n - nw - kwv + 1;

/*           ==== Aggressive early deflation ==== */

	    igraphdlaqr2_(wantt, wantz, n, &ktop, &kbot, &nw, &h__[h_offset], ldh, 
		    iloz, ihiz, &z__[z_offset], ldz, &ls, &ld, &wr[1], &wi[1],
		     &h__[kv + h_dim1], ldh, &nho, &h__[kv + kt * h_dim1], 
		    ldh, &nve, &h__[kwv + h_dim1], ldh, &work[1], lwork);

/*           ==== Adjust KBOT accounting for new deflations. ==== */

	    kbot -= ld;

/*           ==== KS points to the shifts. ==== */

	    ks = kbot - ls + 1;

/*           ==== Skip an expensive QR sweep if there is a (partly   
             .    heuristic) reason to expect that many eigenvalues   
             .    will deflate without it.  Here, the QR sweep is   
             .    skipped if many eigenvalues have just been deflated   
             .    or if the remaining active block is small. */

	    if (ld == 0 || ld * 100 <= nw * nibble && kbot - ktop + 1 > min(
		    nmin,nwmax)) {

/*              ==== NS = nominal number of simultaneous shifts.   
                .    This may be lowered (slightly) if DLAQR2   
                .    did not provide that many shifts. ====   

   Computing MIN   
   Computing MAX */
		i__4 = 2, i__5 = kbot - ktop;
		i__2 = min(nsmax,nsr), i__3 = max(i__4,i__5);
		ns = min(i__2,i__3);
		ns -= ns % 2;

/*              ==== If there have been no deflations   
                .    in a multiple of KEXSH iterations,   
                .    then try exceptional shifts.   
                .    Otherwise use shifts provided by   
                .    DLAQR2 above or from the eigenvalues   
                .    of a trailing principal submatrix. ==== */

		if (ndfl % 6 == 0) {
		    ks = kbot - ns + 1;
/* Computing MAX */
		    i__3 = ks + 1, i__4 = ktop + 2;
		    i__2 = max(i__3,i__4);
		    for (i__ = kbot; i__ >= i__2; i__ += -2) {
			ss = (d__1 = h__[i__ + (i__ - 1) * h_dim1], abs(d__1))
				 + (d__2 = h__[i__ - 1 + (i__ - 2) * h_dim1], 
				abs(d__2));
			aa = ss * .75 + h__[i__ + i__ * h_dim1];
			bb = ss;
			cc = ss * -.4375;
			dd = aa;
			igraphdlanv2_(&aa, &bb, &cc, &dd, &wr[i__ - 1], &wi[i__ - 1]
				, &wr[i__], &wi[i__], &cs, &sn);
/* L30: */
		    }
		    if (ks == ktop) {
			wr[ks + 1] = h__[ks + 1 + (ks + 1) * h_dim1];
			wi[ks + 1] = 0.;
			wr[ks] = wr[ks + 1];
			wi[ks] = wi[ks + 1];
		    }
		} else {

/*                 ==== Got NS/2 or fewer shifts? Use DLAHQR   
                   .    on a trailing principal submatrix to   
                   .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9,   
                   .    there is enough space below the subdiagonal   
                   .    to fit an NS-by-NS scratch array.) ==== */

		    if (kbot - ks + 1 <= ns / 2) {
			ks = kbot - ns + 1;
			kt = *n - ns + 1;
			igraphdlacpy_("A", &ns, &ns, &h__[ks + ks * h_dim1], ldh, &
				h__[kt + h_dim1], ldh);
			igraphdlahqr_(&c_false, &c_false, &ns, &c__1, &ns, &h__[kt 
				+ h_dim1], ldh, &wr[ks], &wi[ks], &c__1, &
				c__1, zdum, &c__1, &inf);
			ks += inf;

/*                    ==== In case of a rare QR failure use   
                      .    eigenvalues of the trailing 2-by-2   
                      .    principal submatrix.  ==== */

			if (ks >= kbot) {
			    aa = h__[kbot - 1 + (kbot - 1) * h_dim1];
			    cc = h__[kbot + (kbot - 1) * h_dim1];
			    bb = h__[kbot - 1 + kbot * h_dim1];
			    dd = h__[kbot + kbot * h_dim1];
			    igraphdlanv2_(&aa, &bb, &cc, &dd, &wr[kbot - 1], &wi[
				    kbot - 1], &wr[kbot], &wi[kbot], &cs, &sn)
				    ;
			    ks = kbot - 1;
			}
		    }

		    if (kbot - ks + 1 > ns) {

/*                    ==== Sort the shifts (Helps a little)   
                      .    Bubble sort keeps complex conjugate   
                      .    pairs together. ==== */

