/*  -- translated by f2c (version 20100827).
   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;

/* 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 3.2) --   
       Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..   
       November 2006   


       This subroutine 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.   

       Purpose   
       =======   

       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.   

       Arguments   
       =========   

       WANTT   (input) LOGICAL   
            = .TRUE. : the full Schur form T is required;   
            = .FALSE.: only eigenvalues are required.   

       WANTZ   (input) LOGICAL   
            = .TRUE. : the matrix of Schur vectors Z is required;   
            = .FALSE.: Schur vectors are not required.   

       N     (input) INTEGER   
             The order of the matrix H.  N .GE. 0.   

       ILO   (input) INTEGER   
       IHI   (input) 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.   

       H     (input/output) 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.   

       LDH   (input) INTEGER   
             The leading dimension of the array H. LDH .GE. max(1,N).   

       WR    (output) DOUBLE PRECISION array, dimension (IHI)   
       WI    (output) 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).   

       ILOZ     (input) INTEGER   
       IHIZ     (input) 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.   

       Z     (input/output) 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.)   

       LDZ   (input) INTEGER   
             The leading dimension of the array Z.  if WANTZ is .TRUE.   
             then LDZ.GE.MAX(1,IHIZ).  Otherwize, LDZ.GE.1.   

       WORK  (workspace/output) DOUBLE PRECISION array, dimension LWORK   
             On exit, if LWORK = -1, WORK(1) returns an estimate of   
             the optimal value for LWORK.   

       LWORK (input) 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.   


       INFO  (output) 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 an orthogonal matrix.  The final   
                  value of H is upper Hessenberg and quasi-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.   

       ================================================================   
       Based on contributions by   
          Karen Braman and Ralph Byers, Department of Mathematics,   
          University of Kansas, USA   

       ================================================================   
       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.   

         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.   

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

       ==== 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_ */