			sorted = FALSE_;
			i__2 = ks + 1;
			for (k = kbot; k >= i__2; --k) {
			    if (sorted) {
				goto L60;
			    }
			    sorted = TRUE_;
			    i__3 = k - 1;
			    for (i__ = ks; i__ <= i__3; ++i__) {
				if ((d__1 = wr[i__], abs(d__1)) + (d__2 = wi[
					i__], abs(d__2)) < (d__3 = wr[i__ + 1]
					, abs(d__3)) + (d__4 = wi[i__ + 1], 
					abs(d__4))) {
				    sorted = FALSE_;

				    swap = wr[i__];
				    wr[i__] = wr[i__ + 1];
				    wr[i__ + 1] = swap;

				    swap = wi[i__];
				    wi[i__] = wi[i__ + 1];
				    wi[i__ + 1] = swap;
				}
/* L40: */
			    }
/* L50: */
			}
L60:
			;
		    }

/*                 ==== Shuffle shifts into pairs of real shifts   
                   .    and pairs of complex conjugate shifts   
                   .    assuming complex conjugate shifts are   
                   .    already adjacent to one another. (Yes,   
                   .    they are.)  ==== */

		    i__2 = ks + 2;
		    for (i__ = kbot; i__ >= i__2; i__ += -2) {
			if (wi[i__] != -wi[i__ - 1]) {

			    swap = wr[i__];
			    wr[i__] = wr[i__ - 1];
			    wr[i__ - 1] = wr[i__ - 2];
			    wr[i__ - 2] = swap;

			    swap = wi[i__];
			    wi[i__] = wi[i__ - 1];
			    wi[i__ - 1] = wi[i__ - 2];
			    wi[i__ - 2] = swap;
			}
/* L70: */
		    }
		}

/*              ==== If there are only two shifts and both are   
                .    real, then use only one.  ==== */

		if (kbot - ks + 1 == 2) {
		    if (wi[kbot] == 0.) {
			if ((d__1 = wr[kbot] - h__[kbot + kbot * h_dim1], abs(
				d__1)) < (d__2 = wr[kbot - 1] - h__[kbot + 
				kbot * h_dim1], abs(d__2))) {
			    wr[kbot - 1] = wr[kbot];
			} else {
			    wr[kbot] = wr[kbot - 1];
			}
		    }
		}

/*              ==== Use up to NS of the the smallest magnatiude   
                .    shifts.  If there aren't NS shifts available,   
                .    then use them all, possibly dropping one to   
                .    make the number of shifts even. ====   

   Computing MIN */
		i__2 = ns, i__3 = kbot - ks + 1;
		ns = min(i__2,i__3);
		ns -= ns % 2;
		ks = kbot - ns + 1;

/*              ==== Small-bulge multi-shift QR sweep:   
                .    split workspace under the subdiagonal into   
                .    - a KDU-by-KDU work array U in the lower   
                .      left-hand-corner,   
                .    - a KDU-by-at-least-KDU-but-more-is-better   
                .      (KDU-by-NHo) horizontal work array WH along   
                .      the bottom edge,   
                .    - and an at-least-KDU-but-more-is-better-by-KDU   
                .      (NVE-by-KDU) vertical work WV arrow along   
                .      the left-hand-edge. ==== */

		kdu = ns * 3 - 3;
		ku = *n - kdu + 1;
		kwh = kdu + 1;
		nho = *n - kdu - 3 - (kdu + 1) + 1;
		kwv = kdu + 4;
		nve = *n - kdu - kwv + 1;

/*              ==== Small-bulge multi-shift QR sweep ==== */

		igraphdlaqr5_(wantt, wantz, &kacc22, n, &ktop, &kbot, &ns, &wr[ks], 
			&wi[ks], &h__[h_offset], ldh, iloz, ihiz, &z__[
			z_offset], ldz, &work[1], &c__3, &h__[ku + h_dim1], 
			ldh, &nve, &h__[kwv + h_dim1], ldh, &nho, &h__[ku + 
			kwh * h_dim1], ldh);
	    }

/*           ==== Note progress (or the lack of it). ==== */

	    if (ld > 0) {
		ndfl = 1;
	    } else {
		++ndfl;
	    }

/*           ==== End of main loop ====   
   L80: */
	}

/*        ==== Iteration limit exceeded.  Set INFO to show where   
          .    the problem occurred and exit. ==== */

	*info = kbot;
L90:
	;
    }

/*     ==== Return the optimal value of LWORK. ==== */

    work[1] = (doublereal) lwkopt;

/*     ==== End of DLAQR4 ==== */

    return 0;
} /* igraphdlaqr4_ */

